%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP650+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:21:35 AM UTC 2026
% Result : Theorem 249.61s 86.36s
% Output : Refutation 259.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 2184
% Syntax : Number of formulae : 5622 ( 905 unt; 0 typ; 73 def)
% Number of atoms : 33618 (4837 equ; 0 cnn)
% Maximal formula atoms : 205 ( 5 avg)
% Number of connectives : 113337 (5968 ~;2445 |;14104 &;79938 @)
% ( 434 <=>;10448 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 450 ( 447 usr; 50 con; 0-9 aty)
% Number of variables : 14446 ( 59 ^;13684 !; 630 ?;14446 :)
% ( 0 !>; 0 ?*; 0 @-; 73 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(v3_group_1_decl,type,
v3_group_1: $i > $o ).
thf(v4_group_1_decl,type,
v4_group_1: $i > $o ).
thf(l1_group_1_decl,type,
l1_group_1: $i > $o ).
thf(k3_latsubgr_decl,type,
k3_latsubgr: $i > $i > $i > $i ).
thf(k6_partfun1_decl,type,
k6_partfun1: $i > $i ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(k11_group_4_decl,type,
k11_group_4: $i > $i ).
thf(v10_lattices_decl,type,
v10_lattices: $i > $o ).
thf(v15_lattices_decl,type,
v15_lattices: $i > $o ).
thf(v16_lattices_decl,type,
v16_lattices: $i > $o ).
thf(l3_lattices_decl,type,
l3_lattices: $i > $o ).
thf(v3_filter_0_decl,type,
v3_filter_0: $i > $o ).
thf(m1_lattice4_decl,type,
m1_lattice4: $i > $i > $i > $o ).
thf(v3_lattice4_decl,type,
v3_lattice4: $i > $i > $i > $o ).
thf(r1_lattice4_decl,type,
r1_lattice4: $i > $i > $i > $o ).
thf(v17_lattices_decl,type,
v17_lattices: $i > $o ).
thf(v11_lattices_decl,type,
v11_lattices: $i > $o ).
thf(v13_lattices_decl,type,
v13_lattices: $i > $o ).
thf(v14_lattices_decl,type,
v14_lattices: $i > $o ).
thf(v2_lattice4_decl,type,
v2_lattice4: $i > $i > $i > $o ).
thf(r4_lattice4_decl,type,
r4_lattice4: $i > $i > $i > $o ).
thf(k8_filter_1_decl,type,
k8_filter_1: $i > $i > $i ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v1_finseq_1_decl,type,
v1_finseq_1: $i > $o ).
thf(m2_subset_1_decl,type,
m2_subset_1: $i > $i > $i > $o ).
thf(k1_numbers_decl,type,
k1_numbers: $i ).
thf(k5_numbers_decl,type,
k5_numbers: $i ).
thf(k3_finseq_1_decl,type,
k3_finseq_1: $i > $i ).
thf(k1_nat_1_decl,type,
k1_nat_1: $i > $i > $i ).
thf(np__1_decl,type,
np__1: $i ).
thf(r1_xreal_0_decl,type,
r1_xreal_0: $i > $i > $o ).
thf(k1_funct_1_decl,type,
k1_funct_1: $i > $i > $i ).
thf(k2_finseq_3_decl,type,
k2_finseq_3: $i > $i > $i ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(r3_lattices_decl,type,
r3_lattices: $i > $i > $i > $o ).
thf(k4_lattices_decl,type,
k4_lattices: $i > $i > $i > $i ).
thf(k8_funct_2_decl,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(k4_filter_0_decl,type,
k4_filter_0: $i > $i > $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(r5_binop_1_decl,type,
r5_binop_1: $i > $i > $i > $o ).
thf(k7_filter_1_decl,type,
k7_filter_1: $i > $i > $i > $i > $i ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(r1_xboole_0_decl,type,
r1_xboole_0: $i > $i > $o ).
thf(k2_xboole_0_decl,type,
k2_xboole_0: $i > $i > $i ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(k3_partfun1_decl,type,
k3_partfun1: $i > $i > $i > $i ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(k1_relat_1_decl,type,
k1_relat_1: $i > $i ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(v1_int_1_decl,type,
v1_int_1: $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k6_xcmplx_0_decl,type,
k6_xcmplx_0: $i > $i > $i ).
thf(m1_filter_0_decl,type,
m1_filter_0: $i > $i > $o ).
thf(k7_filter_0_decl,type,
k7_filter_0: $i > $i > $i > $i ).
thf(v1_binop_1_decl,type,
v1_binop_1: $i > $i > $o ).
thf(r6_binop_1_decl,type,
r6_binop_1: $i > $i > $i > $o ).
thf(r4_binop_1_decl,type,
r4_binop_1: $i > $i > $i > $o ).
thf(r1_binop_1_decl,type,
r1_binop_1: $i > $i > $i > $o ).
thf(k1_binop_1_decl,type,
k1_binop_1: $i > $i > $i > $i ).
thf(k3_relat_1_decl,type,
k3_relat_1: $i > $i ).
thf(k3_xboole_0_decl,type,
k3_xboole_0: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k1_finseq_3_decl,type,
k1_finseq_3: $i > $i > $i ).
thf(k2_relat_1_decl,type,
k2_relat_1: $i > $i ).
thf(k4_finseq_1_decl,type,
k4_finseq_1: $i > $i ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(r2_wellord2_decl,type,
r2_wellord2: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(k6_subset_1_decl,type,
k6_subset_1: $i > $i > $i > $i ).
thf(m1_realset1_decl,type,
m1_realset1: $i > $i > $i > $o ).
thf(k1_realset1_decl,type,
k1_realset1: $i > $i > $i ).
thf(v4_lattice3_decl,type,
v4_lattice3: $i > $o ).
thf(r4_lattice3_decl,type,
r4_lattice3: $i > $i > $i > $o ).
thf(r1_lattices_decl,type,
r1_lattices: $i > $i > $i > $o ).
thf(m1_filter_1_decl,type,
m1_filter_1: $i > $i > $i > $o ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(k1_struct_0_decl,type,
k1_struct_0: $i > $i > $i ).
thf(m1_orders_1_decl,type,
m1_orders_1: $i > $i > $o ).
thf(k3_tarski_decl,type,
k3_tarski: $i > $i ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(v3_binop_1_decl,type,
v3_binop_1: $i > $i > $o ).
thf(m2_realset1_decl,type,
m2_realset1: $i > $i > $i > $o ).
thf(k4_card_1_decl,type,
k4_card_1: $i > $i ).
thf(k5_relat_1_decl,type,
k5_relat_1: $i > $i > $i ).
thf(k1_domain_1_decl,type,
k1_domain_1: $i > $i > $i > $i > $i ).
thf(v1_lattice4_decl,type,
v1_lattice4: $i > $i > $i > $o ).
thf(r2_binop_1_decl,type,
r2_binop_1: $i > $i > $i > $o ).
thf(k9_relat_1_decl,type,
k9_relat_1: $i > $i > $i ).
thf(r1_partfun1_decl,type,
r1_partfun1: $i > $i > $o ).
thf(k2_funcop_1_decl,type,
k2_funcop_1: $i > $i > $i ).
thf(v1_filter_0_decl,type,
v1_filter_0: $i > $i > $o ).
thf(k5_partfun1_decl,type,
k5_partfun1: $i > $i > $i > $i ).
thf(g1_group_1_decl,type,
g1_group_1: $i > $i > $i ).
thf(k33_binop_2_decl,type,
k33_binop_2: $i ).
thf(np__0_decl,type,
np__0: $i ).
thf(r3_lattice3_decl,type,
r3_lattice3: $i > $i > $i > $o ).
thf(k6_finseq_1_decl,type,
k6_finseq_1: $i > $i ).
thf(v2_binop_1_decl,type,
v2_binop_1: $i > $i > $o ).
thf(m2_finseq_1_decl,type,
m2_finseq_1: $i > $i > $o ).
thf(r1_filter_0_decl,type,
r1_filter_0: $i > $i > $i > $i > $o ).
thf(r3_binop_1_decl,type,
r3_binop_1: $i > $i > $i > $o ).
thf(m2_filter_1_decl,type,
m2_filter_1: $i > $i > $i > $o ).
thf(m1_finseq_1_decl,type,
m1_finseq_1: $i > $i > $o ).
thf(k2_card_1_decl,type,
k2_card_1: $i > $i ).
thf(k1_card_1_decl,type,
k1_card_1: $i > $i ).
thf(k6_filter_0_decl,type,
k6_filter_0: $i > $i > $i > $i ).
thf(k1_funct_2_decl,type,
k1_funct_2: $i > $i > $i ).
thf(k2_partfun1_decl,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(k1_partfun1_decl,type,
k1_partfun1: $i > $i > $i > $i > $i > $i > $i ).
thf(r7_binop_1_decl,type,
r7_binop_1: $i > $i > $i > $o ).
thf(k1_orders_1_decl,type,
k1_orders_1: $i > $i ).
thf(k2_funct_1_decl,type,
k2_funct_1: $i > $i ).
thf(k3_subset_1_decl,type,
k3_subset_1: $i > $i > $i ).
thf(k6_group_1_decl,type,
k6_group_1: $i > $i > $i > $i ).
thf(k1_group_1_decl,type,
k1_group_1: $i > $i > $i > $i ).
thf(k5_filter_0_decl,type,
k5_filter_0: $i > $i > $i > $i ).
thf(k7_setfam_1_decl,type,
k7_setfam_1: $i > $i > $i ).
thf(k2_funct_2_decl,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(k2_binop_1_decl,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(m4_vectsp_8_decl,type,
m4_vectsp_8: $i > $i > $i > $o ).
thf(m3_vectsp_8_decl,type,
m3_vectsp_8: $i > $i > $i > $o ).
thf(k1_funct_4_decl,type,
k1_funct_4: $i > $i > $i ).
thf(r2_lattice4_decl,type,
r2_lattice4: $i > $i > $i > $o ).
thf(k5_subset_1_decl,type,
k5_subset_1: $i > $i > $i > $i ).
thf(k4_subset_1_decl,type,
k4_subset_1: $i > $i > $i > $i ).
thf(v5_lattice3_decl,type,
v5_lattice3: $i > $o ).
thf(k1_real_1_decl,type,
k1_real_1: $i > $i ).
thf(l1_vectsp_1_decl,type,
l1_vectsp_1: $i > $o ).
thf(v2_group_1_decl,type,
v2_group_1: $i > $o ).
thf(v6_vectsp_1_decl,type,
v6_vectsp_1: $i > $o ).
thf(v8_vectsp_1_decl,type,
v8_vectsp_1: $i > $o ).
thf(k2_enumset1_decl,type,
k2_enumset1: $i > $i > $i > $i > $i ).
thf(k6_domain_1_decl,type,
k6_domain_1: $i > $i > $i ).
thf(k10_relset_1_decl,type,
k10_relset_1: $i > $i > $i > $i > $i ).
thf(v3_lattices_decl,type,
v3_lattices: $i > $o ).
thf(k15_lattice3_decl,type,
k15_lattice3: $i > $i > $i ).
thf(k6_relat_1_decl,type,
k6_relat_1: $i > $i ).
thf(k6_lattices_decl,type,
k6_lattices: $i > $i ).
thf(k10_filter_1_decl,type,
k10_filter_1: $i > $i > $i > $i > $i ).
thf(k3_setfam_1_decl,type,
k3_setfam_1: $i > $i > $i ).
thf(k2_xcmplx_0_decl,type,
k2_xcmplx_0: $i > $i > $i ).
thf(k5_lattices_decl,type,
k5_lattices: $i > $i ).
thf(k8_filter_0_decl,type,
k8_filter_0: $i > $i > $i ).
thf(k2_filter_0_decl,type,
k2_filter_0: $i > $i > $i ).
thf(k7_group_1_decl,type,
k7_group_1: $i > $i > $i ).
thf(k3_group_1_decl,type,
k3_group_1: $i > $i > $i ).
thf(k2_group_1_decl,type,
k2_group_1: $i > $i ).
thf(r1_lattice3_decl,type,
r1_lattice3: $i > $i > $i > $o ).
thf(k3_lattice3_decl,type,
k3_lattice3: $i > $i ).
thf(k4_lattice3_decl,type,
k4_lattice3: $i > $i > $i ).
thf(k7_lattices_decl,type,
k7_lattices: $i > $i > $i ).
thf(a_2_0_lattice3_decl,type,
a_2_0_lattice3: $i > $i > $i ).
thf(k3_filter_0_decl,type,
k3_filter_0: $i > $i > $i ).
thf(a_3_1_filter_0_decl,type,
a_3_1_filter_0: $i > $i > $i > $i ).
thf(v2_filter_0_decl,type,
v2_filter_0: $i > $i > $o ).
thf(k1_filter_0_decl,type,
k1_filter_0: $i > $i ).
thf(k3_funct_2_decl,type,
k3_funct_2: $i > $i > $i > $i > $i ).
thf(r1_realset1_decl,type,
r1_realset1: $i > $i > $i > $o ).
thf(a_2_5_lattice3_decl,type,
a_2_5_lattice3: $i > $i > $i ).
thf(k16_lattice3_decl,type,
k16_lattice3: $i > $i > $i ).
thf(a_2_6_lattice3_decl,type,
a_2_6_lattice3: $i > $i > $i ).
thf(k12_finseq_1_decl,type,
k12_finseq_1: $i > $i > $i ).
thf(m3_lattice4_decl,type,
m3_lattice4: $i > $i > $o ).
thf(k3_lattice4_decl,type,
k3_lattice4: $i > $i > $i ).
thf(k5_group_1_decl,type,
k5_group_1: $i > $i ).
thf(v6_group_1_decl,type,
v6_group_1: $i > $o ).
thf(r3_orders_2_decl,type,
r3_orders_2: $i > $i > $i > $o ).
thf(v7_group_1_decl,type,
v7_group_1: $i > $o ).
thf(k4_finseq_4_decl,type,
k4_finseq_4: $i > $i > $i > $i > $i ).
thf(k3_group_4_decl,type,
k3_group_4: $i > $i > $i ).
thf(k6_setfam_1_decl,type,
k6_setfam_1: $i > $i > $i ).
thf(r2_tarski_decl,type,
r2_tarski: $i > $i > $o ).
thf(k5_lattice4_decl,type,
k5_lattice4: $i > $i ).
thf(u2_lattices_decl,type,
u2_lattices: $i > $i ).
thf(u1_lattices_decl,type,
u1_lattices: $i > $i ).
thf(k9_filter_0_decl,type,
k9_filter_0: $i > $i > $i > $i ).
thf(k4_funct_2_decl,type,
k4_funct_2: $i > $i > $i > $i ).
thf(k3_lattices_decl,type,
k3_lattices: $i > $i > $i > $i ).
thf(k7_binop_2_decl,type,
k7_binop_2: $i > $i ).
thf(k8_setfam_1_decl,type,
k8_setfam_1: $i > $i > $i ).
thf(v6_ordinal1_decl,type,
v6_ordinal1: $i > $o ).
thf(a_2_2_lattice3_decl,type,
a_2_2_lattice3: $i > $i > $i ).
thf(k3_xcmplx_0_decl,type,
k3_xcmplx_0: $i > $i > $i ).
thf(k8_finseq_1_decl,type,
k8_finseq_1: $i > $i > $i > $i ).
thf(v6_lattice3_decl,type,
v6_lattice3: $i > $o ).
thf(a_3_5_lattice3_decl,type,
a_3_5_lattice3: $i > $i > $i > $i ).
thf(k4_lattice4_decl,type,
k4_lattice4: $i > $i > $i ).
thf(g4_vectsp_1_decl,type,
g4_vectsp_1: $i > $i > $i > $i > $i > $i ).
thf(k4_numbers_decl,type,
k4_numbers: $i ).
thf(r2_setfam_1_decl,type,
r2_setfam_1: $i > $i > $o ).
thf(m1_group_2_decl,type,
m1_group_2: $i > $i > $o ).
thf(l1_lattices_decl,type,
l1_lattices: $i > $o ).
thf(v3_funct_2_decl,type,
v3_funct_2: $i > $i > $i > $o ).
thf(m2_lattice4_decl,type,
m2_lattice4: $i > $i > $o ).
thf(r3_lattice4_decl,type,
r3_lattice4: $i > $i > $i > $o ).
thf(a_3_2_domain_1_decl,type,
a_3_2_domain_1: $i > $i > $i > $i ).
thf(a_2_0_lattice4_decl,type,
a_2_0_lattice4: $i > $i > $i ).
thf(k3_binop_1_decl,type,
k3_binop_1: $i > $i > $i ).
thf(k1_setfam_1_decl,type,
k1_setfam_1: $i > $i ).
thf(v1_card_1_decl,type,
v1_card_1: $i > $o ).
thf(a_2_2_domain_1_decl,type,
a_2_2_domain_1: $i > $i > $i ).
thf(k9_filter_1_decl,type,
k9_filter_1: $i > $i ).
thf(k1_int_2_decl,type,
k1_int_2: $i > $i ).
thf(r1_rlvect_1_decl,type,
r1_rlvect_1: $i > $i > $o ).
thf(l2_lattices_decl,type,
l2_lattices: $i > $o ).
thf(k1_subset_1_decl,type,
k1_subset_1: $i > $i ).
thf(k2_subset_1_decl,type,
k2_subset_1: $i > $i ).
thf(k2_struct_0_decl,type,
k2_struct_0: $i > $i > $i > $i ).
thf(v1_group_6_decl,type,
v1_group_6: $i > $i > $i > $o ).
thf(k2_nat_1_decl,type,
k2_nat_1: $i > $i > $i ).
thf(k17_group_2_decl,type,
k17_group_2: $i > $i > $i ).
thf(k2_group_3_decl,type,
k2_group_3: $i > $i > $i > $i ).
thf(k7_rlvect_1_decl,type,
k7_rlvect_1: $i > $i > $i > $i ).
thf(v5_group_1_decl,type,
v5_group_1: $i > $i > $o ).
thf(k2_group_4_decl,type,
k2_group_4: $i > $i ).
thf(k5_setfam_1_decl,type,
k5_setfam_1: $i > $i > $i ).
thf(a_3_1_domain_1_decl,type,
a_3_1_domain_1: $i > $i > $i > $i ).
thf(k14_group_2_decl,type,
k14_group_2: $i > $i > $i ).
thf(a_1_0_filter_1_decl,type,
a_1_0_filter_1: $i > $i ).
thf(k1_finsub_1_decl,type,
k1_finsub_1: $i > $i > $i > $i ).
thf(v2_group_6_decl,type,
v2_group_6: $i > $i > $i > $o ).
thf(r2_lattice3_decl,type,
r2_lattice3: $i > $i > $i > $o ).
thf(k2_vectsp_1_decl,type,
k2_vectsp_1: $i > $i ).
thf(u1_vectsp_1_decl,type,
u1_vectsp_1: $i > $i ).
thf(a_3_3_lattice3_decl,type,
a_3_3_lattice3: $i > $i > $i > $i ).
thf(k4_group_4_decl,type,
k4_group_4: $i > $i > $i > $i ).
thf(k1_finsop_1_decl,type,
k1_finsop_1: $i > $i > $i > $i ).
thf(a_3_9_lattice3_decl,type,
a_3_9_lattice3: $i > $i > $i > $i ).
thf(a_3_10_lattice3_decl,type,
a_3_10_lattice3: $i > $i > $i > $i ).
thf(g3_lattices_decl,type,
g3_lattices: $i > $i > $i > $i ).
thf(a_3_6_lattice3_decl,type,
a_3_6_lattice3: $i > $i > $i > $i ).
thf(m1_eqrel_1_decl,type,
m1_eqrel_1: $i > $i > $o ).
thf(l2_struct_0_decl,type,
l2_struct_0: $i > $o ).
thf(k7_funct_2_decl,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(a_2_0_filter_0_decl,type,
a_2_0_filter_0: $i > $i > $i ).
thf(a_3_7_lattice3_decl,type,
a_3_7_lattice3: $i > $i > $i > $i ).
thf(a_3_8_lattice3_decl,type,
a_3_8_lattice3: $i > $i > $i > $i ).
thf(k1_group_3_decl,type,
k1_group_3: $i > $i ).
thf(v1_group_1_decl,type,
v1_group_1: $i > $o ).
thf(k2_latsubgr_decl,type,
k2_latsubgr: $i > $i > $i ).
thf(k1_latsubgr_decl,type,
k1_latsubgr: $i > $i ).
thf(k9_group_1_decl,type,
k9_group_1: $i > $i ).
thf(a_3_3_domain_1_decl,type,
a_3_3_domain_1: $i > $i > $i > $i ).
thf(a_2_7_lattice3_decl,type,
a_2_7_lattice3: $i > $i > $i ).
thf(k10_group_1_decl,type,
k10_group_1: $i > $i > $i > $i ).
thf(a_1_0_domain_1_decl,type,
a_1_0_domain_1: $i > $i ).
thf(a_2_3_lattice3_decl,type,
a_2_3_lattice3: $i > $i > $i ).
thf(a_2_4_lattice3_decl,type,
a_2_4_lattice3: $i > $i > $i ).
thf(k5_int_1_decl,type,
k5_int_1: $i > $i > $i ).
thf(r1_group_2_decl,type,
r1_group_2: $i > $i > $i > $o ).
thf(k8_group_4_decl,type,
k8_group_4: $i > $i > $i > $i ).
thf(k3_group_3_decl,type,
k3_group_3: $i > $i > $i > $i ).
thf(k4_group_3_decl,type,
k4_group_3: $i > $i > $i > $i ).
thf(k3_group_2_decl,type,
k3_group_2: $i > $i > $i > $i ).
thf(k7_group_2_decl,type,
k7_group_2: $i > $i > $i ).
thf(v1_group_3_decl,type,
v1_group_3: $i > $i > $o ).
thf(v3_group_6_decl,type,
v3_group_6: $i > $i > $i > $o ).
thf(k11_group_6_decl,type,
k11_group_6: $i > $i > $i ).
thf(k6_group_6_decl,type,
k6_group_6: $i > $i > $i ).
thf(k2_group_2_decl,type,
k2_group_2: $i > $i > $i > $i ).
thf(k13_group_2_decl,type,
k13_group_2: $i > $i > $i > $i ).
thf(k6_group_2_decl,type,
k6_group_2: $i > $i ).
thf(k8_group_1_decl,type,
k8_group_1: $i > $i ).
thf(k12_group_2_decl,type,
k12_group_2: $i > $i > $i > $i ).
thf(k16_group_2_decl,type,
k16_group_2: $i > $i > $i ).
thf(k13_group_6_decl,type,
k13_group_6: $i > $i > $i > $i ).
thf(k8_relset_1_decl,type,
k8_relset_1: $i > $i > $i > $i > $i ).
thf(k10_group_2_decl,type,
k10_group_2: $i > $i > $i > $i ).
thf(k4_group_2_decl,type,
k4_group_2: $i > $i > $i > $i ).
thf(k11_group_2_decl,type,
k11_group_2: $i > $i > $i > $i ).
thf(u1_group_1_decl,type,
u1_group_1: $i > $i ).
thf(k2_group_6_decl,type,
k2_group_6: $i > $i > $i > $i ).
thf(m1_group_6_decl,type,
m1_group_6: $i > $i > $i > $o ).
thf(a_3_0_filter_0_decl,type,
a_3_0_filter_0: $i > $i > $i > $i ).
thf(k1_group_6_decl,type,
k1_group_6: $i > $i > $i > $i ).
thf(k9_group_2_decl,type,
k9_group_2: $i > $i > $i > $i ).
thf(k5_group_4_decl,type,
k5_group_4: $i > $i > $i ).
thf(k8_group_3_decl,type,
k8_group_3: $i > $i > $i ).
thf(r4_group_3_decl,type,
r4_group_3: $i > $i > $i > $o ).
thf(k7_group_3_decl,type,
k7_group_3: $i > $i > $i ).
thf(k5_group_3_decl,type,
k5_group_3: $i > $i > $i > $i ).
thf(np__2_decl,type,
np__2: $i ).
thf(a_2_1_domain_1_decl,type,
a_2_1_domain_1: $i > $i > $i ).
thf(k4_group_6_decl,type,
k4_group_6: $i > $i > $i ).
thf(k5_group_2_decl,type,
k5_group_2: $i > $i ).
thf(k7_group_4_decl,type,
k7_group_4: $i > $i > $i > $i ).
thf(k5_group_6_decl,type,
k5_group_6: $i > $i > $i ).
thf(k18_group_2_decl,type,
k18_group_2: $i > $i > $i ).
thf(k7_domain_1_decl,type,
k7_domain_1: $i > $i > $i > $i ).
thf(a_1_0_group_2_decl,type,
a_1_0_group_2: $i > $i ).
thf(k6_group_3_decl,type,
k6_group_3: $i > $i > $i > $i ).
thf(a_3_0_group_2_decl,type,
a_3_0_group_2: $i > $i > $i > $i ).
thf(v4_group_6_decl,type,
v4_group_6: $i > $i > $i > $o ).
thf(k8_group_6_decl,type,
k8_group_6: $i > $i > $i > $i > $i > $i ).
thf(r2_group_6_decl,type,
r2_group_6: $i > $i > $o ).
thf(k9_group_6_decl,type,
k9_group_6: $i > $i > $i > $i ).
thf(k1_group_2_decl,type,
k1_group_2: $i > $i > $i ).
thf(k3_finsub_1_decl,type,
k3_finsub_1: $i > $i > $i > $i ).
thf(a_3_4_lattice3_decl,type,
a_3_4_lattice3: $i > $i > $i > $i ).
thf(k9_group_4_decl,type,
k9_group_4: $i > $i ).
thf(k8_group_2_decl,type,
k8_group_2: $i > $i > $i > $i ).
thf(r1_nat_1_decl,type,
r1_nat_1: $i > $i > $o ).
thf(k12_group_6_decl,type,
k12_group_6: $i > $i > $i > $i ).
thf(v2_group_4_decl,type,
v2_group_4: $i > $i > $o ).
thf(k6_group_4_decl,type,
k6_group_4: $i > $i ).
thf(k10_group_4_decl,type,
k10_group_4: $i > $i ).
thf(k10_domain_1_decl,type,
k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k1_group_4_decl,type,
k1_group_4: $i > $i > $i > $i ).
thf(k9_group_3_decl,type,
k9_group_3: $i > $i > $i ).
thf(a_3_2_lattice3_decl,type,
a_3_2_lattice3: $i > $i > $i > $i ).
thf(k15_group_2_decl,type,
k15_group_2: $i > $i > $i ).
thf(k9_group_5_decl,type,
k9_group_5: $i > $i ).
thf(k7_group_6_decl,type,
k7_group_6: $i > $i > $i > $i ).
thf(k10_group_3_decl,type,
k10_group_3: $i > $i > $i ).
thf(a_1_0_group_4_decl,type,
a_1_0_group_4: $i > $i ).
thf(r6_group_3_decl,type,
r6_group_3: $i > $i > $i > $o ).
thf(k11_group_3_decl,type,
k11_group_3: $i > $i > $i ).
thf(k12_domain_1_decl,type,
k12_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(v1_group_4_decl,type,
v1_group_4: $i > $i > $o ).
thf(p1_s2_card_1_decl,type,
p1_s2_card_1: $i > $o ).
thf(a_1_2_domain_1_decl,type,
a_1_2_domain_1: $i > $i ).
thf(r5_group_3_decl,type,
r5_group_3: $i > $i > $i > $o ).
thf(k2_finseq_4_decl,type,
k2_finseq_4: $i > $i > $i > $i ).
thf(k4_group_1_decl,type,
k4_group_1: $i > $i ).
thf(a_2_0_group_2_decl,type,
a_2_0_group_2: $i > $i > $i ).
thf(a_3_6_domain_1_decl,type,
a_3_6_domain_1: $i > $i > $i > $i ).
thf(k11_relset_1_decl,type,
k11_relset_1: $i > $i > $i > $i > $i ).
thf(k3_finseq_4_decl,type,
k3_finseq_4: $i > $i > $i > $i > $i ).
thf(k8_rlvect_1_decl,type,
k8_rlvect_1: $i > $i > $i > $i > $i ).
thf(a_2_0_group_4_decl,type,
a_2_0_group_4: $i > $i > $i ).
thf(k10_group_6_decl,type,
k10_group_6: $i > $i > $i ).
thf(a_3_5_domain_1_decl,type,
a_3_5_domain_1: $i > $i > $i > $i ).
thf(p1_s1_int_1_decl,type,
p1_s1_int_1: $i > $o ).
thf(a_3_4_domain_1_decl,type,
a_3_4_domain_1: $i > $i > $i > $i ).
thf(k9_domain_1_decl,type,
k9_domain_1: $i > $i > $i > $i > $i > $i ).
thf(k3_group_6_decl,type,
k3_group_6: $i > $i > $i > $i ).
thf(a_3_0_group_6_decl,type,
a_3_0_group_6: $i > $i > $i > $i ).
thf(a_3_0_group_3_decl,type,
a_3_0_group_3: $i > $i > $i > $i ).
thf(a_1_1_domain_1_decl,type,
a_1_1_domain_1: $i > $i ).
thf(k3_group_5_decl,type,
k3_group_5: $i > $i > $i > $i > $i ).
thf(r1_group_6_decl,type,
r1_group_6: $i > $i > $o ).
thf(u2_struct_0_decl,type,
u2_struct_0: $i > $i ).
thf(k2_group_5_decl,type,
k2_group_5: $i > $i > $i > $i ).
thf(a_2_3_group_3_decl,type,
a_2_3_group_3: $i > $i > $i ).
thf(a_2_1_group_3_decl,type,
a_2_1_group_3: $i > $i > $i ).
thf(k11_domain_1_decl,type,
k11_domain_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k13_domain_1_decl,type,
k13_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k8_domain_1_decl,type,
k8_domain_1: $i > $i > $i > $i > $i ).
thf(k4_xcmplx_0_decl,type,
k4_xcmplx_0: $i > $i ).
thf(v3_realset2_decl,type,
v3_realset2: $i > $o ).
thf(a_3_7_domain_1_decl,type,
a_3_7_domain_1: $i > $i > $i > $i ).
thf(f1_s2_group_4_decl,type,
f1_s2_group_4: $i ).
thf(p1_s2_group_4_decl,type,
p1_s2_group_4: $i > $o ).
thf(k6_eqrel_1_decl,type,
k6_eqrel_1: $i > $i > $i > $i ).
thf(a_1_0_group_6_decl,type,
a_1_0_group_6: $i > $i ).
thf(r3_group_3_decl,type,
r3_group_3: $i > $i > $i > $o ).
thf(r1_group_3_decl,type,
r1_group_3: $i > $i > $i > $o ).
thf(a_2_0_group_3_decl,type,
a_2_0_group_3: $i > $i > $i ).
thf(r2_group_3_decl,type,
r2_group_3: $i > $i > $i > $o ).
thf(k6_finseqop_decl,type,
k6_finseqop: $i > $i > $i ).
thf(v1_setwiseo_decl,type,
v1_setwiseo: $i > $i > $o ).
thf(r1_finseqop_decl,type,
r1_finseqop: $i > $i > $i > $o ).
thf(a_2_2_group_3_decl,type,
a_2_2_group_3: $i > $i > $i ).
thf(a_1_1_group_4_decl,type,
a_1_1_group_4: $i > $i ).
thf(k2_finsop_1_decl,type,
k2_finsop_1: $i > $i > $i > $i ).
thf(np__3_decl,type,
np__3: $i ).
thf(v1_finseqop_decl,type,
v1_finseqop: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i > $i > $i ).
thf(sk15_decl,type,
sk15: $i ).
thf(sk19_decl,type,
sk19: $i ).
thf(sk24_decl,type,
sk24: $i ).
thf(sk27_decl,type,
sk27: $i ).
thf(sk37_decl,type,
sk37: $i > $i ).
thf(sk48_decl,type,
sk48: $i ).
thf(sk81_decl,type,
sk81: $i > $i ).
thf(sk82_decl,type,
sk82: $i > $i > $i ).
thf(sk110_decl,type,
sk110: $i ).
thf(sk111_decl,type,
sk111: $i > $i > $i ).
thf(sk118_decl,type,
sk118: $i > $i > $i ).
thf(sk145_decl,type,
sk145: $i ).
thf(sk149_decl,type,
sk149: $i > $i ).
thf(sk150_decl,type,
sk150: $i > $i ).
thf(sk152_decl,type,
sk152: $i ).
thf(sk167_decl,type,
sk167: $i ).
thf(sk179_decl,type,
sk179: $i ).
thf(sk180_decl,type,
sk180: $i > $i > $i ).
thf(sk196_decl,type,
sk196: $i ).
thf(sk235_decl,type,
sk235: $i ).
thf(sk253_decl,type,
sk253: $i ).
thf(sk259_decl,type,
sk259: $i ).
thf(sk261_decl,type,
sk261: $i ).
thf(sk272_decl,type,
sk272: $i ).
thf(sk280_decl,type,
sk280: $i ).
thf(sk297_decl,type,
sk297: $i > $i ).
thf(sk305_decl,type,
sk305: $i > $i ).
thf(sk330_decl,type,
sk330: $i > $i ).
thf(sk335_decl,type,
sk335: $i ).
thf(sk348_decl,type,
sk348: $i > $i ).
thf(sk370_decl,type,
sk370: $i ).
thf(sk378_decl,type,
sk378: $i > $i ).
thf(sk385_decl,type,
sk385: $i ).
thf(sk388_decl,type,
sk388: $i ).
thf(sk397_decl,type,
sk397: $i > $i > $i > $i ).
thf(sk398_decl,type,
sk398: $i > $i > $o ).
thf(sk399_decl,type,
sk399: $i > $i > $i ).
thf(sk400_decl,type,
sk400: $i > $i > $i ).
thf(sk401_decl,type,
sk401: $i > $i > $i ).
thf(sk464_decl,type,
sk464: $i ).
thf(sk481_decl,type,
sk481: $i > $i ).
thf(sk510_decl,type,
sk510: $i ).
thf(sk522_decl,type,
sk522: $i ).
thf(sk524_decl,type,
sk524: $i > $i ).
thf(sk537_decl,type,
sk537: $i ).
thf(sk544_decl,type,
sk544: $i ).
thf(sk545_decl,type,
sk545: $i ).
thf(sk554_decl,type,
sk554: $i > $i ).
thf(sk555_decl,type,
sk555: $i ).
thf(sk561_decl,type,
sk561: $i > $i > $i ).
thf(sk562_decl,type,
sk562: $i > $i > $i ).
thf(sk569_decl,type,
sk569: $i > $i ).
thf(sk581_decl,type,
sk581: $i ).
thf(sk593_decl,type,
sk593: $i ).
thf(sk605_decl,type,
sk605: $i ).
thf(sk607_decl,type,
sk607: $i ).
thf(sk608_decl,type,
sk608: $i ).
thf(sk610_decl,type,
sk610: $i ).
thf(sk611_decl,type,
sk611: $i ).
thf(sk612_decl,type,
sk612: $i ).
thf(sk636_decl,type,
sk636: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k6_partfun1 @ ( A @ ( A @ k3_latsubgr ) ) )
= ( A @ k11_group_4 @ u1_struct_0 @ k6_partfun1 ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k1_binop_1 ) ) )
= D ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( E @ ( D @ ( A @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) )
& ( ( F @ ( E @ ( A @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( C @ ( B @ ( A @ sk3 ) ) @ ( A @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( C @ ( B @ ( A @ sk3 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) )
& ( ( E @ ( D @ ( A @ k1_binop_1 ) ) @ ( C @ ( B @ ( A @ sk3 ) ) @ ( B @ k1_binop_1 ) ) )
= ( E @ ( C @ ( B @ ( A @ sk3 ) ) @ ( B @ k1_binop_1 ) ) @ ( D @ ( C @ ( B @ ( A @ sk3 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ sk4 ) ) @ ( C @ ( B @ ( A @ sk3 ) ) @ ( A @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( D @ ( C @ ( B @ ( A @ sk4 ) ) @ ( B @ k1_binop_1 ) ) @ ( D @ ( C @ ( B @ ( A @ sk3 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ sk4 ) ) @ ( A @ k1_binop_1 ) ) @ ( C @ ( B @ ( A @ sk3 ) ) @ ( B @ k1_binop_1 ) ) )
= ( D @ ( C @ ( B @ ( A @ sk3 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ ( B @ ( A @ sk4 ) ) @ ( C @ ( B @ ( A @ sk3 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ~ ( ( C @ ( np__1 @ r1_xreal_0 ) )
& ( C
= ( B @ ( A @ k6_xcmplx_0 ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( A @ ( D @ ( B @ r4_lattice3 ) ) )
=> ( D @ ( C @ ( B @ r1_lattices ) ) ) ) )
& ( A @ ( C @ ( B @ r4_lattice3 ) ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] :
~ ? [C: $i] :
( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ r4_lattice3 ) ) )
=> ( D @ ( C @ ( A @ r1_lattices ) ) ) ) )
& ( B @ ( C @ ( A @ r4_lattice3 ) ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ sk8 @ ( C @ ( B @ r4_lattice3 ) ) )
=> ( C @ ( A @ ( B @ r1_lattices ) ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( B @ ( C @ m1_filter_1 ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_finseq_1 )
& ( B @ v1_finset_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ ( k5_numbers @ ( B @ m1_relset_1 ) ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( A @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ r1_lattices ) ) ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( @+[A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk24_def,definition,
( sk24
= ( @+[A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( @+[A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk37_def,definition,
( sk37
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_finseq_1 )
& ( B @ v1_finset_1 )
& ( B @ v2_funct_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_finseq_1 ) ) ) ) ) ).
thf(sk48_def,definition,
( sk48
= ( @+[A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk81_def,definition,
( sk81
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ? [C: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ~ ? [C: $i] :
( ~ ? [D: $i] :
( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ) ) ) ).
thf(sk82_def,definition,
( sk82
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ! [D: $i] :
( ( A @ ( D @ r1_tarski ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( B @ sk81 @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk110_def,definition,
( sk110
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ) ) ) ).
thf(sk111_def,definition,
( sk111
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( A @ ( B @ ( C @ m1_relset_1 ) ) ) ) ) ) ).
thf(sk118_def,definition,
( sk118
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( A @ ( B @ ( C @ m1_relset_1 ) ) ) ) ) ) ).
thf(sk145_def,definition,
( sk145
= ( @+[A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk149_def,definition,
( sk149
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( B = C ) ) ) ) ) ) ).
thf(sk150_def,definition,
( sk150
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k1_relat_1 )
= A )
& ( ( A @ sk149 @ k1_relat_1 )
= A ) )
=> ( ( A @ sk149 )
= B ) ) ) ) ) ).
thf(sk152_def,definition,
( sk152
= ( @+[A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk167_def,definition,
( sk167
= ( @+[A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk179_def,definition,
( sk179
= ( @+[A: $i] : ( A @ l1_struct_0 ) ) ) ).
thf(sk180_def,definition,
( sk180
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A
= ( C @ k1_relat_1 ) ) ) ) ) ) ).
thf(sk196_def,definition,
( sk196
= ( @+[A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk235_def,definition,
( sk235
= ( @+[A: $i] : ( A @ l1_lattices ) ) ) ).
thf(sk253_def,definition,
( sk253
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk259_def,definition,
( sk259
= ( @+[A: $i] :
( ( A @ v8_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_vectsp_1 ) ) ) ) ).
thf(sk261_def,definition,
( sk261
= ( @+[A: $i] : ( A @ l2_lattices ) ) ) ).
thf(sk272_def,definition,
( sk272
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk280_def,definition,
( sk280
= ( @+[A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk297_def,definition,
( sk297
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_eqrel_1 ) ) ) ) ).
thf(sk305_def,definition,
( sk305
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_subset_1 ) ) ) ) ).
thf(sk330_def,definition,
( sk330
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk335_def,definition,
( sk335
= ( @+[A: $i] :
( ( A @ v1_group_1 )
& ( A @ l1_group_1 ) ) ) ) ).
thf(sk348_def,definition,
( sk348
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m2_finseq_1 ) ) ) ) ).
thf(sk370_def,definition,
( sk370
= ( @+[A: $i] : ( A @ l1_vectsp_1 ) ) ) ).
thf(sk378_def,definition,
( sk378
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_finseq_1 ) ) ) ) ).
thf(sk385_def,definition,
( sk385
= ( @+[A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk388_def,definition,
( sk388
= ( @+[A: $i] : ( A @ v1_xboole_0 ) ) ) ).
thf(sk397_def,definition,
( sk397
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( A @ r2_hidden ) ) ) ) ) ).
thf(sk399_def,definition,
( sk399
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ).
thf(sk400_def,definition,
( sk400
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ r2_hidden ) )
=> ( C @ ( B @ ( A @ sk399 ) @ r2_hidden ) ) ) ) ) ).
thf(sk401_def,definition,
( sk401
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk464_def,definition,
( sk464
= ( @+[A: $i] :
( ! [B: $i] :
( ( B @ v1_int_1 )
=> ( ( ( B @ p1_s1_int_1 )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s1_int_1 ) ) ) )
& ( k4_numbers @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ) ) ) ).
thf(sk481_def,definition,
( sk481
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ r2_hidden ) ) ) ) ).
thf(sk510_def,definition,
( sk510
= ( @+[A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk522_def,definition,
( sk522
= ( @+[A: $i] : ( A @ v1_card_1 ) ) ) ).
thf(sk524_def,definition,
( sk524
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ? [C: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ) ) ) ).
thf(sk537_def,definition,
( sk537
= ( @+[A: $i] : ( A @ l2_struct_0 ) ) ) ).
thf(sk544_def,definition,
( sk544
= ( @+[A: $i] : ( A @ v1_int_1 ) ) ) ).
thf(sk545_def,definition,
( sk545
= ( @+[A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk554_def,definition,
( sk554
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ k1_tarski ) ) ) ) ).
thf(sk555_def,definition,
( sk555
= ( @+[A: $i] :
~ ( A @ v1_xboole_0 ) ) ) ).
thf(sk561_def,definition,
( sk561
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
=> ( C = B ) ) ) ) ).
thf(sk562_def,definition,
( sk562
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C = B )
=> ( A @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk569_def,definition,
( sk569
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ k1_tarski ) ) ) ) ).
thf(sk581_def,definition,
( sk581
= ( @+[A: $i] :
( ! [B: $i] :
( ( ( f1_s2_group_4 @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( B @ p1_s2_group_4 )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s2_group_4 ) ) ) )
& ( f1_s2_group_4 @ k1_group_3 @ ( A @ r1_tarski ) ) ) ) ) ).
thf(sk593_def,definition,
( sk593
= ( @+[A: $i] : ( A @ l3_lattices ) ) ) ).
thf(sk605_def,definition,
( sk605
= ( @+[A: $i] :
( ( A @ v3_realset2 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ) ) ) ).
thf(sk607_def,definition,
( sk607
= ( @+[A: $i] :
( ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ) ) ) ).
thf(sk608_def,definition,
( sk608
= ( @+[A: $i] :
( ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v2_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ) ) ) ).
thf(sk610_def,definition,
( sk610
= ( @+[A: $i] :
( ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v2_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ) ) ) ).
thf(sk611_def,definition,
( sk611
= ( @+[A: $i] :
( ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ) ) ) ).
thf(sk612_def,definition,
( sk612
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ) ) ) ).
thf(sk636_def,definition,
( sk636
= ( @+[A: $i] : ( A @ l1_group_1 ) ) ) ).
thf(1319,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k6_lattices @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_lattices) ).
thf(8536,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k6_lattices @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).
thf(974,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( B @ k1_relat_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funct_2) ).
thf(6836,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( B @ k1_relat_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(1261,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ! [D: $i] :
( ( C @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( B @ ( C @ ( A @ k12_group_2 ) ) ) )
=> ( ( D @ ( C @ ( A @ k6_group_6 ) @ k3_group_1 ) )
= ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k12_group_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_group_6) ).
thf(8186,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ! [D: $i] :
( ( C @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( B @ ( C @ ( A @ k12_group_2 ) ) ) )
=> ( ( D @ ( C @ ( A @ k6_group_6 ) @ k3_group_1 ) )
= ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k12_group_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_finseq_3 ) @ v1_finseq_1 )
& ( B @ ( A @ k1_finseq_3 ) @ v1_funct_1 )
& ( B @ ( A @ k1_finseq_3 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_finseq_3) ).
thf(2612,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_finseq_3 ) @ v1_finseq_1 )
& ( B @ ( A @ k1_finseq_3 ) @ v1_funct_1 )
& ( B @ ( A @ k1_finseq_3 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(2058,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k2_subset_1 @ ( A @ k1_group_2 ) )
= ( A @ u1_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_group_2) ).
thf(12116,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k2_subset_1 @ ( A @ k1_group_2 ) )
= ( A @ u1_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2058]) ).
thf(520,axiom,
! [A: $i] :
( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_1) ).
thf(4538,plain,
! [A: $i] :
( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(4539,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
| ( ( A @ sk149 )
!= ( A @ sk150 ) ) )
& ( ( A = k1_xboole_0 )
| ( ( A @ sk150 @ k1_relat_1 )
= A ) )
& ( ( A = k1_xboole_0 )
| ( ( A @ sk149 @ k1_relat_1 )
= A ) )
& ( ( A = k1_xboole_0 )
| ( A @ sk150 @ v1_funct_1 ) )
& ( ( A = k1_xboole_0 )
| ( A @ sk150 @ v1_relat_1 ) )
& ( ( A = k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) )
& ( ( A = k1_xboole_0 )
| ( A @ sk149 @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[4538]) ).
thf(4546,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[4539]) ).
thf(4548,plain,
! [A: $i] :
( ( A @ sk149 @ v1_funct_1 )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[4546]) ).
thf(808,axiom,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(6054,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(6055,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[6054]) ).
thf(6056,plain,
k1_xboole_0 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[6055]) ).
thf(784,axiom,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(5951,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(5952,plain,
~ ? [A: $i] : ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[5951]) ).
thf(5953,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[5952]) ).
thf(14700,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,5953]) ).
thf(14701,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[14700]) ).
thf(14707,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[14701]) ).
thf(22693,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( B @ k1_funct_2 ) ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,14707]) ).
thf(22694,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( B @ k1_funct_2 ) ) )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[22693]) ).
thf(22695,plain,
! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ sk149 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[22694:[bind(A,$thf( D @ ( D @ k1_funct_2 ) )),bind(B,$thf( D ))]]) ).
thf(23105,plain,
! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ sk149 @ v1_funct_1 ),
inference(simp,[status(thm)],[22695]) ).
thf(1559,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( A @ k9_group_3 ) @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k9_group_3 ) @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_group_3) ).
thf(9864,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( A @ k9_group_3 ) @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k9_group_3 ) @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1559]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
= ( D @ ( B @ k4_xboole_0 ) @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_zfmisc_1) ).
thf(2278,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
= ( D @ ( B @ k4_xboole_0 ) @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(2279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
= ( D @ ( B @ k4_xboole_0 ) @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ),
inference(cnf,[status(esa)],[2278]) ).
thf(2280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ k4_xboole_0 ) @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ k2_xboole_0 ) )
= ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ),
inference(lifteq,[status(thm)],[2279]) ).
thf(7,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ l3_lattices )
& ( B @ v16_lattices )
& ( B @ v15_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
<=> ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_filter_1) ).
thf(2143,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) )
=> ( ( B @ l3_lattices )
& ( B @ v16_lattices )
& ( B @ v15_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) )
& ( ( ( B @ l3_lattices )
& ( B @ v16_lattices )
& ( B @ v15_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2144,plain,
! [B: $i,A: $i] :
( ( ( B @ l3_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) )
& ( ( B @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) )
& ( ( B @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) )
& ( ( B @ v10_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) )
& ( ~ ( B @ v3_struct_0 )
| ~ ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) )
& ( ( A @ l3_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) )
& ( ( A @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) )
& ( ( A @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) )
& ( ( A @ v10_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) )
& ( ~ ( A @ v3_struct_0 )
| ~ ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) )
& ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ l3_lattices )
| ~ ( B @ v16_lattices )
| ~ ( B @ v15_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) )
& ( ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ l3_lattices )
| ~ ( B @ v16_lattices )
| ~ ( B @ v15_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) )
& ( ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ l3_lattices )
| ~ ( B @ v16_lattices )
| ~ ( B @ v15_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) )
& ( ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ~ ( B @ l3_lattices )
| ~ ( B @ v16_lattices )
| ~ ( B @ v15_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) )
& ( ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v16_lattices )
| ~ ( B @ v15_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ) ),
inference(cnf,[status(esa)],[2143]) ).
thf(2156,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ l3_lattices )
| ~ ( B @ v16_lattices )
| ~ ( B @ v15_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2144]) ).
thf(2163,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ v16_lattices )
| ~ ( B @ v15_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[2156]) ).
thf(1334,axiom,
( ( k1_xboole_0 @ k1_card_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_card_1) ).
thf(8606,plain,
( ( k1_xboole_0 @ k1_card_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).
thf(8607,plain,
( ( k1_xboole_0 @ k1_card_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[8606]) ).
thf(172,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_finseq_1 )
& ( B @ v1_finset_1 )
& ( B @ v2_funct_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_finseq_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finseq_1) ).
thf(2817,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_finseq_1 )
& ( B @ v1_finset_1 )
& ( B @ v2_funct_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_finseq_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(2818,plain,
! [A: $i] :
( ( A @ sk37 @ v1_finseq_1 )
& ( A @ sk37 @ v1_finset_1 )
& ( A @ sk37 @ v2_funct_1 )
& ( A @ sk37 @ v1_funct_1 )
& ( A @ sk37 @ v1_relat_1 )
& ( A @ sk37 @ v1_xboole_0 )
& ( A @ ( A @ sk37 @ m1_finseq_1 ) ) ),
inference(cnf,[status(esa)],[2817]) ).
thf(2823,plain,
! [A: $i] : ( A @ sk37 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[2818]) ).
thf(1050,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(7165,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(7166,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[7165]) ).
thf(7167,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[7166]) ).
thf(1616,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(10195,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1616]) ).
thf(10196,plain,
! [A: $i] :
? [B: $i] :
( ~ ? [C: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[10195]) ).
thf(10197,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk524 @ ( E @ r2_hidden ) )
| ( A @ sk524 @ ( E @ r2_tarski ) )
| ~ ( A @ sk524 @ ( E @ r1_tarski ) ) )
& ( ( A @ sk524 @ ( D @ k1_zfmisc_1 @ r2_hidden ) )
| ~ ( A @ sk524 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk524 @ ( C @ r2_hidden ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ sk524 @ ( B @ r2_hidden ) ) )
& ( A @ sk524 @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[10196]) ).
thf(10198,plain,
! [A: $i] : ( A @ sk524 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[10197]) ).
thf(1526,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(9697,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1526]) ).
thf(9698,plain,
( ! [A: $i] :
( ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) )
=> ( A = k1_xboole_0 ) )
& ! [A: $i] :
( ( A = k1_xboole_0 )
=> ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) ) ) ),
inference(miniscope,[status(thm)],[9697]) ).
thf(9699,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = k1_xboole_0 )
| ( C @ ( C @ sk481 @ r2_hidden ) ) )
& ( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[9698]) ).
thf(9700,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[9699]) ).
thf(9702,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[9700]) ).
thf(9703,plain,
! [A: $i] :
~ ( k1_xboole_0 @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[9702]) ).
thf(16245,plain,
! [B: $i,A: $i] :
( ( ( A @ sk524 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10198,9703]) ).
thf(16246,plain,
! [B: $i,A: $i] :
( ( A @ sk524 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[16245]) ).
thf(16247,plain,
! [B: $i,A: $i] :
( ( ( A @ sk524 )
!= k1_xboole_0 )
| ( A != B ) ),
inference(simp,[status(thm)],[16246]) ).
thf(16248,plain,
! [A: $i] :
( ( A @ sk524 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[16247]) ).
thf(17880,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk524 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,16248]) ).
thf(17881,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk524 ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[17880]) ).
thf(17882,plain,
! [A: $i] :
~ ( A @ sk524 @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[17881:[bind(A,$thf( C @ sk524 )),bind(B,$thf( C ))]]) ).
thf(19375,plain,
! [A: $i] :
~ ( A @ sk524 @ v1_xboole_0 ),
inference(simp,[status(thm)],[17882]) ).
thf(21413,plain,
! [B: $i,A: $i] :
( ( ( A @ sk37 @ v1_xboole_0 )
!= ( B @ sk524 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2823,19375]) ).
thf(21414,plain,
! [B: $i,A: $i] :
( ( A @ sk37 @ v1_xboole_0 )
!= ( B @ sk524 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[21413]) ).
thf(21418,plain,
! [B: $i,A: $i] :
( ( A @ sk37 )
!= ( B @ sk524 ) ),
inference(simp,[status(thm)],[21414]) ).
thf(19020,plain,
! [B: $i,A: $i] :
( ( ( A @ sk37 @ v1_xboole_0 )
!= ( B @ v1_xboole_0 ) )
| ~ $true
| ( B = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2823,7167]) ).
thf(19021,plain,
! [B: $i,A: $i] :
( ( ( A @ sk37 @ v1_xboole_0 )
!= ( B @ v1_xboole_0 ) )
| ( B = k1_xboole_0 ) ),
inference(simp,[status(thm)],[19020]) ).
thf(19022,plain,
! [A: $i] :
( ( A @ sk37 )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[19021:[bind(A,$thf( C )),bind(B,$thf( C @ sk37 ))]]) ).
thf(19422,plain,
! [A: $i] :
( ( A @ sk37 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[19022]) ).
thf(29599,plain,
! [A: $i] :
( ( A @ sk524 )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[21418,19422]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_finset_1) ).
thf(3873,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(552,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(4739,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(4740,plain,
( ( sk167 @ v1_relat_1 )
& ( sk167 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[4739]) ).
thf(4741,plain,
sk167 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[4740]) ).
thf(18766,plain,
! [A: $i] :
( ( ( sk167 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ~ $true
| ( A = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[4741,7167]) ).
thf(18767,plain,
! [A: $i] :
( ( ( sk167 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ( A = k1_xboole_0 ) ),
inference(simp,[status(thm)],[18766]) ).
thf(18768,plain,
sk167 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[18767:[bind(A,$thf( sk167 ))]]) ).
thf(1392,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 ) )
<=> ( ( C @ ( B @ ( A @ k2_group_2 ) ) )
!= k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_group_2) ).
thf(8960,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k2_group_2 ) ) )
!= k1_xboole_0 )
=> ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 ) ) )
& ( ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k2_group_2 ) ) )
!= k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392]) ).
thf(1480,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( C
= ( D @ ( B @ ( A @ k13_group_2 ) ) ) )
& ( C
= ( D @ ( B @ ( A @ k12_group_2 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_group_6) ).
thf(9405,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( C
= ( D @ ( B @ ( A @ k13_group_2 ) ) ) )
& ( C
= ( D @ ( B @ ( A @ k12_group_2 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480]) ).
thf(1536,axiom,
( ( k1_xboole_0 @ k6_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_relat_1) ).
thf(9747,plain,
( ( k1_xboole_0 @ k6_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1536]) ).
thf(9748,plain,
( ( k1_xboole_0 @ k6_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[9747]) ).
thf(1828,axiom,
! [A: $i] :
( ( A @ k6_partfun1 )
= ( A @ k6_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
thf(11229,plain,
! [A: $i] :
( ( A @ k6_partfun1 )
= ( A @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1828]) ).
thf(11230,plain,
! [A: $i] :
( ( A @ k6_partfun1 )
= ( A @ k6_relat_1 ) ),
inference(cnf,[status(esa)],[11229]) ).
thf(11231,plain,
! [A: $i] :
( ( A @ k6_relat_1 )
= ( A @ k6_partfun1 ) ),
inference(lifteq,[status(thm)],[11230]) ).
thf(16259,plain,
( ( k1_xboole_0 @ k6_partfun1 )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[9748,11231]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k6_partfun1 @ ( A @ ( A @ k3_latsubgr ) ) )
= ( A @ k11_group_4 @ u1_struct_0 @ k6_partfun1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_latsubgr) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k6_partfun1 @ ( A @ ( A @ k3_latsubgr ) ) )
= ( A @ k11_group_4 @ u1_struct_0 @ k6_partfun1 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(2113,plain,
~ ! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k6_partfun1 @ ( A @ ( A @ k3_latsubgr ) ) )
= ( A @ k11_group_4 @ u1_struct_0 @ k6_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(2114,plain,
( ( ( sk1 @ u1_struct_0 @ k6_partfun1 @ ( sk1 @ ( sk1 @ k3_latsubgr ) ) )
!= ( sk1 @ k11_group_4 @ u1_struct_0 @ k6_partfun1 ) )
& ( sk1 @ l1_group_1 )
& ( sk1 @ v4_group_1 )
& ( sk1 @ v3_group_1 )
& ~ ( sk1 @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[2113]) ).
thf(2116,plain,
( ( sk1 @ u1_struct_0 @ k6_partfun1 @ ( sk1 @ ( sk1 @ k3_latsubgr ) ) )
!= ( sk1 @ k11_group_4 @ u1_struct_0 @ k6_partfun1 ) ),
inference(cnfConj,[status(thm)],[2114]) ).
thf(2120,plain,
( ( sk1 @ u1_struct_0 @ k6_partfun1 @ ( sk1 @ ( sk1 @ k3_latsubgr ) ) )
!= ( sk1 @ k11_group_4 @ u1_struct_0 @ k6_partfun1 ) ),
inference(lifteq,[status(thm)],[2116]) ).
thf(16260,plain,
( ( ( sk1 @ u1_struct_0 @ k6_partfun1 )
!= ( k1_xboole_0 @ k6_partfun1 ) )
| ( ( k1_xboole_0 @ ( sk1 @ ( sk1 @ k3_latsubgr ) ) )
!= ( sk1 @ k11_group_4 @ u1_struct_0 @ k6_partfun1 ) ) ),
inference(paramod_ordered,[status(thm)],[16259,2120]) ).
thf(16261,plain,
( ( ( sk1 @ u1_struct_0 )
!= k1_xboole_0 )
| ( ( k1_xboole_0 @ ( sk1 @ ( sk1 @ k3_latsubgr ) ) )
!= ( sk1 @ k11_group_4 @ u1_struct_0 @ k6_partfun1 ) ) ),
inference(simp,[status(thm)],[16260]) ).
thf(1390,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_funct_2) ).
thf(8930,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1390]) ).
thf(1170,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r1_xboole_0 ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( D @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_subset_1) ).
thf(7766,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r1_xboole_0 ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( D @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(234,axiom,
? [A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(3095,plain,
? [A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(3096,plain,
( ( sk48 @ v1_xboole_0 )
& ( sk48 @ v2_funct_1 )
& ( sk48 @ v1_funct_1 )
& ( sk48 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[3095]) ).
thf(3100,plain,
sk48 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[3096]) ).
thf(2118,plain,
sk1 @ v4_group_1,
inference(cnfConj,[status(thm)],[2114]) ).
thf(18204,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ v4_group_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,2118]) ).
thf(18205,plain,
( ( k1_xboole_0 @ v4_group_1 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[18204:[bind(A,$thf( sk1 ))]]) ).
thf(20090,plain,
( ( ( sk48 @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_group_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3100,18205]) ).
thf(20091,plain,
( ( ( sk48 @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v4_group_1 ) ),
inference(simp,[status(thm)],[20090]) ).
thf(20092,plain,
( ( sk48 != sk1 )
| ( k1_xboole_0 @ v4_group_1 ) ),
inference(simp,[status(thm)],[20091]) ).
thf(19095,plain,
! [A: $i] :
( ( ( sk48 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ~ $true
| ( A = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[3100,7167]) ).
thf(19096,plain,
! [A: $i] :
( ( ( sk48 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ( A = k1_xboole_0 ) ),
inference(simp,[status(thm)],[19095]) ).
thf(19097,plain,
sk48 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[19096:[bind(A,$thf( sk48 ))]]) ).
thf(24218,plain,
( ( sk1 != k1_xboole_0 )
| ( k1_xboole_0 @ v4_group_1 ) ),
inference(rewrite,[status(thm)],[20092,19097]) ).
thf(24231,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ( sk1 != k1_xboole_0 )
| ( A @ v4_group_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,24218]) ).
thf(24232,plain,
! [A: $i] :
( ( sk1 != k1_xboole_0 )
| ( A @ v4_group_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[24231:[]]) ).
thf(43299,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( B @ v4_group_1 )
| ~ ( B @ v1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,24232]) ).
thf(43300,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B @ v4_group_1 )
| ~ ( B @ v1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[43299]) ).
thf(43301,plain,
! [A: $i] :
( ( A @ v4_group_1 )
| ~ ( A @ v1_xboole_0 )
| ( sk1 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[43300:[bind(A,$thf( sk1 ))]]) ).
thf(43305,plain,
! [A: $i] :
( ( A @ v4_group_1 )
| ~ ( A @ v1_xboole_0 )
| ( sk1 @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[43301]) ).
thf(1893,axiom,
? [A: $i] :
( ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc8_vectsp_1) ).
thf(11467,plain,
? [A: $i] :
( ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1893]) ).
thf(11468,plain,
( ( sk607 @ v7_group_1 )
& ( sk607 @ v4_group_1 )
& ~ ( sk607 @ v3_struct_0 )
& ( sk607 @ l1_group_1 ) ),
inference(cnf,[status(esa)],[11467]) ).
thf(11472,plain,
sk607 @ v7_group_1,
inference(cnfConj,[status(thm)],[11468]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_partfun1) ).
thf(2744,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(187,axiom,
! [A: $i] :
( ( A @ k1_orders_1 )
= ( k1_xboole_0 @ k1_tarski @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_orders_1) ).
thf(2887,plain,
! [A: $i] :
( ( A @ k1_orders_1 )
= ( k1_xboole_0 @ k1_tarski @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(2888,plain,
! [A: $i] :
( ( A @ k1_orders_1 )
= ( k1_xboole_0 @ k1_tarski @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) ) ),
inference(cnf,[status(esa)],[2887]) ).
thf(2889,plain,
! [A: $i] :
( ( k1_xboole_0 @ k1_tarski @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) )
= ( A @ k1_orders_1 ) ),
inference(lifteq,[status(thm)],[2888]) ).
thf(1651,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ? [E: $i] :
( ( ( E @ u1_struct_0 )
= ( D @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) ) )
& ( B @ ( E @ m1_group_2 ) )
& ( E @ v1_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_latsubgr) ).
thf(10373,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ? [E: $i] :
( ( ( E @ u1_struct_0 )
= ( D @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) ) )
& ( B @ ( E @ m1_group_2 ) )
& ( E @ v1_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1651]) ).
thf(1446,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( B @ ( C @ ( A @ k9_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_filter_0) ).
thf(9273,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( B @ ( C @ ( A @ k9_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446]) ).
thf(1609,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( C @ ( D @ ( A @ k13_group_2 ) ) @ ( B @ ( D @ ( A @ k13_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( B @ ( D @ ( A @ k13_group_2 ) ) @ ( C @ ( A @ k4_group_2 ) ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_group_2) ).
thf(10166,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( C @ ( D @ ( A @ k13_group_2 ) ) @ ( B @ ( D @ ( A @ k13_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( B @ ( D @ ( A @ k13_group_2 ) ) @ ( C @ ( A @ k4_group_2 ) ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1609]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( C @ ( B @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_realset1) ).
thf(2292,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( C @ ( B @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(2293,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ m1_realset1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) )
& ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ v1_funct_2 ) ) )
| ~ ( B @ ( A @ ( C @ m1_realset1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) )
& ( ( C @ ( B @ k1_realset1 ) @ v1_funct_1 )
| ~ ( B @ ( A @ ( C @ m1_realset1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ) ),
inference(cnf,[status(esa)],[2292]) ).
thf(2295,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ v1_funct_2 ) ) )
| ~ ( B @ ( A @ ( C @ m1_realset1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[2293]) ).
thf(524,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ~ ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ! [B: $i] :
( ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ m1_orders_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( C @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_orders_1) ).
thf(4571,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ~ ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ! [B: $i] :
( ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( C @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( A @ ( B @ m1_orders_1 ) ) )
& ( ( A @ ( B @ m1_orders_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( C @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(287,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k3_group_1 ) @ ( A @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k3_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_group_1) ).
thf(3345,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k3_group_1 ) @ ( A @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k3_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(1516,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ k8_group_3 ) @ ( B @ ( C @ ( A @ k4_group_3 ) ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_group_3) ).
thf(9653,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ k8_group_3 ) @ ( B @ ( C @ ( A @ k4_group_3 ) ) @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1516]) ).
thf(55,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_finseq_1 )
& ( B @ v1_finset_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ ( k5_numbers @ ( B @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finseq_1) ).
thf(2341,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_finseq_1 )
& ( B @ v1_finset_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ ( k5_numbers @ ( B @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(46,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_xboole_1) ).
thf(2305,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(2306,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(cnf,[status(esa)],[2305]) ).
thf(1199,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( B @ ( np__2 @ ( A @ k6_group_1 ) ) @ ( C @ ( A @ k12_group_2 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_group_2) ).
thf(7890,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( B @ ( np__2 @ ( A @ k6_group_1 ) ) @ ( C @ ( A @ k12_group_2 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_filter_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_filter_1) ).
thf(2336,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_filter_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v17_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v11_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_lattices) ).
thf(2125,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v17_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v11_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2126,plain,
! [A: $i] :
( ( ( A @ v16_lattices )
| ~ ( A @ v17_lattices )
| ( A @ v3_struct_0 )
| ~ ( A @ l3_lattices ) )
& ( ( A @ v15_lattices )
| ~ ( A @ v17_lattices )
| ( A @ v3_struct_0 )
| ~ ( A @ l3_lattices ) )
& ( ( A @ v14_lattices )
| ~ ( A @ v17_lattices )
| ( A @ v3_struct_0 )
| ~ ( A @ l3_lattices ) )
& ( ( A @ v13_lattices )
| ~ ( A @ v17_lattices )
| ( A @ v3_struct_0 )
| ~ ( A @ l3_lattices ) )
& ( ( A @ v11_lattices )
| ~ ( A @ v17_lattices )
| ( A @ v3_struct_0 )
| ~ ( A @ l3_lattices ) )
& ( ~ ( A @ v3_struct_0 )
| ~ ( A @ v17_lattices )
| ( A @ v3_struct_0 )
| ~ ( A @ l3_lattices ) ) ),
inference(cnf,[status(esa)],[2125]) ).
thf(2131,plain,
! [A: $i] :
( ( A @ v14_lattices )
| ~ ( A @ v17_lattices )
| ( A @ v3_struct_0 )
| ~ ( A @ l3_lattices ) ),
inference(cnfConj,[status(thm)],[2126]) ).
thf(1453,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_card_1) ).
thf(9298,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1453]) ).
thf(9299,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(cnf,[status(esa)],[9298]) ).
thf(32926,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9299,9703]) ).
thf(32927,plain,
! [B: $i,A: $i] :
( ( A @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[32926]) ).
thf(32944,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_card_1 )
!= k1_xboole_0 )
| ( ( A @ k1_card_1 )
!= B ) ),
inference(simp,[status(thm)],[32927]) ).
thf(32953,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k1_card_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[32944]) ).
thf(33531,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_zfmisc_1 @ k1_card_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,32953]) ).
thf(33532,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_zfmisc_1 @ k1_card_1 ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[33531]) ).
thf(33533,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ k1_card_1 @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[33532:[bind(A,$thf( D @ k1_zfmisc_1 @ k1_card_1 )),bind(B,$thf( D ))]]) ).
thf(33543,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ k1_card_1 @ v1_xboole_0 ),
inference(simp,[status(thm)],[33533]) ).
thf(1136,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices )
& ~ ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattices) ).
thf(7569,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices )
& ~ ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(163,axiom,
( ( k1_xboole_0 @ v1_finseq_1 )
& ( k1_xboole_0 @ v1_funct_1 )
& ( k1_xboole_0 @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_finseq_1) ).
thf(2774,plain,
( ( k1_xboole_0 @ v1_finseq_1 )
& ( k1_xboole_0 @ v1_funct_1 )
& ( k1_xboole_0 @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(2775,plain,
( ( k1_xboole_0 @ v1_finseq_1 )
& ( k1_xboole_0 @ v1_funct_1 )
& ( k1_xboole_0 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2774]) ).
thf(2778,plain,
k1_xboole_0 @ v1_finseq_1,
inference(cnfConj,[status(thm)],[2775]) ).
thf(1280,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(8288,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(1820,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_group_3 ) ) )
<=> ? [D: $i] :
( ( B
= ( D @ ( C @ ( A @ k2_group_3 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_group_3) ).
thf(11192,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( B
= ( D @ ( C @ ( A @ k2_group_3 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ r1_group_3 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_group_3 ) ) )
=> ? [D: $i] :
( ( B
= ( D @ ( C @ ( A @ k2_group_3 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1820]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ( ( D @ k1_tarski @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= k1_xboole_0 )
& ( B @ ( D @ r2_hidden ) ) )
<=> ( ( C @ k2_relat_1 )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_2) ).
thf(4262,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= B )
=> ! [D: $i] :
~ ( ( ( D @ k1_tarski @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= k1_xboole_0 )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( ! [D: $i] :
~ ( ( ( D @ k1_tarski @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= k1_xboole_0 )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( C @ k2_relat_1 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(1515,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ( ( C @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( C @ ( A @ k7_group_2 ) @ m1_subset_1 ) )
& ( C @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( B @ ( C @ ( A @ k12_group_2 ) ) @ m1_subset_1 ) )
& ( C @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( B @ ( C @ ( A @ k13_group_2 ) ) @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_group_6) ).
thf(9648,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ( ( C @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( C @ ( A @ k7_group_2 ) @ m1_subset_1 ) )
& ( C @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( B @ ( C @ ( A @ k12_group_2 ) ) @ m1_subset_1 ) )
& ( C @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( B @ ( C @ ( A @ k13_group_2 ) ) @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1515]) ).
thf(1109,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ a_1_0_filter_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i,D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A
= ( D @ ( C @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ k1_domain_1 ) ) ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_filter_1) ).
thf(7445,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i,D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A
= ( D @ ( C @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ k1_domain_1 ) ) ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_filter_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_filter_1 @ ( A @ r2_hidden ) )
=> ? [C: $i,D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A
= ( D @ ( C @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ k1_domain_1 ) ) ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(21992,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ v4_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,2118]) ).
thf(21993,plain,
( ( k1_xboole_0 @ v4_group_1 )
| ( sk1 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21992:[bind(A,$thf( sk1 ))]]) ).
thf(1817,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ ( A @ r5_group_3 ) ) )
=> ( B @ ( C @ ( A @ r5_group_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_group_3) ).
thf(11186,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ ( A @ r5_group_3 ) ) )
=> ( B @ ( C @ ( A @ r5_group_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1817]) ).
thf(431,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v6_lattice3 )
<=> ! [B: $i,C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k16_lattice3 ) @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ a_3_5_lattice3 ) ) @ ( A @ k16_lattice3 ) @ ( A @ r3_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_lattice3) ).
thf(4062,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i,C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k16_lattice3 ) @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ a_3_5_lattice3 ) ) @ ( A @ k16_lattice3 ) @ ( A @ r3_lattices ) ) ) )
=> ( A @ v6_lattice3 ) )
& ( ( A @ v6_lattice3 )
=> ! [B: $i,C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k16_lattice3 ) @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ a_3_5_lattice3 ) ) @ ( A @ k16_lattice3 ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(588,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_funct_1) ).
thf(4899,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(446,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(4143,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(4144,plain,
( ~ ( sk110 @ v3_struct_0 )
& ( sk110 @ l1_struct_0 ) ),
inference(cnf,[status(esa)],[4143]) ).
thf(4146,plain,
~ ( sk110 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4144]) ).
thf(19100,plain,
! [A: $i] :
( ( A != sk110 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,4146]) ).
thf(19101,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk110 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19100:[bind(A,$thf( sk110 ))]]) ).
thf(549,axiom,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_subset_1) ).
thf(4729,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(421,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v15_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_filter_0) ).
thf(4022,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v15_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(923,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_partfun1) ).
thf(6651,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(1539,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v3_group_6 ) ) )
<=> ( ( C @ ( B @ ( A @ k9_group_6 ) ) )
= ( B @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_group_6) ).
thf(9754,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k9_group_6 ) ) )
= ( B @ u1_struct_0 ) )
=> ( B @ ( A @ ( C @ v3_group_6 ) ) ) )
& ( ( B @ ( A @ ( C @ v3_group_6 ) ) )
=> ( ( C @ ( B @ ( A @ k9_group_6 ) ) )
= ( B @ u1_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1539]) ).
thf(185,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m1_orders_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_orders_1) ).
thf(2876,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m1_orders_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(1551,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
thf(9833,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1551]) ).
thf(2119,plain,
~ ( sk1 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2114]) ).
thf(18651,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,2119]) ).
thf(18652,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[18651:[bind(A,$thf( sk1 ))]]) ).
thf(20700,plain,
( ( ( sk1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,18652]) ).
thf(20701,plain,
( ( ( sk1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[20700]) ).
thf(20710,plain,
( ( sk1 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[20701]) ).
thf(25551,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ( sk1 != k1_xboole_0 )
| ~ ( A @ v3_struct_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,20710]) ).
thf(25552,plain,
! [A: $i] :
( ( sk1 != k1_xboole_0 )
| ~ ( A @ v3_struct_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[25551:[]]) ).
thf(72,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ v2_funct_1 )
=> ( B @ ( A @ k1_finseq_3 ) @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_finseq_3) ).
thf(2412,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ v2_funct_1 )
=> ( B @ ( A @ k1_finseq_3 ) @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(469,axiom,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(4290,plain,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(526,axiom,
( ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ l1_group_1 )
& ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v7_group_1 )
& ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v4_group_1 )
& ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v3_group_1 )
& ~ ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v3_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_group_1) ).
thf(4582,plain,
( ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ l1_group_1 )
& ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v7_group_1 )
& ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v4_group_1 )
& ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v3_group_1 )
& ~ ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v3_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(4583,plain,
( ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ l1_group_1 )
& ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v7_group_1 )
& ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v4_group_1 )
& ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v3_group_1 )
& ~ ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[4582]) ).
thf(4588,plain,
k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ l1_group_1,
inference(cnfConj,[status(thm)],[4583]) ).
thf(598,axiom,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
thf(4960,plain,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(4961,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
| ~ ( A @ l1_group_1 ) ),
inference(cnf,[status(esa)],[4960]) ).
thf(16425,plain,
! [A: $i] :
( ( ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4588,4961]) ).
thf(16426,plain,
! [A: $i] :
( ( ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[16425]) ).
thf(16427,plain,
k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ l1_struct_0,
inference(pattern_uni,[status(thm)],[16426:[bind(A,$thf( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) ))]]) ).
thf(457,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k4_lattice4 ) @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( C
= ( E @ ( D @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattice4) ).
thf(4183,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( C
= ( E @ ( D @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( B @ ( A @ k4_lattice4 ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ k4_lattice4 ) @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( C
= ( E @ ( D @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(1849,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k7_group_3 ) @ ( C @ ( B @ ( A @ k2_group_3 ) ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_group_3) ).
thf(11313,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k7_group_3 ) @ ( C @ ( B @ ( A @ k2_group_3 ) ) @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1849]) ).
thf(673,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
=> ( A @ ( B @ r1_partfun1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_partfun1) ).
thf(5390,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
=> ( A @ ( B @ r1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_funct_1) ).
thf(2463,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1178,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ m1_finseq_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k1_group_4 ) ) )
= ( C @ ( B @ k1_finseq_3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_group_4) ).
thf(7798,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ m1_finseq_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k1_group_4 ) ) )
= ( C @ ( B @ k1_finseq_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(296,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C
= ( B @ ( A @ k1_funct_4 ) ) )
<=> ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( ~ ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) ) ) )
& ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_4) ).
thf(3397,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( ~ ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) ) ) )
& ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) )
=> ( C
= ( B @ ( A @ k1_funct_4 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_funct_4 ) ) )
=> ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( ~ ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) ) ) )
& ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(1525,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_2_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_2_domain_1) ).
thf(9685,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_2_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_2_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1525]) ).
thf(383,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ k7_setfam_1 ) )
= k1_xboole_0 )
& ( B != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(3830,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ k7_setfam_1 ) )
= k1_xboole_0 )
& ( B != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(1219,axiom,
? [A: $i] : ( A @ l1_vectsp_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_vectsp_1) ).
thf(7990,plain,
? [A: $i] : ( A @ l1_vectsp_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_relat_1) ).
thf(2499,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_xboole_1) ).
thf(2595,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(11470,plain,
~ ( sk607 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[11468]) ).
thf(18677,plain,
! [A: $i] :
( ( A != sk607 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,11470]) ).
thf(18678,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk607 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[18677:[bind(A,$thf( sk607 ))]]) ).
thf(32327,plain,
( ( ( sk607 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,18678]) ).
thf(32328,plain,
( ( ( sk607 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[32327]) ).
thf(32341,plain,
( ( sk607 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[32328]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) @ ( B @ ( A @ ( A @ k3_funct_2 ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_funct_2) ).
thf(3449,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) @ ( B @ ( A @ ( A @ k3_funct_2 ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(814,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k2_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_relat_1) ).
thf(6074,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k2_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(2027,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 )
= ( B @ ( A @ k4_group_6 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_group_6) ).
thf(11998,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 )
= ( B @ ( A @ k4_group_6 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2027]) ).
thf(906,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_binop_1) ).
thf(6555,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) )
=> ( C @ ( B @ ( A @ r2_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(51,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( B @ ( A @ k1_finseq_3 ) @ k2_relat_1 )
= ( B @ ( A @ k2_relat_1 @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_finseq_3) ).
thf(2331,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( B @ ( A @ k1_finseq_3 ) @ k2_relat_1 )
= ( B @ ( A @ k2_relat_1 @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(1966,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k6_group_2 @ ( A @ k13_group_2 ) ) )
= ( A @ u1_struct_0 ) )
& ( ( B @ ( A @ k6_group_2 @ ( A @ k12_group_2 ) ) )
= ( A @ u1_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_group_2) ).
thf(11763,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k6_group_2 @ ( A @ k13_group_2 ) ) )
= ( A @ u1_struct_0 ) )
& ( ( B @ ( A @ k6_group_2 @ ( A @ k12_group_2 ) ) )
= ( A @ u1_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1966]) ).
thf(542,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ k3_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relat_1) ).
thf(4682,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ k3_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(1579,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_xboole_1) ).
thf(9965,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ ( C @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1579]) ).
thf(1340,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k7_group_6 ) ) @ ( C @ ( B @ ( A @ k7_group_6 ) ) @ ( A @ k2_group_2 ) ) )
= ( D @ ( C @ ( B @ ( A @ k6_group_6 ) @ k1_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_group_6) ).
thf(8639,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k7_group_6 ) ) @ ( C @ ( B @ ( A @ k7_group_6 ) ) @ ( A @ k2_group_2 ) ) )
= ( D @ ( C @ ( B @ ( A @ k6_group_6 ) @ k1_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).
thf(1933,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( np__1 @ ( A @ k6_group_1 ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_group_1) ).
thf(11620,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( np__1 @ ( A @ k6_group_1 ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1933]) ).
thf(2825,plain,
! [A: $i] : ( A @ sk37 @ v1_finset_1 ),
inference(cnfConj,[status(thm)],[2818]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_finset_1) ).
thf(2179,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2180,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] : ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(miniscope,[status(thm)],[2179]) ).
thf(2181,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 )
| ~ ( A @ v1_finset_1 ) ),
inference(cnf,[status(esa)],[2180]) ).
thf(14312,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk37 @ v1_finset_1 )
!= ( B @ v1_finset_1 ) )
| ( C @ ( B @ k4_xboole_0 ) @ v1_finset_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2825,2181]) ).
thf(14313,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk37 @ v1_finset_1 )
!= ( B @ v1_finset_1 ) )
| ( C @ ( B @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(simp,[status(thm)],[14312]) ).
thf(14314,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk37 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(pattern_uni,[status(thm)],[14313:[bind(A,$thf( D )),bind(B,$thf( D @ sk37 ))]]) ).
thf(14346,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk37 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(simp,[status(thm)],[14314]) ).
thf(31455,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(rewrite,[status(thm)],[14346,19422]) ).
thf(908,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( B @ v1_finset_1 )
=> ( ( B @ ( A @ r2_wellord2 ) )
=> ( ( A @ k4_card_1 )
= ( B @ k4_card_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_card_1) ).
thf(6566,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( B @ v1_finset_1 )
=> ( ( B @ ( A @ r2_wellord2 ) )
=> ( ( A @ k4_card_1 )
= ( B @ k4_card_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(1870,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( ( D @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_group_1) ).
thf(11385,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( ( D @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1870]) ).
thf(546,axiom,
! [A: $i] : ( A @ k2_card_1 @ ( k1_xboole_0 @ k1_card_1 @ r2_hidden ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_card_1) ).
thf(4710,plain,
! [A: $i] : ( A @ k2_card_1 @ ( k1_xboole_0 @ k1_card_1 @ r2_hidden ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(4711,plain,
! [A: $i] : ( A @ k2_card_1 @ ( k1_xboole_0 @ k1_card_1 @ r2_hidden ) ),
inference(cnf,[status(esa)],[4710]) ).
thf(15024,plain,
! [A: $i] : ( A @ k2_card_1 @ ( k1_xboole_0 @ r2_hidden ) ),
inference(rewrite,[status(thm)],[4711,8607]) ).
thf(15025,plain,
! [B: $i,A: $i] :
( ( ( A @ k2_card_1 @ ( k1_xboole_0 @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15024,9703]) ).
thf(15026,plain,
! [B: $i,A: $i] :
( ( A @ k2_card_1 @ ( k1_xboole_0 @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[15025]) ).
thf(15027,plain,
! [B: $i,A: $i] :
( ( ( A @ k2_card_1 )
!= k1_xboole_0 )
| ( k1_xboole_0 != B ) ),
inference(simp,[status(thm)],[15026]) ).
thf(15028,plain,
! [A: $i] :
( ( A @ k2_card_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[15027]) ).
thf(18076,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k2_card_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,15028]) ).
thf(18077,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k2_card_1 ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[18076]) ).
thf(18078,plain,
! [A: $i] :
~ ( A @ k2_card_1 @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[18077:[bind(A,$thf( C @ k2_card_1 )),bind(B,$thf( C ))]]) ).
thf(19451,plain,
! [A: $i] :
~ ( A @ k2_card_1 @ v1_xboole_0 ),
inference(simp,[status(thm)],[18078]) ).
thf(582,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_filter_0 ) )
=> ( ( ( E @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
& ( E @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) )
=> ( E @ ( D @ ( B @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_filter_0) ).
thf(4877,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_filter_0 ) )
=> ( ( ( E @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
& ( E @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) )
=> ( E @ ( D @ ( B @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(1419,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).
thf(9091,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419]) ).
thf(1096,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_0) ).
thf(7396,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(624,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_finseq_1) ).
thf(5129,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(5130,plain,
( ( sk196 @ v1_finset_1 )
& ( sk196 @ v1_funct_1 )
& ( sk196 @ v1_relat_1 )
& ~ ( sk196 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[5129]) ).
thf(5131,plain,
~ ( sk196 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[5130]) ).
thf(1241,axiom,
! [A: $i] :
( ( k4_numbers @ ( A @ m1_subset_1 ) )
=> ( A @ v1_int_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_int_1) ).
thf(8077,plain,
! [A: $i] :
( ( k4_numbers @ ( A @ m1_subset_1 ) )
=> ( A @ v1_int_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(1488,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k9_group_6 ) ) )
= ( C @ ( B @ ( A @ k13_group_6 ) ) @ u1_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_group_6) ).
thf(9437,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k9_group_6 ) ) )
= ( C @ ( B @ ( A @ k13_group_6 ) ) @ u1_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1488]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t133_funct_2) ).
thf(2250,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1929,axiom,
? [A: $i] :
( ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_group_1) ).
thf(11605,plain,
? [A: $i] :
( ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1929]) ).
thf(11606,plain,
( ( sk611 @ v1_group_1 )
& ~ ( sk611 @ v3_struct_0 )
& ( sk611 @ l1_group_1 ) ),
inference(cnf,[status(esa)],[11605]) ).
thf(11607,plain,
sk611 @ l1_group_1,
inference(cnfConj,[status(thm)],[11606]) ).
thf(16437,plain,
! [A: $i] :
( ( ( sk611 @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11607,4961]) ).
thf(16438,plain,
! [A: $i] :
( ( ( sk611 @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[16437]) ).
thf(16439,plain,
sk611 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[16438:[bind(A,$thf( sk611 ))]]) ).
thf(22484,plain,
! [A: $i] :
( ( A != sk611 )
| ( k1_xboole_0 @ l1_struct_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,16439]) ).
thf(22485,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk611 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22484:[bind(A,$thf( sk611 ))]]) ).
thf(1100,axiom,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_xboole_1) ).
thf(7408,plain,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(7409,plain,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
inference(cnf,[status(esa)],[7408]) ).
thf(949,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k4_lattice4 ) )
= ( B @ ( A @ a_2_0_lattice4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattice4) ).
thf(6744,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k4_lattice4 ) )
= ( B @ ( A @ a_2_0_lattice4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(964,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_card_1) ).
thf(6798,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(38936,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( C @ ( A @ k1_orders_1 @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[2889,2306]) ).
thf(38937,plain,
! [A: $i] : ( k1_xboole_0 @ k1_tarski @ ( A @ k1_orders_1 @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[38936:[bind(A,$thf( D )),bind(B,$thf( D @ k1_zfmisc_1 )),bind(C,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(38981,plain,
! [A: $i] : ( k1_xboole_0 @ k1_tarski @ ( A @ k1_orders_1 @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[38937]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
<=> ( ( B @ ( A @ k4_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(2232,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ k4_xboole_0 ) )
= A )
=> ( B @ ( A @ r1_xboole_0 ) ) )
& ( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k4_xboole_0 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(2233,plain,
( ! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= A )
=> ( B @ ( A @ r1_xboole_0 ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k4_xboole_0 ) )
= A ) ) ),
inference(miniscope,[status(thm)],[2232]) ).
thf(2234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
| ( ( D @ ( C @ k4_xboole_0 ) )
!= C ) )
& ( ( ( B @ ( A @ k4_xboole_0 ) )
= A )
| ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[2233]) ).
thf(2235,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= A )
| ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(cnfConj,[status(thm)],[2234]) ).
thf(2237,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r1_xboole_0 ) )
| ( ( B @ ( A @ k4_xboole_0 ) )
= A ) ),
inference(lifteq,[status(thm)],[2235]) ).
thf(39438,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( A @ k1_orders_1 @ r1_xboole_0 ) )
!= ( C @ ( B @ r1_xboole_0 ) ) )
| ~ $true
| ( ( C @ ( B @ k4_xboole_0 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[38981,2237]) ).
thf(39439,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( A @ k1_orders_1 @ r1_xboole_0 ) )
!= ( C @ ( B @ r1_xboole_0 ) ) )
| ( ( C @ ( B @ k4_xboole_0 ) )
= B ) ),
inference(simp,[status(thm)],[39438]) ).
thf(39440,plain,
! [A: $i] :
( ( k1_xboole_0 @ k1_tarski @ ( A @ k1_orders_1 @ k4_xboole_0 ) )
= ( A @ k1_orders_1 ) ),
inference(pattern_uni,[status(thm)],[39439:[bind(A,$thf( D )),bind(B,$thf( D @ k1_orders_1 )),bind(C,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(39484,plain,
! [A: $i] :
( ( k1_xboole_0 @ k1_tarski @ ( A @ k1_orders_1 @ k4_xboole_0 ) )
= ( A @ k1_orders_1 ) ),
inference(simp,[status(thm)],[39440]) ).
thf(494,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k3_xcmplx_0 ) @ ( C @ k6_group_1 ) ) )
= ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( B @ ( C @ k6_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_group_1) ).
thf(4408,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k3_xcmplx_0 ) @ ( C @ k6_group_1 ) ) )
= ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( B @ ( C @ k6_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(59,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_orders_1 ) )
=> ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_orders_1) ).
thf(2359,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_orders_1 ) )
=> ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(2360,plain,
! [B: $i,A: $i] :
( ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( B @ m1_orders_1 ) )
| ( A @ v1_xboole_0 ) )
& ( ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
| ~ ( A @ ( B @ m1_orders_1 ) )
| ( A @ v1_xboole_0 ) )
& ( ( B @ v1_funct_1 )
| ~ ( A @ ( B @ m1_orders_1 ) )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[2359]) ).
thf(2363,plain,
! [B: $i,A: $i] :
( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( B @ m1_orders_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2360]) ).
thf(1813,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_group_2 @ ( A @ k11_group_3 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t164_group_3) ).
thf(11175,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_group_2 @ ( A @ k11_group_3 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1813]) ).
thf(689,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( ( A @ k3_finseq_1 @ ( C @ r1_xreal_0 ) )
& ( C @ ( np__1 @ r1_xreal_0 ) ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) )
& ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finseq_1) ).
thf(5444,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( ( A @ k3_finseq_1 @ ( C @ r1_xreal_0 ) )
& ( C @ ( np__1 @ r1_xreal_0 ) ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) )
& ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(1440,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ k2_group_1 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k2_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_group_6) ).
thf(9241,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ k2_group_1 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k2_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440]) ).
thf(1711,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( k1_xboole_0 @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_partfun1) ).
thf(10658,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( k1_xboole_0 @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1711]) ).
thf(1653,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_zfmisc_1 ) @ ( A @ k10_group_4 @ m2_relset_1 ) ) )
& ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_zfmisc_1 ) @ ( A @ k10_group_4 @ v1_funct_2 ) ) )
& ( A @ k10_group_4 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_group_4) ).
thf(10387,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_zfmisc_1 ) @ ( A @ k10_group_4 @ m2_relset_1 ) ) )
& ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_zfmisc_1 ) @ ( A @ k10_group_4 @ v1_funct_2 ) ) )
& ( A @ k10_group_4 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1653]) ).
thf(690,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(5454,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(1223,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( B
!= ( E @ k1_tarski ) )
& ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_funct_2) ).
thf(8005,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( B
!= ( E @ k1_tarski ) )
& ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(775,axiom,
k5_numbers != k1_numbers,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_numbers) ).
thf(5898,plain,
k5_numbers != k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(915,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( B @ ( C @ k5_relat_1 ) )
= B )
& ( B @ v2_funct_1 )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( C
= ( A @ k6_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_funct_1) ).
thf(6587,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( B @ ( C @ k5_relat_1 ) )
= B )
& ( B @ v2_funct_1 )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( C
= ( A @ k6_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(810,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
thf(6062,plain,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(6063,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
| ~ ( A @ l2_struct_0 ) ),
inference(cnf,[status(esa)],[6062]) ).
thf(677,axiom,
k1_numbers @ ( k4_numbers @ r1_tarski ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_numbers) ).
thf(5402,plain,
k1_numbers @ ( k4_numbers @ r1_tarski ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(2229,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(2230,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] : ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(miniscope,[status(thm)],[2229]) ).
thf(2231,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) )
| ~ ( B @ ( A @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[2230]) ).
thf(21577,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( k4_numbers @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5402,2231]) ).
thf(21578,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( k4_numbers @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[21577]) ).
thf(21579,plain,
! [A: $i] : ( k4_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[21578:[bind(A,$thf( k4_numbers )),bind(B,$thf( k1_numbers ))]]) ).
thf(21630,plain,
! [A: $i] : ( k4_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[21579]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_xboole_1) ).
thf(2274,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(2275,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
| ~ ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
| ~ ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) ) ) ),
inference(cnf,[status(esa)],[2274]) ).
thf(2276,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ~ ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(cnfConj,[status(thm)],[2275]) ).
thf(41424,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ k4_xboole_0 ) @ ( B @ r1_tarski ) ) )
| ( C @ ( B @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21630,2276]) ).
thf(41425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ k4_xboole_0 ) @ ( B @ r1_tarski ) ) )
| ( C @ ( B @ r1_tarski ) ) ),
inference(simp,[status(thm)],[41424]) ).
thf(41426,plain,
! [A: $i] : ( A @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[41425:[bind(A,$thf( E )),bind(B,$thf( k1_numbers @ ( E @ k4_xboole_0 ) )),bind(C,$thf( E )),bind(D,$thf( k4_numbers ))]]) ).
thf(41461,plain,
! [A: $i] : ( A @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[41426]) ).
thf(47,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ~ ( ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ~ ( ( C @ ( np__1 @ r1_xreal_0 ) )
& ( C
= ( A @ ( B @ k6_xcmplx_0 ) ) ) ) )
& ~ ( A @ ( B @ r1_xreal_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_int_1) ).
thf(2307,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ~ ( ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ~ ( ( C @ ( np__1 @ r1_xreal_0 ) )
& ( C
= ( A @ ( B @ k6_xcmplx_0 ) ) ) ) )
& ~ ( A @ ( B @ r1_xreal_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(2308,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk6 ) @ ( np__1 @ r1_xreal_0 ) )
| ( A @ ( B @ r1_xreal_0 ) )
| ~ ( B @ v1_int_1 )
| ~ ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) ) )
& ( ( ( A @ ( B @ sk6 ) )
= ( A @ ( B @ k6_xcmplx_0 ) ) )
| ( A @ ( B @ r1_xreal_0 ) )
| ~ ( B @ v1_int_1 )
| ~ ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) ) )
& ( ( k5_numbers @ ( k1_numbers @ ( A @ ( B @ sk6 ) @ m2_subset_1 ) ) )
| ( A @ ( B @ r1_xreal_0 ) )
| ~ ( B @ v1_int_1 )
| ~ ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) ) ) ),
inference(cnf,[status(esa)],[2307]) ).
thf(2309,plain,
! [B: $i,A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ ( B @ sk6 ) @ m2_subset_1 ) ) )
| ( A @ ( B @ r1_xreal_0 ) )
| ~ ( B @ v1_int_1 )
| ~ ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) ) ),
inference(cnfConj,[status(thm)],[2308]) ).
thf(911,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relat_1) ).
thf(6576,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(894,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(6473,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(6474,plain,
( ( sk280 @ v1_relat_1 )
& ~ ( sk280 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[6473]) ).
thf(6475,plain,
~ ( sk280 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[6474]) ).
thf(12416,plain,
( ( ( sk280 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,6475]) ).
thf(12417,plain,
( ( sk280 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12416]) ).
thf(12426,plain,
sk280 != k1_xboole_0,
inference(simp,[status(thm)],[12417]) ).
thf(2117,plain,
sk1 @ l1_group_1,
inference(cnfConj,[status(thm)],[2114]) ).
thf(1000,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k16_group_2 ) )
= ( B @ ( A @ k14_group_2 ) @ k1_card_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_group_2) ).
thf(6944,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k16_group_2 ) )
= ( B @ ( A @ k14_group_2 ) @ k1_card_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(1664,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_group_2 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_group_2 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_group_2 ) )
=> ( ( ( E @ ( A @ ( D @ m1_group_6 ) ) )
& ( ( G @ u1_struct_0 )
= ( E @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) ) )
& ( ( F @ u1_struct_0 )
= ( D @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) ) ) )
=> ( G @ ( B @ ( F @ m1_group_6 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_latsubgr) ).
thf(10446,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_group_2 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_group_2 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_group_2 ) )
=> ( ( ( E @ ( A @ ( D @ m1_group_6 ) ) )
& ( ( G @ u1_struct_0 )
= ( E @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) ) )
& ( ( F @ u1_struct_0 )
= ( D @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) ) ) )
=> ( G @ ( B @ ( F @ m1_group_6 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1664]) ).
thf(632,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ v1_finset_1 )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finset_1) ).
