%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP642+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:21:31 AM UTC 2026
% Result : Theorem 74.94s 26.39s
% Output : Refutation 81.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1805
% Syntax : Number of formulae : 3612 ( 261 unt; 0 typ; 0 def)
% Number of atoms : 23188 (3312 equ; 0 cnn)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 79183 (2856 ~; 165 |;10637 &;56751 @)
% ( 345 <=>;8429 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 301 ( 299 usr; 15 con; 0-9 aty)
% Number of variables : 10515 ( 0 ^;10058 !; 457 ?;10515 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_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(v1_group_1_decl,type,
v1_group_1: $i > $o ).
thf(m1_group_2_decl,type,
m1_group_2: $i > $i > $o ).
thf(k1_funct_1_decl,type,
k1_funct_1: $i > $i > $i ).
thf(k1_latsubgr_decl,type,
k1_latsubgr: $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $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_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(k1_relat_1_decl,type,
k1_relat_1: $i > $i ).
thf(k3_xboole_0_decl,type,
k3_xboole_0: $i > $i > $i ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k5_relat_1_decl,type,
k5_relat_1: $i > $i > $i ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(r1_partfun1_decl,type,
r1_partfun1: $i > $i > $o ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k2_relat_1_decl,type,
k2_relat_1: $i > $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k1_funct_4_decl,type,
k1_funct_4: $i > $i > $i ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(k10_relat_1_decl,type,
k10_relat_1: $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(k9_relat_1_decl,type,
k9_relat_1: $i > $i > $i ).
thf(k4_finseq_1_decl,type,
k4_finseq_1: $i > $i ).
thf(k11_finseq_1_decl,type,
k11_finseq_1: $i > $i > $i > $i ).
thf(k2_finseq_1_decl,type,
k2_finseq_1: $i > $i ).
thf(np__3_decl,type,
np__3: $i ).
thf(k2_xboole_0_decl,type,
k2_xboole_0: $i > $i > $i ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k1_binop_1_decl,type,
k1_binop_1: $i > $i > $i > $i ).
thf(r1_binop_1_decl,type,
r1_binop_1: $i > $i > $i > $o ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(k10_finseq_1_decl,type,
k10_finseq_1: $i > $i > $i ).
thf(r1_xboole_0_decl,type,
r1_xboole_0: $i > $i > $o ).
thf(v4_ordinal2_decl,type,
v4_ordinal2: $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(r1_xreal_0_decl,type,
r1_xreal_0: $i > $i > $o ).
thf(k14_finseq_1_decl,type,
k14_finseq_1: $i > $i ).
thf(k8_finseq_1_decl,type,
k8_finseq_1: $i > $i > $i > $i ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(k6_setfam_1_decl,type,
k6_setfam_1: $i > $i > $i ).
thf(k2_funct_1_decl,type,
k2_funct_1: $i > $i ).
thf(m2_finseq_1_decl,type,
m2_finseq_1: $i > $i > $o ).
thf(k3_finseq_1_decl,type,
k3_finseq_1: $i > $i ).
thf(k16_finseq_1_decl,type,
k16_finseq_1: $i > $i > $i > $i ).
thf(k1_card_1_decl,type,
k1_card_1: $i > $i ).
thf(k8_setfam_1_decl,type,
k8_setfam_1: $i > $i > $i ).
thf(k1_funct_2_decl,type,
k1_funct_2: $i > $i > $i ).
thf(m1_finseq_1_decl,type,
m1_finseq_1: $i > $i > $o ).
thf(v3_binop_1_decl,type,
v3_binop_1: $i > $i > $o ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(m3_realset1_decl,type,
m3_realset1: $i > $i > $i > $o ).
thf(r2_binop_1_decl,type,
r2_binop_1: $i > $i > $i > $o ).
thf(k1_realset1_decl,type,
k1_realset1: $i > $i > $i ).
thf(r5_binop_1_decl,type,
r5_binop_1: $i > $i > $i > $o ).
thf(np__2_decl,type,
np__2: $i ).
thf(k1_setfam_1_decl,type,
k1_setfam_1: $i > $i ).
thf(l1_rlvect_1_decl,type,
l1_rlvect_1: $i > $o ).
thf(l2_struct_0_decl,type,
l2_struct_0: $i > $o ).
thf(r3_binop_1_decl,type,
r3_binop_1: $i > $i > $i > $o ).
thf(k5_partfun1_decl,type,
k5_partfun1: $i > $i > $i > $i ).
thf(k4_relset_1_decl,type,
k4_relset_1: $i > $i > $i > $i ).
thf(k4_card_1_decl,type,
k4_card_1: $i > $i ).
thf(k4_funct_4_decl,type,
k4_funct_4: $i > $i > $i > $i > $i ).
thf(r7_binop_1_decl,type,
r7_binop_1: $i > $i > $i > $o ).
thf(k7_funct_2_decl,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(v2_binop_1_decl,type,
v2_binop_1: $i > $i > $o ).
thf(m2_realset1_decl,type,
m2_realset1: $i > $i > $i > $o ).
thf(k3_realset1_decl,type,
k3_realset1: $i > $i > $i > $i ).
thf(k1_group_4_decl,type,
k1_group_4: $i > $i > $i > $i ).
thf(r2_wellord2_decl,type,
r2_wellord2: $i > $i > $o ).
thf(np__1_decl,type,
np__1: $i ).
thf(k12_finseq_1_decl,type,
k12_finseq_1: $i > $i > $i ).
thf(k1_partfun1_decl,type,
k1_partfun1: $i > $i > $i > $i > $i > $i > $i ).
thf(k2_xcmplx_0_decl,type,
k2_xcmplx_0: $i > $i > $i ).
thf(np__0_decl,type,
np__0: $i ).
thf(k6_partfun1_decl,type,
k6_partfun1: $i > $i ).
thf(k3_subset_1_decl,type,
k3_subset_1: $i > $i > $i ).
thf(k2_binop_1_decl,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k7_setfam_1_decl,type,
k7_setfam_1: $i > $i > $i ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(v7_group_1_decl,type,
v7_group_1: $i > $o ).
thf(k3_group_4_decl,type,
k3_group_4: $i > $i > $i ).
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(g1_group_1_decl,type,
g1_group_1: $i > $i > $i ).
thf(r1_setfam_1_decl,type,
r1_setfam_1: $i > $i > $o ).
thf(k3_tarski_decl,type,
k3_tarski: $i > $i ).
thf(v1_int_1_decl,type,
v1_int_1: $i > $o ).
thf(k1_real_1_decl,type,
k1_real_1: $i > $i ).
thf(k7_group_2_decl,type,
k7_group_2: $i > $i > $i ).
thf(r1_rlvect_1_decl,type,
r1_rlvect_1: $i > $i > $o ).
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(g3_lattices_decl,type,
g3_lattices: $i > $i > $i > $i ).
thf(k8_relset_1_decl,type,
k8_relset_1: $i > $i > $i > $i > $i ).
thf(k1_orders_1_decl,type,
k1_orders_1: $i > $i ).
thf(k2_funct_2_decl,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(k6_subset_1_decl,type,
k6_subset_1: $i > $i > $i > $i ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(k9_relset_1_decl,type,
k9_relset_1: $i > $i > $i > $i > $i ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(v4_finsub_1_decl,type,
v4_finsub_1: $i > $o ).
thf(k1_finsub_1_decl,type,
k1_finsub_1: $i > $i > $i > $i ).
thf(k3_funct_2_decl,type,
k3_funct_2: $i > $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(k4_numbers_decl,type,
k4_numbers: $i ).
thf(k2_group_4_decl,type,
k2_group_4: $i > $i ).
thf(k5_group_1_decl,type,
k5_group_1: $i > $i ).
thf(k2_group_1_decl,type,
k2_group_1: $i > $i ).
thf(k1_nat_1_decl,type,
k1_nat_1: $i > $i > $i ).
thf(k1_group_1_decl,type,
k1_group_1: $i > $i > $i > $i ).
thf(v6_group_1_decl,type,
v6_group_1: $i > $o ).
thf(k4_finseq_4_decl,type,
k4_finseq_4: $i > $i > $i > $i > $i ).
thf(r2_tarski_decl,type,
r2_tarski: $i > $i > $o ).
thf(v1_group_6_decl,type,
v1_group_6: $i > $i > $i > $o ).
thf(m1_realset1_decl,type,
m1_realset1: $i > $i > $i > $o ).
thf(k9_group_6_decl,type,
k9_group_6: $i > $i > $i > $i ).
thf(v3_lattices_decl,type,
v3_lattices: $i > $o ).
thf(v6_ordinal1_decl,type,
v6_ordinal1: $i > $o ).
thf(k2_partfun1_decl,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(g4_vectsp_1_decl,type,
g4_vectsp_1: $i > $i > $i > $i > $i > $i ).
thf(m1_orders_1_decl,type,
m1_orders_1: $i > $i > $o ).
thf(k7_domain_1_decl,type,
k7_domain_1: $i > $i > $i > $i ).
thf(k3_xcmplx_0_decl,type,
k3_xcmplx_0: $i > $i > $i ).
thf(l1_lattices_decl,type,
l1_lattices: $i > $o ).
thf(k6_finseq_1_decl,type,
k6_finseq_1: $i > $i ).
thf(a_3_2_domain_1_decl,type,
a_3_2_domain_1: $i > $i > $i > $i ).
thf(k3_binop_1_decl,type,
k3_binop_1: $i > $i > $i ).
thf(k5_group_4_decl,type,
k5_group_4: $i > $i > $i ).
thf(k6_group_1_decl,type,
k6_group_1: $i > $i > $i > $i ).
thf(k1_int_2_decl,type,
k1_int_2: $i > $i ).
thf(k3_group_1_decl,type,
k3_group_1: $i > $i > $i ).
thf(a_2_2_domain_1_decl,type,
a_2_2_domain_1: $i > $i > $i ).