thf(5168,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ v1_finset_1 )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(1360,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( ( B @ ( A @ k16_group_2 ) )
= ( A @ k8_group_1 ) )
& ( B @ ( A @ k14_group_2 ) @ v1_finset_1 ) )
=> ( ( A @ k5_group_2 @ ( B @ ( A @ r1_group_2 ) ) )
& ( A @ v6_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t185_group_2) ).
thf(8723,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( ( B @ ( A @ k16_group_2 ) )
= ( A @ k8_group_1 ) )
& ( B @ ( A @ k14_group_2 ) @ v1_finset_1 ) )
=> ( ( A @ k5_group_2 @ ( B @ ( A @ r1_group_2 ) ) )
& ( A @ v6_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).
thf(1470,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k6_group_6 ) @ v1_group_1 )
& ~ ( B @ ( A @ k6_group_6 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_group_6) ).
thf(9373,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k6_group_6 ) @ v1_group_1 )
& ~ ( B @ ( A @ k6_group_6 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1470]) ).
thf(1778,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k6_group_3 ) ) @ u1_struct_0 )
= ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k12_group_2 ) ) @ ( B @ ( A @ k4_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_group_3) ).
thf(11043,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k6_group_3 ) ) @ u1_struct_0 )
= ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k12_group_2 ) ) @ ( B @ ( A @ k4_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1778]) ).
thf(1016,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( A @ ( B @ k1_setfam_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_setfam_1) ).
thf(7008,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( A @ ( B @ k1_setfam_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(1372,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k3_filter_0 ) @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_filter_0) ).
thf(8797,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k3_filter_0 ) @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).
thf(935,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( C @ v1_int_1 )
=> ( ( ( A @ ( B @ k2_xcmplx_0 ) )
= C )
=> ( C @ ( B @ r1_xreal_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_int_1) ).
thf(6695,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( C @ v1_int_1 )
=> ( ( ( A @ ( B @ k2_xcmplx_0 ) )
= C )
=> ( C @ ( B @ r1_xreal_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(848,axiom,
? [A: $i] :
( ( A @ v8_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_vectsp_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc9_vectsp_1) ).
thf(6213,plain,
? [A: $i] :
( ( A @ v8_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_vectsp_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(6214,plain,
( ( sk259 @ v8_vectsp_1 )
& ( sk259 @ v6_vectsp_1 )
& ( sk259 @ v7_group_1 )
& ( sk259 @ v4_group_1 )
& ( sk259 @ v2_group_1 )
& ~ ( sk259 @ v3_struct_0 )
& ( sk259 @ l1_vectsp_1 ) ),
inference(cnf,[status(esa)],[6213]) ).
thf(6217,plain,
sk259 @ v8_vectsp_1,
inference(cnfConj,[status(thm)],[6214]) ).
thf(22456,plain,
! [A: $i] :
( ( A != sk259 )
| ( k1_xboole_0 @ v8_vectsp_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,6217]) ).
thf(22457,plain,
( ( k1_xboole_0 @ v8_vectsp_1 )
| ( sk259 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22456:[bind(A,$thf( sk259 ))]]) ).
thf(1511,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_group_4 ) )
<=> ? [C: $i] :
( ( ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( C @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k5_group_4 ) )
!= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) )
& ( ( C @ ( A @ k5_group_4 ) )
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_group_4) ).
thf(9604,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ? [C: $i] :
( ( ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( C @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k5_group_4 ) )
!= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) )
& ( ( C @ ( A @ k5_group_4 ) )
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( A @ ( B @ v1_group_4 ) ) )
& ( ( A @ ( B @ v1_group_4 ) )
=> ? [C: $i] :
( ( ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( C @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k5_group_4 ) )
!= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) )
& ( ( C @ ( A @ k5_group_4 ) )
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1511]) ).
thf(2075,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ v6_group_1 )
=> ( B @ v6_group_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_group_2) ).
thf(12172,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ v6_group_1 )
=> ( B @ v6_group_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2075]) ).
thf(604,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
<=> ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_relat_1) ).
thf(5000,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
=> ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(2107,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k6_group_4 @ m1_group_2 ) )
& ( A @ k6_group_4 @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_group_4) ).
thf(12299,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k6_group_4 @ m1_group_2 ) )
& ( A @ k6_group_4 @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2107]) ).
thf(2776,plain,
k1_xboole_0 @ v1_relat_1,
inference(cnfConj,[status(thm)],[2775]) ).
thf(132,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k4_finseq_1 )
= ( A @ k1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_finseq_1) ).
thf(2659,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k4_finseq_1 )
= ( A @ k1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1474,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(9383,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474]) ).
thf(6219,plain,
sk259 @ v7_group_1,
inference(cnfConj,[status(thm)],[6214]) ).
thf(1876,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ v1_int_1 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k6_group_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_group_1) ).
thf(11409,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ v1_int_1 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k6_group_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1876]) ).
thf(1692,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k3_filter_0 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_filter_0) ).
thf(10567,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k3_filter_0 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1692]) ).
thf(969,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k1_funct_4 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_funct_4) ).
thf(6813,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k1_funct_4 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(101,axiom,
( ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v3_group_1 )
& ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v4_group_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_group_1) ).
thf(2527,plain,
( ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v3_group_1 )
& ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v4_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
thf(3040,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(1543,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ ( B @ v2_filter_0 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_filter_0) ).
thf(9769,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) ) ) ) )
=> ( A @ ( B @ v2_filter_0 ) ) )
& ( ( A @ ( B @ v2_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1543]) ).
thf(1084,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_funct_2) ).
thf(7322,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(1423,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k7_group_2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_group_2) ).
thf(9120,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k7_group_2 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1423]) ).
thf(1642,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( A @ v4_group_1 )
=> ( ( C @ ( B @ ( D @ ( A @ k4_group_2 ) ) @ ( A @ k2_group_2 ) ) )
= ( C @ ( D @ ( A @ k3_group_2 ) ) @ ( B @ ( A @ k2_group_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_group_2) ).
thf(10331,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( A @ v4_group_1 )
=> ( ( C @ ( B @ ( D @ ( A @ k4_group_2 ) ) @ ( A @ k2_group_2 ) ) )
= ( C @ ( D @ ( A @ k3_group_2 ) ) @ ( B @ ( A @ k2_group_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1642]) ).
thf(30,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( k5_numbers @ ( k1_numbers @ ( A @ k3_finseq_1 @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_finseq_1) ).
thf(2248,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( k5_numbers @ ( k1_numbers @ ( A @ k3_finseq_1 @ m2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1245,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_finseq_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_finseq_1) ).
thf(8118,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_finseq_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(568,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k4_card_1 )
= ( A @ k1_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_card_1) ).
thf(4807,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k4_card_1 )
= ( A @ k1_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(1724,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ~ ( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( B
= ( F @ ( E @ ( A @ k4_lattices ) ) ) ) ) ) )
& ( D @ ( C @ ( A @ k5_filter_0 ) ) @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_filter_0) ).
thf(10711,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ~ ( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( B
= ( F @ ( E @ ( A @ k4_lattices ) ) ) ) ) ) )
& ( D @ ( C @ ( A @ k5_filter_0 ) ) @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1724]) ).
thf(890,axiom,
! [A: $i] : ( A @ k2_card_1 @ v1_card_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_card_1) ).
thf(6441,plain,
! [A: $i] : ( A @ k2_card_1 @ v1_card_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(401,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( C @ ( B @ ( A @ r1_lattice4 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_filter_0 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_lattice4) ).
thf(3910,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_filter_0 ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r1_lattice4 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_lattice4 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_filter_0 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(634,axiom,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_partfun1) ).
thf(5173,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(754,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_relat_1) ).
thf(5793,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(1627,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_group_2 ) ) )
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( C @ ( A @ k2_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_group_2) ).
thf(10244,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_group_2 ) ) )
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( C @ ( A @ k2_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1627]) ).
thf(237,axiom,
k1_numbers @ ( k5_numbers @ r1_tarski ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_numbers) ).
thf(3108,plain,
k1_numbers @ ( k5_numbers @ r1_tarski ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1056,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_subset_1) ).
thf(7198,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(1277,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
<=> ( ( B @ ( A @ k9_group_3 ) )
= ( B @ k1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_group_3) ).
thf(8271,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( ( B @ ( A @ k9_group_3 ) )
= ( B @ k1_tarski ) )
=> ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) ) )
& ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k9_group_3 ) )
= ( B @ k1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).
thf(653,axiom,
! [A: $i] :
( ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) )
<=> ( A @ k3_tarski @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_finset_1) ).
thf(5265,plain,
! [A: $i] :
( ( ( A @ k3_tarski @ v1_finset_1 )
=> ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) ) )
& ( ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) )
=> ( A @ k3_tarski @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(459,axiom,
! [A: $i,B: $i] : ( B @ ( B @ r2_setfam_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_setfam_1) ).
thf(4214,plain,
! [A: $i] : ( A @ ( A @ r2_setfam_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(4215,plain,
! [A: $i] : ( A @ ( A @ r2_setfam_1 ) ),
inference(cnf,[status(esa)],[4214]) ).
thf(1174,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ( ( B @ ( A @ ( C @ m1_group_6 ) ) )
=> ( C @ ( A @ k6_group_6 ) @ ( C @ ( B @ ( A @ k1_group_6 ) ) @ ( B @ k6_group_6 ) @ m1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_group_6) ).
thf(7781,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ( ( B @ ( A @ ( C @ m1_group_6 ) ) )
=> ( C @ ( A @ k6_group_6 ) @ ( C @ ( B @ ( A @ k1_group_6 ) ) @ ( B @ k6_group_6 ) @ m1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(534,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( B
= ( A @ k2_relat_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
thf(4614,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k2_relat_1 ) ) )
& ( ( B
= ( A @ k2_relat_1 ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(1634,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( A @ k3_group_3 ) ) )
= ( D @ ( C @ ( A @ k2_group_3 ) ) @ ( D @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ u1_struct_0 @ k7_domain_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_group_3) ).
thf(10294,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( A @ k3_group_3 ) ) )
= ( D @ ( C @ ( A @ k2_group_3 ) ) @ ( D @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ u1_struct_0 @ k7_domain_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1634]) ).
thf(1753,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_xboole_1) ).
thf(10876,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1753]) ).
thf(1508,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) ) )
& ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k3_filter_0 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_filter_0) ).
thf(9572,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) ) )
& ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k3_filter_0 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1508]) ).
thf(1395,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_tarski @ ( A @ k5_partfun1 ) ) )
= ( D @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t164_funct_2) ).
thf(8988,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_tarski @ ( A @ k5_partfun1 ) ) )
= ( D @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395]) ).
thf(1884,axiom,
? [A: $i] :
( ( A @ v3_realset2 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_group_6) ).
thf(11433,plain,
? [A: $i] :
( ( A @ v3_realset2 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1884]) ).
thf(11434,plain,
( ( sk605 @ v3_realset2 )
& ( sk605 @ v4_group_1 )
& ( sk605 @ v3_group_1 )
& ( sk605 @ v2_group_1 )
& ~ ( sk605 @ v3_struct_0 )
& ( sk605 @ l1_group_1 ) ),
inference(cnf,[status(esa)],[11433]) ).
thf(11440,plain,
~ ( sk605 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[11434]) ).
thf(802,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_funct_4 ) @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_4) ).
thf(6017,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_funct_4 ) @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(2033,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ m1_group_2 ) )
=> ( C @ ( D @ ( B @ ( A @ k9_group_2 ) ) @ m1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_group_2) ).
thf(12013,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ m1_group_2 ) )
=> ( C @ ( D @ ( B @ ( A @ k9_group_2 ) ) @ m1_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2033]) ).
thf(944,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_subset_1) ).
thf(6732,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(1787,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k6_partfun1 @ ( A @ k6_eqrel_1 ) ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_eqrel_1) ).
thf(11080,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k6_partfun1 @ ( A @ k6_eqrel_1 ) ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1787]) ).
thf(2115,plain,
sk1 @ v3_group_1,
inference(cnfConj,[status(thm)],[2114]) ).
thf(18331,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ v3_group_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,2115]) ).
thf(18332,plain,
( ( k1_xboole_0 @ v3_group_1 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[18331:[bind(A,$thf( sk1 ))]]) ).
thf(20104,plain,
( ( ( sk48 @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_group_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3100,18332]) ).
thf(20105,plain,
( ( ( sk48 @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v3_group_1 ) ),
inference(simp,[status(thm)],[20104]) ).
thf(20108,plain,
( ( sk48 != sk1 )
| ( k1_xboole_0 @ v3_group_1 ) ),
inference(simp,[status(thm)],[20105]) ).
thf(25025,plain,
( ( sk1 != k1_xboole_0 )
| ( k1_xboole_0 @ v3_group_1 ) ),
inference(rewrite,[status(thm)],[20108,19097]) ).
thf(25038,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ( sk1 != k1_xboole_0 )
| ( A @ v3_group_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,25025]) ).
thf(25039,plain,
! [A: $i] :
( ( sk1 != k1_xboole_0 )
| ( A @ v3_group_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25038:[]]) ).
thf(2079,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ r1_rlvect_1 ) )
| ( D @ ( B @ r1_rlvect_1 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ r1_rlvect_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_latsubgr) ).
thf(12193,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ r1_rlvect_1 ) )
| ( D @ ( B @ r1_rlvect_1 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ r1_rlvect_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2079]) ).
thf(119,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B @ ( D @ v2_binop_1 ) )
& ( A @ ( C @ v2_binop_1 ) ) )
<=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v2_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_filter_1) ).
thf(2607,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v2_binop_1 ) )
=> ( ( B @ ( D @ v2_binop_1 ) )
& ( A @ ( C @ v2_binop_1 ) ) ) )
& ( ( ( B @ ( D @ v2_binop_1 ) )
& ( A @ ( C @ v2_binop_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v2_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(1385,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_partfun1) ).
thf(8915,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1385]) ).
thf(1158,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C
= ( B @ ( A @ k3_filter_0 ) ) )
<=> ( ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_filter_0) ).
thf(7669,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( ( ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( C
= ( B @ ( A @ k3_filter_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_filter_0 ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(1496,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(9494,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496]) ).
thf(1107,axiom,
! [A: $i] : ( A @ k1_card_1 @ v1_card_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_card_1) ).
thf(7440,plain,
! [A: $i] : ( A @ k1_card_1 @ v1_card_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(7441,plain,
! [A: $i] : ( A @ k1_card_1 @ v1_card_1 ),
inference(cnf,[status(esa)],[7440]) ).
thf(13654,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_card_1 )
!= ( A @ k1_card_1 ) )
| ( k1_xboole_0 @ v1_card_1 ) ),
inference(paramod_ordered,[status(thm)],[8607,7441]) ).
thf(13655,plain,
k1_xboole_0 @ v1_card_1,
inference(pattern_uni,[status(thm)],[13654:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_xboole_1) ).
thf(3017,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ( ( B @ ( A @ r1_xreal_0 ) )
=> ( k5_numbers @ ( A @ ( B @ k6_xcmplx_0 ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_int_1) ).
thf(2194,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ( ( B @ ( A @ r1_xreal_0 ) )
=> ( k5_numbers @ ( A @ ( B @ k6_xcmplx_0 ) @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2195,plain,
! [B: $i,A: $i] :
( ( k5_numbers @ ( A @ ( B @ k6_xcmplx_0 ) @ r2_hidden ) )
| ~ ( B @ ( A @ r1_xreal_0 ) )
| ~ ( B @ v1_int_1 )
| ~ ( A @ v1_int_1 ) ),
inference(cnf,[status(esa)],[2194]) ).
thf(11609,plain,
sk611 @ v1_group_1,
inference(cnfConj,[status(thm)],[11606]) ).
thf(21898,plain,
! [A: $i] :
( ( A != sk611 )
| ( k1_xboole_0 @ v1_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,11609]) ).
thf(21899,plain,
( ( k1_xboole_0 @ v1_group_1 )
| ( sk611 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21898:[bind(A,$thf( sk611 ))]]) ).
thf(1578,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C
= ( B @ ( A @ k10_group_6 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k2_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_group_6) ).
thf(9956,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k2_group_1 ) ) )
=> ( C
= ( B @ ( A @ k10_group_6 ) ) ) )
& ( ( C
= ( B @ ( A @ k10_group_6 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k2_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1578]) ).
thf(980,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(6860,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(6861,plain,
! [A: $i] : ( A @ ( A @ sk305 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[6860]) ).
thf(71,axiom,
? [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_realset1) ).
thf(2408,plain,
? [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(2409,plain,
! [A: $i] :
( ( ~ ( A @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ v1_xboole_0 )
| ~ ( sk15 @ ( A @ m1_subset_1 ) ) )
& ~ ( sk15 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[2408]) ).
thf(2411,plain,
! [A: $i] :
( ~ ( A @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ v1_xboole_0 )
| ~ ( sk15 @ ( A @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[2409]) ).
thf(16581,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk305 @ m1_subset_1 ) )
!= ( sk15 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6861,2411]) ).
thf(16582,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk305 @ m1_subset_1 ) )
!= ( sk15 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[16581]) ).
thf(16583,plain,
~ ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[16582:[bind(A,$thf( sk15 )),bind(B,$thf( sk15 @ sk305 ))]]) ).
thf(16630,plain,
( ( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,16583]) ).
thf(16631,plain,
( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[16630]) ).
thf(16645,plain,
( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[16631]) ).
thf(879,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lattices @ ( A @ k7_lattices ) )
= ( A @ k5_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_lattice4) ).
thf(6391,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lattices @ ( A @ k7_lattices ) )
= ( A @ k5_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(2086,axiom,
? [A: $i] : ( A @ l1_group_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_group_1) ).
thf(12216,plain,
? [A: $i] : ( A @ l1_group_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2086]) ).
thf(12217,plain,
sk636 @ l1_group_1,
inference(cnf,[status(esa)],[12216]) ).
thf(16422,plain,
! [A: $i] :
( ( ( sk636 @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12217,4961]) ).
thf(16423,plain,
! [A: $i] :
( ( ( sk636 @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[16422]) ).
thf(16424,plain,
sk636 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[16423:[bind(A,$thf( sk636 ))]]) ).
thf(493,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
<=> ( ( C @ k1_relat_1 @ ( A @ r2_hidden ) )
| ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_funct_4) ).
thf(4403,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 @ ( A @ r2_hidden ) )
| ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k1_funct_4 ) @ k1_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k1_funct_4 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( C @ k1_relat_1 @ ( A @ r2_hidden ) )
| ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(956,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_binop_1) ).
thf(6764,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) )
=> ( B @ ( C @ ( A @ r6_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(1497,axiom,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(9497,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1497]) ).
thf(9498,plain,
( ! [A: $i] : ( A @ k1_tarski @ v1_finset_1 )
& ~ ? [A: $i] : ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(miniscope,[status(thm)],[9497]) ).
thf(9499,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[9498]) ).
thf(9501,plain,
! [A: $i] : ( A @ k1_tarski @ v1_finset_1 ),
inference(cnfConj,[status(thm)],[9499]) ).
thf(9502,plain,
! [A: $i] : ( A @ k1_tarski @ v1_finset_1 ),
inference(simp,[status(thm)],[9501]) ).
thf(14329,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ v1_finset_1 )
!= ( B @ v1_finset_1 ) )
| ( C @ ( B @ k4_xboole_0 ) @ v1_finset_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9502,2181]) ).
thf(14330,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ v1_finset_1 )
!= ( B @ v1_finset_1 ) )
| ( C @ ( B @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(simp,[status(thm)],[14329]) ).
thf(14331,plain,
! [B: $i,A: $i] : ( A @ ( B @ k1_tarski @ k4_xboole_0 ) @ v1_finset_1 ),
inference(pattern_uni,[status(thm)],[14330:[bind(A,$thf( D )),bind(B,$thf( D @ k1_tarski ))]]) ).
thf(14347,plain,
! [B: $i,A: $i] : ( A @ ( B @ k1_tarski @ k4_xboole_0 ) @ v1_finset_1 ),
inference(simp,[status(thm)],[14331]) ).
thf(1438,axiom,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( A @ u1_struct_0 @ ( A @ u1_vectsp_1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_vectsp_1) ).
thf(9212,plain,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( A @ u1_struct_0 @ ( A @ u1_vectsp_1 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1438]) ).
thf(1503,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( D @ ( A @ k6_group_3 ) ) @ ( C @ ( B @ ( D @ ( A @ k6_group_3 ) ) @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_group_3) ).
thf(9526,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( D @ ( A @ k6_group_3 ) ) @ ( C @ ( B @ ( D @ ( A @ k6_group_3 ) ) @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1503]) ).
thf(900,axiom,
! [A: $i] :
( ( A = k4_numbers )
<=> ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
<=> ~ ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( B
!= ( C @ k1_real_1 ) )
& ( B != C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_int_1) ).
thf(6505,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( ~ ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( B
!= ( C @ k1_real_1 ) )
& ( B != C ) ) )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ~ ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( B
!= ( C @ k1_real_1 ) )
& ( B != C ) ) ) ) )
=> ( A = k4_numbers ) )
& ( ( A = k4_numbers )
=> ! [B: $i] :
( ( ~ ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( B
!= ( C @ k1_real_1 ) )
& ( B != C ) ) )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ~ ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( B
!= ( C @ k1_real_1 ) )
& ( B != C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(1795,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k14_group_2 ) @ v1_finset_1 )
=> ( ? [C: $i] :
( ( ( B @ ( A @ k17_group_2 ) )
= ( C @ k4_card_1 ) )
& ( C
= ( B @ ( A @ k15_group_2 ) ) )
& ( C @ v1_finset_1 ) )
& ? [C: $i] :
( ( ( B @ ( A @ k17_group_2 ) )
= ( C @ k4_card_1 ) )
& ( C
= ( B @ ( A @ k14_group_2 ) ) )
& ( C @ v1_finset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t176_group_2) ).
thf(11112,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k14_group_2 ) @ v1_finset_1 )
=> ( ? [C: $i] :
( ( ( B @ ( A @ k17_group_2 ) )
= ( C @ k4_card_1 ) )
& ( C
= ( B @ ( A @ k15_group_2 ) ) )
& ( C @ v1_finset_1 ) )
& ? [C: $i] :
( ( ( B @ ( A @ k17_group_2 ) )
= ( C @ k4_card_1 ) )
& ( C
= ( B @ ( A @ k14_group_2 ) ) )
& ( C @ v1_finset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1795]) ).
thf(2092,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_2_group_3 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( B @ k7_group_3 ) @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ u1_struct_0 @ k6_domain_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_group_3) ).
thf(12244,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ( C @ ( B @ k7_group_3 ) @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ u1_struct_0 @ k6_domain_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_2_group_3 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_2_group_3 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( B @ k7_group_3 ) @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ u1_struct_0 @ k6_domain_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2092]) ).
thf(363,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( B
= ( A @ k4_card_1 ) )
<=> ( ( B @ k1_card_1 )
= ( A @ k1_card_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_card_1) ).
thf(3745,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( ( ( B @ k1_card_1 )
= ( A @ k1_card_1 ) )
=> ( B
= ( A @ k4_card_1 ) ) )
& ( ( B
= ( A @ k4_card_1 ) )
=> ( ( B @ k1_card_1 )
= ( A @ k1_card_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(1613,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ v6_group_1 )
=> ( ( C @ k9_group_1 )
= ( B @ ( C @ ( A @ k6_group_3 ) ) @ k9_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_group_3) ).
thf(10181,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ v6_group_1 )
=> ( ( C @ k9_group_1 )
= ( B @ ( C @ ( A @ k6_group_3 ) ) @ k9_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1613]) ).
thf(1137,axiom,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( A = B )
<=> ( B @ ( A @ r2_wellord2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_card_1) ).
thf(7573,plain,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( ( B @ ( A @ r2_wellord2 ) )
=> ( A = B ) )
& ( ( A = B )
=> ( B @ ( A @ r2_wellord2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(1272,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(8247,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(8248,plain,
( ( sk385 @ v1_finset_1 )
& ~ ( sk385 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[8247]) ).
thf(8250,plain,
sk385 @ v1_finset_1,
inference(cnfConj,[status(thm)],[8248]) ).
thf(14315,plain,
! [B: $i,A: $i] :
( ( ( sk385 @ v1_finset_1 )
!= ( A @ v1_finset_1 ) )
| ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8250,2181]) ).
thf(14316,plain,
! [B: $i,A: $i] :
( ( ( sk385 @ v1_finset_1 )
!= ( A @ v1_finset_1 ) )
| ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(simp,[status(thm)],[14315]) ).
thf(14317,plain,
! [A: $i] : ( A @ ( sk385 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(pattern_uni,[status(thm)],[14316:[bind(A,$thf( sk385 ))]]) ).
thf(14348,plain,
! [A: $i] : ( A @ ( sk385 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(simp,[status(thm)],[14317]) ).
thf(15005,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk385 @ k4_xboole_0 ) @ v1_finset_1 )
!= ( B @ v1_finset_1 ) )
| ( C @ ( B @ k4_xboole_0 ) @ v1_finset_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14348,2181]) ).
thf(15006,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk385 @ k4_xboole_0 ) @ v1_finset_1 )
!= ( B @ v1_finset_1 ) )
| ( C @ ( B @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(simp,[status(thm)],[15005]) ).
thf(15007,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( sk385 @ k4_xboole_0 ) @ k4_xboole_0 ) @ v1_finset_1 ),
inference(pattern_uni,[status(thm)],[15006:[bind(A,$thf( E )),bind(B,$thf( E @ ( sk385 @ k4_xboole_0 ) )),bind(C,$thf( C ))]]) ).
thf(15013,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( sk385 @ k4_xboole_0 ) @ k4_xboole_0 ) @ v1_finset_1 ),
inference(simp,[status(thm)],[15007]) ).
thf(1099,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ ( A @ r2_wellord2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_card_1) ).
thf(7405,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ ( A @ r2_wellord2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ k6_relat_1 @ ( C @ k5_relat_1 ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_partfun1) ).
thf(3332,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ k6_relat_1 @ ( C @ k5_relat_1 ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(405,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t175_orders_1) ).
thf(3942,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(1932,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_struct_0) ).
thf(11616,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1932]) ).
thf(11617,plain,
( ~ ( sk612 @ v3_struct_0 )
& ( sk612 @ l2_struct_0 ) ),
inference(cnf,[status(esa)],[11616]) ).
thf(11618,plain,
sk612 @ l2_struct_0,
inference(cnfConj,[status(thm)],[11617]) ).
thf(22433,plain,
! [A: $i] :
( ( A != sk612 )
| ( k1_xboole_0 @ l2_struct_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,11618]) ).
thf(22434,plain,
( ( k1_xboole_0 @ l2_struct_0 )
| ( sk612 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22433:[bind(A,$thf( sk612 ))]]) ).
thf(584,axiom,
! [A: $i,B: $i] :
( ( A @ k6_relat_1 @ ( B @ k6_relat_1 @ k5_relat_1 ) )
= ( B @ ( A @ k3_xboole_0 ) @ k6_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_funct_1) ).
thf(4884,plain,
! [A: $i,B: $i] :
( ( A @ k6_relat_1 @ ( B @ k6_relat_1 @ k5_relat_1 ) )
= ( B @ ( A @ k3_xboole_0 ) @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(1131,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ( ( C @ ( D @ r1_rlvect_1 ) )
=> ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( D @ r1_rlvect_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_group_4) ).
thf(7556,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ( ( C @ ( D @ r1_rlvect_1 ) )
=> ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( D @ r1_rlvect_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(456,axiom,
k4_numbers @ ( k5_numbers @ r1_tarski ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_numbers) ).
thf(4182,plain,
k4_numbers @ ( k5_numbers @ r1_tarski ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(21617,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( k5_numbers @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4182,2231]) ).
thf(21618,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( k5_numbers @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[21617]) ).
thf(21619,plain,
! [A: $i] : ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k4_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[21618:[bind(A,$thf( k5_numbers )),bind(B,$thf( k4_numbers ))]]) ).
thf(21644,plain,
! [A: $i] : ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k4_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[21619]) ).
thf(43657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k4_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ k4_xboole_0 ) @ ( B @ r1_tarski ) ) )
| ( C @ ( B @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21644,2276]) ).
thf(43658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k4_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ k4_xboole_0 ) @ ( B @ r1_tarski ) ) )
| ( C @ ( B @ r1_tarski ) ) ),
inference(simp,[status(thm)],[43657]) ).
thf(43659,plain,
! [A: $i] : ( A @ ( k4_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[43658:[bind(A,$thf( E )),bind(B,$thf( k4_numbers @ ( E @ k4_xboole_0 ) )),bind(C,$thf( E )),bind(D,$thf( k5_numbers ))]]) ).
thf(43693,plain,
! [A: $i] : ( A @ ( k4_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[43659]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_xboole_1) ).
thf(2187,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(2188,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
| ~ ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[2187]) ).
thf(45236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( k4_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43693,2188]) ).
thf(45237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( k4_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) ) ),
inference(simp,[status(thm)],[45236]) ).
thf(45238,plain,
! [A: $i] : ( A @ ( k4_numbers @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[45237:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k4_numbers )),bind(D,$thf( A ))]]) ).
thf(1646,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) @ ( A @ k3_lattices ) ) )
= ( B @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) )
=> ( A @ v11_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_lattices) ).
thf(10358,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) @ ( A @ k3_lattices ) ) )
= ( B @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) )
=> ( A @ v11_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1646]) ).
thf(871,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ k1_group_1 ) ) )
= ( C @ ( D @ ( B @ k1_group_1 ) ) ) )
=> ( ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( C @ ( B @ k1_group_1 ) ) )
= ( C @ ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k1_group_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_group_1) ).
thf(6359,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ k1_group_1 ) ) )
= ( C @ ( D @ ( B @ k1_group_1 ) ) ) )
=> ( ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( C @ ( B @ k1_group_1 ) ) )
= ( C @ ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k1_group_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(1001,axiom,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(6947,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(6948,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(lifteq,[status(thm)],[6947]) ).
thf(38575,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_orders_1 ) ) ),
inference(paramod_ordered,[status(thm)],[6948,2889]) ).
thf(38576,plain,
( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k4_xboole_0 ) )
= ( k1_xboole_0 @ k1_orders_1 ) ),
inference(pattern_uni,[status(thm)],[38575:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(38681,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k4_xboole_0 ) )
!= ( A @ ( B @ k1_tarski @ k4_xboole_0 ) ) )
| ( k1_xboole_0 @ k1_orders_1 @ v1_finset_1 ) ),
inference(paramod_ordered,[status(thm)],[38576,14347]) ).
thf(38682,plain,
k1_xboole_0 @ k1_orders_1 @ v1_finset_1,
inference(pattern_uni,[status(thm)],[38681:[bind(A,$thf( k1_xboole_0 @ k1_tarski )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(38870,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_orders_1 @ v1_finset_1 )
!= ( A @ v1_finset_1 ) )
| ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38682,2181]) ).
thf(38871,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_orders_1 @ v1_finset_1 )
!= ( A @ v1_finset_1 ) )
| ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(simp,[status(thm)],[38870]) ).
thf(38872,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ k1_orders_1 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(pattern_uni,[status(thm)],[38871:[bind(A,$thf( k1_xboole_0 @ k1_orders_1 )),bind(B,$thf( B ))]]) ).
thf(38887,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ k1_orders_1 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(simp,[status(thm)],[38872]) ).
thf(460,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(4216,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(4217,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( B @ sk118 ) @ v1_funct_2 ) ) )
& ( A @ ( B @ sk118 ) @ v1_funct_1 )
& ( A @ ( B @ sk118 ) @ v1_relat_1 )
& ( B @ ( A @ ( A @ ( B @ sk118 ) @ m1_relset_1 ) ) ) ),
inference(cnf,[status(esa)],[4216]) ).
thf(4220,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk118 ) @ v1_funct_1 ),
inference(cnfConj,[status(thm)],[4217]) ).
thf(517,axiom,
! [A: $i] :
( ( ( A @ v1_card_1 )
& ( A @ v1_finset_1 ) )
=> ? [B: $i] :
( ( A
= ( B @ k1_card_1 ) )
& ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_card_1) ).
thf(4528,plain,
! [A: $i] :
( ( ( A @ v1_card_1 )
& ( A @ v1_finset_1 ) )
=> ? [B: $i] :
( ( A
= ( B @ k1_card_1 ) )
& ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(1899,axiom,
? [A: $i] :
( ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v2_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_group_1) ).
thf(11491,plain,
? [A: $i] :
( ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v2_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1899]) ).
thf(11492,plain,
( ( sk608 @ v4_group_1 )
& ( sk608 @ v3_group_1 )
& ( sk608 @ v2_group_1 )
& ( sk608 @ v1_group_1 )
& ~ ( sk608 @ v3_struct_0 )
& ( sk608 @ l1_group_1 ) ),
inference(cnf,[status(esa)],[11491]) ).
thf(11494,plain,
~ ( sk608 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[11492]) ).
thf(19109,plain,
! [A: $i] :
( ( A != sk608 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,11494]) ).
thf(19110,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk608 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19109:[bind(A,$thf( sk608 ))]]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_xboole_1) ).
thf(2182,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(2183,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A )
| ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[2182]) ).
thf(2184,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r1_xboole_0 ) )
| ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
inference(lifteq,[status(thm)],[2183]) ).
thf(1236,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D
= ( C @ k2_funct_1 ) )
& ( A @ ( B @ ( C @ v4_group_6 ) ) ) )
=> ( B @ ( A @ ( D @ v4_group_6 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_group_6) ).
thf(8057,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D
= ( C @ k2_funct_1 ) )
& ( A @ ( B @ ( C @ v4_group_6 ) ) ) )
=> ( B @ ( A @ ( D @ v4_group_6 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(1086,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset_1) ).
thf(7338,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(7339,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[7338]) ).
thf(14725,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[6948,7339]) ).
thf(14726,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ),
inference(pattern_uni,[status(thm)],[14725:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(48,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v4_lattice3 )
<=> ! [B: $i] :
? [C: $i] :
( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ r4_lattice3 ) ) )
=> ( D @ ( C @ ( A @ r1_lattices ) ) ) ) )
& ( B @ ( C @ ( A @ r4_lattice3 ) ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_lattice3) ).
thf(2313,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
? [C: $i] :
( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ r4_lattice3 ) ) )
=> ( D @ ( C @ ( A @ r1_lattices ) ) ) ) )
& ( B @ ( C @ ( A @ r4_lattice3 ) ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) )
=> ( A @ v4_lattice3 ) )
& ( ( A @ v4_lattice3 )
=> ! [B: $i] :
? [C: $i] :
( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ r4_lattice3 ) ) )
=> ( D @ ( C @ ( A @ r1_lattices ) ) ) ) )
& ( B @ ( C @ ( A @ r4_lattice3 ) ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(2314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ v4_lattice3 )
| ~ ( A @ ( D @ sk9 ) @ ( D @ ( A @ r1_lattices ) ) )
| ~ ( A @ sk8 @ ( D @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) )
& ( ( A @ v4_lattice3 )
| ( A @ sk8 @ ( A @ ( D @ sk9 ) @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ sk8 @ ( D @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) )
& ( ( A @ v4_lattice3 )
| ( A @ u1_struct_0 @ ( A @ ( D @ sk9 ) @ m1_subset_1 ) )
| ~ ( A @ sk8 @ ( D @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) )
& ( ( C @ ( A @ ( B @ sk7 ) @ ( A @ r1_lattices ) ) )
| ~ ( B @ ( C @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ v4_lattice3 )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) )
& ( ( B @ ( A @ ( B @ sk7 ) @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ v4_lattice3 )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) )
& ( ( A @ u1_struct_0 @ ( A @ ( B @ sk7 ) @ m1_subset_1 ) )
| ~ ( A @ v4_lattice3 )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ) ),
inference(cnf,[status(esa)],[2313]) ).
thf(2316,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk7 ) @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ v4_lattice3 )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2314]) ).
thf(305,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_funct_1) ).
thf(3446,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(627,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( ( A @ k2_group_4 )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_group_4) ).
thf(5146,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( ( A @ k2_group_4 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(146,axiom,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finseq_1) ).
thf(2712,plain,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(771,axiom,
? [A: $i] : ( A @ l1_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(5886,plain,
? [A: $i] : ( A @ l1_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(5887,plain,
sk235 @ l1_lattices,
inference(cnf,[status(esa)],[5886]) ).
thf(4291,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
| ~ ( A @ l1_lattices ) ),
inference(cnf,[status(esa)],[4290]) ).
thf(15753,plain,
! [A: $i] :
( ( ( sk235 @ l1_lattices )
!= ( A @ l1_lattices ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5887,4291]) ).
thf(15754,plain,
! [A: $i] :
( ( ( sk235 @ l1_lattices )
!= ( A @ l1_lattices ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[15753]) ).
thf(15755,plain,
sk235 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[15754:[bind(A,$thf( sk235 ))]]) ).
thf(2071,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( B @ ( A @ r4_group_3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r4_group_3) ).
thf(12158,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( B @ ( A @ r4_group_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2071]) ).
thf(747,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B
= ( A @ k2_funct_1 ) )
<=> ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
& ( ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
thf(5713,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
& ( ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) )
=> ( B
= ( A @ k2_funct_1 ) ) )
& ( ( B
= ( A @ k2_funct_1 ) )
=> ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
& ( ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r1_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r2_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_binop_1) ).
thf(2627,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r2_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r1_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r1_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r2_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(1808,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_2) ).
thf(11160,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1808]) ).
thf(1832,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k6_group_2 @ ( A @ k15_group_2 ) )
= ( A @ u1_struct_0 @ k1_tarski ) )
& ( ( A @ k6_group_2 @ ( A @ k14_group_2 ) )
= ( A @ u1_struct_0 @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t172_group_2) ).
thf(11239,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k6_group_2 @ ( A @ k15_group_2 ) )
= ( A @ u1_struct_0 @ k1_tarski ) )
& ( ( A @ k6_group_2 @ ( A @ k14_group_2 ) )
= ( A @ u1_struct_0 @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1832]) ).
thf(1463,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k13_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k4_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_group_2) ).
thf(9356,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k13_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k4_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k3_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( A @ k3_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_relat_1) ).
thf(2459,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k3_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( A @ k3_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(240,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_subset_1) ).
thf(3121,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(904,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_subset_1) ).
thf(6551,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(11619,plain,
~ ( sk612 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[11617]) ).
thf(18239,plain,
! [A: $i] :
( ( A != sk612 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,11619]) ).
thf(18240,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk612 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[18239:[bind(A,$thf( sk612 ))]]) ).
thf(111,axiom,
! [A: $i,B: $i] : ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_xboole_1) ).
thf(2580,plain,
! [A: $i,B: $i] : ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(1195,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k6_group_6 ) )
= ( B @ ( A @ k5_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ g1_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_group_6) ).
thf(7871,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k6_group_6 ) )
= ( B @ ( A @ k5_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ g1_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(751,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_xboole_0 ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t186_partfun1) ).
thf(5782,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_xboole_0 ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(866,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( B @ ( F @ ( E @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) )
=> ( ( B @ ( F @ ( D @ ( A @ k4_lattices ) ) @ ( E @ ( C @ ( A @ k4_lattices ) ) @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
& ( B @ ( F @ ( D @ ( A @ k3_lattices ) ) @ ( E @ ( C @ ( A @ k3_lattices ) ) @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_filter_1) ).
thf(6336,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( B @ ( F @ ( E @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) )
=> ( ( B @ ( F @ ( D @ ( A @ k4_lattices ) ) @ ( E @ ( C @ ( A @ k4_lattices ) ) @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
& ( B @ ( F @ ( D @ ( A @ k3_lattices ) ) @ ( E @ ( C @ ( A @ k3_lattices ) ) @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(636,axiom,
! [A: $i] :
( ( A @ v1_card_1 )
=> ( A @ k2_card_1 @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_card_1) ).
thf(5178,plain,
! [A: $i] :
( ( A @ v1_card_1 )
=> ( A @ k2_card_1 @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(1163,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_group_3 ) ) @ ( D @ ( A @ k5_group_3 ) ) )
= ( B @ ( D @ ( C @ ( A @ k3_group_2 ) ) @ ( A @ k5_group_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_group_3) ).
thf(7716,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_group_3 ) ) @ ( D @ ( A @ k5_group_3 ) ) )
= ( B @ ( D @ ( C @ ( A @ k3_group_2 ) ) @ ( A @ k5_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(966,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_xboole_1) ).
thf(6804,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(1225,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k5_group_4 ) @ m1_group_2 ) )
& ( B @ ( A @ k5_group_4 ) @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_group_4) ).
thf(8012,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k5_group_4 ) @ m1_group_2 ) )
& ( B @ ( A @ k5_group_4 ) @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(2051,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k3_group_3 ) ) )
!= k1_xboole_0 )
<=> ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_group_3) ).
thf(12077,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k3_group_3 ) ) )
!= k1_xboole_0 ) )
& ( ( ( C @ ( B @ ( A @ k3_group_3 ) ) )
!= k1_xboole_0 )
=> ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2051]) ).
thf(453,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).
thf(4172,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(4173,plain,
~ ? [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
= k1_xboole_0 ),
inference(miniscope,[status(thm)],[4172]) ).
thf(4174,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(cnf,[status(esa)],[4173]) ).
thf(4175,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(lifteq,[status(thm)],[4174]) ).
thf(22846,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ k1_tarski @ k2_xboole_0 ) ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,4175]) ).
thf(22847,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ k1_tarski @ k2_xboole_0 ) ) )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[22846]) ).
thf(22848,plain,
! [B: $i,A: $i] : ( A @ ( B @ k1_tarski @ k2_xboole_0 ) @ sk149 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[22847:[bind(A,$thf( E @ ( F @ k1_tarski @ k2_xboole_0 ) )),bind(B,$thf( F )),bind(C,$thf( E ))]]) ).
thf(23159,plain,
! [B: $i,A: $i] : ( A @ ( B @ k1_tarski @ k2_xboole_0 ) @ sk149 @ v1_funct_1 ),
inference(simp,[status(thm)],[22848]) ).
thf(1771,axiom,
? [A: $i] :
( ! [B: $i] :
( ( ( f1_s2_group_4 @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
<=> ( B @ p1_s2_group_4 ) ) )
& ( f1_s2_group_4 @ k1_group_3 @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_group_4) ).
thf(10991,plain,
? [A: $i] :
( ! [B: $i] :
( ( ( f1_s2_group_4 @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( B @ p1_s2_group_4 )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s2_group_4 ) ) ) )
& ( f1_s2_group_4 @ k1_group_3 @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1771]) ).
thf(2146,plain,
! [B: $i,A: $i] :
( ( B @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2144]) ).
thf(1914,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_group_3 ) ) @ ( A @ k3_group_3 ) ) )
= ( D @ ( C @ ( A @ k2_group_2 ) ) @ ( B @ ( A @ k3_group_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_group_3) ).
thf(11549,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_group_3 ) ) @ ( A @ k3_group_3 ) ) )
= ( D @ ( C @ ( A @ k2_group_2 ) ) @ ( B @ ( A @ k3_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1914]) ).
thf(42439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41461,2188]) ).
thf(42440,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) ) ),
inference(simp,[status(thm)],[42439]) ).
thf(42441,plain,
! [A: $i] : ( A @ ( k1_numbers @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[42440:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_numbers )),bind(D,$thf( A ))]]) ).
thf(1970,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ k1_group_1 ) ) )
= ( C @ ( D @ ( B @ k1_group_1 ) ) ) )
=> ( ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( C @ ( B @ k1_group_1 ) ) )
= ( C @ ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k1_group_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_group_1) ).
thf(11786,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ k1_group_1 ) ) )
= ( C @ ( D @ ( B @ k1_group_1 ) ) ) )
=> ( ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( C @ ( B @ k1_group_1 ) ) )
= ( C @ ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k1_group_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1970]) ).
thf(1982,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ m1_group_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_group_2) ).
thf(11816,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ m1_group_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1982]) ).
thf(397,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m3_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_lattice4) ).
thf(3895,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m3_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(21779,plain,
! [A: $i] :
( ( A
!= ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,16645]) ).
thf(21780,plain,
! [A: $i] :
( ( A
!= ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) ) )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[21779]) ).
thf(21781,plain,
sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ sk149 @ v1_funct_1,
inference(pattern_uni,[status(thm)],[21780:[bind(A,$thf( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) ))]]) ).
thf(1643,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r2_wellord2 ) )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_card_1) ).
thf(10334,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ( k1_xboole_0 @ ( A @ r2_wellord2 ) ) )
& ( ( k1_xboole_0 @ ( A @ r2_wellord2 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1643]) ).
thf(10335,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( k1_xboole_0 @ ( A @ r2_wellord2 ) ) )
& ! [A: $i] :
( ( k1_xboole_0 @ ( A @ r2_wellord2 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[10334]) ).
thf(10336,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( B @ r2_wellord2 ) )
| ( B != k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( A @ r2_wellord2 ) ) ) ),
inference(cnf,[status(esa)],[10335]) ).
thf(10338,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r2_wellord2 ) )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[10336]) ).
thf(10340,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r2_wellord2 ) )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[10338]) ).
thf(10341,plain,
k1_xboole_0 @ ( k1_xboole_0 @ r2_wellord2 ),
inference(simp,[status(thm)],[10340]) ).
thf(26094,plain,
( ( ( sk612 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,18240]) ).
thf(26095,plain,
( ( ( sk612 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[26094]) ).
thf(26108,plain,
( ( sk612 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[26095]) ).
thf(806,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_realset1) ).
thf(6046,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
= ( B @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_funct_2) ).
thf(3276,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
= ( B @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(110,axiom,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc8_finseq_1) ).
thf(2573,plain,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(2574,plain,
( ( sk19 @ v1_finseq_1 )
& ( sk19 @ v1_finset_1 )
& ( sk19 @ v1_funct_1 )
& ( sk19 @ v1_relat_1 )
& ~ ( sk19 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[2573]) ).
thf(2575,plain,
sk19 @ v1_finseq_1,
inference(cnfConj,[status(thm)],[2574]) ).
thf(1284,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( D @ ( A @ k4_lattices ) ) @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ r3_lattices ) ) )
& ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_filter_1) ).
thf(8303,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( D @ ( A @ k4_lattices ) ) @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ r3_lattices ) ) )
& ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).
thf(1097,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relset_1) ).
thf(7400,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(1948,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ k2_group_3 ) ) )
= B )
& ( ( C @ ( A @ k3_group_1 ) @ ( C @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ k2_group_3 ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_group_3) ).
thf(11684,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ k2_group_3 ) ) )
= B )
& ( ( C @ ( A @ k3_group_1 ) @ ( C @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ k2_group_3 ) ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1948]) ).
thf(1051,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_zfmisc_1) ).
thf(7168,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(56,axiom,
! [A: $i,B: $i] :
~ ( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_zfmisc_1) ).
thf(2348,plain,
! [A: $i,B: $i] :
~ ( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1452,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
<=> ( A @ ( B @ m1_finseq_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_finseq_1) ).
thf(9292,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_finseq_1 ) )
=> ( A @ ( B @ m2_finseq_1 ) ) )
& ( ( A @ ( B @ m2_finseq_1 ) )
=> ( A @ ( B @ m1_finseq_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452]) ).
thf(985,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( B @ ( A @ k6_group_6 ) @ ( A @ ( B @ ( A @ k11_group_6 ) @ v3_group_6 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_group_6) ).
thf(6872,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( B @ ( A @ k6_group_6 ) @ ( A @ ( B @ ( A @ k11_group_6 ) @ v3_group_6 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(1931,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_group_2 @ k9_group_1 )
= np__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_group_2) ).
thf(11613,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_group_2 @ k9_group_1 )
= np__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1931]) ).
thf(1595,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_3_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_3_domain_1) ).
thf(10078,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_3_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_3_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1595]) ).
thf(1925,axiom,
? [A: $i] :
( ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v2_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_group_1) ).
thf(11583,plain,
? [A: $i] :
( ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v2_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1925]) ).
thf(11584,plain,
( ( sk610 @ v7_group_1 )
& ( sk610 @ v4_group_1 )
& ( sk610 @ v3_group_1 )
& ( sk610 @ v2_group_1 )
& ( sk610 @ v1_group_1 )
& ~ ( sk610 @ v3_struct_0 )
& ( sk610 @ l1_group_1 ) ),
inference(cnf,[status(esa)],[11583]) ).
thf(11588,plain,
sk610 @ l1_group_1,
inference(cnfConj,[status(thm)],[11584]) ).
thf(777,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t176_orders_1) ).
thf(5903,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(1168,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k2_filter_0 ) )
= ( C @ ( A @ k2_filter_0 ) ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_filter_1) ).
thf(7761,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k2_filter_0 ) )
= ( C @ ( A @ k2_filter_0 ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(283,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relset_1) ).
thf(3335,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(1384,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( D @ ( C @ m1_group_2 ) )
=> ( ( B @ ( D @ ( A @ k13_group_2 ) ) @ ( B @ ( C @ ( A @ k13_group_2 ) ) @ r1_tarski ) )
& ( B @ ( D @ ( A @ k12_group_2 ) ) @ ( B @ ( C @ ( A @ k12_group_2 ) ) @ r1_tarski ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_group_3) ).
thf(8911,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( D @ ( C @ m1_group_2 ) )
=> ( ( B @ ( D @ ( A @ k13_group_2 ) ) @ ( B @ ( C @ ( A @ k13_group_2 ) ) @ r1_tarski ) )
& ( B @ ( D @ ( A @ k12_group_2 ) ) @ ( B @ ( C @ ( A @ k12_group_2 ) ) @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384]) ).
thf(17913,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ l1_group_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,2117]) ).
thf(17914,plain,
( ( k1_xboole_0 @ l1_group_1 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[17913:[bind(A,$thf( sk1 ))]]) ).
thf(19571,plain,
( ( ( sk167 @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_group_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4741,17914]) ).
thf(19572,plain,
( ( ( sk167 @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_group_1 ) ),
inference(simp,[status(thm)],[19571]) ).
thf(19581,plain,
( ( sk167 != sk1 )
| ( k1_xboole_0 @ l1_group_1 ) ),
inference(simp,[status(thm)],[19572]) ).
thf(21457,plain,
( ( sk1 != k1_xboole_0 )
| ( k1_xboole_0 @ l1_group_1 ) ),
inference(rewrite,[status(thm)],[19581,18768]) ).
thf(21466,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ( sk1 != k1_xboole_0 )
| ( A @ l1_group_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,21457]) ).
thf(21467,plain,
! [A: $i] :
( ( sk1 != k1_xboole_0 )
| ( A @ l1_group_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[21466:[]]) ).
thf(852,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(6236,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
& ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_binop_1) ).
thf(2216,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
& ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r6_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
& ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(11590,plain,
~ ( sk610 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[11584]) ).
thf(18703,plain,
! [A: $i] :
( ( A != sk610 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,11590]) ).
thf(18704,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk610 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[18703:[bind(A,$thf( sk610 ))]]) ).
thf(33576,plain,
( ( ( sk610 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,18704]) ).
thf(33577,plain,
( ( ( sk610 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[33576]) ).
thf(33590,plain,
( ( sk610 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[33577]) ).
thf(1660,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(10427,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1660]) ).
thf(1209,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ( ( C @ ( D @ ( B @ k13_group_2 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( E @ ( D @ r1_rlvect_1 ) )
& ( A
= ( C @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_group_2) ).
thf(7944,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ( ( ? [E: $i] :
( ( E @ ( D @ r1_rlvect_1 ) )
& ( A
= ( C @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ ( B @ k13_group_2 ) ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( D @ ( B @ k13_group_2 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( E @ ( D @ r1_rlvect_1 ) )
& ( A
= ( C @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(11436,plain,
sk605 @ v3_group_1,
inference(cnfConj,[status(thm)],[11434]) ).
thf(790,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_relat_1) ).
thf(5977,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(3766,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(413,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_funct_4) ).
thf(3994,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(206,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 )
& ( ( A @ k2_relat_1 )
= ( B @ k2_relat_1 ) ) )
=> ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_finseq_1) ).
thf(2985,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 )
& ( ( A @ k2_relat_1 )
= ( B @ k2_relat_1 ) ) )
=> ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(511,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ ( C @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
thf(4496,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ ( C @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
=> ( C @ ( A @ k4_xboole_0 ) @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_xboole_1) ).
thf(2227,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
=> ( C @ ( A @ k4_xboole_0 ) @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1042,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ( ( B @ ( np__1 @ k2_group_4 @ ( B @ k3_finseq_1 @ ( k4_numbers @ k1_finsop_1 ) ) @ ( A @ k4_group_4 ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_group_4) ).
thf(7136,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ( ( B @ ( np__1 @ k2_group_4 @ ( B @ k3_finseq_1 @ ( k4_numbers @ k1_finsop_1 ) ) @ ( A @ k4_group_4 ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(1249,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(8133,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(1064,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_partfun1) ).
thf(7235,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(231,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v14_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_0) ).
thf(3088,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v14_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(2108,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_group_4 @ k5_lattices )
= ( A @ k5_group_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_group_4) ).
thf(12303,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_group_4 @ k5_lattices )
= ( A @ k5_group_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2108]) ).
thf(1472,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(9379,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472]) ).
thf(567,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_xboole_1) ).
thf(4803,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(4124,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(268,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_orders_1 @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_orders_1) ).
thf(3281,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_orders_1 @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_realset1 ) ) )
<=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_realset1) ).
thf(3466,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ r1_realset1 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_realset1 ) ) )
=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(1192,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_domain_1 ) ) )
= ( B @ ( C @ ( A @ k7_domain_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k7_domain_1) ).
thf(7856,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_domain_1 ) ) )
= ( B @ ( C @ ( A @ k7_domain_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(246,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relat_1) ).
thf(3140,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) )
=> ( E @ ( C @ k3_xboole_0 ) @ ( D @ ( B @ k3_xboole_0 ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_zfmisc_1) ).
thf(4030,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) )
=> ( E @ ( C @ k3_xboole_0 ) @ ( D @ ( B @ k3_xboole_0 ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(10,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_lattice4) ).
thf(2172,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2173,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
| ~ ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ ( B @ ( C @ m1_lattice4 ) ) )
| ~ ( B @ l3_lattices )
| ~ ( B @ v3_filter_0 )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[2172]) ).
thf(1349,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
<=> ( A @ k1_zfmisc_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_finset_1) ).
thf(8678,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_finset_1 )
=> ( A @ v1_finset_1 ) )
& ( ( A @ v1_finset_1 )
=> ( A @ k1_zfmisc_1 @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349]) ).
thf(533,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m1_filter_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( B @ ( E @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_filter_1) ).
thf(4607,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( B @ ( E @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) )
=> ( B @ ( A @ ( C @ m1_filter_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_filter_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( B @ ( E @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(1289,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ( ( C @ ( D @ ( B @ k11_group_2 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ( C @ ( F @ r2_hidden ) )
& ( E @ ( D @ r1_rlvect_1 ) )
& ( A
= ( F @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_group_2) ).
thf(8330,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ( ( ? [E: $i] :
( ? [F: $i] :
( ( C @ ( F @ r2_hidden ) )
& ( E @ ( D @ r1_rlvect_1 ) )
& ( A
= ( F @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ ( B @ k11_group_2 ) ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( D @ ( B @ k11_group_2 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ? [F: $i] :
( ( C @ ( F @ r2_hidden ) )
& ( E @ ( D @ r1_rlvect_1 ) )
& ( A
= ( F @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(820,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( C @ r1_tarski ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_funct_2) ).
thf(6102,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( C @ r1_tarski ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(1323,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k3_funct_2 ) ) ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_2) ).
thf(8546,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k3_funct_2 ) ) ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_zfmisc_1) ).
thf(2516,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(449,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(4156,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(1897,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k8_group_3 ) )
= ( B @ ( A @ a_2_2_group_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_group_3) ).
thf(11481,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k8_group_3 ) )
= ( B @ ( A @ a_2_2_group_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1897]) ).
thf(394,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) )
= ( A @ k2_relat_1 @ k6_relat_1 ) )
& ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_1) ).
thf(3880,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) )
= ( A @ k2_relat_1 @ k6_relat_1 ) )
& ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(5,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r4_lattice4 ) ) )
& ( A @ v17_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_lattice4) ).
thf(2133,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r4_lattice4 ) ) )
& ( A @ v17_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2134,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ r4_lattice4 ) ) )
| ~ ( A @ ( B @ ( C @ v2_lattice4 ) ) )
| ~ ( A @ ( B @ ( C @ m1_lattice4 ) ) )
| ~ ( B @ l3_lattices )
| ~ ( B @ v17_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) )
& ( ( A @ v17_lattices )
| ~ ( A @ ( B @ ( C @ v2_lattice4 ) ) )
| ~ ( A @ ( B @ ( C @ m1_lattice4 ) ) )
| ~ ( B @ l3_lattices )
| ~ ( B @ v17_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ) ),
inference(cnf,[status(esa)],[2133]) ).
thf(2136,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ r4_lattice4 ) ) )
| ~ ( A @ ( B @ ( C @ v2_lattice4 ) ) )
| ~ ( A @ ( B @ ( C @ m1_lattice4 ) ) )
| ~ ( B @ l3_lattices )
| ~ ( B @ v17_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2134]) ).
thf(1402,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ k6_lattices @ ( B @ ( A @ r3_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattices) ).
thf(9013,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ k6_lattices @ ( B @ ( A @ r3_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402]) ).
thf(750,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C
= ( B @ ( A @ k8_filter_0 ) ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( B @ g3_lattices ) ) ) )
& ( E
= ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( D
= ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_filter_0) ).
thf(5750,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( B @ g3_lattices ) ) ) )
& ( E
= ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( D
= ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C
= ( B @ ( A @ k8_filter_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k8_filter_0 ) ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( B @ g3_lattices ) ) ) )
& ( E
= ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( D
= ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(1805,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k5_lattices @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattices) ).
thf(11151,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k5_lattices @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1805]) ).
thf(102,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
~ ( ( B = np__0 )
& ( A @ k4_finseq_1 @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finseq_3) ).
thf(2531,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
~ ( ( B = np__0 )
& ( A @ k4_finseq_1 @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(1141,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k12_group_2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_group_2) ).
thf(7592,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k12_group_2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(503,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_zfmisc_1) ).
thf(4467,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( C
= ( B @ ( A @ ( C @ k3_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_partfun1) ).
thf(2405,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( C
= ( B @ ( A @ ( C @ k3_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(25558,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ( sk1 != k1_xboole_0 )
| ~ ( A @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,20710]) ).
thf(25559,plain,
! [A: $i] :
( ( sk1 != k1_xboole_0 )
| ~ ( A @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25558:[]]) ).
thf(2020,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k3_group_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_group_1) ).
thf(11977,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k3_group_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2020]) ).
thf(21700,plain,
! [A: $i] :
( ( A != sk607 )
| ( k1_xboole_0 @ v7_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,11472]) ).
thf(21701,plain,
( ( k1_xboole_0 @ v7_group_1 )
| ( sk607 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21700:[bind(A,$thf( sk607 ))]]) ).
thf(1080,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_group_2 ) ) )
= ( C @ ( B @ ( A @ a_3_0_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_group_2) ).
thf(7311,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_group_2 ) ) )
= ( C @ ( B @ ( A @ a_3_0_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(1628,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ m2_finseq_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_finseq_1) ).
thf(10247,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ m2_finseq_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1628]) ).
thf(10248,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ m2_finseq_1 ) ),
inference(cnf,[status(esa)],[10247]) ).
thf(514,axiom,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(4507,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(4508,plain,
( ( sk145 @ v2_funct_1 )
& ( sk145 @ v1_funct_1 )
& ( sk145 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[4507]) ).
thf(4511,plain,
sk145 @ v2_funct_1,
inference(cnfConj,[status(thm)],[4508]) ).
thf(663,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ~ ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_subset_1) ).
thf(5352,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ~ ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ~ ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(1331,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ~ ( ! [C: $i] :
( ( C @ v1_finset_1 )
=> ~ ( ( ( C @ k4_card_1 )
= ( B @ ( A @ k11_group_3 ) @ ( A @ k17_group_2 ) ) )
& ( C
= ( B @ ( A @ k9_group_3 ) ) ) ) )
& ( ( B @ ( A @ k11_group_3 ) @ ( A @ k14_group_2 ) @ v1_finset_1 )
| ( B @ ( A @ k9_group_3 ) @ v1_finset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t162_group_3) ).
thf(8583,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ~ ( ! [C: $i] :
( ( C @ v1_finset_1 )
=> ~ ( ( ( C @ k4_card_1 )
= ( B @ ( A @ k11_group_3 ) @ ( A @ k17_group_2 ) ) )
& ( C
= ( B @ ( A @ k9_group_3 ) ) ) ) )
& ( ( B @ ( A @ k11_group_3 ) @ ( A @ k14_group_2 ) @ v1_finset_1 )
| ( B @ ( A @ k9_group_3 ) @ v1_finset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(2069,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k2_group_1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_group_1) ).
thf(12154,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k2_group_1 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2069]) ).
thf(1725,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(10719,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) )
=> ( B
= ( A @ k1_tarski ) ) )
& ( ( B
= ( A @ k1_tarski ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1725]) ).
thf(220,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ ( A @ k1_finseq_3 ) @ k4_finseq_1 )
= ( A @ k4_finseq_1 ) )
=> ( A @ k2_relat_1 @ ( B @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_finseq_3) ).
thf(3043,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ ( A @ k1_finseq_3 ) @ k4_finseq_1 )
= ( A @ k4_finseq_1 ) )
=> ( A @ k2_relat_1 @ ( B @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(1258,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( D @ ( A @ ( B @ k8_relset_1 ) ) ) )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_relset_1) ).
thf(8178,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( D @ ( A @ ( B @ k8_relset_1 ) ) ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(379,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r2_hidden ) )
=> ( D @ ( B @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_filter_0) ).
thf(3820,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r2_hidden ) )
=> ( D @ ( B @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(2654,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(1667,axiom,
? [A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).
thf(10453,plain,
? [A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1667]) ).
thf(10454,plain,
( ( sk545 @ v3_lattices )
& ~ ( sk545 @ v3_struct_0 )
& ( sk545 @ l3_lattices ) ),
inference(cnf,[status(esa)],[10453]) ).
thf(10457,plain,
sk545 @ v3_lattices,
inference(cnfConj,[status(thm)],[10454]) ).
thf(22492,plain,
! [A: $i] :
( ( A != sk545 )
| ( k1_xboole_0 @ v3_lattices )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,10457]) ).
thf(22493,plain,
( ( k1_xboole_0 @ v3_lattices )
| ( sk545 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22492:[bind(A,$thf( sk545 ))]]) ).
thf(1454,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k2_group_2 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_group_2) ).
thf(9300,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ? [F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ k2_group_2 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ k2_group_2 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ? [F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454]) ).
thf(1759,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k1_group_3 @ ( B @ r2_hidden ) )
<=> ? [C: $i] :
( ( B = C )
& ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_latsubgr) ).
thf(10903,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ? [C: $i] :
( ( B = C )
& ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( A @ k1_group_3 @ ( B @ r2_hidden ) ) )
& ( ( A @ k1_group_3 @ ( B @ r2_hidden ) )
=> ? [C: $i] :
( ( B = C )
& ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1759]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i,F: $i] :
( ( ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) )
=> ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) ) ) )
& ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_2) ).
thf(4439,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i,F: $i] :
( ( ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) )
=> ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) ) ) )
& ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(1640,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k14_group_2 ) @ v1_finset_1 )
=> ( B @ ( A @ k6_group_6 ) @ v6_group_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_group_6) ).
thf(10326,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k14_group_2 ) @ v1_finset_1 )
=> ( B @ ( A @ k6_group_6 ) @ v6_group_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1640]) ).
thf(2015,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= ( C @ ( B @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_group_3) ).
thf(11949,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= ( C @ ( B @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2015]) ).
thf(685,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
<=> ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_partfun1) ).
thf(5429,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(411,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
<=> ( ( B @ ( A @ k1_funct_4 ) )
= ( A @ ( B @ k1_funct_4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_4) ).
thf(3976,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k1_funct_4 ) )
= ( A @ ( B @ k1_funct_4 ) ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= ( A @ ( B @ k1_funct_4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(50,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v15_lattices )
<=> ( ( A @ v14_lattices )
& ( A @ v13_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_lattices) ).
thf(2326,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( ( A @ v14_lattices )
& ( A @ v13_lattices ) )
=> ( A @ v15_lattices ) )
& ( ( A @ v15_lattices )
=> ( ( A @ v14_lattices )
& ( A @ v13_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(2327,plain,
! [A: $i] :
( ( ( A @ v15_lattices )
| ~ ( A @ v14_lattices )
| ~ ( A @ v13_lattices )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) )
& ( ( A @ v14_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) )
& ( ( A @ v13_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ) ),
inference(cnf,[status(esa)],[2326]) ).
thf(2328,plain,
! [A: $i] :
( ( A @ v13_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2327]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_funcop_1 ) @ ( B @ ( A @ k2_funcop_1 ) @ r1_tarski ) )
=> ( ( B = D )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_funct_4) ).
thf(2916,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_funcop_1 ) @ ( B @ ( A @ k2_funcop_1 ) @ r1_tarski ) )
=> ( ( B = D )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(1763,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ( ? [D: $i] :
( ( C @ ( D @ v2_group_4 ) )
& ( C @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( B @ ( C @ k6_group_4 @ r1_rlvect_1 ) )
<=> ! [D: $i] :
( ( ( C @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( C @ ( D @ v2_group_4 ) )
=> ( B @ ( D @ r1_rlvect_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_group_4) ).
thf(10935,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ( ? [D: $i] :
( ( C @ ( D @ v2_group_4 ) )
& ( C @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( ! [D: $i] :
( ( ( C @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( C @ ( D @ v2_group_4 ) )
=> ( B @ ( D @ r1_rlvect_1 ) ) ) )
=> ( B @ ( C @ k6_group_4 @ r1_rlvect_1 ) ) )
& ( ( B @ ( C @ k6_group_4 @ r1_rlvect_1 ) )
=> ! [D: $i] :
( ( ( C @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( C @ ( D @ v2_group_4 ) )
=> ( B @ ( D @ r1_rlvect_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1763]) ).
thf(2080,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_group_4 @ u1_struct_0 )
= ( A @ k1_group_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_group_4) ).
thf(12197,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_group_4 @ u1_struct_0 )
= ( A @ k1_group_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2080]) ).
thf(11495,plain,
sk608 @ v1_group_1,
inference(cnfConj,[status(thm)],[11492]) ).
thf(21902,plain,
! [A: $i] :
( ( A != sk608 )
| ( k1_xboole_0 @ v1_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,11495]) ).
thf(21903,plain,
( ( k1_xboole_0 @ v1_group_1 )
| ( sk608 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21902:[bind(A,$thf( sk608 ))]]) ).
thf(553,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
<=> ( B @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_subset_1) ).
thf(4743,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ ( C @ m2_subset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
=> ( B @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(1203,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( D
= ( C @ ( B @ ( A @ k13_group_6 ) ) ) )
<=> ( ( D @ u1_struct_0 )
= ( A @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_group_6) ).
thf(7914,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( ( ( D @ u1_struct_0 )
= ( A @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k13_group_6 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k13_group_6 ) ) ) )
=> ( ( D @ u1_struct_0 )
= ( A @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(1944,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 )
& ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( B @ ( A @ r6_group_3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r6_group_3) ).
thf(11667,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 )
& ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( B @ ( A @ r6_group_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1944]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
<=> ( ( B @ k1_relat_1 @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
thf(3425,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( B @ k1_relat_1 @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( B @ k1_relat_1 @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(579,axiom,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_realset1) ).
thf(4866,plain,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(1420,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( D @ ( A @ k10_group_2 ) ) @ ( A @ k2_group_2 ) ) )
= ( C @ ( D @ ( A @ k11_group_2 ) ) @ ( B @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_group_2) ).
thf(9099,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( D @ ( A @ k10_group_2 ) ) @ ( A @ k2_group_2 ) ) )
= ( C @ ( D @ ( A @ k11_group_2 ) ) @ ( B @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1420]) ).
thf(153,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k3_relat_1 )
= ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
thf(2735,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k3_relat_1 )
= ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_partfun1) ).
thf(4422,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(2060,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k8_group_1 @ v1_card_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_group_1) ).
thf(12122,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k8_group_1 @ v1_card_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2060]) ).
thf(1397,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( B @ ( A @ k15_group_2 ) @ ( B @ ( A @ k14_group_2 ) @ r2_wellord2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t166_group_2) ).
thf(8996,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( B @ ( A @ k15_group_2 ) @ ( B @ ( A @ k14_group_2 ) @ r2_wellord2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397]) ).
thf(770,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(5883,plain,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(901,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_subset_1) ).
thf(6538,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ r3_binop_1 ) ) )
& ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_binop_1) ).
thf(3131,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ r3_binop_1 ) ) )
& ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(239,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
<=> ( ( B @ ( A @ ( C @ m3_vectsp_8 ) ) )
& ( B @ ( A @ ( C @ m4_vectsp_8 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_vectsp_8) ).
thf(3116,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( B @ ( A @ ( C @ m3_vectsp_8 ) ) )
& ( B @ ( A @ ( C @ m4_vectsp_8 ) ) ) )
=> ( B @ ( A @ ( C @ m1_lattice4 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( B @ ( A @ ( C @ m3_vectsp_8 ) ) )
& ( B @ ( A @ ( C @ m4_vectsp_8 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(21834,plain,
! [A: $i] :
( ( A != sk610 )
| ( k1_xboole_0 @ l1_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,11588]) ).
thf(21835,plain,
( ( k1_xboole_0 @ l1_group_1 )
| ( sk610 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21834:[bind(A,$thf( sk610 ))]]) ).
thf(1268,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v4_group_6 ) ) )
<=> ( ( B @ ( A @ ( C @ v2_group_6 ) ) )
& ( B @ ( A @ ( C @ v3_group_6 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_group_6) ).
thf(8225,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( B @ ( A @ ( C @ v2_group_6 ) ) )
& ( B @ ( A @ ( C @ v3_group_6 ) ) ) )
=> ( B @ ( A @ ( C @ v4_group_6 ) ) ) )
& ( ( B @ ( A @ ( C @ v4_group_6 ) ) )
=> ( ( B @ ( A @ ( C @ v2_group_6 ) ) )
& ( B @ ( A @ ( C @ v3_group_6 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(2102,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 )
& ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( B @ ( A @ r1_group_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_group_2) ).
thf(12286,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 )
& ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( B @ ( A @ r1_group_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2102]) ).
thf(7406,plain,
~ ? [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ r2_wellord2 ) ),
inference(miniscope,[status(thm)],[7405]) ).
thf(7407,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ ( A @ r2_wellord2 ) ),
inference(cnf,[status(esa)],[7406]) ).
thf(14717,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ~ ( k1_xboole_0 @ k1_tarski @ ( A @ r2_wellord2 ) ) ),
inference(paramod_ordered,[status(thm)],[6948,7407]) ).
thf(14718,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ r2_wellord2 ) ),
inference(pattern_uni,[status(thm)],[14717:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(221,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] : ( A @ k4_finseq_1 @ ( B @ ( A @ k1_finseq_3 ) @ k4_finseq_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_finseq_3) ).
thf(3046,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] : ( A @ k4_finseq_1 @ ( B @ ( A @ k1_finseq_3 ) @ k4_finseq_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(38917,plain,
( ( ( sk608 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,19110]) ).
thf(38918,plain,
( ( ( sk608 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[38917]) ).
thf(38931,plain,
( ( sk608 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[38918]) ).
thf(11496,plain,
sk608 @ l1_group_1,
inference(cnfConj,[status(thm)],[11492]) ).
thf(16431,plain,
! [A: $i] :
( ( ( sk608 @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11496,4961]) ).
thf(16432,plain,
! [A: $i] :
( ( ( sk608 @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[16431]) ).
thf(16433,plain,
sk608 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[16432:[bind(A,$thf( sk608 ))]]) ).
thf(21974,plain,
! [A: $i] :
( ( A != sk608 )
| ( k1_xboole_0 @ l1_struct_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,16433]) ).
thf(21975,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk608 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21974:[bind(A,$thf( sk608 ))]]) ).
thf(286,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k6_lattices @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_filter_0) ).
thf(3342,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k6_lattices @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(1750,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( C @ ( B @ ( C @ ( A @ k8_group_4 ) ) @ ( C @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_group_4) ).
thf(10865,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( C @ ( B @ ( C @ ( A @ k8_group_4 ) ) @ ( C @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1750]) ).
thf(1459,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ( ( C @ ( A @ k4_group_6 ) @ ( B @ ( C @ ( A @ k13_group_2 ) ) @ r2_hidden ) )
& ( C @ ( A @ k4_group_6 ) @ ( B @ ( C @ ( A @ k12_group_2 ) ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_group_6) ).
thf(9332,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ( ( C @ ( A @ k4_group_6 ) @ ( B @ ( C @ ( A @ k13_group_2 ) ) @ r2_hidden ) )
& ( C @ ( A @ k4_group_6 ) @ ( B @ ( C @ ( A @ k12_group_2 ) ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459]) ).
thf(1159,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ~ ( A @ ( C @ v2_group_4 ) ) )
=> ( B @ ( A @ k6_group_4 @ r1_rlvect_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_group_4) ).
thf(7683,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ~ ( A @ ( C @ v2_group_4 ) ) )
=> ( B @ ( A @ k6_group_4 @ r1_rlvect_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(1630,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ v1_group_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_group_3) ).
thf(10251,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ v1_group_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1630]) ).
thf(461,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(4222,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(4223,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(cnf,[status(esa)],[4222]) ).
thf(4224,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(lifteq,[status(thm)],[4223]) ).
thf(987,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g3_lattices ) ) )
= ( F @ ( E @ ( D @ g3_lattices ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(6878,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g3_lattices ) ) )
= ( F @ ( E @ ( D @ g3_lattices ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(98,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ ( B @ v1_filter_0 ) )
<=> ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( B = C )
| ( C
= ( A @ u1_struct_0 ) ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_filter_0) ).
thf(2501,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( B = C )
| ( C
= ( A @ u1_struct_0 ) ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) )
=> ( A @ ( B @ v1_filter_0 ) ) )
& ( ( A @ ( B @ v1_filter_0 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( B = C )
| ( C
= ( A @ u1_struct_0 ) ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(2013,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_subset_1 @ ( A @ k1_group_2 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_group_2) ).
thf(11944,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_subset_1 @ ( A @ k1_group_2 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2013]) ).
thf(654,axiom,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(5274,plain,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(857,axiom,
? [A: $i] : ( A @ l2_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(6257,plain,
? [A: $i] : ( A @ l2_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(6258,plain,
sk261 @ l2_lattices,
inference(cnf,[status(esa)],[6257]) ).
thf(543,axiom,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(4685,plain,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(4686,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
| ~ ( A @ l2_lattices ) ),
inference(cnf,[status(esa)],[4685]) ).
thf(16065,plain,
! [A: $i] :
( ( ( sk261 @ l2_lattices )
!= ( A @ l2_lattices ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6258,4686]) ).
thf(16066,plain,
! [A: $i] :
( ( ( sk261 @ l2_lattices )
!= ( A @ l2_lattices ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[16065]) ).
thf(16067,plain,
sk261 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[16066:[bind(A,$thf( sk261 ))]]) ).
thf(28,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(2243,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(2244,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(cnf,[status(esa)],[2243]) ).
thf(38730,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k4_xboole_0 ) )
!= ( B @ ( A @ k4_xboole_0 ) ) )
| ( A @ ( k1_xboole_0 @ k1_orders_1 @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[38576,2244]) ).
thf(38731,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_orders_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[38730:[bind(A,$thf( k1_xboole_0 @ k1_tarski )),bind(B,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(867,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
<=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(6340,plain,
! [A: $i,B: $i] :
( ( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(6341,plain,
( ! [A: $i,B: $i] :
( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(miniscope,[status(thm)],[6340]) ).
thf(6342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( D @ ( C @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( D != k1_xboole_0 ) )
& ( ( ( D @ ( C @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( C != k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[6341]) ).
thf(6345,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[6342]) ).
thf(6349,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[6345]) ).
thf(6350,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[6349]) ).
thf(1172,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i,D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( A @ ( B @ k13_group_6 ) ) @ r1_rlvect_1 ) )
<=> ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_group_6) ).
thf(7771,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i,D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ ( A @ ( B @ k13_group_6 ) ) @ r1_rlvect_1 ) ) )
& ( ( C @ ( D @ ( A @ ( B @ k13_group_6 ) ) @ r1_rlvect_1 ) )
=> ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(1371,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( B @ m1_filter_0 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
<=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_filter_0) ).
thf(8785,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) )
=> ( A @ ( B @ m1_filter_0 ) ) )
& ( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).
thf(1152,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_card_1) ).
thf(7652,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(560,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ~ ( A @ ( C @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
& ~ ( ~ ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) )
& ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_xboole_0) ).
thf(4778,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ~ ( A @ ( C @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
& ~ ( ~ ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) )
& ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(1888,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_group_3 ) ) )
<=> ? [D: $i] :
( ( B
= ( D @ ( C @ ( A @ k4_group_3 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_group_3) ).
thf(11448,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( B
= ( D @ ( C @ ( A @ k4_group_3 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ r3_group_3 ) ) ) )
& ( ( C @ ( B @ ( A @ r3_group_3 ) ) )
=> ? [D: $i] :
( ( B
= ( D @ ( C @ ( A @ k4_group_3 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1888]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= A )
& ( ( B @ k2_relat_1 )
= A ) )
=> ( ( C @ ( B @ ( A @ k4_funct_2 ) ) @ k2_relat_1 )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funct_2) ).
thf(3776,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= A )
& ( ( B @ k2_relat_1 )
= A ) )
=> ( ( C @ ( B @ ( A @ k4_funct_2 ) ) @ k2_relat_1 )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(1386,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t175_partfun1) ).
thf(8919,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_zfmisc_1) ).
thf(2682,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(1814,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( C @ ( B @ ( A @ k7_group_4 ) ) )
= ( B @ ( C @ ( A @ k7_group_4 ) ) ) )
=> ( ( C @ ( B @ ( A @ k8_group_4 ) ) @ u1_struct_0 )
= ( C @ ( B @ ( A @ k7_group_4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_group_4) ).
thf(11178,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( C @ ( B @ ( A @ k7_group_4 ) ) )
= ( B @ ( C @ ( A @ k7_group_4 ) ) ) )
=> ( ( C @ ( B @ ( A @ k8_group_4 ) ) @ u1_struct_0 )
= ( C @ ( B @ ( A @ k7_group_4 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1814]) ).
thf(242,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( ( A @ ( B @ k1_funct_4 ) )
= B )
& ( ( B @ ( A @ k1_funct_4 ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_funct_4) ).
thf(3125,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( ( A @ ( B @ k1_funct_4 ) )
= B )
& ( ( B @ ( A @ k1_funct_4 ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(1821,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k3_group_3 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_group_3) ).
thf(11200,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k3_group_3 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1821]) ).
thf(930,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v11_lattices )
=> ( B @ ( A @ k8_filter_0 ) @ v11_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_filter_0) ).
thf(6676,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v11_lattices )
=> ( B @ ( A @ k8_filter_0 ) @ v11_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(17611,plain,
! [A: $i] :
( ( ( sk612 @ l2_struct_0 )
!= ( A @ l2_struct_0 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11618,6063]) ).
thf(17612,plain,
! [A: $i] :
( ( ( sk612 @ l2_struct_0 )
!= ( A @ l2_struct_0 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[17611]) ).
thf(17613,plain,
sk612 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[17612:[bind(A,$thf( sk612 ))]]) ).
thf(328,axiom,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
thf(3542,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(1240,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v7_group_1 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k1_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_group_1) ).
thf(8069,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k1_group_1 ) ) ) ) ) )
=> ( A @ v7_group_1 ) )
& ( ( A @ v7_group_1 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_partfun1) ).
thf(2185,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(631,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
thf(5160,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(939,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_xboole_1) ).
thf(6713,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(1265,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_funct_2) ).
thf(8208,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_partfun1) ).
thf(2562,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(1700,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( B @ ( A @ k4_group_6 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_group_6) ).
thf(10606,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( B @ ( A @ k4_group_6 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1700]) ).
thf(732,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k2_relat_1 @ ( A @ r2_hidden ) )
& ( B @ v2_funct_1 ) )
=> ( ( A
= ( A @ ( B @ ( B @ k2_funct_1 @ k5_relat_1 ) @ k1_funct_1 ) ) )
& ( A
= ( A @ ( B @ k2_funct_1 @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
thf(5640,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k2_relat_1 @ ( A @ r2_hidden ) )
& ( B @ v2_funct_1 ) )
=> ( ( A
= ( A @ ( B @ ( B @ k2_funct_1 @ k5_relat_1 ) @ k1_funct_1 ) ) )
& ( A
= ( A @ ( B @ k2_funct_1 @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_partfun1) ).
thf(2488,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(1612,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C
= ( B @ ( A @ k10_group_3 ) ) )
<=> ( ( C @ u1_struct_0 )
= ( B @ ( A @ a_2_3_group_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_group_3) ).
thf(10174,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( ( ( C @ u1_struct_0 )
= ( B @ ( A @ a_2_3_group_3 ) ) )
=> ( C
= ( B @ ( A @ k10_group_3 ) ) ) )
& ( ( C
= ( B @ ( A @ k10_group_3 ) ) )
=> ( ( C @ u1_struct_0 )
= ( B @ ( A @ a_2_3_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1612]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(2897,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(925,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( A @ ( B @ k9_relat_1 ) @ ( A @ r2_wellord2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_card_1) ).
thf(6662,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( A @ ( B @ k9_relat_1 ) @ ( A @ r2_wellord2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_xboole_1) ).
thf(2213,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(2214,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] : ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(miniscope,[status(thm)],[2213]) ).
thf(2215,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ ( B @ ( A @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[2214]) ).
thf(17030,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( k5_numbers @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3108,2215]) ).
thf(17031,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( k5_numbers @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[17030]) ).
thf(17032,plain,
! [A: $i] : ( k1_numbers @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[17031:[bind(A,$thf( k5_numbers )),bind(B,$thf( k1_numbers ))]]) ).
thf(17062,plain,
! [A: $i] : ( k1_numbers @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[17032]) ).
thf(17326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17062,2188]) ).
thf(17327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) ) ),
inference(simp,[status(thm)],[17326]) ).
thf(17328,plain,
! [A: $i] : ( k1_numbers @ ( A @ k2_xboole_0 ) @ ( k5_numbers @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[17327:[bind(A,$thf( A )),bind(B,$thf( k5_numbers )),bind(C,$thf( A )),bind(D,$thf( k1_numbers ))]]) ).
thf(17576,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( A @ k2_xboole_0 ) @ ( k5_numbers @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17328,2215]) ).
thf(17577,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( A @ k2_xboole_0 ) @ ( k5_numbers @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[17576]) ).
thf(17578,plain,
! [B: $i,A: $i] : ( k1_numbers @ ( B @ k2_xboole_0 ) @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[17577:[bind(A,$thf( E )),bind(B,$thf( k5_numbers )),bind(C,$thf( k1_numbers @ ( E @ k2_xboole_0 ) )),bind(D,$thf( D ))]]) ).
thf(17581,plain,
! [B: $i,A: $i] : ( k1_numbers @ ( B @ k2_xboole_0 ) @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[17578]) ).
thf(39020,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_orders_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38731,2215]) ).
thf(39021,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_orders_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[39020]) ).
thf(39022,plain,
! [A: $i] : ( k1_xboole_0 @ k1_tarski @ ( A @ ( k1_xboole_0 @ k1_orders_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[39021:[bind(A,$thf( k1_xboole_0 @ k1_orders_1 )),bind(B,$thf( k1_xboole_0 @ k1_tarski )),bind(C,$thf( C ))]]) ).
thf(39044,plain,
! [A: $i] : ( k1_xboole_0 @ k1_tarski @ ( A @ ( k1_xboole_0 @ k1_orders_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[39022]) ).
thf(2072,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= B )
| ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= B ) )
=> ( C
= ( A @ k2_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_group_1) ).
thf(12161,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= B )
| ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= B ) )
=> ( C
= ( A @ k2_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2072]) ).
thf(864,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_lattice4) ).
thf(6332,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( A @ ( B @ ( C @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_enumset1) ).
thf(4568,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( A @ ( B @ ( C @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(602,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) ) )
=> ( ( D @ ( C @ r1_xboole_0 ) )
| ( C = D ) ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_zfmisc_1) ).
thf(4984,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) ) )
=> ( ( D @ ( C @ r1_xboole_0 ) )
| ( C = D ) ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(1878,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_group_2 @ ( A @ k16_group_2 ) )
= ( A @ k8_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t182_group_2) ).
thf(11416,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_group_2 @ ( A @ k16_group_2 ) )
= ( A @ k8_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1878]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_partfun1 ) ) ) )
=> ( ( B @ k3_relat_1 )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_orders_1) ).
thf(2466,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_partfun1 ) ) ) )
=> ( ( B @ k3_relat_1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1936,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ r1_group_6 ) )
& ( B @ ( A @ r1_group_6 ) ) )
=> ( C @ ( A @ r1_group_6 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_group_6) ).
thf(11628,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ r1_group_6 ) )
& ( B @ ( A @ r1_group_6 ) ) )
=> ( C @ ( A @ r1_group_6 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1936]) ).
thf(1672,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finset_1) ).
thf(10469,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1672]) ).
thf(1894,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_group_1 @ v2_binop_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_group_1) ).
thf(11473,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_group_1 @ v2_binop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1894]) ).
thf(355,axiom,
! [A: $i] : ( A @ k6_relat_1 @ v2_funct_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_1) ).
thf(3713,plain,
! [A: $i] : ( A @ k6_relat_1 @ v2_funct_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(58,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( E @ ( B @ r4_binop_1 ) ) )
& ( D @ ( C @ ( A @ r4_binop_1 ) ) ) )
<=> ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r4_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_filter_1) ).
thf(2354,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r4_binop_1 ) ) )
=> ( ( F @ ( E @ ( B @ r4_binop_1 ) ) )
& ( D @ ( C @ ( A @ r4_binop_1 ) ) ) ) )
& ( ( ( F @ ( E @ ( B @ r4_binop_1 ) ) )
& ( D @ ( C @ ( A @ r4_binop_1 ) ) ) )
=> ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r4_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(2355,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( B @ r4_binop_1 ) ) )
| ~ ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r4_binop_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) )
& ( ( D @ ( C @ ( A @ r4_binop_1 ) ) )
| ~ ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r4_binop_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) )
& ( ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r4_binop_1 ) ) )
| ~ ( F @ ( E @ ( B @ r4_binop_1 ) ) )
| ~ ( D @ ( C @ ( A @ r4_binop_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[2354]) ).
thf(2356,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r4_binop_1 ) ) )
| ~ ( F @ ( E @ ( B @ r4_binop_1 ) ) )
| ~ ( D @ ( C @ ( A @ r4_binop_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2355]) ).
thf(1156,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( B @ ( D @ ( A @ k6_group_3 ) ) @ ( B @ ( C @ ( A @ k6_group_3 ) ) @ ( A @ k9_group_2 ) ) @ ( B @ ( D @ ( C @ ( A @ k9_group_2 ) ) @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_group_3) ).
thf(7665,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( B @ ( D @ ( A @ k6_group_3 ) ) @ ( B @ ( C @ ( A @ k6_group_3 ) ) @ ( A @ k9_group_2 ) ) @ ( B @ ( D @ ( C @ ( A @ k9_group_2 ) ) @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(656,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
=> ( B @ ( A @ ( A @ k5_partfun1 ) ) @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_funct_2) ).
thf(5279,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
=> ( B @ ( A @ ( A @ k5_partfun1 ) ) @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(1710,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ u1_struct_0 @ k12_finseq_1 ) @ ( A @ u1_struct_0 @ k8_finseq_1 ) ) @ ( A @ k3_group_4 ) )
= ( B @ ( A @ k3_group_4 ) @ ( C @ ( A @ k1_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_group_4) ).
thf(10655,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ u1_struct_0 @ k12_finseq_1 ) @ ( A @ u1_struct_0 @ k8_finseq_1 ) ) @ ( A @ k3_group_4 ) )
= ( B @ ( A @ k3_group_4 ) @ ( C @ ( A @ k1_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1710]) ).
thf(826,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_zfmisc_1) ).
thf(6130,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(1965,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k9_group_2 ) ) )
= ( C @ ( B @ ( A @ k8_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_group_2) ).
thf(11760,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k9_group_2 ) ) )
= ( C @ ( B @ ( A @ k8_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1965]) ).
thf(1194,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_4_lattice3 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_4_lattice3) ).
thf(7862,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_4_lattice3 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_4_lattice3 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(323,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k5_lattices )
= ( k1_xboole_0 @ ( A @ k15_lattice3 ) ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattice3) ).
thf(3517,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k5_lattices )
= ( k1_xboole_0 @ ( A @ k15_lattice3 ) ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(1546,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v6_group_1 )
=> ( ( A @ k5_group_2 @ ( A @ k17_group_2 ) )
= ( A @ k9_group_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t183_group_2) ).
thf(9800,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v6_group_1 )
=> ( ( A @ k5_group_2 @ ( A @ k17_group_2 ) )
= ( A @ k9_group_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1546]) ).
thf(873,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_relset_1) ).
thf(6365,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(1348,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_filter_0) ).
thf(8674,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).
thf(1713,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(10665,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1713]) ).
thf(559,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
<=> ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_partfun1) ).
thf(4771,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(813,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(6071,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(1383,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 ) )
=> ( ( ( E @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( ( E @ ( D @ ( A @ k5_filter_0 ) ) @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( E @ ( D @ ( A @ k5_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_filter_0) ).
thf(8907,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 ) )
=> ( ( ( E @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( ( E @ ( D @ ( A @ k5_filter_0 ) ) @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( E @ ( D @ ( A @ k5_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383]) ).
thf(1484,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(9420,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1484]) ).
thf(1941,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ r1_group_6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_group_6) ).
thf(11641,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ r1_group_6 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1941]) ).
thf(1829,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 )
& ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r1_group_2 ) ) )
=> ( B @ ( C @ ( A @ r1_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_group_2) ).
thf(11232,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 )
& ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r1_group_2 ) ) )
=> ( B @ ( C @ ( A @ r1_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1829]) ).
thf(180,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_partfun1) ).
thf(2857,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(1892,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ( ( B @ ( A @ ( C @ m1_group_6 ) ) )
=> ( ( B @ ( A @ ( C @ m1_group_6 ) ) )
& ( B @ ( C @ v1_group_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_group_6) ).
thf(11463,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ( ( B @ ( A @ ( C @ m1_group_6 ) ) )
=> ( ( B @ ( A @ ( C @ m1_group_6 ) ) )
& ( B @ ( C @ v1_group_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1892]) ).
thf(644,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ ( B @ v1_filter_0 ) )
<=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_filter_0) ).
thf(5214,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) )
=> ( A @ ( B @ v1_filter_0 ) ) )
& ( ( A @ ( B @ v1_filter_0 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(1105,axiom,
? [A: $i] :
( ( A @ v1_group_1 )
& ( A @ l1_group_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_group_1) ).
thf(7433,plain,
? [A: $i] :
( ( A @ v1_group_1 )
& ( A @ l1_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(7434,plain,
( ( sk335 @ v1_group_1 )
& ( sk335 @ l1_group_1 ) ),
inference(cnf,[status(esa)],[7433]) ).
thf(7435,plain,
sk335 @ l1_group_1,
inference(cnfConj,[status(thm)],[7434]) ).
thf(16434,plain,
! [A: $i] :
( ( ( sk335 @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7435,4961]) ).
thf(16435,plain,
! [A: $i] :
( ( ( sk335 @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[16434]) ).
thf(16436,plain,
sk335 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[16435:[bind(A,$thf( sk335 ))]]) ).
thf(22160,plain,
! [A: $i] :
( ( A != sk335 )
| ( k1_xboole_0 @ l1_struct_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,16436]) ).
thf(22161,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk335 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22160:[bind(A,$thf( sk335 ))]]) ).
thf(1856,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ r2_group_6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_group_6) ).
thf(11331,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ r2_group_6 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1856]) ).
thf(9,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( ( A @ k3_finseq_1 )
= ( np__1 @ ( C @ k1_nat_1 ) ) )
=> ( ( ( D @ ( A @ ( B @ k2_finseq_3 ) @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) ) )
| ( D @ ( B @ r1_xreal_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_finseq_3) ).
thf(2169,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( ( A @ k3_finseq_1 )
= ( np__1 @ ( C @ k1_nat_1 ) ) )
=> ( ( ( D @ ( A @ ( B @ k2_finseq_3 ) @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) ) )
| ( D @ ( B @ r1_xreal_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1381,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( B @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funct_2) ).
thf(8902,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( B @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1381]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relat_1) ).
thf(2403,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1838,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_group_3 ) ) )
<=> ? [D: $i] :
( ( C
= ( D @ ( B @ ( A @ k2_group_3 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_group_3) ).
thf(11264,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( C
= ( D @ ( B @ ( A @ k2_group_3 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ r1_group_3 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_group_3 ) ) )
=> ? [D: $i] :
( ( C
= ( D @ ( B @ ( A @ k2_group_3 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1838]) ).
thf(1842,axiom,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( A @ l1_group_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_vectsp_1) ).
thf(11285,plain,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( A @ l1_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1842]) ).
thf(458,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ~ ( ( C @ v2_funct_1 )
<=> ! [D: $i,E: $i] :
( ( ( A @ ( D @ ( E @ m2_relset_1 ) ) )
& ( A @ ( D @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( A @ ( D @ ( F @ m2_relset_1 ) ) )
& ( A @ ( D @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( C @ ( E @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) )
= ( C @ ( F @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_2) ).
thf(4194,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ~ ( ( ! [D: $i,E: $i] :
( ( ( A @ ( D @ ( E @ m2_relset_1 ) ) )
& ( A @ ( D @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( A @ ( D @ ( F @ m2_relset_1 ) ) )
& ( A @ ( D @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( C @ ( E @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) )
= ( C @ ( F @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) )
=> ( C @ v2_funct_1 ) )
& ( ( C @ v2_funct_1 )
=> ! [D: $i,E: $i] :
( ( ( A @ ( D @ ( E @ m2_relset_1 ) ) )
& ( A @ ( D @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( A @ ( D @ ( F @ m2_relset_1 ) ) )
& ( A @ ( D @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( C @ ( E @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) )
= ( C @ ( F @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(623,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m1_lattice4 ) ) )
=> ( ( D @ ( C @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lattice4) ).
thf(5127,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m1_lattice4 ) ) )
=> ( ( D @ ( C @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(899,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( D @ k2_relat_1 @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).
thf(6502,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( D @ k2_relat_1 @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(1919,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_group_6 ) ) )
= ( C @ ( B @ ( A @ k8_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_group_6) ).
thf(11564,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_group_6 ) ) )
= ( C @ ( B @ ( A @ k8_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1919]) ).
thf(1912,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_group_3 ) ) )
<=> ? [D: $i] :
( ( C
= ( D @ ( B @ ( A @ k4_group_3 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_group_3) ).
thf(11538,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( C
= ( D @ ( B @ ( A @ k4_group_3 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ r3_group_3 ) ) ) )
& ( ( C @ ( B @ ( A @ r3_group_3 ) ) )
=> ? [D: $i] :
( ( C
= ( D @ ( B @ ( A @ k4_group_3 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1912]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( C @ ( D @ ( A @ ( B @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_enumset1) ).
thf(4179,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( C @ ( D @ ( A @ ( B @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(640,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( B @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) )
<=> ~ ( A @ ( B @ r1_xreal_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_card_1) ).