thf(v2_group_6_decl,type,
v2_group_6: $i > $i > $i > $o ).
thf(k6_xcmplx_0_decl,type,
k6_xcmplx_0: $i > $i > $i ).
thf(l2_lattices_decl,type,
l2_lattices: $i > $o ).
thf(k2_card_1_decl,type,
k2_card_1: $i > $i ).
thf(v4_group_6_decl,type,
v4_group_6: $i > $i > $i > $o ).
thf(k13_group_6_decl,type,
k13_group_6: $i > $i > $i > $i ).
thf(k1_subset_1_decl,type,
k1_subset_1: $i > $i ).
thf(k2_subset_1_decl,type,
k2_subset_1: $i > $i ).
thf(k7_rlvect_1_decl,type,
k7_rlvect_1: $i > $i > $i > $i ).
thf(u1_lattices_decl,type,
u1_lattices: $i > $i ).
thf(k8_funct_2_decl,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(k8_group_4_decl,type,
k8_group_4: $i > $i > $i > $i ).
thf(k2_realset1_decl,type,
k2_realset1: $i > $i > $i > $i ).
thf(k5_setfam_1_decl,type,
k5_setfam_1: $i > $i > $i ).
thf(v1_card_1_decl,type,
v1_card_1: $i > $o ).
thf(a_3_1_domain_1_decl,type,
a_3_1_domain_1: $i > $i > $i > $i ).
thf(k8_rlvect_1_decl,type,
k8_rlvect_1: $i > $i > $i > $i > $i ).
thf(k2_vectsp_1_decl,type,
k2_vectsp_1: $i > $i ).
thf(u1_vectsp_1_decl,type,
u1_vectsp_1: $i > $i ).
thf(k2_finsop_1_decl,type,
k2_finsop_1: $i > $i > $i > $i ).
thf(u1_group_1_decl,type,
u1_group_1: $i > $i ).
thf(k8_group_6_decl,type,
k8_group_6: $i > $i > $i > $i > $i > $i ).
thf(m1_eqrel_1_decl,type,
m1_eqrel_1: $i > $i > $o ).
thf(k6_domain_1_decl,type,
k6_domain_1: $i > $i > $i ).
thf(a_3_3_domain_1_decl,type,
a_3_3_domain_1: $i > $i > $i > $i ).
thf(a_1_0_domain_1_decl,type,
a_1_0_domain_1: $i > $i ).
thf(u2_lattices_decl,type,
u2_lattices: $i > $i ).
thf(k10_group_1_decl,type,
k10_group_1: $i > $i > $i > $i ).
thf(k2_group_2_decl,type,
k2_group_2: $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(k13_group_2_decl,type,
k13_group_2: $i > $i > $i > $i ).
thf(r4_group_3_decl,type,
r4_group_3: $i > $i > $i > $o ).
thf(r3_group_3_decl,type,
r3_group_3: $i > $i > $i > $o ).
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(r1_group_3_decl,type,
r1_group_3: $i > $i > $i > $o ).
thf(k2_group_3_decl,type,
k2_group_3: $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(k7_group_3_decl,type,
k7_group_3: $i > $i > $i ).
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(k1_group_2_decl,type,
k1_group_2: $i > $i > $i ).
thf(k14_group_2_decl,type,
k14_group_2: $i > $i > $i ).
thf(k6_group_2_decl,type,
k6_group_2: $i > $i ).
thf(k15_group_2_decl,type,
k15_group_2: $i > $i > $i ).
thf(k7_group_1_decl,type,
k7_group_1: $i > $i > $i ).
thf(k8_group_3_decl,type,
k8_group_3: $i > $i > $i ).
thf(k5_group_3_decl,type,
k5_group_3: $i > $i > $i > $i ).
thf(m1_group_6_decl,type,
m1_group_6: $i > $i > $i > $o ).
thf(r1_realset1_decl,type,
r1_realset1: $i > $i > $i > $o ).
thf(a_2_1_domain_1_decl,type,
a_2_1_domain_1: $i > $i > $i ).
thf(v1_group_3_decl,type,
v1_group_3: $i > $i > $o ).
thf(k4_group_6_decl,type,
k4_group_6: $i > $i > $i ).
thf(k9_group_1_decl,type,
k9_group_1: $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(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(v3_group_6_decl,type,
v3_group_6: $i > $i > $i > $o ).
thf(k17_group_2_decl,type,
k17_group_2: $i > $i > $i ).
thf(k7_binop_2_decl,type,
k7_binop_2: $i > $i ).
thf(k3_finsub_1_decl,type,
k3_finsub_1: $i > $i > $i > $i ).
thf(v1_setwiseo_decl,type,
v1_setwiseo: $i > $i > $o ).
thf(k9_group_4_decl,type,
k9_group_4: $i > $i ).
thf(k1_group_3_decl,type,
k1_group_3: $i > $i ).
thf(k5_funct_4_decl,type,
k5_funct_4: $i > $i > $i > $i > $i > $i ).
thf(k6_group_6_decl,type,
k6_group_6: $i > $i > $i ).
thf(k12_group_6_decl,type,
k12_group_6: $i > $i > $i > $i ).
thf(k11_group_6_decl,type,
k11_group_6: $i > $i > $i ).
thf(r1_nat_1_decl,type,
r1_nat_1: $i > $i > $o ).
thf(k10_domain_1_decl,type,
k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k9_group_2_decl,type,
k9_group_2: $i > $i > $i > $i ).
thf(r1_group_2_decl,type,
r1_group_2: $i > $i > $i > $o ).
thf(k10_group_4_decl,type,
k10_group_4: $i > $i ).
thf(k1_group_6_decl,type,
k1_group_6: $i > $i > $i > $i ).
thf(k7_group_6_decl,type,
k7_group_6: $i > $i > $i > $i ).
thf(v2_group_4_decl,type,
v2_group_4: $i > $i > $o ).
thf(a_2_2_group_3_decl,type,
a_2_2_group_3: $i > $i > $i ).
thf(k10_group_3_decl,type,
k10_group_3: $i > $i > $i ).
thf(k6_group_4_decl,type,
k6_group_4: $i > $i ).
thf(a_1_0_group_4_decl,type,
a_1_0_group_4: $i > $i ).
thf(k33_binop_2_decl,type,
k33_binop_2: $i ).
thf(k8_group_2_decl,type,
k8_group_2: $i > $i > $i > $i ).
thf(a_2_1_group_3_decl,type,
a_2_1_group_3: $i > $i > $i ).
thf(a_1_0_finseq_1_decl,type,
a_1_0_finseq_1: $i > $i ).
thf(k12_domain_1_decl,type,
k12_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k6_lattices_decl,type,
k6_lattices: $i > $i ).
thf(v1_group_4_decl,type,
v1_group_4: $i > $i > $o ).
thf(k9_group_3_decl,type,
k9_group_3: $i > $i > $i ).
thf(k11_group_3_decl,type,
k11_group_3: $i > $i > $i ).
thf(p1_s2_card_1_decl,type,
p1_s2_card_1: $i > $o ).
thf(k2_nat_1_decl,type,
k2_nat_1: $i > $i > $i ).
thf(k16_group_2_decl,type,
k16_group_2: $i > $i > $i ).
thf(k5_group_2_decl,type,
k5_group_2: $i > $i ).
thf(a_1_2_domain_1_decl,type,
a_1_2_domain_1: $i > $i ).
thf(k9_domain_1_decl,type,
k9_domain_1: $i > $i > $i > $i > $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(v5_group_1_decl,type,
v5_group_1: $i > $i > $o ).
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(k3_finseq_4_decl,type,
k3_finseq_4: $i > $i > $i > $i > $i ).
thf(a_2_0_group_4_decl,type,
a_2_0_group_4: $i > $i > $i ).
thf(a_3_5_domain_1_decl,type,
a_3_5_domain_1: $i > $i > $i > $i ).
thf(k10_group_6_decl,type,
k10_group_6: $i > $i > $i ).
thf(a_1_0_group_2_decl,type,
a_1_0_group_2: $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(a_1_0_group_6_decl,type,
a_1_0_group_6: $i > $i ).
thf(k2_group_5_decl,type,
k2_group_5: $i > $i > $i > $i ).
thf(k11_group_4_decl,type,
k11_group_4: $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(m1_ordinal1_decl,type,
m1_ordinal1: $i > $i > $o ).
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(r2_group_6_decl,type,
r2_group_6: $i > $i > $o ).
thf(k3_latsubgr_decl,type,
k3_latsubgr: $i > $i > $i > $i ).
thf(k11_domain_1_decl,type,
k11_domain_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(f1_s2_funct_2_decl,type,
f1_s2_funct_2: $i ).
thf(f3_s2_funct_2_decl,type,
f3_s2_funct_2: $i > $i ).
thf(f2_s2_funct_2_decl,type,
f2_s2_funct_2: $i ).
thf(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(a_2_3_group_3_decl,type,
a_2_3_group_3: $i > $i > $i ).
thf(k4_xcmplx_0_decl,type,
k4_xcmplx_0: $i > $i ).
thf(r1_ordinal1_decl,type,
r1_ordinal1: $i > $i > $o ).
thf(v3_realset2_decl,type,
v3_realset2: $i > $o ).
thf(f1_s1_funct_2_decl,type,
f1_s1_funct_2: $i ).
thf(f2_s1_funct_2_decl,type,
f2_s1_funct_2: $i ).
thf(p1_s1_funct_2_decl,type,
p1_s1_funct_2: $i > $i > $o ).
thf(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(a_3_7_domain_1_decl,type,
a_3_7_domain_1: $i > $i > $i > $i ).
thf(k9_group_5_decl,type,
k9_group_5: $i > $i ).
thf(k5_lattices_decl,type,
k5_lattices: $i > $i ).
thf(k2_group_6_decl,type,
k2_group_6: $i > $i > $i > $i ).
thf(k6_finseqop_decl,type,
k6_finseqop: $i > $i > $i ).
thf(k2_latsubgr_decl,type,
k2_latsubgr: $i > $i > $i ).
thf(r1_finseqop_decl,type,
r1_finseqop: $i > $i > $i > $o ).
thf(r6_group_3_decl,type,
r6_group_3: $i > $i > $i > $o ).
thf(a_1_1_group_4_decl,type,
a_1_1_group_4: $i > $i ).
thf(k3_group_6_decl,type,
k3_group_6: $i > $i > $i > $i ).
thf(v1_finseqop_decl,type,
v1_finseqop: $i > $i > $o ).
thf(1373,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/sandbox/benchmark/theBenchmark.p',t72_group_1) ).
thf(8607,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)],[1373]) ).
thf(1237,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_4_domain_1) ).
thf(7854,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)],[1237]) ).
thf(651,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_eqrel_1) ).
thf(4899,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)],[651]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',t131_partfun1) ).
thf(1840,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)],[11]) ).
thf(1725,axiom,
! [A: $i] :
( ( A @ k6_finseq_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_finseq_1) ).
thf(10081,plain,
! [A: $i] :
( ( A @ k6_finseq_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1725]) ).
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 @ 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/sandbox/benchmark/theBenchmark.p',t27_group_2) ).
thf(8646,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)],[1384]) ).
thf(1666,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/sandbox/benchmark/theBenchmark.p',existence_m1_group_2) ).
thf(9907,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)],[1666]) ).
thf(1149,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/sandbox/benchmark/theBenchmark.p',t132_funct_2) ).
thf(7396,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)],[1149]) ).
thf(1675,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/sandbox/benchmark/theBenchmark.p',t63_group_2) ).
thf(9929,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)],[1675]) ).
thf(1361,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/sandbox/benchmark/theBenchmark.p',d11_group_3) ).
thf(8536,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)],[1361]) ).
thf(773,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(5509,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(1132,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/sandbox/benchmark/theBenchmark.p',t30_group_3) ).
thf(7304,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)],[1132]) ).
thf(1699,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/sandbox/benchmark/theBenchmark.p',t110_group_2) ).
thf(10007,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)],[1699]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= ( D @ ( C @ k10_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_funct_2) ).
thf(3873,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= ( D @ ( C @ k10_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(1478,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/sandbox/benchmark/theBenchmark.p',d16_group_2) ).
thf(9131,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)],[1478]) ).
thf(175,axiom,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k1_relat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(2630,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)],[175]) ).
thf(1546,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/sandbox/benchmark/theBenchmark.p',dt_k8_group_2) ).
thf(9405,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)],[1546]) ).
thf(1438,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/sandbox/benchmark/theBenchmark.p',t33_group_4) ).
thf(8930,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)],[1438]) ).
thf(1222,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_5_domain_1) ).
thf(7766,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)],[1222]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ k4_finseq_1 )
= ( np__3 @ k2_finseq_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finseq_3) ).
thf(1879,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ k4_finseq_1 )
= ( np__3 @ k2_finseq_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1062,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/sandbox/benchmark/theBenchmark.p',redefinition_m2_subset_1) ).
thf(6836,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)],[1062]) ).
thf(1489,axiom,
k4_numbers != k1_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_numbers) ).
thf(9208,plain,
k4_numbers != k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1489]) ).
thf(446,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_partfun1) ).
thf(3944,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)],[446]) ).
thf(1087,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/sandbox/benchmark/theBenchmark.p',t34_group_2) ).
thf(6979,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)],[1087]) ).
thf(170,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/sandbox/benchmark/theBenchmark.p',t171_partfun1) ).
thf(2612,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)],[170]) ).
thf(919,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(6167,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)],[919]) ).
thf(106,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/sandbox/benchmark/theBenchmark.p',d6_binop_1) ).
thf(2295,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)],[106]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',fc2_realset1) ).
thf(2306,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)],[109]) ).
thf(1662,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/sandbox/benchmark/theBenchmark.p',t92_group_2) ).
thf(9886,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)],[1662]) ).
thf(1177,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/sandbox/benchmark/theBenchmark.p',d19_vectsp_1) ).
thf(7569,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)],[1177]) ).
thf(859,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_group_2) ).
thf(5896,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)],[859]) ).
thf(727,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/sandbox/benchmark/theBenchmark.p',cc4_vectsp_1) ).
thf(5260,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)],[727]) ).
thf(1279,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/sandbox/benchmark/theBenchmark.p',t14_group_4) ).
thf(8097,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)],[1279]) ).
thf(1157,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/sandbox/benchmark/theBenchmark.p',t28_group_2) ).
thf(7445,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)],[1157]) ).
thf(1026,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/sandbox/benchmark/theBenchmark.p',d1_orders_1) ).
thf(6651,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)],[1026]) ).
thf(348,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/sandbox/benchmark/theBenchmark.p',t52_xboole_1) ).
thf(3434,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)],[348]) ).
thf(290,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/sandbox/benchmark/theBenchmark.p',t15_binop_1) ).
thf(3167,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)],[290]) ).
thf(1653,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/sandbox/benchmark/theBenchmark.p',t80_group_2) ).
thf(9833,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)],[1653]) ).
thf(944,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/sandbox/benchmark/theBenchmark.p',t105_group_3) ).
thf(6283,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)],[944]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( B @ v4_ordinal2 )
=> ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ! [D: $i] :
( ( D @ v4_ordinal2 )
=> ! [E: $i] :
( ( E @ v4_ordinal2 )
=> ! [F: $i] :
( ( F @ v4_ordinal2 )
=> ~ ( ( F @ ( E @ r1_xreal_0 ) )
& ( ( E @ ( A @ k14_finseq_1 @ k1_funct_1 ) )
= D )
& ( ( F @ ( A @ k14_finseq_1 @ k1_funct_1 ) )
= C )
& ( A @ k14_finseq_1 @ k3_finseq_1 @ ( F @ r1_xreal_0 ) )
& ( E @ ( np__1 @ r1_xreal_0 ) )
& ~ ( C @ ( D @ r1_xreal_0 ) )
& ( B @ k2_finseq_1 @ ( A @ r1_tarski ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_finseq_3) ).
thf(4183,plain,
! [A: $i,B: $i] :
( ( B @ v4_ordinal2 )
=> ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ! [D: $i] :
( ( D @ v4_ordinal2 )
=> ! [E: $i] :
( ( E @ v4_ordinal2 )
=> ! [F: $i] :
( ( F @ v4_ordinal2 )
=> ~ ( ( F @ ( E @ r1_xreal_0 ) )
& ( ( E @ ( A @ k14_finseq_1 @ k1_funct_1 ) )
= D )
& ( ( F @ ( A @ k14_finseq_1 @ k1_funct_1 ) )
= C )
& ( A @ k14_finseq_1 @ k3_finseq_1 @ ( F @ r1_xreal_0 ) )
& ( E @ ( np__1 @ r1_xreal_0 ) )
& ~ ( C @ ( D @ r1_xreal_0 ) )
& ( B @ k2_finseq_1 @ ( A @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(1323,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/sandbox/benchmark/theBenchmark.p',t44_setfam_1) ).
thf(8338,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)],[1323]) ).
thf(409,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k10_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t172_relat_1) ).
thf(3698,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k10_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(1109,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( A @ a_1_2_domain_1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_domain_1) ).
thf(7100,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)],[1109]) ).
thf(945,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/sandbox/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(6285,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)],[945]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ ( A @ k4_relset_1 ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_2) ).
thf(3397,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ ( A @ k4_relset_1 ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(1740,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/sandbox/benchmark/theBenchmark.p',t78_group_2) ).
thf(10134,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)],[1740]) ).
thf(1415,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/sandbox/benchmark/theBenchmark.p',d11_group_1) ).
thf(8784,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)],[1415]) ).
thf(1613,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/sandbox/benchmark/theBenchmark.p',d15_group_3) ).
thf(9685,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)],[1613]) ).
thf(155,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k2_relat_1 @ v1_relat_1 )
& ( A @ k2_relat_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(2544,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)],[155]) ).
thf(983,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/sandbox/benchmark/theBenchmark.p',d4_group_3) ).
thf(6448,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)],[983]) ).
thf(1610,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/sandbox/benchmark/theBenchmark.p',dt_k9_group_2) ).
thf(9676,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)],[1610]) ).
thf(1007,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/sandbox/benchmark/theBenchmark.p',t67_group_1) ).
thf(6566,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)],[1007]) ).
thf(616,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ k6_partfun1 @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k6_partfun1 @ v1_partfun1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_partfun1) ).
thf(4728,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)],[616]) ).
thf(1493,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_xboole_1) ).
thf(9222,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)],[1493]) ).
thf(671,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/sandbox/benchmark/theBenchmark.p',t178_orders_1) ).
thf(4992,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)],[671]) ).