thf(5193,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( ~ ( A @ ( B @ r1_xreal_0 ) )
=> ( B @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ) )
& ( ( B @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) )
=> ~ ( A @ ( B @ r1_xreal_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(538,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k1_relat_1 @ v1_relat_1 )
& ( A @ k1_relat_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(4664,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k1_relat_1 @ v1_relat_1 )
& ( A @ k1_relat_1 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(676,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ~ ( ( C @ ( E @ ( D @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( B @ ( D @ ( A @ k2_filter_0 ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( C @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_lattice4) ).
thf(5397,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ~ ( ( C @ ( E @ ( D @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( B @ ( D @ ( A @ k2_filter_0 ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( C @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(1333,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ? [E: $i] :
( ( ( E @ u1_struct_0 )
= ( D @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k3_funct_2 ) ) ) ) )
& ( A @ ( E @ m1_group_2 ) )
& ( E @ v1_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_latsubgr) ).
thf(8600,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ? [E: $i] :
( ( ( E @ u1_struct_0 )
= ( D @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k3_funct_2 ) ) ) ) )
& ( A @ ( E @ m1_group_2 ) )
& ( E @ v1_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).
thf(475,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ( C @ k2_relat_1 )
= B )
<=> ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( B @ ( E @ m2_relset_1 ) ) )
& ( D @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( B @ ( F @ m2_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( E @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_2) ).
thf(4317,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( B @ ( E @ m2_relset_1 ) ) )
& ( D @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( B @ ( F @ m2_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( E @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) )
=> ( ( C @ k2_relat_1 )
= B ) )
& ( ( ( C @ k2_relat_1 )
= B )
=> ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( B @ ( E @ m2_relset_1 ) ) )
& ( D @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( B @ ( F @ m2_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( E @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(229,axiom,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k1_relat_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_finseq_1) ).
thf(3084,plain,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k1_relat_1 @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1297,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_group_6 ) ) )
<=> ( C @ v2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_group_6) ).
thf(8367,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ v2_funct_1 )
=> ( B @ ( A @ ( C @ v2_group_6 ) ) ) )
& ( ( B @ ( A @ ( C @ v2_group_6 ) ) )
=> ( C @ v2_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297]) ).
thf(43989,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( B @ v3_group_1 )
| ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,25039]) ).
thf(43990,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B @ v3_group_1 )
| ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[43989]) ).
thf(43991,plain,
! [A: $i] :
( ( A @ v3_group_1 )
| ~ ( A @ v1_xboole_0 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[43990:[bind(A,$thf( sk1 ))]]) ).
thf(43993,plain,
! [A: $i] :
( ( A @ v3_group_1 )
| ~ ( A @ v1_xboole_0 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[43991]) ).
thf(7436,plain,
sk335 @ v1_group_1,
inference(cnfConj,[status(thm)],[7434]) ).
thf(38894,plain,
( ( ( sk110 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,19101]) ).
thf(38895,plain,
( ( ( sk110 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[38894]) ).
thf(38908,plain,
( ( sk110 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[38895]) ).
thf(345,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_xboole_0 ) )
& ( C @ ( B @ r1_xboole_0 ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_subset_1) ).
thf(3657,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_xboole_0 ) )
& ( C @ ( B @ r1_xboole_0 ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(1799,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k10_group_3 ) @ m1_group_2 ) )
& ( B @ ( A @ k10_group_3 ) @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_group_3) ).
thf(11132,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k10_group_3 ) @ m1_group_2 ) )
& ( B @ ( A @ k10_group_3 ) @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1799]) ).
thf(1059,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( B
= ( A @ k5_group_2 ) )
<=> ( ( B @ u1_struct_0 )
= ( A @ k2_group_1 @ ( A @ u1_struct_0 @ k6_domain_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_group_2) ).
thf(7215,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( ( B @ u1_struct_0 )
= ( A @ k2_group_1 @ ( A @ u1_struct_0 @ k6_domain_1 ) ) )
=> ( B
= ( A @ k5_group_2 ) ) )
& ( ( B
= ( A @ k5_group_2 ) )
=> ( ( B @ u1_struct_0 )
= ( A @ k2_group_1 @ ( A @ u1_struct_0 @ k6_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(2024,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k5_group_2 @ v7_group_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_group_3) ).
thf(11991,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k5_group_2 @ v7_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2024]) ).
thf(597,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k9_filter_1 @ k3_relat_1 )
= ( A @ u1_struct_0 ) )
& ( ( A @ k9_filter_1 @ k2_relat_1 )
= ( A @ u1_struct_0 ) )
& ( ( A @ k9_filter_1 @ k1_relat_1 )
= ( A @ u1_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_filter_1) ).
thf(4952,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k9_filter_1 @ k3_relat_1 )
= ( A @ u1_struct_0 ) )
& ( ( A @ k9_filter_1 @ k2_relat_1 )
= ( A @ u1_struct_0 ) )
& ( ( A @ k9_filter_1 @ k1_relat_1 )
= ( A @ u1_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(487,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ ( B @ v1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
<=> ~ ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_filter_0) ).
thf(4383,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ ( B @ v1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ~ ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ~ ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(1211,axiom,
! [A: $i] :
( ( A @ ( A @ k6_finseq_1 @ m2_finseq_1 ) )
& ( A @ k6_finseq_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_finseq_1) ).
thf(7956,plain,
! [A: $i] :
( ( A @ ( A @ k6_finseq_1 @ m2_finseq_1 ) )
& ( A @ k6_finseq_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(7957,plain,
( ! [A: $i] : ( A @ ( A @ k6_finseq_1 @ m2_finseq_1 ) )
& ! [A: $i] : ( A @ k6_finseq_1 @ v1_xboole_0 ) ),
inference(miniscope,[status(thm)],[7956]) ).
thf(7958,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ k6_finseq_1 @ m2_finseq_1 ) )
& ( A @ k6_finseq_1 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[7957]) ).
thf(7959,plain,
! [A: $i] : ( A @ k6_finseq_1 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[7958]) ).
thf(1148,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(7633,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(7634,plain,
~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[7633]) ).
thf(7635,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[7634]) ).
thf(13670,plain,
! [B: $i,A: $i] :
( ( ( A @ k6_finseq_1 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7959,7635]) ).
thf(13671,plain,
! [B: $i,A: $i] :
( ( A @ k6_finseq_1 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13670]) ).
thf(13679,plain,
! [B: $i,A: $i] :
( ( A @ k6_finseq_1 )
!= ( B @ k1_zfmisc_1 ) ),
inference(simp,[status(thm)],[13671]) ).
thf(1626,axiom,
! [A: $i] :
( ( A @ k6_finseq_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_finseq_1) ).
thf(10241,plain,
! [A: $i] :
( ( A @ k6_finseq_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1626]) ).
thf(10242,plain,
! [A: $i] :
( ( A @ k6_finseq_1 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[10241]) ).
thf(10243,plain,
! [A: $i] :
( ( A @ k6_finseq_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[10242]) ).
thf(15534,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[13679,10243]) ).
thf(22571,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_zfmisc_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,15534]) ).
thf(22572,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_zfmisc_1 ) )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[22571]) ).
thf(22573,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ sk149 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[22572:[bind(A,$thf( C @ k1_zfmisc_1 )),bind(B,$thf( C ))]]) ).
thf(23064,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ sk149 @ v1_funct_1 ),
inference(simp,[status(thm)],[22573]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(4460,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1603,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k3_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(10117,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k3_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1603]) ).
thf(1956,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r2_group_3 ) ) )
& ( C @ ( B @ ( A @ r2_group_3 ) ) ) )
=> ( D @ ( B @ ( A @ r2_group_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_group_3) ).
thf(11716,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r2_group_3 ) ) )
& ( C @ ( B @ ( A @ r2_group_3 ) ) ) )
=> ( D @ ( B @ ( A @ r2_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1956]) ).
thf(1230,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_group_3 ) ) )
= ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( B @ ( A @ k3_group_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_group_3) ).
thf(8037,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_group_3 ) ) )
= ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( B @ ( A @ k3_group_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(564,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ r3_lattices ) ) )
<=> ( ( F @ ( E @ ( B @ r3_lattices ) ) )
& ( D @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_1) ).
thf(4793,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( ( F @ ( E @ ( B @ r3_lattices ) ) )
& ( D @ ( C @ ( A @ r3_lattices ) ) ) )
=> ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ r3_lattices ) ) ) )
& ( ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ r3_lattices ) ) )
=> ( ( F @ ( E @ ( B @ r3_lattices ) ) )
& ( D @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(492,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( A @ k3_filter_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_filter_0) ).
thf(4400,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( A @ k3_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(1213,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ u1_struct_0 @ k1_subset_1 @ ( B @ ( A @ k3_group_2 ) ) )
= k1_xboole_0 )
& ( ( A @ u1_struct_0 @ k1_subset_1 @ ( B @ ( A @ k4_group_2 ) ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_group_2) ).
thf(7965,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ u1_struct_0 @ k1_subset_1 @ ( B @ ( A @ k3_group_2 ) ) )
= k1_xboole_0 )
& ( ( A @ u1_struct_0 @ k1_subset_1 @ ( B @ ( A @ k4_group_2 ) ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(516,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k4_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_subset_1) ).
thf(4514,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k4_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(1518,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relset_1) ).
thf(9661,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1518]) ).
thf(1874,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( B @ v4_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_group_2) ).
thf(11404,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( B @ v4_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1874]) ).
thf(21790,plain,
! [A: $i] :
( ( A != sk636 )
| ( k1_xboole_0 @ l1_struct_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,16424]) ).
thf(21791,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk636 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21790:[bind(A,$thf( sk636 ))]]) ).
thf(1495,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_5_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ~ ( C @ ( E @ r2_hidden ) )
<=> ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_5_domain_1) ).
thf(9475,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
=> ~ ( C @ ( E @ r2_hidden ) ) )
& ( ~ ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_5_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_5_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
=> ~ ( C @ ( E @ r2_hidden ) ) )
& ( ~ ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1495]) ).
thf(1801,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r2_wellord2 ) )
& ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ r2_wellord2 ) )
& ( B @ ( A @ r2_wellord2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_card_1) ).
thf(11139,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r2_wellord2 ) )
& ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ r2_wellord2 ) )
& ( B @ ( A @ r2_wellord2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1801]) ).
thf(1120,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k1_zfmisc_1 )
= ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_zfmisc_1) ).
thf(7500,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k1_zfmisc_1 )
= ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(1961,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ k2_group_3 ) ) )
= ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k2_group_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_group_3) ).
thf(11740,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ k2_group_3 ) ) )
= ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k2_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1961]) ).
thf(1588,axiom,
? [A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_lattices) ).
thf(10025,plain,
? [A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1588]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( D @ v1_partfun1 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_partfun1) ).
thf(4595,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( D @ v1_partfun1 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(1637,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k6_group_6 ) @ k2_group_1 )
= ( B @ ( A @ k7_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_group_6) ).
thf(10309,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k6_group_6 ) @ k2_group_1 )
= ( B @ ( A @ k7_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1637]) ).
thf(312,axiom,
! [A: $i] :
( ( ( A @ k6_relat_1 @ k2_relat_1 )
= A )
& ( ( A @ k6_relat_1 @ k1_relat_1 )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_relat_1) ).
thf(3476,plain,
! [A: $i] :
( ( ( A @ k6_relat_1 @ k2_relat_1 )
= A )
& ( ( A @ k6_relat_1 @ k1_relat_1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(3477,plain,
( ! [A: $i] :
( ( A @ k6_relat_1 @ k2_relat_1 )
= A )
& ! [A: $i] :
( ( A @ k6_relat_1 @ k1_relat_1 )
= A ) ),
inference(miniscope,[status(thm)],[3476]) ).
thf(3478,plain,
! [B: $i,A: $i] :
( ( ( B @ k6_relat_1 @ k2_relat_1 )
= B )
& ( ( A @ k6_relat_1 @ k1_relat_1 )
= A ) ),
inference(cnf,[status(esa)],[3477]) ).
thf(3479,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ k1_relat_1 )
= A ),
inference(cnfConj,[status(thm)],[3478]) ).
thf(3481,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ k1_relat_1 )
= A ),
inference(lifteq,[status(thm)],[3479]) ).
thf(16255,plain,
! [A: $i] :
( ( A @ k6_partfun1 @ k1_relat_1 )
= A ),
inference(rewrite,[status(thm)],[3481,11231]) ).
thf(87,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ ( A @ k1_finseq_3 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) )
=> ( A @ k2_relat_1 @ ( B @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_finseq_3) ).
thf(2469,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ ( A @ k1_finseq_3 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) )
=> ( A @ k2_relat_1 @ ( B @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(887,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(6419,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(1007,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( D @ ( A @ k7_group_2 ) @ ( C @ ( A @ k11_group_2 ) ) @ ( A @ k2_group_2 ) ) )
= ( B @ ( D @ ( A @ k11_group_2 ) ) @ ( C @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_group_2) ).
thf(6964,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( D @ ( A @ k7_group_2 ) @ ( C @ ( A @ k11_group_2 ) ) @ ( A @ k2_group_2 ) ) )
= ( B @ ( D @ ( A @ k11_group_2 ) ) @ ( C @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(709,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v13_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_filter_0) ).
thf(5541,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v13_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(1752,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ r2_wellord2 ) )
<=> ? [C: $i] :
( A
= ( C @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_card_1) ).
thf(10868,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ k1_tarski ) )
=> ( B @ k1_tarski @ ( A @ r2_wellord2 ) ) )
& ( ( B @ k1_tarski @ ( A @ r2_wellord2 ) )
=> ? [C: $i] :
( A
= ( C @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1752]) ).
thf(10869,plain,
( ! [A: $i] :
( ? [B: $i] :
( A
= ( B @ k1_tarski ) )
=> ! [B: $i] : ( B @ k1_tarski @ ( A @ r2_wellord2 ) ) )
& ! [A: $i] :
( ? [B: $i] : ( B @ k1_tarski @ ( A @ r2_wellord2 ) )
=> ? [B: $i] :
( A
= ( B @ k1_tarski ) ) ) ),
inference(miniscope,[status(thm)],[10868]) ).
thf(10870,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ k1_tarski @ ( C @ r2_wellord2 ) )
| ( C
!= ( D @ k1_tarski ) ) )
& ( ( A
= ( A @ sk569 @ k1_tarski ) )
| ~ ( B @ k1_tarski @ ( A @ r2_wellord2 ) ) ) ),
inference(cnf,[status(esa)],[10869]) ).
thf(10872,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ k1_tarski @ ( A @ r2_wellord2 ) )
| ( A
!= ( B @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[10870]) ).
thf(10874,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ k1_tarski @ ( A @ r2_wellord2 ) )
| ( A
!= ( B @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[10872]) ).
thf(10875,plain,
! [B: $i,A: $i] : ( B @ k1_tarski @ ( A @ k1_tarski @ r2_wellord2 ) ),
inference(simp,[status(thm)],[10874]) ).
thf(31129,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ r2_wellord2 ) )
!= ( C @ k1_zfmisc_1 @ ( C @ r2_wellord2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10875,7407]) ).
thf(31130,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r2_wellord2 ) )
!= ( C @ k1_zfmisc_1 @ ( C @ r2_wellord2 ) ) ),
inference(simp,[status(thm)],[31129]) ).
thf(31140,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ k1_tarski )
!= ( C @ k1_zfmisc_1 ) )
| ( ( A @ k1_tarski )
!= C ) ),
inference(simp,[status(thm)],[31130]) ).
thf(31143,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski )
!= ( A @ k1_tarski @ k1_zfmisc_1 ) ),
inference(simp,[status(thm)],[31140]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( E @ ( B @ r5_binop_1 ) ) )
& ( D @ ( C @ ( A @ r5_binop_1 ) ) ) )
<=> ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r5_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_filter_1) ).
thf(2174,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r5_binop_1 ) ) )
=> ( ( F @ ( E @ ( B @ r5_binop_1 ) ) )
& ( D @ ( C @ ( A @ r5_binop_1 ) ) ) ) )
& ( ( ( F @ ( E @ ( B @ r5_binop_1 ) ) )
& ( D @ ( C @ ( A @ r5_binop_1 ) ) ) )
=> ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r5_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2175,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( B @ r5_binop_1 ) ) )
| ~ ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r5_binop_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) )
& ( ( D @ ( C @ ( A @ r5_binop_1 ) ) )
| ~ ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r5_binop_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) )
& ( ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r5_binop_1 ) ) )
| ~ ( F @ ( E @ ( B @ r5_binop_1 ) ) )
| ~ ( D @ ( C @ ( A @ r5_binop_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[2174]) ).
thf(2178,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( B @ r5_binop_1 ) ) )
| ~ ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r5_binop_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2175]) ).
thf(1809,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ ( A @ k8_group_4 ) ) @ u1_struct_0 )
= ( C @ ( B @ ( A @ k7_group_4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_group_4) ).
thf(11163,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ ( A @ k8_group_4 ) ) @ u1_struct_0 )
= ( C @ ( B @ ( A @ k7_group_4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1809]) ).
thf(39517,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( A @ ( k1_xboole_0 @ k1_orders_1 @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39044,2188]) ).
thf(39518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( A @ ( k1_xboole_0 @ k1_orders_1 @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) ) ),
inference(simp,[status(thm)],[39517]) ).
thf(39519,plain,
! [A: $i] : ( k1_xboole_0 @ k1_tarski @ ( A @ k2_xboole_0 ) @ ( k1_xboole_0 @ k1_orders_1 @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[39518:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 @ k1_orders_1 )),bind(C,$thf( A )),bind(D,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(495,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ~ ( ( A @ ( C @ v1_filter_0 ) )
& ( C @ ( B @ r2_hidden ) ) ) )
& ( B
!= ( A @ k5_lattices ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_filter_0) ).
thf(4411,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ~ ( ( A @ ( C @ v1_filter_0 ) )
& ( C @ ( B @ r2_hidden ) ) ) )
& ( B
!= ( A @ k5_lattices ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(1760,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_filter_0 ) )
& ( B @ ( C @ m1_filter_0 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_1_filter_0 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( E @ ( G @ ( F @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( G @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_filter_0) ).
thf(10913,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_filter_0 ) )
& ( B @ ( C @ m1_filter_0 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( E @ ( G @ ( F @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( G @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_1_filter_0 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_1_filter_0 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( E @ ( G @ ( F @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( G @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1760]) ).
thf(1681,axiom,
( ( k1_xboole_0 @ k1_setfam_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_setfam_1) ).
thf(10519,plain,
( ( k1_xboole_0 @ k1_setfam_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1681]) ).
thf(858,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v5_lattice3 )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ ( B @ k15_lattice3 ) @ ( B @ k4_lattices ) ) )
= ( C @ ( B @ ( A @ a_3_8_lattice3 ) ) @ ( B @ k15_lattice3 ) ) )
& ( ( A @ ( B @ k15_lattice3 ) @ ( C @ ( B @ k4_lattices ) ) )
= ( C @ ( B @ ( A @ a_3_7_lattice3 ) ) @ ( B @ k15_lattice3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_lattice3) ).
thf(6259,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v5_lattice3 )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ ( B @ k15_lattice3 ) @ ( B @ k4_lattices ) ) )
= ( C @ ( B @ ( A @ a_3_8_lattice3 ) ) @ ( B @ k15_lattice3 ) ) )
& ( ( A @ ( B @ k15_lattice3 ) @ ( C @ ( B @ k4_lattices ) ) )
= ( C @ ( B @ ( A @ a_3_7_lattice3 ) ) @ ( B @ k15_lattice3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(1436,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( ( B @ ( D @ ( A @ k13_group_2 ) ) )
= ( C @ ( D @ ( A @ k13_group_2 ) ) ) )
<=> ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k1_group_1 ) ) @ ( D @ r1_rlvect_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_group_2) ).
thf(9204,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k1_group_1 ) ) @ ( D @ r1_rlvect_1 ) )
=> ( ( B @ ( D @ ( A @ k13_group_2 ) ) )
= ( C @ ( D @ ( A @ k13_group_2 ) ) ) ) )
& ( ( ( B @ ( D @ ( A @ k13_group_2 ) ) )
= ( C @ ( D @ ( A @ k13_group_2 ) ) ) )
=> ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k1_group_1 ) ) @ ( D @ r1_rlvect_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436]) ).
thf(22480,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,2119]) ).
thf(22481,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ( sk1 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22480:[bind(A,$thf( sk1 ))]]) ).
thf(1557,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_mcart_1) ).
thf(9854,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1557]) ).
thf(10720,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) )
=> ( B
= ( A @ k1_tarski ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ k1_tarski ) )
=> ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) ) ) ),
inference(miniscope,[status(thm)],[10719]) ).
thf(10721,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ k1_tarski ) )
| ~ ( F @ ( E @ ( F @ sk562 ) @ r2_hidden ) )
| ( ( E @ ( F @ sk561 ) )
!= E ) )
& ( ( F
= ( E @ k1_tarski ) )
| ( ( E @ ( F @ sk562 ) )
= E )
| ( ( E @ ( F @ sk561 ) )
!= E ) )
& ( ( F
= ( E @ k1_tarski ) )
| ~ ( F @ ( E @ ( F @ sk562 ) @ r2_hidden ) )
| ( F @ ( E @ ( F @ sk561 ) @ r2_hidden ) ) )
& ( ( F
= ( E @ k1_tarski ) )
| ( ( E @ ( F @ sk562 ) )
= E )
| ( F @ ( E @ ( F @ sk561 ) @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
| ( D != A )
| ( B
!= ( A @ k1_tarski ) ) )
& ( ( C = A )
| ~ ( B @ ( C @ r2_hidden ) )
| ( B
!= ( A @ k1_tarski ) ) ) ),
inference(cnf,[status(esa)],[10720]) ).
thf(10726,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ r2_hidden ) )
| ( C != A )
| ( B
!= ( A @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[10721]) ).
thf(10728,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ r2_hidden ) )
| ( C != A )
| ( B
!= ( A @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[10726]) ).
thf(10729,plain,
! [A: $i] : ( A @ k1_tarski @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[10728]) ).
thf(797,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ~ ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_xboole_0 ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t185_partfun1) ).
thf(6002,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ~ ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_xboole_0 ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(1984,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k2_group_1 @ ( A @ k3_group_1 ) )
= ( A @ k2_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_group_1) ).
thf(11821,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k2_group_1 @ ( A @ k3_group_1 ) )
= ( A @ k2_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1984]) ).
thf(1262,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ r1_tarski ) )
<=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(8190,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) )
=> ( B @ k1_tarski @ ( A @ r1_tarski ) ) )
& ( ( B @ k1_tarski @ ( A @ r1_tarski ) )
=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(32918,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_card_1 )
!= ( A @ k1_card_1 ) )
| ( A @ k1_zfmisc_1 @ k1_card_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[8607,9299]) ).
thf(32919,plain,
k1_xboole_0 @ k1_zfmisc_1 @ k1_card_1 @ ( k1_xboole_0 @ r2_hidden ),
inference(pattern_uni,[status(thm)],[32918:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(32958,plain,
k1_xboole_0 @ k1_tarski @ k1_card_1 @ ( k1_xboole_0 @ r2_hidden ),
inference(rewrite,[status(thm)],[32919,6948]) ).
thf(32972,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ k1_card_1 @ ( k1_xboole_0 @ r2_hidden ) )
!= ( k1_xboole_0 @ ( A @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32958,9703]) ).
thf(32973,plain,
! [A: $i] :
( ( k1_xboole_0 @ k1_tarski @ k1_card_1 @ ( k1_xboole_0 @ r2_hidden ) )
!= ( k1_xboole_0 @ ( A @ r2_hidden ) ) ),
inference(simp,[status(thm)],[32972]) ).
thf(33001,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ k1_card_1 )
!= k1_xboole_0 )
| ( k1_xboole_0 != A ) ),
inference(simp,[status(thm)],[32973]) ).
thf(33008,plain,
( ( k1_xboole_0 @ k1_tarski @ k1_card_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[33001]) ).
thf(1657,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) ) )
=> ( ( C @ ( A @ k3_filter_0 ) )
= ( B @ ( A @ k2_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_filter_0) ).
thf(10419,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) ) )
=> ( ( C @ ( A @ k3_filter_0 ) )
= ( B @ ( A @ k2_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1657]) ).
thf(1176,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( k1_xboole_0 @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relset_1) ).
thf(7786,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( k1_xboole_0 @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(1885,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_group_4 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_group_4) ).
thf(11441,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_group_4 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1885]) ).
thf(2035,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( A @ k8_group_1 @ ( B @ k8_group_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_group_2) ).
thf(12018,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( A @ k8_group_1 @ ( B @ k8_group_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2035]) ).
thf(734,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ k1_relat_1 @ ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
thf(5663,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ k1_relat_1 @ ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(1449,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( C @ v1_int_1 )
=> ! [D: $i] :
( ( ( D @ l1_group_1 )
& ( D @ v4_group_1 )
& ( D @ v3_group_1 )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( D @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( D @ u1_struct_0 @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( E @ ( D @ k8_rlvect_1 ) ) ) @ ( C @ k2_group_4 @ ( B @ k2_group_4 @ ( A @ k2_group_4 @ ( k4_numbers @ k3_finseq_4 ) ) ) @ ( D @ k4_group_4 ) ) )
= ( G @ ( C @ ( D @ k6_group_1 ) ) @ ( F @ ( B @ ( D @ k6_group_1 ) ) @ ( E @ ( A @ ( D @ k6_group_1 ) ) @ ( D @ k8_rlvect_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_group_4) ).
thf(9283,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( C @ v1_int_1 )
=> ! [D: $i] :
( ( ( D @ l1_group_1 )
& ( D @ v4_group_1 )
& ( D @ v3_group_1 )
& ~ ( D @ v3_struct_0 ) )
=> ! [E: $i] :
( ( D @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( D @ u1_struct_0 @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( E @ ( D @ k8_rlvect_1 ) ) ) @ ( C @ k2_group_4 @ ( B @ k2_group_4 @ ( A @ k2_group_4 @ ( k4_numbers @ k3_finseq_4 ) ) ) @ ( D @ k4_group_4 ) ) )
= ( G @ ( C @ ( D @ k6_group_1 ) ) @ ( F @ ( B @ ( D @ k6_group_1 ) ) @ ( E @ ( A @ ( D @ k6_group_1 ) ) @ ( D @ k8_rlvect_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1449]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_realset1) ).
thf(2324,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1228,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B
= ( B @ ( A @ a_2_1_domain_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_domain_1) ).
thf(8029,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B
= ( B @ ( A @ a_2_1_domain_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(1460,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_0_group_4 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( E @ ( B @ k7_group_2 ) @ ( C @ r1_tarski ) )
& ( D
= ( E @ u1_struct_0 ) )
& ( B @ ( E @ m1_group_2 ) )
& ( E @ v1_group_1 ) )
& ( A = D )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_group_4) ).
thf(9336,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( E @ ( B @ k7_group_2 ) @ ( C @ r1_tarski ) )
& ( D
= ( E @ u1_struct_0 ) )
& ( B @ ( E @ m1_group_2 ) )
& ( E @ v1_group_1 ) )
& ( A = D )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_group_4 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_group_4 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( E @ ( B @ k7_group_2 ) @ ( C @ r1_tarski ) )
& ( D
= ( E @ u1_struct_0 ) )
& ( B @ ( E @ m1_group_2 ) )
& ( E @ v1_group_1 ) )
& ( A = D )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460]) ).
thf(772,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( B @ ( C @ ( D @ ( A @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_enumset1) ).
thf(5888,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( B @ ( C @ ( D @ ( A @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(617,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( C @ v2_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_partfun1) ).
thf(5084,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( C @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(721,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( k1_xboole_0 @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_partfun1) ).
thf(5597,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( k1_xboole_0 @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(1076,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k2_funct_2 ) ) ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_2) ).
thf(7290,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k2_funct_2 ) ) ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(21715,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk524 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,16248]) ).
thf(21716,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk524 ) )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[21715]) ).
thf(21717,plain,
! [A: $i] : ( A @ sk524 @ sk149 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[21716:[bind(A,$thf( C @ sk524 )),bind(B,$thf( C ))]]) ).
thf(23115,plain,
! [A: $i] : ( A @ sk524 @ sk149 @ v1_funct_1 ),
inference(simp,[status(thm)],[21717]) ).
thf(919,axiom,
! [A: $i] :
( ( A @ k6_relat_1 @ k2_funct_1 )
= ( A @ k6_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_funct_1) ).
thf(6615,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ k2_funct_1 )
= ( A @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(6616,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ k2_funct_1 )
= ( A @ k6_relat_1 ) ),
inference(cnf,[status(esa)],[6615]) ).
thf(6617,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ k2_funct_1 )
= ( A @ k6_relat_1 ) ),
inference(lifteq,[status(thm)],[6616]) ).
thf(30232,plain,
! [A: $i] :
( ( A @ k6_partfun1 @ k2_funct_1 )
= ( A @ k6_partfun1 ) ),
inference(rewrite,[status(thm)],[6617,11231]) ).
thf(30237,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k6_partfun1 )
!= ( A @ k6_partfun1 ) )
| ( ( k1_xboole_0 @ k2_funct_1 )
= ( A @ k6_partfun1 ) ) ),
inference(paramod_ordered,[status(thm)],[16259,30232]) ).
thf(30238,plain,
( ( k1_xboole_0 @ k2_funct_1 )
= ( k1_xboole_0 @ k6_partfun1 ) ),
inference(pattern_uni,[status(thm)],[30237:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(30253,plain,
( ( k1_xboole_0 @ k2_funct_1 )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[30238,16259]) ).
thf(210,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_finseq_3 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_finseq_3) ).
thf(2996,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_finseq_3 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(22126,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ v3_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,2115]) ).
thf(22127,plain,
( ( k1_xboole_0 @ v3_group_1 )
| ( sk1 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22126:[bind(A,$thf( sk1 ))]]) ).
thf(1304,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( C @ v2_group_6 ) ) )
=> ( ( B @ u1_struct_0 @ ( C @ ( A @ ( B @ k13_group_6 ) ) @ u1_struct_0 @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( B @ ( C @ ( A @ ( B @ k13_group_6 ) ) @ ( C @ k2_funct_1 @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( C @ ( A @ ( B @ k13_group_6 ) ) @ u1_struct_0 @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_group_6) ).
thf(8416,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( C @ v2_group_6 ) ) )
=> ( ( B @ u1_struct_0 @ ( C @ ( A @ ( B @ k13_group_6 ) ) @ u1_struct_0 @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( B @ ( C @ ( A @ ( B @ k13_group_6 ) ) @ ( C @ k2_funct_1 @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( C @ ( A @ ( B @ k13_group_6 ) ) @ u1_struct_0 @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).
thf(1844,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_realset2 )
=> ( ( A @ k5_group_2 )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_group_6) ).
thf(11293,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_realset2 )
=> ( ( A @ k5_group_2 )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1844]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_xboole_1) ).
thf(2782,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(572,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( E @ ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( E @ ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ ( C @ k6_group_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_group_6) ).
thf(4820,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( E @ ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( E @ ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ ( C @ k6_group_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(254,axiom,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( ( ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v8_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_vectsp_1) ).
thf(3163,plain,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( ( ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v8_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(80,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k2_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relat_1) ).
thf(2451,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k2_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1506,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ~ ( ! [D: $i] :
( ( D @ v1_finset_1 )
=> ! [E: $i] :
( ( E @ v1_finset_1 )
=> ~ ( ( ( C @ k9_group_1 )
= ( E @ k4_card_1 ) )
& ( ( C @ k9_group_1 )
= ( D @ k4_card_1 ) )
& ( E
= ( B @ ( C @ ( A @ k13_group_2 ) ) ) )
& ( D
= ( B @ ( C @ ( A @ k12_group_2 ) ) ) ) ) ) )
& ( C @ v6_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_group_2) ).
thf(9548,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ~ ( ! [D: $i] :
( ( D @ v1_finset_1 )
=> ! [E: $i] :
( ( E @ v1_finset_1 )
=> ~ ( ( ( C @ k9_group_1 )
= ( E @ k4_card_1 ) )
& ( ( C @ k9_group_1 )
= ( D @ k4_card_1 ) )
& ( E
= ( B @ ( C @ ( A @ k13_group_2 ) ) ) )
& ( D
= ( B @ ( C @ ( A @ k12_group_2 ) ) ) ) ) ) )
& ( C @ v6_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1506]) ).
thf(1217,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(7986,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(207,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(2988,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(2989,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2988]) ).
thf(2990,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2989]) ).
thf(2236,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= A ) ),
inference(cnfConj,[status(thm)],[2234]) ).
thf(2238,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= A ) ),
inference(lifteq,[status(thm)],[2236]) ).
thf(2239,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= A ) ),
inference(simp,[status(thm)],[2238]) ).
thf(24246,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( C @ ( B @ r1_xboole_0 ) )
| ( k1_xboole_0 != B ) ),
inference(paramod_ordered,[status(thm)],[2990,2239]) ).
thf(24247,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r1_xboole_0 ) )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[24246:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(24259,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[24247]) ).
thf(25179,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_xboole_0 ) )
!= ( C @ ( B @ r1_xboole_0 ) ) )
| ~ $true
| ( ( C @ ( C @ ( B @ k2_xboole_0 ) @ k4_xboole_0 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[24259,2184]) ).
thf(25180,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_xboole_0 ) )
!= ( C @ ( B @ r1_xboole_0 ) ) )
| ( ( C @ ( C @ ( B @ k2_xboole_0 ) @ k4_xboole_0 ) )
= B ) ),
inference(simp,[status(thm)],[25179]) ).
thf(25181,plain,
! [A: $i] :
( ( A @ ( A @ ( k1_xboole_0 @ k2_xboole_0 ) @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[25180:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(2364,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(2365,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[2364]) ).
thf(2366,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[2365]) ).
thf(2367,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[2366]) ).
thf(2368,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk12 ) )
= A ),
inference(cnf,[status(esa)],[2367]) ).
thf(59829,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk12 ) )
= A ),
inference(lifteq,[status(thm)],[2368]) ).
thf(59846,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( k1_xboole_0 @ k2_xboole_0 ) @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk12 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[25181,59829]) ).
thf(59847,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk12 ) )
= ( A @ ( k1_xboole_0 @ k2_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[59846:[bind(A,$thf( E )),bind(B,$thf( E @ ( k1_xboole_0 @ k2_xboole_0 ) )),bind(C,$thf( E ))]]) ).
thf(59863,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk12 ) )
= ( A @ ( k1_xboole_0 @ k2_xboole_0 ) ) ),
inference(simp,[status(thm)],[59847]) ).
thf(59842,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk12 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[2990,59829]) ).
thf(59843,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk12 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[59842:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(60659,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_xboole_0 ) )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[59863,59843]) ).
thf(10992,plain,
! [A: $i] :
( ( ( sk581 @ ( A @ r2_hidden ) )
| ~ ( A @ p1_s2_group_4 )
| ~ ( f1_s2_group_4 @ ( A @ m1_group_2 ) )
| ~ ( A @ v1_group_1 ) )
& ( ( A @ p1_s2_group_4 )
| ~ ( sk581 @ ( A @ r2_hidden ) )
| ~ ( f1_s2_group_4 @ ( A @ m1_group_2 ) )
| ~ ( A @ v1_group_1 ) )
& ( f1_s2_group_4 @ k1_group_3 @ ( sk581 @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[10991]) ).
thf(10993,plain,
f1_s2_group_4 @ k1_group_3 @ ( sk581 @ r1_tarski ),
inference(cnfConj,[status(thm)],[10992]) ).
thf(17040,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s2_group_4 @ k1_group_3 @ ( sk581 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10993,2215]) ).
thf(17041,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s2_group_4 @ k1_group_3 @ ( sk581 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[17040]) ).
thf(17042,plain,
! [A: $i] : ( f1_s2_group_4 @ k1_group_3 @ ( A @ ( sk581 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[17041:[bind(A,$thf( sk581 )),bind(B,$thf( f1_s2_group_4 @ k1_group_3 )),bind(C,$thf( C ))]]) ).
thf(17061,plain,
! [A: $i] : ( f1_s2_group_4 @ k1_group_3 @ ( A @ ( sk581 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[17042]) ).
thf(17597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( f1_s2_group_4 @ k1_group_3 @ ( A @ ( sk581 @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17061,2188]) ).
thf(17598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( f1_s2_group_4 @ k1_group_3 @ ( A @ ( sk581 @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) ) ),
inference(simp,[status(thm)],[17597]) ).
thf(17599,plain,
! [A: $i] : ( f1_s2_group_4 @ k1_group_3 @ ( A @ k2_xboole_0 ) @ ( sk581 @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[17598:[bind(A,$thf( A )),bind(B,$thf( sk581 )),bind(C,$thf( A )),bind(D,$thf( f1_s2_group_4 @ k1_group_3 ))]]) ).
thf(60717,plain,
! [B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k2_xboole_0 ) )
!= ( f1_s2_group_4 @ k1_group_3 @ ( B @ k2_xboole_0 ) ) )
| ( k1_xboole_0 @ ( sk581 @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[60659,17599]) ).
thf(60718,plain,
k1_xboole_0 @ ( sk581 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[60717:[bind(A,$thf( f1_s2_group_4 @ k1_group_3 )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(311,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ? [B: $i] :
( ( ( B @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_funct_1) ).
thf(3473,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ? [B: $i] :
( ( ( B @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(842,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k5_relat_1 ) )
= A )
& ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ k5_relat_1 ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_funct_1) ).
thf(6189,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k5_relat_1 ) )
= A )
& ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ k5_relat_1 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(828,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
thf(6135,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(740,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_funct_1 @ v1_funct_1 )
& ( A @ k2_funct_1 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(5680,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_funct_1 @ v1_funct_1 )
& ( A @ k2_funct_1 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(1553,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k6_group_6 ) @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C
= ( B @ ( A @ k11_group_6 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( B @ ( A @ k12_group_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_group_6) ).
thf(9837,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k6_group_6 ) @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( B @ ( A @ k12_group_2 ) ) ) ) )
=> ( C
= ( B @ ( A @ k11_group_6 ) ) ) )
& ( ( C
= ( B @ ( A @ k11_group_6 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( B @ ( A @ k12_group_2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1553]) ).
thf(782,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_eqrel_1) ).
thf(5946,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( A @ ( E @ k1_relat_1 @ ( D @ k2_relat_1 @ k3_xboole_0 ) @ r1_tarski ) )
=> ( ( B @ ( A @ ( E @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( A @ ( C @ k1_partfun1 ) ) ) ) ) )
= ( B @ ( C @ ( E @ ( D @ k5_relat_1 ) @ k3_partfun1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_partfun1) ).
thf(3438,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( A @ ( E @ k1_relat_1 @ ( D @ k2_relat_1 @ k3_xboole_0 ) @ r1_tarski ) )
=> ( ( B @ ( A @ ( E @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( A @ ( C @ k1_partfun1 ) ) ) ) ) )
= ( B @ ( C @ ( E @ ( D @ k5_relat_1 ) @ k3_partfun1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( ( C @ ( E @ ( D @ k5_relat_1 ) @ k1_funct_1 ) )
= ( C @ ( D @ k1_funct_1 ) @ ( E @ k1_funct_1 ) ) )
| ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_2) ).
thf(4147,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( ( C @ ( E @ ( D @ k5_relat_1 ) @ k1_funct_1 ) )
= ( C @ ( D @ k1_funct_1 ) @ ( E @ k1_funct_1 ) ) )
| ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_funct_2) ).
thf(3525,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(2056,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_group_1 @ ( A @ k2_group_3 ) ) )
= ( A @ k2_group_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_group_3) ).
thf(12105,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_group_1 @ ( A @ k2_group_3 ) ) )
= ( A @ k2_group_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2056]) ).
thf(1728,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( D @ ( C @ ( A @ k9_group_2 ) ) @ ( A @ k12_group_2 ) ) )
= ( B @ ( D @ ( A @ k12_group_2 ) ) @ ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_group_2) ).
thf(10757,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( D @ ( C @ ( A @ k9_group_2 ) ) @ ( A @ k12_group_2 ) ) )
= ( B @ ( D @ ( A @ k12_group_2 ) ) @ ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1728]) ).
thf(1788,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k14_group_2 ) @ v1_finset_1 )
=> ( ( B @ ( A @ k6_group_6 ) @ k9_group_1 )
= ( B @ ( A @ k17_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_group_6) ).
thf(11083,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k14_group_2 ) @ v1_finset_1 )
=> ( ( B @ ( A @ k6_group_6 ) @ k9_group_1 )
= ( B @ ( A @ k17_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1788]) ).
thf(2820,plain,
! [A: $i] : ( A @ ( A @ sk37 @ m1_finseq_1 ) ),
inference(cnfConj,[status(thm)],[2818]) ).
thf(21427,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ m1_finseq_1 ) ),
inference(rewrite,[status(thm)],[2820,19422]) ).
thf(41,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( ( C @ ( D @ r1_xreal_0 ) )
& ( D @ ( B @ r1_xreal_0 ) )
& ( A @ k4_finseq_1 @ ( B @ r2_hidden ) )
& ( ( A @ k3_finseq_1 )
= ( np__1 @ ( C @ k1_nat_1 ) ) ) )
=> ( ( D @ ( A @ ( B @ k2_finseq_3 ) @ k1_funct_1 ) )
= ( np__1 @ ( D @ k1_nat_1 ) @ ( A @ k1_funct_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_finseq_3) ).
thf(2289,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( ( C @ ( D @ r1_xreal_0 ) )
& ( D @ ( B @ r1_xreal_0 ) )
& ( A @ k4_finseq_1 @ ( B @ r2_hidden ) )
& ( ( A @ k3_finseq_1 )
= ( np__1 @ ( C @ k1_nat_1 ) ) ) )
=> ( ( D @ ( A @ ( B @ k2_finseq_3 ) @ k1_funct_1 ) )
= ( np__1 @ ( D @ k1_nat_1 ) @ ( A @ k1_funct_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(2290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( B @ k2_finseq_3 ) @ k1_funct_1 ) )
= ( np__1 @ ( D @ k1_nat_1 ) @ ( A @ k1_funct_1 ) ) )
| ~ ( C @ ( D @ r1_xreal_0 ) )
| ~ ( D @ ( B @ r1_xreal_0 ) )
| ~ ( A @ k4_finseq_1 @ ( B @ r2_hidden ) )
| ( ( A @ k3_finseq_1 )
!= ( np__1 @ ( C @ k1_nat_1 ) ) )
| ~ ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
| ~ ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
| ~ ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2289]) ).
thf(2291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ r1_xreal_0 ) )
| ~ ( D @ ( B @ r1_xreal_0 ) )
| ~ ( A @ k4_finseq_1 @ ( B @ r2_hidden ) )
| ~ ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
| ~ ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
| ~ ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( ( D @ ( A @ ( B @ k2_finseq_3 ) @ k1_funct_1 ) )
= ( np__1 @ ( D @ k1_nat_1 ) @ ( A @ k1_funct_1 ) ) )
| ( ( A @ k3_finseq_1 )
!= ( np__1 @ ( C @ k1_nat_1 ) ) ) ),
inference(lifteq,[status(thm)],[2290]) ).
thf(1953,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_group_3 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_group_3) ).
thf(11709,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_group_3 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1953]) ).
thf(1734,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k13_group_2 ) ) @ ( B @ ( A @ k11_group_2 ) ) )
= ( C @ ( B @ ( A @ k13_group_2 ) ) ) )
& ( ( B @ ( B @ ( A @ k7_group_4 ) ) @ ( C @ ( A @ k4_group_2 ) ) )
= ( C @ ( B @ ( A @ k13_group_2 ) ) ) )
& ( ( B @ ( B @ ( A @ k7_group_4 ) ) @ ( C @ ( A @ k3_group_2 ) ) )
= ( C @ ( B @ ( A @ k12_group_2 ) ) ) )
& ( ( C @ ( B @ ( A @ k12_group_2 ) ) @ ( B @ ( A @ k10_group_2 ) ) )
= ( C @ ( B @ ( A @ k12_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_group_6) ).
thf(10786,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k13_group_2 ) ) @ ( B @ ( A @ k11_group_2 ) ) )
= ( C @ ( B @ ( A @ k13_group_2 ) ) ) )
& ( ( B @ ( B @ ( A @ k7_group_4 ) ) @ ( C @ ( A @ k4_group_2 ) ) )
= ( C @ ( B @ ( A @ k13_group_2 ) ) ) )
& ( ( B @ ( B @ ( A @ k7_group_4 ) ) @ ( C @ ( A @ k3_group_2 ) ) )
= ( C @ ( B @ ( A @ k12_group_2 ) ) ) )
& ( ( C @ ( B @ ( A @ k12_group_2 ) ) @ ( B @ ( A @ k10_group_2 ) ) )
= ( C @ ( B @ ( A @ k12_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1734]) ).
thf(975,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_wellord2 ) )
=> ( ( A @ k2_card_1 )
= ( B @ k2_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_card_1) ).
thf(6841,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_wellord2 ) )
=> ( ( A @ k2_card_1 )
= ( B @ k2_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(2251,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
| ( A != k1_xboole_0 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) )
& ( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
| ( B = k1_xboole_0 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) ) ),
inference(cnf,[status(esa)],[2250]) ).
thf(2252,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
| ( B = k1_xboole_0 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[2251]) ).
thf(2254,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( B = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[2252]) ).
thf(1341,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(8642,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
& ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341]) ).
thf(105,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ r3_lattice3 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ ( A @ r1_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattice3) ).
thf(2540,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ ( A @ r1_lattices ) ) ) ) )
=> ( C @ ( B @ ( A @ r3_lattice3 ) ) ) )
& ( ( C @ ( B @ ( A @ r3_lattice3 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ ( A @ r1_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1482,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k12_finseq_1 ) @ ( A @ k3_group_4 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_group_4) ).
thf(9415,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k12_finseq_1 ) @ ( A @ k3_group_4 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482]) ).
thf(1227,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k12_group_2 ) ) )
= ( C @ ( B @ ( A @ k13_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_group_3) ).
thf(8018,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k12_group_2 ) ) )
= ( C @ ( B @ ( A @ k13_group_2 ) ) ) ) )
=> ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) ) )
& ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k12_group_2 ) ) )
= ( C @ ( B @ ( A @ k13_group_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(1523,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k3_group_2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_group_2) ).
thf(9680,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k3_group_2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1523]) ).
thf(581,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( A @ k1_relat_1 )
= k1_xboole_0 )
<=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
thf(4871,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
=> ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
& ( ( ( A @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(1887,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( B @ ( A @ k5_group_2 @ m1_group_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_group_2) ).
thf(11446,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( B @ ( A @ k5_group_2 @ m1_group_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1887]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( C @ ( D @ r1_tarski ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( E @ ( D @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_partfun1) ).
thf(3093,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( C @ ( D @ r1_tarski ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( E @ ( D @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(625,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
| ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(5135,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
| ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(565,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
thf(4798,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(3714,plain,
! [A: $i] : ( A @ k6_relat_1 @ v2_funct_1 ),
inference(cnf,[status(esa)],[3713]) ).
thf(13542,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k6_relat_1 )
!= ( A @ k6_relat_1 ) )
| ( k1_xboole_0 @ v2_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[9748,3714]) ).
thf(13543,plain,
k1_xboole_0 @ v2_funct_1,
inference(pattern_uni,[status(thm)],[13542:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(52,axiom,
! [A: $i,B: $i] : ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) @ ( k1_xboole_0 @ k1_tarski @ k2_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_zfmisc_1) ).
thf(2334,plain,
! [A: $i,B: $i] : ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) @ ( k1_xboole_0 @ k1_tarski @ k2_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(2335,plain,
! [B: $i,A: $i] : ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) @ ( k1_xboole_0 @ k1_tarski @ k2_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ r1_tarski ) ),
inference(cnf,[status(esa)],[2334]) ).
thf(1043,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_1_domain_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_domain_1) ).
thf(7139,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_1_domain_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_1_domain_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(889,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funct_4) ).
thf(6438,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(2777,plain,
k1_xboole_0 @ v1_funct_1,
inference(cnfConj,[status(thm)],[2775]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_zfmisc_1) ).
thf(3152,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1544,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_group_1 )
<=> ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= C ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_group_1) ).
thf(9781,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= C ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
=> ( A @ v2_group_1 ) )
& ( ( A @ v2_group_1 )
=> ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= C ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1544]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(3771,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(569,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( A @ k2_funct_1 @ k2_funct_1 )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_1) ).
thf(4810,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( A @ k2_funct_1 @ k2_funct_1 )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(907,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( k4_numbers @ ( C @ m2_finseq_1 ) )
=> ( ( ( C @ k3_finseq_1 )
= A )
=> ( ( B @ k2_group_1 @ ( A @ ( B @ u1_struct_0 @ k1_finsop_1 ) ) @ ( C @ ( B @ k4_group_4 ) ) )
= ( B @ k2_group_1 @ ( A @ ( B @ u1_struct_0 @ k1_finsop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_group_4) ).
thf(6562,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( k4_numbers @ ( C @ m2_finseq_1 ) )
=> ( ( ( C @ k3_finseq_1 )
= A )
=> ( ( B @ k2_group_1 @ ( A @ ( B @ u1_struct_0 @ k1_finsop_1 ) ) @ ( C @ ( B @ k4_group_4 ) ) )
= ( B @ k2_group_1 @ ( A @ ( B @ u1_struct_0 @ k1_finsop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(1317,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k1_setfam_1 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_setfam_1) ).
thf(8530,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_setfam_1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).
thf(8531,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_setfam_1 )
= A ),
inference(cnf,[status(esa)],[8530]) ).
thf(8532,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_setfam_1 )
= A ),
inference(lifteq,[status(thm)],[8531]) ).
thf(1537,axiom,
np__0 = k1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_card_1) ).
thf(9749,plain,
np__0 = k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1537]) ).
thf(1332,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ ( C @ ( B @ ( A @ k1_group_6 ) ) @ m1_group_6 ) ) )
& ( B @ ( C @ ( B @ ( A @ k1_group_6 ) ) @ v1_group_3 ) )
& ( C @ ( B @ ( A @ k1_group_6 ) ) @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_group_6) ).
thf(8595,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ ( C @ ( B @ ( A @ k1_group_6 ) ) @ m1_group_6 ) ) )
& ( B @ ( C @ ( B @ ( A @ k1_group_6 ) ) @ v1_group_3 ) )
& ( C @ ( B @ ( A @ k1_group_6 ) ) @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).
thf(672,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( B @ v2_funct_1 ) )
=> ( ( A
= ( A @ ( B @ k2_funct_1 @ ( B @ k5_relat_1 ) @ k1_funct_1 ) ) )
& ( A
= ( A @ ( B @ k1_funct_1 ) @ ( B @ k2_funct_1 @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_funct_1) ).
thf(5384,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( B @ v2_funct_1 ) )
=> ( ( A
= ( A @ ( B @ k2_funct_1 @ ( B @ k5_relat_1 ) @ k1_funct_1 ) ) )
& ( A
= ( A @ ( B @ k1_funct_1 ) @ ( B @ k2_funct_1 @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(1568,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ m2_lattice4 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_lattice4) ).
thf(9914,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) )
=> ( A @ ( B @ m2_lattice4 ) ) )
& ( ( A @ ( B @ m2_lattice4 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1568]) ).
thf(1624,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_partfun1) ).
thf(10233,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1624]) ).
thf(735,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(5665,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(614,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_2) ).
thf(5045,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(716,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
thf(5572,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(1161,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k7_group_4 ) ) )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_group_4) ).
thf(7707,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k7_group_4 ) ) )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(1774,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ r3_lattice3 ) ) )
=> ( C @ ( A @ k16_lattice3 ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lattice3) ).
thf(11004,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ r3_lattice3 ) ) )
=> ( C @ ( A @ k16_lattice3 ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1774]) ).
thf(2011,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( B @ ( A @ k15_group_2 ) )
= ( A @ u1_struct_0 @ k1_tarski ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_group_2) ).
thf(11939,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( B @ ( A @ k15_group_2 ) )
= ( A @ u1_struct_0 @ k1_tarski ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2011]) ).
thf(916,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k7_setfam_1 ) ) )
<=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
<=> ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
thf(6591,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k7_setfam_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k7_setfam_1 ) ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(19030,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ k1_tarski @ k2_xboole_0 ) ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,4175]) ).
thf(19031,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ k1_tarski @ k2_xboole_0 ) ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[19030]) ).
thf(19032,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ k1_tarski @ k2_xboole_0 ) @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[19031:[bind(A,$thf( E @ ( F @ k1_tarski @ k2_xboole_0 ) )),bind(B,$thf( F )),bind(C,$thf( E ))]]) ).
thf(19429,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ k1_tarski @ k2_xboole_0 ) @ v1_xboole_0 ),
inference(simp,[status(thm)],[19032]) ).
thf(31536,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_tarski @ k2_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,19429]) ).
thf(31537,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k1_tarski @ k2_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[31536]) ).
thf(31549,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[31537]) ).
thf(1115,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(7473,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(17055,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( k5_numbers @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4182,2215]) ).
thf(17056,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( k5_numbers @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[17055]) ).
thf(17057,plain,
! [A: $i] : ( k4_numbers @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[17056:[bind(A,$thf( k5_numbers )),bind(B,$thf( k4_numbers ))]]) ).
thf(17060,plain,
! [A: $i] : ( k4_numbers @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[17057]) ).
thf(17311,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17060,2188]) ).
thf(17312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) ) ),
inference(simp,[status(thm)],[17311]) ).
thf(17313,plain,
! [A: $i] : ( k4_numbers @ ( A @ k2_xboole_0 ) @ ( k5_numbers @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[17312:[bind(A,$thf( A )),bind(B,$thf( k5_numbers )),bind(C,$thf( A )),bind(D,$thf( k4_numbers ))]]) ).
thf(17565,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( A @ k2_xboole_0 ) @ ( k5_numbers @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17313,2215]) ).
thf(17566,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( A @ k2_xboole_0 ) @ ( k5_numbers @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[17565]) ).
thf(17567,plain,
! [B: $i,A: $i] : ( k4_numbers @ ( B @ k2_xboole_0 ) @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[17566:[bind(A,$thf( E )),bind(B,$thf( k5_numbers )),bind(C,$thf( k4_numbers @ ( E @ k2_xboole_0 ) )),bind(D,$thf( D ))]]) ).
thf(17572,plain,
! [B: $i,A: $i] : ( k4_numbers @ ( B @ k2_xboole_0 ) @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[17567]) ).
thf(40824,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( B @ k2_xboole_0 ) @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( E @ ( D @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( E @ ( D @ k2_xboole_0 ) @ ( C @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17572,2188]) ).
thf(40825,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( B @ k2_xboole_0 ) @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( E @ ( D @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( E @ ( D @ k2_xboole_0 ) @ ( C @ r1_tarski ) ) ),
inference(simp,[status(thm)],[40824]) ).
thf(40826,plain,
! [B: $i,A: $i] : ( k4_numbers @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) @ ( k5_numbers @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[40825:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( k5_numbers )),bind(D,$thf( A )),bind(E,$thf( k4_numbers @ ( F @ k2_xboole_0 ) ))]]) ).
thf(40896,plain,
! [B: $i,A: $i] : ( k4_numbers @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) @ ( k5_numbers @ r1_tarski ) ),
inference(simp,[status(thm)],[40826]) ).
thf(1896,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k3_xcmplx_0 ) @ ( C @ k6_group_1 ) ) )
= ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( B @ ( C @ k6_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_group_1) ).
thf(11478,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k3_xcmplx_0 ) @ ( C @ k6_group_1 ) ) )
= ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( B @ ( C @ k6_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1896]) ).
thf(1023,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( ( B @ ( D @ ( A @ k12_group_2 ) ) )
= ( C @ ( D @ ( A @ k12_group_2 ) ) ) )
<=> ( B @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) @ ( D @ r1_rlvect_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_group_2) ).
thf(7036,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( ( B @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) @ ( D @ r1_rlvect_1 ) )
=> ( ( B @ ( D @ ( A @ k12_group_2 ) ) )
= ( C @ ( D @ ( A @ k12_group_2 ) ) ) ) )
& ( ( ( B @ ( D @ ( A @ k12_group_2 ) ) )
= ( C @ ( D @ ( A @ k12_group_2 ) ) ) )
=> ( B @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) @ ( D @ r1_rlvect_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(922,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( B @ ( A @ ( D @ ( C @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_enumset1) ).
thf(6648,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( B @ ( A @ ( D @ ( C @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(175,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B @ ( D @ v1_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) ) )
<=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_filter_1) ).
thf(2833,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_binop_1 ) )
=> ( ( B @ ( D @ v1_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) ) ) )
& ( ( ( B @ ( D @ v1_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(258,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ k1_zfmisc_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ k1_zfmisc_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ~ ( ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v4_lattice3 )
& ( C @ v10_lattices )
& ( C @ v3_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ~ ( ! [D: $i] :
( ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ k15_lattice3 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) )
& ( ( C @ u1_struct_0 )
= A ) ) )
& ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( A @ k1_zfmisc_1 @ k10_relset_1 ) ) ) @ ( B @ ( A @ ( A @ k1_zfmisc_1 @ k8_funct_2 ) ) ) )
= ( C @ k3_tarski @ ( B @ k1_funct_1 ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k6_domain_1 ) @ ( B @ ( A @ ( A @ k1_zfmisc_1 @ k8_funct_2 ) ) ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_lattice3) ).
thf(3189,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ k1_zfmisc_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ k1_zfmisc_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ~ ( ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v4_lattice3 )
& ( C @ v10_lattices )
& ( C @ v3_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ~ ( ! [D: $i] :
( ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ k15_lattice3 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) )
& ( ( C @ u1_struct_0 )
= A ) ) )
& ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( A @ k1_zfmisc_1 @ k10_relset_1 ) ) ) @ ( B @ ( A @ ( A @ k1_zfmisc_1 @ k8_funct_2 ) ) ) )
= ( C @ k3_tarski @ ( B @ k1_funct_1 ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k6_domain_1 ) @ ( B @ ( A @ ( A @ k1_zfmisc_1 @ k8_funct_2 ) ) ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_xboole_1) ).
thf(2281,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(933,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(6685,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(2410,plain,
~ ( sk15 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[2409]) ).
thf(12418,plain,
( ( ( sk15 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,2410]) ).
thf(12419,plain,
( ( sk15 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12418]) ).
thf(12430,plain,
sk15 != k1_xboole_0,
inference(simp,[status(thm)],[12419]) ).
thf(953,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) )
=> ( ( A @ ( C @ ( B @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_4) ).
thf(6755,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) )
=> ( ( A @ ( C @ ( B @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(1330,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m3_vectsp_8 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k4_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_vectsp_8) ).
thf(8575,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k4_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_lattices ) ) ) ) ) )
=> ( B @ ( A @ ( C @ m3_vectsp_8 ) ) ) )
& ( ( B @ ( A @ ( C @ m3_vectsp_8 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k4_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(620,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v11_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( A @ v11_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_lattice4) ).
thf(5096,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v11_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( A @ v11_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(947,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_eqrel_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(6740,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_eqrel_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(1093,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k12_group_2 ) ) )
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( C @ ( A @ k10_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_group_3) ).
thf(7381,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k12_group_2 ) ) )
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( C @ ( A @ k10_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(298,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v3_filter_0 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_filter_0 ) )
=> ! [H: $i] :
( ( A @ u1_struct_0 @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( A @ u1_struct_0 @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( A @ u1_struct_0 @ ( J @ m1_subset_1 ) )
=> ( ( ( ( J @ ( I @ ( B @ ( A @ r1_filter_0 ) ) ) )
& ( I @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
=> ( J @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
& ( ( ( F @ ( E @ ( G @ ( C @ r1_filter_0 ) ) ) )
& ( E @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) )
=> ( F @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_filter_0) ).
thf(3421,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v3_filter_0 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_filter_0 ) )
=> ! [H: $i] :
( ( A @ u1_struct_0 @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( A @ u1_struct_0 @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( A @ u1_struct_0 @ ( J @ m1_subset_1 ) )
=> ( ( ( ( J @ ( I @ ( B @ ( A @ r1_filter_0 ) ) ) )
& ( I @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
=> ( J @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
& ( ( ( F @ ( E @ ( G @ ( C @ r1_filter_0 ) ) ) )
& ( E @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) )
=> ( F @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(1625,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( ( B @ ( A @ k17_group_2 ) )
= np__1 )
& ( B @ ( A @ k14_group_2 ) @ v1_finset_1 ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t181_group_2) ).
thf(10238,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( ( B @ ( A @ k17_group_2 ) )
= np__1 )
& ( B @ ( A @ k14_group_2 ) @ v1_finset_1 ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1625]) ).
thf(1861,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_group_2 @ ( A @ k11_group_3 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t165_group_3) ).
thf(11346,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_group_2 @ ( A @ k11_group_3 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1861]) ).
thf(1015,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ( ( B @ ( A @ ( C @ m1_group_6 ) ) )
=> ( ( C @ ( A @ k6_group_6 ) @ ( C @ ( B @ ( A @ k1_group_6 ) ) @ ( B @ k6_group_6 ) @ m1_group_2 ) )
& ( C @ ( A @ k6_group_6 ) @ ( C @ ( B @ ( A @ k1_group_6 ) ) @ ( B @ k6_group_6 ) @ v1_group_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_group_6) ).
thf(7004,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ( ( B @ ( A @ ( C @ m1_group_6 ) ) )
=> ( ( C @ ( A @ k6_group_6 ) @ ( C @ ( B @ ( A @ k1_group_6 ) ) @ ( B @ k6_group_6 ) @ m1_group_2 ) )
& ( C @ ( A @ k6_group_6 ) @ ( C @ ( B @ ( A @ k1_group_6 ) ) @ ( B @ k6_group_6 ) @ v1_group_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(1207,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k12_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k3_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_group_2) ).
thf(7936,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k12_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k3_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(1800,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_group_1 @ ( A @ u1_struct_0 @ k3_binop_1 ) )
= ( A @ k2_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_group_1) ).
thf(11136,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_group_1 @ ( A @ u1_struct_0 @ k3_binop_1 ) )
= ( A @ k2_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1800]) ).
thf(1978,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ k2_group_1 )
= ( A @ k2_group_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_group_2) ).
thf(11806,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ k2_group_1 )
= ( A @ k2_group_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1978]) ).
thf(2528,plain,
( ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v3_group_1 )
& ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v4_group_1 ) ),
inference(cnf,[status(esa)],[2527]) ).
thf(2530,plain,
k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v3_group_1,
inference(cnfConj,[status(thm)],[2528]) ).
thf(6221,plain,
sk259 @ v4_group_1,
inference(cnfConj,[status(thm)],[6214]) ).
thf(2031,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k3_group_6 ) ) )
= ( C @ ( B @ ( A @ k8_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_group_6) ).
thf(12008,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k3_group_6 ) ) )
= ( C @ ( B @ ( A @ k8_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2031]) ).
thf(1958,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v4_group_1 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_group_1) ).
thf(11723,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k1_group_1 ) ) ) ) ) ) )
=> ( A @ v4_group_1 ) )
& ( ( A @ v4_group_1 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1958]) ).
thf(897,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( B @ ( A @ ( D @ v1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_partfun1) ).
thf(6498,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( B @ ( A @ ( D @ v1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(252,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( ~ ( A @ ( np__0 @ r1_xreal_0 ) )
=> ( np__1 @ k1_real_1 @ ( A @ r1_xreal_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_int_1) ).
thf(3157,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( ~ ( A @ ( np__0 @ r1_xreal_0 ) )
=> ( np__1 @ k1_real_1 @ ( A @ r1_xreal_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(649,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_xboole_1) ).
thf(5246,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(2055,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( C @ ( D @ m1_group_2 ) )
=> ( ( ( B = D )
& ( A @ v6_group_1 ) )
=> ( ( B @ ( A @ k17_group_2 ) )
= ( C @ ( A @ k17_group_2 ) @ ( D @ ( C @ k17_group_2 ) @ k2_nat_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t179_group_2) ).
thf(12101,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( C @ ( D @ m1_group_2 ) )
=> ( ( ( B = D )
& ( A @ v6_group_1 ) )
=> ( ( B @ ( A @ k17_group_2 ) )
= ( C @ ( A @ k17_group_2 ) @ ( D @ ( C @ k17_group_2 ) @ k2_nat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2055]) ).
thf(6,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v17_lattices )
<=> ( ( A @ v11_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_lattices) ).
thf(2137,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( ( A @ v11_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices ) )
=> ( A @ v17_lattices ) )
& ( ( A @ v17_lattices )
=> ( ( A @ v11_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(3361,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(365,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ v3_struct_0 )
<=> ( A @ u1_struct_0 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_struct_0) ).
thf(3756,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( ( A @ u1_struct_0 @ v1_xboole_0 )
=> ( A @ v3_struct_0 ) )
& ( ( A @ v3_struct_0 )
=> ( A @ u1_struct_0 @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(519,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k9_filter_1 @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_filter_1) ).
thf(4536,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k9_filter_1 @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(1090,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(7363,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(7364,plain,
! [A: $i] :
( ( A @ sk330 @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( A @ sk330 @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[7363]) ).
thf(7366,plain,
! [A: $i] : ( A @ sk330 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[7364]) ).
thf(14696,plain,
! [B: $i,A: $i] :
( ( ( A @ sk330 @ v1_xboole_0 )
!= ( B @ ( B @ k1_funct_2 ) @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7366,5953]) ).
thf(14697,plain,
! [B: $i,A: $i] :
( ( A @ sk330 @ v1_xboole_0 )
!= ( B @ ( B @ k1_funct_2 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[14696]) ).
thf(14708,plain,
! [B: $i,A: $i] :
( ( A @ sk330 )
!= ( B @ ( B @ k1_funct_2 ) ) ),
inference(simp,[status(thm)],[14697]) ).
thf(18716,plain,
! [B: $i,A: $i] :
( ( ( A @ sk330 @ v1_xboole_0 )
!= ( B @ v1_xboole_0 ) )
| ~ $true
| ( B = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7366,7167]) ).
thf(18717,plain,
! [B: $i,A: $i] :
( ( ( A @ sk330 @ v1_xboole_0 )
!= ( B @ v1_xboole_0 ) )
| ( B = k1_xboole_0 ) ),
inference(simp,[status(thm)],[18716]) ).
thf(18718,plain,
! [A: $i] :
( ( A @ sk330 )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[18717:[bind(A,$thf( C )),bind(B,$thf( C @ sk330 ))]]) ).
thf(19324,plain,
! [A: $i] :
( ( A @ sk330 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[18718]) ).
thf(59548,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[14708,19324]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k3_relat_1 )
= ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_relat_1) ).
thf(2240,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k3_relat_1 )
= ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(2241,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ k3_relat_1 )
= ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k2_xboole_0 ) ) )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2240]) ).
thf(2242,plain,
! [B: $i,A: $i] :
( ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_relat_1 )
| ( ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) @ k3_relat_1 ) ) ),
inference(lifteq,[status(thm)],[2241]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(2286,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1505,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_4_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ( ( D @ ( E @ r2_hidden ) )
& ~ ( C @ ( E @ r2_hidden ) ) )
| ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_4_domain_1) ).
thf(9533,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ( ( D @ ( E @ r2_hidden ) )
& ~ ( C @ ( E @ r2_hidden ) ) )
| ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_4_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_4_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ( ( D @ ( E @ r2_hidden ) )
& ~ ( C @ ( E @ r2_hidden ) ) )
| ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1505]) ).
thf(21832,plain,
! [A: $i] :
( ( A != sk605 )
| ( k1_xboole_0 @ v3_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,11436]) ).
thf(21833,plain,
( ( k1_xboole_0 @ v3_group_1 )
| ( sk605 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21832:[bind(A,$thf( sk605 ))]]) ).
thf(280,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k5_lattices )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_filter_0) ).
thf(3327,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k5_lattices )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1744,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k8_finseq_1 ) ) @ ( A @ k3_group_4 ) )
= ( C @ ( A @ k3_group_4 ) @ ( B @ ( A @ k3_group_4 ) @ ( A @ k1_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_group_4) ).
thf(10839,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k8_finseq_1 ) ) @ ( A @ k3_group_4 ) )
= ( C @ ( A @ k3_group_4 ) @ ( B @ ( A @ k3_group_4 ) @ ( A @ k1_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1744]) ).
thf(545,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
<=> ? [C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= C )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_partfun1) ).
thf(4701,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ? [C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= C )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ? [C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= C )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) ) )
<=> ! [F: $i] :
( ( E @ ( F @ r2_hidden ) )
<=> ~ ( ( F != D )
& ( F != C )
& ( F != B )
& ( F != A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_enumset1) ).
thf(3226,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( ~ ( ( F != D )
& ( F != C )
& ( F != B )
& ( F != A ) )
=> ( E @ ( F @ r2_hidden ) ) )
& ( ( E @ ( F @ r2_hidden ) )
=> ~ ( ( F != D )
& ( F != C )
& ( F != B )
& ( F != A ) ) ) )
=> ( E
= ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) ) ) )
& ( ( E
= ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) ) )
=> ! [F: $i] :
( ( ~ ( ( F != D )
& ( F != C )
& ( F != B )
& ( F != A ) )
=> ( E @ ( F @ r2_hidden ) ) )
& ( ( E @ ( F @ r2_hidden ) )
=> ~ ( ( F != D )
& ( F != C )
& ( F != B )
& ( F != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(1902,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( B @ ( A @ k7_group_4 ) ) )
= ( B @ ( A @ k7_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_group_4) ).
thf(11505,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( B @ ( A @ k7_group_4 ) ) )
= ( B @ ( A @ k7_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1902]) ).
thf(1802,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( C @ ( C @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_group_4) ).
thf(11143,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( C @ ( C @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1802]) ).
thf(760,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(5819,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(1992,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k6_group_2 @ ( A @ k6_group_6 ) @ v3_realset2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_group_6) ).
thf(11853,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k6_group_2 @ ( A @ k6_group_6 ) @ v3_realset2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1992]) ).
thf(1569,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( B @ ( A @ k9_group_3 ) @ k1_card_1 )
= ( B @ ( A @ k11_group_3 ) @ ( A @ k16_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t161_group_3) ).
thf(9923,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( B @ ( A @ k9_group_3 ) @ k1_card_1 )
= ( B @ ( A @ k11_group_3 ) @ ( A @ k16_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1569]) ).
thf(1160,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k10_group_4 ) )
<=> ! [C: $i] :
( ( A @ k1_group_3 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_group_3 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_group_2 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_group_2 ) )
=> ( ( ( D = F )
& ( C = E ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( A @ k9_group_2 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_group_4) ).
thf(7688,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k1_group_3 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_group_3 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_group_2 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_group_2 ) )
=> ( ( ( D = F )
& ( C = E ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( A @ k9_group_2 ) ) ) ) ) ) ) ) )
=> ( B
= ( A @ k10_group_4 ) ) )
& ( ( B
= ( A @ k10_group_4 ) )
=> ! [C: $i] :
( ( A @ k1_group_3 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_group_3 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_group_2 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_group_2 ) )
=> ( ( ( D = F )
& ( C = E ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( A @ k9_group_2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(1762,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_setfam_1) ).
thf(10933,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1762]) ).
thf(762,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(5824,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(961,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( E @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_partfun1) ).
thf(6787,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( E @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(2109,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ r1_rlvect_1 ) )
=> ( B @ ( A @ k3_group_1 ) @ ( C @ r1_rlvect_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_group_2) ).
thf(12306,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ r1_rlvect_1 ) )
=> ( B @ ( A @ k3_group_1 ) @ ( C @ r1_rlvect_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2109]) ).
thf(1407,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r2_hidden ) )
=> ( B @ ( C @ ( A @ k5_group_4 ) @ r1_rlvect_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_group_4) ).
thf(9024,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r2_hidden ) )
=> ( B @ ( C @ ( A @ k5_group_4 ) @ r1_rlvect_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1407]) ).
thf(60707,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k2_xboole_0 ) )
!= ( k4_numbers @ ( C @ k2_xboole_0 ) @ ( B @ k2_xboole_0 ) ) )
| ( k1_xboole_0 @ ( k5_numbers @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[60659,40896]) ).
thf(60708,plain,
k1_xboole_0 @ ( k5_numbers @ r1_tarski ),
inference(pattern_uni,[status(thm)],[60707:[bind(A,$thf( k4_numbers @ ( D @ k2_xboole_0 ) )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D ))]]) ).
thf(788,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ k2_enumset1 ) ) ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_enumset1) ).
thf(5970,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ k2_enumset1 ) ) ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v15_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_lattices) ).
thf(2202,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v15_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(2203,plain,
! [A: $i] :
( ( ( A @ v15_lattices )
| ~ ( A @ v14_lattices )
| ~ ( A @ v13_lattices )
| ( A @ v3_struct_0 )
| ~ ( A @ l3_lattices ) )
& ( ~ ( A @ v3_struct_0 )
| ~ ( A @ v14_lattices )
| ~ ( A @ v13_lattices )
| ( A @ v3_struct_0 )
| ~ ( A @ l3_lattices ) ) ),
inference(cnf,[status(esa)],[2202]) ).
thf(2205,plain,
! [A: $i] :
( ( A @ v15_lattices )
| ~ ( A @ v14_lattices )
| ~ ( A @ v13_lattices )
| ( A @ v3_struct_0 )
| ~ ( A @ l3_lattices ) ),
inference(cnfConj,[status(thm)],[2203]) ).
thf(10455,plain,
sk545 @ l3_lattices,
inference(cnfConj,[status(thm)],[10454]) ).
thf(801,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ l2_lattices )
& ( A @ l1_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(6013,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ l2_lattices )
& ( A @ l1_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(6014,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
| ~ ( A @ l3_lattices ) )
& ( ( A @ l1_lattices )
| ~ ( A @ l3_lattices ) ) ),
inference(cnf,[status(esa)],[6013]) ).
thf(6016,plain,
! [A: $i] :
( ( A @ l2_lattices )
| ~ ( A @ l3_lattices ) ),
inference(cnfConj,[status(thm)],[6014]) ).
thf(17081,plain,
! [A: $i] :
( ( ( sk545 @ l3_lattices )
!= ( A @ l3_lattices ) )
| ( A @ l2_lattices )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10455,6016]) ).
thf(17082,plain,
! [A: $i] :
( ( ( sk545 @ l3_lattices )
!= ( A @ l3_lattices ) )
| ( A @ l2_lattices ) ),
inference(simp,[status(thm)],[17081]) ).
thf(17083,plain,
sk545 @ l2_lattices,
inference(pattern_uni,[status(thm)],[17082:[bind(A,$thf( sk545 ))]]) ).
thf(22379,plain,
! [A: $i] :
( ( A != sk545 )
| ( k1_xboole_0 @ l2_lattices )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,17083]) ).
thf(22380,plain,
( ( k1_xboole_0 @ l2_lattices )
| ( sk545 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22379:[bind(A,$thf( sk545 ))]]) ).
thf(21802,plain,
! [A: $i] :
( ( A != sk235 )
| ( k1_xboole_0 @ l1_struct_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,15755]) ).
thf(21803,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk235 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21802:[bind(A,$thf( sk235 ))]]) ).
thf(1589,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_setfam_1) ).
thf(10029,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1589]) ).
thf(1078,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ ( E @ v4_group_6 ) ) )
& ( B @ ( A @ ( D @ v4_group_6 ) ) ) )
=> ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_group_6 ) ) ) ) @ v4_group_6 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_group_6) ).
thf(7305,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ ( E @ v4_group_6 ) ) )
& ( B @ ( A @ ( D @ v4_group_6 ) ) ) )
=> ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_group_6 ) ) ) ) @ v4_group_6 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(1063,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(7230,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(744,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_subset_1) ).
thf(5695,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(1388,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ k7_rlvect_1 ) ) @ ( B @ k2_group_4 @ ( A @ k2_group_4 @ ( k4_numbers @ k2_finseq_4 ) ) @ ( C @ k4_group_4 ) ) )
= ( E @ ( B @ ( C @ k6_group_1 ) ) @ ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( C @ k7_rlvect_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_group_4) ).
thf(8924,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ k7_rlvect_1 ) ) @ ( B @ k2_group_4 @ ( A @ k2_group_4 @ ( k4_numbers @ k2_finseq_4 ) ) @ ( C @ k4_group_4 ) ) )
= ( E @ ( B @ ( C @ k6_group_1 ) ) @ ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( C @ k7_rlvect_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388]) ).
thf(1549,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_subset_1 )
= ( A @ a_1_1_domain_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_domain_1) ).
thf(9822,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_subset_1 )
= ( A @ a_1_1_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1549]) ).
thf(786,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( B @ ( k1_xboole_0 @ ( A @ k5_partfun1 ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t172_partfun1) ).
thf(5961,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( B @ ( k1_xboole_0 @ ( A @ k5_partfun1 ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(532,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ r1_partfun1 ) )
& ( B @ k1_relat_1 @ ( D @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) ) )
=> ( ( B @ ( A @ k1_funct_4 ) @ ( D @ ( C @ k1_funct_4 ) @ k5_relat_1 ) )
= ( B @ ( D @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ k1_funct_4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funct_4) ).
thf(4604,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ r1_partfun1 ) )
& ( B @ k1_relat_1 @ ( D @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) ) )
=> ( ( B @ ( A @ k1_funct_4 ) @ ( D @ ( C @ k1_funct_4 ) @ k5_relat_1 ) )
= ( B @ ( D @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ k1_funct_4 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(1343,axiom,
~ ( k4_numbers @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_numbers) ).
thf(8651,plain,
~ ( k4_numbers @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).
thf(8652,plain,
~ ( k4_numbers @ v1_xboole_0 ),
inference(polarity_switch,[status(thm)],[8651]) ).
thf(12420,plain,
( ( ( k4_numbers @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,8652]) ).
thf(12421,plain,
( ( k4_numbers @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12420]) ).
thf(12425,plain,
k4_numbers != k1_xboole_0,
inference(simp,[status(thm)],[12421]) ).
thf(845,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( C @ ( B @ ( A @ r2_lattice4 ) ) )
<=> ( ( A @ k6_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k6_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_lattice4) ).
thf(6200,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( ( ( A @ k6_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k6_lattices ) )
=> ( C @ ( B @ ( A @ r2_lattice4 ) ) ) )
& ( ( C @ ( B @ ( A @ r2_lattice4 ) ) )
=> ( ( A @ k6_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k6_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(1408,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( C @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( E @ ( D @ ( A @ k1_group_1 ) ) )
= ( D @ ( E @ ( A @ k1_group_1 ) ) ) ) ) ) )
=> ( ( C @ ( B @ ( A @ k2_group_2 ) ) )
= ( B @ ( C @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_group_2) ).
thf(9026,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( C @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( E @ ( D @ ( A @ k1_group_1 ) ) )
= ( D @ ( E @ ( A @ k1_group_1 ) ) ) ) ) ) )
=> ( ( C @ ( B @ ( A @ k2_group_2 ) ) )
= ( B @ ( C @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1408]) ).
thf(1316,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funct_2) ).
thf(8523,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).
thf(1044,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( D @ ( A @ k12_group_2 ) ) @ ( C @ ( A @ k4_group_2 ) ) )
= ( C @ ( D @ ( A @ k13_group_2 ) ) @ ( B @ ( A @ k3_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_group_2) ).
thf(7148,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( D @ ( A @ k12_group_2 ) ) @ ( C @ ( A @ k4_group_2 ) ) )
= ( C @ ( D @ ( A @ k13_group_2 ) ) @ ( B @ ( A @ k3_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(979,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ m1_group_2 ) )
<=> ( C @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_group_4) ).
thf(6856,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( ( C @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) )
=> ( C @ ( B @ m1_group_2 ) ) )
& ( ( C @ ( B @ m1_group_2 ) )
=> ( C @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(388,axiom,
! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(3857,plain,
! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_partfun1) ).
thf(5406,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(630,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k5_setfam_1 ) @ ( A @ k2_subset_1 @ ( A @ k6_subset_1 ) ) )
= ( B @ ( A @ k7_setfam_1 ) @ ( A @ k6_setfam_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).
thf(5157,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k5_setfam_1 ) @ ( A @ k2_subset_1 @ ( A @ k6_subset_1 ) ) )
= ( B @ ( A @ k7_setfam_1 ) @ ( A @ k6_setfam_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(954,axiom,
k4_numbers != k1_numbers,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_numbers) ).
thf(6758,plain,
k4_numbers != k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(6759,plain,
k4_numbers != k1_numbers,
inference(polarity_switch,[status(thm)],[6758]) ).
thf(6760,plain,
k4_numbers != k1_numbers,
inference(lifteq,[status(thm)],[6759]) ).
thf(1524,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( D @ ( A @ k13_group_2 ) ) @ ( C @ ( A @ k4_group_2 ) ) )
= ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( D @ ( A @ k13_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_group_2) ).
thf(9682,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( D @ ( A @ k13_group_2 ) ) @ ( C @ ( A @ k4_group_2 ) ) )
= ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( D @ ( A @ k13_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1524]) ).
thf(320,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ r1_partfun1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_partfun1) ).
thf(3503,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ r1_partfun1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(2025,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ k8_group_1 )
= ( B @ ( C @ ( A @ k6_group_3 ) ) @ k8_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_group_3) ).
thf(11993,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ k8_group_1 )
= ( B @ ( C @ ( A @ k6_group_3 ) ) @ k8_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2025]) ).
thf(587,axiom,
! [A: $i] :
( ( A @ k6_relat_1 @ v1_funct_1 )
& ( A @ k6_relat_1 @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(4893,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ v1_funct_1 )
& ( A @ k6_relat_1 @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(336,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_4) ).
thf(3591,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(1055,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C
= ( B @ ( A @ k5_group_6 ) ) )
<=> ! [D: $i] :
( ( B @ ( A @ k4_group_6 ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k4_group_6 ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
=> ( ( ( E = G )
& ( D = F ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ k2_binop_1 ) ) ) ) ) )
= ( G @ ( F @ ( A @ k2_group_2 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_group_6) ).
thf(7179,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( B @ ( A @ k4_group_6 ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k4_group_6 ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
=> ( ( ( E = G )
& ( D = F ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ k2_binop_1 ) ) ) ) ) )
= ( G @ ( F @ ( A @ k2_group_2 ) ) ) ) ) ) ) ) )
=> ( C
= ( B @ ( A @ k5_group_6 ) ) ) )
& ( ( C
= ( B @ ( A @ k5_group_6 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ k4_group_6 ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k4_group_6 ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
=> ( ( ( E = G )
& ( D = F ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ k2_binop_1 ) ) ) ) ) )
= ( G @ ( F @ ( A @ k2_group_2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(599,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k6_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_subset_1) ).
thf(4962,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k6_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(1114,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( A @ k2_group_2 ) ) @ ( D @ ( B @ ( A @ k2_group_2 ) ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) @ ( D @ ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) @ ( A @ k2_group_2 ) ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_group_2) ).
thf(7471,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( A @ k2_group_2 ) ) @ ( D @ ( B @ ( A @ k2_group_2 ) ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) @ ( D @ ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) @ ( A @ k2_group_2 ) ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(3303,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(1263,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_zfmisc_1 @ r1_tarski ) )
=> ( ~ ( B @ ( A @ r2_wellord2 ) )
& ( B @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_card_1) ).
thf(8201,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_zfmisc_1 @ r1_tarski ) )
=> ( ~ ( B @ ( A @ r2_wellord2 ) )
& ( B @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(527,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( ( A @ ( np__0 @ r1_xreal_0 ) )
=> ( k5_numbers @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_int_1) ).
thf(4589,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( ( A @ ( np__0 @ r1_xreal_0 ) )
=> ( k5_numbers @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(883,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v7_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k10_group_1 ) ) @ ( A @ ( B @ k6_group_1 ) ) )
= ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k10_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_group_1) ).
thf(6406,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v7_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k10_group_1 ) ) @ ( A @ ( B @ k6_group_1 ) ) )
= ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k10_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(1233,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ l1_group_1 )
& ( B @ v7_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( C @ ( A @ ( B @ k13_group_6 ) ) @ v7_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_group_6) ).
thf(8046,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ l1_group_1 )
& ( B @ v7_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( C @ ( A @ ( B @ k13_group_6 ) ) @ v7_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(332,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ v6_group_1 )
<=> ( A @ u1_struct_0 @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_group_1) ).
thf(3567,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( ( A @ u1_struct_0 @ v1_finset_1 )
=> ( A @ v6_group_1 ) )
& ( ( A @ v6_group_1 )
=> ( A @ u1_struct_0 @ v1_finset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(2099,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_group_4 @ u1_lattices )
= ( A @ k10_group_4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_group_4) ).
thf(12275,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_group_4 @ u1_lattices )
= ( A @ k10_group_4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2099]) ).
thf(1389,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_partfun1) ).
thf(8927,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1389]) ).
thf(6015,plain,
! [A: $i] :
( ( A @ l1_lattices )
| ~ ( A @ l3_lattices ) ),
inference(cnfConj,[status(thm)],[6014]) ).
thf(1095,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( A @ k14_group_2 ) @ v1_finset_1 )
=> ( ( C @ ( A @ k17_group_2 ) )
= ( B @ ( C @ ( A @ k6_group_3 ) ) @ ( A @ k17_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_group_3) ).
thf(7393,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( A @ k14_group_2 ) @ v1_finset_1 )
=> ( ( C @ ( A @ k17_group_2 ) )
= ( B @ ( C @ ( A @ k6_group_3 ) ) @ ( A @ k17_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(16416,plain,
! [A: $i] :
( ( ( sk1 @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2117,4961]) ).
thf(16417,plain,
! [A: $i] :
( ( ( sk1 @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[16416]) ).
thf(16418,plain,
sk1 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[16417:[bind(A,$thf( sk1 ))]]) ).
thf(18965,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,16418]) ).
thf(18966,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[18965:[bind(A,$thf( sk1 ))]]) ).
thf(20715,plain,
( ( ( sk1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,18966]) ).
thf(20716,plain,
( ( ( sk1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[20715]) ).
thf(20725,plain,
( ( sk1 != k1_xboole_0 )
| ( k1_xboole_0 @ l1_struct_0 ) ),
inference(simp,[status(thm)],[20716]) ).
thf(1299,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ( ( C @ ( D @ ( B @ k10_group_2 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ( F @ ( D @ r1_rlvect_1 ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_group_2) ).
thf(8375,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ( ( ? [E: $i] :
( ? [F: $i] :
( ( F @ ( D @ r1_rlvect_1 ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ ( B @ k10_group_2 ) ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( D @ ( B @ k10_group_2 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ? [F: $i] :
( ( F @ ( D @ r1_rlvect_1 ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).
thf(1165,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ u1_struct_0 )
!= B ) )
& ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( A @ k3_group_1 ) @ r2_hidden ) ) ) )
& ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k1_group_1 ) ) @ r2_hidden ) ) ) ) )
& ( B != k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_group_2) ).
thf(7725,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ u1_struct_0 )
!= B ) )
& ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( A @ k3_group_1 ) @ r2_hidden ) ) ) )
& ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k1_group_1 ) ) @ r2_hidden ) ) ) ) )
& ( B != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(1848,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) ) )
& ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= ( C @ ( B @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_group_3) ).
thf(11307,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) ) )
& ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= ( C @ ( B @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1848]) ).
thf(1489,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k11_group_6 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ k6_group_6 ) @ ( A @ ( B @ ( A @ k11_group_6 ) @ v1_group_6 ) ) )
& ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k11_group_6 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k11_group_6 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_group_6) ).
thf(9440,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k11_group_6 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ k6_group_6 ) @ ( A @ ( B @ ( A @ k11_group_6 ) @ v1_group_6 ) ) )
& ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k11_group_6 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k11_group_6 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1489]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_funct_2) ).
thf(3265,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(1130,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ r1_rlvect_1 ) )
<=> ( ( B @ ( C @ ( A @ k13_group_2 ) ) )
= ( C @ ( A @ k7_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_group_2) ).
thf(7550,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( ( B @ ( C @ ( A @ k13_group_2 ) ) )
= ( C @ ( A @ k7_group_2 ) ) )
=> ( B @ ( C @ r1_rlvect_1 ) ) )
& ( ( B @ ( C @ r1_rlvect_1 ) )
=> ( ( B @ ( C @ ( A @ k13_group_2 ) ) )
= ( C @ ( A @ k7_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(1182,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(7814,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(1399,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k2_struct_0 ) ) @ ( B @ ( A @ r4_lattice3 ) ) )
<=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_lattice3) ).
thf(9004,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( D @ ( C @ ( A @ k2_struct_0 ) ) @ ( B @ ( A @ r4_lattice3 ) ) ) )
& ( ( D @ ( C @ ( A @ k2_struct_0 ) ) @ ( B @ ( A @ r4_lattice3 ) ) )
=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399]) ).
thf(21745,plain,
! [A: $i] :
( ( A != sk280 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,12426]) ).
thf(21746,plain,
! [A: $i] :
( ( A != sk280 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[21745]) ).
thf(21747,plain,
sk280 @ sk149 @ v1_funct_1,
inference(pattern_uni,[status(thm)],[21746:[bind(A,$thf( sk280 ))]]) ).
thf(609,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( A @ ( B @ k3_tarski @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t177_orders_1) ).
thf(5017,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( A @ ( B @ k3_tarski @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(326,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_binop_1) ).
thf(3531,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) )
=> ( B @ ( C @ ( A @ r6_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(1811,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ m1_group_2 ) )
& ( B @ ( A @ m1_group_2 ) ) )
=> ( C @ ( A @ m1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_group_2) ).
thf(11170,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ m1_group_2 ) )
& ( B @ ( A @ m1_group_2 ) ) )
=> ( C @ ( A @ m1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1811]) ).
thf(2155,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ~ ( B @ l3_lattices )
| ~ ( B @ v16_lattices )
| ~ ( B @ v15_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2144]) ).
thf(2164,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ~ ( B @ v16_lattices )
| ~ ( B @ v15_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[2155]) ).
thf(687,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_relat_1) ).
thf(5438,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(2081,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k10_group_2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_group_2) ).
thf(12200,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k10_group_2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2081]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( C @ ( A @ ( D @ ( B @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_enumset1) ).
thf(3186,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( C @ ( A @ ( D @ ( B @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(811,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_xboole_1) ).
thf(6064,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1193,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ( ( B @ ( A @ ( C @ u1_group_1 @ ( C @ u1_struct_0 @ g1_group_1 ) @ m1_group_6 ) ) )
=> ( ( C @ ( B @ ( A @ k1_group_6 ) ) )
= ( C @ u1_group_1 @ ( C @ u1_struct_0 @ g1_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_group_6) ).
thf(7859,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ( ( B @ ( A @ ( C @ u1_group_1 @ ( C @ u1_struct_0 @ g1_group_1 ) @ m1_group_6 ) ) )
=> ( ( C @ ( B @ ( A @ k1_group_6 ) ) )
= ( C @ u1_group_1 @ ( C @ u1_struct_0 @ g1_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(809,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_xboole_0 ) ) )
=> ( B @ ( A @ k3_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_zfmisc_1) ).
thf(6058,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_xboole_0 ) ) )
=> ( B @ ( A @ k3_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(2342,plain,
! [A: $i] :
( ( A @ sk11 @ v1_finseq_1 )
& ( A @ sk11 @ v1_finset_1 )
& ( A @ sk11 @ v1_funct_1 )
& ( A @ sk11 @ v1_relat_1 )
& ( A @ ( k5_numbers @ ( A @ sk11 @ m1_relset_1 ) ) ) ),
inference(cnf,[status(esa)],[2341]) ).
thf(2343,plain,
! [A: $i] : ( A @ sk11 @ v1_finset_1 ),
inference(cnfConj,[status(thm)],[2342]) ).
thf(14335,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk11 @ v1_finset_1 )
!= ( B @ v1_finset_1 ) )
| ( C @ ( B @ k4_xboole_0 ) @ v1_finset_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2343,2181]) ).
thf(14336,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk11 @ v1_finset_1 )
!= ( B @ v1_finset_1 ) )
| ( C @ ( B @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(simp,[status(thm)],[14335]) ).
thf(14337,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk11 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(pattern_uni,[status(thm)],[14336:[bind(A,$thf( D )),bind(B,$thf( D @ sk11 ))]]) ).
thf(14342,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk11 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(simp,[status(thm)],[14337]) ).
thf(34,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(2268,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(2269,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[2268]) ).
thf(2270,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[2269]) ).
thf(138,axiom,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finseq_1) ).
thf(2685,plain,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(2686,plain,
( ( sk24 @ v1_finseq_1 )
& ( sk24 @ v1_finset_1 )
& ( sk24 @ v2_funct_1 )
& ( sk24 @ v1_funct_1 )
& ( sk24 @ v1_relat_1 )
& ( sk24 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[2685]) ).
thf(2691,plain,
sk24 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[2686]) ).
thf(16619,plain,
( ( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk24 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2691,16583]) ).
thf(16620,plain,
( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk24 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[16619]) ).
thf(16644,plain,
( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) )
!= sk24 ),
inference(simp,[status(thm)],[16620]) ).
thf(16969,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
!= ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) ) )
| ( A != sk24 ) ),
inference(paramod_ordered,[status(thm)],[2270,16644]) ).
thf(16973,plain,
( ( k1_xboole_0 @ ( sk24 @ k4_xboole_0 ) )
!= ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) ) ),
inference(simp,[status(thm)],[16969]) ).
thf(26509,plain,
( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) )
!= sk24 ),
inference(rewrite,[status(thm)],[16973,2270]) ).
thf(1072,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_filter_0) ).
thf(7269,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(1889,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_group_2 ) @ ( A @ k3_group_3 ) ) )
= ( C @ ( B @ ( A @ k3_group_3 ) ) @ ( A @ k1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_group_3) ).
thf(11456,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_group_2 ) @ ( A @ k3_group_3 ) ) )
= ( C @ ( B @ ( A @ k3_group_3 ) ) @ ( A @ k1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1889]) ).
thf(1101,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( B @ k4_finseq_1 @ ( B @ k4_finseq_1 @ ( D @ m2_relset_1 ) ) )
& ( B @ k4_finseq_1 @ ( B @ k4_finseq_1 @ ( D @ v3_funct_2 ) ) )
& ( B @ k4_finseq_1 @ ( B @ k4_finseq_1 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C
= ( B @ ( D @ k5_relat_1 ) ) )
=> ( ( B @ ( A @ k3_group_4 ) )
= ( C @ ( A @ k3_group_4 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_group_4) ).
thf(7410,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( B @ k4_finseq_1 @ ( B @ k4_finseq_1 @ ( D @ m2_relset_1 ) ) )
& ( B @ k4_finseq_1 @ ( B @ k4_finseq_1 @ ( D @ v3_funct_2 ) ) )
& ( B @ k4_finseq_1 @ ( B @ k4_finseq_1 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C
= ( B @ ( D @ k5_relat_1 ) ) )
=> ( ( B @ ( A @ k3_group_4 ) )
= ( C @ ( A @ k3_group_4 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(982,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ( ( B @ ( A @ k7_group_2 ) @ ( C @ k2_relat_1 @ r1_tarski ) )
=> ( C @ ( A @ k3_group_4 ) @ ( B @ r1_rlvect_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_group_4) ).
thf(6865,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ( ( B @ ( A @ k7_group_2 ) @ ( C @ k2_relat_1 @ r1_tarski ) )
=> ( C @ ( A @ k3_group_4 ) @ ( B @ r1_rlvect_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(682,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_0 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_filter_0) ).
thf(5416,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_0 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(22236,plain,
! [A: $i] :
( ( A != sk235 )
| ( k1_xboole_0 @ l1_lattices )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,5887]) ).
thf(22237,plain,
( ( k1_xboole_0 @ l1_lattices )
| ( sk235 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22236:[bind(A,$thf( sk235 ))]]) ).
thf(223,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ ( A @ k1_finseq_3 ) )
= A )
<=> ( A @ k2_relat_1 @ ( B @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_finseq_3) ).