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 @ 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/sandbox/benchmark/theBenchmark.p',t12_group_1) ).
thf(8077,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)],[1275]) ).
thf(1497,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/sandbox/benchmark/theBenchmark.p',t33_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] :
( ( ( 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)],[1497]) ).
thf(1186,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/sandbox/benchmark/theBenchmark.p',t12_group_2) ).
thf(7601,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)],[1186]) ).
thf(1341,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/sandbox/benchmark/theBenchmark.p',t55_subset_1) ).
thf(8450,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)],[1341]) ).
thf(989,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/sandbox/benchmark/theBenchmark.p',t60_group_6) ).
thf(6463,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)],[989]) ).
thf(149,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/sandbox/benchmark/theBenchmark.p',t25_partfun1) ).
thf(2527,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)],[149]) ).
thf(248,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/sandbox/benchmark/theBenchmark.p',t17_binop_1) ).
thf(3012,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)],[248]) ).
thf(811,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/sandbox/benchmark/theBenchmark.p',d11_group_2) ).
thf(5669,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)],[811]) ).
thf(1484,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/sandbox/benchmark/theBenchmark.p',t67_group_6) ).
thf(9191,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)],[1484]) ).
thf(780,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/sandbox/benchmark/theBenchmark.p',t44_subset_1) ).
thf(5529,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)],[780]) ).
thf(926,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_card_1) ).
thf(6194,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)],[926]) ).
thf(887,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/sandbox/benchmark/theBenchmark.p',t25_funct_2) ).
thf(6022,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)],[887]) ).
thf(1012,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/sandbox/benchmark/theBenchmark.p',d8_group_2) ).
thf(6587,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)],[1012]) ).
thf(923,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/sandbox/benchmark/theBenchmark.p',t69_group_1) ).
thf(6177,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)],[923]) ).
thf(701,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/sandbox/benchmark/theBenchmark.p',d20_binop_1) ).
thf(5141,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)],[701]) ).
thf(709,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/sandbox/benchmark/theBenchmark.p',t23_int_1) ).
thf(5168,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)],[709]) ).
thf(1167,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/sandbox/benchmark/theBenchmark.p',t134_group_2) ).
thf(7517,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)],[1167]) ).
thf(1338,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/sandbox/benchmark/theBenchmark.p',t2_realset1) ).
thf(8434,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)],[1338]) ).
thf(842,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/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(5820,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)],[842]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',t9_relset_1) ).
thf(1882,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)],[20]) ).
thf(1480,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/sandbox/benchmark/theBenchmark.p',t71_group_3) ).
thf(9163,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)],[1480]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',t46_funct_1) ).
thf(2231,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)],[92]) ).
thf(173,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/sandbox/benchmark/theBenchmark.p',t62_relat_1) ).
thf(2622,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)],[173]) ).
thf(1531,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/sandbox/benchmark/theBenchmark.p',t84_group_3) ).
thf(9351,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)],[1531]) ).
thf(430,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/sandbox/benchmark/theBenchmark.p',d19_binop_1) ).
thf(3858,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)],[430]) ).
thf(521,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/sandbox/benchmark/theBenchmark.p',dt_k3_group_4) ).
thf(4311,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)],[521]) ).
thf(905,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/sandbox/benchmark/theBenchmark.p',t142_group_2) ).
thf(6106,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)],[905]) ).
thf(563,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/sandbox/benchmark/theBenchmark.p',t29_partfun1) ).
thf(4515,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)],[563]) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(2495,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)],[141]) ).
thf(1192,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k3_finsub_1 ) ) )
= ( B @ ( C @ ( A @ k3_finsub_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_finsub_1) ).
thf(7641,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k3_finsub_1 ) ) )
= ( B @ ( C @ ( A @ k3_finsub_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(723,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/sandbox/benchmark/theBenchmark.p',d17_binop_1) ).
thf(5242,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)],[723]) ).
thf(1664,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/sandbox/benchmark/theBenchmark.p',t56_group_2) ).
thf(9901,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)],[1664]) ).
thf(451,axiom,
! [A: $i] : ( A @ k3_tarski @ ( A @ k1_setfam_1 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_setfam_1) ).
thf(3959,plain,
! [A: $i] : ( A @ k3_tarski @ ( A @ k1_setfam_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',t12_funct_4) ).
thf(2248,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)],[99]) ).
thf(1282,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(8118,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)],[1282]) ).
thf(1671,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/sandbox/benchmark/theBenchmark.p',t124_group_3) ).
thf(9918,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)],[1671]) ).
thf(1774,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/sandbox/benchmark/theBenchmark.p',t85_group_4) ).
thf(10262,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)],[1774]) ).
thf(1215,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/sandbox/benchmark/theBenchmark.p',t53_group_6) ).
thf(7726,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)],[1215]) ).
thf(981,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
thf(6441,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)],[981]) ).
thf(42,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/sandbox/benchmark/theBenchmark.p',t48_funct_1) ).
thf(2014,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)],[42]) ).
thf(957,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/sandbox/benchmark/theBenchmark.p',t136_group_2) ).
thf(6323,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)],[957]) ).
thf(1769,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/sandbox/benchmark/theBenchmark.p',t180_group_2) ).
thf(10244,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)],[1769]) ).
thf(1340,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/sandbox/benchmark/theBenchmark.p',t53_group_3) ).
thf(8447,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)],[1340]) ).
thf(345,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/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(3402,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)],[345]) ).
thf(1781,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/sandbox/benchmark/theBenchmark.p',t52_group_2) ).
thf(10294,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)],[1781]) ).
thf(1141,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/sandbox/benchmark/theBenchmark.p',d6_group_6) ).
thf(7341,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)],[1141]) ).
thf(1446,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/sandbox/benchmark/theBenchmark.p',t32_group_1) ).
thf(8988,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)],[1446]) ).
thf(800,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/sandbox/benchmark/theBenchmark.p',t172_group_2) ).
thf(5614,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)],[800]) ).
thf(1535,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/sandbox/benchmark/theBenchmark.p',t19_latsubgr) ).
thf(9364,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)],[1535]) ).
thf(556,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_relset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(4487,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_relset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(994,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/sandbox/benchmark/theBenchmark.p',t118_group_2) ).
thf(6480,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)],[994]) ).
thf(1507,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/sandbox/benchmark/theBenchmark.p',t66_funct_2) ).
thf(9268,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)],[1507]) ).
thf(681,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/sandbox/benchmark/theBenchmark.p',t1_group_6) ).
thf(5037,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)],[681]) ).
thf(590,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finset_1) ).
thf(4633,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)],[590]) ).
thf(260,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/sandbox/benchmark/theBenchmark.p',t156_relat_1) ).
thf(3049,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)],[260]) ).
thf(964,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/sandbox/benchmark/theBenchmark.p',t65_partfun1) ).
thf(6359,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)],[964]) ).
thf(465,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/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
thf(4026,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)],[465]) ).
thf(192,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/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
thf(2712,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)],[192]) ).
thf(1568,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/sandbox/benchmark/theBenchmark.p',t103_group_2) ).
thf(9494,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)],[1568]) ).
thf(595,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/sandbox/benchmark/theBenchmark.p',t16_subset_1) ).
thf(4650,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)],[595]) ).
thf(37,axiom,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(1988,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)],[37]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_funct_2) ).
thf(3562,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',t26_card_1) ).
thf(2146,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)],[72]) ).
thf(427,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/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(3848,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)],[427]) ).
thf(1318,axiom,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(8320,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_funct_1) ).
thf(3017,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(749,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_xboole_1) ).
thf(5425,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)],[749]) ).
thf(1683,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/sandbox/benchmark/theBenchmark.p',t55_group_4) ).
thf(9956,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)],[1683]) ).
thf(1084,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/sandbox/benchmark/theBenchmark.p',t40_funct_2) ).
thf(6971,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)],[1084]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(3217,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(1577,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/sandbox/benchmark/theBenchmark.p',t106_group_2) ).
thf(9526,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)],[1577]) ).
thf(346,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/sandbox/benchmark/theBenchmark.p',t67_partfun1) ).
thf(3429,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)],[346]) ).
thf(1322,axiom,
k5_numbers != k1_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_numbers) ).
thf(8335,plain,
k5_numbers != k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322]) ).
thf(1363,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/sandbox/benchmark/theBenchmark.p',t10_group_1) ).
thf(8551,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)],[1363]) ).
thf(1078,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/sandbox/benchmark/theBenchmark.p',t42_group_2) ).
thf(6939,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)],[1078]) ).
thf(1381,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finset_1) ).
thf(8635,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)],[1381]) ).
thf(245,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/sandbox/benchmark/theBenchmark.p',t20_funct_4) ).
thf(3004,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)],[245]) ).
thf(639,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/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(4839,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)],[639]) ).
thf(333,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/sandbox/benchmark/theBenchmark.p',t36_funct_2) ).
thf(3332,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)],[333]) ).
thf(594,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/sandbox/benchmark/theBenchmark.p',t140_zfmisc_1) ).
thf(4647,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)],[594]) ).
thf(339,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(3367,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(1431,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_2_domain_1) ).
thf(8879,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)],[1431]) ).
thf(504,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/sandbox/benchmark/theBenchmark.p',t152_funct_2) ).
thf(4220,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)],[504]) ).
thf(1270,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/sandbox/benchmark/theBenchmark.p',t14_latsubgr) ).
thf(8057,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)],[1270]) ).
thf(1407,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/sandbox/benchmark/theBenchmark.p',t50_group_3) ).
thf(8747,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)],[1407]) ).
thf(1794,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/sandbox/benchmark/theBenchmark.p',t83_group_3) ).
thf(10346,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)],[1794]) ).
thf(1554,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/sandbox/benchmark/theBenchmark.p',redefinition_r2_group_6) ).
thf(9428,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)],[1554]) ).
thf(1388,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/sandbox/benchmark/theBenchmark.p',t100_group_3) ).
thf(8667,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)],[1388]) ).
thf(335,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/sandbox/benchmark/theBenchmark.p',t25_binop_1) ).
thf(3338,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)],[335]) ).
thf(71,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
<=> ! [B: $i] :
? [C: $i] : ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t159_funct_1) ).
thf(2141,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i] :
? [C: $i] : ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k10_relat_1 ) @ r1_tarski ) )
=> ( A @ v2_funct_1 ) )
& ( ( A @ v2_funct_1 )
=> ! [B: $i] :
? [C: $i] : ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(735,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(5316,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(1492,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/sandbox/benchmark/theBenchmark.p',t7_group_6) ).
thf(9218,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)],[1492]) ).
thf(1022,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/sandbox/benchmark/theBenchmark.p',t11_funct_2) ).
thf(6634,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)],[1022]) ).
thf(576,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/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(4564,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)],[576]) ).
thf(935,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/sandbox/benchmark/theBenchmark.p',t28_subset_1) ).
thf(6241,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)],[935]) ).
thf(279,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/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(3121,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)],[279]) ).
thf(328,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/sandbox/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(3313,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)],[328]) ).
thf(1427,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/sandbox/benchmark/theBenchmark.p',t16_xboole_1) ).
thf(8838,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)],[1427]) ).
thf(820,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/sandbox/benchmark/theBenchmark.p',t5_mcart_1) ).
thf(5708,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)],[820]) ).
thf(966,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/sandbox/benchmark/theBenchmark.p',d13_group_2) ).
thf(6370,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)],[966]) ).
thf(1213,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/sandbox/benchmark/theBenchmark.p',t133_group_2) ).
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 ) )
=> ( ( ( 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)],[1213]) ).
thf(219,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/sandbox/benchmark/theBenchmark.p',t51_funct_1) ).
thf(2844,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)],[219]) ).
thf(382,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/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(3577,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)],[382]) ).
thf(1510,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/sandbox/benchmark/theBenchmark.p',d17_group_2) ).
thf(9278,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)],[1510]) ).
thf(1219,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/sandbox/benchmark/theBenchmark.p',t2_mcart_1) ).
thf(7748,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)],[1219]) ).
thf(414,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/sandbox/benchmark/theBenchmark.p',dt_m2_realset1) ).
thf(3717,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)],[414]) ).
thf(624,axiom,
? [A: $i] : ( A @ l1_lattices ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(4762,plain,
? [A: $i] : ( A @ l1_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(1792,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/sandbox/benchmark/theBenchmark.p',reflexivity_r1_group_2) ).
thf(10341,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)],[1792]) ).
thf(1609,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/sandbox/benchmark/theBenchmark.p',t164_group_2) ).
thf(9672,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)],[1609]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',symmetry_r1_partfun1) ).
thf(2575,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)],[162]) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',t19_relat_1) ).
thf(2548,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)],[156]) ).
thf(514,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( np__1 @ ( A @ k2_xcmplx_0 ) @ k1_tarski @ ( A @ k2_finseq_1 @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finseq_3) ).
thf(4266,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( np__1 @ ( A @ k2_xcmplx_0 ) @ k1_tarski @ ( A @ k2_finseq_1 @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(1422,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/sandbox/benchmark/theBenchmark.p',t20_group_1) ).
thf(8816,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)],[1422]) ).
thf(1216,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/sandbox/benchmark/theBenchmark.p',dt_k11_group_6) ).
thf(7729,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)],[1216]) ).
thf(1619,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/sandbox/benchmark/theBenchmark.p',t150_group_3) ).
thf(9708,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)],[1619]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_funct_1) ).
thf(2516,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(995,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_zfmisc_1) ).
thf(6483,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)],[995]) ).
thf(490,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/sandbox/benchmark/theBenchmark.p',t25_xboole_1) ).
thf(4156,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)],[490]) ).
thf(657,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/sandbox/benchmark/theBenchmark.p',t50_funct_2) ).
thf(4941,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)],[657]) ).
thf(1796,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/sandbox/benchmark/theBenchmark.p',t84_group_4) ).
thf(10351,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)],[1796]) ).
thf(340,axiom,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(3370,plain,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(717,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finset_1) ).
thf(5227,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)],[717]) ).
thf(990,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/sandbox/benchmark/theBenchmark.p',t118_group_3) ).
thf(6466,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)],[990]) ).
thf(877,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/sandbox/benchmark/theBenchmark.p',t69_card_1) ).
thf(5977,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)],[877]) ).
thf(1075,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/sandbox/benchmark/theBenchmark.p',t156_group_3) ).
thf(6909,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)],[1075]) ).
thf(130,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/sandbox/benchmark/theBenchmark.p',t132_partfun1) ).
thf(2432,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)],[130]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',t121_funct_1) ).
thf(1914,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)],[24]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) )
= ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_funct_1) ).
thf(2020,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) )
= ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1627,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/sandbox/benchmark/theBenchmark.p',t1_latsubgr) ).
thf(9735,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)],[1627]) ).
thf(586,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/sandbox/benchmark/theBenchmark.p',t59_card_1) ).
thf(4618,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)],[586]) ).
thf(271,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ! [C: $i] :
~ ( ( ( C @ k1_tarski @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_funct_1) ).
thf(3088,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ! [C: $i] :
~ ( ( ( C @ k1_tarski @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(1456,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/sandbox/benchmark/theBenchmark.p',t12_group_6) ).
thf(9027,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)],[1456]) ).
thf(1470,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(9096,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1470]) ).
thf(1724,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/sandbox/benchmark/theBenchmark.p',t181_group_2) ).
thf(10078,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)],[1724]) ).
thf(864,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/sandbox/benchmark/theBenchmark.p',d2_group_2) ).
thf(5921,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)],[864]) ).
thf(1694,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/sandbox/benchmark/theBenchmark.p',t66_group_2) ).
thf(9994,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)],[1694]) ).
thf(843,axiom,
! [A: $i] :
( ~ ( ( A @ ( A @ r1_xboole_0 ) )
& ( A != k1_xboole_0 ) )
& ~ ( ( A = k1_xboole_0 )
& ~ ( A @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_xboole_1) ).
thf(5825,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)],[843]) ).
thf(822,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/sandbox/benchmark/theBenchmark.p',t147_group_2) ).
thf(5723,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)],[822]) ).
thf(868,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset_1) ).
thf(5938,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(835,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_zfmisc_1) ).
thf(5770,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)],[835]) ).
thf(1347,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/sandbox/benchmark/theBenchmark.p',t30_finset_1) ).
thf(8472,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)],[1347]) ).
thf(1309,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/sandbox/benchmark/theBenchmark.p',d8_group_6) ).
thf(8256,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)],[1309]) ).
thf(228,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/sandbox/benchmark/theBenchmark.p',d2_funct_2) ).
thf(2886,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)],[228]) ).
thf(466,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/sandbox/benchmark/theBenchmark.p',d12_group_6) ).
thf(4030,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)],[466]) ).
thf(1350,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/sandbox/benchmark/theBenchmark.p',t160_group_3) ).
thf(8487,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)],[1350]) ).
thf(422,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/sandbox/benchmark/theBenchmark.p',t143_partfun1) ).
thf(3809,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)],[422]) ).
thf(1320,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/sandbox/benchmark/theBenchmark.p',t90_group_6) ).
thf(8330,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)],[1320]) ).
thf(69,axiom,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_finseq_1) ).
thf(2136,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)],[69]) ).
thf(948,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/sandbox/benchmark/theBenchmark.p',redefinition_k10_group_1) ).
thf(6291,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)],[948]) ).
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 ) )
=> ( ( ( 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/sandbox/benchmark/theBenchmark.p',t32_funct_2) ).
thf(4948,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)],[658]) ).
thf(150,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/sandbox/benchmark/theBenchmark.p',t26_finset_1) ).
thf(2531,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)],[150]) ).
thf(510,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k4_card_1 )
= np__1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_card_1) ).
thf(4249,plain,
! [A: $i] :
( ( A @ k1_tarski @ k4_card_1 )
= np__1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(739,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ( ( B @ k2_finseq_1 @ ( A @ r2_hidden ) )
=> ( ( B @ k2_finseq_1 @ ( C @ ( A @ k6_xcmplx_0 ) @ r2_hidden ) )
| ( C @ ( A @ r1_xreal_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finseq_3) ).
thf(5352,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ( ( B @ k2_finseq_1 @ ( A @ r2_hidden ) )
=> ( ( B @ k2_finseq_1 @ ( C @ ( A @ k6_xcmplx_0 ) @ r2_hidden ) )
| ( C @ ( A @ r1_xreal_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(781,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(5533,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)],[781]) ).
thf(1370,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/sandbox/benchmark/theBenchmark.p',t22_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 @ 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)],[1370]) ).
thf(833,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/sandbox/benchmark/theBenchmark.p',t12_latsubgr) ).
thf(5765,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)],[833]) ).
thf(549,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/sandbox/benchmark/theBenchmark.p',t58_domain_1) ).
thf(4422,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)],[549]) ).
thf(318,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/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(3275,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)],[318]) ).
thf(1002,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/sandbox/benchmark/theBenchmark.p',t39_subset_1) ).
thf(6538,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)],[1002]) ).
thf(861,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/sandbox/benchmark/theBenchmark.p',t68_group_6) ).
thf(5910,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)],[861]) ).
thf(1144,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/sandbox/benchmark/theBenchmark.p',t14_group_2) ).
thf(7349,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)],[1144]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_realset1) ).
thf(2444,plain,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(1385,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/sandbox/benchmark/theBenchmark.p',t8_funct_2) ).
thf(8654,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)],[1385]) ).
thf(1791,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/sandbox/benchmark/theBenchmark.p',t65_group_4) ).
thf(10337,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)],[1791]) ).
thf(8,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/sandbox/benchmark/theBenchmark.p',t156_funct_1) ).
thf(1832,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)],[8]) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(2126,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)],[67]) ).
thf(1476,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/sandbox/benchmark/theBenchmark.p',d2_group_6) ).
thf(9123,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)],[1476]) ).
thf(592,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/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
thf(4637,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)],[592]) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(2654,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)],[182]) ).
thf(311,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/sandbox/benchmark/theBenchmark.p',t7_setfam_1) ).
thf(3248,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)],[311]) ).
thf(507,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/sandbox/benchmark/theBenchmark.p',cc5_vectsp_1) ).
thf(4238,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)],[507]) ).
thf(1374,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/sandbox/benchmark/theBenchmark.p',t10_latsubgr) ).
thf(8610,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)],[1374]) ).
thf(795,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/sandbox/benchmark/theBenchmark.p',t47_group_6) ).
thf(5585,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)],[795]) ).
thf(169,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/sandbox/benchmark/theBenchmark.p',t11_binop_1) ).
thf(2603,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)],[169]) ).
thf(566,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/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(4524,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)],[566]) ).
thf(444,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( ( A @ k2_finseq_1 )
= ( B @ k2_finseq_1 ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_finseq_1) ).