thf(3054,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( A @ k2_relat_1 @ ( B @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k1_finseq_3 ) )
= A ) )
& ( ( ( B @ ( A @ k1_finseq_3 ) )
= A )
=> ( A @ k2_relat_1 @ ( B @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(2296,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ m1_realset1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[2293]) ).
thf(525,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ~ ( B @ ( np__0 @ r1_xreal_0 ) )
=> ( ( C @ ( B @ ( A @ k6_group_1 ) ) )
= ( B @ k1_int_2 @ ( C @ ( A @ k5_group_1 @ ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) @ ( A @ k3_group_1 ) ) ) )
& ( ( B @ ( np__0 @ r1_xreal_0 ) )
=> ( ( C @ ( B @ ( A @ k6_group_1 ) ) )
= ( B @ k1_int_2 @ ( C @ ( A @ k5_group_1 @ ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_group_1) ).
thf(4576,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ~ ( B @ ( np__0 @ r1_xreal_0 ) )
=> ( ( C @ ( B @ ( A @ k6_group_1 ) ) )
= ( B @ k1_int_2 @ ( C @ ( A @ k5_group_1 @ ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) @ ( A @ k3_group_1 ) ) ) )
& ( ( B @ ( np__0 @ r1_xreal_0 ) )
=> ( ( C @ ( B @ ( A @ k6_group_1 ) ) )
= ( B @ k1_int_2 @ ( C @ ( A @ k5_group_1 @ ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(1442,axiom,
! [A: $i] :
( ( ( A @ l1_vectsp_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v8_vectsp_1 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_group_1 @ ( A @ k1_group_1 ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_vectsp_1) ).
thf(9252,plain,
! [A: $i] :
( ( ( A @ l1_vectsp_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_group_1 @ ( A @ k1_group_1 ) ) )
= B ) )
=> ( A @ v8_vectsp_1 ) )
& ( ( A @ v8_vectsp_1 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_group_1 @ ( A @ k1_group_1 ) ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442]) ).
thf(706,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( k1_xboole_0 @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( k1_xboole_0 @ k5_relat_1 ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_relat_1) ).
thf(5519,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( k1_xboole_0 @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( k1_xboole_0 @ k5_relat_1 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(1709,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ( ( ( B @ ( A @ k3_xcmplx_0 ) )
= ( np__1 @ k1_real_1 ) )
<=> ( ( ( B
= ( np__1 @ k1_real_1 ) )
& ( A = np__1 ) )
| ( ( B = np__1 )
& ( A
= ( np__1 @ k1_real_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_int_1) ).
thf(10639,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ( ( ( ( ( B
= ( np__1 @ k1_real_1 ) )
& ( A = np__1 ) )
| ( ( B = np__1 )
& ( A
= ( np__1 @ k1_real_1 ) ) ) )
=> ( ( B @ ( A @ k3_xcmplx_0 ) )
= ( np__1 @ k1_real_1 ) ) )
& ( ( ( B @ ( A @ k3_xcmplx_0 ) )
= ( np__1 @ k1_real_1 ) )
=> ( ( ( B
= ( np__1 @ k1_real_1 ) )
& ( A = np__1 ) )
| ( ( B = np__1 )
& ( A
= ( np__1 @ k1_real_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1709]) ).
thf(6741,plain,
! [A: $i] : ( A @ ( A @ sk297 @ m1_eqrel_1 ) ),
inference(cnf,[status(esa)],[6740]) ).
thf(2083,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k2_group_1 @ ( A @ r2_group_3 ) ) )
| ( A @ k2_group_1 @ ( B @ ( A @ r2_group_3 ) ) ) )
=> ( B
= ( A @ k2_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_group_3) ).
thf(12205,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k2_group_1 @ ( A @ r2_group_3 ) ) )
| ( A @ k2_group_1 @ ( B @ ( A @ r2_group_3 ) ) ) )
=> ( B
= ( A @ k2_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2083]) ).
thf(2016,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ? [D: $i] :
( ( ( B @ ( D @ ( A @ k1_group_1 ) ) )
= C )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
& ? [D: $i] :
( ( ( D @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) )
& ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k1_group_1 ) ) ) ) ) ) ) )
=> ( ( A @ v3_group_1 )
& ( A @ v4_group_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_group_1) ).
thf(11952,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ? [D: $i] :
( ( ( B @ ( D @ ( A @ k1_group_1 ) ) )
= C )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
& ? [D: $i] :
( ( ( D @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) )
& ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k1_group_1 ) ) ) ) ) ) ) )
=> ( ( A @ v3_group_1 )
& ( A @ v4_group_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2016]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_funcop_1 ) @ ( C @ ( A @ k2_funcop_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_funct_4) ).
thf(2496,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_funcop_1 ) @ ( C @ ( A @ k2_funcop_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(2062,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E = C )
& ( D = B ) )
=> ( ( E @ ( D @ ( A @ k11_group_4 @ k4_lattices ) ) )
= ( C @ ( B @ ( A @ k9_group_2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_latsubgr) ).
thf(12127,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E = C )
& ( D = B ) )
=> ( ( E @ ( D @ ( A @ k11_group_4 @ k4_lattices ) ) )
= ( C @ ( B @ ( A @ k9_group_2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2062]) ).
thf(430,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ k1_relat_1 ) )
=> ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_1) ).
thf(4059,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ k1_relat_1 ) )
=> ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(2049,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_group_3 @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_group_3) ).
thf(12073,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_group_3 @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2049]) ).
thf(27368,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ~ ( A @ v3_struct_0 )
| ( sk1 @ sk149 @ v1_funct_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,22481]) ).
thf(27369,plain,
! [A: $i] :
( ~ ( A @ v3_struct_0 )
| ( sk1 @ sk149 @ v1_funct_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[27368:[]]) ).
thf(2074,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k7_group_1 ) @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_group_1) ).
thf(12169,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k7_group_1 ) @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2074]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(2382,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(6442,plain,
! [A: $i] : ( A @ k2_card_1 @ v1_card_1 ),
inference(cnf,[status(esa)],[6441]) ).
thf(330,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k4_filter_0 ) ) )
= ( D @ ( C @ ( A @ k4_filter_0 ) ) @ ( B @ ( A @ k4_filter_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_filter_1) ).
thf(3550,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k4_filter_0 ) ) )
= ( D @ ( C @ ( A @ k4_filter_0 ) ) @ ( B @ ( A @ k4_filter_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(1900,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k2_group_1 @ ( A @ k7_group_1 ) )
= np__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_group_1) ).
thf(11499,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k2_group_1 @ ( A @ k7_group_1 ) )
= np__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1900]) ).
thf(657,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( D
= ( C @ ( B @ ( A @ k5_partfun1 ) ) ) )
<=> ! [E: $i] :
( ( D @ ( E @ r2_hidden ) )
<=> ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_partfun1) ).
thf(5281,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ! [E: $i] :
( ( ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( ( D @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k5_partfun1 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k5_partfun1 ) ) ) )
=> ! [E: $i] :
( ( ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( ( D @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(10026,plain,
( ( sk510 @ v3_lattices )
& ( sk510 @ l3_lattices ) ),
inference(cnf,[status(esa)],[10025]) ).
thf(10027,plain,
sk510 @ l3_lattices,
inference(cnfConj,[status(thm)],[10026]) ).
thf(17026,plain,
! [A: $i] :
( ( ( sk510 @ l3_lattices )
!= ( A @ l3_lattices ) )
| ( A @ l1_lattices )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10027,6015]) ).
thf(17027,plain,
! [A: $i] :
( ( ( sk510 @ l3_lattices )
!= ( A @ l3_lattices ) )
| ( A @ l1_lattices ) ),
inference(simp,[status(thm)],[17026]) ).
thf(17028,plain,
sk510 @ l1_lattices,
inference(pattern_uni,[status(thm)],[17027:[bind(A,$thf( sk510 ))]]) ).
thf(22385,plain,
! [A: $i] :
( ( A != sk510 )
| ( k1_xboole_0 @ l1_lattices )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,17028]) ).
thf(22386,plain,
( ( k1_xboole_0 @ l1_lattices )
| ( sk510 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22385:[bind(A,$thf( sk510 ))]]) ).
thf(1822,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k7_group_3 ) @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_group_3) ).
thf(11202,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k7_group_3 ) @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1822]) ).
thf(297,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ a_3_1_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_filter_0) ).
thf(3418,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ a_3_1_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(590,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B
= ( C @ k1_relat_1 ) ) ) )
& ~ ( ( B != k1_xboole_0 )
& ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_1) ).
thf(4907,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B
= ( C @ k1_relat_1 ) ) ) )
& ~ ( ( B != k1_xboole_0 )
& ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(4908,plain,
~ ? [A: $i,B: $i] :
( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B
= ( C @ k1_relat_1 ) ) ) )
& ~ ( ( B != k1_xboole_0 )
& ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[4907]) ).
thf(4909,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk180 ) @ k2_relat_1 @ r1_tarski ) )
| ( B != k1_xboole_0 ) )
& ( ( B
= ( A @ ( B @ sk180 ) @ k1_relat_1 ) )
| ( B != k1_xboole_0 ) )
& ( ( A @ ( B @ sk180 ) @ v1_funct_1 )
| ( B != k1_xboole_0 ) )
& ( ( A @ ( B @ sk180 ) @ v1_relat_1 )
| ( B != k1_xboole_0 ) )
& ( ( A @ ( A @ ( B @ sk180 ) @ k2_relat_1 @ r1_tarski ) )
| ( A = k1_xboole_0 ) )
& ( ( B
= ( A @ ( B @ sk180 ) @ k1_relat_1 ) )
| ( A = k1_xboole_0 ) )
& ( ( A @ ( B @ sk180 ) @ v1_funct_1 )
| ( A = k1_xboole_0 ) )
& ( ( A @ ( B @ sk180 ) @ v1_relat_1 )
| ( A = k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[4908]) ).
thf(4913,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk180 ) @ v1_funct_1 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[4909]) ).
thf(4924,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk180 ) @ v1_funct_1 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[4913]) ).
thf(4925,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ sk180 ) @ v1_funct_1 ),
inference(simp,[status(thm)],[4924]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( C @ v2_funct_1 )
<=> ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_2) ).
thf(3795,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) )
=> ( C @ v2_funct_1 ) )
& ( ( C @ v2_funct_1 )
=> ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(32,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ ( A @ k1_finseq_3 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_finseq_3) ).
thf(2257,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ ( A @ k2_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k1_finseq_3 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k1_finseq_3 ) )
= k1_xboole_0 )
=> ( B @ ( A @ k2_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(2258,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i] :
( ( B @ ( A @ k2_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k1_finseq_3 ) )
= k1_xboole_0 ) )
& ! [B: $i] :
( ( ( B @ ( A @ k1_finseq_3 ) )
= k1_xboole_0 )
=> ( B @ ( A @ k2_relat_1 @ r1_tarski ) ) ) ) ),
inference(miniscope,[status(thm)],[2257]) ).
thf(2259,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ( C @ ( A @ k1_finseq_3 ) )
= k1_xboole_0 )
| ~ ( C @ ( A @ k2_relat_1 @ r1_tarski ) )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) )
& ( ( B @ ( A @ k2_relat_1 @ r1_tarski ) )
| ( ( B @ ( A @ k1_finseq_3 ) )
!= k1_xboole_0 )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[2258]) ).
thf(2261,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k1_finseq_3 ) )
= k1_xboole_0 )
| ~ ( B @ ( A @ k2_relat_1 @ r1_tarski ) )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[2259]) ).
thf(2263,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ k2_relat_1 @ r1_tarski ) )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( ( B @ ( A @ k1_finseq_3 ) )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[2261]) ).
thf(2264,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ k2_relat_1 @ r1_tarski ) )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( ( B @ ( A @ k1_finseq_3 ) )
= k1_xboole_0 ) ),
inference(simp,[status(thm)],[2263]) ).
thf(11439,plain,
sk605 @ v4_group_1,
inference(cnfConj,[status(thm)],[11434]) ).
thf(1188,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ! [E: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F
= ( D @ u1_struct_0 @ ( C @ u1_struct_0 @ k2_xboole_0 ) ) )
=> ( ( D @ ( C @ ( A @ k8_group_4 ) ) @ u1_struct_0 @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) )
= ( F @ ( A @ k5_group_4 ) @ u1_struct_0 @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_latsubgr) ).
thf(7834,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ! [E: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F
= ( D @ u1_struct_0 @ ( C @ u1_struct_0 @ k2_xboole_0 ) ) )
=> ( ( D @ ( C @ ( A @ k8_group_4 ) ) @ u1_struct_0 @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) )
= ( F @ ( A @ k5_group_4 ) @ u1_struct_0 @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(1162,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ( ( B @ ( A @ ( B @ ( C @ ( A @ k9_group_2 ) ) @ m1_group_6 ) ) )
& ( B @ ( B @ ( C @ ( A @ k9_group_2 ) ) @ v1_group_3 ) )
& ( B @ ( A @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ m1_group_6 ) ) )
& ( B @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ v1_group_3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_group_6) ).
thf(7710,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ( ( B @ ( A @ ( B @ ( C @ ( A @ k9_group_2 ) ) @ m1_group_6 ) ) )
& ( B @ ( B @ ( C @ ( A @ k9_group_2 ) ) @ v1_group_3 ) )
& ( B @ ( A @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ m1_group_6 ) ) )
& ( B @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ v1_group_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(1335,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ k4_group_2 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( A
= ( D @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_group_2) ).
thf(8608,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( A
= ( D @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ ( B @ k4_group_2 ) ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( D @ ( B @ k4_group_2 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( A
= ( D @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).
thf(1926,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ u1_struct_0 @ k2_subset_1 @ ( B @ ( A @ k3_group_2 ) ) )
= ( A @ u1_struct_0 ) )
& ( ( A @ u1_struct_0 @ k2_subset_1 @ ( B @ ( A @ k4_group_2 ) ) )
= ( A @ u1_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_group_2) ).
thf(11592,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ u1_struct_0 @ k2_subset_1 @ ( B @ ( A @ k3_group_2 ) ) )
= ( A @ u1_struct_0 ) )
& ( ( A @ u1_struct_0 @ k2_subset_1 @ ( B @ ( A @ k4_group_2 ) ) )
= ( A @ u1_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1926]) ).
thf(1600,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_1_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_domain_1) ).
thf(10099,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_1_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_1_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1600]) ).
thf(547,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ~ ( ~ ( D @ ( F @ ( C @ ( B @ k2_funct_2 ) ) ) @ ( F @ ( E @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ ( C @ ( A @ k3_funct_2 ) ) ) @ ( D @ ( E @ ( B @ ( A @ k3_funct_2 ) ) ) @ r1_tarski ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_funct_2) ).
thf(4712,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ~ ( ~ ( D @ ( F @ ( C @ ( B @ k2_funct_2 ) ) ) @ ( F @ ( E @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ ( C @ ( A @ k3_funct_2 ) ) ) @ ( D @ ( E @ ( B @ ( A @ k3_funct_2 ) ) ) @ r1_tarski ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(824,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(6122,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(6123,plain,
( ( sk253 @ v1_funct_1 )
& ( sk253 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[6122]) ).
thf(6124,plain,
sk253 @ v1_relat_1,
inference(cnfConj,[status(thm)],[6123]) ).
thf(1859,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( np__2 @ ( A @ k6_group_1 ) ) )
= ( B @ ( B @ ( A @ k1_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_group_1) ).
thf(11339,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( np__2 @ ( A @ k6_group_1 ) ) )
= ( B @ ( B @ ( A @ k1_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1859]) ).
thf(1024,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k11_group_4 @ u1_struct_0 @ ( A @ k11_group_4 @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ k11_group_4 @ u1_struct_0 @ ( A @ k11_group_4 @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D
= ( C @ ( B @ ( A @ k3_latsubgr ) ) ) )
<=> ! [E: $i] :
( ( ( A @ ( E @ m1_group_2 ) )
& ( E @ v1_group_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F
= ( E @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( F @ ( B @ k5_group_4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_latsubgr) ).
thf(7042,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k11_group_4 @ u1_struct_0 @ ( A @ k11_group_4 @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ k11_group_4 @ u1_struct_0 @ ( A @ k11_group_4 @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( ( ( A @ ( E @ m1_group_2 ) )
& ( E @ v1_group_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F
= ( E @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( F @ ( B @ k5_group_4 ) ) ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k3_latsubgr ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k3_latsubgr ) ) ) )
=> ! [E: $i] :
( ( ( A @ ( E @ m1_group_2 ) )
& ( E @ v1_group_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F
= ( E @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( F @ ( B @ k5_group_4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(1370,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_4) ).
thf(8778,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370]) ).
thf(75,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_finseq_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_funct_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_finseq_1) ).
thf(2428,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_finseq_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_funct_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(729,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(5630,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_2) ).
thf(5670,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(419,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ v1_finset_1 )
<=> ( A @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_finset_1) ).
thf(4016,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ v1_finset_1 )
=> ( A @ k1_relat_1 @ v1_finset_1 ) )
& ( ( A @ k1_relat_1 @ v1_finset_1 )
=> ( A @ v1_finset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1611,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( A @ k2_group_3 ) ) @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k2_group_3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_group_6) ).
thf(10171,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( A @ k2_group_3 ) ) @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k2_group_3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1611]) ).
thf(2249,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ k3_finseq_1 @ m2_subset_1 ) ) )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2248]) ).
thf(1558,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( F @ m2_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ k3_group_5 ) ) ) @ ( F @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( F @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( F @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( F @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_group_5 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_group_6) ).
thf(9861,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( F @ m2_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ k3_group_5 ) ) ) @ ( F @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( F @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( F @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( F @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_group_5 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1558]) ).
thf(855,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B
= ( A @ u1_struct_0 ) )
& ( B
= ( A @ k1_filter_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_0) ).
thf(6247,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B
= ( A @ u1_struct_0 ) )
& ( B
= ( A @ k1_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(796,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k8_filter_1 ) @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_filter_1) ).
thf(6000,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k8_filter_1 ) @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(1243,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ~ ( A @ ( C @ v2_group_4 ) ) )
=> ( ( B
= ( A @ k6_group_4 ) )
<=> ( B
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) ) ) )
& ( ? [C: $i] :
( ( A @ ( C @ v2_group_4 ) )
& ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( B
= ( A @ k6_group_4 ) )
<=> ( ( B @ u1_struct_0 )
= ( A @ a_1_0_group_4 @ k1_setfam_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_group_4) ).
thf(8091,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ~ ( A @ ( C @ v2_group_4 ) ) )
=> ( ( ( B
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) )
=> ( B
= ( A @ k6_group_4 ) ) )
& ( ( B
= ( A @ k6_group_4 ) )
=> ( B
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) ) ) ) )
& ( ? [C: $i] :
( ( A @ ( C @ v2_group_4 ) )
& ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( ( ( B @ u1_struct_0 )
= ( A @ a_1_0_group_4 @ k1_setfam_1 ) )
=> ( B
= ( A @ k6_group_4 ) ) )
& ( ( B
= ( A @ k6_group_4 ) )
=> ( ( B @ u1_struct_0 )
= ( A @ a_1_0_group_4 @ k1_setfam_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(1768,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_2_lattice3 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( C @ ( B @ k4_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_2_lattice3) ).
thf(10975,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( C @ ( B @ k4_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_2_lattice3 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_2_lattice3 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( C @ ( B @ k4_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1768]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(4397,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(1481,axiom,
! [A: $i,B: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k16_lattice3 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_lattice3) ).
thf(9412,plain,
! [A: $i,B: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k16_lattice3 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481]) ).
thf(1311,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A = k1_xboole_0 )
=> ( ( A @ ( B @ m1_eqrel_1 ) )
<=> ( B = k1_xboole_0 ) ) )
& ( ( A != k1_xboole_0 )
=> ( ( A @ ( B @ m1_eqrel_1 ) )
<=> ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r1_xboole_0 ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( C != k1_xboole_0 ) ) ) )
& ( ( B @ ( A @ k5_setfam_1 ) )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_eqrel_1) ).
thf(8476,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A = k1_xboole_0 )
=> ( ( ( B = k1_xboole_0 )
=> ( A @ ( B @ m1_eqrel_1 ) ) )
& ( ( A @ ( B @ m1_eqrel_1 ) )
=> ( B = k1_xboole_0 ) ) ) )
& ( ( A != k1_xboole_0 )
=> ( ( ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r1_xboole_0 ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( C != k1_xboole_0 ) ) ) )
& ( ( B @ ( A @ k5_setfam_1 ) )
= A ) )
=> ( A @ ( B @ m1_eqrel_1 ) ) )
& ( ( A @ ( B @ m1_eqrel_1 ) )
=> ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r1_xboole_0 ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( C != k1_xboole_0 ) ) ) )
& ( ( B @ ( A @ k5_setfam_1 ) )
= A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311]) ).
thf(804,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_4 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_4) ).
thf(6032,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_4 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(1167,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( B @ ( B @ ( A @ k6_group_2 @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) )
& ( B @ ( A @ k6_group_2 @ ( B @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_group_2) ).
thf(7757,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( B @ ( B @ ( A @ k6_group_2 @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) )
& ( B @ ( A @ k6_group_2 @ ( B @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(2277,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ r1_xboole_0 ) )
| ~ ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(cnfConj,[status(thm)],[2275]) ).
thf(957,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_partfun1) ).
thf(6773,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(704,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( k1_xboole_0 @ ( B @ v1_partfun1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_partfun1) ).
thf(5512,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( k1_xboole_0 @ ( B @ v1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(1575,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( C @ v2_group_6 ) ) )
=> ( C @ ( A @ ( B @ k13_group_6 ) ) @ ( B @ r1_group_6 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_group_6) ).
thf(9949,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( C @ v2_group_6 ) ) )
=> ( C @ ( A @ ( B @ k13_group_6 ) ) @ ( B @ r1_group_6 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1575]) ).
thf(21972,plain,
! [A: $i] :
( ( A != sk636 )
| ( k1_xboole_0 @ l1_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,12217]) ).
thf(21973,plain,
( ( k1_xboole_0 @ l1_group_1 )
| ( sk636 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21972:[bind(A,$thf( sk636 ))]]) ).
thf(1197,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ r1_rlvect_1 ) )
<=> ( ( B @ ( C @ ( A @ k12_group_2 ) ) )
= ( C @ ( A @ k7_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_group_2) ).
thf(7881,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( ( B @ ( C @ ( A @ k12_group_2 ) ) )
= ( C @ ( A @ k7_group_2 ) ) )
=> ( B @ ( C @ r1_rlvect_1 ) ) )
& ( ( B @ ( C @ r1_rlvect_1 ) )
=> ( ( B @ ( C @ ( A @ k12_group_2 ) ) )
= ( C @ ( A @ k7_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(661,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(5347,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(5348,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[5347]) ).
thf(5349,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[5348]) ).
thf(1221,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_group_6 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_group_6) ).
thf(7994,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_group_6 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(1898,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ~ ( ( B = k1_xboole_0 )
& ( ( B @ ( A @ k1_group_2 ) )
!= k1_xboole_0 ) )
& ~ ( ( ( B @ ( A @ k1_group_2 ) )
= k1_xboole_0 )
& ( B != k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_group_2) ).
thf(11484,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ~ ( ( B = k1_xboole_0 )
& ( ( B @ ( A @ k1_group_2 ) )
!= k1_xboole_0 ) )
& ~ ( ( ( B @ ( A @ k1_group_2 ) )
= k1_xboole_0 )
& ( B != k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1898]) ).
thf(11587,plain,
sk610 @ v3_group_1,
inference(cnfConj,[status(thm)],[11584]) ).
thf(1826,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r2_group_3 ) ) )
<=> ( C @ ( B @ ( A @ r1_group_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r2_group_3) ).
thf(11223,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r1_group_3 ) ) )
=> ( C @ ( B @ ( A @ r2_group_3 ) ) ) )
& ( ( C @ ( B @ ( A @ r2_group_3 ) ) )
=> ( C @ ( B @ ( A @ r1_group_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1826]) ).
thf(2078,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k3_group_1 ) )
= ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_group_1) ).
thf(12190,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k3_group_1 ) )
= ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2078]) ).
thf(759,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_xboole_1) ).
thf(5815,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(11471,plain,
sk607 @ v4_group_1,
inference(cnfConj,[status(thm)],[11468]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_relset_1) ).
thf(4344,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(437,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relat_1) ).
thf(4091,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
thf(3752,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(1555,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ k3_group_1 ) @ ( D @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ ( D @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_group_6) ).
thf(9849,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ k3_group_1 ) @ ( D @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ ( D @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1555]) ).
thf(561,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_zfmisc_1) ).
thf(4785,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k1_relat_1 @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relset_1) ).
thf(4499,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k1_relat_1 @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(251,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v5_lattice3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_lattice3) ).
thf(3154,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v5_lattice3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(244,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v14_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r2_lattice4 ) ) )
& ( A @ v14_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_lattice4) ).
thf(3134,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v14_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r2_lattice4 ) ) )
& ( A @ v14_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(468,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C
= ( D @ ( B @ k1_funct_1 ) ) )
& ( B @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_1) ).
thf(4284,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C
= ( D @ ( B @ k1_funct_1 ) ) )
& ( B @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(870,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( k1_xboole_0 @ k1_funct_4 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_4) ).
thf(6356,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( k1_xboole_0 @ k1_funct_4 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(1655,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( A @ ( B @ k1_setfam_1 @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_orders_1) ).
thf(10394,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( A @ ( B @ k1_setfam_1 @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1655]) ).
thf(773,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_relat_1) ).
thf(5891,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(5892,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[5891]) ).
thf(5893,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[5892]) ).
thf(703,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v5_lattice3 )
<=> ! [B: $i,C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ a_3_3_lattice3 ) ) @ ( A @ k15_lattice3 ) @ ( B @ ( A @ k15_lattice3 ) @ ( C @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_lattice3) ).
thf(5507,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i,C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ a_3_3_lattice3 ) ) @ ( A @ k15_lattice3 ) @ ( B @ ( A @ k15_lattice3 ) @ ( C @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) )
=> ( A @ v5_lattice3 ) )
& ( ( A @ v5_lattice3 )
=> ! [B: $i,C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ a_3_3_lattice3 ) ) @ ( A @ k15_lattice3 ) @ ( B @ ( A @ k15_lattice3 ) @ ( C @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(622,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( ~ ( A @ ( B @ v5_group_1 ) )
=> ( ( C
= ( B @ ( A @ k7_group_1 ) ) )
<=> ( ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( ( B @ ( D @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) )
=> ( ( D @ ( C @ r1_xreal_0 ) )
| ( D = np__0 ) ) ) )
& ( C != np__0 )
& ( ( B @ ( C @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) ) ) ) )
& ( ( A @ ( B @ v5_group_1 ) )
=> ( ( C
= ( B @ ( A @ k7_group_1 ) ) )
<=> ( C = np__0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_group_1) ).
thf(5102,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( ~ ( A @ ( B @ v5_group_1 ) )
=> ( ( ( ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( ( B @ ( D @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) )
=> ( ( D @ ( C @ r1_xreal_0 ) )
| ( D = np__0 ) ) ) )
& ( C != np__0 )
& ( ( B @ ( C @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) ) )
=> ( C
= ( B @ ( A @ k7_group_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k7_group_1 ) ) )
=> ( ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( ( B @ ( D @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) )
=> ( ( D @ ( C @ r1_xreal_0 ) )
| ( D = np__0 ) ) ) )
& ( C != np__0 )
& ( ( B @ ( C @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) ) ) ) ) )
& ( ( A @ ( B @ v5_group_1 ) )
=> ( ( ( C = np__0 )
=> ( C
= ( B @ ( A @ k7_group_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k7_group_1 ) ) )
=> ( C = np__0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(1380,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( A @ k2_group_2 ) ) )
= ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( D @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ u1_struct_0 @ k7_domain_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_group_2) ).
thf(8899,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( A @ k2_group_2 ) ) )
= ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( D @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ u1_struct_0 @ k7_domain_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1380]) ).
thf(840,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) )
= ( B @ ( A @ a_2_0_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_filter_0) ).
thf(6178,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) )
= ( B @ ( A @ a_2_0_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(2579,plain,
~ ( sk19 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[2574]) ).
thf(12422,plain,
( ( ( sk19 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,2579]) ).
thf(12423,plain,
( ( sk19 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12422]) ).
thf(12428,plain,
sk19 != k1_xboole_0,
inference(simp,[status(thm)],[12423]) ).
thf(22445,plain,
! [A: $i] :
( ( A != sk19 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,12428]) ).
thf(22446,plain,
! [A: $i] :
( ( A != sk19 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[22445]) ).
thf(22447,plain,
sk19 @ sk149 @ v1_funct_1,
inference(pattern_uni,[status(thm)],[22446:[bind(A,$thf( sk19 ))]]) ).
thf(2004,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E = C )
& ( D = B ) )
=> ( ( E @ ( D @ ( A @ k11_group_4 @ r3_lattices ) ) )
<=> ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_latsubgr) ).
thf(11908,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E = C )
& ( D = B ) )
=> ( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) )
=> ( E @ ( D @ ( A @ k11_group_4 @ r3_lattices ) ) ) )
& ( ( E @ ( D @ ( A @ k11_group_4 @ r3_lattices ) ) )
=> ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2004]) ).
thf(2132,plain,
! [A: $i] :
( ( A @ v15_lattices )
| ~ ( A @ v17_lattices )
| ( A @ v3_struct_0 )
| ~ ( A @ l3_lattices ) ),
inference(cnfConj,[status(thm)],[2126]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( B @ ( A @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_partfun1) ).
thf(2890,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( B @ ( A @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(4157,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk111 ) @ v1_funct_1 )
& ( A @ ( B @ sk111 ) @ v1_relat_1 )
& ( B @ ( A @ ( A @ ( B @ sk111 ) @ m1_relset_1 ) ) ) ),
inference(cnf,[status(esa)],[4156]) ).
thf(4160,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk111 ) @ v1_funct_1 ),
inference(cnfConj,[status(thm)],[4157]) ).
thf(537,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k8_filter_0 ) @ v3_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_filter_0) ).
thf(4661,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k8_filter_0 ) @ v3_filter_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_realset1) ).
thf(2396,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(1866,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k1_group_1 ) ) ) )
<=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k3_group_1 ) )
= ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_group_1) ).
thf(11371,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k3_group_1 ) )
= ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) ) )
=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k1_group_1 ) ) ) ) )
& ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k1_group_1 ) ) ) )
=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k3_group_1 ) )
= ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1866]) ).
thf(1135,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ k5_group_2 @ ( A @ k5_group_2 @ ( B @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) )
& ( A @ k5_group_2 @ ( B @ ( A @ k5_group_2 @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_group_2) ).
thf(7565,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ k5_group_2 @ ( A @ k5_group_2 @ ( B @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) )
& ( A @ k5_group_2 @ ( B @ ( A @ k5_group_2 @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(322,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_relat_1) ).
thf(3514,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(2042,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( C @ m1_group_2 ) )
=> ( ( A @ ( C @ r1_rlvect_1 ) )
=> ( A @ ( B @ r1_rlvect_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_group_2) ).
thf(12037,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( C @ m1_group_2 ) )
=> ( ( A @ ( C @ r1_rlvect_1 ) )
=> ( A @ ( B @ r1_rlvect_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2042]) ).
thf(420,axiom,
~ ( k1_numbers @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_numbers) ).
thf(4020,plain,
~ ( k1_numbers @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(4021,plain,
~ ( k1_numbers @ v1_xboole_0 ),
inference(polarity_switch,[status(thm)],[4020]) ).
thf(310,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_0 @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_filter_0) ).
thf(3471,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_0 @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_setfam_1 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_setfam_1) ).
thf(3286,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_setfam_1 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(767,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k4_filter_0 ) ) )
= ( C @ ( B @ ( A @ a_3_6_lattice3 ) ) @ ( A @ k15_lattice3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_lattice3) ).
thf(5843,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k4_filter_0 ) ) )
= ( C @ ( B @ ( A @ a_3_6_lattice3 ) ) @ ( A @ k15_lattice3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(1670,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(10464,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1670]) ).
thf(10465,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[10464]) ).
thf(1270,axiom,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
thf(8234,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(8235,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(cnf,[status(esa)],[8234]) ).
thf(8236,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(lifteq,[status(thm)],[8235]) ).
thf(31058,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ),
inference(rewrite,[status(thm)],[10465,8236]) ).
thf(913,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k3_lattice3 @ u1_struct_0 @ ( B @ ( A @ k4_lattice3 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattice3) ).
thf(6582,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k3_lattice3 @ u1_struct_0 @ ( B @ ( A @ k4_lattice3 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(1338,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k11_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( B @ ( D @ ( A @ k10_group_2 ) ) @ ( C @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_group_2) ).
thf(8623,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k11_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( B @ ( D @ ( A @ k10_group_2 ) ) @ ( C @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k4_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(2958,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k4_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k4_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(467,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ! [E: $i] :
( ( D @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C = E )
=> ( ( C @ ( A @ ( B @ k6_group_1 ) ) )
= ( E @ ( A @ ( D @ k6_group_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_group_4) ).
thf(4280,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ! [E: $i] :
( ( D @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C = E )
=> ( ( C @ ( A @ ( B @ k6_group_1 ) ) )
= ( E @ ( A @ ( D @ k6_group_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(1678,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_mcart_1) ).
thf(10502,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1678]) ).
thf(173,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_relat_1) ).
thf(2826,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1649,axiom,
? [A: $i] : ( A @ l2_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_struct_0) ).
thf(10369,plain,
? [A: $i] : ( A @ l2_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1649]) ).
thf(183,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ( ~ ( A @ ( B @ r1_xreal_0 ) )
=> ( np__1 @ ( B @ k6_xcmplx_0 ) @ ( A @ r1_xreal_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_int_1) ).
thf(2872,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ( ~ ( A @ ( B @ r1_xreal_0 ) )
=> ( np__1 @ ( B @ k6_xcmplx_0 ) @ ( A @ r1_xreal_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(1910,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_group_1 ) @ ( A @ k3_group_1 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_group_1) ).
thf(11532,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_group_1 ) @ ( A @ k3_group_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1910]) ).
thf(19,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_binop_1) ).
thf(2198,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r4_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r6_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(2199,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
| ~ ( B @ ( C @ ( A @ r4_binop_1 ) ) )
| ~ ( A @ ( C @ v1_binop_1 ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( A @ v1_xboole_0 ) )
& ( ( B @ ( C @ ( A @ r4_binop_1 ) ) )
| ~ ( B @ ( C @ ( A @ r6_binop_1 ) ) )
| ~ ( A @ ( C @ v1_binop_1 ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[2198]) ).
thf(2200,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ r4_binop_1 ) ) )
| ~ ( B @ ( C @ ( A @ r6_binop_1 ) ) )
| ~ ( A @ ( C @ v1_binop_1 ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2199]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
= D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_binop_1) ).
thf(2206,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
= D ) )
=> ( C @ ( B @ ( A @ r1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(2207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
| ( ( A @ ( B @ ( C @ sk2 ) ) @ ( B @ ( C @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk2 ) ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( B @ m1_subset_1 ) ) )
& ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk2 ) ) @ m1_subset_1 ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( B @ m1_subset_1 ) ) )
& ( ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
= D )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r1_binop_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( B @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[2206]) ).
thf(2208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
= D )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r1_binop_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[2207]) ).
thf(2211,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r1_binop_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( B @ m1_subset_1 ) )
| ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
= D ) ),
inference(lifteq,[status(thm)],[2208]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( B @ ( C @ ( A @ k3_xboole_0 ) @ ( D @ k3_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_partfun1) ).
thf(2741,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( B @ ( C @ ( A @ k3_xboole_0 ) @ ( D @ k3_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(406,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k2_relat_1 )
= ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relat_1) ).
thf(3958,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k2_relat_1 )
= ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(1375,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ r2_setfam_1 ) )
=> ( ( A @ k1_setfam_1 @ ( B @ k1_setfam_1 @ r1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_setfam_1) ).
thf(8810,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ r2_setfam_1 ) )
=> ( ( A @ k1_setfam_1 @ ( B @ k1_setfam_1 @ r1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(9380,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(cnf,[status(esa)],[9379]) ).
thf(13059,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,7635]) ).
thf(13060,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13059]) ).
thf(13065,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[13060]) ).
thf(13550,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[6948,13065]) ).
thf(13551,plain,
( ( k1_xboole_0 @ k1_tarski )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[13550:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(781,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_setfam_1 ) )
<=> ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r1_tarski ) )
& ( A @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_setfam_1) ).
thf(5937,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r1_tarski ) )
& ( A @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r2_setfam_1 ) ) )
& ( ( B @ ( A @ r2_setfam_1 ) )
=> ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r1_tarski ) )
& ( A @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(1347,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ r1_tarski ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( E @ ( C @ ( A @ k2_group_2 ) ) @ ( D @ ( B @ ( A @ k2_group_2 ) ) @ r1_tarski ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_group_3) ).
thf(8672,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ r1_tarski ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( E @ ( C @ ( A @ k2_group_2 ) ) @ ( D @ ( B @ ( A @ k2_group_2 ) ) @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347]) ).
thf(1298,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ v6_group_1 )
=> ( ( B @ ( A @ k14_group_2 ) @ v1_finset_1 )
& ( B @ ( A @ k15_group_2 ) @ v1_finset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t164_group_2) ).
thf(8371,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ v6_group_1 )
=> ( ( B @ ( A @ k14_group_2 ) @ v1_finset_1 )
& ( B @ ( A @ k15_group_2 ) @ v1_finset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).
thf(135,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ m1_finseq_1 ) )
<=> ( A @ ( B @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_finseq_1) ).
thf(2670,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( B @ m1_finseq_1 ) ) )
& ( ( A @ ( B @ m1_finseq_1 ) )
=> ( A @ ( B @ k2_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(378,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( A @ k7_lattices ) )
= ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k9_filter_0 ) ) ) )
& ( ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k9_filter_0 ) ) ) )
& ( ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( A @ k7_lattices ) )
= ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) @ ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_filter_1) ).
thf(3810,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( A @ k7_lattices ) )
= ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k9_filter_0 ) ) ) )
& ( ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k9_filter_0 ) ) ) )
& ( ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( A @ k7_lattices ) )
= ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) @ ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(694,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ v2_group_6 ) ) )
=> ( ( C @ ( D @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_group_6) ).
thf(5465,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ v2_group_6 ) ) )
=> ( ( C @ ( D @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(1500,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
=> ( ( C = D )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_2) ).
thf(9512,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
=> ( ( C = D )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1500]) ).
thf(836,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( B @ ( C @ ( D @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_enumset1) ).
thf(6163,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( B @ ( C @ ( D @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(428,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ k2_xboole_0 ) )
= C )
=> ! [D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( A @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_partfun1) ).
thf(4053,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ k2_xboole_0 ) )
= C )
=> ! [D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( A @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(4585,plain,
~ ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4583]) ).
thf(76,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( B @ r1_binop_1 ) ) )
& ( E @ ( C @ ( A @ r1_binop_1 ) ) ) )
<=> ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_filter_1) ).
thf(2433,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_binop_1 ) ) )
=> ( ( F @ ( D @ ( B @ r1_binop_1 ) ) )
& ( E @ ( C @ ( A @ r1_binop_1 ) ) ) ) )
& ( ( ( F @ ( D @ ( B @ r1_binop_1 ) ) )
& ( E @ ( C @ ( A @ r1_binop_1 ) ) ) )
=> ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_partfun1) ).
thf(2477,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(548,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ ( B @ r3_lattice3 ) ) )
<=> ( B @ ( A @ a_2_0_lattice3 ) @ ( C @ ( B @ k7_lattices ) @ ( B @ r4_lattice3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_lattice3) ).
thf(4725,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ a_2_0_lattice3 ) @ ( C @ ( B @ k7_lattices ) @ ( B @ r4_lattice3 ) ) )
=> ( A @ ( C @ ( B @ r3_lattice3 ) ) ) )
& ( ( A @ ( C @ ( B @ r3_lattice3 ) ) )
=> ( B @ ( A @ a_2_0_lattice3 ) @ ( C @ ( B @ k7_lattices ) @ ( B @ r4_lattice3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k5_relat_1 ) @ k1_funct_1 ) )
= ( A @ ( C @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
thf(3090,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k5_relat_1 ) @ k1_funct_1 ) )
= ( A @ ( C @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(1026,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( A @ k1_setfam_1 @ ( B @ k1_setfam_1 @ r1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_setfam_1) ).
thf(7063,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( A @ k1_setfam_1 @ ( B @ k1_setfam_1 @ r1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(1312,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_group_3 @ k1_zfmisc_1 @ ( B @ ( A @ k9_group_3 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_group_3) ).
thf(8503,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_group_3 @ k1_zfmisc_1 @ ( B @ ( A @ k9_group_3 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).
thf(1300,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
thf(8386,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
thf(1081,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k5_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(7314,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k5_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(603,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v3_funct_2 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( B @ r1_tarski ) )
=> ( ( ( B @ ( C @ ( A @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( A @ ( A @ k3_funct_2 ) ) ) )
= B )
& ( ( B @ ( C @ ( A @ ( A @ k3_funct_2 ) ) ) @ ( C @ ( A @ ( A @ k2_funct_2 ) ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_funct_2) ).
thf(4994,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v3_funct_2 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( B @ r1_tarski ) )
=> ( ( ( B @ ( C @ ( A @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( A @ ( A @ k3_funct_2 ) ) ) )
= B )
& ( ( B @ ( C @ ( A @ ( A @ k3_funct_2 ) ) ) @ ( C @ ( A @ ( A @ k2_funct_2 ) ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(1696,axiom,
! [A: $i] :
( ( ( A @ l1_vectsp_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v6_vectsp_1 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_group_1 @ ( B @ ( A @ k1_group_1 ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_vectsp_1) ).
thf(10583,plain,
! [A: $i] :
( ( ( A @ l1_vectsp_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_group_1 @ ( B @ ( A @ k1_group_1 ) ) )
= B ) )
=> ( A @ v6_vectsp_1 ) )
& ( ( A @ v6_vectsp_1 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_group_1 @ ( B @ ( A @ k1_group_1 ) ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1696]) ).
thf(1121,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_zfmisc_1 ) @ ( A @ k9_group_4 @ m2_relset_1 ) ) )
& ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_zfmisc_1 ) @ ( A @ k9_group_4 @ v1_funct_2 ) ) )
& ( A @ k9_group_4 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_group_4) ).
thf(7503,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_zfmisc_1 ) @ ( A @ k9_group_4 @ m2_relset_1 ) ) )
& ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_zfmisc_1 ) @ ( A @ k9_group_4 @ v1_funct_2 ) ) )
& ( A @ k9_group_4 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(1259,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ ( A @ k9_group_2 ) ) @ ( A @ k1_latsubgr @ k1_funct_1 ) )
= ( C @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ k3_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_latsubgr) ).
thf(8181,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ ( A @ k9_group_2 ) ) @ ( A @ k1_latsubgr @ k1_funct_1 ) )
= ( C @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ k3_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(3543,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[3542]) ).
thf(3544,plain,
( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[3543]) ).
thf(3546,plain,
( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3544]) ).
thf(611,axiom,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(5038,plain,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(1648,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(10367,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1648]) ).
thf(594,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( B @ ( C @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_filter_0) ).
thf(4942,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( B @ ( C @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(1485,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v4_group_6 ) ) )
=> ( ( ( C @ ( B @ ( A @ k9_group_6 ) ) )
= ( B @ u1_struct_0 ) )
& ( ( C @ k1_relat_1 )
= ( A @ u1_struct_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_group_6) ).
thf(9423,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v4_group_6 ) ) )
=> ( ( ( C @ ( B @ ( A @ k9_group_6 ) ) )
= ( B @ u1_struct_0 ) )
& ( ( C @ k1_relat_1 )
= ( A @ u1_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1485]) ).
thf(22753,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ l1_struct_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,16418]) ).
thf(22754,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk1 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22753:[bind(A,$thf( sk1 ))]]) ).
thf(601,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ v3_filter_0 )
& ( A @ v3_filter_0 ) )
<=> ( B @ ( A @ k8_filter_1 ) @ v3_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_filter_1) ).
thf(4979,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k8_filter_1 ) @ v3_filter_0 )
=> ( ( B @ v3_filter_0 )
& ( A @ v3_filter_0 ) ) )
& ( ( ( B @ v3_filter_0 )
& ( A @ v3_filter_0 ) )
=> ( B @ ( A @ k8_filter_1 ) @ v3_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(1945,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k11_group_3 ) @ m1_group_2 ) )
& ( B @ ( A @ k11_group_3 ) @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_group_3) ).
thf(11670,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k11_group_3 ) @ m1_group_2 ) )
& ( B @ ( A @ k11_group_3 ) @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1945]) ).
thf(217,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A = k1_xboole_0 )
<=> ( ( A @ k4_finseq_1 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finseq_1) ).
thf(3028,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( ( A @ k4_finseq_1 )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( ( A @ k4_finseq_1 )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(403,axiom,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finseq_1) ).
thf(3926,plain,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(2345,plain,
! [A: $i] : ( A @ sk11 @ v1_funct_1 ),
inference(cnfConj,[status(thm)],[2342]) ).
thf(1766,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ~ ( ( C @ ( E @ r2_hidden ) )
<=> ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_7_domain_1) ).
thf(10958,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ~ ( ( ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ~ ( ( ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1766]) ).
thf(860,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_xboole_1) ).
thf(6267,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(2344,plain,
! [A: $i] : ( A @ sk11 @ v1_relat_1 ),
inference(cnfConj,[status(thm)],[2342]) ).
thf(367,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( C @ k1_group_1 ) ) )
= ( D @ ( E @ ( C @ k1_group_1 ) ) ) )
=> ( ( E @ ( B @ ( C @ k6_group_1 ) ) @ ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) )
= ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( E @ ( B @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_group_1) ).
thf(3763,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( C @ k1_group_1 ) ) )
= ( D @ ( E @ ( C @ k1_group_1 ) ) ) )
=> ( ( E @ ( B @ ( C @ k6_group_1 ) ) @ ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) )
= ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( E @ ( B @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(22199,plain,
! [A: $i] :
( ( A != sk545 )
| ( k1_xboole_0 @ l3_lattices )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,10455]) ).
thf(22200,plain,
( ( k1_xboole_0 @ l3_lattices )
| ( sk545 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22199:[bind(A,$thf( sk545 ))]]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v2_funct_1 )
=> ( ( D @ v2_funct_1 )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) )
| ( ( B != k1_xboole_0 )
& ( C = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_funct_2) ).
thf(4104,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v2_funct_1 )
=> ( ( D @ v2_funct_1 )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) )
| ( ( B != k1_xboole_0 )
& ( C = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(1512,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) )
= ( D @ ( B @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattices) ).
thf(9613,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) )
= ( D @ ( B @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) )
= ( D @ ( B @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1512]) ).
thf(1565,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( A @ k3_group_3 ) ) @ ( D @ ( B @ ( A @ k3_group_3 ) ) @ ( A @ k2_group_2 ) ) @ ( D @ ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( A @ k3_group_3 ) ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_group_3) ).
thf(9885,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( A @ k3_group_3 ) ) @ ( D @ ( B @ ( A @ k3_group_3 ) ) @ ( A @ k2_group_2 ) ) @ ( D @ ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( A @ k3_group_3 ) ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1565]) ).
thf(1687,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( B @ k13_group_6 ) ) @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ ( A @ ( B @ k13_group_6 ) ) @ ( B @ ( C @ v1_group_6 ) ) )
& ( C @ ( A @ ( B @ k13_group_6 ) ) @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_group_6) ).
thf(10543,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( B @ k13_group_6 ) ) @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ ( A @ ( B @ k13_group_6 ) ) @ ( B @ ( C @ v1_group_6 ) ) )
& ( C @ ( A @ ( B @ k13_group_6 ) ) @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1687]) ).
thf(2036,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ k5_group_2 @ ( A @ k5_group_2 @ r2_group_6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_group_6) ).
thf(12020,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ k5_group_2 @ ( A @ k5_group_2 @ r2_group_6 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2036]) ).
thf(12414,plain,
( ( ( sk196 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,5131]) ).
thf(12415,plain,
( ( sk196 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12414]) ).
thf(12424,plain,
sk196 != k1_xboole_0,
inference(simp,[status(thm)],[12415]) ).
thf(22703,plain,
! [A: $i] :
( ( A != sk196 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,12424]) ).
thf(22704,plain,
! [A: $i] :
( ( A != sk196 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[22703]) ).
thf(22705,plain,
sk196 @ sk149 @ v1_funct_1,
inference(pattern_uni,[status(thm)],[22704:[bind(A,$thf( sk196 ))]]) ).
thf(550,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
thf(4732,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(1928,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_group_4 @ k6_lattices )
= ( A @ k6_group_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_group_4) ).
thf(11602,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_group_4 @ k6_lattices )
= ( A @ k6_group_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1928]) ).
thf(2228,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ k4_xboole_0 ) @ ( B @ r1_xboole_0 ) )
| ~ ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[2227]) ).
thf(343,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
thf(3643,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(3644,plain,
! [A: $i] :
? [B: $i] :
( ~ ? [C: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ~ ? [C: $i] :
( ~ ? [D: $i] :
( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[3643]) ).
thf(3645,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk81 @ ( F @ r2_hidden ) )
| ( A @ sk81 @ ( F @ r2_tarski ) )
| ~ ( A @ sk81 @ ( F @ r1_tarski ) ) )
& ( ( A @ ( D @ sk82 ) @ ( E @ r2_hidden ) )
| ~ ( D @ ( E @ r1_tarski ) )
| ~ ( A @ sk81 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk81 @ ( A @ ( D @ sk82 ) @ r2_hidden ) )
| ~ ( A @ sk81 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk81 @ ( C @ r2_hidden ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ sk81 @ ( B @ r2_hidden ) ) )
& ( A @ sk81 @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[3644]) ).
thf(3647,plain,
! [A: $i] : ( A @ sk81 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[3645]) ).
thf(1761,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( D
= ( C @ ( B @ ( A @ k6_group_3 ) ) ) )
<=> ( ( D @ u1_struct_0 )
= ( C @ ( B @ ( A @ k7_group_2 ) @ ( A @ k4_group_3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_group_3) ).
thf(10926,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( ( ( D @ u1_struct_0 )
= ( C @ ( B @ ( A @ k7_group_2 ) @ ( A @ k4_group_3 ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k6_group_3 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k6_group_3 ) ) ) )
=> ( ( D @ u1_struct_0 )
= ( C @ ( B @ ( A @ k7_group_2 ) @ ( A @ k4_group_3 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1761]) ).
thf(794,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k3_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_funct_1) ).
thf(5993,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k3_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(659,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k14_group_2 ) @ v1_finset_1 )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( C
= ( B @ ( A @ k17_group_2 ) ) )
<=> ? [D: $i] :
( ( C
= ( D @ k4_card_1 ) )
& ( D
= ( B @ ( A @ k14_group_2 ) ) )
& ( D @ v1_finset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_group_2) ).
thf(5330,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k14_group_2 ) @ v1_finset_1 )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( ? [D: $i] :
( ( C
= ( D @ k4_card_1 ) )
& ( D
= ( B @ ( A @ k14_group_2 ) ) )
& ( D @ v1_finset_1 ) )
=> ( C
= ( B @ ( A @ k17_group_2 ) ) ) )
& ( ( C
= ( B @ ( A @ k17_group_2 ) ) )
=> ? [D: $i] :
( ( C
= ( D @ k4_card_1 ) )
& ( D
= ( B @ ( A @ k14_group_2 ) ) )
& ( D @ v1_finset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(1695,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( D @ ( A @ k10_group_2 ) ) @ ( B @ ( A @ k4_group_2 ) ) )
= ( B @ ( D @ ( A @ k13_group_2 ) ) @ ( C @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_group_3) ).
thf(10580,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( D @ ( A @ k10_group_2 ) ) @ ( B @ ( A @ k4_group_2 ) ) )
= ( B @ ( D @ ( A @ k13_group_2 ) ) @ ( C @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1695]) ).
thf(1295,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k5_group_2 @ ( A @ k6_group_6 ) @ ( A @ r2_group_6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_group_6) ).
thf(8358,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k5_group_2 @ ( A @ k6_group_6 ) @ ( A @ r2_group_6 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295]) ).
thf(474,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(4315,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(4316,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[4315]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_xboole_1) ).
thf(2245,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(2577,plain,
sk19 @ v1_relat_1,
inference(cnfConj,[status(thm)],[2574]) ).
thf(768,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ k9_relat_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
thf(5847,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k9_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k9_relat_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(1830,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k6_finseq_1 @ ( k4_numbers @ k6_finseq_1 @ ( A @ k4_group_4 ) ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_group_4) ).
thf(11234,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k6_finseq_1 @ ( k4_numbers @ k6_finseq_1 @ ( A @ k4_group_4 ) ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1830]) ).
thf(6215,plain,
~ ( sk259 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[6214]) ).
thf(1128,axiom,
! [A: $i] : ( A @ ( A @ ( A @ k6_relat_1 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_relset_1) ).
thf(7540,plain,
! [A: $i] : ( A @ ( A @ ( A @ k6_relat_1 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(639,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k2_relat_1 @ v1_relat_1 )
& ( A @ k2_relat_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(5189,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k2_relat_1 @ v1_relat_1 )
& ( A @ k2_relat_1 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_2) ).
thf(3105,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(727,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_subset_1) ).
thf(5626,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(44,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ k2_relat_1 )
!= k1_xboole_0 )
=> ( A @ k4_finseq_1 @ ( np__1 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_finseq_3) ).
thf(2300,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ k2_relat_1 )
!= k1_xboole_0 )
=> ( A @ k4_finseq_1 @ ( np__1 @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1075,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ( ( A @ ( C @ ( D @ ( B @ k6_group_3 ) ) @ r1_rlvect_1 ) )
<=> ? [E: $i] :
( ( E @ ( D @ r1_rlvect_1 ) )
& ( A
= ( C @ ( E @ ( B @ k2_group_3 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_group_3) ).
thf(7281,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ( ( ? [E: $i] :
( ( E @ ( D @ r1_rlvect_1 ) )
& ( A
= ( C @ ( E @ ( B @ k2_group_3 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( A @ ( C @ ( D @ ( B @ k6_group_3 ) ) @ r1_rlvect_1 ) ) )
& ( ( A @ ( C @ ( D @ ( B @ k6_group_3 ) ) @ r1_rlvect_1 ) )
=> ? [E: $i] :
( ( E @ ( D @ r1_rlvect_1 ) )
& ( A
= ( C @ ( E @ ( B @ k2_group_3 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(374,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ~ ( ( A @ ( C @ v1_filter_0 ) )
& ( C @ ( B @ r1_tarski ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_filter_0) ).
thf(3782,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ~ ( ( A @ ( C @ v1_filter_0 ) )
& ( C @ ( B @ r1_tarski ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(1747,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_group_3 ) @ k1_card_1 )
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k10_group_3 ) @ ( A @ k16_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_group_3) ).
thf(10848,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_group_3 ) @ k1_card_1 )
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k10_group_3 ) @ ( A @ k16_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1747]) ).
thf(1085,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k8_group_3 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( D @ ( C @ ( B @ r4_group_3 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_group_3) ).
thf(7329,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( D @ ( C @ ( B @ r4_group_3 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ k8_group_3 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k8_group_3 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( D @ ( C @ ( B @ r4_group_3 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(1306,axiom,
! [A: $i,B: $i] :
( ( ( A = k1_xboole_0 )
=> ( ( B
= ( A @ k1_setfam_1 ) )
<=> ( B = k1_xboole_0 ) ) )
& ( ( A != k1_xboole_0 )
=> ( ( B
= ( A @ k1_setfam_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(8424,plain,
! [A: $i,B: $i] :
( ( ( A = k1_xboole_0 )
=> ( ( ( B = k1_xboole_0 )
=> ( B
= ( A @ k1_setfam_1 ) ) )
& ( ( B
= ( A @ k1_setfam_1 ) )
=> ( B = k1_xboole_0 ) ) ) )
& ( ( A != k1_xboole_0 )
=> ( ( ! [C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k1_setfam_1 ) ) )
& ( ( B
= ( A @ k1_setfam_1 ) )
=> ! [C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).
thf(8425,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( ! [B: $i] :
( ( B = k1_xboole_0 )
=> ( B
= ( A @ k1_setfam_1 ) ) )
& ! [B: $i] :
( ( B
= ( A @ k1_setfam_1 ) )
=> ( B = k1_xboole_0 ) ) ) )
& ! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ! [B: $i] :
( ( ! [C: $i] :
( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k1_setfam_1 ) ) )
& ! [B: $i] :
( ( B
= ( A @ k1_setfam_1 ) )
=> ( ! [C: $i] :
( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[8424]) ).
thf(8426,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( J
= ( H @ k1_setfam_1 ) )
| ( J != k1_xboole_0 )
| ( H != k1_xboole_0 ) )
& ( ( I = k1_xboole_0 )
| ( I
!= ( H @ k1_setfam_1 ) )
| ( H != k1_xboole_0 ) )
& ( ( F
= ( A @ k1_setfam_1 ) )
| ~ ( F @ ( A @ ( F @ sk401 ) @ r2_hidden ) )
| ( F @ ( A @ sk398 ) )
| ( A = k1_xboole_0 ) )
& ( ( F
= ( A @ k1_setfam_1 ) )
| ( G @ ( A @ ( F @ sk401 ) @ r2_hidden ) )
| ~ ( A @ ( G @ r2_hidden ) )
| ( F @ ( A @ sk398 ) )
| ( A = k1_xboole_0 ) )
& ( ( F
= ( A @ k1_setfam_1 ) )
| ~ ( F @ ( A @ sk398 ) )
| ~ ( A @ ( F @ sk400 ) @ ( A @ ( F @ sk399 ) @ r2_hidden ) )
| ( A = k1_xboole_0 ) )
& ( ( F
= ( A @ k1_setfam_1 ) )
| ~ ( F @ ( A @ sk398 ) )
| ( A @ ( A @ ( F @ sk400 ) @ r2_hidden ) )
| ( A = k1_xboole_0 ) )
& ( ( F
= ( A @ k1_setfam_1 ) )
| ~ ( F @ ( A @ sk398 ) )
| ( F @ ( A @ ( F @ sk399 ) @ r2_hidden ) )
| ( A = k1_xboole_0 ) )
& ( ( B @ ( E @ r2_hidden ) )
| ~ ( A @ ( B @ ( E @ sk397 ) ) @ ( E @ r2_hidden ) )
| ( B
!= ( A @ k1_setfam_1 ) )
| ( A = k1_xboole_0 ) )
& ( ( B @ ( E @ r2_hidden ) )
| ( A @ ( A @ ( B @ ( E @ sk397 ) ) @ r2_hidden ) )
| ( B
!= ( A @ k1_setfam_1 ) )
| ( A = k1_xboole_0 ) )
& ( ( D @ ( C @ r2_hidden ) )
| ~ ( A @ ( D @ r2_hidden ) )
| ~ ( B @ ( C @ r2_hidden ) )
| ( B
!= ( A @ k1_setfam_1 ) )
| ( A = k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[8425]) ).
thf(8428,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k1_setfam_1 ) )
| ( B != k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[8426]) ).
thf(8445,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k1_setfam_1 ) )
| ( B != k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[8428]) ).
thf(8446,plain,
( ( k1_xboole_0 @ k1_setfam_1 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[8445]) ).
thf(1287,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ k5_group_3 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( C @ ( B @ k2_group_3 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_group_3) ).
thf(8314,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( C @ ( B @ k2_group_3 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ ( B @ k5_group_3 ) ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( D @ ( B @ k5_group_3 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( C @ ( B @ k2_group_3 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_xboole_1) ).
thf(2840,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_partfun1) ).
thf(5098,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(965,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( ( np__0 @ ( A @ k5_int_1 ) )
= np__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_int_1) ).
thf(6801,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( ( np__0 @ ( A @ k5_int_1 ) )
= np__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(61,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ r4_lattice3 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( A @ r1_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattice3) ).
thf(2369,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( A @ r1_lattices ) ) ) ) )
=> ( C @ ( B @ ( A @ r4_lattice3 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_lattice3 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( A @ r1_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(2370,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( A @ r1_lattices ) ) ) ) )
=> ( C @ ( B @ ( A @ r4_lattice3 ) ) ) )
& ! [C: $i] :
( ( C @ ( B @ ( A @ r4_lattice3 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( A @ r1_lattices ) ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[2369]) ).
thf(2371,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ ( A @ r4_lattice3 ) ) )
| ~ ( B @ ( A @ ( B @ ( E @ sk13 ) ) @ ( A @ r1_lattices ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) )
& ( ( E @ ( B @ ( A @ r4_lattice3 ) ) )
| ( E @ ( A @ ( B @ ( E @ sk13 ) ) @ r2_hidden ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) )
& ( ( E @ ( B @ ( A @ r4_lattice3 ) ) )
| ( A @ u1_struct_0 @ ( A @ ( B @ ( E @ sk13 ) ) @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) )
& ( ( B @ ( D @ ( A @ r1_lattices ) ) )
| ~ ( C @ ( D @ r2_hidden ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ) ),
inference(cnf,[status(esa)],[2370]) ).
thf(2374,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r4_lattice3 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk13 ) ) @ r2_hidden ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2371]) ).
thf(2377,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r4_lattice3 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk13 ) ) @ r2_hidden ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[2374]) ).
thf(999,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_xboole_0 ) )
<=> ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
thf(6940,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( C @ ( B @ r1_xboole_0 ) ) )
& ( ( C @ ( B @ r1_xboole_0 ) )
=> ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(539,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ( ( C @ ( D @ r1_rlvect_1 ) )
=> ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( D @ r1_rlvect_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_group_4) ).
thf(4668,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ( ( C @ ( D @ r1_rlvect_1 ) )
=> ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( D @ r1_rlvect_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v2_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ ( B @ k1_binop_1 ) ) )
= ( E @ ( D @ ( C @ ( B @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_binop_1) ).
thf(2801,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ ( B @ k1_binop_1 ) ) )
= ( E @ ( D @ ( C @ ( B @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) ) ) ) ) )
=> ( A @ ( B @ v2_binop_1 ) ) )
& ( ( A @ ( B @ v2_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ ( B @ k1_binop_1 ) ) )
= ( E @ ( D @ ( C @ ( B @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(1212,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_partfun1) ).
thf(7962,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(833,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k3_subset_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(6153,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k3_subset_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(515,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_orders_1) ).
thf(4512,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(605,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( k5_numbers @ ( k1_numbers @ ( B @ ( A @ k17_group_2 ) @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k17_group_2) ).
thf(5006,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( k5_numbers @ ( k1_numbers @ ( B @ ( A @ k17_group_2 ) @ m2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(684,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( B @ ( A @ r1_rlvect_1 ) )
<=> ( A @ u1_struct_0 @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_rlvect_1) ).
thf(5423,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ r2_hidden ) )
=> ( B @ ( A @ r1_rlvect_1 ) ) )
& ( ( B @ ( A @ r1_rlvect_1 ) )
=> ( A @ u1_struct_0 @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(18071,plain,
! [A: $i] :
( ( ( sk24 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ~ $true
| ( A = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2691,7167]) ).
thf(18072,plain,
! [A: $i] :
( ( ( sk24 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ( A = k1_xboole_0 ) ),
inference(simp,[status(thm)],[18071]) ).
thf(18073,plain,
sk24 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[18072:[bind(A,$thf( sk24 ))]]) ).
thf(1224,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattices) ).
thf(8009,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(1656,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( D @ u1_struct_0 )
!= B ) )
& ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ r4_group_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_group_3) ).
thf(10413,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( D @ u1_struct_0 )
!= B ) )
& ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ r4_group_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1656]) ).
thf(843,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
thf(6195,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(895,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_2) ).
thf(6477,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(507,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( B @ ( A @ k3_binop_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_binop_1) ).
thf(4486,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( B @ ( A @ k3_binop_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(1574,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( C @ m1_group_2 ) )
=> ( ( C @ ( B @ k7_group_2 ) @ ( A @ r2_hidden ) )
<=> ( A @ ( C @ r1_rlvect_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_group_2) ).
thf(9945,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( C @ m1_group_2 ) )
=> ( ( ( A @ ( C @ r1_rlvect_1 ) )
=> ( C @ ( B @ k7_group_2 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k7_group_2 ) @ ( A @ r2_hidden ) )
=> ( A @ ( C @ r1_rlvect_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1574]) ).
thf(145,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k4_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_funct_1) ).
thf(2709,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k4_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(702,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ k6_relat_1 @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
<=> ( ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_1) ).
thf(5502,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ k6_relat_1 @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) ) )
& ( ( A @ k6_relat_1 @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(262,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_binop_1) ).
thf(3218,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k2_struct_0 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_struct_0) ).
thf(4789,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k2_struct_0 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(1238,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( D @ ( A @ k11_group_2 ) ) @ ( A @ k2_group_2 ) ) )
= ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( D @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_group_2) ).
thf(8063,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( D @ ( A @ k11_group_2 ) ) @ ( A @ k2_group_2 ) ) )
= ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( D @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(1337,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( ( D @ ( B @ ( A @ k4_group_2 ) ) @ ( C @ ( B @ ( A @ k4_group_2 ) ) @ r1_tarski ) )
& ( D @ ( B @ ( A @ k3_group_2 ) ) @ ( C @ ( B @ ( A @ k3_group_2 ) ) @ r1_tarski ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_group_3) ).
thf(8619,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( ( D @ ( B @ ( A @ k4_group_2 ) ) @ ( C @ ( B @ ( A @ k4_group_2 ) ) @ r1_tarski ) )
& ( D @ ( B @ ( A @ k3_group_2 ) ) @ ( C @ ( B @ ( A @ k3_group_2 ) ) @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).
thf(1226,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ k1_group_3 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k5_group_2 @ r2_hidden ) )
=> ( A @ k5_group_2 @ ( B @ ( A @ k2_latsubgr ) @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_latsubgr) ).
thf(8016,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ k1_group_3 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k5_group_2 @ r2_hidden ) )
=> ( A @ k5_group_2 @ ( B @ ( A @ k2_latsubgr ) @ ( A @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(1441,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k12_group_6 ) ) @ v1_group_3 ) )
& ( C @ ( B @ ( A @ k12_group_6 ) ) @ v4_group_1 )
& ( C @ ( B @ ( A @ k12_group_6 ) ) @ v3_group_1 )
& ( C @ ( B @ ( A @ k12_group_6 ) ) @ v2_group_1 )
& ( C @ ( B @ ( A @ k12_group_6 ) ) @ v1_group_1 )
& ~ ( C @ ( B @ ( A @ k12_group_6 ) ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_group_6) ).
thf(9244,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k12_group_6 ) ) @ v1_group_3 ) )
& ( C @ ( B @ ( A @ k12_group_6 ) ) @ v4_group_1 )
& ( C @ ( B @ ( A @ k12_group_6 ) ) @ v3_group_1 )
& ( C @ ( B @ ( A @ k12_group_6 ) ) @ v2_group_1 )
& ( C @ ( B @ ( A @ k12_group_6 ) ) @ v1_group_1 )
& ~ ( C @ ( B @ ( A @ k12_group_6 ) ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1441]) ).
thf(1189,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( B @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_group_3) ).
thf(7838,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( B @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(1781,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( B @ ( A @ ( A @ k9_group_5 @ m1_group_6 ) ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( A @ k2_group_5 ) ) @ ( B @ r1_rlvect_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_group_6) ).
thf(11057,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( A @ k2_group_5 ) ) @ ( B @ r1_rlvect_1 ) ) ) )
=> ( B @ ( A @ ( A @ k9_group_5 @ m1_group_6 ) ) ) )
& ( ( B @ ( A @ ( A @ k9_group_5 @ m1_group_6 ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( A @ k2_group_5 ) ) @ ( B @ r1_rlvect_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1781]) ).
thf(1145,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_1) ).
thf(7609,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(7610,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(cnf,[status(esa)],[7609]) ).
thf(352,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_group_1 ) ) )
= ( B @ ( C @ ( A @ k5_group_1 @ ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_group_1) ).
thf(3704,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_group_1 ) ) )
= ( B @ ( C @ ( A @ k5_group_1 @ ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(11435,plain,
sk605 @ l1_group_1,
inference(cnfConj,[status(thm)],[11434]) ).
thf(124,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( k1_xboole_0 @ ( A @ k1_finseq_3 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_finseq_3) ).
thf(2631,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( k1_xboole_0 @ ( A @ k1_finseq_3 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(1605,axiom,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( ( A @ v1_group_1 )
=> ( A
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_group_1) ).
thf(10152,plain,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( ( A @ v1_group_1 )
=> ( A
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1605]) ).
thf(591,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
| ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
thf(4930,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
| ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(1712,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k1_group_3 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ k1_group_3 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C
= ( B @ ( A @ k1_group_3 @ k18_group_2 ) ) )
=> ( ( C @ ( A @ k2_latsubgr ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_latsubgr) ).
thf(10661,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k1_group_3 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ k1_group_3 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C
= ( B @ ( A @ k1_group_3 @ k18_group_2 ) ) )
=> ( ( C @ ( A @ k2_latsubgr ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1712]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( ( ( C @ ( C @ k2_funct_1 @ k5_relat_1 ) )
= ( B @ k6_partfun1 ) )
& ( ( C @ k2_funct_1 @ ( C @ k5_relat_1 ) )
= ( A @ k6_partfun1 ) ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_2) ).
thf(5919,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( ( ( C @ ( C @ k2_funct_1 @ k5_relat_1 ) )
= ( B @ k6_partfun1 ) )
& ( ( C @ k2_funct_1 @ ( C @ k5_relat_1 ) )
= ( A @ k6_partfun1 ) ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(1415,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ( ( B @ ( A @ k17_group_2 ) )
= np__2 )
& ( B @ ( A @ k14_group_2 ) @ v1_finset_1 ) )
=> ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_group_3) ).
thf(9063,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ( ( B @ ( A @ k17_group_2 ) )
= np__2 )
& ( B @ ( A @ k14_group_2 ) @ v1_finset_1 ) )
=> ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415]) ).
thf(758,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(5811,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(2007,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) )
=> ( C @ ( B @ m1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_group_2) ).
thf(11929,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) )
=> ( C @ ( B @ m1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2007]) ).
thf(2066,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( B @ ( A @ r1_group_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_group_3) ).
thf(12142,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( B @ ( A @ r1_group_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2066]) ).
thf(1872,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_finseq_1 ) )
& ( k4_numbers @ ( B @ m1_finseq_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k4_group_4 ) ) @ m2_finseq_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_group_4) ).
thf(11400,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_finseq_1 ) )
& ( k4_numbers @ ( B @ m1_finseq_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k4_group_4 ) ) @ m2_finseq_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1872]) ).
thf(1614,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( C @ r2_hidden ) )
<=> ( C @ ( B @ r1_rlvect_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_latsubgr) ).
thf(10184,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_rlvect_1 ) )
=> ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_rlvect_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1614]) ).
thf(1251,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(8149,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(1790,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ a_1_0_group_6 ) )
=> ( B @ ( A @ k5_group_4 ) @ ( A @ k9_group_5 @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_group_6) ).
thf(11089,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ a_1_0_group_6 ) )
=> ( B @ ( A @ k5_group_4 ) @ ( A @ k9_group_5 @ ( A @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1790]) ).
thf(616,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k4_subset_1 ) ) )
= ( A @ k2_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_subset_1) ).
thf(5081,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k4_subset_1 ) ) )
= ( A @ k2_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(958,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(6780,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(1755,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(10882,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1755]) ).
thf(127,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D )
& ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_binop_1) ).
thf(2638,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D )
& ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D )
& ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(1196,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ ( B @ v1_group_3 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_group_3 ) ) )
= ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_group_3) ).
thf(7874,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_group_3 ) ) )
= ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) ) ) )
=> ( A @ ( B @ v1_group_3 ) ) )
& ( ( A @ ( B @ v1_group_3 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_group_3 ) ) )
= ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k1_setfam_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_setfam_1) ).
thf(7222,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k1_setfam_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(1729,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_rlvect_1 ) ) @ ( A @ k3_group_4 ) )
= ( C @ ( B @ ( A @ k1_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_group_4) ).
thf(10760,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_rlvect_1 ) ) @ ( A @ k3_group_4 ) )
= ( C @ ( B @ ( A @ k1_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1729]) ).
thf(1847,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k2_group_3 ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_group_3) ).
thf(11304,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k2_group_3 ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1847]) ).
thf(4219,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk118 ) @ v1_relat_1 ),
inference(cnfConj,[status(thm)],[4217]) ).
thf(697,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) )
<=> ( B @ ( A @ r1_xreal_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_card_1) ).
thf(5475,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( ( B @ ( A @ r1_xreal_0 ) )
=> ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) ) )
& ( ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) )
=> ( B @ ( A @ r1_xreal_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(6218,plain,
sk259 @ v2_group_1,
inference(cnfConj,[status(thm)],[6214]) ).
thf(1998,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( B @ ( C @ ( A @ k8_group_4 ) ) @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_group_4) ).
thf(11877,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( B @ ( C @ ( A @ k8_group_4 ) ) @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1998]) ).
thf(571,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k9_relat_1 ) )
= ( A @ ( B @ k9_relat_1 ) @ ( C @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_relat_1) ).
thf(4817,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k9_relat_1 ) )
= ( A @ ( B @ k9_relat_1 ) @ ( C @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(2084,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_group_1 ) )
= ( C @ ( A @ k3_group_1 ) ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_group_1) ).
thf(12211,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_group_1 ) )
= ( C @ ( A @ k3_group_1 ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2084]) ).
thf(1355,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k6_group_6 ) @ k8_group_1 )
= ( B @ ( A @ k16_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_group_6) ).
thf(8704,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k6_group_6 ) @ k8_group_1 )
= ( B @ ( A @ k16_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355]) ).
thf(1008,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( C @ ( B @ ( A @ u1_group_1 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_group_1) ).
thf(6967,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( C @ ( B @ ( A @ u1_group_1 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(1190,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] : ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(7841,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] : ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(1292,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k13_group_2 ) ) )
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( C @ ( A @ k11_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_group_3) ).
thf(8346,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k13_group_2 ) ) )
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( C @ ( A @ k11_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).
thf(348,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( ( C @ ( A @ k9_relat_1 ) )
= B )
& ( C @ v1_finset_1 )
& ( A @ k1_relat_1 @ ( C @ r1_tarski ) ) )
& ( A @ k2_relat_1 @ ( B @ r1_tarski ) )
& ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t195_orders_1) ).
thf(3671,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( ( C @ ( A @ k9_relat_1 ) )
= B )
& ( C @ v1_finset_1 )
& ( A @ k1_relat_1 @ ( C @ r1_tarski ) ) )
& ( A @ k2_relat_1 @ ( B @ r1_tarski ) )
& ( B @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( D @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ k3_partfun1 ) ) @ k1_funct_1 ) )
= ( A @ ( D @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_partfun1) ).
thf(2472,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( D @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ k3_partfun1 ) ) @ k1_funct_1 ) )
= ( A @ ( D @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(1504,axiom,
? [A: $i] :
( ! [B: $i] :
( ( B @ v1_int_1 )
=> ( ( A @ ( B @ r2_hidden ) )
<=> ( B @ p1_s1_int_1 ) ) )
& ( k4_numbers @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_int_1) ).
thf(9528,plain,
? [A: $i] :
( ! [B: $i] :
( ( B @ v1_int_1 )
=> ( ( ( B @ p1_s1_int_1 )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s1_int_1 ) ) ) )
& ( k4_numbers @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504]) ).
thf(9529,plain,
! [A: $i] :
( ( ( sk464 @ ( A @ r2_hidden ) )
| ~ ( A @ p1_s1_int_1 )
| ~ ( A @ v1_int_1 ) )
& ( ( A @ p1_s1_int_1 )
| ~ ( sk464 @ ( A @ r2_hidden ) )
| ~ ( A @ v1_int_1 ) )
& ( k4_numbers @ k1_zfmisc_1 @ ( sk464 @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[9528]) ).
thf(9530,plain,
k4_numbers @ k1_zfmisc_1 @ ( sk464 @ m1_subset_1 ),
inference(cnfConj,[status(thm)],[9529]) ).
thf(1976,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_group_2 @ ( A @ k6_group_2 @ ( A @ k9_group_2 ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t105_group_2) ).
thf(11801,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_group_2 @ ( A @ k6_group_2 @ ( A @ k9_group_2 ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1976]) ).
thf(1257,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( C @ ( A @ k1_group_2 ) @ ( A @ k2_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( C @ ( B @ ( A @ k3_group_3 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_group_3) ).
thf(8176,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( C @ ( A @ k1_group_2 ) @ ( A @ k2_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( C @ ( B @ ( A @ k3_group_3 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_xboole_1) ).
thf(2798,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(427,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_4 ) @ v1_funct_1 )
& ( B @ ( A @ k1_funct_4 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_4) ).
thf(4049,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_4 ) @ v1_funct_1 )
& ( B @ ( A @ k1_funct_4 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(981,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ k4_group_3 ) ) @ ( A @ k3_group_3 ) ) )
= ( D @ ( B @ ( A @ k3_group_2 ) ) @ ( C @ ( A @ k3_group_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_group_3) ).
thf(6862,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ k4_group_3 ) ) @ ( A @ k3_group_3 ) ) )
= ( D @ ( B @ ( A @ k3_group_2 ) ) @ ( C @ ( A @ k3_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(764,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
& ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_zfmisc_1) ).
thf(5830,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
& ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(1562,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_partfun1) ).
thf(9872,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1562]) ).
thf(3141,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(cnf,[status(esa)],[3140]) ).
thf(1033,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_mcart_1) ).
thf(7091,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_zfmisc_1) ).
thf(3311,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(1322,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k13_group_2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_group_2) ).
thf(8544,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k13_group_2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322]) ).
thf(1765,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_6_lattice3 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( D @ ( E @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_6_lattice3) ).
thf(10946,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( D @ ( E @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_6_lattice3 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_6_lattice3 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( D @ ( E @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1765]) ).
thf(839,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k6_filter_0 ) ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_filter_0) ).
thf(6175,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k6_filter_0 ) ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(43646,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k4_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21644,2188]) ).
thf(43647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k4_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) ) ),
inference(simp,[status(thm)],[43646]) ).
thf(43648,plain,
! [A: $i] : ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k4_numbers @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[43647:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( k4_numbers )),bind(D,$thf( k5_numbers @ ( E @ k4_xboole_0 ) ))]]) ).
thf(43692,plain,
! [A: $i] : ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k4_numbers @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(simp,[status(thm)],[43648]) ).
thf(22038,plain,
! [A: $i] :
( ( A != sk610 )
| ( k1_xboole_0 @ v3_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,11587]) ).
thf(22039,plain,
( ( k1_xboole_0 @ v3_group_1 )
| ( sk610 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22038:[bind(A,$thf( sk610 ))]]) ).
thf(2088,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ! [E: $i] :
( ( D @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( F = C )
& ( E = B ) )
=> ( ( F @ ( E @ ( D @ k1_group_1 ) ) )
= ( C @ ( B @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_group_2) ).
thf(12223,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ! [E: $i] :
( ( D @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( F = C )
& ( E = B ) )
=> ( ( F @ ( E @ ( D @ k1_group_1 ) ) )
= ( C @ ( B @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2088]) ).
thf(2318,plain,
! [B: $i,A: $i] :
( ( A @ v4_lattice3 )
| ( A @ sk8 @ ( A @ ( B @ sk9 ) @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ sk8 @ ( B @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2314]) ).
thf(2323,plain,
! [B: $i,A: $i] :
( ( A @ v4_lattice3 )
| ( A @ sk8 @ ( A @ ( B @ sk9 ) @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ sk8 @ ( B @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[2318]) ).
thf(1326,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k12_domain_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_domain_1) ).
thf(8555,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k12_domain_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( D
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( ( C @ k2_relat_1 )
= B )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_2) ).
thf(3179,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( D
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( ( C @ k2_relat_1 )
= B )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1499,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_lattice4 ) ) )
<=> ( C @ v2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattice4) ).
thf(9508,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ v2_funct_1 )
=> ( B @ ( A @ ( C @ v1_lattice4 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_lattice4 ) ) )
=> ( C @ v2_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1499]) ).
thf(387,axiom,
! [A: $i,B: $i] :
( ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) )
<=> ? [C: $i] :
( ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= B )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_card_1) ).
thf(3846,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= B )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) ) )
& ( ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) )
=> ? [C: $i] :
( ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= B )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(976,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
thf(6844,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(1273,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k5_group_2 @ v1_group_3 ) )
& ( A @ k5_group_2 @ v4_group_1 )
& ( A @ k5_group_2 @ v3_group_1 )
& ( A @ k5_group_2 @ v2_group_1 )
& ( A @ k5_group_2 @ v1_group_1 )
& ~ ( A @ k5_group_2 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_group_6) ).
thf(8251,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k5_group_2 @ v1_group_3 ) )
& ( A @ k5_group_2 @ v4_group_1 )
& ( A @ k5_group_2 @ v3_group_1 )
& ( A @ k5_group_2 @ v2_group_1 )
& ( A @ k5_group_2 @ v1_group_1 )
& ~ ( A @ k5_group_2 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(1037,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( C @ l3_lattices )
& ( C @ v5_lattice3 )
& ( C @ v4_lattice3 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_8_lattice3 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A
= ( D @ ( E @ ( C @ k4_lattices ) ) ) )
& ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_8_lattice3) ).
thf(7111,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( C @ l3_lattices )
& ( C @ v5_lattice3 )
& ( C @ v4_lattice3 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A
= ( D @ ( E @ ( C @ k4_lattices ) ) ) )
& ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_8_lattice3 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_8_lattice3 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A
= ( D @ ( E @ ( C @ k4_lattices ) ) ) )
& ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(1584,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(10015,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1584]) ).
thf(1676,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m3_vectsp_8 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_vectsp_8) ).
thf(10498,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m3_vectsp_8 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1676]) ).
thf(753,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_xboole_0 ) @ ( B @ ( A @ k1_funct_4 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_4) ).
thf(5791,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_xboole_0 ) @ ( B @ ( A @ k1_funct_4 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(1684,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( A @ k2_group_1 @ ( B @ ( A @ k5_group_3 ) ) )
= ( A @ k2_group_1 @ ( A @ u1_struct_0 @ k6_domain_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_group_3) ).
thf(10528,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( A @ k2_group_1 @ ( B @ ( A @ k5_group_3 ) ) )
= ( A @ k2_group_1 @ ( A @ u1_struct_0 @ k6_domain_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1684]) ).
thf(182,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( ( A @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( A @ v2_funct_1 ) )
=> ( ( A @ k3_finseq_1 )
= np__1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t105_finseq_3) ).
thf(2868,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( ( A @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( A @ v2_funct_1 ) )
=> ( ( A @ k3_finseq_1 )
= np__1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(1083,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) )
<=> ( B @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_group_4) ).
thf(7318,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( ( B @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) )
=> ( C @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) )
& ( ( C @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) )
=> ( B @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(1668,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k7_group_4 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( D @ ( C @ ( A @ k7_group_4 ) ) @ ( B @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_group_4) ).
thf(10458,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k7_group_4 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( D @ ( C @ ( A @ k7_group_4 ) ) @ ( B @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1668]) ).
thf(1364,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( A @ a_1_2_domain_1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_domain_1) ).
thf(8743,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( A @ a_1_2_domain_1 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ k1_funct_1 ) )
= ( B @ ( C @ ( A @ k6_relat_1 @ k5_relat_1 ) @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_1) ).
thf(5620,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ k1_funct_1 ) )
= ( B @ ( C @ ( A @ k6_relat_1 @ k5_relat_1 ) @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(22466,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ( A @ l1_struct_0 )
| ~ ( sk1 @ v1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,18966]) ).
thf(22467,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
| ~ ( sk1 @ v1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22466:[]]) ).
thf(1351,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k2_group_1 @ ( A @ k4_group_2 ) ) )
= B )
& ( ( B @ ( A @ k2_group_1 @ ( A @ k3_group_2 ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_group_2) ).
thf(8687,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k2_group_1 @ ( A @ k4_group_2 ) ) )
= B )
& ( ( B @ ( A @ k2_group_1 @ ( A @ k3_group_2 ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351]) ).
thf(1644,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) @ ( D @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_filter_0) ).
thf(10342,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) @ ( D @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1644]) ).
thf(489,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ k5_group_1 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ k5_group_1 @ v1_funct_2 ) ) )
& ( A @ k5_group_1 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_group_1) ).
thf(4389,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ k5_group_1 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ k5_group_1 @ v1_funct_2 ) ) )
& ( A @ k5_group_1 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(748,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ r1_tarski ) )
=> ( ( B @ ( A @ k16_lattice3 ) @ ( C @ ( A @ k16_lattice3 ) @ ( A @ r3_lattices ) ) )
& ( C @ ( A @ k15_lattice3 ) @ ( B @ ( A @ k15_lattice3 ) @ ( A @ r3_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_lattice3) ).
thf(5743,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ r1_tarski ) )
=> ( ( B @ ( A @ k16_lattice3 ) @ ( C @ ( A @ k16_lattice3 ) @ ( A @ r3_lattices ) ) )
& ( C @ ( A @ k15_lattice3 ) @ ( B @ ( A @ k15_lattice3 ) @ ( A @ r3_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(17911,plain,
! [A: $i] :
( ( A != sk605 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,11440]) ).
thf(17912,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk605 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[17911:[bind(A,$thf( sk605 ))]]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ r1_tarski ) )
=> ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t165_funct_2) ).
thf(3441,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ r1_tarski ) )
=> ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(2310,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk6 ) )
= ( A @ ( B @ k6_xcmplx_0 ) ) )
| ( A @ ( B @ r1_xreal_0 ) )
| ~ ( B @ v1_int_1 )
| ~ ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) ) ),
inference(cnfConj,[status(thm)],[2308]) ).
thf(2312,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ r1_xreal_0 ) )
| ~ ( B @ v1_int_1 )
| ~ ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
| ( ( A @ ( B @ sk6 ) )
= ( A @ ( B @ k6_xcmplx_0 ) ) ) ),
inference(lifteq,[status(thm)],[2310]) ).
thf(1733,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_3_group_3 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( ( D @ ( C @ ( B @ k4_group_3 ) ) )
= C )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_group_3) ).
thf(10776,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ( ( D @ ( C @ ( B @ k4_group_3 ) ) )
= C )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_3_group_3 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_3_group_3 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( ( D @ ( C @ ( B @ k4_group_3 ) ) )
= C )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1733]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_xboole_1) ).
thf(2455,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(1715,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ~ ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_domain_1) ).
thf(10671,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ~ ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ~ ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1715]) ).
thf(1705,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v5_group_1 ) )
<=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( ( B @ ( C @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) )
=> ( C = np__0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_group_1) ).
thf(10620,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( ( B @ ( C @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) )
=> ( C = np__0 ) ) )
=> ( A @ ( B @ v5_group_1 ) ) )
& ( ( A @ ( B @ v5_group_1 ) )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( ( B @ ( C @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) )
=> ( C = np__0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1705]) ).
thf(1736,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k2_group_1 @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k5_group_4 ) @ ( B @ ( A @ k5_group_4 ) @ ( A @ r1_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_group_4) ).
thf(10798,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k2_group_1 @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k5_group_4 ) @ ( B @ ( A @ k5_group_4 ) @ ( A @ r1_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1736]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k7_filter_0 ) ) @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_0) ).
thf(2196,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k7_filter_0 ) ) @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1564,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(9878,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1564]) ).
thf(1779,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(11046,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1779]) ).
thf(910,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k1_funct_4 ) )
= ( C @ ( B @ k1_funct_4 ) @ ( A @ k1_funct_4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funct_4) ).
thf(6573,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k1_funct_4 ) )
= ( C @ ( B @ k1_funct_4 ) @ ( A @ k1_funct_4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(577,axiom,
! [A: $i,B: $i] : ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_zfmisc_1) ).
thf(4861,plain,
! [A: $i,B: $i] : ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(1719,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( B @ ( C @ ( A @ r5_group_3 ) ) )
<=> ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k7_group_2 ) @ ( A @ r4_group_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_group_3) ).
thf(10688,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k7_group_2 ) @ ( A @ r4_group_3 ) ) )
=> ( B @ ( C @ ( A @ r5_group_3 ) ) ) )
& ( ( B @ ( C @ ( A @ r5_group_3 ) ) )
=> ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k7_group_2 ) @ ( A @ r4_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1719]) ).
thf(1011,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ m1_group_2 ) )
<=> ( ( ( B @ u1_group_1 )
= ( B @ u1_struct_0 @ ( A @ u1_group_1 @ k1_realset1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_group_2) ).
thf(6978,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( ( ( B @ u1_group_1 )
= ( B @ u1_struct_0 @ ( A @ u1_group_1 @ k1_realset1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) )
=> ( A @ ( B @ m1_group_2 ) ) )
& ( ( A @ ( B @ m1_group_2 ) )
=> ( ( ( B @ u1_group_1 )
= ( B @ u1_struct_0 @ ( A @ u1_group_1 @ k1_realset1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(1486,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k10_group_6 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( B @ ( A @ k10_group_6 ) @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k10_group_6 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k10_group_6 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_group_6) ).
thf(9429,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k10_group_6 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( B @ ( A @ k10_group_6 ) @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k10_group_6 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k10_group_6 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1486]) ).
thf(1598,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k11_group_2 ) ) )
= ( C @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_group_2) ).
thf(10094,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k11_group_2 ) ) )
= ( C @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1598]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
<=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_realset1) ).
thf(3294,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m1_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(1185,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_lattice4) ).
thf(7821,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(551,axiom,
k5_numbers != k4_numbers,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_numbers) ).
thf(4736,plain,
k5_numbers != k4_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(1254,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
= ( B @ ( C @ ( A @ k5_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_filter_0) ).
thf(8159,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
= ( B @ ( C @ ( A @ k5_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(1269,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( C @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ ( A @ k16_lattice3 ) @ ( A @ r3_lattices ) ) )
& ( C @ ( A @ k15_lattice3 ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_lattice3) ).
thf(8230,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( C @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ ( A @ k16_lattice3 ) @ ( A @ r3_lattices ) ) )
& ( C @ ( A @ k15_lattice3 ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(2002,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B = C )
=> ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_latsubgr) ).
thf(11892,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B = C )
=> ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2002]) ).
thf(1077,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_0_group_2 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i,F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_group_2) ).
thf(7293,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [E: $i,F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_0_group_2 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_0_group_2 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(2044,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ k1_group_3 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_group_3) ).
thf(12045,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ k1_group_3 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2044]) ).
thf(5134,plain,
sk196 @ v1_finset_1,
inference(cnfConj,[status(thm)],[5130]) ).
thf(14326,plain,
! [B: $i,A: $i] :
( ( ( sk196 @ v1_finset_1 )
!= ( A @ v1_finset_1 ) )
| ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5134,2181]) ).
thf(14327,plain,
! [B: $i,A: $i] :
( ( ( sk196 @ v1_finset_1 )
!= ( A @ v1_finset_1 ) )
| ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(simp,[status(thm)],[14326]) ).
thf(14328,plain,
! [A: $i] : ( A @ ( sk196 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(pattern_uni,[status(thm)],[14327:[bind(A,$thf( sk196 ))]]) ).
thf(14345,plain,
! [A: $i] : ( A @ ( sk196 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(simp,[status(thm)],[14328]) ).
thf(14995,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk196 @ k4_xboole_0 ) @ v1_finset_1 )
!= ( B @ v1_finset_1 ) )
| ( C @ ( B @ k4_xboole_0 ) @ v1_finset_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14345,2181]) ).
thf(14996,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk196 @ k4_xboole_0 ) @ v1_finset_1 )
!= ( B @ v1_finset_1 ) )
| ( C @ ( B @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(simp,[status(thm)],[14995]) ).
thf(14997,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( sk196 @ k4_xboole_0 ) @ k4_xboole_0 ) @ v1_finset_1 ),
inference(pattern_uni,[status(thm)],[14996:[bind(A,$thf( E )),bind(B,$thf( E @ ( sk196 @ k4_xboole_0 ) )),bind(C,$thf( C ))]]) ).
thf(15001,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( sk196 @ k4_xboole_0 ) @ k4_xboole_0 ) @ v1_finset_1 ),
inference(simp,[status(thm)],[14997]) ).
thf(1550,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(9825,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1550]) ).
thf(1157,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m2_finseq_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_finseq_1) ).
thf(7667,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m2_finseq_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(7668,plain,
! [A: $i] : ( A @ ( A @ sk348 @ m2_finseq_1 ) ),
inference(cnf,[status(esa)],[7667]) ).
thf(1087,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(7340,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( D @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_xboole_1) ).
thf(2536,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( D @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(2087,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ( ( A @ ( D @ ( C @ ( B @ k8_group_2 ) ) @ r1_rlvect_1 ) )
<=> ( ( A @ ( D @ r1_rlvect_1 ) )
& ( A @ ( C @ r1_rlvect_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_group_2) ).
thf(12218,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ( ( ( ( A @ ( D @ r1_rlvect_1 ) )
& ( A @ ( C @ r1_rlvect_1 ) ) )
=> ( A @ ( D @ ( C @ ( B @ k8_group_2 ) ) @ r1_rlvect_1 ) ) )
& ( ( A @ ( D @ ( C @ ( B @ k8_group_2 ) ) @ r1_rlvect_1 ) )
=> ( ( A @ ( D @ r1_rlvect_1 ) )
& ( A @ ( C @ r1_rlvect_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2087]) ).
thf(2000,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ v6_group_1 )
& ( B @ ( A @ r1_group_6 ) ) )
=> ( B @ v6_group_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_group_6) ).
thf(11888,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ v6_group_1 )
& ( B @ ( A @ r1_group_6 ) ) )
=> ( B @ v6_group_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2000]) ).
thf(1618,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( D
= ( C @ ( B @ ( A @ k8_group_2 ) ) ) )
<=> ( ( D @ u1_struct_0 )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_group_2) ).
thf(10207,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( ( ( D @ u1_struct_0 )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k8_group_2 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k8_group_2 ) ) ) )
=> ( ( D @ u1_struct_0 )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1618]) ).
thf(1791,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_xboole_1) ).
thf(11093,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1791]) ).
thf(1622,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ( C @ ( B @ ( A @ k2_group_6 ) ) @ ( B @ k6_group_6 ) @ ( C @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ k1_group_6 ) ) @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ k6_group_6 ) @ r2_group_6 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_group_6) ).
thf(10222,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ( C @ ( B @ ( A @ k2_group_6 ) ) @ ( B @ k6_group_6 ) @ ( C @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ k1_group_6 ) ) @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ k6_group_6 ) @ r2_group_6 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1622]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( D @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ r2_wellord2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_card_1) ).
thf(2284,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( D @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ r2_wellord2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(2285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ r2_wellord2 ) )
| ~ ( B @ ( D @ r2_hidden ) )
| ~ ( A @ ( C @ r2_hidden ) )
| ~ ( B @ ( A @ r2_wellord2 ) ) ),
inference(cnf,[status(esa)],[2284]) ).
thf(952,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( C @ k2_relat_1 )
= ( A @ ( C @ k1_funct_1 ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_2) ).
thf(6752,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( C @ k2_relat_1 )
= ( A @ ( C @ k1_funct_1 ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(718,axiom,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k1_relat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(5576,plain,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k1_relat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(11608,plain,
~ ( sk611 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[11606]) ).
thf(1798,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(11129,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1798]) ).
thf(340,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(3611,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(1467,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_filter_0 ) ) @ ( C @ ( D @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_filter_1) ).
thf(9365,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_filter_0 ) ) @ ( C @ ( D @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1467]) ).
thf(200,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ k3_finseq_1 )
= np__0 )
<=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_finseq_1) ).