thf(3938,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( ( A @ k2_finseq_1 )
= ( B @ k2_finseq_1 ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(1129,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/sandbox/benchmark/theBenchmark.p',d5_group_4) ).
thf(7277,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)],[1129]) ).
thf(1783,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/sandbox/benchmark/theBenchmark.p',t82_group_4) ).
thf(10305,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)],[1783]) ).
thf(1004,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/sandbox/benchmark/theBenchmark.p',t5_group_2) ).
thf(6552,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)],[1004]) ).
thf(401,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/sandbox/benchmark/theBenchmark.p',t149_funct_2) ).
thf(3644,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)],[401]) ).
thf(474,axiom,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_subset_1) ).
thf(4070,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(278,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/sandbox/benchmark/theBenchmark.p',t9_realset1) ).
thf(3116,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)],[278]) ).
thf(1301,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/sandbox/benchmark/theBenchmark.p',t18_funct_2) ).
thf(8225,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)],[1301]) ).
thf(941,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/sandbox/benchmark/theBenchmark.p',t58_group_3) ).
thf(6274,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)],[941]) ).
thf(1555,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/sandbox/benchmark/theBenchmark.p',t165_group_3) ).
thf(9432,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)],[1555]) ).
thf(1585,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/sandbox/benchmark/theBenchmark.p',t173_group_2) ).
thf(9561,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)],[1585]) ).
thf(1798,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/sandbox/benchmark/theBenchmark.p',t97_group_2) ).
thf(10356,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)],[1798]) ).
thf(1691,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/sandbox/benchmark/theBenchmark.p',t85_group_6) ).
thf(9988,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)],[1691]) ).
thf(830,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(5759,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',t26_binop_1) ).
thf(1871,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)],[16]) ).
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 @ ( 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/sandbox/benchmark/theBenchmark.p',t92_group_3) ).
thf(8806,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)],[1420]) ).
thf(23,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/sandbox/benchmark/theBenchmark.p',d5_binop_1) ).
thf(1907,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)],[23]) ).
thf(897,axiom,
! [A: $i] : ( A @ k1_card_1 @ v1_card_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_card_1) ).
thf(6066,plain,
! [A: $i] : ( A @ k1_card_1 @ v1_card_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1196,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(7652,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)],[1196]) ).
thf(360,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/sandbox/benchmark/theBenchmark.p',t51_setfam_1) ).
thf(3485,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)],[360]) ).
thf(7,axiom,
? [A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(1826,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)],[7]) ).
thf(1032,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/sandbox/benchmark/theBenchmark.p',t7_subset_1) ).
thf(6676,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)],[1032]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_relat_1) ).
thf(2185,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)],[81]) ).
thf(1667,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/sandbox/benchmark/theBenchmark.p',t73_group_3) ).
thf(9909,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)],[1667]) ).
thf(734,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/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(5289,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)],[734]) ).
thf(668,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/sandbox/benchmark/theBenchmark.p',t41_xboole_1) ).
thf(4984,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)],[668]) ).
thf(551,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/sandbox/benchmark/theBenchmark.p',t156_funct_2) ).
thf(4428,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)],[551]) ).
thf(258,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/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(3043,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)],[258]) ).
thf(1071,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/sandbox/benchmark/theBenchmark.p',t82_group_3) ).
thf(6873,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)],[1071]) ).
thf(193,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/sandbox/benchmark/theBenchmark.p',d7_binop_1) ).
thf(2745,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)],[193]) ).
thf(161,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/sandbox/benchmark/theBenchmark.p',t27_binop_1) ).
thf(2571,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)],[161]) ).
thf(1201,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/sandbox/benchmark/theBenchmark.p',t102_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 @ 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)],[1201]) ).
thf(731,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/sandbox/benchmark/theBenchmark.p',t32_group_4) ).
thf(5279,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)],[731]) ).
thf(1092,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/sandbox/benchmark/theBenchmark.p',t24_group_6) ).
thf(7011,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)],[1092]) ).
thf(1327,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/sandbox/benchmark/theBenchmark.p',t142_group_3) ).
thf(8389,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)],[1327]) ).
thf(535,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/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).
thf(4358,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)],[535]) ).
thf(1757,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/sandbox/benchmark/theBenchmark.p',rc1_group_2) ).
thf(10206,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)],[1757]) ).
thf(684,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(5052,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)],[684]) ).
thf(903,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/sandbox/benchmark/theBenchmark.p',t83_zfmisc_1) ).
thf(6098,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)],[903]) ).
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 @ 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/sandbox/benchmark/theBenchmark.p',t22_group_1) ).
thf(9039,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)],[1459]) ).
thf(968,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/sandbox/benchmark/theBenchmark.p',t22_group_2) ).
thf(6382,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)],[968]) ).
thf(719,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/sandbox/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(5231,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)],[719]) ).
thf(1551,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/sandbox/benchmark/theBenchmark.p',t84_group_6) ).
thf(9420,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)],[1551]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',d1_funct_4) ).
thf(1922,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)],[27]) ).
thf(884,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/sandbox/benchmark/theBenchmark.p',t71_group_1) ).
thf(6010,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)],[884]) ).
thf(1646,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/sandbox/benchmark/theBenchmark.p',cc1_group_1) ).
thf(9800,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)],[1646]) ).
thf(726,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/sandbox/benchmark/theBenchmark.p',t87_xboole_1) ).
thf(5256,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)],[726]) ).
thf(854,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(5868,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)],[854]) ).
thf(1211,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/sandbox/benchmark/theBenchmark.p',t34_group_3) ).
thf(7711,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)],[1211]) ).
thf(853,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/sandbox/benchmark/theBenchmark.p',t97_group_3) ).
thf(5866,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)],[853]) ).
thf(1597,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/sandbox/benchmark/theBenchmark.p',t10_group_2) ).
thf(9612,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)],[1597]) ).
thf(533,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(4353,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)],[533]) ).
thf(1033,axiom,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r2_hidden ) )
<=> ~ ( A @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_card_1) ).
thf(6681,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)],[1033]) ).
thf(778,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/sandbox/benchmark/theBenchmark.p',t146_group_2) ).
thf(5521,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)],[778]) ).
thf(714,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_xboole_1) ).
thf(5199,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)],[714]) ).
thf(1120,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/sandbox/benchmark/theBenchmark.p',t29_group_4) ).
thf(7209,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)],[1120]) ).
thf(1081,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/sandbox/benchmark/theBenchmark.p',t162_group_3) ).
thf(6951,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)],[1081]) ).
thf(1103,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/sandbox/benchmark/theBenchmark.p',t186_group_2) ).
thf(7060,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)],[1103]) ).
thf(1479,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/sandbox/benchmark/theBenchmark.p',t20_xboole_1) ).
thf(9155,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)],[1479]) ).
thf(494,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/sandbox/benchmark/theBenchmark.p',dt_k7_domain_1) ).
thf(4179,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)],[494]) ).
thf(596,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(4664,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(1679,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/sandbox/benchmark/theBenchmark.p',t169_group_2) ).
thf(9941,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)],[1679]) ).
thf(1722,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/sandbox/benchmark/theBenchmark.p',t81_group_6) ).
thf(10074,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)],[1722]) ).
thf(558,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/sandbox/benchmark/theBenchmark.p',t31_xboole_1) ).
thf(4492,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)],[558]) ).
thf(441,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/sandbox/benchmark/theBenchmark.p',t64_zfmisc_1) ).
thf(3919,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)],[441]) ).
thf(573,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/sandbox/benchmark/theBenchmark.p',t71_group_6) ).
thf(4551,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)],[573]) ).
thf(1122,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/sandbox/benchmark/theBenchmark.p',t154_funct_2) ).
thf(7215,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)],[1122]) ).
thf(1376,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( k5_numbers @ ( k1_numbers @ ( A @ k4_card_1 @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_card_1) ).
thf(8615,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)],[1376]) ).
thf(1362,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(8543,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)],[1362]) ).
thf(485,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/sandbox/benchmark/theBenchmark.p',t105_zfmisc_1) ).
thf(4141,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)],[485]) ).
thf(1300,axiom,
! [A: $i,B: $i] :
~ ( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_zfmisc_1) ).
thf(8220,plain,
! [A: $i,B: $i] :
~ ( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
thf(449,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/sandbox/benchmark/theBenchmark.p',dt_k3_binop_1) ).
thf(3951,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)],[449]) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',t26_funct_4) ).
thf(2158,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)],[73]) ).
thf(1283,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_ordinal1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_ordinal1) ).
thf(8126,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_ordinal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',t14_funct_4) ).
thf(1963,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)],[32]) ).
thf(675,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) )
= ( D @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_partfun1) ).
thf(5020,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) )
= ( D @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(767,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/sandbox/benchmark/theBenchmark.p',commutativity_k10_group_1) ).
thf(5493,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)],[767]) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',t147_relat_1) ).
thf(1875,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)],[17]) ).
thf(120,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/sandbox/benchmark/theBenchmark.p',t49_funct_1) ).
thf(2388,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)],[120]) ).
thf(151,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/sandbox/benchmark/theBenchmark.p',t53_relat_1) ).
thf(2533,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)],[151]) ).
thf(1097,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/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
thf(7032,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)],[1097]) ).
thf(1113,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/sandbox/benchmark/theBenchmark.p',d12_group_3) ).
thf(7112,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)],[1113]) ).
thf(1637,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/sandbox/benchmark/theBenchmark.p',dt_k17_group_2) ).
thf(9768,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)],[1637]) ).
thf(1506,axiom,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ k1_card_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_card_1) ).
thf(9266,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)],[1506]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',t29_funct_4) ).
thf(1847,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)],[12]) ).
thf(1589,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/sandbox/benchmark/theBenchmark.p',t90_group_3) ).
thf(9580,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)],[1589]) ).
thf(1702,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/sandbox/benchmark/theBenchmark.p',t54_group_4) ).