thf(2932,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A = k1_xboole_0 )
=> ( ( A @ k3_finseq_1 )
= np__0 ) )
& ( ( ( A @ k3_finseq_1 )
= np__0 )
=> ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(314,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_filter_0) ).
thf(3486,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(344,axiom,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(3654,plain,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(1464,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( A @ k2_group_1 @ ( B @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_group_3) ).
thf(9359,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( A @ k2_group_1 @ ( B @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464]) ).
thf(1658,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ v6_group_1 )
=> ( A @ k9_group_1 @ ( B @ k9_group_1 @ r1_xreal_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_group_2) ).
thf(10423,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ v6_group_1 )
=> ( A @ k9_group_1 @ ( B @ k9_group_1 @ r1_xreal_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1658]) ).
thf(971,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_1) ).
thf(6827,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(818,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k2_filter_0 ) @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_filter_0) ).
thf(6097,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k2_filter_0 ) @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(2017,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= ( A @ k2_group_1 ) )
& ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( A @ k2_group_1 ) ) )
=> ( C
= ( B @ ( A @ k3_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_group_1) ).
thf(11965,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= ( A @ k2_group_1 ) )
& ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( A @ k2_group_1 ) ) )
=> ( C
= ( B @ ( A @ k3_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2017]) ).
thf(668,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k9_filter_1 )
= ( A @ a_1_0_filter_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_1) ).
thf(5374,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k9_filter_1 )
= ( A @ a_1_0_filter_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(628,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(5149,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(45,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] : ( A @ k2_relat_1 @ ( B @ ( A @ k1_finseq_3 ) @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_finseq_3) ).
thf(2303,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] : ( A @ k2_relat_1 @ ( B @ ( A @ k1_finseq_3 ) @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(2304,plain,
! [B: $i,A: $i] :
( ( A @ k2_relat_1 @ ( B @ ( A @ k1_finseq_3 ) @ k2_relat_1 @ r1_tarski ) )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2303]) ).
thf(8249,plain,
~ ( sk385 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[8248]) ).
thf(12412,plain,
( ( ( sk385 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,8249]) ).
thf(12413,plain,
( ( sk385 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12412]) ).
thf(12429,plain,
sk385 != k1_xboole_0,
inference(simp,[status(thm)],[12413]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_binop_1) ).
thf(2598,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r5_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(434,axiom,
( ( k1_xboole_0 @ k4_card_1 )
= np__0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_card_1) ).
thf(4084,plain,
( ( k1_xboole_0 @ k4_card_1 )
= np__0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(4085,plain,
( ( k1_xboole_0 @ k4_card_1 )
= np__0 ),
inference(lifteq,[status(thm)],[4084]) ).
thf(9750,plain,
np__0 = k1_xboole_0,
inference(lifteq,[status(thm)],[9749]) ).
thf(12795,plain,
( ( k1_xboole_0 @ k4_card_1 )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[4085,9750]) ).
thf(670,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(5380,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v3_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ k1_binop_1 ) ) )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_binop_1) ).
thf(2387,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ k1_binop_1 ) ) )
= C ) )
=> ( A @ ( B @ v3_binop_1 ) ) )
& ( ( A @ ( B @ v3_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ k1_binop_1 ) ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(9500,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[9499]) ).
thf(13187,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,9500]) ).
thf(13188,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13187]) ).
thf(13194,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[13188]) ).
thf(22927,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_tarski ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,13194]) ).
thf(22928,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_tarski ) )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[22927]) ).
thf(22929,plain,
! [A: $i] : ( A @ k1_tarski @ sk149 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[22928:[bind(A,$thf( C @ k1_tarski )),bind(B,$thf( C ))]]) ).
thf(23199,plain,
! [A: $i] : ( A @ k1_tarski @ sk149 @ v1_funct_1 ),
inference(simp,[status(thm)],[22929]) ).
thf(1122,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ( ( C @ ( A @ k4_group_6 ) @ ( B @ r2_hidden ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_group_6) ).
thf(7508,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ( ( C @ ( A @ k4_group_6 ) @ ( B @ r2_hidden ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(362,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k9_relat_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(3743,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k9_relat_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(5899,plain,
k5_numbers != k1_numbers,
inference(polarity_switch,[status(thm)],[5898]) ).
thf(5900,plain,
k5_numbers != k1_numbers,
inference(lifteq,[status(thm)],[5899]) ).
thf(1864,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_group_3 ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_group_3) ).
thf(11360,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_group_3 ) ) )
= B ) ) )
=> ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) ) )
& ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_group_3 ) ) )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1864]) ).
thf(1303,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( np__1 @ ( A @ k2_xcmplx_0 ) @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( C @ ( B @ k1_group_1 ) ) ) )
& ( ( C @ ( np__1 @ ( A @ k2_xcmplx_0 ) @ ( B @ k6_group_1 ) ) )
= ( C @ ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k1_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_group_1) ).
thf(8410,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( np__1 @ ( A @ k2_xcmplx_0 ) @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( C @ ( B @ k1_group_1 ) ) ) )
& ( ( C @ ( np__1 @ ( A @ k2_xcmplx_0 ) @ ( B @ k6_group_1 ) ) )
= ( C @ ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k1_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(1698,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) )
<=> ? [C: $i] :
( A
= ( C @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_card_1) ).
thf(10596,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ k1_tarski ) )
=> ( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) ) )
& ( ( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) )
=> ? [C: $i] :
( A
= ( C @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1698]) ).
thf(10597,plain,
( ! [A: $i] :
( ? [B: $i] :
( A
= ( B @ k1_tarski ) )
=> ! [B: $i] :
( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) ) )
& ! [A: $i] :
( ? [B: $i] :
( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) )
=> ? [B: $i] :
( A
= ( B @ k1_tarski ) ) ) ),
inference(miniscope,[status(thm)],[10596]) ).
thf(10598,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( C @ k1_card_1 )
= ( E @ k1_tarski @ k1_card_1 ) )
| ( C
!= ( D @ k1_tarski ) ) )
& ( ( A
= ( A @ sk554 @ k1_tarski ) )
| ( ( A @ k1_card_1 )
!= ( B @ k1_tarski @ k1_card_1 ) ) ) ),
inference(cnf,[status(esa)],[10597]) ).
thf(10600,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_card_1 )
= ( C @ k1_tarski @ k1_card_1 ) )
| ( A
!= ( B @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[10598]) ).
thf(10602,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_card_1 )
= ( C @ k1_tarski @ k1_card_1 ) )
| ( A
!= ( B @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[10600]) ).
thf(10603,plain,
! [B: $i,A: $i] :
( ( A @ k1_tarski @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) ),
inference(simp,[status(thm)],[10602]) ).
thf(789,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( C @ r1_tarski ) )
& ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( B @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_lattice4) ).
thf(5973,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( C @ r1_tarski ) )
& ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(2029,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ ( A @ r1_group_6 ) )
=> ( A @ ( B @ r1_group_6 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_group_6) ).
thf(12004,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ ( A @ r1_group_6 ) )
=> ( A @ ( B @ r1_group_6 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2029]) ).
thf(327,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ ( A @ k12_finseq_1 ) @ m2_finseq_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_finseq_1) ).
thf(3540,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ ( A @ k12_finseq_1 ) @ m2_finseq_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(1177,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_6_lattice3 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( D @ ( E @ ( C @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_6_lattice3) ).
thf(7789,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [E: $i] :
( ( D @ ( E @ ( C @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_6_lattice3 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_6_lattice3 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( D @ ( E @ ( C @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(1816,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k6_group_2 @ ( A @ m1_group_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_group_2) ).
thf(11184,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k6_group_2 @ ( A @ m1_group_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1816]) ).
thf(1404,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(9017,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).
thf(1362,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( C @ l3_lattices )
& ( C @ v6_lattice3 )
& ( C @ v4_lattice3 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_10_lattice3 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A
= ( D @ ( E @ ( C @ k3_lattices ) ) ) )
& ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_10_lattice3) ).
thf(8732,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( C @ l3_lattices )
& ( C @ v6_lattice3 )
& ( C @ v4_lattice3 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A
= ( D @ ( E @ ( C @ k3_lattices ) ) ) )
& ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_10_lattice3 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_10_lattice3 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A
= ( D @ ( E @ ( C @ k3_lattices ) ) ) )
& ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362]) ).
thf(1663,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( A @ k3_group_1 ) @ r2_hidden ) ) ) )
=> ( ( B @ ( A @ k1_group_2 ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_group_2) ).
thf(10438,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( A @ k3_group_1 ) @ r2_hidden ) ) ) )
=> ( ( B @ ( A @ k1_group_2 ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1663]) ).
thf(1850,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k15_group_2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_group_2) ).
thf(11315,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k15_group_2 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1850]) ).
thf(1591,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_0_filter_0 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i,F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k4_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_filter_0) ).
thf(10047,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [E: $i,F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k4_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_0_filter_0 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_0_filter_0 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k4_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1591]) ).
thf(1754,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( A @ v4_group_1 )
=> ( ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( D @ ( A @ k4_group_2 ) ) )
= ( C @ ( D @ ( A @ k4_group_2 ) ) @ ( B @ ( A @ k2_group_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_group_2) ).
thf(10879,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( A @ v4_group_1 )
=> ( ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( D @ ( A @ k4_group_2 ) ) )
= ( C @ ( D @ ( A @ k4_group_2 ) ) @ ( B @ ( A @ k2_group_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1754]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k7_filter_0 ) ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_filter_0) ).
thf(3760,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k7_filter_0 ) ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(992,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= ( C @ k2_relat_1 ) )
& ( C @ v2_funct_1 )
& ( B @ v2_funct_1 )
& ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k3_group_4 ) )
= ( C @ ( A @ k3_group_4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_group_4) ).
thf(6908,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= ( C @ k2_relat_1 ) )
& ( C @ v2_funct_1 )
& ( B @ v2_funct_1 )
& ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k3_group_4 ) )
= ( C @ ( A @ k3_group_4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(408,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( B @ ( A @ k15_lattice3 ) )
= ( B @ ( A @ a_2_2_lattice3 ) @ ( A @ k16_lattice3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_lattice3) ).
thf(3967,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( B @ ( A @ k15_lattice3 ) )
= ( B @ ( A @ a_2_2_lattice3 ) @ ( A @ k16_lattice3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ~ ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(2766,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) )
& ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ~ ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(17037,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( k4_numbers @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5402,2215]) ).
thf(17038,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( k4_numbers @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[17037]) ).
thf(17039,plain,
! [A: $i] : ( k1_numbers @ ( A @ ( k4_numbers @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[17038:[bind(A,$thf( k4_numbers )),bind(B,$thf( k1_numbers ))]]) ).
thf(17067,plain,
! [A: $i] : ( k1_numbers @ ( A @ ( k4_numbers @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[17039]) ).
thf(17552,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( A @ ( k4_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17067,2215]) ).
thf(17553,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( A @ ( k4_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[17552]) ).
thf(17554,plain,
! [B: $i,A: $i] : ( k1_numbers @ ( A @ ( B @ ( k4_numbers @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[17553:[bind(A,$thf( F )),bind(B,$thf( F @ ( k4_numbers @ k4_xboole_0 ) )),bind(C,$thf( k1_numbers )),bind(D,$thf( D ))]]) ).
thf(17559,plain,
! [B: $i,A: $i] : ( k1_numbers @ ( A @ ( B @ ( k4_numbers @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[17554]) ).
thf(1554,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k4_group_3 ) ) )
= ( C @ ( B @ ( A @ k3_group_1 ) @ ( A @ k3_group_2 ) ) @ ( B @ ( A @ k4_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_group_3) ).
thf(9846,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k4_group_3 ) ) )
= ( C @ ( B @ ( A @ k3_group_1 ) @ ( A @ k3_group_2 ) ) @ ( B @ ( A @ k4_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1554]) ).
thf(1706,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( D @ ( A @ k12_group_2 ) ) )
= ( C @ ( D @ ( A @ k12_group_2 ) ) @ ( B @ ( A @ k3_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_group_2) ).
thf(10629,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( D @ ( A @ k12_group_2 ) ) )
= ( C @ ( D @ ( A @ k12_group_2 ) ) @ ( B @ ( A @ k3_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1706]) ).
thf(2111,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k11_group_4 @ v4_lattice3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_latsubgr) ).
thf(12310,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k11_group_4 @ v4_lattice3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2111]) ).
thf(21774,plain,
! [A: $i] :
( ( A != sk259 )
| ( k1_xboole_0 @ v7_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,6219]) ).
thf(21775,plain,
( ( k1_xboole_0 @ v7_group_1 )
| ( sk259 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21774:[bind(A,$thf( sk259 ))]]) ).
thf(1837,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_group_2) ).
thf(11261,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1837]) ).
thf(1930,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ k1_group_1 ) ) )
= ( C @ ( D @ ( B @ k1_group_1 ) ) ) )
=> ( ( D @ ( C @ ( B @ k1_group_1 ) ) @ ( A @ ( B @ k6_group_1 ) ) )
= ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k1_group_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_group_1) ).
thf(11610,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ k1_group_1 ) ) )
= ( C @ ( D @ ( B @ k1_group_1 ) ) ) )
=> ( ( D @ ( C @ ( B @ k1_group_1 ) ) @ ( A @ ( B @ k6_group_1 ) ) )
= ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k1_group_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1930]) ).
thf(666,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( B @ ( A @ r2_wellord2 ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_card_1) ).
thf(5369,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( B @ ( A @ r2_wellord2 ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(238,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v3_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_binop_1) ).
thf(3109,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= C ) )
=> ( A @ ( B @ v3_binop_1 ) ) )
& ( ( A @ ( B @ v3_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(1186,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_subset_1) ).
thf(7826,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(1594,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ v6_group_1 )
=> ( ( A @ k9_group_1 )
= ( B @ ( A @ k17_group_2 ) @ ( B @ k9_group_1 @ k2_nat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t177_group_2) ).
thf(10075,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ v6_group_1 )
=> ( ( A @ k9_group_1 )
= ( B @ ( A @ k17_group_2 ) @ ( B @ k9_group_1 @ k2_nat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1594]) ).
thf(2005,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_group_2 ) )
= ( B @ ( A @ a_2_0_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_group_2) ).
thf(11916,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_group_2 ) )
= ( B @ ( A @ a_2_0_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2005]) ).
thf(435,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ k2_relat_1 @ k6_relat_1 ) )
& ( ( B @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_1) ).
thf(4086,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ k2_relat_1 @ k6_relat_1 ) )
& ( ( B @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(1394,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k13_group_2 ) ) @ ( C @ ( B @ ( A @ k12_group_2 ) ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_group_3) ).
thf(8980,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k13_group_2 ) ) @ ( C @ ( B @ ( A @ k12_group_2 ) ) @ r1_tarski ) ) )
=> ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) ) )
& ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k13_group_2 ) ) @ ( C @ ( B @ ( A @ k12_group_2 ) ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394]) ).
thf(1997,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_group_3) ).
thf(11873,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1997]) ).
thf(21760,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ~ ( A @ v3_struct_0 )
| ~ ( sk1 @ v1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,18652]) ).
thf(21761,plain,
! [A: $i] :
( ~ ( A @ v3_struct_0 )
| ~ ( sk1 @ v1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21760:[]]) ).
thf(1053,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( A @ k2_group_1 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_latsubgr) ).
thf(7174,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( A @ k2_group_1 @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(41413,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21630,2188]) ).
thf(41414,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) ) ),
inference(simp,[status(thm)],[41413]) ).
thf(41415,plain,
! [A: $i] : ( k4_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[41414:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( k1_numbers )),bind(D,$thf( k4_numbers @ ( E @ k4_xboole_0 ) ))]]) ).
thf(41460,plain,
! [A: $i] : ( k4_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(simp,[status(thm)],[41415]) ).
thf(2009,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_group_4 )
= ( A @ k10_group_4 @ ( A @ k9_group_4 @ ( A @ k1_group_3 @ g3_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_group_4) ).
thf(11933,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_group_4 )
= ( A @ k10_group_4 @ ( A @ k9_group_4 @ ( A @ k1_group_3 @ g3_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2009]) ).
thf(481,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v2_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_1) ).
thf(4361,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v2_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(698,axiom,
! [A: $i,B: $i] :
( ( B @ k6_partfun1 @ ( A @ k6_partfun1 @ k1_funct_4 ) )
= ( B @ ( A @ k2_xboole_0 ) @ k6_partfun1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_4) ).
thf(5479,plain,
! [A: $i,B: $i] :
( ( B @ k6_partfun1 @ ( A @ k6_partfun1 @ k1_funct_4 ) )
= ( B @ ( A @ k2_xboole_0 ) @ k6_partfun1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(633,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( C @ ( D @ ( B @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_enumset1) ).
thf(5170,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( C @ ( D @ ( B @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(1256,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(8174,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(480,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v2_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_binop_1) ).
thf(4352,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) )
=> ( A @ ( B @ v2_binop_1 ) ) )
& ( ( A @ ( B @ v2_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(1806,axiom,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ k1_card_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_card_1) ).
thf(11153,plain,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ k1_card_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1806]) ).
thf(940,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_int_1 )
& ( A @ v1_int_1 ) )
=> ( B @ ( A @ k5_int_1 ) @ v1_int_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_int_1) ).
thf(6716,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_int_1 )
& ( A @ v1_int_1 ) )
=> ( B @ ( A @ k5_int_1 ) @ v1_int_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(787,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(5964,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(1247,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) )
= ( A @ k6_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattices) ).
thf(8127,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) )
= ( A @ k6_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(24224,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ( sk1 != k1_xboole_0 )
| ( A @ v4_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,24218]) ).
thf(24225,plain,
! [A: $i] :
( ( sk1 != k1_xboole_0 )
| ( A @ v4_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[24224:[]]) ).
thf(55585,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( B @ v4_group_1 )
| ( B @ sk149 @ v1_funct_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,24225]) ).
thf(55586,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B @ v4_group_1 )
| ( B @ sk149 @ v1_funct_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[55585]) ).
thf(55587,plain,
! [A: $i] :
( ( A @ v4_group_1 )
| ( A @ sk149 @ v1_funct_1 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[55586:[bind(A,$thf( sk1 ))]]) ).
thf(55648,plain,
! [A: $i] :
( ( A @ v4_group_1 )
| ( A @ sk149 @ v1_funct_1 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[55587]) ).
thf(125,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relat_1) ).
thf(2634,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(884,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(6409,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(400,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= A ) )
& ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( B @ ( A @ k6_setfam_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_setfam_1) ).
thf(3903,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= A ) )
& ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( B @ ( A @ k6_setfam_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(749,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_xboole_1) ).
thf(5747,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(746,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( B @ v1_finset_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k4_card_1 @ ( A @ k4_card_1 @ r1_xreal_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_card_1) ).
thf(5711,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( B @ v1_finset_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k4_card_1 @ ( A @ k4_card_1 @ r1_xreal_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(161,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( E @ ( B @ r6_binop_1 ) ) )
& ( D @ ( C @ ( A @ r6_binop_1 ) ) ) )
<=> ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r6_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_filter_1) ).
thf(2761,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r6_binop_1 ) ) )
=> ( ( F @ ( E @ ( B @ r6_binop_1 ) ) )
& ( D @ ( C @ ( A @ r6_binop_1 ) ) ) ) )
& ( ( ( F @ ( E @ ( B @ r6_binop_1 ) ) )
& ( D @ ( C @ ( A @ r6_binop_1 ) ) ) )
=> ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r6_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(2101,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k7_group_4 ) ) )
= ( B @ ( C @ ( A @ k7_group_4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_group_4) ).
thf(12282,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k7_group_4 ) ) )
= ( B @ ( C @ ( A @ k7_group_4 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2101]) ).
thf(1264,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_group_3) ).
thf(8205,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_relat_1) ).
thf(3279,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(585,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k4_card_1 )
= np__1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_card_1) ).
thf(4887,plain,
! [A: $i] :
( ( A @ k1_tarski @ k4_card_1 )
= np__1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(4888,plain,
! [A: $i] :
( ( A @ k1_tarski @ k4_card_1 )
= np__1 ),
inference(cnf,[status(esa)],[4887]) ).
thf(4889,plain,
! [A: $i] :
( ( A @ k1_tarski @ k4_card_1 )
= np__1 ),
inference(lifteq,[status(thm)],[4888]) ).
thf(1703,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattices) ).
thf(10614,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1703]) ).
thf(1726,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ k4_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_lattices ) ) ) )
& ( ( E @ ( D @ ( A @ k3_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattice4) ).
thf(10740,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ k4_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_lattices ) ) ) )
& ( ( E @ ( D @ ( A @ k3_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_lattices ) ) ) ) ) ) )
=> ( B @ ( A @ ( C @ m1_lattice4 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ k4_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_lattices ) ) ) )
& ( ( E @ ( D @ ( A @ k3_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1726]) ).
thf(1433,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ( A @ u1_struct_0 @ k2_subset_1 @ ( B @ ( A @ k2_group_2 ) ) )
= ( A @ u1_struct_0 ) )
& ( ( B @ ( A @ u1_struct_0 @ k2_subset_1 @ ( A @ k2_group_2 ) ) )
= ( A @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_group_2) ).
thf(9176,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ( A @ u1_struct_0 @ k2_subset_1 @ ( B @ ( A @ k2_group_2 ) ) )
= ( A @ u1_struct_0 ) )
& ( ( B @ ( A @ u1_struct_0 @ k2_subset_1 @ ( A @ k2_group_2 ) ) )
= ( A @ u1_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1433]) ).
thf(557,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_funct_4) ).
thf(4765,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(1907,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_group_6 ) ) )
=> ( A @ ( C @ m1_group_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_group_6) ).
thf(11524,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_group_6 ) ) )
=> ( A @ ( C @ m1_group_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1907]) ).
thf(505,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( D @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
& ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_zfmisc_1) ).
thf(4476,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( D @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
& ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(1411,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( B @ ( C @ k3_xboole_0 ) @ ( A @ ( C @ k3_xboole_0 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_xboole_1) ).
thf(9044,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( B @ ( C @ k3_xboole_0 ) @ ( A @ ( C @ k3_xboole_0 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411]) ).
thf(1530,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k10_group_2 ) ) )
= ( C @ ( B @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_group_3) ).
thf(9716,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k10_group_2 ) ) )
= ( C @ ( B @ ( A @ k11_group_2 ) ) ) ) )
=> ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) ) )
& ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k10_group_2 ) ) )
= ( C @ ( B @ ( A @ k11_group_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1530]) ).
thf(1913,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k3_group_3 ) ) )
= ( C @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ u1_struct_0 @ k6_domain_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_group_3) ).
thf(11546,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k3_group_3 ) ) )
= ( C @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ u1_struct_0 @ k6_domain_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1913]) ).
thf(1305,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_lattice4 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).
thf(8422,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_lattice4 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(1400,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( D @ ( B @ ( A @ k4_lattices ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lattices) ).
thf(9008,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( D @ ( B @ ( A @ k4_lattices ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400]) ).
thf(1234,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ ( A @ k9_group_2 ) ) @ u1_struct_0 )
= ( C @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ k3_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_latsubgr) ).
thf(8049,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ ( A @ k9_group_2 ) ) @ u1_struct_0 )
= ( C @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ k3_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( D @ ( B @ ( C @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_enumset1) ).
thf(3306,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( D @ ( B @ ( C @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(1102,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_group_1 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ k2_group_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_group_1) ).
thf(7414,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_group_1 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= C ) ) )
=> ( B
= ( A @ k2_group_1 ) ) )
& ( ( B
= ( A @ k2_group_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(158,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( A @ k2_relat_1 @ ( B @ r2_hidden ) )
& ( A @ v2_funct_1 ) )
=> ( ( B @ k1_tarski @ ( A @ k1_finseq_3 ) @ k3_finseq_1 )
= ( np__1 @ ( A @ k3_finseq_1 @ k6_xcmplx_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_finseq_3) ).
thf(2748,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( A @ k2_relat_1 @ ( B @ r2_hidden ) )
& ( A @ v2_funct_1 ) )
=> ( ( B @ k1_tarski @ ( A @ k1_finseq_3 ) @ k3_finseq_1 )
= ( np__1 @ ( A @ k3_finseq_1 @ k6_xcmplx_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(1620,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( D @ r2_hidden ) )
& ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( D @ ( C @ ( A @ k1_group_1 ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_latsubgr) ).
thf(10217,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( D @ r2_hidden ) )
& ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( D @ ( C @ ( A @ k1_group_1 ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1620]) ).
thf(1742,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( C @ ( B @ ( A @ k4_filter_0 ) ) ) )
<=> ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_0) ).
thf(10819,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k4_filter_0 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k4_filter_0 ) ) ) )
=> ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1742]) ).
thf(800,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_eqrel_1) ).
thf(6011,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(1985,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ a_1_0_group_2 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( A
= ( C @ ( B @ u1_struct_0 @ k6_domain_1 ) ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_group_2) ).
thf(11824,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ( A
= ( C @ ( B @ u1_struct_0 @ k6_domain_1 ) ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_group_2 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_group_2 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( A
= ( C @ ( B @ u1_struct_0 @ k6_domain_1 ) ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1985]) ).
thf(2094,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D = B )
=> ( ( D @ ( C @ k3_group_1 ) )
= ( B @ ( A @ k3_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_group_2) ).
thf(12255,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D = B )
=> ( ( D @ ( C @ k3_group_1 ) )
= ( B @ ( A @ k3_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2094]) ).
thf(1422,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( C @ ( B @ ( A @ k5_group_3 ) ) )
= ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_group_3) ).
thf(9104,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( C @ ( B @ ( A @ k5_group_3 ) ) )
= ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) ) ) ) ) )
=> ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) ) )
& ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( C @ ( B @ ( A @ k5_group_3 ) ) )
= ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422]) ).
thf(18322,plain,
! [A: $i] :
( ( A != sk259 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,6215]) ).
thf(18323,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk259 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[18322:[bind(A,$thf( sk259 ))]]) ).
thf(26578,plain,
( ( ( sk259 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,18323]) ).
thf(26579,plain,
( ( ( sk259 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[26578]) ).
thf(26592,plain,
( ( sk259 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[26579]) ).
thf(589,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(4905,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(4906,plain,
sk179 @ l1_struct_0,
inference(cnf,[status(esa)],[4905]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ k1_binop_1 ) ) )
= D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_binop_1) ).
thf(2440,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ k1_binop_1 ) ) )
= D ) )
=> ( C @ ( B @ ( A @ r2_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ k1_binop_1 ) ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(1969,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
<=> ( A @ u1_struct_0 @ ( A @ u1_group_1 @ v1_binop_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_group_3) ).
thf(11777,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ u1_struct_0 @ ( A @ u1_group_1 @ v1_binop_1 ) )
=> ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) ) )
& ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_group_1 @ v1_binop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1969]) ).
thf(167,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( k5_numbers @ k1_zfmisc_1 @ ( A @ k4_finseq_1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_finseq_1) ).
thf(2793,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( k5_numbers @ k1_zfmisc_1 @ ( A @ k4_finseq_1 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1855,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( B @ ( A @ r2_group_3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_group_3) ).
thf(11328,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( B @ ( A @ r2_group_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1855]) ).
thf(1967,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ k5_group_2 @ ( B @ ( A @ k10_group_6 ) @ ( B @ ( A @ k13_group_6 ) ) @ ( B @ r1_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_group_6) ).
thf(11769,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( B @ k5_group_2 @ ( B @ ( A @ k10_group_6 ) @ ( B @ ( A @ k13_group_6 ) ) @ ( B @ r1_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1967]) ).
thf(1545,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( D
= ( C @ ( B @ ( A @ k12_group_6 ) ) ) )
<=> ( ( D @ u1_struct_0 )
= ( C @ ( B @ ( A @ a_3_0_group_6 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_group_6) ).
thf(9793,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( ( ( D @ u1_struct_0 )
= ( C @ ( B @ ( A @ a_3_0_group_6 ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k12_group_6 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k12_group_6 ) ) ) )
=> ( ( D @ u1_struct_0 )
= ( C @ ( B @ ( A @ a_3_0_group_6 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1545]) ).
thf(2217,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ( ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
| ( ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) )
& ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ m1_subset_1 ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) )
& ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk4 ) ) @ m1_subset_1 ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) )
& ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk3 ) ) @ m1_subset_1 ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) )
& ( ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
| ~ ( A @ ( F @ m1_subset_1 ) )
| ~ ( A @ ( E @ m1_subset_1 ) )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) )
& ( ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
| ~ ( A @ ( F @ m1_subset_1 ) )
| ~ ( A @ ( E @ m1_subset_1 ) )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ) ),
inference(cnf,[status(esa)],[2216]) ).
thf(2221,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ m1_subset_1 ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[2217]) ).
thf(1154,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(7656,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_1) ).
thf(2189,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(997,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ k3_lattice3 )
= ( B @ k3_lattice3 ) )
=> ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_lattice3) ).
thf(6931,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ k3_lattice3 )
= ( B @ k3_lattice3 ) )
=> ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(1535,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k6_relat_1 )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relset_1) ).
thf(9744,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k6_relat_1 )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1535]) ).
thf(1748,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( D @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_0_group_6 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ( E @ ( D @ ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ k2_group_1 ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_group_6) ).
thf(10851,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( D @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [E: $i] :
( ( ( E @ ( D @ ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ k2_group_1 ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_0_group_6 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_0_group_6 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ( E @ ( D @ ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ k2_group_1 ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1748]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_zfmisc_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_zfmisc_1) ).
thf(3841,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_zfmisc_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(1179,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 )
= ( A @ u1_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_filter_0) ).
thf(7802,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 )
= ( A @ u1_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(1602,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k4_filter_0 ) ) )
= ( C @ ( B @ ( A @ k4_filter_0 ) ) ) )
& ( ( B @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_filter_0 ) ) )
= ( B @ ( C @ ( A @ k4_filter_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_filter_1) ).
thf(10111,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k4_filter_0 ) ) )
= ( C @ ( B @ ( A @ k4_filter_0 ) ) ) )
& ( ( B @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_filter_0 ) ) )
= ( B @ ( C @ ( A @ k4_filter_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1602]) ).
thf(650,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ m1_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_filter_1) ).
thf(5249,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ m1_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(766,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_relat_1) ).
thf(5840,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(2662,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(1035,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( B @ ( C @ ( A @ k13_group_2 ) ) @ ( B @ ( C @ ( A @ k13_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( B @ ( np__2 @ ( A @ k6_group_1 ) ) @ ( C @ ( A @ k13_group_2 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_group_2) ).
thf(7106,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( B @ ( C @ ( A @ k13_group_2 ) ) @ ( B @ ( C @ ( A @ k13_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( B @ ( np__2 @ ( A @ k6_group_1 ) ) @ ( C @ ( A @ k13_group_2 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(1426,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ r1_rlvect_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_rlvect_1) ).
thf(9139,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ r1_rlvect_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1426]) ).
thf(416,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ ( B @ k3_xcmplx_0 ) @ ( C @ k6_group_1 ) ) )
= ( D @ ( B @ ( C @ k6_group_1 ) ) @ ( A @ ( C @ k6_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_group_1) ).
thf(4004,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ ( B @ k3_xcmplx_0 ) @ ( C @ k6_group_1 ) ) )
= ( D @ ( B @ ( C @ k6_group_1 ) ) @ ( A @ ( C @ k6_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k1_struct_0 ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_struct_0) ).
thf(2338,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k1_struct_0 ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(6420,plain,
( ( sk272 @ v1_funct_1 )
& ( sk272 @ v1_xboole_0 )
& ( sk272 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[6419]) ).
thf(6422,plain,
sk272 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[6420]) ).
thf(18542,plain,
! [A: $i] :
( ( ( sk272 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ~ $true
| ( A = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[6422,7167]) ).
thf(18543,plain,
! [A: $i] :
( ( ( sk272 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ( A = k1_xboole_0 ) ),
inference(simp,[status(thm)],[18542]) ).
thf(18544,plain,
sk272 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[18543:[bind(A,$thf( sk272 ))]]) ).
thf(472,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_funct_2) ).
thf(4308,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(2529,plain,
k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v4_group_1,
inference(cnfConj,[status(thm)],[2528]) ).
thf(1339,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ~ ( ( A != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B = k1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_2) ).
thf(8626,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ~ ( ( A != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B = k1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339]) ).
thf(1041,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_zfmisc_1) ).
thf(7133,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1845,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_group_3 ) ) )
=> ( B @ ( C @ ( A @ r3_group_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_group_3) ).
thf(11296,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_group_3 ) ) )
=> ( B @ ( C @ ( A @ r3_group_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1845]) ).
thf(1183,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_relset_1) ).
thf(7817,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(3,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v3_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r1_lattice4 ) ) )
& ( A @ v3_filter_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_lattice4) ).
thf(2121,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v3_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r1_lattice4 ) ) )
& ( A @ v3_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1923,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ k6_group_2 @ ( B @ ( A @ k6_group_2 @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_group_3) ).
thf(11578,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ k6_group_2 @ ( B @ ( A @ k6_group_2 @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1923]) ).
thf(346,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k5_lattice4 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k7_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattice4) ).
thf(3660,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k7_lattices ) ) ) )
=> ( B
= ( A @ k5_lattice4 ) ) )
& ( ( B
= ( A @ k5_lattice4 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k7_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( B @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( B @ ( B @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ l1_struct_0 ) )
=> ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ g4_vectsp_1 ) ) ) ) )
= ( J @ ( I @ ( H @ ( G @ ( F @ g4_vectsp_1 ) ) ) ) ) )
=> ( ( E = J )
& ( D = I )
& ( C = H )
& ( B = G )
& ( A = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g4_vectsp_1) ).
thf(4131,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( B @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( B @ ( B @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ l1_struct_0 ) )
=> ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ g4_vectsp_1 ) ) ) ) )
= ( J @ ( I @ ( H @ ( G @ ( F @ g4_vectsp_1 ) ) ) ) ) )
=> ( ( E = J )
& ( D = I )
& ( C = H )
& ( B = G )
& ( A = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(1952,axiom,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( ( ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_group_1) ).
thf(11705,plain,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( ( ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1952]) ).
thf(756,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ k6_partfun1 @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k6_partfun1 @ v1_partfun1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
thf(5803,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ k6_partfun1 @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k6_partfun1 @ v1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(5804,plain,
( ! [A: $i] : ( A @ ( A @ ( A @ k6_partfun1 @ m2_relset_1 ) ) )
& ! [A: $i] : ( A @ ( A @ ( A @ k6_partfun1 @ v1_partfun1 ) ) ) ),
inference(miniscope,[status(thm)],[5803]) ).
thf(5805,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ k6_partfun1 @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k6_partfun1 @ v1_partfun1 ) ) ) ),
inference(cnf,[status(esa)],[5804]) ).
thf(5807,plain,
! [A: $i] : ( A @ ( A @ ( A @ k6_partfun1 @ m2_relset_1 ) ) ),
inference(cnfConj,[status(thm)],[5805]) ).
thf(5808,plain,
! [A: $i] : ( A @ ( A @ ( A @ k6_partfun1 @ m2_relset_1 ) ) ),
inference(simp,[status(thm)],[5807]) ).
thf(17314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17060,2215]) ).
thf(17315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[17314]) ).
thf(17316,plain,
! [B: $i,A: $i] : ( k4_numbers @ ( A @ ( B @ ( k5_numbers @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[17315:[bind(A,$thf( F )),bind(B,$thf( F @ ( k5_numbers @ k4_xboole_0 ) )),bind(C,$thf( k4_numbers )),bind(D,$thf( D ))]]) ).
thf(17321,plain,
! [B: $i,A: $i] : ( k4_numbers @ ( A @ ( B @ ( k5_numbers @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[17316]) ).
thf(1513,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C != k1_xboole_0 )
=> ( ( C @ ( B @ ( A @ k3_group_3 ) ) )
= B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_group_3) ).
thf(9635,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C != k1_xboole_0 )
=> ( ( C @ ( B @ ( A @ k3_group_3 ) ) )
= B ) ) ) )
=> ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) ) )
& ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C != k1_xboole_0 )
=> ( ( C @ ( B @ ( A @ k3_group_3 ) ) )
= B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1513]) ).
thf(613,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k7_rlvect_1 ) ) @ m2_finseq_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_rlvect_1) ).
thf(5043,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k7_rlvect_1 ) ) @ m2_finseq_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(1374,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ k1_setfam_1 @ ( A @ k1_setfam_1 @ k3_xboole_0 ) )
= ( B @ ( A @ k3_setfam_1 ) @ k1_setfam_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_setfam_1) ).
thf(8807,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ k1_setfam_1 @ ( A @ k1_setfam_1 @ k3_xboole_0 ) )
= ( B @ ( A @ k3_setfam_1 ) @ k1_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374]) ).
thf(1266,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_xboole_1) ).
thf(8215,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(739,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(5678,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(5679,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(cnf,[status(esa)],[5678]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_xboole_1) ).
thf(2729,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(3707,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(1717,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) @ ( A @ k4_lattices ) ) )
= ( B @ ( D @ ( A @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattices) ).
thf(10683,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) @ ( A @ k4_lattices ) ) )
= ( B @ ( D @ ( A @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1717]) ).
thf(1701,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(10608,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1701]) ).
thf(10609,plain,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[10608]) ).
thf(10610,plain,
~ ( sk555 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[10609]) ).
thf(12438,plain,
( ( ( sk555 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,10610]) ).
thf(12439,plain,
( ( sk555 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12438]) ).
thf(12445,plain,
sk555 != k1_xboole_0,
inference(simp,[status(thm)],[12439]) ).
thf(22477,plain,
! [A: $i] :
( ( A != sk555 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,12445]) ).
thf(22478,plain,
! [A: $i] :
( ( A != sk555 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[22477]) ).
thf(22479,plain,
sk555 @ sk149 @ v1_funct_1,
inference(pattern_uni,[status(thm)],[22478:[bind(A,$thf( sk555 ))]]) ).
thf(795,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(5996,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(18402,plain,
! [A: $i] :
( ( A != sk611 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,11608]) ).
thf(18403,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk611 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[18402:[bind(A,$thf( sk611 ))]]) ).
thf(2176,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r5_binop_1 ) ) )
| ~ ( F @ ( E @ ( B @ r5_binop_1 ) ) )
| ~ ( D @ ( C @ ( A @ r5_binop_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2175]) ).
thf(1542,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ k1_orders_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_orders_1) ).
thf(9765,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ( B @ k1_orders_1 @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
& ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( B @ k1_orders_1 @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1542]) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_relat_1) ).
thf(3358,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(2149,plain,
! [B: $i,A: $i] :
( ( B @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2144]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_xboole_1) ).
thf(2585,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_xboole_1) ).
thf(2717,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(936,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_partfun1) ).
thf(6699,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(11591,plain,
sk610 @ v1_group_1,
inference(cnfConj,[status(thm)],[11584]) ).
thf(1357,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k11_group_6 ) @ ( B @ ( A @ k6_group_6 ) @ ( A @ k13_group_6 ) ) )
= ( B @ ( A @ k6_group_6 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_group_6) ).
thf(8713,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k11_group_6 ) @ ( B @ ( A @ k6_group_6 ) @ ( A @ k13_group_6 ) ) )
= ( B @ ( A @ k6_group_6 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).
thf(1017,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k7_lattices ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_lattices) ).
thf(7010,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k7_lattices ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(1281,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( C @ ( B @ ( A @ k4_funct_2 ) ) @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ ( B @ ( A @ k4_funct_2 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k4_funct_2 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_funct_2) ).
thf(8290,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( C @ ( B @ ( A @ k4_funct_2 ) ) @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ ( B @ ( A @ k4_funct_2 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k4_funct_2 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(1231,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k6_group_6 ) @ k1_group_1 ) ) @ ( B @ ( A @ k7_group_6 ) ) )
= ( D @ ( B @ ( A @ k7_group_6 ) ) @ ( C @ ( B @ ( A @ k7_group_6 ) ) @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_group_6) ).
thf(8040,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k6_group_6 ) @ k1_group_1 ) ) @ ( B @ ( A @ k7_group_6 ) ) )
= ( D @ ( B @ ( A @ k7_group_6 ) ) @ ( C @ ( B @ ( A @ k7_group_6 ) ) @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(1047,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( A @ ( D @ v1_group_3 ) ) )
=> ( ( ( D @ ( A @ k4_group_6 ) @ ( C @ r2_hidden ) )
& ( D @ ( A @ k4_group_6 ) @ ( B @ r2_hidden ) ) )
=> ( D @ ( A @ k4_group_6 ) @ ( C @ ( B @ ( A @ k2_group_2 ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_group_6) ).
thf(7155,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( A @ ( D @ v1_group_3 ) ) )
=> ( ( ( D @ ( A @ k4_group_6 ) @ ( C @ r2_hidden ) )
& ( D @ ( A @ k4_group_6 ) @ ( B @ r2_hidden ) ) )
=> ( D @ ( A @ k4_group_6 ) @ ( C @ ( B @ ( A @ k2_group_2 ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(1960,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k7_group_2 ) @ ( A @ k1_group_2 ) )
= ( B @ ( A @ k7_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_group_2) ).
thf(11737,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k7_group_2 ) @ ( A @ k1_group_2 ) )
= ( B @ ( A @ k7_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1960]) ).
thf(1424,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k6_group_2 @ v1_group_3 ) )
& ( A @ k6_group_2 @ v4_group_1 )
& ( A @ k6_group_2 @ v3_group_1 )
& ( A @ k6_group_2 @ v2_group_1 )
& ( A @ k6_group_2 @ v1_group_1 )
& ~ ( A @ k6_group_2 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_group_6) ).
thf(9122,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k6_group_2 @ v1_group_3 ) )
& ( A @ k6_group_2 @ v4_group_1 )
& ( A @ k6_group_2 @ v3_group_1 )
& ( A @ k6_group_2 @ v2_group_1 )
& ( A @ k6_group_2 @ v1_group_1 )
& ~ ( A @ k6_group_2 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424]) ).
thf(2059,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k3_group_1 ) @ ( A @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k3_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_group_1) ).
thf(12119,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k3_group_1 ) @ ( A @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k3_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2059]) ).
thf(912,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( C @ ( D @ k9_relat_1 ) @ ( E @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_funct_2) ).
thf(6578,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( C @ ( D @ k9_relat_1 ) @ ( E @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(615,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k3_setfam_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k3_xboole_0 ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_setfam_1) ).
thf(5048,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k3_xboole_0 ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k3_xboole_0 ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k3_setfam_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_setfam_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k3_xboole_0 ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k3_xboole_0 ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(1804,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_xboole_1) ).
thf(11148,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1804]) ).
thf(1882,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( B @ ( A @ k14_group_2 ) )
= ( A @ u1_struct_0 @ k1_tarski ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t173_group_2) ).
thf(11427,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( B @ ( A @ k14_group_2 ) )
= ( A @ u1_struct_0 @ k1_tarski ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1882]) ).
thf(271,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k5_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_subset_1) ).
thf(3289,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k5_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(1149,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k4_lattice4 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattice4) ).
thf(7636,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k4_lattice4 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(476,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( B @ ( A @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_funct_4) ).
thf(4340,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( B @ ( A @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(294,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ ( B @ r4_lattice3 ) ) )
<=> ( B @ ( A @ a_2_0_lattice3 ) @ ( C @ ( B @ k7_lattices ) @ ( B @ r3_lattice3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattice3) ).
thf(3375,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ a_2_0_lattice3 ) @ ( C @ ( B @ k7_lattices ) @ ( B @ r3_lattice3 ) ) )
=> ( A @ ( C @ ( B @ r4_lattice3 ) ) ) )
& ( ( A @ ( C @ ( B @ r4_lattice3 ) ) )
=> ( B @ ( A @ a_2_0_lattice3 ) @ ( C @ ( B @ k7_lattices ) @ ( B @ r3_lattice3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(1068,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k2_group_2 ) ) )
= ( D @ ( B @ ( A @ k1_group_1 ) ) @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ u1_struct_0 @ k7_domain_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_group_2) ).
thf(7257,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k2_group_2 ) ) )
= ( D @ ( B @ ( A @ k1_group_1 ) ) @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ u1_struct_0 @ k7_domain_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(1782,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(11063,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1782]) ).
thf(376,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= ( A @ ( B @ k1_funct_4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_funct_4) ).
thf(3792,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= ( A @ ( B @ k1_funct_4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(1210,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k2_group_2 ) ) )
= ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ u1_struct_0 @ k6_domain_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_group_2) ).
thf(7953,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k2_group_2 ) ) )
= ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ u1_struct_0 @ k6_domain_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(851,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ( ( ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( B @ k4_finseq_1 @ ( D @ r2_hidden ) )
=> ( ( np__1 @ ( D @ ( B @ k3_finseq_1 @ k6_xcmplx_0 ) @ k2_xcmplx_0 ) @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ ( A @ u1_struct_0 @ ( k5_numbers @ k4_finseq_4 ) ) ) @ ( A @ k3_group_1 ) ) ) ) )
& ( ( B @ k3_finseq_1 )
= ( C @ k3_finseq_1 ) ) )
=> ( ( B @ ( A @ k3_group_4 ) )
= ( C @ ( A @ k3_group_4 ) @ ( A @ k3_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_group_4) ).
thf(6228,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ( ( ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( B @ k4_finseq_1 @ ( D @ r2_hidden ) )
=> ( ( np__1 @ ( D @ ( B @ k3_finseq_1 @ k6_xcmplx_0 ) @ k2_xcmplx_0 ) @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ ( A @ u1_struct_0 @ ( k5_numbers @ k4_finseq_4 ) ) ) @ ( A @ k3_group_1 ) ) ) ) )
& ( ( B @ k3_finseq_1 )
= ( C @ k3_finseq_1 ) ) )
=> ( ( B @ ( A @ k3_group_4 ) )
= ( C @ ( A @ k3_group_4 ) @ ( A @ k3_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(707,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( D @ k2_relat_1 )
= B )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v2_funct_1 ) )
=> ( ( ( E @ v2_funct_1 )
& ( D @ v2_funct_1 ) )
| ( ( B != k1_xboole_0 )
& ( C = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_funct_2) ).
thf(5525,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( D @ k2_relat_1 )
= B )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v2_funct_1 ) )
=> ( ( ( E @ v2_funct_1 )
& ( D @ v2_funct_1 ) )
| ( ( B != k1_xboole_0 )
& ( C = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(791,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ ( A @ ( B @ k1_funct_1 ) @ ( A @ k1_tarski @ k2_funcop_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_4) ).
thf(5979,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ ( A @ ( B @ k1_funct_1 ) @ ( A @ k1_tarski @ k2_funcop_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(2047,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) @ ( C @ ( A @ k1_group_1 ) ) )
= B )
& ( ( B @ ( C @ ( A @ k1_group_1 ) ) @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) )
= B )
& ( ( C @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k1_group_1 ) ) )
= B )
& ( ( C @ ( A @ k3_group_1 ) @ ( C @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k1_group_1 ) ) )
= B )
& ( ( B @ ( C @ ( A @ k3_group_1 ) @ ( C @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= B )
& ( ( B @ ( C @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= B )
& ( ( C @ ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= B )
& ( ( C @ ( A @ k3_group_1 ) @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_group_3) ).
thf(12052,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) @ ( C @ ( A @ k1_group_1 ) ) )
= B )
& ( ( B @ ( C @ ( A @ k1_group_1 ) ) @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) )
= B )
& ( ( C @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k1_group_1 ) ) )
= B )
& ( ( C @ ( A @ k3_group_1 ) @ ( C @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k1_group_1 ) ) )
= B )
& ( ( B @ ( C @ ( A @ k3_group_1 ) @ ( C @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= B )
& ( ( B @ ( C @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= B )
& ( ( C @ ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= B )
& ( ( C @ ( A @ k3_group_1 ) @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2047]) ).
thf(1175,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(7783,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(7784,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[7783]) ).
thf(7785,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[7784]) ).
thf(2052,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= C ) ) )
=> ( B
= ( A @ k2_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_group_1) ).
thf(12087,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= C ) ) )
=> ( B
= ( A @ k2_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2052]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( B @ k5_relat_1 ) )
= ( D @ ( B @ k5_relat_1 ) ) )
& ( ( D @ k1_relat_1 )
= A )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( C = D ) ) ) )
& ( A @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( A
= ( B @ k2_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_funct_1) ).
thf(3686,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( B @ k5_relat_1 ) )
= ( D @ ( B @ k5_relat_1 ) ) )
& ( ( D @ k1_relat_1 )
= A )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( C = D ) ) ) )
& ( A @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( A
= ( B @ k2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(1286,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( A @ v4_group_1 )
=> ( ( B @ ( C @ ( A @ k3_group_2 ) ) @ ( D @ ( A @ k4_group_2 ) ) )
= ( B @ ( D @ ( A @ k4_group_2 ) ) @ ( C @ ( A @ k3_group_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_group_2) ).
thf(8311,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( A @ v4_group_1 )
=> ( ( B @ ( C @ ( A @ k3_group_2 ) ) @ ( D @ ( A @ k4_group_2 ) ) )
= ( B @ ( D @ ( A @ k4_group_2 ) ) @ ( C @ ( A @ k3_group_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(1890,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ ( A @ k2_group_1 @ v5_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_group_1) ).
thf(11459,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ ( A @ k2_group_1 @ v5_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1890]) ).
thf(1413,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k12_group_6 ) ) @ r1_rlvect_1 ) )
<=> ( ( C @ ( D @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k2_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_group_6) ).
thf(9049,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( ( C @ ( D @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k2_group_1 ) )
=> ( C @ ( D @ ( B @ ( A @ k12_group_6 ) ) @ r1_rlvect_1 ) ) )
& ( ( C @ ( D @ ( B @ ( A @ k12_group_6 ) ) @ r1_rlvect_1 ) )
=> ( ( C @ ( D @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k2_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413]) ).
thf(1918,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k8_group_3 ) )
= ( B @ ( A @ a_2_1_group_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_group_3) ).
thf(11561,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k8_group_3 ) )
= ( B @ ( A @ a_2_1_group_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1918]) ).
thf(190,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_xboole_1) ).
thf(2894,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1058,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k18_group_2 ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k18_group_2) ).
thf(7212,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k18_group_2 ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(483,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v13_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r3_lattice4 ) ) )
& ( A @ v13_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattice4) ).
thf(4365,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v13_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r3_lattice4 ) ) )
& ( A @ v13_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(22295,plain,
! [A: $i] :
( ( A != sk610 )
| ( k1_xboole_0 @ v1_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,11591]) ).
thf(22296,plain,
( ( k1_xboole_0 @ v1_group_1 )
| ( sk610 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22295:[bind(A,$thf( sk610 ))]]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( B @ k3_partfun1 ) ) @ ( A @ ( A @ k5_partfun1 ) ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t162_funct_2) ).
thf(2524,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( B @ k3_partfun1 ) ) @ ( A @ ( A @ k5_partfun1 ) ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(1092,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_3_lattice3 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( D @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_lattice3) ).
thf(7372,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_3_lattice3 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_3_lattice3 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( D @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(2373,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r4_lattice3 ) ) )
| ( A @ u1_struct_0 @ ( A @ ( B @ ( C @ sk13 ) ) @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2371]) ).
thf(2376,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r4_lattice3 ) ) )
| ( A @ u1_struct_0 @ ( A @ ( B @ ( C @ sk13 ) ) @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[2373]) ).
thf(59860,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( A @ ( C @ sk12 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[2270,59829]) ).
thf(59861,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ sk12 ) )
= A ),
inference(pattern_uni,[status(thm)],[59860:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ ( C @ k1_funct_1 ) @ k1_tarski @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_partfun1) ).
thf(4465,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ ( C @ k1_funct_1 ) @ k1_tarski @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(33029,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski @ k1_card_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,33008]) ).
thf(33030,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski @ k1_card_1 ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[33029]) ).
thf(33031,plain,
~ ( k1_xboole_0 @ k1_tarski @ k1_card_1 @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[33030:[bind(A,$thf( k1_xboole_0 @ k1_tarski @ k1_card_1 ))]]) ).
thf(34165,plain,
! [B: $i,A: $i] :
( ( ( B @ k1_tarski @ k1_card_1 )
!= ( k1_xboole_0 @ k1_tarski @ k1_card_1 ) )
| ~ ( A @ k1_tarski @ k1_card_1 @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[10603,33031]) ).
thf(34166,plain,
! [A: $i] :
~ ( A @ k1_tarski @ k1_card_1 @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[34165:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(1714,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(10668,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1714]) ).
thf(1775,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k15_group_2 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( D
= ( E @ ( B @ ( A @ k13_group_2 ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_group_2) ).
thf(11006,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( D
= ( E @ ( B @ ( A @ k13_group_2 ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( B @ ( A @ k13_group_2 ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) )
=> ( C
= ( B @ ( A @ k15_group_2 ) ) ) )
& ( ( C
= ( B @ ( A @ k15_group_2 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( D
= ( E @ ( B @ ( A @ k13_group_2 ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( B @ ( A @ k13_group_2 ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1775]) ).
thf(17329,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17062,2215]) ).
thf(17330,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[17329]) ).
thf(17331,plain,
! [B: $i,A: $i] : ( k1_numbers @ ( A @ ( B @ ( k5_numbers @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[17330:[bind(A,$thf( F )),bind(B,$thf( F @ ( k5_numbers @ k4_xboole_0 ) )),bind(C,$thf( k1_numbers )),bind(D,$thf( D ))]]) ).
thf(17336,plain,
! [B: $i,A: $i] : ( k1_numbers @ ( A @ ( B @ ( k5_numbers @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[17331]) ).
thf(1146,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k12_group_6 ) ) @ m1_group_2 ) )
& ( C @ ( B @ ( A @ k12_group_6 ) ) @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_group_6) ).
thf(7611,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k12_group_6 ) ) @ m1_group_2 ) )
& ( C @ ( B @ ( A @ k12_group_6 ) ) @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(1483,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( B @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_filter_0) ).
thf(9418,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( B @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1483]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( D @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_funct_4) ).
thf(4000,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( D @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(1659,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( A @ ( I @ m1_subset_1 ) )
& ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_domain_1 ) ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_domain_1) ).
thf(10425,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( A @ ( I @ m1_subset_1 ) )
& ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_domain_1 ) ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1659]) ).
thf(1606,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_funct_2) ).
thf(10155,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1606]) ).
thf(3545,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[3543]) ).
thf(3547,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3545]) ).
thf(691,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_struct_0 ) ) )
= ( B @ ( C @ ( A @ k2_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_struct_0) ).
thf(5456,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_struct_0 ) ) )
= ( B @ ( C @ ( A @ k2_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(21557,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( k5_numbers @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3108,2231]) ).
thf(21558,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( k5_numbers @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[21557]) ).
thf(21559,plain,
! [A: $i] : ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[21558:[bind(A,$thf( k5_numbers )),bind(B,$thf( k1_numbers ))]]) ).
thf(21647,plain,
! [A: $i] : ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[21559]) ).
thf(780,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_setfam_1) ).
thf(5933,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k7_setfam_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r2_hidden ) ) )
& ( ( B @ ( A @ k7_setfam_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(226,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
<=> ? [C: $i] :
( ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_partfun1) ).
thf(3070,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ? [C: $i] :
( ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ? [C: $i] :
( ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_realset1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_realset1) ).
thf(2727,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(1938,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_group_6 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m1_group_6 ) ) )
=> ( ( D @ ( C @ ( A @ k9_group_2 ) ) )
= ( D @ ( C @ ( B @ k9_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_group_6) ).
thf(11633,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_group_6 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m1_group_6 ) ) )
=> ( ( D @ ( C @ ( A @ k9_group_2 ) ) )
= ( D @ ( C @ ( B @ k9_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1938]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) ) ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_xboole_1) ).
thf(3319,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) ) ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(369,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( D @ ( B @ ( A @ k9_filter_0 ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_filter_1) ).
thf(3768,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( D @ ( B @ ( A @ k9_filter_0 ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(1853,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k9_group_2 ) ) )
= ( B @ ( C @ ( A @ k9_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k9_group_2) ).
thf(11323,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k9_group_2 ) ) )
= ( B @ ( C @ ( A @ k9_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1853]) ).
thf(21515,plain,
( ( ( sk605 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,17912]) ).
thf(21516,plain,
( ( ( sk605 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[21515]) ).
thf(21523,plain,
( ( sk605 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[21516]) ).
thf(1274,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_group_3 @ ( A @ k1_latsubgr @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_group_3 @ ( A @ k1_latsubgr @ v1_funct_2 ) ) )
& ( A @ k1_latsubgr @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_latsubgr) ).
thf(8259,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_group_3 @ ( A @ k1_latsubgr @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_group_3 @ ( A @ k1_latsubgr @ v1_funct_2 ) ) )
& ( A @ k1_latsubgr @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).
thf(25031,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ( sk1 != k1_xboole_0 )
| ( A @ v3_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,25025]) ).
thf(25032,plain,
! [A: $i] :
( ( sk1 != k1_xboole_0 )
| ( A @ v3_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[25031:[]]) ).
thf(55870,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( B @ v3_group_1 )
| ( B @ sk149 @ v1_funct_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,25032]) ).
thf(55871,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B @ v3_group_1 )
| ( B @ sk149 @ v1_funct_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[55870]) ).
thf(55872,plain,
! [A: $i] :
( ( A @ v3_group_1 )
| ( A @ sk149 @ v1_funct_1 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[55871:[bind(A,$thf( sk1 ))]]) ).
thf(55947,plain,
! [A: $i] :
( ( A @ v3_group_1 )
| ( A @ sk149 @ v1_funct_1 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[55872]) ).
thf(994,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ ( A @ r1_group_2 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ r1_rlvect_1 ) )
<=> ( D @ ( C @ r1_rlvect_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_group_2) ).
thf(6916,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ r1_rlvect_1 ) )
=> ( D @ ( B @ r1_rlvect_1 ) ) )
& ( ( D @ ( B @ r1_rlvect_1 ) )
=> ( D @ ( C @ r1_rlvect_1 ) ) ) ) )
=> ( C @ ( B @ ( A @ r1_group_2 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_group_2 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ r1_rlvect_1 ) )
=> ( D @ ( B @ r1_rlvect_1 ) ) )
& ( ( D @ ( B @ r1_rlvect_1 ) )
=> ( D @ ( C @ r1_rlvect_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(2858,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2857]) ).
thf(2859,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2858]) ).
thf(984,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_xboole_1) ).
thf(6870,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(2218,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ( ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
| ( ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[2217]) ).
thf(2225,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
| ( ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ),
inference(lifteq,[status(thm)],[2218]) ).
thf(1005,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( C @ ( A @ k3_group_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_latsubgr) ).
thf(6959,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) @ ( C @ ( A @ k3_group_1 ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(510,axiom,
! [A: $i] : ( A @ k3_tarski @ ( A @ k1_setfam_1 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_setfam_1) ).
thf(4494,plain,
! [A: $i] : ( A @ k3_tarski @ ( A @ k1_setfam_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(1841,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_group_6 ) ) )
<=> ( B @ ( C @ m1_group_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_group_6) ).
thf(11279,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_group_2 ) )
=> ( B @ ( A @ ( C @ m1_group_6 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_group_6 ) ) )
=> ( B @ ( C @ m1_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1841]) ).
thf(21893,plain,
! [A: $i] :
( ( A != sk612 )
| ( k1_xboole_0 @ l1_struct_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,17613]) ).
thf(21894,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk612 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21893:[bind(A,$thf( sk612 ))]]) ).
thf(1002,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_filter_0) ).
thf(6949,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(1293,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v4_group_6 ) ) )
=> ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ k2_funct_1 @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_group_6) ).
thf(8349,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v4_group_6 ) ) )
=> ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ k2_funct_1 @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(339,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( D @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) @ ( B @ r2_hidden ) )
=> ( D @ ( A @ k3_filter_0 ) @ ( B @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_filter_0) ).
thf(3609,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( D @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) @ ( B @ r2_hidden ) )
=> ( D @ ( A @ k3_filter_0 ) @ ( B @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ r2_wellord2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_card_1) ).
thf(2657,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ r2_wellord2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(4159,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk111 ) @ v1_relat_1 ),
inference(cnfConj,[status(thm)],[4157]) ).
thf(22701,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ( sk1 != k1_xboole_0 )
| ( A @ l1_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,21457]) ).
thf(22702,plain,
! [A: $i] :
( ( sk1 != k1_xboole_0 )
| ( A @ l1_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22701:[]]) ).
thf(1951,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ r2_group_6 ) )
=> ( A @ ( B @ r2_group_6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r2_group_6) ).
thf(11703,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ r2_group_6 ) )
=> ( A @ ( B @ r2_group_6 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1951]) ).
thf(1118,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ ( B @ ( A @ r4_lattice3 ) ) )
& ( C @ ( B @ r2_hidden ) ) )
=> ( ( C @ ( A @ k15_lattice3 ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattice3) ).
thf(7487,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ ( B @ ( A @ r4_lattice3 ) ) )
& ( C @ ( B @ r2_hidden ) ) )
=> ( ( C @ ( A @ k15_lattice3 ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(1310,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ r1_tarski ) )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(8470,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_tarski ) ) )
& ( ( B @ ( A @ k1_tarski @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310]) ).
thf(1029,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k10_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k2_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_group_2) ).
thf(7073,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k10_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k2_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(1979,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k8_group_3 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_group_3) ).
thf(11809,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k8_group_3 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1979]) ).
thf(2010,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ k5_group_2 )
= ( A @ k5_group_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_group_2) ).
thf(11936,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ k5_group_2 )
= ( A @ k5_group_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2010]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(3086,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(1877,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ r1_rlvect_1 ) )
=> ( D @ ( C @ r1_rlvect_1 ) ) ) )
=> ( C @ ( B @ m1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_group_2) ).
thf(11411,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ r1_rlvect_1 ) )
=> ( D @ ( C @ r1_rlvect_1 ) ) ) )
=> ( C @ ( B @ m1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1877]) ).
thf(1977,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k8_group_3 ) @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k8_group_3 ) @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_group_3) ).
thf(11804,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k8_group_3 ) @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k8_group_3 ) @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1977]) ).
thf(38526,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( B @ ( A @ k1_orders_1 @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[2889,2244]) ).
thf(38527,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_orders_1 @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[38526:[bind(A,$thf( D )),bind(B,$thf( D @ k1_zfmisc_1 )),bind(C,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(38668,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_orders_1 @ r1_tarski ) ),
inference(simp,[status(thm)],[38527]) ).
thf(228,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( A @ k7_setfam_1 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(3081,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( A @ k7_setfam_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(1527,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( C @ ( A @ k8_setfam_1 ) @ ( B @ r2_hidden ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_setfam_1) ).
thf(9706,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r2_hidden ) ) )
=> ( C @ ( A @ k8_setfam_1 ) @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k8_setfam_1 ) @ ( B @ r2_hidden ) )
=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( E @ v2_funct_1 )
& ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ k2_relat_1 )
= C ) )
=> ( ( ( D @ k2_relat_1 )
= B )
| ( C = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_funct_2) ).
thf(3283,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( E @ v2_funct_1 )
& ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ k2_relat_1 )
= C ) )
=> ( ( ( D @ k2_relat_1 )
= B )
| ( C = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A )
<=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(2674,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ r2_hidden ) )
=> ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A ) )
& ( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A )
=> ~ ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(265,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ l3_lattices )
& ( B @ v14_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ k6_lattices )
= ( B @ k6_lattices @ ( A @ k6_lattices @ ( B @ ( A @ k10_filter_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_filter_1) ).
thf(3272,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ l3_lattices )
& ( B @ v14_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ k6_lattices )
= ( B @ k6_lattices @ ( A @ k6_lattices @ ( B @ ( A @ k10_filter_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(566,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t105_zfmisc_1) ).
thf(4801,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(1379,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ ( A @ r5_group_3 ) ) )
<=> ? [D: $i] :
( ( D @ ( B @ ( A @ k6_group_3 ) ) @ ( C @ ( A @ r1_group_2 ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_group_3) ).
thf(8894,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( ? [D: $i] :
( ( D @ ( B @ ( A @ k6_group_3 ) ) @ ( C @ ( A @ r1_group_2 ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ r5_group_3 ) ) ) )
& ( ( C @ ( B @ ( A @ r5_group_3 ) ) )
=> ? [D: $i] :
( ( D @ ( B @ ( A @ k6_group_3 ) ) @ ( C @ ( A @ r1_group_2 ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379]) ).
thf(1350,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( ( A != np__0 )
=> ( ( A @ ( A @ k5_int_1 ) )
= np__1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_int_1) ).
thf(8684,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( ( A != np__0 )
=> ( ( A @ ( A @ k5_int_1 ) )
= np__1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).
thf(1796,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( C @ ( A @ k1_group_2 ) @ ( B @ ( A @ k4_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( B @ ( C @ ( A @ k5_group_3 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_group_3) ).
thf(11124,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( C @ ( A @ k1_group_2 ) @ ( B @ ( A @ k4_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( B @ ( C @ ( A @ k5_group_3 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1796]) ).
thf(724,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_binop_1) ).
thf(5612,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ( A @ ( B @ v1_binop_1 ) ) )
& ( ( A @ ( B @ v1_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(2077,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( ( B @ ( D @ ( A @ k13_group_2 ) ) )
= ( C @ ( D @ ( A @ k13_group_2 ) ) ) )
<=> ~ ( C @ ( D @ ( A @ k13_group_2 ) ) @ ( B @ ( D @ ( A @ k13_group_2 ) ) @ r1_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_group_2) ).
thf(12184,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( ~ ( C @ ( D @ ( A @ k13_group_2 ) ) @ ( B @ ( D @ ( A @ k13_group_2 ) ) @ r1_xboole_0 ) )
=> ( ( B @ ( D @ ( A @ k13_group_2 ) ) )
= ( C @ ( D @ ( A @ k13_group_2 ) ) ) ) )
& ( ( ( B @ ( D @ ( A @ k13_group_2 ) ) )
= ( C @ ( D @ ( A @ k13_group_2 ) ) ) )
=> ~ ( C @ ( D @ ( A @ k13_group_2 ) ) @ ( B @ ( D @ ( A @ k13_group_2 ) ) @ r1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2077]) ).
thf(425,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( A
= ( A @ k1_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_card_1) ).
thf(4032,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( A
= ( A @ k1_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( A @ ( A @ ( A @ ( B @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_funct_2) ).
thf(2991,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( A @ ( A @ ( A @ ( B @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(1927,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k7_group_3 ) @ ( B @ r2_hidden ) )
<=> ( C @ ( B @ ( A @ r2_group_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_group_3) ).
thf(11598,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ r2_group_3 ) ) )
=> ( C @ ( A @ k7_group_3 ) @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k7_group_3 ) @ ( B @ r2_hidden ) )
=> ( C @ ( B @ ( A @ r2_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1927]) ).
thf(2095,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ v6_group_1 )
<=> ( B @ ( C @ ( A @ k6_group_3 ) ) @ v6_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_group_3) ).
thf(12259,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( B @ ( C @ ( A @ k6_group_3 ) ) @ v6_group_1 )
=> ( C @ v6_group_1 ) )
& ( ( C @ v6_group_1 )
=> ( B @ ( C @ ( A @ k6_group_3 ) ) @ v6_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2095]) ).
thf(1669,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_domain_1 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_domain_1) ).
thf(10461,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_domain_1 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1669]) ).
thf(1519,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
<=> ( k4_numbers @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_int_1) ).
thf(9663,plain,
! [A: $i] :
( ( ( k4_numbers @ ( A @ r2_hidden ) )
=> ( A @ v1_int_1 ) )
& ( ( A @ v1_int_1 )
=> ( k4_numbers @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1519]) ).
thf(10456,plain,
~ ( sk545 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[10454]) ).
thf(18762,plain,
! [A: $i] :
( ( A != sk545 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,10456]) ).
thf(18763,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( sk545 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[18762:[bind(A,$thf( sk545 ))]]) ).
thf(34268,plain,
( ( ( sk545 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,18763]) ).
thf(34269,plain,
( ( ( sk545 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[34268]) ).
thf(34282,plain,
( ( sk545 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[34269]) ).
thf(1662,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattices) ).
thf(10435,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1662]) ).
thf(2713,plain,
( ( sk27 @ v1_finseq_1 )
& ( sk27 @ v1_funct_1 )
& ( sk27 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2712]) ).
thf(2716,plain,
sk27 @ v1_finseq_1,
inference(cnfConj,[status(thm)],[2713]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_funct_1) ).
thf(4381,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(662,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_xboole_1) ).
thf(5350,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(803,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) )
& ( B != k1_xboole_0 ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_lattice4) ).
thf(6019,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) )
& ( B != k1_xboole_0 ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(647,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( A @ k1_funct_4 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k1_funct_4) ).
thf(5239,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( A @ k1_funct_4 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(1835,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( A @ k16_group_2 ) )
= ( B @ ( C @ ( A @ k6_group_3 ) ) @ ( A @ k16_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_group_3) ).
thf(11254,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( A @ k16_group_2 ) )
= ( B @ ( C @ ( A @ k6_group_3 ) ) @ ( A @ k16_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1835]) ).
thf(1556,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ! [D: $i] :
( ( k4_numbers @ ( D @ m2_finseq_1 ) )
=> ( ( B @ ( A @ k7_group_2 ) @ ( C @ k2_relat_1 @ r1_tarski ) )
=> ( C @ ( D @ ( A @ k4_group_4 ) ) @ ( A @ k3_group_4 ) @ ( B @ r1_rlvect_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_group_4) ).
thf(9852,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ! [D: $i] :
( ( k4_numbers @ ( D @ m2_finseq_1 ) )
=> ( ( B @ ( A @ k7_group_2 ) @ ( C @ k2_relat_1 @ r1_tarski ) )
=> ( C @ ( D @ ( A @ k4_group_4 ) ) @ ( A @ k3_group_4 ) @ ( B @ r1_rlvect_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1556]) ).
thf(1683,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ m1_finseq_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k1_group_4 ) ) @ m2_finseq_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_group_4) ).
thf(10525,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ m1_finseq_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k1_group_4 ) ) @ m2_finseq_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1683]) ).
thf(2032,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ v3_realset2 )
& ( A @ v3_realset2 ) )
=> ( B @ ( A @ r2_group_6 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_group_6) ).
thf(12011,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ v3_realset2 )
& ( A @ v3_realset2 ) )
=> ( B @ ( A @ r2_group_6 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2032]) ).
thf(2157,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ l3_lattices )
| ~ ( B @ v16_lattices )
| ~ ( B @ v15_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2144]) ).
thf(2161,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ v16_lattices )
| ~ ( B @ v15_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[2157]) ).
thf(2091,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( D @ ( B @ m1_group_2 ) )
=> ( C @ ( D @ ( A @ k8_group_4 ) ) @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ m1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_group_4) ).
thf(12242,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( D @ ( B @ m1_group_2 ) )
=> ( C @ ( D @ ( A @ k8_group_4 ) ) @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ m1_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2091]) ).
thf(1126,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( B @ ( B @ ( A @ k8_group_2 ) ) @ ( A @ r1_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_group_2) ).
thf(7534,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( B @ ( B @ ( A @ k8_group_2 ) ) @ ( A @ r1_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(1831,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_group_2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_group_2) ).
thf(11237,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_group_2 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1831]) ).
thf(2100,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k6_group_2 @ v1_group_3 ) )
& ( A @ ( A @ k5_group_2 @ v1_group_3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_group_3) ).
thf(12278,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k6_group_2 @ v1_group_3 ) )
& ( A @ ( A @ k5_group_2 @ v1_group_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2100]) ).
thf(1580,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k9_group_4 ) )
<=> ! [C: $i] :
( ( A @ k1_group_3 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_group_3 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_group_2 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_group_2 ) )
=> ( ( ( D = F )
& ( C = E ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( A @ k8_group_4 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_group_4) ).
thf(9967,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k1_group_3 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_group_3 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_group_2 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_group_2 ) )
=> ( ( ( D = F )
& ( C = E ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( A @ k8_group_4 ) ) ) ) ) ) ) ) )
=> ( B
= ( A @ k9_group_4 ) ) )
& ( ( B
= ( A @ k9_group_4 ) )
=> ! [C: $i] :
( ( A @ k1_group_3 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_group_3 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_group_2 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_group_2 ) )
=> ( ( ( D = F )
& ( C = E ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ ( A @ k1_group_3 @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( A @ k8_group_4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1580]) ).
thf(11586,plain,
sk610 @ v7_group_1,
inference(cnfConj,[status(thm)],[11584]) ).
thf(22490,plain,
! [A: $i] :
( ( A != sk610 )
| ( k1_xboole_0 @ v7_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,11586]) ).
thf(22491,plain,
( ( k1_xboole_0 @ v7_group_1 )
| ( sk610 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22490:[bind(A,$thf( sk610 ))]]) ).
thf(711,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( k4_numbers @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m2_finseq_1 ) )
=> ( ( D
= ( C @ ( B @ ( A @ k4_group_4 ) ) ) )
<=> ( ! [E: $i] :
( ( k5_numbers @ ( k1_numbers @ ( E @ m2_subset_1 ) ) )
=> ( ( C @ k4_finseq_1 @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ ( A @ u1_struct_0 @ ( k5_numbers @ k4_finseq_4 ) ) ) @ ( E @ ( B @ ( k4_numbers @ ( k5_numbers @ k4_finseq_4 ) ) ) @ k2_group_4 @ ( A @ k6_group_1 ) ) ) ) ) )
& ( ( D @ k3_finseq_1 )
= ( C @ k3_finseq_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_group_4) ).
thf(5546,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( k4_numbers @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m2_finseq_1 ) )
=> ( ( ( ! [E: $i] :
( ( k5_numbers @ ( k1_numbers @ ( E @ m2_subset_1 ) ) )
=> ( ( C @ k4_finseq_1 @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ ( A @ u1_struct_0 @ ( k5_numbers @ k4_finseq_4 ) ) ) @ ( E @ ( B @ ( k4_numbers @ ( k5_numbers @ k4_finseq_4 ) ) ) @ k2_group_4 @ ( A @ k6_group_1 ) ) ) ) ) )
& ( ( D @ k3_finseq_1 )
= ( C @ k3_finseq_1 ) ) )
=> ( D
= ( C @ ( B @ ( A @ k4_group_4 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k4_group_4 ) ) ) )
=> ( ! [E: $i] :
( ( k5_numbers @ ( k1_numbers @ ( E @ m2_subset_1 ) ) )
=> ( ( C @ k4_finseq_1 @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ ( A @ u1_struct_0 @ ( k5_numbers @ k4_finseq_4 ) ) ) @ ( E @ ( B @ ( k4_numbers @ ( k5_numbers @ k4_finseq_4 ) ) ) @ k2_group_4 @ ( A @ k6_group_1 ) ) ) ) ) )
& ( ( D @ k3_finseq_1 )
= ( C @ k3_finseq_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(2190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) )
& ( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_funct_2 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) )
& ( ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) ) ),
inference(cnf,[status(esa)],[2189]) ).
thf(2193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[2190]) ).
thf(5039,plain,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
inference(cnf,[status(esa)],[5038]) ).
thf(371,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_1) ).
thf(3773,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(1702,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( B @ ( A @ k2_group_2 ) ) )
= ( D @ ( B @ ( A @ k2_group_2 ) ) @ ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_group_2) ).
thf(10611,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( B @ ( A @ k2_group_2 ) ) )
= ( D @ ( B @ ( A @ k2_group_2 ) ) @ ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1702]) ).
thf(1437,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_subset_1) ).
thf(9210,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1437]) ).
thf(444,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ l3_lattices )
& ( B @ v13_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ k5_lattices )
= ( B @ k5_lattices @ ( A @ k5_lattices @ ( B @ ( A @ k10_filter_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_filter_1) ).
thf(4127,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ l3_lattices )
& ( B @ v13_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ k5_lattices )
= ( B @ k5_lattices @ ( A @ k5_lattices @ ( B @ ( A @ k10_filter_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(2220,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk4 ) ) @ m1_subset_1 ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[2217]) ).
thf(714,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ ( B @ u1_struct_0 @ k1_finsop_1 ) ) @ ( B @ k3_group_4 ) )
= ( C @ ( A @ ( B @ k6_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_group_4) ).
thf(5567,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ ( B @ u1_struct_0 @ k1_finsop_1 ) ) @ ( B @ k3_group_4 ) )
= ( C @ ( A @ ( B @ k6_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ( C @ ( B @ r1_partfun1 ) )
& ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_funct_2) ).
thf(4096,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ( C @ ( B @ r1_partfun1 ) )
& ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(882,axiom,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_subset_1) ).
thf(6403,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(1324,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k14_group_2 ) )
= ( B @ ( A @ k15_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_group_3) ).
thf(8549,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k14_group_2 ) )
= ( B @ ( A @ k15_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).
thf(22154,plain,
! [A: $i] :
( ( A != sk259 )
| ( k1_xboole_0 @ v2_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,6218]) ).
thf(22155,plain,
( ( k1_xboole_0 @ v2_group_1 )
| ( sk259 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22154:[bind(A,$thf( sk259 ))]]) ).
thf(1252,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( A @ k9_group_3 ) @ ( B @ r2_hidden ) )
<=> ( C @ ( B @ ( A @ r6_group_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_group_3) ).
thf(8152,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( ( C @ ( B @ ( A @ r6_group_3 ) ) )
=> ( C @ ( A @ k9_group_3 ) @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k9_group_3 ) @ ( B @ r2_hidden ) )
=> ( C @ ( B @ ( A @ r6_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(607,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( A @ ( C @ ( B @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_enumset1) ).
thf(5011,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( A @ ( C @ ( B @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(359,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k16_lattice3 ) )
= B )
& ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k15_lattice3 ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattice3) ).
thf(3726,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k16_lattice3 ) )
= B )
& ( ( B @ ( A @ k1_struct_0 ) @ ( A @ k15_lattice3 ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(227,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( C @ r1_tarski ) )
& ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( B @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_filter_0) ).
thf(3077,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( C @ r1_tarski ) )
& ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(536,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
<=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ ( C @ k5_relat_1 ) ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
& ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_1) ).
thf(4645,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ ( C @ k5_relat_1 ) ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
& ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( B = C ) ) ) )
=> ( A @ v2_funct_1 ) )
& ( ( A @ v2_funct_1 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ ( C @ k5_relat_1 ) ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
& ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( B = C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(1632,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ r5_group_3 ) ) )
<=> ? [D: $i] :
( ( ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) )
= ( D @ ( C @ ( A @ k6_group_3 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_group_3) ).
thf(10257,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ? [D: $i] :
( ( ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) )
= ( D @ ( C @ ( A @ k6_group_3 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ r5_group_3 ) ) ) )
& ( ( C @ ( B @ ( A @ r5_group_3 ) ) )
=> ? [D: $i] :
( ( ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) )
= ( D @ ( C @ ( A @ k6_group_3 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1632]) ).
thf(1216,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
thf(7983,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(1378,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( A @ k3_group_1 ) @ r2_hidden ) ) ) )
& ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k1_group_1 ) ) @ r2_hidden ) ) ) ) ) )
=> ( ( B @ ( B @ ( A @ k2_group_2 ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_group_2) ).
thf(8862,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( A @ k3_group_1 ) @ r2_hidden ) ) ) )
& ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k1_group_1 ) ) @ r2_hidden ) ) ) ) ) )
=> ( ( B @ ( B @ ( A @ k2_group_2 ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378]) ).
thf(1164,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ? [D: $i] :
( ( ( D @ u1_struct_0 )
= ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( B @ ( A @ k3_group_1 ) @ ( A @ k4_group_2 ) ) ) )
& ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_group_2) ).
thf(7719,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ? [D: $i] :
( ( ( D @ u1_struct_0 )
= ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( B @ ( A @ k3_group_1 ) @ ( A @ k4_group_2 ) ) ) )
& ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relset_1) ).
thf(3330,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
| ( A @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(2738,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
| ( A @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1901,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k2_group_3 ) ) )
= ( D @ ( C @ ( A @ k2_group_3 ) ) @ ( D @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ k1_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_group_3) ).
thf(11502,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k2_group_3 ) ) )
= ( D @ ( C @ ( A @ k2_group_3 ) ) @ ( D @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ k1_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1901]) ).
thf(1346,axiom,
( ! [A: $i] :
( ( A @ v1_card_1 )
=> ( ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s2_card_1 ) ) )
=> ( A @ p1_s2_card_1 ) ) )
=> ! [A: $i] :
( ( A @ v1_card_1 )
=> ( A @ p1_s2_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_card_1) ).
thf(8665,plain,
( ! [A: $i] :
( ( A @ v1_card_1 )
=> ( ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s2_card_1 ) ) )
=> ( A @ p1_s2_card_1 ) ) )
=> ! [A: $i] :
( ( A @ v1_card_1 )
=> ( A @ p1_s2_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).
thf(1645,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_2_lattice3 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( D @ ( B @ r4_lattice3 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_lattice3) ).
thf(10348,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ ( B @ r4_lattice3 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_2_lattice3 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_2_lattice3 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( D @ ( B @ r4_lattice3 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1645]) ).
thf(33526,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_zfmisc_1 @ k1_card_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,32953]) ).
thf(33527,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_zfmisc_1 @ k1_card_1 ) )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[33526]) ).
thf(33528,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_card_1 @ sk149 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[33527:[bind(A,$thf( D @ k1_zfmisc_1 @ k1_card_1 )),bind(B,$thf( D ))]]) ).
thf(33541,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_card_1 @ sk149 @ v1_funct_1 ),
inference(simp,[status(thm)],[33528]) ).
thf(2006,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ a_1_0_group_6 @ ( A @ r2_hidden ) )
<=> ? [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ( B @ k2_group_5 ) ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_group_6) ).
thf(11919,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ( B @ k2_group_5 ) ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_group_6 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_group_6 @ ( A @ r2_hidden ) )
=> ? [C: $i,D: $i] :
( ( A
= ( D @ ( C @ ( B @ k2_group_5 ) ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2006]) ).
thf(1880,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( B @ ( A @ r3_group_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t105_group_3) ).
thf(11423,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( B @ ( A @ r3_group_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1880]) ).
thf(618,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_zfmisc_1) ).
thf(5086,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(1365,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k5_lattice4 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k5_lattice4 @ v1_funct_2 ) ) )
& ( A @ k5_lattice4 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattice4) ).
thf(8745,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k5_lattice4 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k5_lattice4 @ v1_funct_2 ) ) )
& ( A @ k5_lattice4 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).
thf(285,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( k5_numbers @ ( k1_numbers @ ( B @ ( A @ k7_group_1 ) @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_group_1) ).
thf(3340,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( k5_numbers @ ( k1_numbers @ ( B @ ( A @ k7_group_1 ) @ m2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(2054,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_group_1 @ v1_finseqop ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_group_1) ).
thf(12099,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_group_1 @ v1_finseqop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2054]) ).
thf(337,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
<=> ( C @ ( A @ k4_lattice3 ) @ ( B @ ( A @ k4_lattice3 ) @ ( A @ k3_lattice3 @ r3_orders_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lattice3) ).
thf(3594,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k4_lattice3 ) @ ( B @ ( A @ k4_lattice3 ) @ ( A @ k3_lattice3 @ r3_orders_2 ) ) )
=> ( C @ ( B @ ( A @ r3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( C @ ( A @ k4_lattice3 ) @ ( B @ ( A @ k4_lattice3 ) @ ( A @ k3_lattice3 @ r3_orders_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(2018,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= B ) ) )
=> ( A @ v7_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_group_3) ).
thf(11968,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= B ) ) )
=> ( A @ v7_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2018]) ).
thf(241,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_2) ).
thf(3123,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_realset1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_realset1) ).
thf(2759,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(301,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_0 @ v2_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_lattice4) ).
thf(3436,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_0 @ v2_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(1291,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] : ( C @ ( B @ ( A @ a_3_4_lattice3 ) ) @ ( A @ k16_lattice3 ) @ ( C @ ( A @ k16_lattice3 ) @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_lattice3) ).
thf(8344,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] : ( C @ ( B @ ( A @ a_3_4_lattice3 ) ) @ ( A @ k16_lattice3 ) @ ( C @ ( A @ k16_lattice3 ) @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(7341,plain,
( ! [A: $i,B: $i] :
( ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = B ) )
& ! [A: $i,B: $i] :
( ( A = B )
=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ) ),
inference(miniscope,[status(thm)],[7340]) ).
thf(7342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C = D )
| ~ ( C @ ( D @ r1_tarski ) )
| ~ ( D @ ( C @ r1_tarski ) ) )
& ( ( A @ ( B @ r1_tarski ) )
| ( A != B ) )
& ( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[7341]) ).
thf(7343,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[7342]) ).
thf(7346,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[7343]) ).
thf(7347,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(simp,[status(thm)],[7346]) ).
thf(16628,plain,
( ( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk167 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4741,16583]) ).
thf(16629,plain,
( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk167 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[16628]) ).
thf(16643,plain,
( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) )
!= sk167 ),
inference(simp,[status(thm)],[16629]) ).
thf(16823,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
!= ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) ) )
| ( A != sk167 ) ),
inference(paramod_ordered,[status(thm)],[2270,16643]) ).
thf(16827,plain,
( ( k1_xboole_0 @ ( sk167 @ k4_xboole_0 ) )
!= ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) ) ),
inference(simp,[status(thm)],[16823]) ).
thf(21675,plain,
( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) )
!= sk167 ),
inference(rewrite,[status(thm)],[16827,2270]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_xboole_1) ).
thf(2706,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(1113,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
<=> ( ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_filter_0) ).
thf(7465,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) )
=> ( C @ ( B @ ( A @ r3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( E @ v1_partfun1 ) ) )
& ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_partfun1) ).
thf(5539,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( E @ v1_partfun1 ) ) )
& ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(21895,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k2_card_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,15028]) ).
thf(21896,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k2_card_1 ) )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[21895]) ).
thf(21897,plain,
! [A: $i] : ( A @ k2_card_1 @ sk149 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[21896:[bind(A,$thf( C @ k2_card_1 )),bind(B,$thf( C ))]]) ).
thf(23196,plain,
! [A: $i] : ( A @ k2_card_1 @ sk149 @ v1_funct_1 ),
inference(simp,[status(thm)],[21897]) ).
thf(1127,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ l3_lattices )
& ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(7536,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ l3_lattices )
& ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( A @ ( D @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_partfun1) ).
thf(2457,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( A @ ( D @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(2068,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v2_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_group_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_group_2) ).
thf(12146,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v2_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_group_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2068]) ).
thf(1451,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( A @ k1_funct_2 ) @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_2) ).
thf(9290,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( A @ k1_funct_2 ) @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).
thf(29620,plain,
( ( ( sk611 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,18403]) ).
thf(29621,plain,
( ( ( sk611 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[29620]) ).
thf(29634,plain,
( ( sk611 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[29621]) ).
thf(903,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_finset_1) ).
thf(6549,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(865,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( A @ k2_funct_1 @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
thf(6334,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( A @ k2_funct_1 @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(1547,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v6_ordinal1 )
& ( A != k1_xboole_0 )
& ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_finset_1) ).
thf(9803,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v6_ordinal1 )
& ( A != k1_xboole_0 )
& ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1547]) ).
thf(2073,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ ( A @ k2_group_1 @ v1_group_4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_group_4) ).
thf(12167,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ ( A @ k2_group_1 @ v1_group_4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2073]) ).
thf(2003,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E = C )
& ( D = B ) )
=> ( ( E @ ( D @ ( A @ k11_group_4 @ r3_lattices ) ) )
<=> ( C @ ( A @ ( B @ m1_group_6 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_latsubgr) ).
thf(11900,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E = C )
& ( D = B ) )
=> ( ( ( C @ ( A @ ( B @ m1_group_6 ) ) )
=> ( E @ ( D @ ( A @ k11_group_4 @ r3_lattices ) ) ) )
& ( ( E @ ( D @ ( A @ k11_group_4 @ r3_lattices ) ) )
=> ( C @ ( A @ ( B @ m1_group_6 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2003]) ).
thf(1972,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( B @ k2_group_1 @ ( C @ r1_rlvect_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_group_2) ).
thf(11792,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( B @ k2_group_1 @ ( C @ r1_rlvect_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1972]) ).
thf(290,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_zfmisc_1) ).
thf(3355,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(1020,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ( ( C @ ( D @ ( B @ k12_group_2 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( E @ ( D @ r1_rlvect_1 ) )
& ( A
= ( E @ ( C @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_group_2) ).
thf(7021,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ( ( ? [E: $i] :
( ( E @ ( D @ r1_rlvect_1 ) )
& ( A
= ( E @ ( C @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ ( B @ k12_group_2 ) ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( D @ ( B @ k12_group_2 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( E @ ( D @ r1_rlvect_1 ) )
& ( A
= ( E @ ( C @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(20723,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ( A @ l1_struct_0 )
| ~ ( sk1 @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,18966]) ).
thf(20724,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
| ~ ( sk1 @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[20723:[]]) ).
thf(719,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ l3_lattices )
& ( B @ v11_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
<=> ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v11_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_filter_1) ).
thf(5578,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v11_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) )
=> ( ( B @ l3_lattices )
& ( B @ v11_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) )
& ( ( ( B @ l3_lattices )
& ( B @ v11_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v11_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(357,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
thf(3719,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(1777,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ~ ( ( C @ ( E @ r2_hidden ) )
& ( E @ ( D @ ( A @ r3_lattices ) ) ) ) )
& ( B @ ( D @ r2_hidden ) ) ) )
=> ( C @ ( A @ k15_lattice3 ) @ ( B @ ( A @ k15_lattice3 ) @ ( A @ r3_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattice3) ).
thf(11038,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ~ ( ( C @ ( E @ r2_hidden ) )
& ( E @ ( D @ ( A @ r3_lattices ) ) ) ) )
& ( B @ ( D @ r2_hidden ) ) ) )
=> ( C @ ( A @ k15_lattice3 ) @ ( B @ ( A @ k15_lattice3 ) @ ( A @ r3_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1777]) ).
thf(2358,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( B @ r4_binop_1 ) ) )
| ~ ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r4_binop_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2355]) ).
thf(417,axiom,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(4007,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(4008,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
inference(cnf,[status(esa)],[4007]) ).
thf(4009,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
inference(lifteq,[status(thm)],[4008]) ).
thf(4495,plain,
! [A: $i] : ( A @ k3_tarski @ ( A @ k1_setfam_1 @ r1_tarski ) ),
inference(cnf,[status(esa)],[4494]) ).
thf(21533,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_zfmisc_1 @ k3_tarski )
!= ( B @ k3_tarski ) )
| ( A @ ( B @ k1_setfam_1 @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[4009,4495]) ).
thf(21534,plain,
! [A: $i] : ( A @ ( A @ k1_zfmisc_1 @ k1_setfam_1 @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[21533:[bind(A,$thf( C )),bind(B,$thf( C @ k1_zfmisc_1 ))]]) ).
thf(21551,plain,
! [A: $i] : ( A @ ( A @ k1_zfmisc_1 @ k1_setfam_1 @ r1_tarski ) ),
inference(simp,[status(thm)],[21534]) ).
thf(1552,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k1_setfam_1 @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_setfam_1) ).
thf(9835,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k1_setfam_1 @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1552]) ).
thf(2026,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( ( D @ ( C @ m1_group_2 ) )
& ( D @ ( B @ m1_group_2 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ m1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_group_4) ).
thf(11996,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( ( D @ ( C @ m1_group_2 ) )
& ( D @ ( B @ m1_group_2 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ m1_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2026]) ).
thf(1393,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_rlvect_1 ) )
=> ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k7_group_3 ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_group_3) ).
thf(8970,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_rlvect_1 ) )
=> ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k7_group_3 ) @ r1_tarski ) ) ) )
=> ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) ) )
& ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_rlvect_1 ) )
=> ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k7_group_3 ) @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393]) ).
thf(2096,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( C @ v6_group_1 )
| ( B @ v6_group_1 ) )
=> ( C @ ( B @ ( A @ k9_group_2 ) ) @ v6_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_group_2) ).
thf(12263,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( C @ v6_group_1 )
| ( B @ v6_group_1 ) )
=> ( C @ ( B @ ( A @ k9_group_2 ) ) @ v6_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2096]) ).
thf(4586,plain,
k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v7_group_1,
inference(cnfConj,[status(thm)],[4583]) ).
thf(1916,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ m1_group_2 ) )
& ( C @ ( B @ ( A @ k9_group_2 ) ) @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_group_2) ).
thf(11554,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ m1_group_2 ) )
& ( C @ ( B @ ( A @ k9_group_2 ) ) @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1916]) ).
thf(2346,plain,
! [A: $i] : ( A @ sk11 @ v1_finseq_1 ),
inference(cnfConj,[status(thm)],[2342]) ).
thf(349,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( A @ ( B @ k5_relat_1 ) @ v2_funct_1 ) )
=> ( ( A @ v2_funct_1 )
& ( B @ v2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funct_1) ).
thf(3678,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( A @ ( B @ k5_relat_1 ) @ v2_funct_1 ) )
=> ( ( A @ v2_funct_1 )
& ( B @ v2_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(2040,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k7_group_3 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_group_3) ).
thf(12032,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k7_group_3 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2040]) ).
thf(2361,plain,
! [B: $i,A: $i] :
( ( B @ v1_funct_1 )
| ~ ( A @ ( B @ m1_orders_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2360]) ).
thf(2311,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk6 ) @ ( np__1 @ r1_xreal_0 ) )
| ( A @ ( B @ r1_xreal_0 ) )
| ~ ( B @ v1_int_1 )
| ~ ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) ) ),
inference(cnfConj,[status(thm)],[2308]) ).
thf(1507,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ r1_rlvect_1 ) )
<=> ( D @ ( C @ r1_rlvect_1 ) ) ) )
=> ( ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) )
= ( C @ u1_group_1 @ ( C @ u1_struct_0 @ g1_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_group_2) ).
thf(9560,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ r1_rlvect_1 ) )
=> ( D @ ( B @ r1_rlvect_1 ) ) )
& ( ( D @ ( B @ r1_rlvect_1 ) )
=> ( D @ ( C @ r1_rlvect_1 ) ) ) ) )
=> ( ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) )
= ( C @ u1_group_1 @ ( C @ u1_struct_0 @ g1_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1507]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( B @ k5_relat_1 ) )
= ( D @ ( B @ k5_relat_1 ) ) )
& ( ( D @ k1_relat_1 )
= A )
& ( ( C @ k1_relat_1 )
= A )
& ( A
= ( B @ k2_relat_1 ) ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_funct_1) ).
thf(3101,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( B @ k5_relat_1 ) )
= ( D @ ( B @ k5_relat_1 ) ) )
& ( ( D @ k1_relat_1 )
= A )
& ( ( C @ k1_relat_1 )
= A )
& ( A
= ( B @ k2_relat_1 ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(1745,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( A @ k1_setfam_1 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_setfam_1) ).
thf(10842,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( A @ k1_setfam_1 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1745]) ).
thf(948,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_subset_1) ).
thf(6742,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(10370,plain,
sk537 @ l2_struct_0,
inference(cnf,[status(esa)],[10369]) ).
thf(1596,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(10088,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1596]) ).
thf(626,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( B @ ( A @ ( A @ ( B @ k1_partfun1 ) ) ) ) ) )
= ( B @ k6_partfun1 ) )
=> ( ( C @ k2_relat_1 )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_funct_2) ).
thf(5143,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( B @ ( A @ ( A @ ( B @ k1_partfun1 ) ) ) ) ) )
= ( B @ k6_partfun1 ) )
=> ( ( C @ k2_relat_1 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(4912,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk180 ) @ k2_relat_1 @ r1_tarski ) )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[4909]) ).
thf(4928,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk180 ) @ k2_relat_1 @ r1_tarski ) )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[4912]) ).
thf(4929,plain,
! [A: $i] : ( A @ ( A @ ( k1_xboole_0 @ sk180 ) @ k2_relat_1 @ r1_tarski ) ),
inference(simp,[status(thm)],[4928]) ).