thf(10025,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)],[1702]) ).
thf(876,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/sandbox/benchmark/theBenchmark.p',t53_group_1) ).
thf(5974,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)],[876]) ).
thf(547,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/sandbox/benchmark/theBenchmark.p',t25_finset_1) ).
thf(4411,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)],[547]) ).
thf(1264,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/sandbox/benchmark/theBenchmark.p',t96_group_1) ).
thf(8029,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)],[1264]) ).
thf(690,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/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(5084,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)],[690]) ).
thf(581,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/sandbox/benchmark/theBenchmark.p',t14_xboole_1) ).
thf(4600,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)],[581]) ).
thf(1465,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/sandbox/benchmark/theBenchmark.p',t61_funct_2) ).
thf(9071,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)],[1465]) ).
thf(850,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(5856,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)],[850]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(3527,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)],[372]) ).
thf(393,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/sandbox/benchmark/theBenchmark.p',t66_zfmisc_1) ).
thf(3621,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)],[393]) ).
thf(1611,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/sandbox/benchmark/theBenchmark.p',t19_group_1) ).
thf(9680,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)],[1611]) ).
thf(1126,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/sandbox/benchmark/theBenchmark.p',t38_funct_4) ).
thf(7258,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)],[1126]) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',t195_orders_1) ).
thf(2007,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)],[41]) ).
thf(606,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( k5_numbers @ k1_zfmisc_1 @ ( A @ k2_finseq_1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_finseq_1) ).
thf(4696,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( k5_numbers @ k1_zfmisc_1 @ ( A @ k2_finseq_1 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(872,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/sandbox/benchmark/theBenchmark.p',d11_card_1) ).
thf(5957,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)],[872]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',t3_funct_2) ).
thf(2237,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)],[95]) ).
thf(752,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( B @ k2_finseq_1 @ ( A @ r2_hidden ) )
<=> ( ( B @ ( A @ r1_xreal_0 ) )
& ( A @ ( np__1 @ r1_xreal_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_finseq_1) ).
thf(5433,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( ( ( B @ ( A @ r1_xreal_0 ) )
& ( A @ ( np__1 @ r1_xreal_0 ) ) )
=> ( B @ k2_finseq_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ k2_finseq_1 @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ r1_xreal_0 ) )
& ( A @ ( np__1 @ r1_xreal_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(728,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(5264,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)],[728]) ).
thf(1517,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/sandbox/benchmark/theBenchmark.p',t168_group_2) ).
thf(9304,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)],[1517]) ).
thf(1515,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/sandbox/benchmark/theBenchmark.p',t54_group_2) ).
thf(9298,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)],[1515]) ).
thf(371,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/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(3524,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)],[371]) ).
thf(1224,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(7792,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(857,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/sandbox/benchmark/theBenchmark.p',t1_realset1) ).
thf(5892,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)],[857]) ).
thf(1512,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/sandbox/benchmark/theBenchmark.p',t65_group_2) ).
thf(9283,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)],[1512]) ).
thf(206,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_4 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_4) ).
thf(2794,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)],[206]) ).
thf(299,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/sandbox/benchmark/theBenchmark.p',t28_funct_2) ).
thf(3199,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)],[299]) ).
thf(1576,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/sandbox/benchmark/theBenchmark.p',t10_group_6) ).
thf(9520,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)],[1576]) ).
thf(1030,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/sandbox/benchmark/theBenchmark.p',t56_group_3) ).
thf(6670,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)],[1030]) ).
thf(1526,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/sandbox/benchmark/theBenchmark.p',t107_group_2) ).
thf(9330,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)],[1526]) ).
thf(642,axiom,
! [A: $i] :
( ( A @ v4_finsub_1 )
<=> ! [B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( ( A @ ( C @ ( B @ k4_xboole_0 ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k2_xboole_0 ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_finsub_1) ).
thf(4857,plain,
! [A: $i] :
( ( ! [B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( ( A @ ( C @ ( B @ k4_xboole_0 ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k2_xboole_0 ) @ r2_hidden ) ) ) )
=> ( A @ v4_finsub_1 ) )
& ( ( A @ v4_finsub_1 )
=> ! [B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( ( A @ ( C @ ( B @ k4_xboole_0 ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k2_xboole_0 ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(1124,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/sandbox/benchmark/theBenchmark.p',t7_funct_2) ).
thf(7245,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)],[1124]) ).
thf(1334,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/sandbox/benchmark/theBenchmark.p',t42_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 @ ( 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)],[1334]) ).
thf(404,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/sandbox/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(3670,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)],[404]) ).
thf(1439,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/sandbox/benchmark/theBenchmark.p',t38_subset_1) ).
thf(8934,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)],[1439]) ).
thf(911,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(6135,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
<=> ( A @ ( B @ k2_relat_1 @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t173_relat_1) ).
thf(2880,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k2_relat_1 @ r1_xboole_0 ) )
=> ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
=> ( A @ ( B @ k2_relat_1 @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(1650,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/sandbox/benchmark/theBenchmark.p',dt_m1_group_2) ).
thf(9811,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)],[1650]) ).
thf(870,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/sandbox/benchmark/theBenchmark.p',t54_group_1) ).
thf(5946,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)],[870]) ).
thf(950,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/sandbox/benchmark/theBenchmark.p',t152_group_2) ).
thf(6300,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)],[950]) ).
thf(783,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/sandbox/benchmark/theBenchmark.p',symmetry_r4_group_3) ).
thf(5541,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)],[783]) ).
thf(679,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/sandbox/benchmark/theBenchmark.p',t43_xboole_1) ).
thf(5032,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)],[679]) ).
thf(1169,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/sandbox/benchmark/theBenchmark.p',t73_card_1) ).
thf(7532,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)],[1169]) ).
thf(1560,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/sandbox/benchmark/theBenchmark.p',t100_group_2) ).
thf(9457,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)],[1560]) ).
thf(1358,axiom,
? [A: $i] : ( A @ l2_struct_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_struct_0) ).
thf(8526,plain,
? [A: $i] : ( A @ l2_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).
thf(479,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/sandbox/benchmark/theBenchmark.p',t5_xboole_0) ).
thf(4115,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)],[479]) ).
thf(1802,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( ( B @ ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ k1_funct_1 ) )
= D )
& ( ( A @ ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ k1_funct_1 ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_4) ).
thf(10378,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( ( B @ ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ k1_funct_1 ) )
= D )
& ( ( A @ ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ k1_funct_1 ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1802]) ).
thf(831,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/sandbox/benchmark/theBenchmark.p',t18_group_6) ).
thf(5761,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)],[831]) ).
thf(604,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/sandbox/benchmark/theBenchmark.p',t9_xboole_1) ).
thf(4686,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)],[604]) ).
thf(113,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/sandbox/benchmark/theBenchmark.p',rc6_finseq_1) ).
thf(2335,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)],[113]) ).
thf(1409,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/sandbox/benchmark/theBenchmark.p',t12_group_3) ).
thf(8759,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)],[1409]) ).
thf(916,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/sandbox/benchmark/theBenchmark.p',t10_subset_1) ).
thf(6157,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)],[916]) ).
thf(1348,axiom,
! [A: $i] :
~ ( ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ~ ( B @ k2_finseq_1 @ ( A @ r2_wellord2 ) ) )
& ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_finseq_1) ).
thf(8479,plain,
! [A: $i] :
~ ( ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ~ ( B @ k2_finseq_1 @ ( A @ r2_wellord2 ) ) )
& ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k10_relat_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc18_finseq_1) ).
thf(2777,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k10_relat_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(285,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/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)],[285]) ).
thf(1039,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/sandbox/benchmark/theBenchmark.p',t5_group_4) ).
thf(6717,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)],[1039]) ).
thf(1299,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/sandbox/benchmark/theBenchmark.p',d15_group_2) ).
thf(8196,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)],[1299]) ).
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 @ 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/sandbox/benchmark/theBenchmark.p',t43_group_4) ).
thf(8664,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)],[1387]) ).
thf(1332,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/sandbox/benchmark/theBenchmark.p',t145_group_2) ).
thf(8411,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)],[1332]) ).
thf(1519,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/sandbox/benchmark/theBenchmark.p',t123_group_3) ).
thf(9309,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)],[1519]) ).
thf(844,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/sandbox/benchmark/theBenchmark.p',t108_group_3) ).
thf(5834,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)],[844]) ).
thf(836,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/sandbox/benchmark/theBenchmark.p',t88_group_3) ).
thf(5773,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)],[836]) ).
thf(984,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/sandbox/benchmark/theBenchmark.p',t25_group_6) ).
thf(6451,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)],[984]) ).
thf(1502,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/sandbox/benchmark/theBenchmark.p',t77_xboole_1) ).
thf(9255,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)],[1502]) ).
thf(1250,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
<=> ( k4_numbers @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_int_1) ).
thf(7954,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)],[1250]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_funct_2) ).
thf(4701,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(699,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/sandbox/benchmark/theBenchmark.p',t79_int_1) ).
thf(5137,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)],[699]) ).
thf(539,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_partfun1) ).
thf(4379,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
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 ) )
=> ( ( 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/sandbox/benchmark/theBenchmark.p',t28_group_4) ).
thf(8992,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)],[1448]) ).
thf(553,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
<=> ( A @ ( B @ m1_finseq_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_finseq_1) ).
thf(4475,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)],[553]) ).
thf(790,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/sandbox/benchmark/theBenchmark.p',t10_group_3) ).
thf(5572,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)],[790]) ).
thf(686,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/sandbox/benchmark/theBenchmark.p',rc9_vectsp_1) ).
thf(5059,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)],[686]) ).
thf(1162,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/sandbox/benchmark/theBenchmark.p',d6_card_1) ).
thf(7473,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)],[1162]) ).
thf(867,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/sandbox/benchmark/theBenchmark.p',t111_group_3) ).
thf(5929,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)],[867]) ).
thf(1806,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/sandbox/benchmark/theBenchmark.p',t71_group_4) ).
thf(10404,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)],[1806]) ).