thf(1635,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_lattices @ ( A @ k4_lattices ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattices) ).
thf(10297,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_lattices @ ( A @ k4_lattices ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1635]) ).
thf(1773,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_domain_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_domain_1) ).
thf(11002,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_domain_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1773]) ).
thf(1661,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ( A @ k2_group_1 @ ( B @ ( A @ k13_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) ) )
& ( ( A @ k2_group_1 @ ( B @ ( A @ k12_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_group_2) ).
thf(10429,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ( A @ k2_group_1 @ ( B @ ( A @ k13_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) ) )
& ( ( A @ k2_group_1 @ ( B @ ( A @ k12_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1661]) ).
thf(1142,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( C @ ( B @ ( D @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_filter_0) ).
thf(7594,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( C @ ( B @ ( D @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(414,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_partfun1) ).
thf(3996,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_partfun1) ).
thf(2538,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(484,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_binop_1) ).
thf(4369,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r5_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(1968,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( B @ ( A @ k3_group_1 ) @ ( A @ k2_group_3 ) ) )
= ( B @ ( A @ k3_group_1 ) ) )
& ( ( B @ ( A @ k3_group_1 ) @ ( B @ ( A @ k2_group_3 ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_group_3) ).
thf(11771,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( B @ ( A @ k3_group_1 ) @ ( A @ k2_group_3 ) ) )
= ( B @ ( A @ k3_group_1 ) ) )
& ( ( B @ ( A @ k3_group_1 ) @ ( B @ ( A @ k2_group_3 ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1968]) ).
thf(1461,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k2_struct_0 ) ) @ ( B @ ( A @ r3_lattice3 ) ) )
<=> ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lattice3) ).
thf(9349,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) )
=> ( D @ ( C @ ( A @ k2_struct_0 ) ) @ ( B @ ( A @ r3_lattice3 ) ) ) )
& ( ( D @ ( C @ ( A @ k2_struct_0 ) ) @ ( B @ ( A @ r3_lattice3 ) ) )
=> ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1461]) ).
thf(1040,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( A @ v4_group_1 )
=> ( ( B @ ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( A @ k3_group_2 ) ) )
= ( B @ ( D @ ( A @ k3_group_2 ) ) @ ( C @ ( A @ k3_group_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_group_2) ).
thf(7130,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( A @ v4_group_1 )
=> ( ( B @ ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( A @ k3_group_2 ) ) )
= ( B @ ( D @ ( A @ k3_group_2 ) ) @ ( C @ ( A @ k3_group_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(2151,plain,
! [B: $i,A: $i] :
( ( A @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2144]) ).
thf(1903,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_group_2 )
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_group_2) ).
thf(11508,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_group_2 )
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1903]) ).
thf(2063,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_group_4 ) @ u1_struct_0 )
= ( B @ ( A @ a_2_0_group_4 ) @ k1_setfam_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_group_4) ).
thf(12131,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_group_4 ) @ u1_struct_0 )
= ( B @ ( A @ a_2_0_group_4 ) @ k1_setfam_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2063]) ).
thf(2085,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k5_group_2 @ v3_realset2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_group_6) ).
thf(12214,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k5_group_2 @ v3_realset2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2085]) ).
thf(2106,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( D @ ( C @ ( A @ k9_group_2 ) ) @ ( B @ ( A @ k9_group_2 ) ) @ ( D @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_group_2) ).
thf(12297,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( D @ ( C @ ( A @ k9_group_2 ) ) @ ( B @ ( A @ k9_group_2 ) ) @ ( D @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2106]) ).
thf(2089,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 )
& ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r1_group_2 ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_group_2) ).
thf(12227,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 )
& ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( B = C )
=> ( C @ ( B @ ( A @ r1_group_2 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_group_2 ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2089]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k2_xboole_0 ) @ k4_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_zfmisc_1) ).
thf(2493,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k2_xboole_0 ) @ k4_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(73,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( B @ v1_finset_1 )
=> ( ( ( A @ k2_relat_1 @ ( B @ r1_tarski ) )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k1_finseq_3 ) @ k3_finseq_1 )
= ( B @ k4_card_1 @ ( A @ k3_finseq_1 @ k6_xcmplx_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_finseq_3) ).
thf(2415,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( B @ v1_finset_1 )
=> ( ( ( A @ k2_relat_1 @ ( B @ r1_tarski ) )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k1_finseq_3 ) @ k3_finseq_1 )
= ( B @ k4_card_1 @ ( A @ k3_finseq_1 @ k6_xcmplx_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(1373,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k6_group_3 ) ) @ ( B @ m1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_group_3) ).
thf(8799,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k6_group_3 ) ) @ ( B @ m1_group_2 ) ) )
=> ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) ) )
& ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k6_group_3 ) ) @ ( B @ m1_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373]) ).
thf(1617,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ k3_group_3 ) ) @ ( A @ k4_group_3 ) ) )
= ( D @ ( B @ ( A @ k4_group_2 ) ) @ ( C @ ( A @ k3_group_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_group_3) ).
thf(10204,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ k3_group_3 ) ) @ ( A @ k4_group_3 ) ) )
= ( D @ ( B @ ( A @ k4_group_2 ) ) @ ( C @ ( A @ k3_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1617]) ).
thf(1471,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(9377,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471]) ).
thf(891,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v17_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_0_lattice3 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( C @ k7_lattices ) ) )
& ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice3) ).
thf(6443,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v17_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( C @ k7_lattices ) ) )
& ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_lattice3 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_lattice3 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( C @ k7_lattices ) ) )
& ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(1593,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_5_lattice3 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k3_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_5_lattice3) ).
thf(10066,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k3_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_5_lattice3 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_5_lattice3 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k3_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1593]) ).
thf(43653,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( k1_xboole_0 @ k2_xboole_0 ) @ k4_xboole_0 ) )
!= ( k5_numbers @ ( B @ k4_xboole_0 ) ) )
| ( k1_xboole_0 @ ( k4_numbers @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[25181,21644]) ).
thf(43654,plain,
k1_xboole_0 @ ( k4_numbers @ ( k5_numbers @ ( k1_xboole_0 @ k2_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ),
inference(pattern_uni,[status(thm)],[43653:[bind(A,$thf( k5_numbers )),bind(B,$thf( k5_numbers @ ( k1_xboole_0 @ k2_xboole_0 ) ))]]) ).
thf(44304,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( k4_numbers @ ( k5_numbers @ ( k1_xboole_0 @ k2_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43654,2188]) ).
thf(44305,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( k4_numbers @ ( k5_numbers @ ( k1_xboole_0 @ k2_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(simp,[status(thm)],[44304]) ).
thf(44306,plain,
k1_xboole_0 @ ( k4_numbers @ k2_xboole_0 ) @ ( k5_numbers @ ( k1_xboole_0 @ k2_xboole_0 ) @ r1_tarski ),
inference(pattern_uni,[status(thm)],[44305:[bind(A,$thf( k5_numbers @ ( k1_xboole_0 @ k2_xboole_0 ) )),bind(B,$thf( k4_numbers )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(44634,plain,
k4_numbers @ ( k5_numbers @ ( k1_xboole_0 @ k2_xboole_0 ) @ r1_tarski ),
inference(rewrite,[status(thm)],[44306,5349]) ).
thf(44669,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( k5_numbers @ ( k1_xboole_0 @ k2_xboole_0 ) @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44634,2215]) ).
thf(44670,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( k5_numbers @ ( k1_xboole_0 @ k2_xboole_0 ) @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[44669]) ).
thf(44671,plain,
! [A: $i] : ( k4_numbers @ ( A @ ( k5_numbers @ ( k1_xboole_0 @ k2_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[44670:[bind(A,$thf( k5_numbers @ ( k1_xboole_0 @ k2_xboole_0 ) )),bind(B,$thf( k4_numbers )),bind(C,$thf( C ))]]) ).
thf(44700,plain,
! [A: $i] : ( k4_numbers @ ( A @ ( k5_numbers @ ( k1_xboole_0 @ k2_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[44671]) ).
thf(60663,plain,
! [A: $i] : ( k4_numbers @ ( A @ ( k1_xboole_0 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[44700,60659]) ).
thf(63090,plain,
k4_numbers @ ( k1_xboole_0 @ r1_tarski ),
inference(rewrite,[status(thm)],[60663,2990]) ).
thf(831,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
thf(6147,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(898,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_xboole_1) ).
thf(6500,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(2041,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ( ( A @ k2_group_1 @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( B @ ( A @ u1_struct_0 @ k1_group_4 ) ) @ ( A @ k3_group_4 ) )
= ( B @ ( A @ k3_group_4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_group_4) ).
thf(12034,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ( ( A @ k2_group_1 @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( B @ ( A @ u1_struct_0 @ k1_group_4 ) ) @ ( A @ k3_group_4 ) )
= ( B @ ( A @ k3_group_4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2041]) ).
thf(970,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v4_lattice3 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ r3_lattice3 ) ) )
=> ( C @ ( D @ ( A @ r1_lattices ) ) ) ) )
& ( B @ ( C @ ( A @ r3_lattice3 ) ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_vectsp_8) ).
thf(6815,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ r3_lattice3 ) ) )
=> ( C @ ( D @ ( A @ r1_lattices ) ) ) ) )
& ( B @ ( C @ ( A @ r3_lattice3 ) ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) )
=> ( A @ v4_lattice3 ) )
& ( ( A @ v4_lattice3 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ r3_lattice3 ) ) )
=> ( C @ ( D @ ( A @ r1_lattices ) ) ) ) )
& ( B @ ( C @ ( A @ r3_lattice3 ) ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(1271,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_2) ).
thf(8237,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(194,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ v15_lattices )
& ( A @ v15_lattices ) )
<=> ( B @ ( A @ k8_filter_1 ) @ v15_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_filter_1) ).
thf(2906,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
=> ( ( B @ v15_lattices )
& ( A @ v15_lattices ) ) )
& ( ( ( B @ v15_lattices )
& ( A @ v15_lattices ) )
=> ( B @ ( A @ k8_filter_1 ) @ v15_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(844,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(6197,plain,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(1144,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(7607,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(822,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ( B @ ( A @ k7_setfam_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_setfam_1) ).
thf(6112,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ( B @ ( A @ k7_setfam_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(1246,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
<=> ( B
= ( A @ k2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_subset_1) ).
thf(8120,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B
= ( A @ k2_subset_1 ) )
=> ( B @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) ) )
& ( ( B @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B
= ( A @ k2_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(763,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) )
= ( B @ u1_lattices @ ( A @ u1_lattices @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_filter_1 ) ) ) @ ( B @ u2_lattices @ ( A @ u2_lattices @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_filter_1 ) ) ) @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ g3_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_filter_1) ).
thf(5827,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) )
= ( B @ u1_lattices @ ( A @ u1_lattices @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_filter_1 ) ) ) @ ( B @ u2_lattices @ ( A @ u2_lattices @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_filter_1 ) ) ) @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ g3_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(1757,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k5_group_4 ) @ ( B @ ( A @ k5_group_4 ) @ m1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_group_4) ).
thf(10898,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k5_group_4 ) @ ( B @ ( A @ k5_group_4 ) @ m1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1757]) ).
thf(3480,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ k2_relat_1 )
= A ),
inference(cnfConj,[status(thm)],[3478]) ).
thf(3482,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ k2_relat_1 )
= A ),
inference(lifteq,[status(thm)],[3480]) ).
thf(3483,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ k2_relat_1 )
= A ),
inference(simp,[status(thm)],[3482]) ).
thf(16258,plain,
! [A: $i] :
( ( A @ k6_partfun1 @ k2_relat_1 )
= A ),
inference(rewrite,[status(thm)],[3483,11231]) ).
thf(360,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( B @ ( A @ k8_filter_0 ) @ u1_lattices )
= ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( ( B @ ( A @ k8_filter_0 ) @ u2_lattices )
= ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( ( B @ ( A @ k8_filter_0 ) @ u1_struct_0 )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_filter_0) ).
thf(3732,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( B @ ( A @ k8_filter_0 ) @ u1_lattices )
= ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( ( B @ ( A @ k8_filter_0 ) @ u2_lattices )
= ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( ( B @ ( A @ k8_filter_0 ) @ u1_struct_0 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(1412,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(9047,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412]) ).
thf(1352,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_2) ).
thf(8693,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).
thf(43,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A
= ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ k3_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_partfun1) ).
thf(2297,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A
= ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ k3_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(2298,plain,
! [A: $i] :
( ( A
= ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ k3_partfun1 ) ) ) )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2297]) ).
thf(2299,plain,
! [A: $i] :
( ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ k3_partfun1 ) ) )
= A ) ),
inference(lifteq,[status(thm)],[2298]) ).
thf(1308,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k2_xcmplx_0 ) @ ( C @ k6_group_1 ) ) )
= ( D @ ( B @ ( C @ k6_group_1 ) ) @ ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_group_1) ).
thf(8461,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k2_xcmplx_0 ) @ ( C @ k6_group_1 ) ) )
= ( D @ ( B @ ( C @ k6_group_1 ) ) @ ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).
thf(776,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_lattice4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_lattice4) ).
thf(5901,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_lattice4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(1435,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_6_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ( C @ ( E @ r2_hidden ) )
<=> ~ ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_6_domain_1) ).
thf(9185,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ~ ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ~ ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_6_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_6_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ~ ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ~ ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435]) ).
thf(1863,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( ( B @ ( D @ ( A @ k1_group_1 ) ) )
= C )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_group_1) ).
thf(11355,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( ( B @ ( D @ ( A @ k1_group_1 ) ) )
= C )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1863]) ).
thf(769,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ v1_partfun1 ) ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funct_4) ).
thf(5880,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ v1_partfun1 ) ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(43986,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( B @ v3_group_1 )
| ~ ( B @ v1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,25039]) ).
thf(43987,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B @ v3_group_1 )
| ~ ( B @ v1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[43986]) ).
thf(43988,plain,
! [A: $i] :
( ( A @ v3_group_1 )
| ~ ( A @ v1_xboole_0 )
| ( sk1 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[43987:[bind(A,$thf( sk1 ))]]) ).
thf(43992,plain,
! [A: $i] :
( ( A @ v3_group_1 )
| ~ ( A @ v1_xboole_0 )
| ( sk1 @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[43988]) ).
thf(1639,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_7_lattice3 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k15_lattice3 ) ) )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_7_lattice3) ).
thf(10316,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k15_lattice3 ) ) )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_7_lattice3 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_7_lattice3 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k15_lattice3 ) ) )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1639]) ).
thf(1089,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_lattices @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lattices) ).
thf(7360,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_lattices @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(1403,axiom,
! [A: $i,B: $i] :
( ( B @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(9015,plain,
! [A: $i,B: $i] :
( ( B @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403]) ).
thf(1731,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_mcart_1) ).
thf(10766,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1731]) ).
thf(454,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( B @ ( A @ k3_filter_0 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_filter_0) ).
thf(4176,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( B @ ( A @ k3_filter_0 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(319,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_funct_2) ).
thf(3500,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(245,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( B @ k5_relat_1 ) @ v2_funct_1 ) )
=> ( B @ v2_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_1) ).
thf(3138,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( B @ k5_relat_1 ) @ v2_funct_1 ) )
=> ( B @ v2_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(2375,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r4_lattice3 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk13 ) ) @ ( A @ r1_lattices ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2371]) ).
thf(2378,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r4_lattice3 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk13 ) ) @ ( A @ r1_lattices ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[2375]) ).
thf(755,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ ( B @ v2_filter_0 ) )
& ( B
!= ( A @ k1_filter_0 ) ) )
<=> ( A @ ( B @ v1_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_filter_0) ).
thf(5795,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ ( B @ v1_filter_0 ) )
=> ( ( A @ ( B @ v2_filter_0 ) )
& ( B
!= ( A @ k1_filter_0 ) ) ) )
& ( ( ( A @ ( B @ v2_filter_0 ) )
& ( B
!= ( A @ k1_filter_0 ) ) )
=> ( A @ ( B @ v1_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(1328,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( D @ ( C @ ( A @ k7_group_4 ) ) @ ( B @ ( A @ k3_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_group_4) ).
thf(8561,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( D @ ( C @ ( A @ k7_group_4 ) ) @ ( B @ ( A @ k3_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).
thf(946,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k7_setfam_1 ) )
= ( C @ ( A @ k7_setfam_1 ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_setfam_1) ).
thf(6737,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k7_setfam_1 ) )
= ( C @ ( A @ k7_setfam_1 ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(1957,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ l1_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_group_2) ).
thf(11718,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ l1_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1957]) ).
thf(11438,plain,
sk605 @ v2_group_1,
inference(cnfConj,[status(thm)],[11434]) ).
thf(2021,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k8_rlvect_1 ) ) ) @ ( A @ k3_group_4 ) )
= ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k1_group_1 ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k8_rlvect_1 ) ) ) @ ( A @ k3_group_4 ) )
= ( D @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_group_4) ).
thf(11979,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k8_rlvect_1 ) ) ) @ ( A @ k3_group_4 ) )
= ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k1_group_1 ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k8_rlvect_1 ) ) ) @ ( A @ k3_group_4 ) )
= ( D @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2021]) ).
thf(4509,plain,
sk145 @ v1_relat_1,
inference(cnfConj,[status(thm)],[4508]) ).
thf(1079,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k3_group_2 ) ) )
= ( C @ ( B @ ( A @ k4_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_group_2) ).
thf(7307,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k3_group_2 ) ) )
= ( C @ ( B @ ( A @ k4_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(2197,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ k7_filter_0 ) ) @ m1_filter_0 ) )
| ~ ( A @ ( C @ m1_filter_0 ) )
| ~ ( A @ ( B @ m1_filter_0 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v17_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[2196]) ).
thf(1875,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( A @ k1_group_2 ) )
= ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k3_group_1 ) @ ( A @ u1_struct_0 @ k7_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_group_2) ).
thf(11406,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( A @ k1_group_2 ) )
= ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k3_group_1 ) @ ( A @ u1_struct_0 @ k7_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1875]) ).
thf(1529,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v7_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k10_group_1 ) ) @ ( A @ ( B @ k6_group_1 ) ) )
= ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k10_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_group_1) ).
thf(9713,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v7_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k10_group_1 ) ) @ ( A @ ( B @ k6_group_1 ) ) )
= ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k10_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1529]) ).
thf(6216,plain,
sk259 @ v6_vectsp_1,
inference(cnfConj,[status(thm)],[6214]) ).
thf(2034,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ k4_group_1 )
= ( B @ u1_struct_0 @ ( A @ k4_group_1 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_relset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_group_2) ).
thf(12015,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ k4_group_1 )
= ( B @ u1_struct_0 @ ( A @ k4_group_1 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_relset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2034]) ).
thf(1571,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_2) ).
thf(9931,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1571]) ).
thf(816,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_binop_1) ).
thf(6087,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(1818,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r4_group_3 ) ) )
=> ( B @ ( C @ ( A @ r4_group_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r4_group_3) ).
thf(11188,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r4_group_3 ) ) )
=> ( B @ ( C @ ( A @ r4_group_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1818]) ).
thf(1206,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( C @ ( B @ ( A @ k7_group_4 ) ) )
= ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k10_group_2 ) ) ) )
& ( ( C @ ( B @ ( A @ k7_group_4 ) ) )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k11_group_2 ) ) ) )
& ( ( C @ ( B @ ( A @ k7_group_4 ) ) )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_group_4) ).
thf(7928,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( C @ ( B @ ( A @ k7_group_4 ) ) )
= ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k10_group_2 ) ) ) )
& ( ( C @ ( B @ ( A @ k7_group_4 ) ) )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k11_group_2 ) ) ) )
& ( ( C @ ( B @ ( A @ k7_group_4 ) ) )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_filter_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_filter_1) ).
thf(2874,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_filter_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(1786,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( C @ ( B @ ( B @ ( D @ ( C @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_relset_1) ).
thf(11078,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( C @ ( B @ ( B @ ( D @ ( C @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1786]) ).
thf(973,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_filter_0) ).
thf(6834,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(20708,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ~ ( A @ v3_struct_0 )
| ~ ( sk1 @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,18652]) ).
thf(20709,plain,
! [A: $i] :
( ~ ( A @ v3_struct_0 )
| ~ ( sk1 @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[20708:[]]) ).
thf(1665,axiom,
? [A: $i] : ( A @ v1_int_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_int_1) ).
thf(10449,plain,
? [A: $i] : ( A @ v1_int_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1665]) ).
thf(10450,plain,
sk544 @ v1_int_1,
inference(cnf,[status(esa)],[10449]) ).
thf(43287,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( B @ l1_group_1 )
| ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,21467]) ).
thf(43288,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B @ l1_group_1 )
| ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[43287]) ).
thf(43289,plain,
! [A: $i] :
( ( A @ l1_group_1 )
| ~ ( A @ v1_xboole_0 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[43288:[bind(A,$thf( sk1 ))]]) ).
thf(43292,plain,
! [A: $i] :
( ( A @ l1_group_1 )
| ~ ( A @ v1_xboole_0 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[43289]) ).
thf(665,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_relat_1) ).
thf(5367,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(1410,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( A @ k7_group_2 ) @ ( B @ r2_hidden ) )
=> ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k3_group_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_group_2) ).
thf(9042,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( A @ k7_group_2 ) @ ( B @ r2_hidden ) )
=> ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k3_group_1 ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1410]) ).
thf(798,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_partfun1) ).
thf(6004,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(38959,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k4_xboole_0 ) )
!= ( B @ ( A @ k4_xboole_0 ) ) )
| ( B @ ( k1_xboole_0 @ k1_orders_1 @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[38576,2306]) ).
thf(38960,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_orders_1 @ r1_xboole_0 ),
inference(pattern_uni,[status(thm)],[38959:[bind(A,$thf( k1_xboole_0 @ k1_tarski )),bind(B,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(39049,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_orders_1 @ r1_xboole_0 ) )
!= ( B @ ( A @ r1_xboole_0 ) ) )
| ~ $true
| ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[38960,2184]) ).
thf(39050,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_orders_1 @ r1_xboole_0 ) )
!= ( B @ ( A @ r1_xboole_0 ) ) )
| ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
inference(simp,[status(thm)],[39049]) ).
thf(39051,plain,
( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_orders_1 @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( k1_xboole_0 @ k1_orders_1 ) ),
inference(pattern_uni,[status(thm)],[39050:[bind(A,$thf( k1_xboole_0 @ k1_orders_1 )),bind(B,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(59844,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_orders_1 @ k2_xboole_0 ) @ k4_xboole_0 ) )
!= ( B @ ( A @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ k1_orders_1 @ ( B @ sk12 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[39051,59829]) ).
thf(59845,plain,
( ( k1_xboole_0 @ k1_orders_1 @ ( k1_xboole_0 @ k1_tarski @ sk12 ) )
= ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_orders_1 @ k2_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[59844:[bind(A,$thf( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_orders_1 @ k2_xboole_0 ) )),bind(B,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(59850,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k4_xboole_0 ) )
!= ( B @ ( A @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ k1_orders_1 @ ( B @ sk12 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[38576,59829]) ).
thf(59851,plain,
( ( k1_xboole_0 @ k1_orders_1 @ ( k1_xboole_0 @ k1_tarski @ sk12 ) )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(pattern_uni,[status(thm)],[59850:[bind(A,$thf( k1_xboole_0 @ k1_tarski )),bind(B,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(60002,plain,
( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_orders_1 @ k2_xboole_0 ) )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(rewrite,[status(thm)],[59845,59851]) ).
thf(1171,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_subset_1 @ ( B @ ( A @ k4_subset_1 ) ) )
= ( A @ k2_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_subset_1) ).
thf(7768,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_subset_1 @ ( B @ ( A @ k4_subset_1 ) ) )
= ( A @ k2_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(22040,plain,
! [A: $i] :
( ( A != sk607 )
| ( k1_xboole_0 @ v4_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,11471]) ).
thf(22041,plain,
( ( k1_xboole_0 @ v4_group_1 )
| ( sk607 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22040:[bind(A,$thf( sk607 ))]]) ).
thf(2014,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ m1_group_2 ) )
=> ( D @ ( C @ ( A @ k9_group_2 ) ) @ ( D @ ( B @ ( A @ k9_group_2 ) ) @ m1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_group_2) ).
thf(11947,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ m1_group_2 ) )
=> ( D @ ( C @ ( A @ k9_group_2 ) ) @ ( D @ ( B @ ( A @ k9_group_2 ) ) @ m1_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2014]) ).
thf(1934,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ v7_group_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_group_2) ).
thf(11623,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ v7_group_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1934]) ).
thf(2129,plain,
! [A: $i] :
( ( A @ v11_lattices )
| ~ ( A @ v17_lattices )
| ( A @ v3_struct_0 )
| ~ ( A @ l3_lattices ) ),
inference(cnfConj,[status(thm)],[2126]) ).
thf(1740,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_realset2 )
<=> ( ( A @ v6_group_1 )
& ( ( A @ k9_group_1 )
= np__1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_group_6) ).
thf(10810,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( ( A @ v6_group_1 )
& ( ( A @ k9_group_1 )
= np__1 ) )
=> ( A @ v3_realset2 ) )
& ( ( A @ v3_realset2 )
=> ( ( A @ v6_group_1 )
& ( ( A @ k9_group_1 )
= np__1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1740]) ).
thf(1253,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(8156,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(774,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) @ r1_tarski ) )
& ( B @ ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_relat_1) ).
thf(5894,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) @ r1_tarski ) )
& ( B @ ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(1974,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_group_3 ) @ ( A @ k2_group_2 ) ) )
= ( B @ ( A @ k7_group_3 ) @ ( C @ ( A @ k2_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_group_3) ).
thf(11796,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_group_3 ) @ ( A @ k2_group_2 ) ) )
= ( B @ ( A @ k7_group_3 ) @ ( C @ ( A @ k2_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1974]) ).
thf(1517,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_funct_2) ).
thf(9655,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1517]) ).
thf(1819,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k11_group_2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_group_2) ).
thf(11190,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k11_group_2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1819]) ).
thf(2046,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_group_2 @ ( A @ k7_group_2 ) @ ( A @ k5_group_3 ) ) )
= ( B @ ( A @ a_2_0_group_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_group_3) ).
thf(12049,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_group_2 @ ( A @ k7_group_2 ) @ ( A @ k5_group_3 ) ) )
= ( B @ ( A @ a_2_0_group_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2046]) ).
thf(11498,plain,
sk608 @ v3_group_1,
inference(cnfConj,[status(thm)],[11492]) ).
thf(501,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(4462,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(1432,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k2_group_2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_group_2) ).
thf(9174,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k2_group_2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1432]) ).
thf(1879,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ m1_group_2 ) )
& ( B @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ m1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_group_2) ).
thf(11419,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ m1_group_2 ) )
& ( B @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ m1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1879]) ).
thf(635,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( C @ ( A @ ( B @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_enumset1) ).
thf(5175,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( C @ ( A @ ( B @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(1314,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k6_group_6 ) @ u1_group_1 )
= ( B @ ( A @ k5_group_6 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_group_6) ).
thf(8517,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k6_group_6 ) @ u1_group_1 )
= ( B @ ( A @ k5_group_6 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314]) ).
thf(33,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k2_relat_1 @ ( B @ r2_hidden ) )
=> ( A @ k4_finseq_1 @ ( np__1 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_finseq_3) ).
thf(2265,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k2_relat_1 @ ( B @ r2_hidden ) )
=> ( A @ k4_finseq_1 @ ( np__1 @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(2266,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ? [B: $i] : ( A @ k2_relat_1 @ ( B @ r2_hidden ) )
=> ( A @ k4_finseq_1 @ ( np__1 @ r2_hidden ) ) ) ),
inference(miniscope,[status(thm)],[2265]) ).
thf(2267,plain,
! [B: $i,A: $i] :
( ( A @ k4_finseq_1 @ ( np__1 @ r2_hidden ) )
| ~ ( A @ k2_relat_1 @ ( B @ r2_hidden ) )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2266]) ).
thf(1784,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_zfmisc_1) ).
thf(11073,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1784]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_relat_1) ).
thf(4028,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(869,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( C @ ( B @ ( D @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_enumset1) ).
thf(6353,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( C @ ( B @ ( D @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(1200,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ( ( ( B @ ( A @ k3_xcmplx_0 ) )
= np__1 )
<=> ( ( ( B
= ( np__1 @ k1_real_1 ) )
& ( A
= ( np__1 @ k1_real_1 ) ) )
| ( ( B = np__1 )
& ( A = np__1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_int_1) ).
thf(7892,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ( ( ( ( ( B
= ( np__1 @ k1_real_1 ) )
& ( A
= ( np__1 @ k1_real_1 ) ) )
| ( ( B = np__1 )
& ( A = np__1 ) ) )
=> ( ( B @ ( A @ k3_xcmplx_0 ) )
= np__1 ) )
& ( ( ( B @ ( A @ k3_xcmplx_0 ) )
= np__1 )
=> ( ( ( B
= ( np__1 @ k1_real_1 ) )
& ( A
= ( np__1 @ k1_real_1 ) ) )
| ( ( B = np__1 )
& ( A = np__1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(722,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k3_filter_0 ) )
= ( A @ u1_struct_0 ) )
& ( ( B @ ( A @ k3_filter_0 ) )
= ( A @ k1_filter_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_filter_0) ).
thf(5599,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k3_filter_0 ) )
= ( A @ u1_struct_0 ) )
& ( ( B @ ( A @ k3_filter_0 ) )
= ( A @ k1_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(1366,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ! [E: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( C = F )
& ( B = E ) )
=> ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ k4_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ k3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_filter_0) ).
thf(8750,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ! [E: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( C = F )
& ( B = E ) )
=> ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ k4_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ k3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).
thf(1764,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( C @ ( B @ ( A @ k13_group_6 ) ) @ m1_group_2 ) )
& ( C @ ( B @ ( A @ k13_group_6 ) ) @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_group_6) ).
thf(10942,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( C @ ( B @ ( A @ k13_group_6 ) ) @ m1_group_2 ) )
& ( C @ ( B @ ( A @ k13_group_6 ) ) @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1764]) ).
thf(1294,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( np__1 @ k7_binop_2 @ ( A @ k6_group_1 ) ) )
= ( B @ ( A @ k3_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_group_1) ).
thf(8355,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( np__1 @ k7_binop_2 @ ( A @ k6_group_1 ) ) )
= ( B @ ( A @ k3_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294]) ).
thf(1921,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k4_group_3 ) ) @ ( A @ k4_group_3 ) ) )
= C )
& ( ( B @ ( A @ k3_group_1 ) @ ( B @ ( C @ ( A @ k4_group_3 ) ) @ ( A @ k4_group_3 ) ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_group_3) ).
thf(11569,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k4_group_3 ) ) @ ( A @ k4_group_3 ) ) )
= C )
& ( ( B @ ( A @ k3_group_1 ) @ ( B @ ( C @ ( A @ k4_group_3 ) ) @ ( A @ k4_group_3 ) ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1921]) ).
thf(1621,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_4) ).
thf(10219,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1621]) ).
thf(1034,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m1_group_6 ) ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E = C )
=> ( ( ( E @ ( D @ ( B @ k13_group_2 ) ) )
= ( C @ ( D @ ( A @ k13_group_2 ) ) ) )
& ( ( E @ ( D @ ( B @ k12_group_2 ) ) )
= ( C @ ( D @ ( A @ k12_group_2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_group_6) ).
thf(7098,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m1_group_6 ) ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E = C )
=> ( ( ( E @ ( D @ ( B @ k13_group_2 ) ) )
= ( C @ ( D @ ( A @ k13_group_2 ) ) ) )
& ( ( E @ ( D @ ( B @ k12_group_2 ) ) )
= ( C @ ( D @ ( A @ k12_group_2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(950,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_finset_1) ).
thf(6747,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_funct_1) ).
thf(5392,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= ( C @ ( D @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_binop_1) ).
thf(2785,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= ( C @ ( D @ ( B @ k1_binop_1 ) ) ) ) ) )
=> ( A @ ( B @ v1_binop_1 ) ) )
& ( ( A @ ( B @ v1_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= ( C @ ( D @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1153,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(7654,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(116,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] : ( A @ k3_finseq_1 @ ( B @ ( A @ k1_finseq_3 ) @ k3_finseq_1 @ r1_xreal_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_finseq_3) ).
thf(2593,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] : ( A @ k3_finseq_1 @ ( B @ ( A @ k1_finseq_3 ) @ k3_finseq_1 @ r1_xreal_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(931,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( ( D @ ( B @ k5_relat_1 ) )
= ( A @ k6_relat_1 ) )
& ( ( B @ ( C @ k5_relat_1 ) )
= ( D @ k1_relat_1 @ k6_relat_1 ) )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_relat_1) ).
thf(6678,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( ( D @ ( B @ k5_relat_1 ) )
= ( A @ k6_relat_1 ) )
& ( ( B @ ( C @ k5_relat_1 ) )
= ( D @ k1_relat_1 @ k6_relat_1 ) )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_funcop_1 ) @ ( B @ ( A @ k2_funcop_1 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_4) ).
thf(3006,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_funcop_1 ) @ ( B @ ( A @ k2_funcop_1 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(1398,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( ( B @ ( A @ k4_group_6 ) )
= ( B @ ( A @ k15_group_2 ) ) )
& ( ( B @ ( A @ k4_group_6 ) )
= ( B @ ( A @ k14_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_group_6) ).
thf(8998,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( ( B @ ( A @ k4_group_6 ) )
= ( B @ ( A @ k15_group_2 ) ) )
& ( ( B @ ( A @ k4_group_6 ) )
= ( B @ ( A @ k14_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1398]) ).
thf(1229,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_2) ).
thf(8032,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(1937,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k9_group_2 ) ) @ u1_struct_0 )
= ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k3_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_latsubgr) ).
thf(11630,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k9_group_2 ) ) @ u1_struct_0 )
= ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k3_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1937]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_filter_1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_filter_1) ).
thf(2647,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_filter_1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(637,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( C @ ( B @ ( A @ k2_struct_0 ) ) @ ( A @ k16_lattice3 ) ) )
& ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( C @ ( B @ ( A @ k2_struct_0 ) ) @ ( A @ k15_lattice3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattice3) ).
thf(5180,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( C @ ( B @ ( A @ k2_struct_0 ) ) @ ( A @ k16_lattice3 ) ) )
& ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( C @ ( B @ ( A @ k2_struct_0 ) ) @ ( A @ k15_lattice3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(977,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_2) ).
thf(6847,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(1981,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ v3_realset2 )
& ( B @ ( A @ r2_group_6 ) ) )
=> ( B @ v3_realset2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_group_6) ).
thf(11814,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ v3_realset2 )
& ( B @ ( A @ r2_group_6 ) ) )
=> ( B @ v3_realset2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1981]) ).
thf(43639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k4_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ k4_xboole_0 ) @ ( B @ r1_tarski ) ) )
| ( D @ ( B @ r1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21644,2277]) ).
thf(43640,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k4_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ k4_xboole_0 ) @ ( B @ r1_tarski ) ) )
| ( D @ ( B @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[43639]) ).
thf(43641,plain,
! [A: $i] : ( k5_numbers @ ( k4_numbers @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[43640:[bind(A,$thf( E )),bind(B,$thf( k4_numbers @ ( E @ k4_xboole_0 ) )),bind(C,$thf( E )),bind(D,$thf( k5_numbers ))]]) ).
thf(43718,plain,
! [A: $i] : ( k5_numbers @ ( k4_numbers @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[43641]) ).
thf(1417,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k4_group_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k3_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_group_1) ).
thf(9074,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k3_group_1 ) ) ) )
=> ( B
= ( A @ k4_group_1 ) ) )
& ( ( B
= ( A @ k4_group_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k3_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1417]) ).
thf(29930,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ( A @ l1_struct_0 )
| ( sk1 @ sk149 @ v1_funct_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,22754]) ).
thf(29931,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
| ( sk1 @ sk149 @ v1_funct_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[29930:[]]) ).
thf(1769,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ~ ( B @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
thf(10985,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ~ ( B @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1769]) ).
thf(107,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A
= ( B @ k6_finseq_1 ) )
<=> ( ( A @ k3_finseq_1 )
= np__0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_finseq_1) ).
thf(2553,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( ( A @ k3_finseq_1 )
= np__0 )
=> ( A
= ( B @ k6_finseq_1 ) ) )
& ( ( A
= ( B @ k6_finseq_1 ) )
=> ( ( A @ k3_finseq_1 )
= np__0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(905,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k8_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_setfam_1) ).
thf(6553,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k8_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(1027,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k8_group_3 ) @ ( B @ r2_hidden ) )
<=> ( C @ ( B @ ( A @ r4_group_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_group_3) ).
thf(7066,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ r4_group_3 ) ) )
=> ( C @ ( A @ k8_group_3 ) @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k8_group_3 ) @ ( B @ r2_hidden ) )
=> ( C @ ( B @ ( A @ r4_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(39387,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k1_orders_1 @ k4_xboole_0 ) @ v1_finset_1 )
!= ( B @ v1_finset_1 ) )
| ( C @ ( B @ k4_xboole_0 ) @ v1_finset_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38887,2181]) ).
thf(39388,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k1_orders_1 @ k4_xboole_0 ) @ v1_finset_1 )
!= ( B @ v1_finset_1 ) )
| ( C @ ( B @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(simp,[status(thm)],[39387]) ).
thf(39389,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( k1_xboole_0 @ k1_orders_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ v1_finset_1 ),
inference(pattern_uni,[status(thm)],[39388:[bind(A,$thf( E )),bind(B,$thf( E @ ( k1_xboole_0 @ k1_orders_1 @ k4_xboole_0 ) )),bind(C,$thf( C ))]]) ).
thf(39433,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( k1_xboole_0 @ k1_orders_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ v1_finset_1 ),
inference(simp,[status(thm)],[39389]) ).
thf(199,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_partfun1) ).
thf(2928,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(1242,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( C @ v1_finset_1 )
=> ~ ( ( ( C @ k4_card_1 )
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k10_group_3 ) @ ( A @ k17_group_2 ) ) )
& ( C
= ( B @ ( A @ k7_group_3 ) ) ) ) )
& ( ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k10_group_3 ) @ ( A @ k14_group_2 ) @ v1_finset_1 )
| ( B @ ( A @ k7_group_3 ) @ v1_finset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_group_3) ).
thf(8079,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( C @ v1_finset_1 )
=> ~ ( ( ( C @ k4_card_1 )
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k10_group_3 ) @ ( A @ k17_group_2 ) ) )
& ( C
= ( B @ ( A @ k7_group_3 ) ) ) ) )
& ( ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k10_group_3 ) @ ( A @ k14_group_2 ) @ v1_finset_1 )
| ( B @ ( A @ k7_group_3 ) @ v1_finset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(1792,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( ( D @ u1_struct_0 )
= ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k3_xboole_0 ) ) )
=> ( C @ ( B @ ( A @ k8_group_2 ) ) @ ( D @ ( A @ r1_group_2 ) ) ) ) )
& ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( D
= ( C @ ( B @ ( A @ k8_group_2 ) ) ) )
=> ( ( D @ u1_struct_0 )
= ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k3_xboole_0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_group_2) ).
thf(11095,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( ( D @ u1_struct_0 )
= ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k3_xboole_0 ) ) )
=> ( C @ ( B @ ( A @ k8_group_2 ) ) @ ( D @ ( A @ r1_group_2 ) ) ) ) )
& ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( D
= ( C @ ( B @ ( A @ k8_group_2 ) ) ) )
=> ( ( D @ u1_struct_0 )
= ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k3_xboole_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1792]) ).
thf(680,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( C @ ( D @ ( B @ ( A @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_enumset1) ).
thf(5410,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( C @ ( D @ ( B @ ( A @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(692,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(5459,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(2329,plain,
! [A: $i] :
( ( A @ v14_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2327]) ).
thf(178,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_xboole_1) ).
thf(2842,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(1004,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relset_1) ).
thf(6956,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(765,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m3_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattice4) ).
thf(5838,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m3_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(396,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_partfun1) ).
thf(3893,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(1133,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(7561,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(195,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v15_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_lattices) ).
thf(2911,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v15_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(521,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_binop_1) ).
thf(4554,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(1906,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_group_1 @ ( B @ ( A @ k2_group_3 ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_group_3) ).
thf(11521,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_group_1 @ ( B @ ( A @ k2_group_3 ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1906]) ).
thf(2578,plain,
sk19 @ v1_finset_1,
inference(cnfConj,[status(thm)],[2574]) ).
thf(22486,plain,
! [A: $i] :
( ( A != sk605 )
| ( k1_xboole_0 @ v2_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,11438]) ).
thf(22487,plain,
( ( k1_xboole_0 @ v2_group_1 )
| ( sk605 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22486:[bind(A,$thf( sk605 ))]]) ).
thf(1278,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_subset_1) ).
thf(8280,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(1143,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ? [D: $i] :
( ( C
= ( D @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ k11_group_6 ) @ ( C @ ( A @ ( B @ k13_group_6 ) ) @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ k6_group_6 ) @ ( B @ k8_group_6 ) ) ) ) ) )
& ( C @ ( A @ ( B @ k13_group_6 ) ) @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ k6_group_6 ) @ ( D @ v4_group_6 ) ) )
& ( C @ ( A @ ( B @ k13_group_6 ) ) @ u1_struct_0 @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ k6_group_6 ) @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( B @ k13_group_6 ) ) @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ k6_group_6 ) @ ( D @ v1_group_6 ) ) )
& ( C @ ( A @ ( B @ k13_group_6 ) ) @ u1_struct_0 @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ k6_group_6 ) @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_group_6) ).
thf(7598,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ? [D: $i] :
( ( C
= ( D @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ k11_group_6 ) @ ( C @ ( A @ ( B @ k13_group_6 ) ) @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ k6_group_6 ) @ ( B @ k8_group_6 ) ) ) ) ) )
& ( C @ ( A @ ( B @ k13_group_6 ) ) @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ k6_group_6 ) @ ( D @ v4_group_6 ) ) )
& ( C @ ( A @ ( B @ k13_group_6 ) ) @ u1_struct_0 @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ k6_group_6 ) @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( B @ k13_group_6 ) ) @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ k6_group_6 ) @ ( D @ v1_group_6 ) ) )
& ( C @ ( A @ ( B @ k13_group_6 ) ) @ u1_struct_0 @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ k6_group_6 ) @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(1538,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( A @ v4_group_1 )
=> ( ( B @ ( C @ ( A @ k4_group_2 ) ) @ ( D @ ( A @ k4_group_2 ) ) )
= ( B @ ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( A @ k4_group_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_group_2) ).
thf(9751,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( A @ v4_group_1 )
=> ( ( B @ ( C @ ( A @ k4_group_2 ) ) @ ( D @ ( A @ k4_group_2 ) ) )
= ( B @ ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( A @ k4_group_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1538]) ).
thf(699,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( D @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) )
& ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B
= ( C @ ( A @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_xboole_1) ).
thf(5482,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( D @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) )
& ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B
= ( C @ ( A @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(733,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k15_lattice3 ) ) )
<=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ r4_lattice3 ) ) )
=> ( D @ ( C @ ( A @ r1_lattices ) ) ) ) )
& ( B @ ( C @ ( A @ r4_lattice3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_lattice3) ).
thf(5646,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ r4_lattice3 ) ) )
=> ( D @ ( C @ ( A @ r1_lattices ) ) ) ) )
& ( B @ ( C @ ( A @ r4_lattice3 ) ) ) )
=> ( C
= ( B @ ( A @ k15_lattice3 ) ) ) )
& ( ( C
= ( B @ ( A @ k15_lattice3 ) ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ r4_lattice3 ) ) )
=> ( D @ ( C @ ( A @ r1_lattices ) ) ) ) )
& ( B @ ( C @ ( A @ r4_lattice3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(861,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ k1_group_3 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C
= ( B @ ( A @ k2_latsubgr ) ) )
<=> ( ( C @ u1_struct_0 )
= ( B @ ( A @ k1_latsubgr @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_group_3 @ k2_funct_2 ) ) ) @ ( A @ u1_struct_0 @ k6_setfam_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_latsubgr) ).
thf(6270,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ k1_group_3 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( ( ( C @ u1_struct_0 )
= ( B @ ( A @ k1_latsubgr @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_group_3 @ k2_funct_2 ) ) ) @ ( A @ u1_struct_0 @ k6_setfam_1 ) ) )
=> ( C
= ( B @ ( A @ k2_latsubgr ) ) ) )
& ( ( C
= ( B @ ( A @ k2_latsubgr ) ) )
=> ( ( C @ u1_struct_0 )
= ( B @ ( A @ k1_latsubgr @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_group_3 @ k2_funct_2 ) ) ) @ ( A @ u1_struct_0 @ k6_setfam_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
<=> ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).
thf(2418,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
=> ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1235,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m4_vectsp_8 ) ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m4_vectsp_8) ).
thf(8052,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m4_vectsp_8 ) ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(856,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_filter_0 ) )
=> ( ( ( E @ ( D @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
& ( E @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) )
=> ( E @ ( D @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_filter_0) ).
thf(6255,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_filter_0 ) )
=> ( ( ( E @ ( D @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
& ( E @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) )
=> ( E @ ( D @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(1021,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( B @ ( C @ m1_group_2 ) )
<=> ( C @ ( B @ ( C @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_group_2) ).
thf(7030,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( ( C @ ( B @ ( C @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) )
=> ( B @ ( C @ m1_group_2 ) ) )
& ( ( B @ ( C @ m1_group_2 ) )
=> ( C @ ( B @ ( C @ ( A @ k9_group_2 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(1428,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r2_hidden ) )
=> ( ( D @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_filter_0) ).
thf(9143,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r2_hidden ) )
=> ( ( D @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k3_relat_1 @ ( A @ k3_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t180_orders_1) ).
thf(2401,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k3_relat_1 @ ( A @ k3_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(875,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_3_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_domain_1) ).
thf(6377,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_3_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(2210,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
| ( ( A @ ( B @ ( C @ sk2 ) ) @ ( B @ ( C @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk2 ) ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[2207]) ).
thf(2212,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( B @ m1_subset_1 ) )
| ( ( A @ ( B @ ( C @ sk2 ) ) @ ( B @ ( C @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk2 ) ) ) ) ),
inference(lifteq,[status(thm)],[2210]) ).
thf(22218,plain,
! [A: $i] :
( ( A != sk179 )
| ( k1_xboole_0 @ l1_struct_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,4906]) ).
thf(22219,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk179 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22218:[bind(A,$thf( sk179 ))]]) ).
thf(1917,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= ( A @ k2_group_1 ) )
=> ( B
= ( A @ k2_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_group_3) ).
thf(11558,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= ( A @ k2_group_1 ) )
=> ( B
= ( A @ k2_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1917]) ).
thf(22162,plain,
! [A: $i] :
( ( A != sk608 )
| ( k1_xboole_0 @ l1_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,11496]) ).
thf(22163,plain,
( ( k1_xboole_0 @ l1_group_1 )
| ( sk608 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22162:[bind(A,$thf( sk608 ))]]) ).
thf(667,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) )
=> ( A @ v14_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_filter_0) ).
thf(5372,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) )
=> ( A @ v14_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(2170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( B @ k2_finseq_3 ) @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) ) )
| ( D @ ( B @ r1_xreal_0 ) )
| ( ( A @ k3_finseq_1 )
!= ( np__1 @ ( C @ k1_nat_1 ) ) )
| ~ ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
| ~ ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
| ~ ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2169]) ).
thf(2171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ r1_xreal_0 ) )
| ~ ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
| ~ ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
| ~ ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( ( D @ ( A @ ( B @ k2_finseq_3 ) @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) ) )
| ( ( A @ k3_finseq_1 )
!= ( np__1 @ ( C @ k1_nat_1 ) ) ) ),
inference(lifteq,[status(thm)],[2170]) ).
thf(917,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( A @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( A = B )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(6609,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( A @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( A = B )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(1117,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
<=> ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(7479,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r1_xboole_0 ) ) )
& ( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(1954,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k5_group_2 @ v6_group_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_group_2) ).
thf(11711,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k5_group_2 @ v6_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1954]) ).
thf(669,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_filter_1) ).
thf(5377,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(641,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relat_1) ).
thf(5197,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_xboole_1) ).
thf(2550,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(880,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ r1_tarski ) )
=> ( ( B @ k3_tarski @ ( A @ k15_lattice3 ) )
= ( B @ ( A @ a_2_7_lattice3 ) @ ( A @ k15_lattice3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattice3) ).
thf(6394,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ r1_tarski ) )
=> ( ( B @ k3_tarski @ ( A @ k15_lattice3 ) )
= ( B @ ( A @ a_2_7_lattice3 ) @ ( A @ k15_lattice3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(121,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( B @ ( A @ m2_finseq_1 ) )
=> ( B @ ( C @ ( A @ k1_finseq_3 ) @ m2_finseq_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_finseq_3) ).
thf(2620,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( B @ ( A @ m2_finseq_1 ) )
=> ( B @ ( C @ ( A @ k1_finseq_3 ) @ m2_finseq_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(1586,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( A @ k2_group_5 ) ) @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k2_group_5 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_group_6) ).
thf(10020,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( A @ k2_group_5 ) ) @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k2_group_5 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1586]) ).
thf(1688,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( D @ ( A @ k11_group_2 ) ) @ ( B @ ( A @ k4_group_2 ) ) )
= ( C @ ( B @ ( A @ k4_group_2 ) ) @ ( D @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_group_3) ).
thf(10549,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( D @ ( A @ k11_group_2 ) ) @ ( B @ ( A @ k4_group_2 ) ) )
= ( C @ ( B @ ( A @ k4_group_2 ) ) @ ( D @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1688]) ).
thf(1473,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( C @ ( B @ ( A @ k7_group_4 ) ) @ ( A @ k5_group_4 ) @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_group_4) ).
thf(9381,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( C @ ( B @ ( A @ k7_group_4 ) ) @ ( A @ k5_group_4 ) @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1473]) ).
thf(1833,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k1_group_1 ) ) ) )
<=> ( ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_group_1) ).
thf(11245,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) ) )
=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k1_group_1 ) ) ) ) )
& ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k1_group_1 ) ) ) )
=> ( ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1833]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r2_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_binop_1) ).
thf(3159,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r2_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r2_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1180,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) )
= ( B @ k3_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(7805,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) )
= ( B @ k3_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(41406,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ k4_xboole_0 ) @ ( B @ r1_tarski ) ) )
| ( D @ ( B @ r1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21630,2277]) ).
thf(41407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ k4_xboole_0 ) @ ( B @ r1_tarski ) ) )
| ( D @ ( B @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[41406]) ).
thf(41408,plain,
! [A: $i] : ( k4_numbers @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[41407:[bind(A,$thf( E )),bind(B,$thf( k1_numbers @ ( E @ k4_xboole_0 ) )),bind(C,$thf( E )),bind(D,$thf( k4_numbers ))]]) ).
thf(41459,plain,
! [A: $i] : ( k4_numbers @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[41408]) ).
thf(2030,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_group_3 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_group_3) ).
thf(12006,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_group_3 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2030]) ).
thf(1202,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( B @ ( A @ k15_group_2 ) )
= ( A @ a_1_0_group_2 ) )
=> ( A @ k5_group_2 @ ( B @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t171_group_2) ).
thf(7911,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( B @ ( A @ k15_group_2 ) )
= ( A @ a_1_0_group_2 ) )
=> ( A @ k5_group_2 @ ( B @ ( A @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(2287,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[2286]) ).
thf(2288,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[2287]) ).
thf(1633,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( B @ m1_filter_0 ) )
<=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r3_lattices ) ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) ) ) )
& ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_filter_0) ).
thf(10264,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r3_lattices ) ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) ) ) )
& ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) )
=> ( A @ ( B @ m1_filter_0 ) ) )
& ( ( A @ ( B @ m1_filter_0 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r3_lattices ) ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) ) ) )
& ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1633]) ).
thf(293,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
!= C ) )
& ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_partfun1) ).
thf(3363,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
!= C ) )
& ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(1738,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k4_xcmplx_0 @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k3_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_group_1) ).
thf(10803,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k4_xcmplx_0 @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k3_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1738]) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ~ ( C @ v2_funct_1 )
& ? [D: $i] :
( ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
& ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
& ( B != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funct_2) ).
thf(3142,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ~ ( C @ v2_funct_1 )
& ? [D: $i] :
( ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
& ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
& ( B != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(1401,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_finseq_1 ) )
& ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k3_group_4 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_group_4) ).
thf(9011,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_finseq_1 ) )
& ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k3_group_4 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1401]) ).
thf(1723,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( A @ k9_filter_1 @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) )
<=> ( C @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_1) ).
thf(10707,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( A @ k9_filter_1 @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) ) )
& ( ( A @ k9_filter_1 @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( C @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1723]) ).
thf(1860,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ r2_group_6 ) )
<=> ( B @ ( A @ r1_group_6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r2_group_6) ).
thf(11342,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ r1_group_6 ) )
=> ( B @ ( A @ r2_group_6 ) ) )
& ( ( B @ ( A @ r2_group_6 ) )
=> ( B @ ( A @ r1_group_6 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1860]) ).
thf(1132,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ ( B @ k6_group_1 ) ) )
= ( B @ k2_group_1 ) )
=> ( A @ ( C @ ( B @ k7_group_1 ) @ r1_nat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_group_1) ).
thf(7558,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ ( B @ k6_group_1 ) ) )
= ( B @ k2_group_1 ) )
=> ( A @ ( C @ ( B @ k7_group_1 ) @ r1_nat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(26270,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ( sk1 != k1_xboole_0 )
| ( A @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,20725]) ).
thf(26271,plain,
! [A: $i] :
( ( sk1 != k1_xboole_0 )
| ( A @ l1_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26270:[]]) ).
thf(2110,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_group_3 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_group_3) ).
thf(12308,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_group_3 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2110]) ).
thf(678,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_2) ).
thf(5403,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t161_funct_2) ).
thf(2999,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1534,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ k2_group_1 @ ( A @ u1_struct_0 @ k18_group_2 ) ) )
=> ( A @ k5_group_2 @ ( B @ ( A @ k5_group_4 ) @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_latsubgr) ).
thf(9740,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ k2_group_1 @ ( A @ u1_struct_0 @ k18_group_2 ) ) )
=> ( A @ k5_group_2 @ ( B @ ( A @ k5_group_4 ) @ ( A @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534]) ).
thf(288,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ k2_group_1 @ ( A @ ( B @ k6_group_1 ) ) )
= ( B @ k2_group_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_group_1) ).
thf(3348,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ k2_group_1 @ ( A @ ( B @ k6_group_1 ) ) )
= ( B @ k2_group_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(619,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( C @ ( B @ ( A @ r4_lattice4 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ k7_lattices ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k7_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattice4) ).
thf(5089,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ k7_lattices ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k7_lattices ) ) ) )
=> ( C @ ( B @ ( A @ r4_lattice4 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_lattice4 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ k7_lattices ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k7_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(432,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ k4_lattice4 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattice4) ).
thf(4067,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ k4_lattice4 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k4_lattice4 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(658,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( E @ k2_relat_1 )
= C )
& ( ( D @ k2_relat_1 )
= B ) )
=> ( ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ k2_relat_1 )
= C )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funct_2) ).
thf(5326,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( E @ k2_relat_1 )
= C )
& ( ( D @ k2_relat_1 )
= B ) )
=> ( ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ k2_relat_1 )
= C )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(586,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 @ ( A @ k8_filter_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_filter_0) ).
thf(4890,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 @ ( A @ k8_filter_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(1839,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ r4_group_3 ) ) )
<=> ( C @ ( B @ ( A @ r2_group_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_group_3) ).
thf(11272,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ r2_group_3 ) ) )
=> ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ r4_group_3 ) ) ) )
& ( ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ r4_group_3 ) ) )
=> ( C @ ( B @ ( A @ r2_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1839]) ).
thf(11493,plain,
sk608 @ v4_group_1,
inference(cnfConj,[status(thm)],[11492]) ).
thf(1387,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( C @ ( D @ ( A @ k12_group_2 ) ) @ ( B @ ( D @ ( A @ k12_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( D @ ( A @ k12_group_2 ) ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_group_2) ).
thf(8922,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( C @ ( D @ ( A @ k12_group_2 ) ) @ ( B @ ( D @ ( A @ k12_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( D @ ( A @ k12_group_2 ) ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1387]) ).
thf(139,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( ( A @ k1_card_1 @ k2_card_1 )
= ( np__1 @ ( A @ k1_nat_1 ) @ k1_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_card_1) ).
thf(2693,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( ( A @ k1_card_1 @ k2_card_1 )
= ( np__1 @ ( A @ k1_nat_1 ) @ k1_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(1111,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ~ ( A @ ( np__0 @ r1_xreal_0 ) )
=> ( ( C @ ( A @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ k1_int_2 @ ( B @ k6_group_1 ) ) @ ( B @ k3_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_group_1) ).
thf(7458,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ~ ( A @ ( np__0 @ r1_xreal_0 ) )
=> ( ( C @ ( A @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ k1_int_2 @ ( B @ k6_group_1 ) ) @ ( B @ k3_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(1911,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_group_1 ) @ ( A @ k2_group_3 ) ) )
= ( C @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ k3_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_group_3) ).
thf(11535,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_group_1 ) @ ( A @ k2_group_3 ) ) )
= ( C @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ k3_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1911]) ).
thf(1873,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_group_1 @ ( A @ k4_group_1 @ ( A @ u1_struct_0 @ r1_finseqop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_group_1) ).
thf(11402,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_group_1 @ ( A @ k4_group_1 @ ( A @ u1_struct_0 @ r1_finseqop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1873]) ).
thf(1540,axiom,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_subset_1) ).
thf(9760,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540]) ).
thf(9761,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[9760]) ).
thf(9762,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[9761]) ).
thf(1498,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_vectsp_8 ) ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_vectsp_8) ).
thf(9503,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_vectsp_8 ) ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498]) ).
thf(1510,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( D @ ( C @ r1_partfun1 ) ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_funct_2) ).
thf(9582,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( D @ ( C @ r1_partfun1 ) ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1510]) ).
thf(1307,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k13_group_2 ) ) @ ( C @ ( A @ k7_group_2 ) @ r2_wellord2 ) )
& ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( C @ ( A @ k7_group_2 ) @ r2_wellord2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_group_2) ).
thf(8457,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k13_group_2 ) ) @ ( C @ ( A @ k7_group_2 ) @ r2_wellord2 ) )
& ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( C @ ( A @ k7_group_2 ) @ r2_wellord2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).
thf(960,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_relat_1) ).
thf(6785,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(943,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
thf(6730,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(6476,plain,
sk280 @ v1_relat_1,
inference(cnfConj,[status(thm)],[6474]) ).
thf(1720,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k3_group_3 ) ) )
= ( D @ ( B @ ( A @ k2_group_3 ) ) @ ( C @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ u1_struct_0 @ k7_domain_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_group_3) ).
thf(10692,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k3_group_3 ) ) )
= ( D @ ( B @ ( A @ k2_group_3 ) ) @ ( C @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ u1_struct_0 @ k7_domain_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1720]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
<=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_subset_1) ).
thf(3490,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( C @ ( B @ r1_tarski ) ) )
& ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1046,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(7153,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(7154,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(cnf,[status(esa)],[7153]) ).
thf(1704,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( C @ ( D @ ( A @ k10_group_2 ) ) @ ( B @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_group_2) ).
thf(10617,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( C @ ( D @ ( A @ k10_group_2 ) ) @ ( B @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1704]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_partfun1) ).
thf(4394,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(1707,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_xboole_1) ).
thf(10632,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1707]) ).
thf(1039,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_group_6 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k1_group_1 ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k1_group_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_group_6) ).
thf(7122,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k1_group_1 ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k1_group_1 ) ) ) ) ) )
=> ( B @ ( A @ ( C @ v1_group_6 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_group_6 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k1_group_1 ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k1_group_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(213,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_finseq_3 ) )
= A )
<=> ~ ( A @ k2_relat_1 @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_finseq_3) ).
thf(3009,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ~ ( A @ k2_relat_1 @ ( B @ r2_hidden ) )
=> ( ( B @ k1_tarski @ ( A @ k1_finseq_3 ) )
= A ) )
& ( ( ( B @ k1_tarski @ ( A @ k1_finseq_3 ) )
= A )
=> ~ ( A @ k2_relat_1 @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(1069,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( B @ ( A @ k14_group_2 ) )
= ( A @ a_1_0_group_2 ) )
=> ( A @ k5_group_2 @ ( B @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t170_group_2) ).
thf(7260,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( B @ ( A @ k14_group_2 ) )
= ( A @ a_1_0_group_2 ) )
=> ( A @ k5_group_2 @ ( B @ ( A @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(742,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_partfun1) ).
thf(5688,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(21900,plain,
! [A: $i] :
( ( A != sk335 )
| ( k1_xboole_0 @ v1_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,7436]) ).
thf(21901,plain,
( ( k1_xboole_0 @ v1_group_1 )
| ( sk335 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21900:[bind(A,$thf( sk335 ))]]) ).
thf(989,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k10_group_1 ) ) )
= ( B @ ( C @ ( A @ k10_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k10_group_1) ).
thf(6890,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k10_group_1 ) ) )
= ( B @ ( C @ ( A @ k10_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(1479,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k8_rlvect_1 ) ) ) @ m2_finseq_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_rlvect_1) ).
thf(9403,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k8_rlvect_1 ) ) ) @ m2_finseq_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1479]) ).
thf(1119,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_4_lattice3 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( C @ ( B @ k3_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_4_lattice3) ).
thf(7490,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( C @ ( B @ k3_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_4_lattice3 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_4_lattice3 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( C @ ( B @ k3_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(17017,plain,
! [A: $i] :
( ( ( sk545 @ l3_lattices )
!= ( A @ l3_lattices ) )
| ( A @ l1_lattices )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10455,6015]) ).
thf(17018,plain,
! [A: $i] :
( ( ( sk545 @ l3_lattices )
!= ( A @ l3_lattices ) )
| ( A @ l1_lattices ) ),
inference(simp,[status(thm)],[17017]) ).
thf(17019,plain,
sk545 @ l1_lattices,
inference(pattern_uni,[status(thm)],[17018:[bind(A,$thf( sk545 ))]]) ).
thf(17068,plain,
! [A: $i] :
( ( ( sk545 @ l1_lattices )
!= ( A @ l1_lattices ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17019,4291]) ).
thf(17069,plain,
! [A: $i] :
( ( ( sk545 @ l1_lattices )
!= ( A @ l1_lattices ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[17068]) ).
thf(17070,plain,
sk545 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[17069:[bind(A,$thf( sk545 ))]]) ).
thf(902,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r4_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_binop_1) ).
thf(6540,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r4_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(1531,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( A @ ( C @ ( B @ ( A @ k3_group_6 ) ) @ m1_group_6 ) ) )
& ( C @ ( C @ ( B @ ( A @ k3_group_6 ) ) @ v1_group_3 ) )
& ( C @ ( B @ ( A @ k3_group_6 ) ) @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_group_6) ).
thf(9727,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( A @ ( C @ ( B @ ( A @ k3_group_6 ) ) @ m1_group_6 ) ) )
& ( C @ ( C @ ( B @ ( A @ k3_group_6 ) ) @ v1_group_3 ) )
& ( C @ ( B @ ( A @ k3_group_6 ) ) @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1531]) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
<=> ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
& ( C @ ( B @ ( A @ r4_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_binop_1) ).
thf(2665,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
& ( C @ ( B @ ( A @ r4_binop_1 ) ) ) )
=> ( C @ ( B @ ( A @ r6_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
=> ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
& ( C @ ( B @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(47198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ k4_xboole_0 ) @ ( B @ r1_tarski ) ) )
| ( D @ ( B @ r1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21647,2277]) ).
thf(47199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ k4_xboole_0 ) @ ( B @ r1_tarski ) ) )
| ( D @ ( B @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[47198]) ).
thf(47200,plain,
! [A: $i] : ( k5_numbers @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[47199:[bind(A,$thf( E )),bind(B,$thf( k1_numbers @ ( E @ k4_xboole_0 ) )),bind(C,$thf( E )),bind(D,$thf( k5_numbers ))]]) ).
thf(47272,plain,
! [A: $i] : ( k5_numbers @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[47200]) ).
thf(14332,plain,
! [B: $i,A: $i] :
( ( ( sk19 @ v1_finset_1 )
!= ( A @ v1_finset_1 ) )
| ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2578,2181]) ).
thf(14333,plain,
! [B: $i,A: $i] :
( ( ( sk19 @ v1_finset_1 )
!= ( A @ v1_finset_1 ) )
| ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(simp,[status(thm)],[14332]) ).
thf(14334,plain,
! [A: $i] : ( A @ ( sk19 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(pattern_uni,[status(thm)],[14333:[bind(A,$thf( sk19 ))]]) ).
thf(14349,plain,
! [A: $i] : ( A @ ( sk19 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(simp,[status(thm)],[14334]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v3_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_filter_1) ).
thf(4813,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v3_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(1215,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( B @ ( A @ k6_group_6 ) @ l1_group_1 )
& ( B @ ( A @ k6_group_6 ) @ v7_group_1 )
& ( B @ ( A @ k6_group_6 ) @ v4_group_1 )
& ( B @ ( A @ k6_group_6 ) @ v3_group_1 )
& ~ ( B @ ( A @ k6_group_6 ) @ v3_struct_0 ) )
<=> ( B @ ( A @ ( A @ k9_group_5 @ m1_group_6 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_group_6) ).
thf(7975,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( B @ ( A @ ( A @ k9_group_5 @ m1_group_6 ) ) )
=> ( ( B @ ( A @ k6_group_6 ) @ l1_group_1 )
& ( B @ ( A @ k6_group_6 ) @ v7_group_1 )
& ( B @ ( A @ k6_group_6 ) @ v4_group_1 )
& ( B @ ( A @ k6_group_6 ) @ v3_group_1 )
& ~ ( B @ ( A @ k6_group_6 ) @ v3_struct_0 ) ) )
& ( ( ( B @ ( A @ k6_group_6 ) @ l1_group_1 )
& ( B @ ( A @ k6_group_6 ) @ v7_group_1 )
& ( B @ ( A @ k6_group_6 ) @ v4_group_1 )
& ( B @ ( A @ k6_group_6 ) @ v3_group_1 )
& ~ ( B @ ( A @ k6_group_6 ) @ v3_struct_0 ) )
=> ( B @ ( A @ ( A @ k9_group_5 @ m1_group_6 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(850,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_funct_1 )
= ( A @ k2_funct_1 @ ( B @ k2_funct_1 @ k5_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_1) ).
thf(6225,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_funct_1 )
= ( A @ k2_funct_1 @ ( B @ k2_funct_1 @ k5_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(1151,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_filter_0) ).
thf(7650,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_zfmisc_1) ).
thf(2271,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1416,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(9069,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1416]) ).
thf(1443,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(9259,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1443]) ).
thf(259,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k5_relat_1 ) )
= A )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( B
= ( B @ k1_relat_1 @ k6_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funct_1) ).
thf(3206,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k5_relat_1 ) )
= A )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( B
= ( B @ k1_relat_1 @ k6_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(17549,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( A @ ( k4_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17067,2188]) ).
thf(17550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( A @ ( k4_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) ) ),
inference(simp,[status(thm)],[17549]) ).
thf(17551,plain,
! [A: $i] : ( k1_numbers @ ( A @ k2_xboole_0 ) @ ( k4_numbers @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[17550:[bind(A,$thf( A )),bind(B,$thf( k4_numbers )),bind(C,$thf( A )),bind(D,$thf( k1_numbers ))]]) ).
thf(17587,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( A @ k2_xboole_0 ) @ ( k4_numbers @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17551,2215]) ).
thf(17588,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( A @ k2_xboole_0 ) @ ( k4_numbers @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[17587]) ).
thf(17589,plain,
! [B: $i,A: $i] : ( k1_numbers @ ( B @ k2_xboole_0 ) @ ( A @ ( k4_numbers @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[17588:[bind(A,$thf( E )),bind(B,$thf( k4_numbers )),bind(C,$thf( k1_numbers @ ( E @ k2_xboole_0 ) )),bind(D,$thf( D ))]]) ).
thf(17592,plain,
! [B: $i,A: $i] : ( k1_numbers @ ( B @ k2_xboole_0 ) @ ( A @ ( k4_numbers @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[17589]) ).
thf(41310,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( B @ k2_xboole_0 ) @ ( A @ ( k4_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( E @ ( D @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( E @ ( D @ k2_xboole_0 ) @ ( C @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17592,2188]) ).
thf(41311,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( B @ k2_xboole_0 ) @ ( A @ ( k4_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( E @ ( D @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( E @ ( D @ k2_xboole_0 ) @ ( C @ r1_tarski ) ) ),
inference(simp,[status(thm)],[41310]) ).
thf(41312,plain,
! [B: $i,A: $i] : ( k1_numbers @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) @ ( k4_numbers @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[41311:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( k4_numbers )),bind(D,$thf( A )),bind(E,$thf( k1_numbers @ ( F @ k2_xboole_0 ) ))]]) ).
thf(41371,plain,
! [B: $i,A: $i] : ( k1_numbers @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) @ ( k4_numbers @ r1_tarski ) ),
inference(simp,[status(thm)],[41312]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ k3_partfun1 ) ) @ ( C @ ( A @ ( E @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_partfun1) ).
thf(2652,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ k3_partfun1 ) ) @ ( C @ ( A @ ( E @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(530,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r1_xboole_0 ) )
& ( A @ ( C @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( D @ ( C @ k2_xboole_0 ) ) ) )
=> ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_xboole_1) ).
thf(4598,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r1_xboole_0 ) )
& ( A @ ( C @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( D @ ( C @ k2_xboole_0 ) ) ) )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(1629,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_lattice4) ).
thf(10249,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1629]) ).
thf(1751,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(10867,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1751]) ).
thf(11469,plain,
sk607 @ l1_group_1,
inference(cnfConj,[status(thm)],[11468]) ).
thf(16440,plain,
! [A: $i] :
( ( ( sk607 @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11469,4961]) ).
thf(16441,plain,
! [A: $i] :
( ( ( sk607 @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[16440]) ).
thf(16442,plain,
sk607 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[16441:[bind(A,$thf( sk607 ))]]) ).
thf(1597,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_lattices) ).
thf(10091,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1597]) ).
thf(1514,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v6_group_1 )
=> ( B @ ( A @ k8_group_3 ) @ v1_finset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_group_3) ).
thf(9646,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v6_group_1 )
=> ( B @ ( A @ k8_group_3 ) @ v1_finset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1514]) ).
thf(1785,axiom,
? [A: $i] : ( A @ l3_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(11076,plain,
? [A: $i] : ( A @ l3_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1785]) ).
thf(11077,plain,
sk593 @ l3_lattices,
inference(cnf,[status(esa)],[11076]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r4_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_binop_1) ).
thf(2878,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r4_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(2070,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( C @ ( D @ ( A @ k12_group_2 ) ) @ ( B @ ( D @ ( A @ k12_group_2 ) ) @ r2_wellord2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_group_2) ).
thf(12156,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( C @ ( D @ ( A @ k12_group_2 ) ) @ ( B @ ( D @ ( A @ k12_group_2 ) ) @ r2_wellord2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2070]) ).
thf(2122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ r1_lattice4 ) ) )
| ~ ( A @ ( B @ ( C @ v3_lattice4 ) ) )
| ~ ( A @ ( B @ ( C @ m1_lattice4 ) ) )
| ~ ( B @ l3_lattices )
| ~ ( B @ v3_filter_0 )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) )
& ( ( A @ v3_filter_0 )
| ~ ( A @ ( B @ ( C @ v3_lattice4 ) ) )
| ~ ( A @ ( B @ ( C @ m1_lattice4 ) ) )
| ~ ( B @ l3_lattices )
| ~ ( B @ v3_filter_0 )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ) ),
inference(cnf,[status(esa)],[2121]) ).
thf(2124,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ r1_lattice4 ) ) )
| ~ ( A @ ( B @ ( C @ v3_lattice4 ) ) )
| ~ ( A @ ( B @ ( C @ m1_lattice4 ) ) )
| ~ ( B @ l3_lattices )
| ~ ( B @ v3_filter_0 )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2122]) ).
thf(1244,axiom,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( A @ u1_struct_0 @ ( A @ k2_vectsp_1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_vectsp_1) ).
thf(8116,plain,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( A @ u1_struct_0 @ ( A @ k2_vectsp_1 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(1776,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( D @ r1_tarski ) ) )
=> ( A @ ( D @ r1_tarski ) ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_xboole_1) ).
thf(11030,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( D @ r1_tarski ) ) )
=> ( A @ ( D @ r1_tarski ) ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1776]) ).
thf(1045,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k5_lattices @ ( A @ r3_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattices) ).
thf(7151,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k5_lattices @ ( A @ r3_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(583,axiom,
! [A: $i] :
( ( A @ l1_lattices )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
& ( A @ u1_lattices @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(4879,plain,
! [A: $i] :
( ( A @ l1_lattices )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
& ( A @ u1_lattices @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(1313,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( C @ v1_finset_1 )
=> ~ ( ( ( C @ k4_card_1 )
= ( B @ ( A @ k10_group_3 ) @ ( A @ k17_group_2 ) ) )
& ( C
= ( B @ ( A @ k8_group_3 ) ) ) ) )
& ( ( B @ ( A @ k10_group_3 ) @ ( A @ k14_group_2 ) @ v1_finset_1 )
| ( B @ ( A @ k8_group_3 ) @ v1_finset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_group_3) ).
thf(8505,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( C @ v1_finset_1 )
=> ~ ( ( ( C @ k4_card_1 )
= ( B @ ( A @ k10_group_3 ) @ ( A @ k17_group_2 ) ) )
& ( C
= ( B @ ( A @ k8_group_3 ) ) ) ) )
& ( ( B @ ( A @ k10_group_3 ) @ ( A @ k14_group_2 ) @ v1_finset_1 )
| ( B @ ( A @ k8_group_3 ) @ v1_finset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).
thf(470,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= A )
& ( B @ v2_funct_1 ) )
=> ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v3_funct_2 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_funct_2) ).
thf(4292,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= A )
& ( B @ v2_funct_1 ) )
=> ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v3_funct_2 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(1573,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( C @ ( A @ ( B @ k13_group_6 ) ) @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ k6_group_6 ) @ r2_group_6 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_group_6) ).
thf(9943,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( C @ ( A @ ( B @ k13_group_6 ) ) @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ k6_group_6 ) @ r2_group_6 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1573]) ).
thf(1220,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_filter_0) ).
thf(7992,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(1288,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v4_group_6 ) ) )
<=> ( ( C @ v2_funct_1 )
& ( ( C @ ( B @ ( A @ k9_group_6 ) ) )
= ( B @ u1_struct_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_group_6) ).
thf(8323,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ v2_funct_1 )
& ( ( C @ ( B @ ( A @ k9_group_6 ) ) )
= ( B @ u1_struct_0 ) ) )
=> ( B @ ( A @ ( C @ v4_group_6 ) ) ) )
& ( ( B @ ( A @ ( C @ v4_group_6 ) ) )
=> ( ( C @ v2_funct_1 )
& ( ( C @ ( B @ ( A @ k9_group_6 ) ) )
= ( B @ u1_struct_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).
thf(12410,plain,
( ( ( k1_xboole_0 @ v1_xboole_0 )
!= ( k1_numbers @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6056,4021]) ).
thf(12411,plain,
( ( k1_xboole_0 @ v1_xboole_0 )
!= ( k1_numbers @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12410]) ).
thf(12427,plain,
k1_xboole_0 != k1_numbers,
inference(simp,[status(thm)],[12411]) ).
thf(22867,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ( A != k1_numbers )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,12427]) ).
thf(22868,plain,
! [A: $i] :
( ( A != k1_numbers )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22867:[]]) ).
thf(23170,plain,
k1_numbers @ sk149 @ v1_funct_1,
inference(simp,[status(thm)],[22868]) ).
thf(576,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ r1_partfun1 ) )
& ( D @ ( B @ r1_partfun1 ) ) )
=> ( C @ ( B @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_funct_2) ).
thf(4859,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ r1_partfun1 ) )
& ( D @ ( B @ r1_partfun1 ) ) )
=> ( C @ ( B @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(2105,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( ( B @ ( C @ ( A @ k6_group_3 ) ) )
= A )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_group_3) ).
thf(12294,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( ( B @ ( C @ ( A @ k6_group_3 ) ) )
= A )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2105]) ).
thf(1522,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k14_group_2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k14_group_2) ).
thf(9678,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k14_group_2 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1522]) ).
thf(222,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) )
<=> ( ( A @ k4_finseq_1 )
= ( B @ k4_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_finseq_3) ).
thf(3048,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( A @ k4_finseq_1 )
= ( B @ k4_finseq_1 ) )
=> ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) )
& ( ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) )
=> ( ( A @ k4_finseq_1 )
= ( B @ k4_finseq_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(2332,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k1_finseq_3 ) @ k2_relat_1 )
= ( B @ ( A @ k2_relat_1 @ k4_xboole_0 ) ) )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2331]) ).
thf(2333,plain,
! [B: $i,A: $i] :
( ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( ( B @ ( A @ k1_finseq_3 ) @ k2_relat_1 )
= ( B @ ( A @ k2_relat_1 @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[2332]) ).
thf(179,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
<=> ? [B: $i] :
( ( A
= ( B @ k2_relat_1 ) )
& ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_finseq_1) ).
thf(2846,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( A
= ( B @ k2_relat_1 ) )
& ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ v1_finset_1 ) )
& ( ( A @ v1_finset_1 )
=> ? [B: $i] :
( ( A
= ( B @ k2_relat_1 ) )
& ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(2253,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
| ( A != k1_xboole_0 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[2251]) ).
thf(2255,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[2253]) ).
thf(2256,plain,
! [B: $i,A: $i] :
( ( A @ ( k1_xboole_0 @ ( A @ ( k1_xboole_0 @ ( B @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
| ~ ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(simp,[status(thm)],[2255]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_zfmisc_1) ).
thf(2564,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) )
& ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(1447,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_relset_1) ).
thf(9276,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447]) ).
thf(2050,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( A @ k6_group_2 @ ( B @ m1_group_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_group_2) ).
thf(12075,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( A @ k6_group_2 @ ( B @ m1_group_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2050]) ).
thf(272,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(3292,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(192,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ v2_funct_1 )
=> ( ( B @ ( A @ k1_finseq_3 ) @ k3_finseq_1 )
= ( A @ k2_relat_1 @ ( B @ k3_xboole_0 ) @ k4_card_1 @ ( A @ k3_finseq_1 @ k6_xcmplx_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_finseq_3) ).
thf(2899,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ v2_funct_1 )
=> ( ( B @ ( A @ k1_finseq_3 ) @ k3_finseq_1 )
= ( A @ k2_relat_1 @ ( B @ k3_xboole_0 ) @ k4_card_1 @ ( A @ k3_finseq_1 @ k6_xcmplx_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(926,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ r1_filter_0 ) ) ) )
<=> ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_filter_0) ).
thf(6664,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
=> ( D @ ( C @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ r1_filter_0 ) ) ) )
=> ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(5133,plain,
sk196 @ v1_funct_1,
inference(cnfConj,[status(thm)],[5130]) ).
thf(1964,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 )
& ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r6_group_3 ) ) )
=> ( B @ ( C @ ( A @ r6_group_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r6_group_3) ).
thf(11758,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 )
& ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r6_group_3 ) ) )
=> ( B @ ( C @ ( A @ r6_group_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1964]) ).
thf(22482,plain,
! [A: $i] :
( ( A != sk537 )
| ( k1_xboole_0 @ l2_struct_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,10370]) ).
thf(22483,plain,
( ( k1_xboole_0 @ l2_struct_0 )
| ( sk537 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22482:[bind(A,$thf( sk537 ))]]) ).
thf(2090,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= D )
<=> ( B
= ( C @ ( A @ k3_group_1 ) @ ( D @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_group_1) ).
thf(12234,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B
= ( C @ ( A @ k3_group_1 ) @ ( D @ ( A @ k1_group_1 ) ) ) )
=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= D ) )
& ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= D )
=> ( B
= ( C @ ( A @ k3_group_1 ) @ ( D @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2090]) ).
thf(1699,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_filter_0) ).
thf(10604,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1699]) ).
thf(452,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_4 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k1_funct_4 ) @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_funct_4) ).
thf(4168,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_4 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k1_funct_4 ) @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(827,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relat_1) ).
thf(6132,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(1028,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_xboole_1) ).
thf(7070,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_2) ).
thf(3571,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(793,axiom,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k2_relat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(5991,plain,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k2_relat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_xboole_1) ).
thf(2582,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(1935,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( A @ k2_group_1 @ ( B @ r1_rlvect_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_group_2) ).
thf(11626,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( A @ k2_group_1 @ ( B @ r1_rlvect_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1935]) ).
thf(1457,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ! [D: $i] :
( ( ( C @ ( A @ k6_group_6 ) @ ( D @ m1_group_2 ) )
& ( C @ ( A @ k6_group_6 ) @ ( D @ v1_group_3 ) )
& ( D @ v1_group_1 ) )
=> ( ( ( B @ ( A @ ( C @ m1_group_6 ) ) )
& ( D
= ( C @ ( B @ ( A @ k1_group_6 ) ) @ ( B @ k6_group_6 ) ) ) )
=> ( B @ ( A @ k6_group_6 ) @ ( D @ ( C @ ( A @ k6_group_6 ) @ k6_group_6 ) @ r2_group_6 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_group_6) ).
thf(9317,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ! [D: $i] :
( ( ( C @ ( A @ k6_group_6 ) @ ( D @ m1_group_2 ) )
& ( C @ ( A @ k6_group_6 ) @ ( D @ v1_group_3 ) )
& ( D @ v1_group_1 ) )
=> ( ( ( B @ ( A @ ( C @ m1_group_6 ) ) )
& ( D
= ( C @ ( B @ ( A @ k1_group_6 ) ) @ ( B @ k6_group_6 ) ) ) )
=> ( B @ ( A @ k6_group_6 ) @ ( D @ ( C @ ( A @ k6_group_6 ) @ k6_group_6 ) @ r2_group_6 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1457]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( C @ ( B @ ( A @ k3_partfun1 ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k3_partfun1 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_partfun1) ).
thf(2942,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( C @ ( B @ ( A @ k3_partfun1 ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k3_partfun1 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(715,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_partfun1) ).
thf(5570,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(1922,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_group_4 @ u2_lattices )
= ( A @ k9_group_4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_group_4) ).
thf(11575,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_group_4 @ u2_lattices )
= ( A @ k9_group_4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1922]) ).
thf(4914,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk180 ) @ v1_relat_1 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[4909]) ).
thf(4921,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk180 ) @ v1_relat_1 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[4914]) ).
thf(4922,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ sk180 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[4921]) ).
thf(1650,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( ( C @ ( D @ r1_rlvect_1 ) )
& ( B @ ( D @ r1_rlvect_1 ) ) )
=> ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( D @ r1_rlvect_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_group_2) ).
thf(10371,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( ( C @ ( D @ r1_rlvect_1 ) )
& ( B @ ( D @ r1_rlvect_1 ) ) )
=> ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( D @ r1_rlvect_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1650]) ).
thf(15015,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk19 @ k4_xboole_0 ) @ v1_finset_1 )
!= ( B @ v1_finset_1 ) )
| ( C @ ( B @ k4_xboole_0 ) @ v1_finset_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14349,2181]) ).
thf(15016,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk19 @ k4_xboole_0 ) @ v1_finset_1 )
!= ( B @ v1_finset_1 ) )
| ( C @ ( B @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(simp,[status(thm)],[15015]) ).
thf(15017,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( sk19 @ k4_xboole_0 ) @ k4_xboole_0 ) @ v1_finset_1 ),
inference(pattern_uni,[status(thm)],[15016:[bind(A,$thf( E )),bind(B,$thf( E @ ( sk19 @ k4_xboole_0 ) )),bind(C,$thf( C ))]]) ).
thf(15021,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( sk19 @ k4_xboole_0 ) @ k4_xboole_0 ) @ v1_finset_1 ),
inference(simp,[status(thm)],[15017]) ).
thf(554,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_xboole_1) ).
thf(4749,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(1147,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B
= ( C @ ( A @ k16_lattice3 ) ) )
<=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( A @ r3_lattice3 ) ) )
=> ( B @ ( D @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( B @ ( A @ r3_lattice3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattice3) ).
thf(7615,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( A @ r3_lattice3 ) ) )
=> ( B @ ( D @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( B @ ( A @ r3_lattice3 ) ) ) )
=> ( B
= ( C @ ( A @ k16_lattice3 ) ) ) )
& ( ( B
= ( C @ ( A @ k16_lattice3 ) ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( A @ r3_lattice3 ) ) )
=> ( B @ ( D @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( B @ ( A @ r3_lattice3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(872,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) )
=> ( ( A @ k2_card_1 )
= ( B @ k2_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_card_1) ).
thf(6362,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) )
=> ( ( A @ k2_card_1 )
= ( B @ k2_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(1406,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( B @ ( A @ k4_lattice4 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice4) ).
thf(9022,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( B @ ( A @ k4_lattice4 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406]) ).
thf(646,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funct_1) ).
thf(5229,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(2103,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( A @ k1_group_2 ) )
= ( B @ ( A @ k1_group_2 ) @ ( C @ ( A @ k1_group_2 ) @ ( A @ k2_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_group_2) ).
thf(12289,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( A @ k1_group_2 ) )
= ( B @ ( A @ k1_group_2 ) @ ( C @ ( A @ k1_group_2 ) @ ( A @ k2_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2103]) ).
thf(1031,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ k1_tarski ) )
=> ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_zfmisc_1) ).
thf(7085,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ k1_tarski ) )
=> ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(2715,plain,
sk27 @ v1_funct_1,
inference(cnfConj,[status(thm)],[2713]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_partfun1) ).
thf(3640,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(1116,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(7475,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(853,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ? [C: $i] :
( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
& ( A @ ( C @ m1_subset_1 ) ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k3_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_binop_1) ).
thf(6238,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ? [C: $i] :
( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
& ( A @ ( C @ m1_subset_1 ) ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ( C
= ( B @ ( A @ k3_binop_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(723,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ v13_lattices )
& ( A @ v13_lattices ) )
<=> ( B @ ( A @ k8_filter_1 ) @ v13_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_filter_1) ).
thf(5607,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k8_filter_1 ) @ v13_lattices )
=> ( ( B @ v13_lattices )
& ( A @ v13_lattices ) ) )
& ( ( ( B @ v13_lattices )
& ( A @ v13_lattices ) )
=> ( B @ ( A @ k8_filter_1 ) @ v13_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(426,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B
= ( A @ k6_relat_1 ) )
<=> ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= C ) )
& ( ( B @ k1_relat_1 )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
thf(4035,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= C ) )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( B
= ( A @ k6_relat_1 ) ) )
& ( ( B
= ( A @ k6_relat_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= C ) )
& ( ( B @ k1_relat_1 )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(1891,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_group_3 ) ) )
=> ( B @ ( C @ ( A @ r1_group_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_group_3) ).
thf(11461,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_group_3 ) ) )
=> ( B @ ( C @ ( A @ r1_group_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1891]) ).
thf(1570,axiom,
! [A: $i,B: $i] :
~ ( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_zfmisc_1) ).
thf(9926,plain,
! [A: $i,B: $i] :
~ ( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1570]) ).
thf(779,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
=> ( ( ( ( D @ k2_relat_1 )
= A )
& ( C @ v2_funct_1 ) )
| ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_funct_2) ).
thf(5927,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
=> ( ( ( ( D @ k2_relat_1 )
= A )
& ( C @ v2_funct_1 ) )
| ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(705,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(5514,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(998,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( C @ k8_group_1 )
= ( B @ ( C @ ( A @ k13_group_2 ) ) @ k1_card_1 ) )
& ( ( C @ k8_group_1 )
= ( B @ ( C @ ( A @ k12_group_2 ) ) @ k1_card_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_group_2) ).
thf(6934,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( C @ k8_group_1 )
= ( B @ ( C @ ( A @ k13_group_2 ) ) @ k1_card_1 ) )
& ( ( C @ k8_group_1 )
= ( B @ ( C @ ( A @ k12_group_2 ) ) @ k1_card_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(1356,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ k4_lattices ) ) )
= ( F @ ( E @ ( B @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k10_filter_1 ) ) ) ) )
& ( ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ k3_lattices ) ) )
= ( F @ ( E @ ( B @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k10_filter_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_filter_1) ).
thf(8707,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ k4_lattices ) ) )
= ( F @ ( E @ ( B @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k10_filter_1 ) ) ) ) )
& ( ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ k3_lattices ) ) )
= ( F @ ( E @ ( B @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k10_filter_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).
thf(465,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_partfun1) ).
thf(4272,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(593,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
thf(4939,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(921,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( E @ v1_partfun1 ) ) ) ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t162_partfun1) ).
thf(6621,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( E @ v1_partfun1 ) ) ) ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(2192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_funct_2 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[2190]) ).
thf(541,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( B @ m3_lattice4 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_lattice4) ).
thf(4673,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) )
=> ( A @ ( B @ m3_lattice4 ) ) )
& ( ( A @ ( B @ m3_lattice4 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(261,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v3_filter_0 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_filter_0 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( F @ ( B @ ( A @ r1_filter_0 ) ) ) )
& ( D @ ( D @ ( E @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_filter_0) ).
thf(3214,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v3_filter_0 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_filter_0 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( F @ ( B @ ( A @ r1_filter_0 ) ) ) )
& ( D @ ( D @ ( E @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(2076,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= ( A @ k2_group_1 ) )
| ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( A @ k2_group_1 ) ) )
=> ( ( C
= ( B @ ( A @ k3_group_1 ) ) )
& ( B
= ( C @ ( A @ k3_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_group_1) ).
thf(12174,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= ( A @ k2_group_1 ) )
| ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( A @ k2_group_1 ) ) )
=> ( ( C
= ( B @ ( A @ k3_group_1 ) ) )
& ( B
= ( C @ ( A @ k3_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2076]) ).
thf(1267,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k6_group_6 ) @ v4_group_1 )
& ( B @ ( A @ k6_group_6 ) @ v3_group_1 )
& ( B @ ( A @ k6_group_6 ) @ v2_group_1 )
& ( B @ ( A @ k6_group_6 ) @ v1_group_1 )
& ~ ( B @ ( A @ k6_group_6 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_group_6) ).
thf(8218,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k6_group_6 ) @ v4_group_1 )
& ( B @ ( A @ k6_group_6 ) @ v3_group_1 )
& ( B @ ( A @ k6_group_6 ) @ v2_group_1 )
& ( B @ ( A @ k6_group_6 ) @ v1_group_1 )
& ~ ( B @ ( A @ k6_group_6 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(1962,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 )
& ( B @ ( A @ r1_group_6 ) ) )
=> ( ( B @ l1_group_1 )
& ( B @ v7_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_group_6) ).
thf(11743,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 )
& ( B @ ( A @ r1_group_6 ) ) )
=> ( ( B @ l1_group_1 )
& ( B @ v7_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1962]) ).
thf(1592,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( B
= ( D @ ( C @ ( A @ k13_group_2 ) ) ) )
& ( B
= ( D @ ( C @ ( A @ k12_group_2 ) ) ) ) ) )
& ( C @ ( A @ k4_group_6 ) @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_group_6) ).
thf(10059,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ( B
= ( D @ ( C @ ( A @ k13_group_2 ) ) ) )
& ( B
= ( D @ ( C @ ( A @ k12_group_2 ) ) ) ) ) )
& ( C @ ( A @ k4_group_6 ) @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1592]) ).
thf(991,axiom,
! [A: $i,B: $i] :
( ( B @ k6_partfun1 @ ( A @ k6_partfun1 @ r1_tarski ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funct_4) ).
thf(6902,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k6_partfun1 @ ( A @ k6_partfun1 @ r1_tarski ) ) )
& ( ( B @ k6_partfun1 @ ( A @ k6_partfun1 @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_partfun1) ).
thf(2588,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(701,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_enumset1) ).
thf(5499,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(1577,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ k5_group_3 ) ) @ ( A @ k3_group_3 ) ) )
= ( B @ ( D @ ( C @ ( A @ k2_group_2 ) ) @ ( A @ k5_group_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_group_3) ).
thf(9953,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ k5_group_3 ) ) @ ( A @ k3_group_3 ) ) )
= ( B @ ( D @ ( C @ ( A @ k2_group_2 ) ) @ ( A @ k5_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1577]) ).
thf(384,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( A @ k4_finseq_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) )
& ( ( A @ k4_finseq_1 )
= ( B @ k4_finseq_1 ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finseq_1) ).
thf(3833,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( A @ k4_finseq_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) )
& ( ( A @ k4_finseq_1 )
= ( B @ k4_finseq_1 ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(1049,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) )
=> ( ( A @ k1_setfam_1 @ ( B @ r1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_setfam_1) ).
thf(7159,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) )
=> ( ( A @ k1_setfam_1 @ ( B @ r1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ ( B @ ( A @ k5_partfun1 ) ) )
= ( B @ ( A @ k1_funct_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_funct_2) ).
thf(2732,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ ( B @ ( A @ k5_partfun1 ) ) )
= ( B @ ( A @ k1_funct_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1694,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ ( A @ r1_group_6 ) )
<=> ? [C: $i] :
( ( B @ ( A @ ( C @ v4_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_group_6) ).
thf(10572,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ( B @ ( A @ ( C @ v4_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ r1_group_6 ) ) )
& ( ( B @ ( A @ r1_group_6 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v4_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1694]) ).
thf(535,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ v3_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_filter_1) ).
thf(4641,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ v3_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(1382,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( ( A @ k9_group_1 )
= ( B @ k9_group_1 ) )
& ( A @ v6_group_1 ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_group_2) ).
thf(8904,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( ( A @ k9_group_1 )
= ( B @ k9_group_1 ) )
& ( A @ v6_group_1 ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( C @ k2_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_funct_2) ).
thf(4469,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( C @ k2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(1993,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_group_1 ) )
= ( A @ k2_group_1 ) )
=> ( B
= ( A @ k2_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_group_1) ).
thf(11855,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_group_1 ) )
= ( A @ k2_group_1 ) )
=> ( B
= ( A @ k2_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1993]) ).
thf(260,axiom,
! [A: $i] :
~ ( ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ~ ( B @ ( A @ r2_wellord2 ) ) )
& ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_card_1) ).
thf(3209,plain,
! [A: $i] :
~ ( ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ~ ( B @ ( A @ r2_wellord2 ) ) )
& ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(1509,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k6_group_3 ) ) @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) )
& ( C @ ( B @ ( A @ k3_group_1 ) @ ( B @ ( C @ ( A @ k6_group_3 ) ) @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_group_3) ).
thf(9578,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k6_group_3 ) ) @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) )
& ( C @ ( B @ ( A @ k3_group_1 ) @ ( B @ ( C @ ( A @ k6_group_3 ) ) @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1509]) ).
thf(1682,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( B @ ( A @ k5_group_2 @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) )
& ( B @ ( B @ ( A @ k5_group_2 @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_group_4) ).
thf(10521,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( B @ ( A @ k5_group_2 @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) )
& ( B @ ( B @ ( A @ k5_group_2 @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1682]) ).
thf(148,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_struct_0 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_struct_0) ).
thf(2720,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_struct_0 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1797,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_group_6 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_group_6) ).
thf(11126,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_group_6 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1797]) ).
thf(1282,axiom,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r2_hidden ) )
<=> ~ ( A @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_card_1) ).
thf(8295,plain,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( ~ ( A @ ( B @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) )
& ( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).
thf(1376,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C
= ( B @ ( A @ k5_group_4 ) ) )
<=> ( ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( D @ u1_struct_0 @ ( B @ r1_tarski ) )
=> ( D @ ( C @ m1_group_2 ) ) ) )
& ( C @ u1_struct_0 @ ( B @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_group_4) ).
thf(8813,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( ( ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( D @ u1_struct_0 @ ( B @ r1_tarski ) )
=> ( D @ ( C @ m1_group_2 ) ) ) )
& ( C @ u1_struct_0 @ ( B @ r1_tarski ) ) )
=> ( C
= ( B @ ( A @ k5_group_4 ) ) ) )
& ( ( C
= ( B @ ( A @ k5_group_4 ) ) )
=> ( ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( D @ u1_struct_0 @ ( B @ r1_tarski ) )
=> ( D @ ( C @ m1_group_2 ) ) ) )
& ( C @ u1_struct_0 @ ( B @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376]) ).
thf(2154,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v16_lattices )
| ~ ( B @ v15_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2144]) ).
thf(2160,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ v16_lattices )
| ~ ( B @ v15_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[2154]) ).
thf(1654,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_domain_1 ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_domain_1) ).
thf(10392,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_domain_1 ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1654]) ).
thf(1494,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ v6_group_1 )
=> ( C @ ( A @ ( B @ k13_group_6 ) ) @ v6_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_group_6) ).
thf(9473,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ v6_group_1 )
=> ( C @ ( A @ ( B @ k13_group_6 ) ) @ v6_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1494]) ).
thf(2023,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( np__3 @ ( A @ k6_group_1 ) ) )
= ( B @ ( B @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_group_1) ).
thf(11988,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( np__3 @ ( A @ k6_group_1 ) ) )
= ( B @ ( B @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2023]) ).
thf(1187,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( C @ ( D @ ( A @ k13_group_2 ) ) @ ( B @ ( D @ ( A @ k12_group_2 ) ) @ r2_wellord2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_group_2) ).
thf(7832,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( C @ ( D @ ( A @ k13_group_2 ) ) @ ( B @ ( D @ ( A @ k12_group_2 ) ) @ r2_wellord2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(878,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ r2_wellord2 ) )
& ( C @ ( A @ r2_wellord2 ) )
& ( D @ ( C @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ r2_wellord2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_card_1) ).
thf(6389,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ r2_wellord2 ) )
& ( C @ ( A @ r2_wellord2 ) )
& ( D @ ( C @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ r2_wellord2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(2222,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
| ~ ( A @ ( F @ m1_subset_1 ) )
| ~ ( A @ ( E @ m1_subset_1 ) )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[2217]) ).
thf(2224,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ m1_subset_1 ) )
| ~ ( A @ ( E @ m1_subset_1 ) )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ),
inference(lifteq,[status(thm)],[2222]) ).
thf(1679,axiom,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
& ( A @ k1_subset_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_subset_1) ).
thf(10509,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
& ( A @ k1_subset_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1679]) ).
thf(21766,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ l1_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,2117]) ).
thf(21767,plain,
( ( k1_xboole_0 @ l1_group_1 )
| ( sk1 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21766:[bind(A,$thf( sk1 ))]]) ).
thf(741,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_partfun1) ).
thf(5684,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(1708,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( np__0 @ r1_xreal_0 ) )
=> ( ( C @ ( A @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ k1_int_2 @ ( B @ k6_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_group_1) ).
thf(10636,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( np__0 @ r1_xreal_0 ) )
=> ( ( C @ ( A @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ k1_int_2 @ ( B @ k6_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1708]) ).
thf(652,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k6_lattices @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_filter_0) ).
thf(5262,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k6_lattices @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(1301,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ k3_group_2 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_group_2) ).
thf(8396,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ ( B @ k3_group_2 ) ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( D @ ( B @ k3_group_2 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k1_group_1 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).
thf(1886,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( C @ k1_group_1 ) ) )
= ( D @ ( E @ ( C @ k1_group_1 ) ) ) )
=> ( ( E @ ( B @ ( C @ k6_group_1 ) ) @ ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) )
= ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( E @ ( B @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_group_1) ).
thf(11443,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( C @ k1_group_1 ) ) )
= ( D @ ( E @ ( C @ k1_group_1 ) ) ) )
=> ( ( E @ ( B @ ( C @ k6_group_1 ) ) @ ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) )
= ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( E @ ( B @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1886]) ).
thf(522,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_finseq_1) ).
thf(4561,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(479,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( C @ ( B @ ( A @ r3_lattice4 ) ) )
<=> ( ( A @ k5_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k5_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattice4) ).
thf(4346,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( ( ( A @ k5_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k5_lattices ) )
=> ( C @ ( B @ ( A @ r3_lattice4 ) ) ) )
& ( ( C @ ( B @ ( A @ r3_lattice4 ) ) )
=> ( ( A @ k5_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k5_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(1439,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( B
= ( A @ k1_group_3 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_group_3) ).
thf(9214,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) ) ) )
=> ( B
= ( A @ k1_group_3 ) ) )
& ( ( B
= ( A @ k1_group_3 ) )
=> ! [C: $i] :
( ( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1439]) ).
thf(1641,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_group_2 ) ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k2_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_group_2) ).
thf(10328,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_group_2 ) ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k2_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1641]) ).
thf(3304,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[3303]) ).
thf(3305,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[3304]) ).
thf(1104,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(7429,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(2019,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ( ( B @ ( A @ k3_group_4 ) )
= ( A @ u1_group_1 @ ( B @ ( A @ u1_struct_0 @ k2_finsop_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_group_4) ).
thf(11974,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ( ( B @ ( A @ k3_group_4 ) )
= ( A @ u1_group_1 @ ( B @ ( A @ u1_struct_0 @ k2_finsop_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2019]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v11_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v17_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_lattices) ).
thf(2165,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v11_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v17_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1608,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k2_xboole_0 ) ) )
=> ( D @ ( A @ k5_group_4 ) @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_latsubgr) ).
thf(10162,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k2_xboole_0 ) ) )
=> ( D @ ( A @ k5_group_4 ) @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1608]) ).
thf(993,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_group_2 ) ) )
= ( B @ ( C @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_group_2) ).
thf(6912,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_group_2 ) ) )
= ( B @ ( C @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(1214,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ k1_tarski ) )
=> ( ( B @ ( A @ k7_setfam_1 ) )
= ( k1_xboole_0 @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_setfam_1) ).
thf(7971,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ k1_tarski ) )
=> ( ( B @ ( A @ k7_setfam_1 ) )
= ( k1_xboole_0 @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( B != C )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_zfmisc_1) ).
thf(3722,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( B != C )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(2061,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k7_group_2 ) )
= ( B @ u1_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_group_2) ).
thf(12124,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k7_group_2 ) )
= ( B @ u1_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2061]) ).
thf(1581,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(9986,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1581]) ).
thf(17023,plain,
! [A: $i] :
( ( ( sk593 @ l3_lattices )
!= ( A @ l3_lattices ) )
| ( A @ l1_lattices )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11077,6015]) ).
thf(17024,plain,
! [A: $i] :
( ( ( sk593 @ l3_lattices )
!= ( A @ l3_lattices ) )
| ( A @ l1_lattices ) ),
inference(simp,[status(thm)],[17023]) ).
thf(17025,plain,
sk593 @ l1_lattices,
inference(pattern_uni,[status(thm)],[17024:[bind(A,$thf( sk593 ))]]) ).
thf(17071,plain,
! [A: $i] :
( ( ( sk593 @ l1_lattices )
!= ( A @ l1_lattices ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17025,4291]) ).
thf(17072,plain,
! [A: $i] :
( ( ( sk593 @ l1_lattices )
!= ( A @ l1_lattices ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[17071]) ).
thf(17073,plain,
sk593 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[17072:[bind(A,$thf( sk593 ))]]) ).
thf(1434,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( np__0 @ ( A @ r1_xreal_0 ) )
=> ( ( C @ ( A @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ k1_int_2 @ ( B @ k6_group_1 ) ) @ ( B @ k3_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_group_1) ).
thf(9182,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( np__0 @ ( A @ r1_xreal_0 ) )
=> ( ( C @ ( A @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ k1_int_2 @ ( B @ k6_group_1 ) ) @ ( B @ k3_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1434]) ).
thf(655,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_1_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_domain_1) ).
thf(5276,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_1_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(1671,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k2_group_2 ) ) )
= ( D @ ( C @ ( A @ k2_group_2 ) ) @ ( D @ ( B @ ( A @ k2_group_2 ) ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_group_2) ).
thf(10466,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k2_group_2 ) ) )
= ( D @ ( C @ ( A @ k2_group_2 ) ) @ ( D @ ( B @ ( A @ k2_group_2 ) ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1671]) ).
thf(1810,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r4_group_3 ) ) )
<=> ( C @ ( B @ ( A @ r3_group_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r4_group_3) ).
thf(11166,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r3_group_3 ) ) )
=> ( C @ ( B @ ( A @ r4_group_3 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_group_3 ) ) )
=> ( C @ ( B @ ( A @ r3_group_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1810]) ).
thf(1218,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( D @ ( B @ ( A @ k2_group_2 ) ) @ ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) @ ( B @ ( A @ k2_group_2 ) ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_group_2) ).
thf(7988,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( D @ ( B @ ( A @ k2_group_2 ) ) @ ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) @ ( B @ ( A @ k2_group_2 ) ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( C @ k2_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_xboole_1) ).
thf(4768,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( C @ k2_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(1604,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k12_group_2 ) ) @ ( C @ ( B @ ( A @ k13_group_2 ) ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_group_3) ).
thf(10144,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k12_group_2 ) ) @ ( C @ ( B @ ( A @ k13_group_2 ) ) @ r1_tarski ) ) )
=> ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) ) )
& ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k12_group_2 ) ) @ ( C @ ( B @ ( A @ k13_group_2 ) ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1604]) ).
thf(1749,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k15_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ r2_hidden ) )
& ( B @ ( A @ k14_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t165_group_2) ).
thf(10861,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k15_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ r2_hidden ) )
& ( B @ ( A @ k14_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1749]) ).
thf(1155,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_funct_2) ).
thf(7662,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(2028,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( B @ u1_struct_0 )
= ( A @ u1_struct_0 ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_group_2) ).
thf(12001,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( B @ u1_struct_0 )
= ( A @ u1_struct_0 ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2028]) ).
thf(783,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k4_funct_2 ) ) )
= ( C @ ( B @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_funct_2) ).
thf(5948,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k4_funct_2 ) ) )
= ( C @ ( B @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(4145,plain,
sk110 @ l1_struct_0,
inference(cnfConj,[status(thm)],[4144]) ).
thf(712,axiom,
! [A: $i,B: $i] :
~ ( ( ( B @ ( A @ k2_xboole_0 ) @ k1_setfam_1 )
!= ( B @ k1_setfam_1 @ ( A @ k1_setfam_1 @ k3_xboole_0 ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_setfam_1) ).
thf(5560,plain,
! [A: $i,B: $i] :
~ ( ( ( B @ ( A @ k2_xboole_0 ) @ k1_setfam_1 )
!= ( B @ k1_setfam_1 @ ( A @ k1_setfam_1 @ k3_xboole_0 ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(1946,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_group_4 @ l3_lattices )
& ( A @ k11_group_4 @ v10_lattices )
& ( A @ k11_group_4 @ v3_lattices )
& ~ ( A @ k11_group_4 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_group_4) ).
thf(11674,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_group_4 @ l3_lattices )
& ( A @ k11_group_4 @ v10_lattices )
& ( A @ k11_group_4 @ v3_lattices )
& ~ ( A @ k11_group_4 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1946]) ).
thf(2337,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( B @ sk10 ) @ m1_filter_1 ) ) )
| ~ ( B @ v1_relat_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[2336]) ).
thf(2082,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_group_2 @ ( A @ k17_group_2 ) )
= np__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t180_group_2) ).
thf(12202,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_group_2 @ ( A @ k17_group_2 ) )
= np__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2082]) ).
thf(6125,plain,
sk253 @ v1_funct_1,
inference(cnfConj,[status(thm)],[6123]) ).
thf(2219,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk3 ) ) @ m1_subset_1 ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[2217]) ).
thf(4562,plain,
( ( sk152 @ v1_finset_1 )
& ( sk152 @ v2_funct_1 )
& ( sk152 @ v1_funct_1 )
& ( sk152 @ v1_relat_1 )
& ( sk152 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[4561]) ).
thf(4563,plain,
sk152 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[4562]) ).
thf(16617,plain,
( ( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4563,16583]) ).
thf(16618,plain,
( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[16617]) ).
thf(16646,plain,
( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) )
!= sk152 ),
inference(simp,[status(thm)],[16618]) ).
thf(16992,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
!= ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) ) )
| ( A != sk152 ) ),
inference(paramod_ordered,[status(thm)],[2270,16646]) ).
thf(16996,plain,
( ( k1_xboole_0 @ ( sk152 @ k4_xboole_0 ) )
!= ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) ) ),
inference(simp,[status(thm)],[16992]) ).
thf(26544,plain,
( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) )
!= sk152 ),
inference(rewrite,[status(thm)],[16996,2270]) ).
thf(1647,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( B @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_group_4) ).
thf(10365,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( B @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1647]) ).
thf(1836,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( C @ m1_group_2 ) )
& ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( B @ m1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_group_4) ).
thf(11257,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( C @ m1_group_2 ) )
& ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( B @ m1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1836]) ).
thf(17090,plain,
! [A: $i] :
( ( ( sk510 @ l3_lattices )
!= ( A @ l3_lattices ) )
| ( A @ l2_lattices )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10027,6016]) ).
thf(17091,plain,
! [A: $i] :
( ( ( sk510 @ l3_lattices )
!= ( A @ l3_lattices ) )
| ( A @ l2_lattices ) ),
inference(simp,[status(thm)],[17090]) ).
thf(17092,plain,
sk510 @ l2_lattices,
inference(pattern_uni,[status(thm)],[17091:[bind(A,$thf( sk510 ))]]) ).
thf(710,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t153_relat_1) ).
thf(5543,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(2319,plain,
! [B: $i,A: $i] :
( ( A @ v4_lattice3 )
| ~ ( A @ ( B @ sk9 ) @ ( B @ ( A @ r1_lattices ) ) )
| ~ ( A @ sk8 @ ( B @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2314]) ).
thf(2322,plain,
! [B: $i,A: $i] :
( ( A @ v4_lattice3 )
| ~ ( A @ ( B @ sk9 ) @ ( B @ ( A @ r1_lattices ) ) )
| ~ ( A @ sk8 @ ( B @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[2319]) ).
thf(382,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v11_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_filter_0) ).
thf(3828,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v11_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(1794,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k6_finseq_1 @ ( A @ k3_group_4 ) )
= ( A @ k2_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_group_4) ).
thf(11109,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k6_finseq_1 @ ( A @ k3_group_4 ) )
= ( A @ k2_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1794]) ).
thf(142,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ ( A @ k1_finseq_3 ) @ k3_finseq_1 )
= ( A @ k3_finseq_1 ) )
=> ( A @ k2_relat_1 @ ( B @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_finseq_3) ).
thf(2701,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ ( A @ k1_finseq_3 ) @ k3_finseq_1 )
= ( A @ k3_finseq_1 ) )
=> ( A @ k2_relat_1 @ ( B @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(1139,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_subset_1) ).
thf(7583,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ r2_binop_1 ) ) )
& ( B @ ( C @ ( A @ r1_binop_1 ) ) ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_binop_1) ).
thf(2903,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ r2_binop_1 ) ) )
& ( B @ ( C @ ( A @ r1_binop_1 ) ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1567,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ k2_filter_0 ) )
= ( A @ u1_struct_0 ) )
& ~ ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_filter_0) ).
thf(9911,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ k2_filter_0 ) )
= ( A @ u1_struct_0 ) )
& ~ ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567]) ).
thf(26263,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ( sk1 != k1_xboole_0 )
| ( A @ l1_struct_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,20725]) ).
thf(26264,plain,
! [A: $i] :
( ( sk1 != k1_xboole_0 )
| ( A @ l1_struct_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[26263:[]]) ).
thf(1014,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( B @ v1_xboole_0 ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( A @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(6994,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xboole_0 ) ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( ( A @ ( B @ r2_hidden ) )
=> ( A @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( C @ ( B @ r1_tarski ) )
& ( ( C @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( A @ ( C @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(4117,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( C @ ( B @ r1_tarski ) )
& ( ( C @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( A @ ( C @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(1191,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_group_3 ) )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v2_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_group_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_group_3) ).
thf(7847,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_group_3 ) )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v2_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_group_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(846,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k1_funct_4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funct_4) ).
thf(6206,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k1_funct_4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(1487,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k4_filter_0 ) ) @ ( D @ ( B @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_filter_1) ).
thf(9435,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k4_filter_0 ) ) @ ( D @ ( B @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1487]) ).
thf(1475,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k12_finseq_1 ) @ ( B @ ( A @ u1_struct_0 @ k8_finseq_1 ) ) @ ( A @ k3_group_4 ) )
= ( C @ ( B @ ( A @ k3_group_4 ) @ ( A @ k1_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_group_4) ).
thf(9386,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k12_finseq_1 ) @ ( B @ ( A @ u1_struct_0 @ k8_finseq_1 ) ) @ ( A @ k3_group_4 ) )
= ( C @ ( B @ ( A @ k3_group_4 ) @ ( A @ k1_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1475]) ).
thf(638,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_xboole_1) ).
thf(5186,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(356,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( ( A @ k1_card_1 @ v1_finset_1 )
& ( A @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_card_1) ).
thf(3715,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( ( A @ k1_card_1 @ v1_finset_1 )
& ( A @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(1943,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k1_group_1 ) ) ) )
<=> ( ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) )
= ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_group_1) ).
thf(11661,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) )
= ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) ) )
=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k1_group_1 ) ) ) ) )
& ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k1_group_1 ) ) ) )
=> ( ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) )
= ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1943]) ).
thf(1895,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= ( C @ ( D @ ( A @ k2_group_3 ) ) ) )
=> ( B = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_group_3) ).
thf(11475,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= ( C @ ( D @ ( A @ k2_group_3 ) ) ) )
=> ( B = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1895]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_xboole_0 ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ k3_tarski @ ( C @ r1_tarski ) ) )
=> ( A @ k3_tarski @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_setfam_1) ).
thf(4164,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_xboole_0 ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ k3_tarski @ ( C @ r1_tarski ) ) )
=> ( A @ k3_tarski @ ( C @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(1815,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_group_2 @ ( A @ k14_group_2 ) )
= ( A @ a_1_0_group_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_group_2) ).
thf(11181,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_group_2 @ ( A @ k14_group_2 ) )
= ( A @ a_1_0_group_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1815]) ).
thf(1204,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( ( C @ ( E @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( E @ ( C @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_filter_0) ).
thf(7921,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( ( C @ ( E @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( E @ ( C @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(1999,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k7_group_3 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( D @ ( C @ ( B @ r2_group_3 ) ) )
& ( D = A )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_group_3) ).
thf(11879,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( D @ ( C @ ( B @ r2_group_3 ) ) )
& ( D = A )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ k7_group_3 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k7_group_3 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( D @ ( C @ ( B @ r2_group_3 ) ) )
& ( D = A )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1999]) ).
thf(1309,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) )
<=> ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_lattices) ).
thf(8464,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) )
& ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) )
=> ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(2246,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(cnf,[status(esa)],[2245]) ).
thf(2247,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) ) ),
inference(lifteq,[status(thm)],[2246]) ).
thf(643,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_realset1) ).
thf(5208,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(2948,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(1361,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( D @ ( A @ k13_group_2 ) ) @ ( A @ k2_group_2 ) ) )
= ( C @ ( B @ ( A @ k3_group_2 ) ) @ ( D @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_group_3) ).
thf(8729,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( D @ ( A @ k13_group_2 ) ) @ ( A @ k2_group_2 ) ) )
= ( C @ ( B @ ( A @ k3_group_2 ) ) @ ( D @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_relat_1) ).
thf(3488,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(1353,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v6_group_1 )
=> ( B @ v1_finset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_group_2) ).
thf(8696,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v6_group_1 )
=> ( B @ v1_finset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353]) ).
thf(886,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k5_subset_1 ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(6415,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k5_subset_1 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(1285,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(8309,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(8310,plain,
sk388 @ v1_xboole_0,
inference(cnf,[status(esa)],[8309]) ).
thf(16621,plain,
( ( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk388 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8310,16583]) ).
thf(16622,plain,
( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk388 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[16621]) ).
thf(16648,plain,
( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) )
!= sk388 ),
inference(simp,[status(thm)],[16622]) ).
thf(17003,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
!= ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) ) )
| ( A != sk388 ) ),
inference(paramod_ordered,[status(thm)],[2270,16648]) ).
thf(17007,plain,
( ( k1_xboole_0 @ ( sk388 @ k4_xboole_0 ) )
!= ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) ) ),
inference(simp,[status(thm)],[17003]) ).
thf(27078,plain,
( ( sk15 @ sk305 @ k1_tarski @ ( sk15 @ k4_xboole_0 ) )
!= sk388 ),
inference(rewrite,[status(thm)],[17007,2270]) ).
thf(1110,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(7456,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(17087,plain,
! [A: $i] :
( ( ( sk593 @ l3_lattices )
!= ( A @ l3_lattices ) )
| ( A @ l2_lattices )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11077,6016]) ).
thf(17088,plain,
! [A: $i] :
( ( ( sk593 @ l3_lattices )
!= ( A @ l3_lattices ) )
| ( A @ l2_lattices ) ),
inference(simp,[status(thm)],[17087]) ).
thf(17089,plain,
sk593 @ l2_lattices,
inference(pattern_uni,[status(thm)],[17088:[bind(A,$thf( sk593 ))]]) ).
thf(1173,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_0) ).
thf(7779,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(1599,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( C @ ( A @ k9_group_3 ) @ ( B @ ( C @ ( A @ k6_group_3 ) ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_group_3) ).
thf(10097,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( C @ ( A @ k9_group_3 ) @ ( B @ ( C @ ( A @ k6_group_3 ) ) @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1599]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_finseq_1 ) )
& ( A @ ( B @ m1_finseq_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ k8_finseq_1 ) ) @ m2_finseq_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_finseq_1) ).
thf(4057,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_finseq_1 ) )
& ( A @ ( B @ m1_finseq_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ k8_finseq_1 ) ) @ m2_finseq_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(176,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_xboole_1) ).
thf(2838,plain,
! [A: $i,B: $i] : ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(1587,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( B @ ( A @ k7_group_2 ) @ ( A @ k5_group_4 ) @ ( A @ r1_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_group_4) ).
thf(10023,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( B @ ( A @ k7_group_2 ) @ ( A @ k5_group_4 ) @ ( A @ r1_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1587]) ).
thf(409,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(3970,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(728,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_finset_1) ).
thf(5628,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(1987,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ m1_group_2 ) )
& ( C @ ( B @ ( A @ k8_group_4 ) ) @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_group_4) ).
thf(11835,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ m1_group_2 ) )
& ( C @ ( B @ ( A @ k8_group_4 ) ) @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1987]) ).
thf(1756,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ a_1_0_group_4 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ? [D: $i] :
( ( B @ ( D @ v2_group_4 ) )
& ( C
= ( D @ u1_struct_0 ) )
& ( B @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
& ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_group_4) ).
thf(10885,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ? [D: $i] :
( ( B @ ( D @ v2_group_4 ) )
& ( C
= ( D @ u1_struct_0 ) )
& ( B @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
& ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_group_4 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_group_4 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ? [D: $i] :
( ( B @ ( D @ v2_group_4 ) )
& ( C
= ( D @ u1_struct_0 ) )
& ( B @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
& ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1756]) ).
thf(1685,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ u1_struct_0 @ k1_subset_1 @ ( B @ ( A @ k2_group_2 ) ) )
= k1_xboole_0 )
& ( ( B @ ( A @ u1_struct_0 @ k1_subset_1 @ ( A @ k2_group_2 ) ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_group_2) ).
thf(10531,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ u1_struct_0 @ k1_subset_1 @ ( B @ ( A @ k2_group_2 ) ) )
= k1_xboole_0 )
& ( ( B @ ( A @ u1_struct_0 @ k1_subset_1 @ ( A @ k2_group_2 ) ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1685]) ).
thf(1521,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ! [D: $i] :
( ( k4_numbers @ ( D @ m2_finseq_1 ) )
=> ! [E: $i] :
( ( k4_numbers @ ( E @ m2_finseq_1 ) )
=> ( ( ( ( C @ k3_finseq_1 )
= ( E @ k3_finseq_1 ) )
& ( ( B @ k3_finseq_1 )
= ( D @ k3_finseq_1 ) ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k8_finseq_1 ) ) @ ( E @ ( D @ ( k4_numbers @ k8_finseq_1 ) ) @ ( A @ k4_group_4 ) ) )
= ( C @ ( E @ ( A @ k4_group_4 ) ) @ ( B @ ( D @ ( A @ k4_group_4 ) ) @ ( A @ u1_struct_0 @ k8_finseq_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_group_4) ).
thf(9675,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ! [D: $i] :
( ( k4_numbers @ ( D @ m2_finseq_1 ) )
=> ! [E: $i] :
( ( k4_numbers @ ( E @ m2_finseq_1 ) )
=> ( ( ( ( C @ k3_finseq_1 )
= ( E @ k3_finseq_1 ) )
& ( ( B @ k3_finseq_1 )
= ( D @ k3_finseq_1 ) ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k8_finseq_1 ) ) @ ( E @ ( D @ ( k4_numbers @ k8_finseq_1 ) ) @ ( A @ k4_group_4 ) ) )
= ( C @ ( E @ ( A @ k4_group_4 ) ) @ ( B @ ( D @ ( A @ k4_group_4 ) ) @ ( A @ u1_struct_0 @ k8_finseq_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521]) ).
thf(1138,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_subset_1) ).
thf(7580,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( B = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(1329,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(8564,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r2_hidden ) ) )
& ( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(2379,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1955,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( A @ v4_group_1 )
=> ( ( D @ ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( A @ k2_group_2 ) ) )
= ( D @ ( C @ ( A @ k2_group_2 ) ) @ ( B @ ( A @ k2_group_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_group_2) ).
thf(11713,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( A @ v4_group_1 )
=> ( ( D @ ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( A @ k2_group_2 ) ) )
= ( D @ ( C @ ( A @ k2_group_2 ) ) @ ( B @ ( A @ k2_group_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1955]) ).
thf(1430,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
<=> ( ( B @ ( A @ k11_group_3 ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t163_group_3) ).
thf(9151,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( ( B @ ( A @ k11_group_3 ) )
= A )
=> ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) ) )
& ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k11_group_3 ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1430]) ).
thf(600,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k2_xcmplx_0 ) @ ( C @ k6_group_1 ) ) )
= ( D @ ( B @ ( C @ k6_group_1 ) ) @ ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_group_1) ).
thf(4976,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k2_xcmplx_0 ) @ ( C @ k6_group_1 ) ) )
= ( D @ ( B @ ( C @ k6_group_1 ) ) @ ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(1112,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( C @ ( A @ k12_group_2 ) ) )
= ( B @ ( C @ ( A @ k13_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_group_2) ).
thf(7461,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( C @ ( A @ k12_group_2 ) ) )
= ( B @ ( C @ ( A @ k13_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(1767,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ r2_hidden ) )
=> ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k2_filter_0 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_filter_0) ).
thf(10973,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ r2_hidden ) )
=> ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k2_filter_0 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1767]) ).
thf(1067,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
<=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(7251,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(874,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r7_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_binop_1) ).
thf(6369,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r7_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r7_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(1462,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_lattices @ ( A @ k3_lattices ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_lattices) ).
thf(9353,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_lattices @ ( A @ k3_lattices ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462]) ).
thf(508,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v14_lattices )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k6_lattices )
= ( A @ k6_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_filter_0) ).
thf(4488,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v14_lattices )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k6_lattices )
= ( A @ k6_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(1466,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( B @ ( D @ ( A @ k4_group_3 ) ) @ ( B @ ( C @ ( A @ k4_group_3 ) ) @ ( A @ k2_group_2 ) ) @ ( B @ ( D @ ( C @ ( A @ k2_group_2 ) ) @ ( A @ k4_group_3 ) ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_group_3) ).
thf(9363,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( B @ ( D @ ( A @ k4_group_3 ) ) @ ( B @ ( C @ ( A @ k4_group_3 ) ) @ ( A @ k2_group_2 ) ) @ ( B @ ( D @ ( C @ ( A @ k2_group_2 ) ) @ ( A @ k4_group_3 ) ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1466]) ).
thf(1607,axiom,
? [A: $i] : ( A @ v1_card_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_card_1) ).
thf(10160,plain,
? [A: $i] : ( A @ v1_card_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1607]) ).
thf(4510,plain,
sk145 @ v1_funct_1,
inference(cnfConj,[status(thm)],[4508]) ).
thf(2357,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ r4_binop_1 ) ) )
| ~ ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r4_binop_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2355]) ).
thf(2320,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ sk7 ) @ ( A @ r1_lattices ) ) )
| ~ ( B @ ( C @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ v4_lattice3 )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2314]) ).
thf(1237,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( k4_numbers @ ( A @ k2_group_4 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_group_4) ).
thf(8061,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( k4_numbers @ ( A @ k2_group_4 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(10028,plain,
sk510 @ v3_lattices,
inference(cnfConj,[status(thm)],[10026]) ).
thf(757,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_partfun1) ).
thf(5809,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(1857,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ ( A @ r2_group_6 ) )
=> ( ( A @ k8_group_1 )
= ( B @ k8_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_group_6) ).
thf(11334,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ ( A @ r2_group_6 ) )
=> ( ( A @ k8_group_1 )
= ( B @ k8_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1857]) ).
thf(2692,plain,
sk24 @ v1_finset_1,
inference(cnfConj,[status(thm)],[2686]) ).
thf(14321,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ v1_finset_1 )
!= ( A @ v1_finset_1 ) )
| ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2692,2181]) ).
thf(14322,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ v1_finset_1 )
!= ( A @ v1_finset_1 ) )
| ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(simp,[status(thm)],[14321]) ).
thf(14323,plain,
! [A: $i] : ( A @ ( sk24 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(pattern_uni,[status(thm)],[14322:[bind(A,$thf( sk24 ))]]) ).
thf(14343,plain,
! [A: $i] : ( A @ ( sk24 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(simp,[status(thm)],[14323]) ).
thf(14772,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk24 @ k4_xboole_0 ) @ v1_finset_1 )
!= ( B @ v1_finset_1 ) )
| ( C @ ( B @ k4_xboole_0 ) @ v1_finset_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14343,2181]) ).
thf(14773,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk24 @ k4_xboole_0 ) @ v1_finset_1 )
!= ( B @ v1_finset_1 ) )
| ( C @ ( B @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(simp,[status(thm)],[14772]) ).
thf(14774,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( sk24 @ k4_xboole_0 ) @ k4_xboole_0 ) @ v1_finset_1 ),
inference(pattern_uni,[status(thm)],[14773:[bind(A,$thf( E )),bind(B,$thf( E @ ( sk24 @ k4_xboole_0 ) )),bind(C,$thf( C ))]]) ).
thf(14778,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( sk24 @ k4_xboole_0 ) @ k4_xboole_0 ) @ v1_finset_1 ),
inference(simp,[status(thm)],[14774]) ).
thf(35714,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( k1_xboole_0 @ k4_xboole_0 ) @ k4_xboole_0 ) @ v1_finset_1 ),
inference(rewrite,[status(thm)],[14778,18073]) ).
thf(9927,plain,
~ ? [A: $i,B: $i] :
( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[9926]) ).
thf(9928,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[9927]) ).
thf(9929,plain,
! [B: $i,A: $i] :
( ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[9928]) ).
thf(9930,plain,
! [A: $i] :
~ ( A @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[9929]) ).
thf(22030,plain,
! [A: $i] :
( ( A != sk605 )
| ( k1_xboole_0 @ v4_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,11439]) ).
thf(22031,plain,
( ( k1_xboole_0 @ v4_group_1 )
| ( sk605 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22030:[bind(A,$thf( sk605 ))]]) ).
thf(463,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k3_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(4235,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k3_tarski ) ) )
& ( ( B
= ( A @ k3_tarski ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(645,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k5_relat_1 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_relat_1) ).
thf(5226,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k5_relat_1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(1862,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k8_group_3 ) )
= ( C @ ( A @ k8_group_3 ) ) )
<=> ~ ( C @ ( A @ k8_group_3 ) @ ( B @ ( A @ k8_group_3 ) @ r1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_group_3) ).
thf(11349,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ~ ( C @ ( A @ k8_group_3 ) @ ( B @ ( A @ k8_group_3 ) @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k8_group_3 ) )
= ( C @ ( A @ k8_group_3 ) ) ) )
& ( ( ( B @ ( A @ k8_group_3 ) )
= ( C @ ( A @ k8_group_3 ) ) )
=> ~ ( C @ ( A @ k8_group_3 ) @ ( B @ ( A @ k8_group_3 ) @ r1_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1862]) ).
thf(1405,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_group_6 ) ) )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_group_6) ).
thf(9019,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_group_6 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_group_6 ) ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ k2_xboole_0 ) ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_xboole_1) ).
thf(4093,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ k2_xboole_0 ) ) ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(1636,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_1_group_3 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( D @ ( C @ ( B @ r4_group_3 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_group_3) ).
thf(10300,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ( D @ ( C @ ( B @ r4_group_3 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_1_group_3 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_1_group_3 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( D @ ( C @ ( B @ r4_group_3 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1636]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(2860,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(664,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( A @ k5_setfam_1 ) )
= ( B @ ( A @ k6_setfam_1 ) @ ( A @ k2_subset_1 @ ( A @ k6_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_setfam_1) ).
thf(5364,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( A @ k5_setfam_1 ) )
= ( B @ ( A @ k6_setfam_1 ) @ ( A @ k2_subset_1 @ ( A @ k6_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r3_binop_1 ) ) )
<=> ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
& ( C @ ( B @ ( A @ r1_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_binop_1) ).
thf(2722,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
& ( C @ ( B @ ( A @ r1_binop_1 ) ) ) )
=> ( C @ ( B @ ( A @ r3_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r3_binop_1 ) ) )
=> ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
& ( C @ ( B @ ( A @ r1_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1103,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ v6_group_1 )
& ( B @ ( A @ r2_group_6 ) ) )
=> ( ( A @ k9_group_1 )
= ( B @ k9_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_group_6) ).
thf(7426,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ v6_group_1 )
& ( B @ ( A @ r2_group_6 ) ) )
=> ( ( A @ k9_group_1 )
= ( B @ k9_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(462,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
<=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_funct_2) ).
thf(4225,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) )
=> ( B @ v2_funct_1 ) )
& ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(477,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_xboole_1) ).
thf(4342,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(2939,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(1325,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k11_group_3 ) )
= ( B @ ( A @ k7_group_2 ) @ ( A @ k10_group_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_group_3) ).
thf(8552,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k11_group_3 ) )
= ( B @ ( A @ k7_group_2 ) @ ( A @ k10_group_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).
thf(1232,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v2_group_4 ) )
=> ( ( ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k5_group_4 ) )
= A )
| ( C @ ( B @ r1_rlvect_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_group_4) ).
thf(8043,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v2_group_4 ) )
=> ( ( ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k5_group_4 ) )
= A )
| ( C @ ( B @ r1_rlvect_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(1939,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( A @ k3_group_3 ) ) )
= ( E @ ( C @ ( A @ k2_group_3 ) ) @ ( D @ ( C @ ( A @ k2_group_3 ) ) @ ( E @ ( B @ ( A @ k2_group_3 ) ) @ ( D @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ u1_struct_0 @ k9_domain_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_group_3) ).
thf(11636,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( A @ k3_group_3 ) ) )
= ( E @ ( C @ ( A @ k2_group_3 ) ) @ ( D @ ( C @ ( A @ k2_group_3 ) ) @ ( E @ ( B @ ( A @ k2_group_3 ) ) @ ( D @ ( B @ ( A @ k2_group_3 ) ) @ ( A @ u1_struct_0 @ k9_domain_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1939]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(3961,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(696,axiom,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( ( A @ k2_vectsp_1 )
= ( A @ u1_vectsp_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_vectsp_1) ).
thf(5472,plain,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( ( A @ k2_vectsp_1 )
= ( A @ u1_vectsp_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(574,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( B @ ( C @ ( A @ k5_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(4838,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( B @ ( C @ ( A @ k5_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(854,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( k5_numbers @ ( k1_numbers @ ( A @ k4_card_1 @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_card_1) ).
thf(6245,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( k5_numbers @ ( k1_numbers @ ( A @ k4_card_1 @ m2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(189,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_finseq_1 @ ( A @ k3_finseq_1 @ r1_xreal_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_finseq_1) ).
thf(2892,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_finseq_1 @ ( A @ k3_finseq_1 @ r1_xreal_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(8150,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[8149]) ).
thf(8151,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[8150]) ).
thf(720,axiom,
k1_numbers @ k1_zfmisc_1 @ ( k5_numbers @ m1_subset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_numbers) ).
thf(5596,plain,
k1_numbers @ k1_zfmisc_1 @ ( k5_numbers @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(2008,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v6_group_1 )
=> ( A @ k1_group_3 @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_group_3) ).
thf(11931,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v6_group_1 )
=> ( A @ k1_group_3 @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2008]) ).
thf(1532,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k12_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( C @ ( A @ k7_group_2 ) @ r1_tarski ) )
& ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k12_group_2 ) ) @ ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( C @ ( A @ k7_group_2 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_group_2) ).
thf(9732,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k12_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( C @ ( A @ k7_group_2 ) @ r1_tarski ) )
& ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k12_group_2 ) ) @ ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( C @ ( A @ k7_group_2 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1532]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
<=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_partfun1) ).
thf(4150,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) )
=> ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(34149,plain,
! [B: $i,A: $i] :
( ( ( B @ k1_tarski @ k1_card_1 )
!= ( k1_xboole_0 @ k1_tarski @ k1_card_1 ) )
| ( ( A @ k1_tarski @ k1_card_1 )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[10603,33008]) ).
thf(34150,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_card_1 )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[34149:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(2043,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( ( B @ ( D @ ( A @ k12_group_2 ) ) )
= ( C @ ( D @ ( A @ k12_group_2 ) ) ) )
<=> ~ ( C @ ( D @ ( A @ k12_group_2 ) ) @ ( B @ ( D @ ( A @ k12_group_2 ) ) @ r1_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_group_2) ).
thf(12039,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( ~ ( C @ ( D @ ( A @ k12_group_2 ) ) @ ( B @ ( D @ ( A @ k12_group_2 ) ) @ r1_xboole_0 ) )
=> ( ( B @ ( D @ ( A @ k12_group_2 ) ) )
= ( C @ ( D @ ( A @ k12_group_2 ) ) ) ) )
& ( ( ( B @ ( D @ ( A @ k12_group_2 ) ) )
= ( C @ ( D @ ( A @ k12_group_2 ) ) ) )
=> ~ ( C @ ( D @ ( A @ k12_group_2 ) ) @ ( B @ ( D @ ( A @ k12_group_2 ) ) @ r1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2043]) ).
thf(1201,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( k1_xboole_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_partfun1) ).
thf(7908,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( k1_xboole_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(5806,plain,
! [A: $i] : ( A @ ( A @ ( A @ k6_partfun1 @ v1_partfun1 ) ) ),
inference(cnfConj,[status(thm)],[5805]) ).
thf(58361,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k6_partfun1 )
!= ( A @ k6_partfun1 ) )
| ( A @ ( A @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16259,5806]) ).
thf(58362,plain,
k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ v1_partfun1 ) ),
inference(pattern_uni,[status(thm)],[58361:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(1250,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k1_group_2 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k3_group_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_group_2) ).
thf(8140,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k3_group_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ k1_group_2 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k1_group_2 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k3_group_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(1013,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_finset_1 )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( B @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_card_1) ).
thf(6992,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_finset_1 )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( B @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(1666,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( A @ k5_group_2 @ ( B @ ( C @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) )
=> ( A @ k5_group_2 @ ( C @ ( A @ r1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_group_3) ).
thf(10451,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( A @ k5_group_2 @ ( B @ ( C @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) )
=> ( A @ k5_group_2 @ ( C @ ( A @ r1_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1666]) ).
thf(1716,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_xboole_1) ).
thf(10680,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1716]) ).
thf(1010,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
= ( C @ ( B @ ( A @ a_3_0_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_0) ).
thf(6975,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
= ( C @ ( B @ ( A @ a_3_0_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(1061,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(7224,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(350,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k7_setfam_1 ) @ ( B @ ( A @ k7_setfam_1 ) @ r1_tarski ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_setfam_1) ).
thf(3684,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k7_setfam_1 ) @ ( B @ ( A @ k7_setfam_1 ) @ r1_tarski ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(6220,plain,
sk259 @ l1_vectsp_1,
inference(cnfConj,[status(thm)],[6214]) ).
thf(1865,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ m1_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_group_4) ).
thf(11369,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ m1_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1865]) ).
thf(1283,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ ( D @ ( B @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( D @ ( B @ ( A @ k8_relset_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_partfun1) ).
thf(8299,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ ( D @ ( B @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( D @ ( B @ ( A @ k8_relset_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).
thf(963,axiom,
! [A: $i] :
( ( A @ l2_lattices )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
& ( A @ u2_lattices @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(6793,plain,
! [A: $i] :
( ( A @ l2_lattices )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
& ( A @ u2_lattices @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(91,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( B @ r2_binop_1 ) ) )
& ( E @ ( C @ ( A @ r2_binop_1 ) ) ) )
<=> ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r2_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_filter_1) ).
thf(2479,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r2_binop_1 ) ) )
=> ( ( F @ ( D @ ( B @ r2_binop_1 ) ) )
& ( E @ ( C @ ( A @ r2_binop_1 ) ) ) ) )
& ( ( ( F @ ( D @ ( B @ r2_binop_1 ) ) )
& ( E @ ( C @ ( A @ r2_binop_1 ) ) ) )
=> ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r2_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1563,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(9876,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1563]) ).
thf(1140,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k4_group_6 ) )
= ( B @ ( A @ k14_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_group_6) ).
thf(7589,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k4_group_6 ) )
= ( B @ ( A @ k14_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(2209,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk2 ) ) @ m1_subset_1 ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[2207]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
<=> ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
thf(4078,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(18083,plain,
! [A: $i] :
( ( ( sk388 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ~ $true
| ( A = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[8310,7167]) ).
thf(18084,plain,
! [A: $i] :
( ( ( sk388 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ( A = k1_xboole_0 ) ),
inference(simp,[status(thm)],[18083]) ).
thf(18085,plain,
sk388 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[18084:[bind(A,$thf( sk388 ))]]) ).
thf(1619,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( B @ k1_tarski @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_subset_1) ).
thf(10214,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( B @ k1_tarski @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1619]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_funct_2) ).
thf(3168,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(1296,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( B @ ( G @ r2_hidden ) )
& ( G @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_mcart_1) ).
thf(8360,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( B @ ( G @ r2_hidden ) )
& ( G @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).
thf(1065,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_latsubgr) ).
thf(7239,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( B @ ( A @ k1_latsubgr @ k1_funct_1 ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(938,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_funct_2) ).
thf(6706,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ k4_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( B @ ( C @ k2_xboole_0 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_xboole_1) ).
thf(2924,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ k4_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( B @ ( C @ k2_xboole_0 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(978,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_group_1 ) )
= ( D @ ( C @ g1_group_1 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_group_1) ).
thf(6850,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_group_1 ) )
= ( D @ ( C @ g1_group_1 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(1995,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ a_1_1_group_4 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ~ ( B @ ( C @ v1_group_4 ) )
& ( A = C )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_1_group_4) ).
thf(11862,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ~ ( B @ ( C @ v1_group_4 ) )
& ( A = C )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_1_group_4 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_1_group_4 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ~ ( B @ ( C @ v1_group_4 ) )
& ( A = C )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1995]) ).
thf(700,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
~ ( ( ( E @ ( D @ k1_funct_1 ) )
= C )
& ( A @ ( E @ r2_hidden ) ) )
& ( ( D @ k2_relat_1 )
= B )
& ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_2) ).
thf(5490,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
~ ( ( ( E @ ( D @ k1_funct_1 ) )
= C )
& ( A @ ( E @ r2_hidden ) ) )
& ( ( D @ k2_relat_1 )
= B )
& ( B @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(792,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
<=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
thf(5981,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( B = C ) )
=> ( A @ v2_funct_1 ) )
& ( ( A @ v2_funct_1 )
=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(1448,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ! [E: $i] :
( ( D @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C = E )
=> ( ( C @ ( A @ ( B @ k6_group_1 ) ) )
= ( E @ ( A @ ( D @ k6_group_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_group_4) ).
thf(9279,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ! [E: $i] :
( ( D @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C = E )
=> ( ( C @ ( A @ ( B @ k6_group_1 ) ) )
= ( E @ ( A @ ( D @ k6_group_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448]) ).
thf(307,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_subset_1) ).
thf(3452,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ~ ( B @ ( D @ r2_hidden ) ) )
& ( ~ ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(1585,axiom,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_card_1 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_card_1) ).
thf(10018,plain,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_card_1 @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1585]) ).
thf(497,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_2_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_domain_1) ).
thf(4424,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_2_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(1354,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ ( D @ ( C @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k7_funct_2 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ ( D @ ( C @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k7_funct_2 ) ) ) ) @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ ( D @ ( C @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k7_funct_2 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k7_funct_2 ) ) ) ) @ v1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_group_6) ).
thf(8698,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ ( D @ ( C @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k7_funct_2 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ ( D @ ( C @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k7_funct_2 ) ) ) ) @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ ( D @ ( C @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k7_funct_2 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k7_funct_2 ) ) ) ) @ v1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354]) ).
thf(57,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_xboole_1) ).
thf(2352,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1012,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ? [D: $i] :
( ( ( D @ u1_struct_0 )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) )
& ( A @ ( D @ m1_group_2 ) )
& ( A @ ( D @ v1_group_3 ) )
& ( D @ v1_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_group_3) ).
thf(6985,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ? [D: $i] :
( ( ( D @ u1_struct_0 )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) )
& ( A @ ( D @ m1_group_2 ) )
& ( A @ ( D @ v1_group_3 ) )
& ( D @ v1_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(595,axiom,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( ( ( A @ v8_vectsp_1 )
& ( A @ v7_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v6_vectsp_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_vectsp_1) ).
thf(4945,plain,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( ( ( A @ v8_vectsp_1 )
& ( A @ v7_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v6_vectsp_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(225,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k1_nat_1 ) @ ( C @ k6_group_1 ) ) )
= ( D @ ( B @ ( C @ k6_group_1 ) ) @ ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_group_1) ).
thf(3067,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k1_nat_1 ) @ ( C @ k6_group_1 ) ) )
= ( D @ ( B @ ( C @ k6_group_1 ) ) @ ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(1739,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ g1_group_1 ) @ l1_group_1 )
& ( B @ ( A @ g1_group_1 ) @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_group_1) ).
thf(10806,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ g1_group_1 ) @ l1_group_1 )
& ( B @ ( A @ g1_group_1 ) @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1739]) ).
thf(1082,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m2_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_lattice4) ).
thf(7316,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m2_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(1169,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ k5_group_4 ) @ ( B @ ( A @ k5_group_4 ) @ ( A @ k9_group_2 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k5_group_4 ) @ m1_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_group_4) ).
thf(7764,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ k5_group_4 ) @ ( B @ ( A @ k5_group_4 ) @ ( A @ k9_group_2 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k5_group_4 ) @ m1_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(140,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k3_finseq_1 )
= ( A @ k1_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_finseq_1) ).
thf(2696,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k3_finseq_1 )
= ( A @ k1_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
=> ( ( A @ ( k5_numbers @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_finseq_1) ).
thf(2828,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
=> ( ( A @ ( k5_numbers @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(1971,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( np__0 @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_group_1) ).
thf(11789,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( np__0 @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1971]) ).
thf(1476,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( D @ ( B @ ( A @ k8_relset_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_partfun1) ).
thf(9389,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( D @ ( B @ ( A @ k8_relset_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1476]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ ( C @ ( B @ ( A @ k2_group_6 ) ) @ m1_group_6 ) ) )
& ( B @ ( C @ ( B @ ( A @ k2_group_6 ) ) @ v1_group_3 ) )
& ( C @ ( B @ ( A @ k2_group_6 ) ) @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_group_6) ).
thf(6970,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ ( C @ ( B @ ( A @ k2_group_6 ) ) @ m1_group_6 ) ) )
& ( B @ ( C @ ( B @ ( A @ k2_group_6 ) ) @ v1_group_3 ) )
& ( C @ ( B @ ( A @ k2_group_6 ) ) @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(812,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_funct_1) ).
thf(6068,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(2039,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ k11_group_4 @ u1_struct_0 @ ( A @ k11_group_4 @ u1_struct_0 @ ( C @ ( B @ ( A @ k3_latsubgr ) ) @ m2_relset_1 ) ) )
& ( B @ k11_group_4 @ u1_struct_0 @ ( A @ k11_group_4 @ u1_struct_0 @ ( C @ ( B @ ( A @ k3_latsubgr ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k3_latsubgr ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_latsubgr) ).
thf(12027,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ k11_group_4 @ u1_struct_0 @ ( A @ k11_group_4 @ u1_struct_0 @ ( C @ ( B @ ( A @ k3_latsubgr ) ) @ m2_relset_1 ) ) )
& ( B @ k11_group_4 @ u1_struct_0 @ ( A @ k11_group_4 @ u1_struct_0 @ ( C @ ( B @ ( A @ k3_latsubgr ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k3_latsubgr ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2039]) ).
thf(1318,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relset_1) ).
thf(8533,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).
thf(329,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k3_lattice4 ) @ m3_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice4) ).
thf(3548,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k3_lattice4 ) @ m3_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(1735,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_group_1 @ ( A @ k2_group_1 @ ( A @ u1_struct_0 @ r3_binop_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_group_1) ).
thf(10796,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_group_1 @ ( A @ k2_group_1 @ ( A @ u1_struct_0 @ r3_binop_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1735]) ).
thf(2347,plain,
! [A: $i] : ( A @ ( k5_numbers @ ( A @ sk11 @ m1_relset_1 ) ) ),
inference(cnfConj,[status(thm)],[2342]) ).
thf(1391,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k6_domain_1 ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
thf(8957,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k6_domain_1 ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391]) ).
thf(16419,plain,
! [A: $i] :
( ( ( sk610 @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11588,4961]) ).
thf(16420,plain,
! [A: $i] :
( ( ( sk610 @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[16419]) ).
thf(16421,plain,
sk610 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[16420:[bind(A,$thf( sk610 ))]]) ).
thf(683,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t171_partfun1) ).
thf(5421,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(4737,plain,
k5_numbers != k4_numbers,
inference(polarity_switch,[status(thm)],[4736]) ).
thf(4738,plain,
k4_numbers != k5_numbers,
inference(lifteq,[status(thm)],[4737]) ).
thf(2325,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( B @ ( A @ ( C @ m1_realset1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[2324]) ).
thf(404,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( ( C @ ( A @ k1_funct_1 ) )
= D )
<=> ( ( D @ ( B @ k1_funct_1 ) )
= C ) ) )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k2_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_1) ).
thf(3928,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( ( ( D @ ( B @ k1_funct_1 ) )
= C )
=> ( ( C @ ( A @ k1_funct_1 ) )
= D ) )
& ( ( ( C @ ( A @ k1_funct_1 ) )
= D )
=> ( ( D @ ( B @ k1_funct_1 ) )
= C ) ) ) )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k2_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(1073,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ m1_relset_1 ) ) )
=> ( ( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( k1_xboole_0 @ ( A @ v2_binop_1 ) )
& ( k1_xboole_0 @ ( A @ v1_binop_1 ) )
& ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_xboole_0 )
& ( A @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_binop_1) ).
thf(7271,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ m1_relset_1 ) ) )
=> ( ( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( k1_xboole_0 @ ( A @ v2_binop_1 ) )
& ( k1_xboole_0 @ ( A @ v1_binop_1 ) )
& ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_xboole_0 )
& ( A @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(929,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_relat_1) ).
thf(6674,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(2490,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(1279,axiom,
! [A: $i,B: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k15_lattice3 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_lattice3) ).
thf(8285,plain,
! [A: $i,B: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k15_lattice3 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(983,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
thf(6867,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(1615,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v6_ordinal1 )
& ( A != k1_xboole_0 )
& ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_finset_1) ).
thf(10188,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v6_ordinal1 )
& ( A != k1_xboole_0 )
& ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1615]) ).
thf(440,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) @ ( A @ r1_partfun1 ) )
=> ( C @ ( A @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_funct_4) ).
thf(4102,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) @ ( A @ r1_partfun1 ) )
=> ( C @ ( A @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_finseq_1 ) )
=> ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_finseq_1) ).
thf(2919,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_finseq_1 ) )
=> ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(1427,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( A @ k9_group_3 ) @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_group_3) ).
thf(9141,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( A @ k9_group_3 ) @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1427]) ).
thf(1560,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( C @ v2_group_6 ) ) )
<=> ( B @ k5_group_2 @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ r1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_group_6) ).
thf(9866,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ k5_group_2 @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ r1_group_2 ) ) )
=> ( A @ ( B @ ( C @ v2_group_6 ) ) ) )
& ( ( A @ ( B @ ( C @ v2_group_6 ) ) )
=> ( B @ k5_group_2 @ ( C @ ( A @ ( B @ k12_group_6 ) ) @ ( B @ r1_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1560]) ).
thf(2223,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
| ~ ( A @ ( F @ m1_subset_1 ) )
| ~ ( A @ ( E @ m1_subset_1 ) )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[2217]) ).
thf(2226,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ m1_subset_1 ) )
| ~ ( A @ ( E @ m1_subset_1 ) )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ),
inference(lifteq,[status(thm)],[2223]) ).
thf(1368,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(8761,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368]) ).
thf(21994,plain,
! [A: $i] :
( ( A != k4_numbers )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,12425]) ).
thf(21995,plain,
! [A: $i] :
( ( A != k4_numbers )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[21994]) ).
thf(21996,plain,
k4_numbers @ sk149 @ v1_funct_1,
inference(pattern_uni,[status(thm)],[21995:[bind(A,$thf( k4_numbers ))]]) ).
thf(2012,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( C @ ( D @ ( A @ k13_group_2 ) ) @ ( B @ ( D @ ( A @ k13_group_2 ) ) @ r2_wellord2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t153_group_2) ).
thf(11942,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( C @ ( D @ ( A @ k13_group_2 ) ) @ ( B @ ( D @ ( A @ k13_group_2 ) ) @ r2_wellord2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2012]) ).
thf(1869,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ v6_group_1 )
=> ( A @ k9_group_1 @ ( B @ k9_group_1 @ r1_nat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_group_2) ).
thf(11383,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ v6_group_1 )
=> ( A @ k9_group_1 @ ( B @ k9_group_1 @ r1_nat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1869]) ).
thf(942,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(6726,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(15537,plain,
! [B: $i,A: $i] :
( ( ( A @ sk81 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3647,9703]) ).
thf(15538,plain,
! [B: $i,A: $i] :
( ( A @ sk81 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[15537]) ).
thf(15539,plain,
! [B: $i,A: $i] :
( ( ( A @ sk81 )
!= k1_xboole_0 )
| ( A != B ) ),
inference(simp,[status(thm)],[15538]) ).
thf(15540,plain,
! [A: $i] :
( ( A @ sk81 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[15539]) ).
thf(22934,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk81 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,15540]) ).
thf(22935,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk81 ) )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[22934]) ).
thf(22936,plain,
! [A: $i] : ( A @ sk81 @ sk149 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[22935:[bind(A,$thf( C @ sk81 )),bind(B,$thf( C ))]]) ).
thf(23205,plain,
! [A: $i] : ( A @ sk81 @ sk149 @ v1_funct_1 ),
inference(simp,[status(thm)],[22936]) ).
thf(1674,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( D @ ( A @ k12_group_2 ) ) @ ( A @ k2_group_2 ) ) )
= ( C @ ( D @ ( A @ k11_group_2 ) ) @ ( B @ ( A @ k3_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_group_3) ).
thf(10479,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( D @ ( A @ k12_group_2 ) ) @ ( A @ k2_group_2 ) ) )
= ( C @ ( D @ ( A @ k11_group_2 ) ) @ ( B @ ( A @ k3_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1674]) ).
thf(115,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_relat_1) ).
thf(2591,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( D @ ( B @ ( A @ k5_partfun1 ) ) ) )
& ! [E: $i] :
( B
!= ( E @ k1_tarski ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_funct_2) ).
thf(3709,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( D @ ( B @ ( A @ k5_partfun1 ) ) ) )
& ! [E: $i] :
( B
!= ( E @ k1_tarski ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(11585,plain,
sk610 @ v4_group_1,
inference(cnfConj,[status(thm)],[11584]) ).
thf(563,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_orders_1) ).
thf(4791,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(1803,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( k1_xboole_0 @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t176_partfun1) ).
thf(11145,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1803]) ).
thf(60695,plain,
! [B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k2_xboole_0 ) )
!= ( k1_xboole_0 @ k1_tarski @ ( B @ k2_xboole_0 ) ) )
| ( k1_xboole_0 @ ( k1_xboole_0 @ k1_orders_1 @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[60659,39519]) ).
thf(60696,plain,
k1_xboole_0 @ ( k1_xboole_0 @ k1_orders_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[60695:[bind(A,$thf( k1_xboole_0 @ k1_tarski )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(1022,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_filter_0) ).
thf(7034,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(730,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( B @ r3_binop_1 ) ) )
& ( E @ ( C @ ( A @ r3_binop_1 ) ) ) )
<=> ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r3_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_filter_1) ).
thf(5632,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r3_binop_1 ) ) )
=> ( ( F @ ( D @ ( B @ r3_binop_1 ) ) )
& ( E @ ( C @ ( A @ r3_binop_1 ) ) ) ) )
& ( ( ( F @ ( D @ ( B @ r3_binop_1 ) ) )
& ( E @ ( C @ ( A @ r3_binop_1 ) ) ) )
=> ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r3_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(16257,plain,
! [A: $i] : ( A @ k6_partfun1 @ v2_funct_1 ),
inference(rewrite,[status(thm)],[3714,11231]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k2_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(3613,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k2_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k2_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(1858,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k16_group_2 ) @ v1_card_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_group_2) ).
thf(11337,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k16_group_2 ) @ v1_card_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1858]) ).
thf(1772,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_realset2 )
<=> ? [B: $i] :
( ( A @ u1_struct_0 )
= ( B @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_group_6) ).
thf(10996,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ? [B: $i] :
( ( A @ u1_struct_0 )
= ( B @ k1_tarski ) )
=> ( A @ v3_realset2 ) )
& ( ( A @ v3_realset2 )
=> ? [B: $i] :
( ( A @ u1_struct_0 )
= ( B @ k1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1772]) ).
thf(1959,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k4_group_1 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k4_group_1 @ v1_funct_2 ) ) )
& ( A @ k4_group_1 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_group_1) ).
thf(11732,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k4_group_1 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k4_group_1 @ v1_funct_2 ) ) )
& ( A @ k4_group_1 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1959]) ).
thf(1722,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ ( B @ k10_group_3 ) @ r1_rlvect_1 ) )
<=> ? [D: $i] :
( ( ( D @ ( C @ ( B @ k4_group_3 ) ) )
= C )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_group_3) ).
thf(10697,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( ( D @ ( C @ ( B @ k4_group_3 ) ) )
= C )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( A @ ( C @ ( B @ k10_group_3 ) @ r1_rlvect_1 ) ) )
& ( ( A @ ( C @ ( B @ k10_group_3 ) @ r1_rlvect_1 ) )
=> ? [D: $i] :
( ( ( D @ ( C @ ( B @ k4_group_3 ) ) )
= C )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1722]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_funct_2) ).
thf(3864,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(972,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( B @ ( A @ ( C @ v3_lattice4 ) ) )
<=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
& ( B @ ( A @ ( C @ v1_lattice4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice4) ).
thf(6829,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
& ( B @ ( A @ ( C @ v1_lattice4 ) ) ) )
=> ( B @ ( A @ ( C @ v3_lattice4 ) ) ) )
& ( ( B @ ( A @ ( C @ v3_lattice4 ) ) )
=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
& ( B @ ( A @ ( C @ v1_lattice4 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(815,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ l3_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v17_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v10_lattices )
& ~ ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_filter_0) ).
thf(6077,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ l3_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v17_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v10_lattices )
& ~ ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(1940,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ k5_group_2 @ ( B @ ( A @ k5_group_2 @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_group_3) ).
thf(11639,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ k5_group_2 @ ( B @ ( A @ k5_group_2 @ ( A @ k6_group_3 ) ) @ ( A @ r1_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1940]) ).
thf(2272,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[2271]) ).
thf(2273,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[2272]) ).
thf(2282,plain,
~ ? [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_xboole_0 ) ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[2281]) ).
thf(2283,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
| ~ ( C @ ( A @ r1_xboole_0 ) )
| ( B @ ( A @ r1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[2282]) ).
thf(1905,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k7_group_3 ) )
= ( A @ k2_group_1 @ ( A @ u1_struct_0 @ k6_domain_1 ) ) )
<=> ( B
= ( A @ k2_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_group_3) ).
thf(11514,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B
= ( A @ k2_group_1 ) )
=> ( ( B @ ( A @ k7_group_3 ) )
= ( A @ k2_group_1 @ ( A @ u1_struct_0 @ k6_domain_1 ) ) ) )
& ( ( ( B @ ( A @ k7_group_3 ) )
= ( A @ k2_group_1 @ ( A @ u1_struct_0 @ k6_domain_1 ) ) )
=> ( B
= ( A @ k2_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1905]) ).
thf(1429,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) )
<=> ( B @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_filter_0) ).
thf(9147,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ r3_lattices ) ) )
=> ( C @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) )
=> ( B @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_subset_1) ).
thf(3484,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(1852,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k8_group_2 ) ) @ m1_group_2 ) )
& ( C @ ( B @ ( A @ k8_group_2 ) ) @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_group_2) ).
thf(11319,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k8_group_2 ) ) @ m1_group_2 ) )
& ( C @ ( B @ ( A @ k8_group_2 ) ) @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1852]) ).
thf(1576,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k10_group_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_group_1) ).
thf(9951,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k10_group_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1576]) ).
thf(381,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k2_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
thf(3825,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k2_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(934,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( B @ ( A @ a_2_4_lattice3 ) @ ( A @ k16_lattice3 ) ) )
& ( B
= ( B @ ( A @ a_2_3_lattice3 ) @ ( A @ k15_lattice3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattice3) ).
thf(6689,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( B @ ( A @ a_2_4_lattice3 ) @ ( A @ k16_lattice3 ) ) )
& ( B
= ( B @ ( A @ a_2_3_lattice3 ) @ ( A @ k15_lattice3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(1986,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_group_2 @ ( A @ k15_group_2 ) )
= ( A @ a_1_0_group_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_group_2) ).
thf(11832,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_group_2 @ ( A @ k15_group_2 ) )
= ( A @ a_1_0_group_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1986]) ).
thf(2135,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ v17_lattices )
| ~ ( A @ ( B @ ( C @ v2_lattice4 ) ) )
| ~ ( A @ ( B @ ( C @ m1_lattice4 ) ) )
| ~ ( B @ l3_lattices )
| ~ ( B @ v17_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2134]) ).
thf(606,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k6_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_filter_0) ).
thf(5008,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k6_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(1421,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( B @ ( A @ k11_group_6 ) @ ( B @ ( A @ k6_group_6 ) @ ( A @ k12_group_6 ) ) @ ( A @ r1_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_group_6) ).
thf(9102,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( B @ ( A @ k11_group_6 ) @ ( B @ ( A @ k6_group_6 ) @ ( A @ k12_group_6 ) ) @ ( A @ r1_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421]) ).
thf(1851,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k8_group_3 ) @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_group_3) ).
thf(11317,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k8_group_3 ) @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1851]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( F @ ( C @ k2_xboole_0 ) @ ( E @ ( B @ k2_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_partfun1) ).
thf(4089,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( F @ ( C @ k2_xboole_0 ) @ ( E @ ( B @ k2_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(671,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_domain_1) ).
thf(5382,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(990,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( C @ l3_lattices )
& ( C @ v6_lattice3 )
& ( C @ v4_lattice3 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_9_lattice3 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( C @ k3_lattices ) ) ) )
& ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_9_lattice3) ).
thf(6893,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( C @ l3_lattices )
& ( C @ v6_lattice3 )
& ( C @ v4_lattice3 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( C @ k3_lattices ) ) ) )
& ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_9_lattice3 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_9_lattice3 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( C @ k3_lattices ) ) ) )
& ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(1369,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( D @ ( C @ ( A @ k8_group_4 ) ) @ r1_rlvect_1 ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ( B
= ( E @ ( F @ ( A @ k4_group_4 ) ) @ ( A @ k3_group_4 ) ) )
& ( D @ ( A @ k7_group_2 ) @ ( C @ ( A @ k7_group_2 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k3_finseq_1 )
= ( F @ k3_finseq_1 ) )
& ( k4_numbers @ ( F @ m2_finseq_1 ) ) )
& ( A @ u1_struct_0 @ ( E @ m2_finseq_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_group_4) ).
thf(8766,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( ? [E: $i] :
( ? [F: $i] :
( ( B
= ( E @ ( F @ ( A @ k4_group_4 ) ) @ ( A @ k3_group_4 ) ) )
& ( D @ ( A @ k7_group_2 ) @ ( C @ ( A @ k7_group_2 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k3_finseq_1 )
= ( F @ k3_finseq_1 ) )
& ( k4_numbers @ ( F @ m2_finseq_1 ) ) )
& ( A @ u1_struct_0 @ ( E @ m2_finseq_1 ) ) )
=> ( B @ ( D @ ( C @ ( A @ k8_group_4 ) ) @ r1_rlvect_1 ) ) )
& ( ( B @ ( D @ ( C @ ( A @ k8_group_4 ) ) @ r1_rlvect_1 ) )
=> ? [E: $i] :
( ? [F: $i] :
( ( B
= ( E @ ( F @ ( A @ k4_group_4 ) ) @ ( A @ k3_group_4 ) ) )
& ( D @ ( A @ k7_group_2 ) @ ( C @ ( A @ k7_group_2 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k3_finseq_1 )
= ( F @ k3_finseq_1 ) )
& ( k4_numbers @ ( F @ m2_finseq_1 ) ) )
& ( A @ u1_struct_0 @ ( E @ m2_finseq_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369]) ).
thf(1003,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( B @ ( A @ k13_group_6 ) ) @ r1_rlvect_1 ) )
& ( B @ ( A @ ( D @ v2_group_6 ) ) ) )
=> ( ( C @ ( D @ k2_funct_1 @ k1_funct_1 ) @ ( D @ k1_funct_1 ) )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_group_6) ).
thf(6953,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( B @ ( A @ k13_group_6 ) ) @ r1_rlvect_1 ) )
& ( B @ ( A @ ( D @ v2_group_6 ) ) ) )
=> ( ( C @ ( D @ k2_funct_1 @ k1_funct_1 ) @ ( D @ k1_funct_1 ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(5132,plain,
sk196 @ v1_relat_1,
inference(cnfConj,[status(thm)],[5130]) ).
thf(1222,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_3_lattice3 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_3_lattice3) ).
thf(7996,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_3_lattice3 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_3_lattice3 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(1018,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k2_filter_0 ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_filter_0) ).
thf(7012,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k2_filter_0 ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(962,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( C @ k1_group_1 ) ) )
= ( D @ ( E @ ( C @ k1_group_1 ) ) ) )
=> ( ( E @ ( B @ ( C @ k6_group_1 ) ) @ ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) )
= ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( E @ ( B @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_group_1) ).
thf(6790,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( C @ k1_group_1 ) ) )
= ( D @ ( E @ ( C @ k1_group_1 ) ) ) )
=> ( ( E @ ( B @ ( C @ k6_group_1 ) ) @ ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) )
= ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( E @ ( B @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(1492,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_mcart_1) ).
thf(9459,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1492]) ).
thf(43302,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( B @ v4_group_1 )
| ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,24232]) ).
thf(43303,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B @ v4_group_1 )
| ~ ( B @ v1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[43302]) ).
thf(43304,plain,
! [A: $i] :
( ( A @ v4_group_1 )
| ~ ( A @ v1_xboole_0 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[43303:[bind(A,$thf( sk1 ))]]) ).
thf(43306,plain,
! [A: $i] :
( ( A @ v4_group_1 )
| ~ ( A @ v1_xboole_0 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[43304]) ).
thf(33020,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski @ k1_card_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,33008]) ).
thf(33021,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski @ k1_card_1 ) )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[33020]) ).
thf(33022,plain,
k1_xboole_0 @ k1_tarski @ k1_card_1 @ sk149 @ v1_funct_1,
inference(pattern_uni,[status(thm)],[33021:[bind(A,$thf( k1_xboole_0 @ k1_tarski @ k1_card_1 ))]]) ).
thf(34169,plain,
! [B: $i,A: $i] :
( ( ( B @ k1_tarski @ k1_card_1 )
!= ( k1_xboole_0 @ k1_tarski @ k1_card_1 ) )
| ( A @ k1_tarski @ k1_card_1 @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[10603,33022]) ).
thf(34170,plain,
! [A: $i] : ( A @ k1_tarski @ k1_card_1 @ sk149 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[34169:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(1990,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_group_4 @ u1_struct_0 )
= ( A @ a_1_1_group_4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_group_4) ).
thf(11847,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_group_4 @ u1_struct_0 )
= ( A @ a_1_1_group_4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1990]) ).
thf(675,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_setfam_1 ) )
= ( A @ ( B @ k3_setfam_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_setfam_1) ).
thf(5394,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_setfam_1 ) )
= ( A @ ( B @ k3_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(1920,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( B @ ( A @ r5_group_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_group_3) ).
thf(11567,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( B @ ( A @ r5_group_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1920]) ).
thf(1094,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_partfun1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ~ ( C @ v1_xboole_0 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_group_6) ).
thf(7384,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_partfun1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ~ ( C @ v1_xboole_0 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(1150,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_5_lattice3 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( E @ ( D @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_5_lattice3) ).
thf(7638,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ l3_lattices )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( E @ ( D @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_5_lattice3 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_5_lattice3 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( E @ ( D @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(418,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( np__1 @ ( A @ k1_nat_1 ) @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( C @ ( B @ k1_group_1 ) ) ) )
& ( ( C @ ( np__1 @ ( A @ k1_nat_1 ) @ ( B @ k6_group_1 ) ) )
= ( C @ ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k1_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_group_1) ).
thf(4010,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( np__1 @ ( A @ k1_nat_1 ) @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( C @ ( B @ k1_group_1 ) ) ) )
& ( ( C @ ( np__1 @ ( A @ k1_nat_1 ) @ ( B @ k6_group_1 ) ) )
= ( C @ ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k1_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( A @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_partfun1) ).
thf(5243,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( A @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(1038,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( D @ ( A @ k5_group_4 ) @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_latsubgr) ).
thf(7120,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( D @ ( A @ k5_group_4 ) @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(2130,plain,
! [A: $i] :
( ( A @ v16_lattices )
| ~ ( A @ v17_lattices )
| ( A @ v3_struct_0 )
| ~ ( A @ l3_lattices ) ),
inference(cnfConj,[status(thm)],[2126]) ).
thf(920,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( D @ ( C @ k5_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) @ ( D @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_2) ).
thf(6618,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( D @ ( C @ k5_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) @ ( D @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_funct_2) ).
thf(3859,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(1631,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( A @ k2_group_2 ) ) )
= ( E @ ( C @ ( A @ k1_group_1 ) ) @ ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( E @ ( B @ ( A @ k1_group_1 ) ) @ ( D @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ u1_struct_0 @ k9_domain_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_group_2) ).
thf(10254,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k7_domain_1 ) ) @ ( A @ k2_group_2 ) ) )
= ( E @ ( C @ ( A @ k1_group_1 ) ) @ ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( E @ ( B @ ( A @ k1_group_1 ) ) @ ( D @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ u1_struct_0 @ k9_domain_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1631]) ).
thf(1491,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ( ( B @ ( C @ ( A @ k6_group_6 ) @ r1_rlvect_1 ) )
<=> ? [D: $i] :
( ( B
= ( D @ ( C @ ( A @ k13_group_2 ) ) ) )
& ( B
= ( D @ ( C @ ( A @ k12_group_2 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_group_6) ).
thf(9449,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) ) )
=> ( ( ? [D: $i] :
( ( B
= ( D @ ( C @ ( A @ k13_group_2 ) ) ) )
& ( B
= ( D @ ( C @ ( A @ k12_group_2 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( B @ ( C @ ( A @ k6_group_6 ) @ r1_rlvect_1 ) ) )
& ( ( B @ ( C @ ( A @ k6_group_6 ) @ r1_rlvect_1 ) )
=> ? [D: $i] :
( ( B
= ( D @ ( C @ ( A @ k13_group_2 ) ) ) )
& ( B
= ( D @ ( C @ ( A @ k12_group_2 ) ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1491]) ).
thf(573,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ( C = k1_xboole_0 )
& ( B
= ( A @ k1_tarski ) ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B = k1_xboole_0 ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B
= ( A @ k1_tarski ) ) )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).
thf(4823,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ( C = k1_xboole_0 )
& ( B
= ( A @ k1_tarski ) ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B = k1_xboole_0 ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B
= ( A @ k1_tarski ) ) )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(1358,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( A = np__0 )
=> ( ( C @ ( A @ ( B @ k6_group_1 ) ) )
= ( B @ k2_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_group_1) ).
thf(8716,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( A = np__0 )
=> ( ( C @ ( A @ ( B @ k6_group_1 ) ) )
= ( B @ k2_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).
thf(1336,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_domain_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_domain_1) ).
thf(8617,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_domain_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).
thf(373,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(3780,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(1533,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_subset_1) ).
thf(9736,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1533]) ).
thf(2152,plain,
! [B: $i,A: $i] :
( ( A @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
| ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2144]) ).
thf(2260,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_relat_1 @ r1_tarski ) )
| ( ( B @ ( A @ k1_finseq_3 ) )
!= k1_xboole_0 )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[2259]) ).
thf(2262,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_relat_1 @ r1_tarski ) )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( ( B @ ( A @ k1_finseq_3 ) )
!= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[2260]) ).
thf(914,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_finseq_3 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_finseq_3) ).
thf(6584,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_finseq_3 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(8119,plain,
! [A: $i] : ( A @ ( A @ sk378 @ m1_finseq_1 ) ),
inference(cnf,[status(esa)],[8118]) ).
thf(1431,axiom,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( B
= ( A @ k2_card_1 ) )
<=> ( ! [C: $i] :
( ( C @ v1_card_1 )
=> ( ( C @ ( A @ k1_card_1 @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) ) )
& ( B @ ( A @ k1_card_1 @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_card_1) ).
thf(9160,plain,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( ( ! [C: $i] :
( ( C @ v1_card_1 )
=> ( ( C @ ( A @ k1_card_1 @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) ) )
& ( B @ ( A @ k1_card_1 @ r2_hidden ) ) )
=> ( B
= ( A @ k2_card_1 ) ) )
& ( ( B
= ( A @ k2_card_1 ) )
=> ( ! [C: $i] :
( ( C @ v1_card_1 )
=> ( ( C @ ( A @ k1_card_1 @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) ) )
& ( B @ ( A @ k1_card_1 @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1431]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_partfun1) ).
thf(2394,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(11497,plain,
sk608 @ v2_group_1,
inference(cnfConj,[status(thm)],[11492]) ).
thf(1868,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_group_1 @ v1_setwiseo ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_group_1) ).
thf(11381,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_group_1 @ v1_setwiseo ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1868]) ).
thf(1444,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( D @ ( C @ ( A @ k9_group_2 ) ) @ ( A @ k13_group_2 ) ) )
= ( B @ ( D @ ( A @ k13_group_2 ) ) @ ( B @ ( C @ ( A @ k13_group_2 ) ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_group_2) ).
thf(9262,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( D @ ( C @ ( A @ k9_group_2 ) ) @ ( A @ k13_group_2 ) ) )
= ( B @ ( D @ ( A @ k13_group_2 ) ) @ ( B @ ( C @ ( A @ k13_group_2 ) ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444]) ).
thf(79,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k3_finseq_1 @ ( A @ k3_finseq_1 @ r1_xreal_0 ) )
<=> ( B @ k4_finseq_1 @ ( A @ k4_finseq_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_finseq_3) ).
thf(2447,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k4_finseq_1 @ ( A @ k4_finseq_1 @ r1_tarski ) )
=> ( B @ k3_finseq_1 @ ( A @ k3_finseq_1 @ r1_xreal_0 ) ) )
& ( ( B @ k3_finseq_1 @ ( A @ k3_finseq_1 @ r1_xreal_0 ) )
=> ( B @ k4_finseq_1 @ ( A @ k4_finseq_1 @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(1843,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k2_group_3 ) ) ) )
& ( ( B @ ( A @ k3_group_1 ) @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k2_group_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_group_6) ).
thf(11287,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k2_group_3 ) ) ) )
& ( ( B @ ( A @ k3_group_1 ) @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k2_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1843]) ).
thf(1691,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( ( C @ ( E @ ( A @ k4_lattices ) ) @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( E @ ( C @ ( A @ k4_lattices ) ) @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_filter_0) ).
thf(10563,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( ( C @ ( E @ ( A @ k4_lattices ) ) @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( E @ ( C @ ( A @ k4_lattices ) ) @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1691]) ).
thf(1106,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k9_group_6 ) ) )
= ( C @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_group_6) ).
thf(7437,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k9_group_6 ) ) )
= ( C @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_partfun1) ).
thf(2956,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(60731,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k2_xboole_0 ) )
!= ( k1_numbers @ ( C @ k2_xboole_0 ) @ ( B @ k2_xboole_0 ) ) )
| ( k1_xboole_0 @ ( k4_numbers @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[60659,41371]) ).
thf(60732,plain,
k1_xboole_0 @ ( k4_numbers @ r1_tarski ),
inference(pattern_uni,[status(thm)],[60731:[bind(A,$thf( k1_numbers @ ( D @ k2_xboole_0 ) )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D ))]]) ).
thf(1824,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k6_group_2 @ m1_group_2 ) )
& ( A @ k6_group_2 @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_group_2) ).
thf(11210,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k6_group_2 @ m1_group_2 ) )
& ( A @ k6_group_2 @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1824]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) @ ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_relat_1) ).
thf(2475,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) @ ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(1991,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ k2_group_1 @ ( A @ ( B @ k6_group_1 ) ) )
= ( B @ k2_group_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_group_1) ).
thf(11850,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ k2_group_1 @ ( A @ ( B @ k6_group_1 ) ) )
= ( B @ k2_group_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1991]) ).
thf(531,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ ( A @ k5_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relat_1) ).
thf(4602,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ ( A @ k5_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(1071,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(7266,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(21884,plain,
! [A: $i] :
( ( A != sk261 )
| ( k1_xboole_0 @ l1_struct_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,16067]) ).
thf(21885,plain,
( ( k1_xboole_0 @ l1_struct_0 )
| ( sk261 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21884:[bind(A,$thf( sk261 ))]]) ).
thf(881,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) )
& ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_1) ).
thf(6397,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) )
& ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(21962,plain,
! [A: $i] :
( ( A != sk15 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,12430]) ).
thf(21963,plain,
! [A: $i] :
( ( A != sk15 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[21962]) ).
thf(21964,plain,
sk15 @ sk149 @ v1_funct_1,
inference(pattern_uni,[status(thm)],[21963:[bind(A,$thf( sk15 ))]]) ).
thf(896,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v6_group_1 )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( B
= ( A @ k9_group_1 ) )
<=> ? [C: $i] :
( ( B
= ( C @ k4_card_1 ) )
& ( C
= ( A @ u1_struct_0 ) )
& ( C @ v1_finset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_group_1) ).
thf(6484,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v6_group_1 )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( ? [C: $i] :
( ( B
= ( C @ k4_card_1 ) )
& ( C
= ( A @ u1_struct_0 ) )
& ( C @ v1_finset_1 ) )
=> ( B
= ( A @ k9_group_1 ) ) )
& ( ( B
= ( A @ k9_group_1 ) )
=> ? [C: $i] :
( ( B
= ( C @ k4_card_1 ) )
& ( C
= ( A @ u1_struct_0 ) )
& ( C @ v1_finset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(841,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_subset_1) ).
thf(6181,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(1520,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( np__2 @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) )
<=> ( ( B @ ( A @ k3_group_1 ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_group_1) ).
thf(9669,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( B @ ( A @ k3_group_1 ) )
= B )
=> ( ( B @ ( np__2 @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) ) )
& ( ( ( B @ ( np__2 @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) )
=> ( ( B @ ( A @ k3_group_1 ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1520]) ).
thf(318,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k5_relat_1 ) @ k5_relat_1 ) )
= ( C @ ( B @ k5_relat_1 ) @ ( A @ k5_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_relat_1) ).
thf(3497,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k5_relat_1 ) @ k5_relat_1 ) )
= ( C @ ( B @ k5_relat_1 ) @ ( A @ k5_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(2098,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_group_6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_group_6) ).
thf(12273,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_group_6 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2098]) ).
thf(386,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v3_filter_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_filter_0) ).
thf(3844,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v3_filter_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_tarski ) ) )
=> ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_partfun1) ).
thf(3585,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_tarski ) ) )
=> ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(300,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
=> ( ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= B )
& ( ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relset_1) ).
thf(3430,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
=> ( ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= B )
& ( ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(1477,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k5_group_2 @ ( A @ k12_group_2 ) ) )
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) ) )
& ( ( B @ ( A @ k5_group_2 @ ( A @ k13_group_2 ) ) )
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t133_group_2) ).
thf(9393,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k5_group_2 @ ( A @ k12_group_2 ) ) )
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) ) )
& ( ( B @ ( A @ k5_group_2 @ ( A @ k13_group_2 ) ) )
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1477]) ).
thf(743,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_filter_0 ) ) )
= ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_filter_0) ).
thf(5692,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_filter_0 ) ) )
= ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(528,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r1_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_binop_1) ).
thf(4591,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r1_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r1_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(338,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m2_finseq_1 ) )
=> ( ( ! [E: $i] :
( ( k5_numbers @ ( k1_numbers @ ( E @ m2_subset_1 ) ) )
=> ( ( B @ k4_finseq_1 @ ( E @ r2_hidden ) )
=> ( ( E @ ( B @ k1_funct_1 ) )
= ( E @ ( D @ ( A @ u1_struct_0 @ ( k5_numbers @ k4_finseq_4 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( k5_numbers @ k4_finseq_4 ) ) ) @ ( A @ k1_group_1 ) ) ) ) ) )
& ( ( B @ k3_finseq_1 )
= ( D @ k3_finseq_1 ) )
& ( ( B @ k3_finseq_1 )
= ( C @ k3_finseq_1 ) )
& ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k3_group_4 ) )
= ( D @ ( A @ k3_group_4 ) @ ( C @ ( A @ k3_group_4 ) @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_group_4) ).
thf(3598,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m2_finseq_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m2_finseq_1 ) )
=> ( ( ! [E: $i] :
( ( k5_numbers @ ( k1_numbers @ ( E @ m2_subset_1 ) ) )
=> ( ( B @ k4_finseq_1 @ ( E @ r2_hidden ) )
=> ( ( E @ ( B @ k1_funct_1 ) )
= ( E @ ( D @ ( A @ u1_struct_0 @ ( k5_numbers @ k4_finseq_4 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( k5_numbers @ k4_finseq_4 ) ) ) @ ( A @ k1_group_1 ) ) ) ) ) )
& ( ( B @ k3_finseq_1 )
= ( D @ k3_finseq_1 ) )
& ( ( B @ k3_finseq_1 )
= ( C @ k3_finseq_1 ) )
& ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k3_group_4 ) )
= ( D @ ( A @ k3_group_4 ) @ ( C @ ( A @ k3_group_4 ) @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(1908,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( D @ ( A @ k4_group_3 ) ) @ ( A @ k4_group_3 ) ) )
= ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( D @ ( A @ k4_group_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_group_3) ).
thf(11526,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( D @ ( A @ k4_group_3 ) ) @ ( A @ k4_group_3 ) ) )
= ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( D @ ( A @ k4_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1908]) ).
thf(612,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k6_relat_1 @ k1_funct_1 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
thf(5040,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k6_relat_1 @ k1_funct_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(1963,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k8_group_1 )
= ( A @ u1_struct_0 @ k1_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_group_1) ).
thf(11755,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k8_group_1 )
= ( A @ u1_struct_0 @ k1_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1963]) ).
thf(249,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_subset_1) ).
thf(3149,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(1721,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ( A @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ v1_group_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_group_3) ).
thf(10695,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ( A @ ( C @ ( B @ ( A @ k9_group_2 ) ) @ v1_group_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1721]) ).
thf(18027,plain,
! [A: $i] :
( ( ( sk152 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ~ $true
| ( A = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[4563,7167]) ).
thf(18028,plain,
! [A: $i] :
( ( ( sk152 @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ( A = k1_xboole_0 ) ),
inference(simp,[status(thm)],[18027]) ).
thf(18029,plain,
sk152 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[18028:[bind(A,$thf( sk152 ))]]) ).
thf(1915,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r4_group_3 ) ) )
& ( C @ ( B @ ( A @ r4_group_3 ) ) ) )
=> ( D @ ( B @ ( A @ r4_group_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_group_3) ).
thf(11552,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r4_group_3 ) ) )
& ( C @ ( B @ ( A @ r4_group_3 ) ) ) )
=> ( D @ ( B @ ( A @ r4_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1915]) ).
thf(488,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
=> ( A @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_subset_1) ).
thf(4387,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
=> ( A @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(2576,plain,
sk19 @ v1_funct_1,
inference(cnfConj,[status(thm)],[2574]) ).
thf(885,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 @ ( B @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_relat_1) ).
thf(6412,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 @ ( B @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(325,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(3529,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(1048,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v6_group_1 )
=> ( A @ k9_group_1 @ ( np__1 @ r1_xreal_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_group_1) ).
thf(7157,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v6_group_1 )
=> ( A @ k9_group_1 @ ( np__1 @ r1_xreal_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(2362,plain,
! [B: $i,A: $i] :
( ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
| ~ ( A @ ( B @ m1_orders_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2360]) ).
thf(862,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_group_6) ).
thf(6277,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
=> ( D = E ) ) ) )
=> ( C @ v2_funct_1 ) )
& ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(2153,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ l3_lattices )
| ~ ( B @ v16_lattices )
| ~ ( B @ v15_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2144]) ).
thf(2162,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
| ~ ( B @ v16_lattices )
| ~ ( B @ v15_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( B @ l3_lattices )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[2153]) ).
thf(1827,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ m1_group_2 ) )
=> ( D @ ( C @ ( A @ k8_group_4 ) ) @ ( B @ m1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_group_4) ).
thf(11227,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ m1_group_2 ) )
=> ( D @ ( C @ ( A @ k8_group_4 ) ) @ ( B @ m1_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1827]) ).
thf(1812,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ k2_group_1 )
= ( C @ k2_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_group_2) ).
thf(11172,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ k2_group_1 )
= ( C @ k2_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1812]) ).
thf(1198,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k10_group_1 ) ) )
= ( C @ ( B @ ( A @ k1_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_group_1) ).
thf(7887,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k10_group_1 ) ) )
= ( C @ ( B @ ( A @ k1_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(43284,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( B @ l1_group_1 )
| ~ ( B @ v1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,21467]) ).
thf(43285,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B @ l1_group_1 )
| ~ ( B @ v1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[43284]) ).
thf(43286,plain,
! [A: $i] :
( ( A @ l1_group_1 )
| ~ ( A @ v1_xboole_0 )
| ( sk1 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[43285:[bind(A,$thf( sk1 ))]]) ).
thf(43291,plain,
! [A: $i] :
( ( A @ l1_group_1 )
| ~ ( A @ v1_xboole_0 )
| ( sk1 @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[43286]) ).
thf(18287,plain,
! [A: $i] :
( ( A != k33_binop_2 )
| ~ ( k1_xboole_0 @ ( k1_numbers @ g1_group_1 ) @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,4585]) ).
thf(18288,plain,
( ~ ( k1_xboole_0 @ ( k1_numbers @ g1_group_1 ) @ v3_struct_0 )
| ~ ( k33_binop_2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[18287:[bind(A,$thf( k33_binop_2 ))]]) ).
thf(1425,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_0_group_2 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k3_group_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_group_2) ).
thf(9130,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k3_group_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_group_2 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_group_2 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k3_group_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425]) ).
thf(6585,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_finseq_3 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[6584]) ).
thf(6586,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_finseq_3 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[6585]) ).
thf(1019,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( C @ ( A @ k10_group_2 ) ) )
= ( B @ ( C @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_group_2) ).
thf(7017,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( C @ ( A @ k10_group_2 ) ) )
= ( B @ ( C @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ ( B @ r3_lattice3 ) ) )
<=> ( C @ ( B @ k4_lattice3 ) @ ( A @ ( B @ k3_lattice3 @ r1_lattice3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_lattice3) ).
thf(3351,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ k4_lattice3 ) @ ( A @ ( B @ k3_lattice3 @ r1_lattice3 ) ) )
=> ( A @ ( C @ ( B @ r3_lattice3 ) ) ) )
& ( ( A @ ( C @ ( B @ r3_lattice3 ) ) )
=> ( C @ ( B @ k4_lattice3 ) @ ( A @ ( B @ k3_lattice3 @ r1_lattice3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(837,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k2_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relat_1) ).
thf(6166,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k2_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(2053,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ( B @ ( A @ k15_group_2 ) @ ( A @ u1_struct_0 @ k5_setfam_1 ) )
= ( A @ u1_struct_0 ) )
& ( ( B @ ( A @ k14_group_2 ) @ ( A @ u1_struct_0 @ k5_setfam_1 ) )
= ( A @ u1_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_group_2) ).
thf(12093,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ( B @ ( A @ k15_group_2 ) @ ( A @ u1_struct_0 @ k5_setfam_1 ) )
= ( A @ u1_struct_0 ) )
& ( ( B @ ( A @ k14_group_2 ) @ ( A @ u1_struct_0 @ k5_setfam_1 ) )
= ( A @ u1_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2053]) ).
thf(1125,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_group_3 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k2_latsubgr ) @ m1_group_2 ) )
& ( B @ ( A @ k2_latsubgr ) @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_latsubgr) ).
thf(7530,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_group_3 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k2_latsubgr ) @ m1_group_2 ) )
& ( B @ ( A @ k2_latsubgr ) @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(1208,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( D
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_lattice4) ).
thf(7939,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( D
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(877,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ ( B @ k2_xcmplx_0 ) @ ( C @ k6_group_1 ) ) )
= ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( D @ ( B @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_group_1) ).
thf(6386,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ ( B @ k2_xcmplx_0 ) @ ( C @ k6_group_1 ) ) )
= ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( D @ ( B @ ( C @ k6_group_1 ) ) @ ( C @ k1_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(909,axiom,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( ( ( A @ v8_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_vectsp_1) ).
thf(6569,plain,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( ( ( A @ v8_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(2294,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k1_realset1 ) @ v1_funct_1 )
| ~ ( B @ ( A @ ( C @ m1_realset1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[2293]) ).
thf(1276,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( C @ m1_group_2 ) )
=> ( ( C @ ( B @ k9_group_3 ) @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ m1_group_2 ) )
& ( A @ v1_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_group_3) ).
thf(8267,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( C @ m1_group_2 ) )
=> ( ( C @ ( B @ k9_group_3 ) @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ m1_group_2 ) )
& ( A @ v1_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(738,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v6_lattice3 )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ ( B @ k16_lattice3 ) @ ( B @ k3_lattices ) ) )
= ( C @ ( B @ ( A @ a_3_10_lattice3 ) ) @ ( B @ k16_lattice3 ) ) )
& ( ( A @ ( B @ k16_lattice3 ) @ ( C @ ( B @ k3_lattices ) ) )
= ( C @ ( B @ ( A @ a_3_9_lattice3 ) ) @ ( B @ k16_lattice3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_lattice3) ).
thf(5672,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v6_lattice3 )
& ( B @ v4_lattice3 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ ( B @ k16_lattice3 ) @ ( B @ k3_lattices ) ) )
= ( C @ ( B @ ( A @ a_3_10_lattice3 ) ) @ ( B @ k16_lattice3 ) ) )
& ( ( A @ ( B @ k16_lattice3 ) @ ( C @ ( B @ k3_lattices ) ) )
= ( C @ ( B @ ( A @ a_3_9_lattice3 ) ) @ ( B @ k16_lattice3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(1455,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_lattices @ ( A @ k3_lattices ) ) )
= ( A @ k6_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattices) ).
thf(9311,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_lattices @ ( A @ k3_lattices ) ) )
= ( A @ k6_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455]) ).
thf(1601,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( ( D @ ( A @ k7_group_2 ) @ ( C @ r2_hidden ) )
& ( D @ ( A @ k7_group_2 ) @ ( B @ r2_hidden ) ) )
=> ( D @ ( A @ k7_group_2 ) @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_group_2) ).
thf(10109,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( ( D @ ( A @ k7_group_2 ) @ ( C @ r2_hidden ) )
& ( D @ ( A @ k7_group_2 ) @ ( B @ r2_hidden ) ) )
=> ( D @ ( A @ k7_group_2 ) @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1601]) ).
thf(1566,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k14_group_2 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( D
= ( E @ ( B @ ( A @ k12_group_2 ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_group_2) ).
thf(9887,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( D
= ( E @ ( B @ ( A @ k12_group_2 ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( B @ ( A @ k12_group_2 ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) )
=> ( C
= ( B @ ( A @ k14_group_2 ) ) ) )
& ( ( C
= ( B @ ( A @ k14_group_2 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( D
= ( E @ ( B @ ( A @ k12_group_2 ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( B @ ( A @ k12_group_2 ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1566]) ).
thf(2315,plain,
! [B: $i,A: $i] :
( ( A @ u1_struct_0 @ ( A @ ( B @ sk7 ) @ m1_subset_1 ) )
| ~ ( A @ v4_lattice3 )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2314]) ).
thf(580,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( A @ k2_card_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_card_1) ).
thf(4869,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( A @ k2_card_1 @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(41219,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( B @ k2_xboole_0 ) @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( E @ ( D @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( E @ ( D @ k2_xboole_0 ) @ ( C @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17581,2188]) ).
thf(41220,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( B @ k2_xboole_0 ) @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) )
!= ( E @ ( D @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( E @ ( D @ k2_xboole_0 ) @ ( C @ r1_tarski ) ) ),
inference(simp,[status(thm)],[41219]) ).
thf(41221,plain,
! [B: $i,A: $i] : ( k1_numbers @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) @ ( k5_numbers @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[41220:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( k5_numbers )),bind(D,$thf( A )),bind(E,$thf( k1_numbers @ ( F @ k2_xboole_0 ) ))]]) ).
thf(41262,plain,
! [B: $i,A: $i] : ( k1_numbers @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) @ ( k5_numbers @ r1_tarski ) ),
inference(simp,[status(thm)],[41221]) ).
thf(122,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r5_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_binop_1) ).
thf(2623,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r5_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r6_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r5_binop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(1315,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( ( B @ k9_group_1 )
= np__1 )
& ( B @ v6_group_1 ) )
=> ( A @ k5_group_2 @ ( B @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_group_2) ).
thf(8520,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( ( B @ k9_group_1 )
= np__1 )
& ( B @ v6_group_1 ) )
=> ( A @ k5_group_2 @ ( B @ ( A @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).
thf(471,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( A @ ( B @ m2_lattice4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_lattice4) ).
thf(4306,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( A @ ( B @ m2_lattice4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(1950,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k1_group_2 ) )
= ( B @ ( A @ k3_group_1 ) @ ( A @ u1_struct_0 @ k6_domain_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_group_2) ).
thf(11700,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k1_group_2 ) )
= ( B @ ( A @ k3_group_1 ) @ ( A @ u1_struct_0 @ k6_domain_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1950]) ).
thf(4917,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( B @ sk180 ) @ k1_relat_1 ) )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[4909]) ).
thf(4926,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk180 ) @ k1_relat_1 )
= B )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[4917]) ).
thf(4927,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ sk180 ) @ k1_relat_1 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[4926]) ).
thf(422,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k4_filter_0 ) ) )
= ( A @ k6_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_filter_0) ).
thf(4025,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k4_filter_0 ) ) )
= ( A @ k6_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( C @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_xboole_1) ).
thf(2779,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( C @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(1458,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k3_group_3 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k2_group_3 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_group_3) ).
thf(9321,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ? [F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k2_group_3 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ k3_group_3 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ k3_group_3 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ? [F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k2_group_3 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458]) ).
thf(27385,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ~ ( A @ v3_struct_0 )
| ( sk1 @ sk149 @ v1_funct_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,22481]) ).
thf(27386,plain,
! [A: $i] :
( ~ ( A @ v3_struct_0 )
| ( sk1 @ sk149 @ v1_funct_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[27385:[]]) ).
thf(47205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21647,2188]) ).
thf(47206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
!= ( D @ ( C @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) )
| ( D @ ( C @ k2_xboole_0 ) @ ( B @ r1_tarski ) ) ),
inference(simp,[status(thm)],[47205]) ).
thf(47207,plain,
! [A: $i] : ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[47206:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( k1_numbers )),bind(D,$thf( k5_numbers @ ( E @ k4_xboole_0 ) ))]]) ).
thf(47273,plain,
! [A: $i] : ( k5_numbers @ ( A @ k4_xboole_0 ) @ ( k1_numbers @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(simp,[status(thm)],[47207]) ).
thf(7991,plain,
sk370 @ l1_vectsp_1,
inference(cnf,[status(esa)],[7990]) ).
thf(807,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_partfun1) ).
thf(6050,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(308,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( B @ ( A @ k7_lattices ) @ ( C @ ( A @ k7_lattices ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_lattices) ).
thf(3464,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( B @ ( A @ k7_lattices ) @ ( C @ ( A @ k7_lattices ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(1502,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_relset_1) ).
thf(9523,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1502]) ).
thf(2138,plain,
! [A: $i] :
( ( ( A @ v17_lattices )
| ~ ( A @ v11_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) )
& ( ( A @ v11_lattices )
| ~ ( A @ v17_lattices )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) )
& ( ( A @ v16_lattices )
| ~ ( A @ v17_lattices )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) )
& ( ( A @ v15_lattices )
| ~ ( A @ v17_lattices )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ) ),
inference(cnf,[status(esa)],[2137]) ).
thf(2142,plain,
! [A: $i] :
( ( A @ v17_lattices )
| ~ ( A @ v11_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2138]) ).
thf(937,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( G @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ! [H: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( H @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( H @ v1_funct_2 ) ) )
& ( H @ v1_funct_1 ) )
=> ( ( F @ ( D @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( H @ ( G @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( H @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( G @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ k1_domain_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_filter_1) ).
thf(6703,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( G @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ! [H: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( H @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( H @ v1_funct_2 ) ) )
& ( H @ v1_funct_1 ) )
=> ( ( F @ ( D @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( H @ ( G @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( H @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( G @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ k1_domain_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(295,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
<=> ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v17_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_filter_1) ).
thf(3379,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v17_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) )
=> ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) )
& ( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v17_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(1465,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( ( B @ ( D @ ( A @ r5_group_3 ) ) )
& ( D @ ( C @ ( A @ r6_group_3 ) ) ) )
=> ( B @ ( C @ ( A @ r5_group_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_group_3) ).
thf(9361,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( ( B @ ( D @ ( A @ r5_group_3 ) ) )
& ( D @ ( C @ ( A @ r6_group_3 ) ) ) )
=> ( B @ ( C @ ( A @ r5_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1465]) ).
thf(2123,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ v3_filter_0 )
| ~ ( A @ ( B @ ( C @ v3_lattice4 ) ) )
| ~ ( A @ ( B @ ( C @ m1_lattice4 ) ) )
| ~ ( B @ l3_lattices )
| ~ ( B @ v3_filter_0 )
| ~ ( B @ v10_lattices )
| ( B @ v3_struct_0 )
| ~ ( A @ l3_lattices )
| ~ ( A @ v16_lattices )
| ~ ( A @ v15_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2122]) ).
thf(1290,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k8_group_2 ) ) @ ( A @ k7_group_2 ) )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_group_2) ).
thf(8341,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k8_group_2 ) ) @ ( A @ k7_group_2 ) )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k3_finsub_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290]) ).
thf(1693,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( D @ ( A @ k5_group_3 ) ) @ ( A @ k4_group_3 ) ) )
= ( B @ ( D @ ( C @ ( A @ k4_group_2 ) ) @ ( A @ k5_group_3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_group_3) ).
thf(10569,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( D @ ( A @ k5_group_3 ) ) @ ( A @ k4_group_3 ) ) )
= ( B @ ( D @ ( C @ ( A @ k4_group_2 ) ) @ ( A @ k5_group_3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1693]) ).
thf(1129,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_wellord2 ) )
<=> ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_card_1) ).
thf(7542,plain,
! [A: $i,B: $i] :
( ( ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) )
=> ( B @ ( A @ r2_wellord2 ) ) )
& ( ( B @ ( A @ r2_wellord2 ) )
=> ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(1924,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ ( A @ k10_group_6 ) @ ( B @ ( A @ k12_group_6 ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_group_6) ).
thf(11580,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ ( A @ k10_group_6 ) @ ( B @ ( A @ k12_group_6 ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1924]) ).
thf(1345,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(8660,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).
thf(1949,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k3_group_1 ) ) )
<=> ( ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= ( A @ k2_group_1 ) )
& ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( A @ k2_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_group_1) ).
thf(11690,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= ( A @ k2_group_1 ) )
& ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( A @ k2_group_1 ) ) )
=> ( C
= ( B @ ( A @ k3_group_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_group_1 ) ) )
=> ( ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= ( A @ k2_group_1 ) )
& ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( A @ k2_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1949]) ).
thf(2301,plain,
! [A: $i] :
( ( A @ k4_finseq_1 @ ( np__1 @ r2_hidden ) )
| ( ( A @ k2_relat_1 )
= k1_xboole_0 )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2300]) ).
thf(2302,plain,
! [A: $i] :
( ( A @ k4_finseq_1 @ ( np__1 @ r2_hidden ) )
| ~ ( A @ v1_finseq_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[2301]) ).
thf(2057,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= D )
<=> ( C
= ( D @ ( B @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_group_1) ).
thf(12108,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( C
= ( D @ ( B @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) ) )
=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= D ) )
& ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= D )
=> ( C
= ( D @ ( B @ ( A @ k3_group_1 ) @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2057]) ).
thf(544,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m3_lattice4 ) )
=> ( ( C
= ( B @ ( A @ k3_lattice4 ) ) )
<=> ( ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_lattice4) ).
thf(4687,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m3_lattice4 ) )
=> ( ( ( ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( C
= ( B @ ( A @ k3_lattice4 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_lattice4 ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_partfun1) ).
thf(2385,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(540,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( B @ ( D @ ( C @ ( A @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t105_enumset1) ).
thf(4670,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( B @ ( D @ ( C @ ( A @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(485,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ~ ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( C @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_4) ).
thf(4378,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ~ ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( C @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(799,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(6007,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(1255,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k5_group_4 ) @ r1_rlvect_1 ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( ( D @ ( E @ ( A @ k4_group_4 ) ) @ ( A @ k3_group_4 ) )
= B )
& ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
& ( ( D @ k3_finseq_1 )
= ( E @ k3_finseq_1 ) )
& ( k4_numbers @ ( E @ m2_finseq_1 ) ) )
& ( A @ u1_struct_0 @ ( D @ m2_finseq_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_group_4) ).
thf(8162,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( ( D @ ( E @ ( A @ k4_group_4 ) ) @ ( A @ k3_group_4 ) )
= B )
& ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
& ( ( D @ k3_finseq_1 )
= ( E @ k3_finseq_1 ) )
& ( k4_numbers @ ( E @ m2_finseq_1 ) ) )
& ( A @ u1_struct_0 @ ( D @ m2_finseq_1 ) ) )
=> ( B @ ( C @ ( A @ k5_group_4 ) @ r1_rlvect_1 ) ) )
& ( ( B @ ( C @ ( A @ k5_group_4 ) @ r1_rlvect_1 ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( ( D @ ( E @ ( A @ k4_group_4 ) ) @ ( A @ k3_group_4 ) )
= B )
& ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
& ( ( D @ k3_finseq_1 )
= ( E @ k3_finseq_1 ) )
& ( k4_numbers @ ( E @ m2_finseq_1 ) ) )
& ( A @ u1_struct_0 @ ( D @ m2_finseq_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(2097,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= B )
<=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k1_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_group_3) ).
thf(12267,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k1_group_1 ) ) ) )
=> ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= B ) )
& ( ( ( C @ ( B @ ( A @ k2_group_3 ) ) )
= B )
=> ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( B @ ( C @ ( A @ k1_group_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2097]) ).
thf(1123,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_group_3 @ ( B @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_group_3 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k1_latsubgr ) )
<=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_latsubgr) ).
thf(7510,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_group_3 @ ( B @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_group_3 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ u1_struct_0 ) ) )
=> ( B
= ( A @ k1_latsubgr ) ) )
& ( ( B
= ( A @ k1_latsubgr ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ u1_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(1947,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k8_group_4 ) ) @ u1_struct_0 )
= ( C @ ( B @ ( A @ k7_group_4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_group_4) ).
thf(11680,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k8_group_4 ) ) @ u1_struct_0 )
= ( C @ ( B @ ( A @ k7_group_4 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1947]) ).
thf(1052,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( ( B @ ( A @ k17_group_2 ) )
= ( A @ k9_group_1 ) )
& ( A @ v6_group_1 ) )
=> ( A @ k5_group_2 @ ( B @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t184_group_2) ).
thf(7171,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( ( B @ ( A @ k17_group_2 ) )
= ( A @ k9_group_1 ) )
& ( A @ v6_group_1 ) )
=> ( A @ k5_group_2 @ ( B @ ( A @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(1528,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_domain_1 ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_domain_1) ).
thf(9711,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_domain_1 ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1528]) ).
thf(1572,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
<=> ( ( C @ k2_relat_1 )
= ( B @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice4) ).
thf(9937,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= ( B @ u1_struct_0 ) )
=> ( B @ ( A @ ( C @ v2_lattice4 ) ) ) )
& ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ k2_relat_1 )
= ( B @ u1_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1572]) ).
thf(11589,plain,
sk610 @ v2_group_1,
inference(cnfConj,[status(thm)],[11584]) ).
thf(1590,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_group_6 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_group_6 ) ) ) ) @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_group_6 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k8_group_6 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_group_6) ).
thf(10041,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_group_6 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_group_6 ) ) ) ) @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( A @ u1_struct_0 @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_group_6 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k8_group_6 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1590]) ).
thf(53530,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( B @ l1_group_1 )
| ( B @ sk149 @ v1_funct_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,22702]) ).
thf(53531,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B @ l1_group_1 )
| ( B @ sk149 @ v1_funct_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[53530]) ).
thf(53532,plain,
! [A: $i] :
( ( A @ l1_group_1 )
| ( A @ sk149 @ v1_funct_1 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[53531:[bind(A,$thf( sk1 ))]]) ).
thf(53589,plain,
! [A: $i] :
( ( A @ l1_group_1 )
| ( A @ sk149 @ v1_funct_1 )
| ~ ( sk1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[53532]) ).
thf(995,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
<=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_subset_1) ).
thf(6925,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) )
& ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(34173,plain,
! [B: $i,A: $i] :
( ( ( B @ k1_tarski @ k1_card_1 )
!= ( k1_xboole_0 @ k1_tarski @ k1_card_1 ) )
| ( A @ k1_tarski @ k1_card_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[10603,32958]) ).
thf(34174,plain,
! [A: $i] : ( A @ k1_tarski @ k1_card_1 @ ( k1_xboole_0 @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[34173:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(785,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_binop_1) ).
thf(5954,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) )
=> ( C @ ( B @ ( A @ r1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(1638,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 )
& ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r6_group_3 ) ) )
<=> ( C @ ( B @ ( A @ r5_group_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r6_group_3) ).
thf(10312,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 )
& ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r5_group_3 ) ) )
=> ( C @ ( B @ ( A @ r6_group_3 ) ) ) )
& ( ( C @ ( B @ ( A @ r6_group_3 ) ) )
=> ( C @ ( B @ ( A @ r5_group_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1638]) ).
thf(1066,axiom,
! [A: $i] :
( ~ ( ( A @ ( A @ r1_xboole_0 ) )
& ( A != k1_xboole_0 ) )
& ~ ( ( A = k1_xboole_0 )
& ~ ( A @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_xboole_1) ).
thf(7242,plain,
! [A: $i] :
( ~ ( ( A @ ( A @ r1_xboole_0 ) )
& ( A != k1_xboole_0 ) )
& ~ ( ( A = k1_xboole_0 )
& ~ ( A @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(11437,plain,
sk605 @ v3_realset2,
inference(cnfConj,[status(thm)],[11434]) ).
thf(1996,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k5_group_2 @ ( A @ u1_struct_0 @ k1_subset_1 @ ( A @ k5_group_4 ) @ ( A @ r1_group_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_group_4) ).
thf(11871,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k5_group_2 @ ( A @ u1_struct_0 @ k1_subset_1 @ ( A @ k5_group_4 ) @ ( A @ r1_group_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1996]) ).
thf(893,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) )
& ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
<=> ( ( B @ k1_relat_1 @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k5_relat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funct_1) ).
thf(6456,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) )
& ! [D: $i] :
( ( ( ( B @ k1_relat_1 @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( B @ k1_relat_1 @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) )
=> ( C
= ( B @ ( A @ k5_relat_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(1989,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k5_group_2 @ m1_group_2 ) )
& ( A @ k5_group_2 @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_group_2) ).
thf(11843,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( A @ k5_group_2 @ m1_group_2 ) )
& ( A @ k5_group_2 @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1989]) ).
thf(2104,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_group_2) ).
thf(12292,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2104]) ).
thf(575,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v1_finset_1 )
=> ~ ( ! [C: $i] :
( ( C @ v1_finset_1 )
=> ~ ( ( ( C @ k4_card_1 )
= ( B @ k4_card_1 @ ( A @ k2_nat_1 ) ) )
& ( C
= ( B @ k3_tarski ) ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
( ( D @ v1_finset_1 )
=> ~ ( ! [E: $i] :
( ( B @ ( E @ r2_hidden ) )
=> ( ( ( E @ ( C @ r1_xboole_0 ) )
& ( E @ ( C @ r2_wellord2 ) ) )
| ( C = E ) ) )
& ( ( D @ k4_card_1 )
= A )
& ( D = C ) ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t186_group_2) ).
thf(4841,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v1_finset_1 )
=> ~ ( ! [C: $i] :
( ( C @ v1_finset_1 )
=> ~ ( ( ( C @ k4_card_1 )
= ( B @ k4_card_1 @ ( A @ k2_nat_1 ) ) )
& ( C
= ( B @ k3_tarski ) ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
( ( D @ v1_finset_1 )
=> ~ ( ! [E: $i] :
( ( B @ ( E @ r2_hidden ) )
=> ( ( ( E @ ( C @ r1_xboole_0 ) )
& ( E @ ( C @ r2_wellord2 ) ) )
| ( C = E ) ) )
& ( ( D @ k4_card_1 )
= A )
& ( D = C ) ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(375,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_partfun1) ).
thf(3790,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(1359,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_setfam_1 ) )
= ( B @ k1_setfam_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(8720,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_setfam_1 ) )
= ( B @ k1_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ k9_relat_1 ) )
= ( C @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_partfun1) ).
thf(3337,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ k9_relat_1 ) )
= ( C @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(928,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_lattices @ ( A @ k7_lattices ) )
= ( A @ k6_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_lattice4) ).
thf(6671,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_lattices @ ( A @ k7_lattices ) )
= ( A @ k6_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(1680,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m2_lattice4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice4) ).
thf(10515,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m2_lattice4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1680]) ).
thf(509,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_xboole_1) ).
thf(4491,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(832,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( D @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_xboole_1) ).
thf(6150,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( D @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(1057,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_group_2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_group_2) ).
thf(7210,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_group_2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(608,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( C @ ( B @ ( D @ ( A @ k6_group_1 ) ) @ ( A @ k2_group_3 ) ) )
= ( C @ ( B @ ( A @ k2_group_3 ) ) @ ( D @ ( A @ k6_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_group_3) ).
thf(5014,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( C @ ( B @ ( D @ ( A @ k6_group_1 ) ) @ ( A @ k2_group_3 ) ) )
= ( C @ ( B @ ( A @ k2_group_3 ) ) @ ( D @ ( A @ k6_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(2065,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k7_group_3 ) @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k7_group_3 ) @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_group_3) ).
thf(12140,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k7_group_3 ) @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k7_group_3 ) @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2065]) ).
thf(1697,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ k10_group_6 ) @ ( D @ ( C @ ( B @ ( A @ k8_group_6 ) ) ) ) )
= ( C @ ( A @ k10_group_6 ) ) )
& ( ( E @ ( B @ ( A @ k10_group_6 ) @ ( C @ ( B @ ( A @ k8_group_6 ) ) ) ) )
= ( C @ ( A @ k10_group_6 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_group_6) ).
thf(10590,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ k10_group_6 ) @ ( D @ ( C @ ( B @ ( A @ k8_group_6 ) ) ) ) )
= ( C @ ( A @ k10_group_6 ) ) )
& ( ( E @ ( B @ ( A @ k10_group_6 ) @ ( C @ ( B @ ( A @ k8_group_6 ) ) ) ) )
= ( C @ ( A @ k10_group_6 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1697]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( B @ ( C @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_realset1) ).
thf(3062,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( B @ ( C @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(959,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k2_nat_1 ) @ ( C @ k6_group_1 ) ) )
= ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( B @ ( C @ k6_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_group_1) ).
thf(6782,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k2_nat_1 ) @ ( C @ k6_group_1 ) ) )
= ( D @ ( A @ ( C @ k6_group_1 ) ) @ ( B @ ( C @ k6_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r7_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_funct_1 ) )
= ( E @ ( B @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_binop_1) ).
thf(2751,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_funct_1 ) )
= ( E @ ( B @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ ( C @ k1_binop_1 ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r7_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r7_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_funct_1 ) )
= ( E @ ( B @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(1652,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(10379,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1652]) ).
thf(713,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ k5_relat_1 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_relat_1) ).
thf(5564,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ k5_relat_1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(1983,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k7_group_2 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_group_2) ).
thf(11818,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ ( A @ k7_group_2 ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1983]) ).
thf(1623,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( A @ ( C @ ( B @ k11_group_3 ) @ r1_rlvect_1 ) )
<=> ? [D: $i] :
( ( C @ ( D @ ( C @ ( B @ k6_group_3 ) ) @ ( B @ r1_group_2 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_group_3) ).
thf(10224,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ ( C @ ( B @ k6_group_3 ) ) @ ( B @ r1_group_2 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( A @ ( C @ ( B @ k11_group_3 ) @ r1_rlvect_1 ) ) )
& ( ( A @ ( C @ ( B @ k11_group_3 ) @ r1_rlvect_1 ) )
=> ? [D: $i] :
( ( C @ ( D @ ( C @ ( B @ k6_group_3 ) ) @ ( B @ r1_group_2 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1623]) ).
thf(277,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ( ~ ( A @ ( B @ r1_xreal_0 ) )
=> ( B @ ( np__1 @ ( A @ k2_xcmplx_0 ) @ r1_xreal_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_int_1) ).
thf(3309,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( B @ v1_int_1 )
=> ( ~ ( A @ ( B @ r1_xreal_0 ) )
=> ( B @ ( np__1 @ ( A @ k2_xcmplx_0 ) @ r1_xreal_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(32473,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_tarski @ k1_zfmisc_1 )
!= ( k1_xboole_0 @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= ( B @ k1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[6948,31143]) ).
thf(32474,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_tarski @ k1_zfmisc_1 )
!= ( k1_xboole_0 @ k1_zfmisc_1 ) )
| ( k1_xboole_0 != B ) ),
inference(simp,[status(thm)],[32473]) ).
thf(32486,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= ( k1_xboole_0 @ k1_zfmisc_1 ) ),
inference(simp,[status(thm)],[32474]) ).
thf(32488,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(rewrite,[status(thm)],[32486,6948]) ).
thf(412,axiom,
! [A: $i,B: $i] :
( ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) )
<=> ? [C: $i] :
( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_card_1) ).
thf(3982,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) ) )
& ( ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) )
=> ? [C: $i] :
( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(380,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k7_binop_2 @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k3_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_group_1) ).
thf(3822,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k7_binop_2 @ ( B @ k6_group_1 ) ) )
= ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k3_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(248,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
<=> ( B @ ( A @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_funct_4) ).
thf(3145,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ k1_funct_4 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ( B @ ( A @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(126,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) )
=> ( B @ ( C @ ( D @ ( A @ r1_filter_0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_filter_0) ).
thf(2636,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) )
=> ( B @ ( C @ ( D @ ( A @ r1_filter_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(1807,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_funct_2) ).
thf(11155,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1807]) ).
thf(1321,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k9_group_6 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_group_6) ).
thf(8542,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k9_group_6 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321]) ).
thf(1493,axiom,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( B
= ( A @ k1_card_1 ) )
<=> ( B @ ( A @ r2_wellord2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_card_1) ).
thf(9466,plain,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( ( B @ ( A @ r2_wellord2 ) )
=> ( B
= ( A @ k1_card_1 ) ) )
& ( ( B
= ( A @ k1_card_1 ) )
=> ( B @ ( A @ r2_wellord2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1493]) ).
thf(398,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ r1_tarski ) )
<=> ( B @ k1_orders_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_orders_1) ).
thf(3897,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ( B @ k1_orders_1 @ ( A @ r2_hidden ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_orders_1 @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(2201,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
| ~ ( B @ ( C @ ( A @ r4_binop_1 ) ) )
| ~ ( A @ ( C @ v1_binop_1 ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2199]) ).
thf(1344,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( D = C ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finset_1) ).
thf(8653,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( D = C ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344]) ).
thf(5275,plain,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[5274]) ).
thf(21542,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k3_tarski )
!= ( A @ k3_tarski ) )
| ( k1_xboole_0 @ ( A @ k1_setfam_1 @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[5275,4495]) ).
thf(21543,plain,
k1_xboole_0 @ ( k1_xboole_0 @ k1_setfam_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[21542:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(21653,plain,
k1_xboole_0 @ ( k1_xboole_0 @ r1_tarski ),
inference(rewrite,[status(thm)],[21543,8446]) ).
thf(838,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_realset1) ).
thf(6169,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(1825,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_0_group_3 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( D @ ( C @ ( B @ r2_group_3 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_group_3) ).
thf(11214,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ( D @ ( C @ ( B @ r2_group_3 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_group_3 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_group_3 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( D @ ( C @ ( B @ r2_group_3 ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1825]) ).
thf(2112,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k1_group_1 ) ) ) ) ) ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
| ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ? [D: $i] :
( ( ( C @ ( D @ ( A @ k1_group_1 ) ) )
= B )
& ( ( D @ ( C @ ( A @ k1_group_1 ) ) )
= B )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
& ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_group_1) ).
thf(12312,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ ( A @ k1_group_1 ) ) )
= ( D @ ( C @ ( A @ k1_group_1 ) ) @ ( B @ ( A @ k1_group_1 ) ) ) ) ) ) )
=> ( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
| ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ? [D: $i] :
( ( ( C @ ( D @ ( A @ k1_group_1 ) ) )
= B )
& ( ( D @ ( C @ ( A @ k1_group_1 ) ) )
= B )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
& ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2112]) ).
thf(556,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m2_filter_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( ( B @ ( G @ ( F @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) )
& ( B @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) )
=> ( B @ ( G @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_filter_1) ).
thf(4755,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( ( B @ ( G @ ( F @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) )
& ( B @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) )
=> ( B @ ( G @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) )
=> ( B @ ( A @ ( C @ m2_filter_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_filter_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( ( B @ ( G @ ( F @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) )
& ( B @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) )
=> ( B @ ( G @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(1980,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( D @ v1_int_1 )
=> ( ( C @ ( B @ ( D @ ( A @ k6_group_1 ) ) @ ( A @ k2_group_3 ) ) )
= ( C @ ( B @ ( A @ k2_group_3 ) ) @ ( D @ ( A @ k6_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_group_3) ).
thf(11811,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( D @ v1_int_1 )
=> ( ( C @ ( B @ ( D @ ( A @ k6_group_1 ) ) @ ( A @ k2_group_3 ) ) )
= ( C @ ( B @ ( A @ k2_group_3 ) ) @ ( D @ ( A @ k6_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1980]) ).
thf(745,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relat_1) ).
thf(5709,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(2186,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ k1_relat_1 @ ( A @ r1_tarski ) )
| ~ ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2185]) ).
thf(823,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k6_lattices )
= ( A @ u1_struct_0 @ ( A @ k15_lattice3 ) ) )
& ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_lattice3) ).
thf(6114,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k6_lattices )
= ( A @ u1_struct_0 @ ( A @ k15_lattice3 ) ) )
& ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(1610,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_group_2 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_group_2 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_group_2 ) )
=> ( ( ( E @ ( B @ ( D @ m1_group_6 ) ) )
& ( ( G @ u1_struct_0 )
= ( E @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k3_funct_2 ) ) ) ) )
& ( ( F @ u1_struct_0 )
= ( D @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k3_funct_2 ) ) ) ) ) )
=> ( G @ ( A @ ( F @ m1_group_6 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_latsubgr) ).
thf(10168,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_group_2 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_group_2 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_group_2 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_group_2 ) )
=> ( ( ( E @ ( B @ ( D @ m1_group_6 ) ) )
& ( ( G @ u1_struct_0 )
= ( E @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k3_funct_2 ) ) ) ) )
& ( ( F @ u1_struct_0 )
= ( D @ u1_struct_0 @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k3_funct_2 ) ) ) ) ) )
=> ( G @ ( A @ ( F @ m1_group_6 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1610]) ).
thf(393,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ v14_lattices )
& ( A @ v14_lattices ) )
<=> ( B @ ( A @ k8_filter_1 ) @ v14_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_filter_1) ).
thf(3875,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k8_filter_1 ) @ v14_lattices )
=> ( ( B @ v14_lattices )
& ( A @ v14_lattices ) ) )
& ( ( ( B @ v14_lattices )
& ( A @ v14_lattices ) )
=> ( B @ ( A @ k8_filter_1 ) @ v14_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_0_lattice4 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i,E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice4) ).
thf(4427,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i,E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_lattice4 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_lattice4 ) @ ( A @ r2_hidden ) )
=> ? [D: $i,E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(1677,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k8_domain_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_domain_1) ).
thf(10500,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k8_domain_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1677]) ).
thf(945,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
& ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_xboole_1) ).
thf(6735,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
& ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(1327,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_group_4 @ r1_rlvect_1 ) )
<=> ~ ( A @ ( B @ v1_group_4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_group_4) ).
thf(8557,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ~ ( A @ ( B @ v1_group_4 ) )
=> ( B @ ( A @ k6_group_4 @ r1_rlvect_1 ) ) )
& ( ( B @ ( A @ k6_group_4 @ r1_rlvect_1 ) )
=> ~ ( A @ ( B @ v1_group_4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( B @ ( C @ ( E @ ( D @ k5_relat_1 ) @ k3_partfun1 ) ) @ ( B @ ( A @ ( E @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( A @ ( C @ k1_partfun1 ) ) ) ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_partfun1) ).
thf(2746,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( B @ ( C @ ( E @ ( D @ k5_relat_1 ) @ k3_partfun1 ) ) @ ( B @ ( A @ ( E @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( A @ ( C @ k1_partfun1 ) ) ) ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1445,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m4_vectsp_8 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k3_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_vectsp_8) ).
thf(9265,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k3_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_lattices ) ) ) ) ) )
=> ( B @ ( A @ ( C @ m4_vectsp_8 ) ) ) )
& ( ( B @ ( A @ ( C @ m4_vectsp_8 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k3_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1445]) ).
thf(681,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_subset_1) ).
thf(5413,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(693,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_zfmisc_1) ).
thf(5462,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(143,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k4_finseq_1 @ ( B @ r2_hidden ) )
=> ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_finseq_3) ).
thf(2704,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k4_finseq_1 @ ( B @ r2_hidden ) )
=> ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(1942,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_group_1 )
<=> ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ? [D: $i] :
( ( ( C @ ( D @ ( A @ k1_group_1 ) ) )
= B )
& ( ( D @ ( C @ ( A @ k1_group_1 ) ) )
= B )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
& ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= C ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_group_1) ).
thf(11644,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ? [D: $i] :
( ( ( C @ ( D @ ( A @ k1_group_1 ) ) )
= B )
& ( ( D @ ( C @ ( A @ k1_group_1 ) ) )
= B )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
& ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= C ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
=> ( A @ v3_group_1 ) )
& ( ( A @ v3_group_1 )
=> ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ? [D: $i] :
( ( ( C @ ( D @ ( A @ k1_group_1 ) ) )
= B )
& ( ( D @ ( C @ ( A @ k1_group_1 ) ) )
= B )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
& ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= C )
& ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= C ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1942]) ).
thf(1673,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_2) ).
thf(10472,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1673]) ).
thf(2093,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( D @ ( C @ ( A @ k8_group_4 ) ) @ ( B @ ( A @ k8_group_4 ) ) @ ( D @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_group_4) ).
thf(12253,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( D @ ( C @ ( A @ k8_group_4 ) ) @ ( B @ ( A @ k8_group_4 ) ) @ ( D @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2093]) ).
thf(688,axiom,
! [A: $i,B: $i] :
( ( B @ k3_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ ( A @ k1_tarski @ k3_setfam_1 ) @ k3_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_setfam_1) ).
thf(5441,plain,
! [A: $i,B: $i] :
( ( B @ k3_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ ( A @ k1_tarski @ k3_setfam_1 ) @ k3_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(1074,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k13_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( B @ ( D @ ( A @ k12_group_2 ) ) @ ( C @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_group_3) ).
thf(7278,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k13_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( B @ ( D @ ( A @ k12_group_2 ) ) @ ( C @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(863,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k1_funct_2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_funct_2) ).
thf(6287,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) ) ) )
=> ( C
= ( B @ ( A @ k1_funct_2 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_funct_2 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(4894,plain,
( ! [A: $i] : ( A @ k6_relat_1 @ v1_funct_1 )
& ! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ) ),
inference(miniscope,[status(thm)],[4893]) ).
thf(4895,plain,
! [B: $i,A: $i] :
( ( B @ k6_relat_1 @ v1_funct_1 )
& ( A @ k6_relat_1 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[4894]) ).
thf(4897,plain,
! [A: $i] : ( A @ k6_relat_1 @ v1_funct_1 ),
inference(cnfConj,[status(thm)],[4895]) ).
thf(4898,plain,
! [A: $i] : ( A @ k6_relat_1 @ v1_funct_1 ),
inference(simp,[status(thm)],[4897]) ).
thf(16256,plain,
! [A: $i] : ( A @ k6_partfun1 @ v1_funct_1 ),
inference(rewrite,[status(thm)],[4898,11231]) ).
thf(1854,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r2_group_3 ) ) )
=> ( B @ ( C @ ( A @ r2_group_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r2_group_3) ).
thf(11326,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r2_group_3 ) ) )
=> ( B @ ( C @ ( A @ r2_group_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1854]) ).
thf(1783,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v3_group_6 ) ) )
<=> ( ( C @ ( B @ ( A @ k13_group_6 ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_group_6) ).
thf(11067,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k13_group_6 ) ) )
= B )
=> ( B @ ( A @ ( C @ v3_group_6 ) ) ) )
& ( ( B @ ( A @ ( C @ v3_group_6 ) ) )
=> ( ( C @ ( B @ ( A @ k13_group_6 ) ) )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1783]) ).
thf(876,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k1_relat_1 )
= ( A @ k2_funct_1 @ k2_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( A @ k2_funct_1 @ k1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
thf(6380,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k1_relat_1 )
= ( A @ k2_funct_1 @ k2_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( A @ k2_funct_1 @ k1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(2714,plain,
sk27 @ v1_relat_1,
inference(cnfConj,[status(thm)],[2713]) ).
thf(1098,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ v3_lattices )
=> ( A
= ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
thf(7402,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ v3_lattices )
=> ( A
= ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(651,axiom,
! [A: $i] :
( ~ ( ! [B: $i] :
~ ( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) )
& ( ( A @ k3_tarski )
!= k1_xboole_0 ) )
& ~ ( ( ( A @ k3_tarski )
= k1_xboole_0 )
& ? [B: $i] :
( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_orders_1) ).
thf(5251,plain,
! [A: $i] :
( ~ ( ! [B: $i] :
~ ( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) )
& ( ( A @ k3_tarski )
!= k1_xboole_0 ) )
& ~ ( ( ( A @ k3_tarski )
= k1_xboole_0 )
& ? [B: $i] :
( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(610,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ v1_finset_1 )
=> ( A @ ( B @ k9_relat_1 ) @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finset_1) ).
thf(5036,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ v1_finset_1 )
=> ( A @ ( B @ k9_relat_1 ) @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(932,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A
= ( A @ a_1_0_domain_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_domain_1) ).
thf(6682,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A
= ( A @ a_1_0_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(2795,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(1181,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( ( B @ ( A @ k9_group_3 ) )
= ( C @ ( A @ k9_group_3 ) ) )
<=> ~ ( C @ ( A @ k9_group_3 ) @ ( B @ ( A @ k9_group_3 ) @ r1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_group_3) ).
thf(7808,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( ~ ( C @ ( A @ k9_group_3 ) @ ( B @ ( A @ k9_group_3 ) @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k9_group_3 ) )
= ( C @ ( A @ k9_group_3 ) ) ) )
& ( ( ( B @ ( A @ k9_group_3 ) )
= ( C @ ( A @ k9_group_3 ) ) )
=> ~ ( C @ ( A @ k9_group_3 ) @ ( B @ ( A @ k9_group_3 ) @ r1_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(1342,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k10_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( D @ ( C @ ( A @ k7_group_4 ) ) @ ( B @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_group_4) ).
thf(8648,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k10_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( D @ ( C @ ( A @ k7_group_4 ) ) @ ( B @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342]) ).
thf(2038,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_group_3 ) ) )
= ( C @ ( B @ ( A @ a_3_0_group_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_group_3) ).
thf(12024,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_group_3 ) ) )
= ( C @ ( B @ ( A @ a_3_0_group_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2038]) ).
thf(918,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funct_1) ).
thf(6612,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(1823,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k6_partfun1 @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ u1_struct_0 @ k6_partfun1 @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k6_partfun1 @ v1_funct_2 ) ) )
& ( A @ u1_struct_0 @ k6_partfun1 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_group_6) ).
thf(11204,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k6_partfun1 @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ u1_struct_0 @ k6_partfun1 @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k6_partfun1 @ v1_funct_2 ) ) )
& ( A @ u1_struct_0 @ k6_partfun1 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1823]) ).
thf(996,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(6929,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(2339,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k1_struct_0 ) )
= ( B @ k1_tarski ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_struct_0 )
| ( A @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[2338]) ).
thf(2340,plain,
! [B: $i,A: $i] :
( ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_struct_0 )
| ( A @ v3_struct_0 )
| ( ( B @ ( A @ k1_struct_0 ) )
= ( B @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[2339]) ).
thf(2037,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ r1_rlvect_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_group_2) ).
thf(12022,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ r1_rlvect_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2037]) ).
thf(3858,plain,
! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ),
inference(cnf,[status(esa)],[3857]) ).
thf(16254,plain,
! [A: $i] : ( A @ k6_partfun1 @ v1_relat_1 ),
inference(rewrite,[status(thm)],[3858,11231]) ).
thf(321,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ ( A @ k16_lattice3 ) )
= ( B @ ( A @ a_2_6_lattice3 ) @ ( A @ k16_lattice3 ) ) )
& ( ( B @ ( A @ k15_lattice3 ) )
= ( B @ ( A @ a_2_5_lattice3 ) @ ( A @ k15_lattice3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattice3) ).
thf(3506,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ ( A @ k16_lattice3 ) )
= ( B @ ( A @ a_2_6_lattice3 ) @ ( A @ k16_lattice3 ) ) )
& ( ( B @ ( A @ k15_lattice3 ) )
= ( B @ ( A @ a_2_5_lattice3 ) @ ( A @ k15_lattice3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(1418,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( B @ ( A @ k6_group_3 ) ) @ m1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_group_3) ).
thf(9083,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( B @ ( A @ k6_group_3 ) ) @ m1_group_2 ) ) )
=> ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) ) )
& ( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( B @ ( A @ k6_group_3 ) ) @ m1_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1418]) ).
thf(642,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ! [E: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( C = F )
& ( B = E ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
<=> ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_filter_0) ).
thf(5200,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ! [E: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( C = F )
& ( B = E ) )
=> ( ( ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ r3_lattices ) ) )
=> ( C @ ( B @ ( A @ r3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ r3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(2001,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k5_group_2 @ ( A @ k6_group_6 ) @ ( A @ ( A @ k5_group_2 @ ( A @ k11_group_6 ) @ v4_group_6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_group_6) ).
thf(11890,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k5_group_2 @ ( A @ k6_group_6 ) @ ( A @ ( A @ k5_group_2 @ ( A @ k11_group_6 ) @ v4_group_6 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2001]) ).
thf(1867,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E = C )
& ( D = B ) )
=> ( ( E @ ( D @ ( A @ k11_group_4 @ k3_lattices ) ) )
= ( C @ ( B @ ( A @ k8_group_4 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_latsubgr) ).
thf(11377,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k11_group_4 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E = C )
& ( D = B ) )
=> ( ( E @ ( D @ ( A @ k11_group_4 @ k3_lattices ) ) )
= ( C @ ( B @ ( A @ k8_group_4 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1867]) ).
thf(1184,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] : ( C @ ( A @ k15_lattice3 ) @ ( B @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ a_3_2_lattice3 ) ) @ ( A @ k15_lattice3 ) @ ( A @ r3_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lattice3) ).
thf(7819,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] : ( C @ ( A @ k15_lattice3 ) @ ( B @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ a_3_2_lattice3 ) ) @ ( A @ k15_lattice3 ) @ ( A @ r3_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(1030,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_0_filter_0 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_0) ).
thf(7076,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_filter_0 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_filter_0 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(986,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k13_group_2 ) ) @ ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k13_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( C @ ( A @ k7_group_2 ) @ r1_tarski ) )
& ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k13_group_2 ) ) @ ( B @ ( C @ ( A @ k13_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( C @ ( A @ k7_group_2 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_group_2) ).
thf(6874,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k13_group_2 ) ) @ ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k13_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( C @ ( A @ k7_group_2 ) @ r1_tarski ) )
& ( B @ ( A @ k3_group_1 ) @ ( C @ ( A @ k13_group_2 ) ) @ ( B @ ( C @ ( A @ k13_group_2 ) ) @ ( A @ k2_group_2 ) ) @ ( C @ ( A @ k7_group_2 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(2127,plain,
! [A: $i] :
( ( A @ v13_lattices )
| ~ ( A @ v17_lattices )
| ( A @ v3_struct_0 )
| ~ ( A @ l3_lattices ) ),
inference(cnfConj,[status(thm)],[2126]) ).
thf(215,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finseq_1) ).
thf(3020,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(361,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ k1_group_1 ) ) )
= ( C @ ( D @ ( B @ k1_group_1 ) ) ) )
=> ( ( D @ ( C @ ( B @ k1_group_1 ) ) @ ( A @ ( B @ k6_group_1 ) ) )
= ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k1_group_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_group_1) ).
thf(3740,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ k1_group_1 ) ) )
= ( C @ ( D @ ( B @ k1_group_1 ) ) ) )
=> ( ( D @ ( C @ ( B @ k1_group_1 ) ) @ ( A @ ( B @ k6_group_1 ) ) )
= ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ k1_group_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(1689,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ v6_group_1 )
=> ( B @ k9_group_1 @ ( C @ ( A @ ( B @ k13_group_6 ) ) @ k9_group_1 @ r1_xreal_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_group_6) ).
thf(10552,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ v6_group_1 )
=> ( B @ k9_group_1 @ ( C @ ( A @ ( B @ k13_group_6 ) ) @ k9_group_1 @ r1_xreal_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1689]) ).
thf(868,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( k5_numbers @ ( k1_numbers @ ( A @ k9_group_1 @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_group_1) ).
thf(6351,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( k5_numbers @ ( k1_numbers @ ( A @ k9_group_1 @ m2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(2353,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(cnf,[status(esa)],[2352]) ).
thf(1205,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ ( B @ ( A @ r3_lattice3 ) ) )
& ( C @ ( B @ r2_hidden ) ) )
=> ( ( C @ ( A @ k16_lattice3 ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_lattice3) ).
thf(7925,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v4_lattice3 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ ( B @ ( A @ r3_lattice3 ) ) )
& ( C @ ( B @ r2_hidden ) ) )
=> ( ( C @ ( A @ k16_lattice3 ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(1468,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( A @ v4_group_1 )
=> ( ( C @ ( B @ ( D @ ( A @ k3_group_2 ) ) @ ( A @ k2_group_2 ) ) )
= ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( D @ ( A @ k3_group_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_group_2) ).
thf(9367,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( A @ v4_group_1 )
=> ( ( C @ ( B @ ( D @ ( A @ k3_group_2 ) ) @ ( A @ k2_group_2 ) ) )
= ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( D @ ( A @ k3_group_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1468]) ).
thf(171,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A = k1_xboole_0 )
<=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finseq_1) ).
thf(2810,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(1871,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ? [D: $i] :
( ( ( D @ u1_struct_0 )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) )
& ( A @ ( D @ m1_group_2 ) ) )
=> ( ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) ) )
& ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( D @ u1_struct_0 )
!= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) ) )
& ( ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_group_2) ).
thf(11390,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ? [D: $i] :
( ( ( D @ u1_struct_0 )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) )
& ( A @ ( D @ m1_group_2 ) ) )
=> ( ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) ) )
& ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( D @ u1_struct_0 )
!= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) ) )
& ( ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) )
= ( B @ ( A @ k7_group_2 ) @ ( C @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1871]) ).
thf(1239,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_zfmisc_1) ).
thf(8066,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(1548,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_0_group_3 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i,F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k2_group_3 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_group_3) ).
thf(9810,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [E: $i,F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k2_group_3 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_0_group_3 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_0_group_3 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k2_group_3 ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1548]) ).
thf(1690,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ k4_group_3 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( A
= ( C @ ( E @ ( B @ k2_group_3 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_group_3) ).
thf(10554,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( A
= ( C @ ( E @ ( B @ k2_group_3 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ ( B @ k4_group_3 ) ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( D @ ( B @ k4_group_3 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( A
= ( C @ ( E @ ( B @ k2_group_3 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1690]) ).
thf(410,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v14_lattices )
=> ( B @ ( A @ k8_filter_0 ) @ v14_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_filter_0) ).
thf(3974,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v14_lattices )
=> ( B @ ( A @ k8_filter_0 ) @ v14_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_xboole_1) ).
thf(3025,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(1088,axiom,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r2_hidden ) )
<=> ( ( A != B )
& ( B @ ( A @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_card_1) ).
thf(7352,plain,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( ( ( A != B )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r2_hidden ) ) )
& ( ( B @ ( A @ r2_hidden ) )
=> ( ( A != B )
& ( B @ ( A @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(951,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_relat_1) ).
thf(6750,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(819,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= ( A @ k1_tarski ) )
=> ( ( B @ k2_relat_1 )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_1) ).
thf(6099,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= ( A @ k1_tarski ) )
=> ( ( B @ k2_relat_1 )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(1743,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ( ( B @ ( np__0 @ k2_group_4 @ ( B @ k3_finseq_1 @ ( k4_numbers @ k1_finsop_1 ) ) @ ( A @ k4_group_4 ) ) )
= ( A @ k2_group_1 @ ( B @ k3_finseq_1 @ ( A @ u1_struct_0 @ k1_finsop_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_group_4) ).
thf(10836,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ( ( B @ ( np__0 @ k2_group_4 @ ( B @ k3_finseq_1 @ ( k4_numbers @ k1_finsop_1 ) ) @ ( A @ k4_group_4 ) ) )
= ( A @ k2_group_1 @ ( B @ k3_finseq_1 @ ( A @ u1_struct_0 @ k1_finsop_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1743]) ).
thf(1409,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ m1_group_2 ) )
& ( A @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ v1_group_3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_group_4) ).
thf(9038,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ m1_group_2 ) )
& ( A @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ v1_group_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409]) ).
thf(7987,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(cnf,[status(esa)],[7986]) ).
thf(13672,plain,
! [B: $i,A: $i] :
( ( ( A @ k6_finseq_1 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7959,9500]) ).
thf(13673,plain,
! [B: $i,A: $i] :
( ( A @ k6_finseq_1 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13672]) ).
thf(13682,plain,
! [B: $i,A: $i] :
( ( A @ k6_finseq_1 )
!= ( B @ k1_tarski ) ),
inference(simp,[status(thm)],[13673]) ).
thf(15662,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[13682,10243]) ).
thf(2064,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k7_group_3 ) )
= ( C @ ( A @ k7_group_3 ) ) )
<=> ~ ( C @ ( A @ k7_group_3 ) @ ( B @ ( A @ k7_group_3 ) @ r1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_group_3) ).
thf(12134,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ~ ( C @ ( A @ k7_group_3 ) @ ( B @ ( A @ k7_group_3 ) @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k7_group_3 ) )
= ( C @ ( A @ k7_group_3 ) ) ) )
& ( ( ( B @ ( A @ k7_group_3 ) )
= ( C @ ( A @ k7_group_3 ) ) )
=> ~ ( C @ ( A @ k7_group_3 ) @ ( B @ ( A @ k7_group_3 ) @ r1_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2064]) ).
thf(1988,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ v7_group_1 )
& ( B @ v4_group_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_group_2) ).
thf(11839,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( B @ v7_group_1 )
& ( B @ v4_group_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1988]) ).
thf(736,axiom,
! [A: $i] : ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ k6_relat_1 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relset_1) ).
thf(5668,plain,
! [A: $i] : ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ k6_relat_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(834,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( B @ ( C @ ( A @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_enumset1) ).
thf(6155,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( D @ ( B @ ( C @ ( A @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(967,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k1_funct_4 ) )
= ( C @ ( A @ k1_funct_4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_funct_4) ).
thf(6807,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k1_funct_4 ) )
= ( C @ ( A @ k1_funct_4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(1062,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_group_3 ) ) )
= ( B @ ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k3_group_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_group_3) ).
thf(7227,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_group_3 ) ) )
= ( B @ ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( A @ k3_group_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(1541,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( A @ ( B @ v2_group_4 ) )
=> ( B @ ( A @ k6_group_4 @ m1_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_group_4) ).
thf(9763,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ v1_group_1 ) )
=> ( ( A @ ( B @ v2_group_4 ) )
=> ( B @ ( A @ k6_group_4 @ m1_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1541]) ).
thf(1973,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_group_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_group_2) ).
thf(11794,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_group_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1973]) ).
thf(731,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( B @ ( A @ k9_filter_0 ) ) )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_filter_1) ).
thf(5637,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( B @ ( A @ k9_filter_0 ) ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(391,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m1_lattice4 ) ) )
=> ( ( B @ ( A @ ( E @ v1_lattice4 ) ) )
=> ( ( D @ ( C @ ( A @ r3_lattices ) ) )
<=> ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_lattice4) ).
thf(3869,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m1_lattice4 ) ) )
=> ( ( B @ ( A @ ( E @ v1_lattice4 ) ) )
=> ( ( ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) )
=> ( D @ ( C @ ( A @ r3_lattices ) ) ) )
& ( ( D @ ( C @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(1770,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( E @ ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( E @ ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ ( C @ k6_group_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_group_6) ).
thf(10988,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l1_group_1 )
& ( C @ v4_group_1 )
& ( C @ v3_group_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_group_6 ) ) )
& ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( A @ ( B @ k6_group_1 ) ) @ ( E @ ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( E @ ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ ( C @ k6_group_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1770]) ).
thf(847,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
| ( B @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(6209,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
| ( B @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(21970,plain,
! [A: $i] :
( ( A != sk259 )
| ( k1_xboole_0 @ v4_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,6221]) ).
thf(21971,plain,
( ( k1_xboole_0 @ v4_group_1 )
| ( sk259 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[21970:[bind(A,$thf( sk259 ))]]) ).
thf(1367,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_funct_2) ).
thf(8758,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).
thf(22201,plain,
! [A: $i] :
( ( A != sk385 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,12429]) ).
thf(22202,plain,
! [A: $i] :
( ( A != sk385 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[22201]) ).
thf(22203,plain,
sk385 @ sk149 @ v1_funct_1,
inference(pattern_uni,[status(thm)],[22202:[bind(A,$thf( sk385 ))]]) ).
thf(1456,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k8_group_3 ) @ k1_card_1 )
= ( B @ ( A @ k10_group_3 ) @ ( A @ k16_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_group_3) ).
thf(9314,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k8_group_3 ) @ k1_card_1 )
= ( B @ ( A @ k10_group_3 ) @ ( A @ k16_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_xboole_1) ).
thf(4484,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(1490,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k10_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( D @ ( A @ k7_group_2 ) @ ( C @ ( A @ k11_group_2 ) ) @ ( B @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_group_2) ).
thf(9446,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k10_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( D @ ( A @ k7_group_2 ) @ ( C @ ( A @ k11_group_2 ) ) @ ( B @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1490]) ).
thf(19102,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk81 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,15540]) ).
thf(19103,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk81 ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[19102]) ).
thf(19104,plain,
! [A: $i] :
~ ( A @ sk81 @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[19103:[bind(A,$thf( C @ sk81 )),bind(B,$thf( C ))]]) ).
thf(19452,plain,
! [A: $i] :
~ ( A @ sk81 @ v1_xboole_0 ),
inference(simp,[status(thm)],[19104]) ).
thf(726,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k7_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_filter_0) ).
thf(5623,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k7_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(6344,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[6342]) ).
thf(6347,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[6344]) ).
thf(6348,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[6347]) ).
thf(1746,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(10845,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1746]) ).
thf(1414,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_funct_2) ).
thf(9055,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1414]) ).
thf(1166,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_domain_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_domain_1) ).
thf(7755,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_domain_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(1881,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_group_1) ).
thf(11425,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_group_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1881]) ).
thf(892,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_setfam_1 ) @ r1_tarski ) )
<=> ( C @ ( A @ k7_setfam_1 ) @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_setfam_1) ).
thf(6452,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k7_setfam_1 ) @ ( B @ r1_tarski ) )
=> ( C @ ( B @ ( A @ k7_setfam_1 ) @ r1_tarski ) ) )
& ( ( C @ ( B @ ( A @ k7_setfam_1 ) @ r1_tarski ) )
=> ( C @ ( A @ k7_setfam_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_funct_2) ).
thf(3886,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(1582,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_zfmisc_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(9992,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( A @ ( C @ r1_tarski ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) )
=> ( B
= ( A @ k1_zfmisc_1 ) ) )
& ( ( B
= ( A @ k1_zfmisc_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ r1_tarski ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1582]) ).
thf(1032,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_group_3 ) )
= ( B @ ( A @ k6_group_2 @ ( A @ k7_group_2 ) @ ( A @ k5_group_3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_group_3) ).
thf(7088,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_group_3 ) )
= ( B @ ( A @ k6_group_2 @ ( A @ k7_group_2 ) @ ( A @ k5_group_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(761,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( ( B @ ( C @ ( A @ k4_funct_2 ) ) )
= B ) )
=> ( C
= ( A @ k6_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_funct_2) ).
thf(5821,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( ( B @ ( C @ ( A @ k4_funct_2 ) ) )
= B ) )
=> ( C
= ( A @ k6_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(592,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( B @ ( C @ ( A @ k4_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(4936,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( B @ ( C @ ( A @ k4_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(695,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ ( B @ r4_lattice3 ) ) )
<=> ( C @ ( B @ k4_lattice3 ) @ ( A @ ( B @ k3_lattice3 @ r2_lattice3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lattice3) ).
thf(5468,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ k4_lattice3 ) @ ( A @ ( B @ k3_lattice3 @ r2_lattice3 ) ) )
=> ( A @ ( C @ ( B @ r4_lattice3 ) ) ) )
& ( ( A @ ( C @ ( B @ r4_lattice3 ) ) )
=> ( C @ ( B @ k4_lattice3 ) @ ( A @ ( B @ k3_lattice3 @ r2_lattice3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(1070,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_xboole_1) ).
thf(7263,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(821,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ r2_hidden ) )
& ( D @ v2_funct_1 ) )
=> ( ( ( C @ ( D @ k1_funct_1 ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
= C )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funct_2) ).
thf(6109,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ r2_hidden ) )
& ( D @ v2_funct_1 ) )
=> ( ( ( C @ ( D @ k1_funct_1 ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
= C )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(1469,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(9370,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469]) ).
thf(1732,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k3_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( C @ ( D @ ( A @ k10_group_2 ) ) @ ( B @ ( A @ k3_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_group_3) ).
thf(10773,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k3_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( C @ ( D @ ( A @ k10_group_2 ) ) @ ( B @ ( A @ k3_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1732]) ).
thf(849,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k5_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_subset_1) ).
thf(6222,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k5_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k6_filter_0 ) ) @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_filter_0) ).
thf(2699,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k6_filter_0 ) ) @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(317,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_relat_1) ).
thf(3494,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(1054,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( D @ ( C @ ( A @ k7_group_4 ) ) @ ( A @ k2_group_2 ) ) )
= ( B @ ( D @ ( A @ k11_group_2 ) ) @ ( C @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_group_4) ).
thf(7176,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( B @ ( D @ ( C @ ( A @ k7_group_4 ) ) @ ( A @ k2_group_2 ) ) )
= ( B @ ( D @ ( A @ k11_group_2 ) ) @ ( C @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(92,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r5_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_binop_1) ).
thf(2484,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r4_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r5_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r5_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(825,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= A )
& ( ( C @ ( B @ ( A @ k4_funct_2 ) ) )
= B ) )
=> ( C
= ( A @ k6_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_funct_2) ).
thf(6126,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= A )
& ( ( C @ ( B @ ( A @ k4_funct_2 ) ) )
= B ) )
=> ( C
= ( A @ k6_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(513,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_realset1 ) @ v1_funct_1 )
& ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_realset1) ).
thf(4501,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_realset1 ) @ v1_funct_1 )
& ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(402,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) )
=> ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_filter_1) ).
thf(3918,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) )
=> ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(1134,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(7563,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(482,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k7_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(4363,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k7_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(924,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 )
= ( A @ k5_lattices @ ( A @ k2_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_filter_0) ).
thf(6658,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 )
= ( A @ k5_lattices @ ( A @ k2_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(2372,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( A @ r1_lattices ) ) )
| ~ ( C @ ( D @ r2_hidden ) )
| ~ ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2371]) ).
thf(1883,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k7_group_1 ) )
= np__1 )
=> ( B
= ( A @ k2_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_group_1) ).
thf(11430,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k7_group_1 ) )
= np__1 )
=> ( B
= ( A @ k2_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1883]) ).
thf(1840,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_group_1 @ ( A @ u1_struct_0 @ k6_finseqop ) )
= ( A @ k4_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_group_1) ).
thf(11276,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_group_1 @ ( A @ u1_struct_0 @ k6_finseqop ) )
= ( A @ k4_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1840]) ).
thf(2067,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( B @ ( C @ ( A @ k8_group_2 ) ) @ ( C @ ( B @ ( A @ k8_group_2 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_group_2) ).
thf(12144,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( B @ ( C @ ( A @ k8_group_2 ) ) @ ( C @ ( B @ ( A @ k8_group_2 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2067]) ).
thf(660,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( B @ ( D @ ( C @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_enumset1) ).
thf(5344,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) )
= ( A @ ( B @ ( D @ ( C @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(888,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ~ ( ( ( ( D @ ( C @ r2_hidden ) )
& ~ ( D @ ( B @ r2_hidden ) ) )
| ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) ) )
& ( A @ ( D @ v1_filter_0 ) ) ) )
& ( B != C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_filter_0) ).
thf(6424,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ~ ( ( ( ( D @ ( C @ r2_hidden ) )
& ~ ( D @ ( B @ r2_hidden ) ) )
| ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) ) )
& ( A @ ( D @ v1_filter_0 ) ) ) )
& ( B != C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(1846,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= ( B @ ( D @ ( A @ k1_group_1 ) ) ) )
| ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( D @ ( B @ ( A @ k1_group_1 ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_group_1) ).
thf(11298,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( B @ ( C @ ( A @ k1_group_1 ) ) )
= ( B @ ( D @ ( A @ k1_group_1 ) ) ) )
| ( ( C @ ( B @ ( A @ k1_group_1 ) ) )
= ( D @ ( B @ ( A @ k1_group_1 ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1846]) ).
thf(17074,plain,
! [A: $i] :
( ( ( sk510 @ l1_lattices )
!= ( A @ l1_lattices ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17028,4291]) ).
thf(17075,plain,
! [A: $i] :
( ( ( sk510 @ l1_lattices )
!= ( A @ l1_lattices ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[17074]) ).
thf(17076,plain,
sk510 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[17075:[bind(A,$thf( sk510 ))]]) ).
thf(1741,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( C @ ( B @ ( A @ k9_group_6 ) ) @ ( B @ k5_group_4 ) @ ( C @ ( B @ ( A @ k13_group_6 ) ) @ ( B @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_group_6) ).
thf(10817,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( C @ ( B @ ( A @ k9_group_6 ) ) @ ( B @ k5_group_4 ) @ ( C @ ( B @ ( A @ k13_group_6 ) ) @ ( B @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1741]) ).
thf(518,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ a_2_2_domain_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_domain_1) ).
thf(4533,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ a_2_2_domain_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(399,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_relat_1) ).
thf(3901,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(22188,plain,
! [A: $i] :
( ( A != sk335 )
| ( k1_xboole_0 @ l1_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,7435]) ).
thf(22189,plain,
( ( k1_xboole_0 @ l1_group_1 )
| ( sk335 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22188:[bind(A,$thf( sk335 ))]]) ).
thf(1561,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ v6_group_1 )
=> ( B @ ( A @ k9_group_3 ) @ v1_finset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t133_group_3) ).
thf(9870,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ v6_group_1 )
=> ( B @ ( A @ k9_group_3 ) @ v1_finset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1561]) ).
thf(4565,plain,
sk152 @ v1_finset_1,
inference(cnfConj,[status(thm)],[4562]) ).
thf(14338,plain,
! [B: $i,A: $i] :
( ( ( sk152 @ v1_finset_1 )
!= ( A @ v1_finset_1 ) )
| ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4565,2181]) ).
thf(14339,plain,
! [B: $i,A: $i] :
( ( ( sk152 @ v1_finset_1 )
!= ( A @ v1_finset_1 ) )
| ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(simp,[status(thm)],[14338]) ).
thf(14340,plain,
! [A: $i] : ( A @ ( sk152 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(pattern_uni,[status(thm)],[14339:[bind(A,$thf( sk152 ))]]) ).
thf(14344,plain,
! [A: $i] : ( A @ ( sk152 @ k4_xboole_0 ) @ v1_finset_1 ),
inference(simp,[status(thm)],[14340]) ).
thf(14787,plain,
! [B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
!= ( B @ ( sk152 @ k4_xboole_0 ) ) )
| ( k1_xboole_0 @ v1_finset_1 ) ),
inference(paramod_ordered,[status(thm)],[2990,14344]) ).
thf(14789,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( sk152 != k1_xboole_0 )
| ( k1_xboole_0 @ v1_finset_1 ) ),
inference(simp,[status(thm)],[14787]) ).
thf(14792,plain,
( ( sk152 != k1_xboole_0 )
| ( k1_xboole_0 @ v1_finset_1 ) ),
inference(simp,[status(thm)],[14789]) ).
thf(19981,plain,
( ( k1_xboole_0 != k1_xboole_0 )
| ( k1_xboole_0 @ v1_finset_1 ) ),
inference(rewrite,[status(thm)],[14792,18029]) ).
thf(19982,plain,
k1_xboole_0 @ v1_finset_1,
inference(simp,[status(thm)],[19981]) ).
thf(1260,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m4_vectsp_8 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m4_vectsp_8) ).
thf(8184,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m4_vectsp_8 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(629,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(5155,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(1675,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ ( B @ v2_group_4 ) )
<=> ( ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ m1_group_2 ) )
=> ( ( C
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) )
| ( ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) )
= C ) ) ) )
& ( ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) )
!= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_group_4) ).
thf(10482,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ( ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ m1_group_2 ) )
=> ( ( C
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) )
| ( ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) )
= C ) ) ) )
& ( ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) )
!= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) ) )
=> ( A @ ( B @ v2_group_4 ) ) )
& ( ( A @ ( B @ v2_group_4 ) )
=> ( ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ m1_group_2 ) )
=> ( ( C
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) )
| ( ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) )
= C ) ) ) )
& ( ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) )
!= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1675]) ).
thf(1091,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v3_group_6 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= D )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_group_6) ).
thf(7367,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ( B @ v1_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_group_6 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v3_group_6 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= D )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(3580,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(1006,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k4_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( B @ ( D @ ( A @ k12_group_2 ) ) @ ( C @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_group_3) ).
thf(6961,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k4_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( B @ ( D @ ( A @ k12_group_2 ) ) @ ( C @ ( A @ k2_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(17614,plain,
! [A: $i] :
( ( ( sk537 @ l2_struct_0 )
!= ( A @ l2_struct_0 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10370,6063]) ).
thf(17615,plain,
! [A: $i] :
( ( ( sk537 @ l2_struct_0 )
!= ( A @ l2_struct_0 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[17614]) ).
thf(17616,plain,
sk537 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[17615:[bind(A,$thf( sk537 ))]]) ).
thf(466,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
<=> ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k1_funct_4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funct_4) ).
thf(4274,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k1_funct_4 ) ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k1_funct_4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(1789,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k4_lattice3 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice3) ).
thf(11086,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k4_lattice3 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1789]) ).
thf(2317,plain,
! [B: $i,A: $i] :
( ( A @ v4_lattice3 )
| ( A @ u1_struct_0 @ ( A @ ( B @ sk9 ) @ m1_subset_1 ) )
| ~ ( A @ sk8 @ ( B @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[2314]) ).
thf(2321,plain,
! [B: $i,A: $i] :
( ( A @ v4_lattice3 )
| ( A @ u1_struct_0 @ ( A @ ( B @ sk9 ) @ m1_subset_1 ) )
| ~ ( A @ sk8 @ ( B @ ( A @ r4_lattice3 ) ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[2317]) ).
thf(1478,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k13_group_2 ) ) @ ( B @ r2_hidden ) )
& ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_group_2) ).
thf(9399,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ ( C @ ( A @ k13_group_2 ) ) @ ( B @ r2_hidden ) )
& ( B @ ( C @ ( A @ k12_group_2 ) ) @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1478]) ).
thf(835,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
<=> ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_realset1) ).
thf(6158,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m2_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(1583,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ u1_struct_0 @ ( A @ u2_struct_0 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_struct_0) ).
thf(10013,plain,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ u1_struct_0 @ ( A @ u2_struct_0 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1583]) ).
thf(1834,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( B @ u1_struct_0 )
= ( C @ u1_struct_0 ) )
=> ( ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) )
= ( C @ u1_group_1 @ ( C @ u1_struct_0 @ g1_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_group_2) ).
thf(11251,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( ( B @ u1_struct_0 )
= ( C @ u1_struct_0 ) )
=> ( ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) )
= ( C @ u1_group_1 @ ( C @ u1_struct_0 @ g1_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1834]) ).
thf(22150,plain,
! [A: $i] :
( ( A != sk605 )
| ( k1_xboole_0 @ l1_group_1 )
| ( A @ sk149 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[4548,11435]) ).
thf(22151,plain,
( ( k1_xboole_0 @ l1_group_1 )
| ( sk605 @ sk149 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[22150:[bind(A,$thf( sk605 ))]]) ).
thf(1396,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ k2_zfmisc_1 ) @ ( B @ ( A @ k5_group_6 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ k2_zfmisc_1 ) @ ( B @ ( A @ k5_group_6 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k5_group_6 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_group_6) ).
thf(8991,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ k2_zfmisc_1 ) @ ( B @ ( A @ k5_group_6 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ ( B @ ( A @ k4_group_6 ) @ k2_zfmisc_1 ) @ ( B @ ( A @ k5_group_6 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k5_group_6 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_partfun1) ).
thf(3299,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(752,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(5789,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(16428,plain,
! [A: $i] :
( ( ( sk605 @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11435,4961]) ).
thf(16429,plain,
! [A: $i] :
( ( ( sk605 @ l1_group_1 )
!= ( A @ l1_group_1 ) )
| ( A @ l1_struct_0 ) ),
inference(simp,[status(thm)],[16428]) ).
thf(16430,plain,
sk605 @ l1_struct_0,
inference(pattern_uni,[status(thm)],[16429:[bind(A,$thf( sk605 ))]]) ).
thf(596,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_xboole_1) ).
thf(4949,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(830,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lattice4) ).
thf(6145,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(18284,plain,
! [A: $i] :
( ( A
!= ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7167,4585]) ).
thf(18285,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[18284:[bind(A,$thf( k33_binop_2 @ ( k1_numbers @ g1_group_1 ) ))]]) ).
thf(1363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(8741,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363]) ).
thf(941,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m2_finseq_1 ) )
=> ~ ( ( B
= ( D @ ( C @ ( A @ k12_finseq_1 ) @ ( A @ k8_finseq_1 ) ) ) )
& ( C
= ( np__1 @ ( B @ k1_funct_1 ) ) ) ) ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_finseq_3) ).
thf(6718,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m2_finseq_1 ) )
=> ~ ( ( B
= ( D @ ( C @ ( A @ k12_finseq_1 ) @ ( A @ k8_finseq_1 ) ) ) )
& ( C
= ( np__1 @ ( B @ k1_funct_1 ) ) ) ) ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(2022,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_group_1 @ ( B @ ( A @ k4_group_3 ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_group_3) ).
thf(11985,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_group_1 @ ( B @ ( A @ k4_group_3 ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2022]) ).
thf(1730,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) )
= ( C @ ( B @ k3_xboole_0 ) @ ( A @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_xboole_1) ).
thf(10763,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) )
= ( C @ ( B @ k3_xboole_0 ) @ ( A @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1730]) ).
thf(450,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_lattices ) @ ( A @ k7_lattices ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattices) ).
thf(4161,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_lattices ) @ ( A @ k7_lattices ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(686,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_1) ).
thf(5436,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(1758,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_2) ).
thf(10900,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1758]) ).
thf(1377,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ k1_group_3 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k9_group_3 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( E @ ( B @ ( A @ r5_group_3 ) ) )
& ( D = E )
& ( A @ ( E @ m1_group_2 ) )
& ( E @ v1_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_group_3) ).
thf(8829,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ k1_group_3 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( ? [E: $i] :
( ( E @ ( B @ ( A @ r5_group_3 ) ) )
& ( D = E )
& ( A @ ( E @ m1_group_2 ) )
& ( E @ v1_group_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( E @ ( B @ ( A @ r5_group_3 ) ) )
& ( D = E )
& ( A @ ( E @ m1_group_2 ) )
& ( E @ v1_group_1 ) ) ) )
=> ( C
= ( B @ ( A @ k9_group_3 ) ) ) )
& ( ( C
= ( B @ ( A @ k9_group_3 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( E @ ( B @ ( A @ r5_group_3 ) ) )
& ( D = E )
& ( A @ ( E @ m1_group_2 ) )
& ( E @ v1_group_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( E @ ( B @ ( A @ r5_group_3 ) ) )
& ( D = E )
& ( A @ ( E @ m1_group_2 ) )
& ( E @ v1_group_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377]) ).
thf(77,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( A @ ( B @ ( C @ v1_lattice4 ) ) ) )
=> ( F @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattice4) ).
thf(2438,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( A @ ( B @ ( C @ v1_lattice4 ) ) ) )
=> ( F @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_1) ).
thf(4752,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_partfun1) ).
thf(4313,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(304,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( A @ k3_subset_1 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(3443,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( A @ k3_subset_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(1737,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ u1_struct_0 @ k12_finseq_1 ) @ ( A @ k2_group_4 @ ( k4_numbers @ k12_finseq_1 ) @ ( B @ k4_group_4 ) ) )
= ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ u1_struct_0 @ k12_finseq_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_group_4) ).
thf(10800,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ u1_struct_0 @ k12_finseq_1 ) @ ( A @ k2_group_4 @ ( k4_numbers @ k12_finseq_1 ) @ ( B @ k4_group_4 ) ) )
= ( C @ ( A @ ( B @ k6_group_1 ) ) @ ( B @ u1_struct_0 @ k12_finseq_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1737]) ).
thf(1036,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k8_group_4 ) ) )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k5_group_4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_group_4) ).
thf(7108,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( C @ ( B @ ( A @ k8_group_4 ) ) )
= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k5_group_4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(968,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finset_1) ).
thf(6810,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(1275,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( D @ ( C @ ( A @ k7_group_4 ) ) @ ( B @ ( A @ k4_group_2 ) ) )
= ( B @ ( D @ ( A @ k13_group_2 ) ) @ ( C @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_group_4) ).
thf(8264,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( D @ ( C @ ( A @ k7_group_4 ) ) @ ( B @ ( A @ k4_group_2 ) ) )
= ( B @ ( D @ ( A @ k13_group_2 ) ) @ ( C @ ( A @ k11_group_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(955,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_zfmisc_1 @ k4_subset_1 ) ) @ ( A @ k7_setfam_1 ) )
= ( C @ ( A @ k7_setfam_1 ) @ ( B @ ( A @ k7_setfam_1 ) @ ( A @ k1_zfmisc_1 @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_setfam_1) ).
thf(6761,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_zfmisc_1 @ k4_subset_1 ) ) @ ( A @ k7_setfam_1 ) )
= ( C @ ( A @ k7_setfam_1 ) @ ( B @ ( A @ k7_setfam_1 ) @ ( A @ k1_zfmisc_1 @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(1248,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ ( A @ k7_group_4 ) ) )
= ( B @ ( C @ ( A @ k7_group_4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_group_4) ).
thf(8130,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( B @ v1_group_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( A @ ( C @ v1_group_3 ) )
& ( C @ v1_group_1 ) )
=> ( ( C @ ( B @ ( A @ k7_group_4 ) ) )
= ( B @ ( C @ ( A @ k7_group_4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(1780,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( C @ l3_lattices )
& ( C @ v5_lattice3 )
& ( C @ v4_lattice3 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_7_lattice3 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( C @ k4_lattices ) ) ) )
& ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_7_lattice3) ).
thf(11048,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( C @ l3_lattices )
& ( C @ v5_lattice3 )
& ( C @ v4_lattice3 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( C @ k4_lattices ) ) ) )
& ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_7_lattice3 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_7_lattice3 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( C @ k4_lattices ) ) ) )
& ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1780]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_xboole_0 ) @ ( C @ k3_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relset_1) ).
thf(2453,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_xboole_0 ) @ ( C @ k3_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1718,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k8_group_1 @ ( C @ ( A @ ( B @ k13_group_6 ) ) @ k8_group_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_group_6) ).
thf(10686,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_group_6 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k8_group_1 @ ( C @ ( A @ ( B @ k13_group_6 ) ) @ k8_group_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1718]) ).
thf(578,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_relat_1 @ k9_relat_1 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t162_funct_1) ).
thf(4863,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_relat_1 @ k9_relat_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(2349,plain,
~ ? [A: $i,B: $i] :
( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(miniscope,[status(thm)],[2348]) ).
thf(2350,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 )
| ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[2349]) ).
thf(2351,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 )
| ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[2350]) ).
thf(829,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k4_subset_1 ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(6141,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k4_subset_1 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(1450,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_lattice4 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_lattice4) ).
thf(9286,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_lattice4 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) @ k2_funct_1 )
= ( A @ ( B @ ( C @ k2_funct_1 @ k3_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_partfun1) ).
thf(2993,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) @ k2_funct_1 )
= ( A @ ( B @ ( C @ k2_funct_1 @ k3_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(805,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= B )
& ( C @ v2_funct_1 ) )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funct_2) ).
thf(6035,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= B )
& ( C @ v2_funct_1 ) )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(2191,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[2190]) ).
thf(927,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( C @ ( B @ r1_partfun1 ) ) )
=> ( ( A @ ( C @ ( B @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_4) ).
thf(6668,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( C @ ( B @ r1_partfun1 ) ) )
=> ( ( A @ ( C @ ( B @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(1975,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( ( D @ ( B @ m1_group_2 ) )
& ( C @ ( B @ m1_group_2 ) ) )
=> ( D @ ( C @ ( A @ k9_group_2 ) ) @ ( B @ m1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_group_2) ).
thf(11799,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_group_2 ) )
=> ( ( ( D @ ( B @ m1_group_2 ) )
& ( C @ ( B @ m1_group_2 ) ) )
=> ( D @ ( C @ ( A @ k9_group_2 ) ) @ ( B @ m1_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1975]) ).
thf(859,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ k3_tarski @ r1_tarski ) ) )
=> ( B @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_setfam_1) ).
thf(6265,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ k3_tarski @ r1_tarski ) ) )
=> ( B @ ( C @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(10161,plain,
sk522 @ v1_card_1,
inference(cnf,[status(esa)],[10160]) ).
thf(2048,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ k5_group_2 )
= ( C @ k5_group_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_group_2) ).
thf(12070,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ( ( B @ k5_group_2 )
= ( C @ k5_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2048]) ).
thf(1994,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k6_group_3 ) ) @ m1_group_2 ) )
& ( C @ ( B @ ( A @ k6_group_3 ) ) @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_group_3) ).
thf(11858,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_group_2 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k6_group_3 ) ) @ m1_group_2 ) )
& ( C @ ( B @ ( A @ k6_group_3 ) ) @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1994]) ).
thf(1904,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k10_group_1 ) ) @ ( A @ k3_group_1 ) )
= ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k3_group_1 ) @ ( A @ k10_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_group_1) ).
thf(11511,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k10_group_1 ) ) @ ( A @ k3_group_1 ) )
= ( C @ ( A @ k3_group_1 ) @ ( B @ ( A @ k3_group_1 ) @ ( A @ k10_group_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1904]) ).
thf(331,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k5_group_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( np__1 @ ( D @ k1_nat_1 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( D @ ( C @ ( B @ ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) @ ( A @ k1_group_1 ) ) ) ) )
& ( ( np__0 @ ( C @ ( B @ ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
= ( A @ k2_group_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_group_1) ).
thf(3553,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( np__1 @ ( D @ k1_nat_1 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( D @ ( C @ ( B @ ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) @ ( A @ k1_group_1 ) ) ) ) )
& ( ( np__0 @ ( C @ ( B @ ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
= ( A @ k2_group_1 ) ) ) )
=> ( B
= ( A @ k5_group_1 ) ) )
& ( ( B
= ( A @ k5_group_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( np__1 @ ( D @ k1_nat_1 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( D @ ( C @ ( B @ ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) @ ( A @ k1_group_1 ) ) ) ) )
& ( ( np__0 @ ( C @ ( B @ ( A @ u1_struct_0 @ ( k5_numbers @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
= ( A @ k2_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(1025,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( D @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( D @ ( C @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( D @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_filter_0) ).
thf(7057,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( D @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( D @ ( C @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( D @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(1727,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
<=> ( B
= ( A @ k1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_subset_1) ).
thf(10750,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B
= ( A @ k1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) )
& ( ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B
= ( A @ k1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1727]) ).
thf(1793,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ( B @ ( A @ k16_group_2 ) )
= ( B @ ( A @ k15_group_2 ) @ k1_card_1 ) )
& ( ( B @ ( A @ k16_group_2 ) )
= ( B @ ( A @ k14_group_2 ) @ k1_card_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t175_group_2) ).
thf(11103,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( ( B @ ( A @ k16_group_2 ) )
= ( B @ ( A @ k15_group_2 ) @ k1_card_1 ) )
& ( ( B @ ( A @ k16_group_2 ) )
= ( B @ ( A @ k14_group_2 ) @ k1_card_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1793]) ).
thf(1302,axiom,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_group_1 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_group_1 @ v1_funct_2 ) ) )
& ( A @ u1_group_1 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_group_1) ).
thf(8405,plain,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_group_1 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_group_1 @ v1_funct_2 ) ) )
& ( A @ u1_group_1 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).
thf(1320,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( B
= ( C @ u1_struct_0 ) )
=> ( C @ ( B @ ( A @ k5_group_4 ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_latsubgr) ).
thf(8538,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( ( B
= ( C @ u1_struct_0 ) )
=> ( C @ ( B @ ( A @ k5_group_4 ) @ ( A @ r1_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320]) ).
thf(1909,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ ( A @ m1_group_2 ) ) )
=> ( ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) )
= ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_group_2) ).
thf(11529,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_group_1 )
& ( B @ v4_group_1 )
& ( B @ v3_group_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ ( B @ m1_group_2 ) )
& ( B @ ( A @ m1_group_2 ) ) )
=> ( ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) )
= ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1909]) ).
thf(817,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ v2_funct_1 )
& ( ( A @ ( B @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) ) )
=> ( B @ k2_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_1) ).
thf(6094,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ v2_funct_1 )
& ( ( A @ ( B @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) ) )
=> ( B @ k2_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(717,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_lattice4 ) )
=> ( A @ ( B @ m2_lattice4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_lattice4) ).
thf(5574,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_lattice4 ) )
=> ( A @ ( B @ m2_lattice4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(988,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ k6_group_2 @ ( A @ k6_group_2 @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) )
& ( A @ k6_group_2 @ ( B @ ( A @ k6_group_2 @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_group_4) ).
thf(6886,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ( A @ k6_group_2 @ ( A @ k6_group_2 @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) )
& ( A @ k6_group_2 @ ( B @ ( A @ k6_group_2 @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(1686,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ r1_rlvect_1 ) ) )
=> ( ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) )
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_group_2) ).
thf(10537,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ r1_rlvect_1 ) ) )
=> ( ( B @ u1_group_1 @ ( B @ u1_struct_0 @ g1_group_1 ) )
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1686]) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_filter_1 ) ) )
=> ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_1) ).
thf(3035,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_filter_1 ) ) )
=> ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(2045,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k6_group_6 ) @ l1_group_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_group_6) ).
thf(12047,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_group_2 ) )
& ( A @ ( B @ v1_group_3 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k6_group_6 ) @ l1_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2045]) ).
thf(2177,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ r5_binop_1 ) ) )
| ~ ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r5_binop_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2175]) ).
thf(1501,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ g1_group_1 ) @ v1_group_1 )
& ~ ( B @ ( A @ g1_group_1 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_group_1) ).
thf(9519,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ g1_group_1 ) @ v1_group_1 )
& ~ ( B @ ( A @ g1_group_1 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1501]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r2_hidden ) )
=> ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_realset1) ).
thf(3669,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r2_hidden ) )
=> ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(1124,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( D @ u1_struct_0 )
!= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) ) )
& ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_group_2) ).
thf(7521,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_group_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_group_2 ) )
=> ~ ( ! [D: $i] :
( ( ( A @ ( D @ m1_group_2 ) )
& ( D @ v1_group_1 ) )
=> ( ( D @ u1_struct_0 )
!= ( C @ ( A @ k7_group_2 ) @ ( B @ ( A @ k7_group_2 ) @ ( A @ k2_group_2 ) ) ) ) )
& ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(1108,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( A @ k1_group_2 ) )
= ( C @ ( A @ k1_group_2 ) @ ( B @ ( A @ k1_group_2 ) @ ( A @ k2_group_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_group_2) ).
thf(7442,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_group_2 ) ) @ ( A @ k1_group_2 ) )
= ( C @ ( A @ k1_group_2 ) @ ( B @ ( A @ k1_group_2 ) @ ( A @ k2_group_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(67655,plain,
$false,
inference(e,[status(thm)],[8536,6836,8186,2612,12116,23105,9864,2280,2163,8607,29599,3873,18768,8960,9405,16261,8930,7766,43305,11472,2744,2889,10373,9273,10166,2295,4571,3345,9653,2341,2306,7890,2336,2131,33543,7569,2778,8288,11192,4262,9648,7445,21993,11186,4062,4899,19101,4729,4022,6651,9754,2876,9833,25552,2412,4290,16427,4183,11313,5390,2463,7798,3397,9685,3830,7990,2499,2595,32341,3449,6074,11998,6555,2331,11763,4682,9965,8639,11620,31455,6566,11385,19451,4877,9091,7396,5131,8077,9437,16248,2250,22485,7409,6744,6798,39484,4408,18678,2363,11175,5444,9241,10658,10387,5454,8005,5898,6587,6063,41461,2309,6576,12426,2117,10198,6944,10446,5168,8723,2231,9373,11043,7008,8797,6695,22457,9604,12172,5000,12299,2776,2659,9383,6219,11409,10567,6813,2527,3040,9769,7322,9120,10331,2248,8118,4807,10711,6441,3910,5173,18652,5793,4960,10244,3108,7198,8271,5265,4215,7781,4614,10294,10876,9572,8988,11440,6017,12013,6732,11080,25039,12193,2607,8915,7669,9494,13655,3017,2195,21899,9956,16645,6391,16424,4403,6764,14347,9212,9526,6505,11112,12244,3745,4739,10181,7573,15013,7405,3332,3942,22434,4884,7556,45238,10358,6359,38887,4220,4528,19110,2184,8057,14726,2316,3446,5146,2712,15755,12158,5713,2627,11160,11239,9356,2459,3121,6551,18240,2580,7871,5782,6336,5178,7716,6804,8012,12077,23159,10991,2146,11549,42441,11786,11816,3895,21781,10341,26108,6046,3276,2575,8303,7400,11684,7168,2348,9292,6872,11613,10078,11588,5903,7761,3335,8911,21467,6236,2216,33590,10427,7944,11436,5977,3766,3994,2985,4496,2227,7136,8133,7235,3088,12303,9379,4803,4124,3281,3466,7856,3140,4030,43693,2173,8678,4607,8330,6102,8546,2516,4156,11481,3880,2136,9013,5750,11151,2531,7592,4467,2405,25559,11977,21701,7311,10248,4511,5352,8583,11491,12154,10719,3043,8178,3820,2654,5953,22493,9300,10903,4439,10326,11949,5429,3976,2328,2916,10935,12197,21903,4743,7914,11667,3425,4866,9099,2735,4422,12122,8996,5883,6538,3131,3116,21835,8225,12286,14718,3046,38931,21975,3342,10865,9332,7683,10251,4224,6878,2501,11944,5274,16067,38731,6350,7771,8785,2274,7652,4778,11448,3776,8919,2682,11178,3125,11200,6676,17613,3542,8069,2185,5160,6713,8208,2562,10606,5640,2488,10174,2897,6662,17581,39044,12161,6332,4568,4984,11416,2466,11628,10469,11473,3713,2356,7665,5279,10655,6130,11760,7862,3517,9800,6365,8674,10665,4771,6071,8907,9420,11641,11232,2857,11463,5214,22161,11331,2169,8902,2403,15028,11264,11285,4194,11609,5127,6502,11564,11538,4179,5193,4664,5397,8600,4317,3084,8367,43993,7436,38908,3657,11132,7215,11991,4952,4383,23064,4460,9497,10117,11716,8037,7633,4793,4507,4400,7965,4514,9661,11404,21791,9475,11495,11139,7500,11740,10025,4595,10309,16255,2469,6419,6964,5541,31143,2178,11163,39519,4411,10913,10519,6259,9204,22481,9854,2237,10729,6002,11821,9298,8190,33008,10419,7786,11441,12018,5663,9283,2324,8029,9336,5888,5084,5597,7290,23115,30253,2996,22127,8416,11293,2782,4820,3163,7441,2451,9548,7986,60718,3473,6189,6135,5680,9837,5946,3438,4147,3525,12105,10757,11083,6054,21427,2291,11709,10786,6841,2254,8642,2540,9415,8018,9680,4871,11446,3093,5135,4798,13543,4686,2335,7139,6438,2777,3152,9781,3771,4810,6562,8532,9749,8595,5384,9914,10233,5665,5045,5572,7707,11004,11939,6591,31549,7473,40896,11478,7036,6648,2833,3189,2281,6685,12430,6755,8575,5096,6740,7381,3421,10238,11346,7004,6947,7936,11136,11806,2530,6221,12008,11723,6498,3157,5246,12101,2137,3361,3756,4536,59548,2242,2286,9533,21833,3327,10839,4701,3226,11505,11143,12217,16433,5819,11853,9923,7688,10933,5824,4588,6787,12306,9024,60708,5970,2205,22380,6860,21803,10029,7305,7230,5695,8924,7408,9822,9703,5961,4604,12425,6200,9026,8523,10243,7148,6856,3857,5406,5157,6760,9682,3503,4216,11993,4893,3591,7179,4962,7471,3303,8201,4589,6406,8046,3567,12275,8927,10875,6015,7393,20725,8375,7725,11307,9440,3265,7550,7814,9004,21747,5017,3531,11170,2364,2164,5438,12200,3186,6064,7859,6058,2118,14342,26509,7269,11456,7410,6865,5416,22237,2232,2307,3054,2296,4576,9252,5519,10639,6741,8250,12205,11952,2496,12127,4059,12073,27369,12169,2382,6442,3550,4172,11499,5281,22386,11202,3418,4925,3795,16259,2264,17061,11439,7834,7710,8608,19422,11592,10099,4712,6124,11339,7042,18332,8778,6122,2428,5630,5670,4016,10171,2249,9861,6247,6000,8091,10975,4397,9412,8476,11619,6032,7757,2277,6773,5512,9949,21973,7881,5349,7994,2133,11484,11587,11223,12190,5815,11471,4344,4091,3752,9849,4785,4499,3154,3134,4284,6356,10394,5893,5507,5102,8899,6178,22447,11908,2132,2890,4160,4661,17599,2396,11371,7565,3514,12037,4021,3471,3286,5843,31058,6582,8623,2958,4280,10502,2826,10369,2872,11532,2200,2211,2741,3958,8810,9380,13551,5937,8672,8371,2670,3810,5465,9512,6163,4053,4585,2433,2477,4725,3090,7063,8651,8503,8386,7314,4994,10583,7503,10247,8181,2179,3546,5038,10367,4942,9423,2181,22754,4979,2213,11670,3028,3926,2345,10958,6267,2344,2313,3763,22200,4104,9613,9885,10543,12020,22705,4732,11602,2228,3647,10926,5993,5330,10580,8358,4316,2245,2577,14348,5847,11234,6215,7540,5189,3105,5626,2300,8530,7281,3782,10848,7329,8446,8314,2840,2115,5098,2990,6801,2377,6940,4668,2801,7962,6153,4512,2685,5006,5423,18073,8009,10413,6195,6477,4486,9945,2359,2709,5502,3218,4789,8063,18205,8619,8016,9244,7838,11057,7610,3704,11435,2631,10152,4930,10661,5919,20710,9063,5811,11929,12142,11400,10184,8149,11089,5081,6780,10882,2638,7874,7222,11467,2268,10760,11304,4219,5475,5951,6218,11877,4817,12211,8704,6967,7841,8346,3671,3643,2472,9530,4291,11801,8176,2798,4049,6862,17328,5830,9872,3141,7091,3311,8544,7435,10946,6175,43692,22039,12223,4582,2323,8555,3179,9508,3846,16436,6844,8251,7111,10015,11496,10498,5791,10528,2868,7318,10458,8743,5620,22467,8687,10342,4389,5743,17912,4315,3441,2312,10776,2455,10671,10620,16583,11229,10798,2196,2240,9878,11046,59829,6573,4861,2172,10195,10688,6978,9429,10094,3294,7821,4736,8159,8230,11892,7293,12045,15001,9825,7668,7340,2536,12218,11888,10207,11093,10222,2285,6752,5576,11608,11129,3611,9365,2932,7609,3486,2125,3654,9359,10423,6827,6097,11965,5374,5149,2304,12429,2598,12795,5380,2387,23199,7508,5134,3743,5900,11360,8410,10603,2243,6475,5973,12004,3540,10455,7789,11184,9017,8732,10438,11315,10047,10879,3760,6908,3967,2766,17559,9846,10629,12310,21775,11261,11610,5369,3109,7826,10075,11916,4086,8980,11873,21761,7174,41460,11933,4361,5479,5170,8174,4352,11153,6716,5964,5887,8234,8127,55648,3476,2634,6409,3903,5747,5711,2761,12282,8247,8205,5402,7407,3279,4889,10614,10740,9176,4765,11524,4476,9044,9716,11546,8422,9008,8049,3306,7414,2748,10217,10819,6011,11824,12255,9750,9104,26592,4906,2440,11777,2408,2793,11328,11769,9793,2221,7656,2189,6931,9744,10851,3841,7802,10111,5249,5840,2662,7106,9139,4004,2338,18544,4308,2529,8626,7133,11296,7817,2121,11578,3660,4131,11705,5808,17321,9635,5043,8807,8215,5679,2729,3707,10683,22479,5996,18403,2176,4685,2292,9765,3358,6615,2149,2585,9502,2717,6699,11591,8713,7010,8290,8040,7155,11737,9122,12119,6578,5048,11148,11427,10993,3289,7636,18704,4340,3375,7257,7165,11063,3792,7953,6228,5525,5979,12052,7785,12087,3686,8311,11459,9049,11561,2894,7212,4365,22296,2524,7372,2376,59861,4465,34166,10668,11006,17336,7611,9418,4000,10425,10155,3547,5456,21647,5933,3070,2727,11633,3319,3768,11323,21523,8259,55947,6916,2859,6870,2225,6959,4494,11279,12216,21894,17083,6949,8349,3609,10334,2657,4159,22702,11703,7487,8470,2188,7073,11809,11936,3086,11411,11804,7440,38668,3081,9706,3283,2674,24232,3272,4801,8894,8684,11124,5612,12184,4032,2991,11598,12259,10461,9663,34282,17028,10435,2716,4381,5350,6019,5239,11254,9852,2817,21644,10525,12011,2161,12242,7534,11237,12278,9967,22491,5546,2193,5039,3773,10611,9210,4127,2220,5567,4096,2326,6403,8549,22155,8152,5011,3726,3077,4645,10257,7983,8249,8862,7719,3330,2738,11502,8665,10348,33541,11919,11423,5086,8745,3340,12099,3594,11968,3123,2759,3436,8344,7347,21675,2706,7465,30232,5539,23196,7536,2457,12146,9290,29634,6549,6334,9803,10596,12167,11618,11900,11792,24218,4887,3355,7021,20724,5578,2573,3719,11038,2358,6016,21551,9835,11996,8970,12263,4586,11554,2346,12445,3678,12032,2361,2311,9560,3101,10842,6742,2119,10370,10088,12428,5143,4929,10297,11002,10429,7594,3996,2538,7783,4369,11771,9349,7130,2151,2229,11508,12131,12214,12297,12227,2493,2415,8799,10204,9377,6443,10066,63090,6147,2774,6217,6500,12034,6815,8237,2906,6197,7607,6112,8120,5827,10898,16258,3732,2284,2257,9047,8693,2299,8461,18966,5901,9185,11355,5880,43992,10316,6340,7360,9015,10766,4176,3500,3138,2378,5795,8561,6737,11718,16439,11438,11979,4509,11586,7307,2197,11406,9713,10457,6216,12015,9931,6087,59843,11188,7928,2874,11583,11078,6834,20709,10450,2182,43292,5367,9042,6004,60002,7768,22041,11470,11947,11623,4009,2129,2343,10810,8156,5894,11796,9655,11190,12049,11498,4462,9174,11419,5175,8517,2267,11073,4028,6353,7892,5599,8750,10942,8355,17914,11569,10219,18763,7098,6747,2410,5392,2785,7654,2593,6678,3006,8998,8032,11630,2647,2289,5180,6847,11814,9528,43718,9074,29931,10985,2278,2553,6553,7066,39433,2928,8652,8079,11095,5410,5459,2329,2842,6956,5838,3893,7561,2911,4554,24225,11521,2578,22487,8280,7598,9751,5482,5646,6270,2418,8052,6255,7030,9143,2401,6377,2212,22219,11558,22163,5372,2171,6609,25032,7479,11711,5377,5197,2550,6394,2620,10020,10549,9381,11245,3159,2369,7805,41459,12006,7911,11590,2288,17313,10264,11607,2244,3363,11605,10803,3142,9011,10707,11342,7558,26271,7339,2303,12308,5403,2999,9740,3348,5089,4067,5326,4890,11272,11493,8922,2693,7458,11535,11402,9762,9503,9582,8457,6785,6730,6476,15534,10692,3490,4084,7154,10617,4394,10632,7122,3009,7260,10456,5688,2239,21901,13065,4907,6890,9403,7490,17070,6540,5886,9727,2665,47272,14349,4813,7975,6225,7650,2271,38981,9069,9259,3206,41371,2652,4598,10249,10867,16442,10091,9646,11077,2878,12156,2124,8116,10449,11030,7151,4879,8505,4292,9943,6056,7992,8323,23170,5678,4859,2202,12294,9678,3048,2333,2846,2256,2564,9276,12075,3292,2899,6664,5133,11758,22483,12234,10604,4168,6132,7070,3571,5991,2582,17019,11626,9317,2942,5570,11575,4922,10371,10027,15021,4749,7615,6362,9022,19429,5229,12289,7085,2715,3640,17551,7475,6238,7635,5607,4035,11461,9926,5927,5514,6934,17060,8707,427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).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP650+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/10.65 % Computer : n026.cluster.edu
% 0.15/10.65 % Model : x86_64 x86_64
% 0.15/10.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.65 % Memory : 8046.5625MB
% 0.15/10.65 % OS : Linux 6.8.0-71-generic
% 0.15/10.65 % CPULimit : 300
% 0.15/10.65 % WCLimit : 300
% 0.15/10.65 % DateTime : Fri Sep 25 15:28:53 UTC 2026
% 0.15/10.65 % CPUTime :
% 0.15/10.65 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.95/11.24 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 4.62/12.23 % [INFO] Parsing done (985ms).
% 4.62/12.25 % [INFO] Running in sequential loop mode.
% 5.69/12.62 % [INFO] eprover registered as external prover.
% 5.69/12.62 % [INFO] Scanning for conjecture ...
% 7.81/13.15 % [INFO] Found a conjecture (or negated_conjecture) and 5673 axioms. Running axiom selection ...
% 11.14/14.94 % [INFO] Axiom selection finished. Selected 2110 axioms (removed 3563 axioms).
% 14.15/16.20 % [INFO] Problem is first-order (TPTP FOF).
% 14.54/16.30 % [INFO] Type checking passed.
% 14.54/16.31 % [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 ...
% 249.61/86.35 % External prover 'e' found a proof!
% 249.61/86.35 % [INFO] Killing All external provers ...
% 249.61/86.35 % Time passed: 75551ms (effective reasoning time: 74095ms)
% 249.61/86.35 % 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)>
% 249.61/86.36 % 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
% 249.61/86.36 % No. of inferences in proof: 5549
% 249.61/86.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 75551 ms resp. 74095 ms w/o parsing
% 259.90/88.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 259.90/88.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------