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 @ ( C @ m1_group_2 ) )
& ( C @ v1_group_1 ) )
=> ( C @ ( A @ k9_group_3 ) @ ( B @ ( C @ ( A @ k6_group_3 ) ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_group_3) ).
thf(10070,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)],[1720]) ).
thf(1339,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/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(8438,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)],[1339]) ).
thf(621,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/sandbox/benchmark/theBenchmark.p',t29_funct_2) ).
thf(4751,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)],[621]) ).
thf(506,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/sandbox/benchmark/theBenchmark.p',t125_zfmisc_1) ).
thf(4230,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)],[506]) ).
thf(655,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_struct_0) ).
thf(4935,plain,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(1245,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/sandbox/benchmark/theBenchmark.p',t39_group_4) ).
thf(7931,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)],[1245]) ).
thf(295,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/sandbox/benchmark/theBenchmark.p',dt_k8_relset_1) ).
thf(3189,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)],[295]) ).
thf(1371,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/sandbox/benchmark/theBenchmark.p',t1_group_3) ).
thf(8586,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)],[1371]) ).
thf(1034,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/sandbox/benchmark/theBenchmark.p',t44_partfun1) ).
thf(6685,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)],[1034]) ).
thf(223,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/sandbox/benchmark/theBenchmark.p',d3_binop_1) ).
thf(2861,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)],[223]) ).
thf(1537,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/sandbox/benchmark/theBenchmark.p',t37_group_1) ).
thf(9369,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)],[1537]) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',t23_binop_1) ).
thf(1896,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)],[22]) ).
thf(1368,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/sandbox/benchmark/theBenchmark.p',d6_realset1) ).
thf(8575,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)],[1368]) ).
thf(1046,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/sandbox/benchmark/theBenchmark.p',t23_group_3) ).
thf(6740,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)],[1046]) ).
thf(1247,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/sandbox/benchmark/theBenchmark.p',t65_group_3) ).
thf(7936,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)],[1247]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(3505,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)],[365]) ).
thf(406,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/sandbox/benchmark/theBenchmark.p',dt_m1_orders_1) ).
thf(3685,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)],[406]) ).
thf(1393,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/sandbox/benchmark/theBenchmark.p',t57_group_3) ).
thf(8686,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)],[1393]) ).
thf(1116,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/sandbox/benchmark/theBenchmark.p',t27_group_1) ).
thf(7194,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)],[1116]) ).
thf(1069,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ r1_tarski ) )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(6863,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)],[1069]) ).
thf(1395,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/sandbox/benchmark/theBenchmark.p',dt_k2_group_1) ).
thf(8691,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)],[1395]) ).
thf(1804,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/sandbox/benchmark/theBenchmark.p',dt_k2_group_3) ).
thf(10388,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)],[1804]) ).
thf(469,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(4040,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(419,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/sandbox/benchmark/theBenchmark.p',t22_int_1) ).
thf(3756,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)],[419]) ).
thf(1805,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/sandbox/benchmark/theBenchmark.p',t5_group_1) ).
thf(10390,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)],[1805]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( ( B @ k2_finseq_1 )
= ( A @ k1_tarski ) )
=> ( ( A = np__1 )
& ( B = np__1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_finseq_3) ).
thf(4536,plain,
! [A: $i,B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( ( B @ k2_finseq_1 )
= ( A @ k1_tarski ) )
=> ( ( A = np__1 )
& ( B = np__1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(210,axiom,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(2809,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(2242,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_finseq_1) ).
thf(2799,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(468,axiom,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(4038,plain,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(194,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k10_relat_1 ) )
= ( A @ k1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t169_relat_1) ).
thf(2750,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k10_relat_1 ) )
= ( A @ k1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(1765,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/sandbox/benchmark/theBenchmark.p',t46_group_4) ).
thf(10233,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)],[1765]) ).
thf(1139,axiom,
! [A: $i,B: $i] :
( ( B @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(7337,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)],[1139]) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
thf(1943,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)],[28]) ).
thf(238,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/sandbox/benchmark/theBenchmark.p',t59_funct_1) ).
thf(2965,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)],[238]) ).
thf(564,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/sandbox/benchmark/theBenchmark.p',t64_group_6) ).
thf(4519,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)],[564]) ).
thf(1673,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/sandbox/benchmark/theBenchmark.p',fc4_group_6) ).
thf(9923,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)],[1673]) ).
thf(1159,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/sandbox/benchmark/theBenchmark.p',dt_k7_group_2) ).
thf(7460,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)],[1159]) ).
thf(1326,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/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(8362,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)],[1326]) ).
thf(588,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/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(4628,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)],[588]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ~ ( ( C
= ( E @ ( D @ k1_funct_1 ) ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( A @ ( D @ k9_relat_1 ) @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_partfun1) ).
thf(4211,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ~ ( ( C
= ( E @ ( D @ k1_funct_1 ) ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( A @ ( D @ k9_relat_1 ) @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(1146,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/sandbox/benchmark/theBenchmark.p',t50_group_6) ).
thf(7354,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)],[1146]) ).
thf(1214,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/sandbox/benchmark/theBenchmark.p',t130_group_2) ).
thf(7722,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)],[1214]) ).
thf(1704,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/sandbox/benchmark/theBenchmark.p',t131_group_3) ).
thf(10029,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)],[1704]) ).
thf(1628,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/sandbox/benchmark/theBenchmark.p',t81_group_2) ).
thf(9738,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)],[1628]) ).
thf(1405,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/sandbox/benchmark/theBenchmark.p',t14_group_3) ).
thf(8742,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)],[1405]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_funct_1) ).
thf(2762,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(1336,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ( C @ ( D @ k10_relat_1 ) @ ( E @ r2_hidden ) )
<=> ( ( C @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funct_2) ).
thf(8421,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ( ( ( C @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ k10_relat_1 ) @ ( E @ r2_hidden ) ) )
& ( ( C @ ( D @ k10_relat_1 ) @ ( E @ r2_hidden ) )
=> ( ( C @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).
thf(1249,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/sandbox/benchmark/theBenchmark.p',t15_relset_1) ).
thf(7952,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)],[1249]) ).
thf(641,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_partfun1) ).
thf(4853,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(649,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_realset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_realset1) ).
thf(4893,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)],[649]) ).
thf(1267,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/sandbox/benchmark/theBenchmark.p',d13_group_4) ).
thf(8046,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)],[1267]) ).
thf(647,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/sandbox/benchmark/theBenchmark.p',t185_partfun1) ).
thf(4888,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)],[647]) ).
thf(1043,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/sandbox/benchmark/theBenchmark.p',t107_group_3) ).
thf(6731,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)],[1043]) ).
thf(874,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/sandbox/benchmark/theBenchmark.p',d10_group_1) ).
thf(5968,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)],[874]) ).
thf(1151,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/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(7410,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)],[1151]) ).
thf(777,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_setfam_1 ) )
& ( B @ ( A @ r1_setfam_1 ) ) )
=> ( C @ ( A @ r1_setfam_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_setfam_1) ).
thf(5519,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_setfam_1 ) )
& ( B @ ( A @ r1_setfam_1 ) ) )
=> ( C @ ( A @ r1_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
& ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
thf(1868,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
& ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1258,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/sandbox/benchmark/theBenchmark.p',t58_setfam_1) ).
thf(7999,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)],[1258]) ).
thf(1524,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/sandbox/benchmark/theBenchmark.p',dt_k6_group_2) ).
thf(9323,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)],[1524]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_relat_1) ).
thf(2954,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1617,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/sandbox/benchmark/theBenchmark.p',redefinition_k2_group_6) ).
thf(9703,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)],[1617]) ).
thf(1353,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/sandbox/benchmark/theBenchmark.p',t31_group_6) ).
thf(8508,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)],[1353]) ).
thf(273,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/sandbox/benchmark/theBenchmark.p',t78_funct_4) ).
thf(3097,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)],[273]) ).
thf(1236,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/sandbox/benchmark/theBenchmark.p',s1_int_1) ).
thf(7849,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)],[1236]) ).
thf(705,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/sandbox/benchmark/theBenchmark.p',t58_card_1) ).
thf(5157,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)],[705]) ).
thf(351,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/sandbox/benchmark/theBenchmark.p',cc1_binop_1) ).
thf(3450,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)],[351]) ).
thf(364,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/sandbox/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(3503,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)],[364]) ).
thf(1161,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/sandbox/benchmark/theBenchmark.p',t3_rlvect_1) ).
thf(7471,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)],[1161]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_xboole_1) ).
thf(3303,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)],[324]) ).
thf(1687,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/sandbox/benchmark/theBenchmark.p',dt_k6_group_3) ).
thf(9968,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)],[1687]) ).
thf(1173,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/sandbox/benchmark/theBenchmark.p',t40_group_6) ).
thf(7550,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)],[1173]) ).
thf(180,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/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).
thf(2646,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)],[180]) ).
thf(429,axiom,
! [A: $i] :
( ( A @ ( A @ k6_finseq_1 @ m2_finseq_1 ) )
& ( A @ k6_finseq_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_finseq_1) ).
thf(3852,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)],[429]) ).
thf(1098,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/sandbox/benchmark/theBenchmark.p',s2_card_1) ).
thf(7037,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)],[1098]) ).
thf(397,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/sandbox/benchmark/theBenchmark.p',t137_zfmisc_1) ).
thf(3635,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)],[397]) ).
thf(75,axiom,
! [A: $i] :
( ? [B: $i] :
( ( B @ k2_finseq_1 @ ( A @ r1_tarski ) )
& ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) ) )
=> ( ( ( A @ k14_finseq_1 )
= k1_xboole_0 )
<=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_finseq_1) ).
thf(2164,plain,
! [A: $i] :
( ? [B: $i] :
( ( B @ k2_finseq_1 @ ( A @ r1_tarski ) )
& ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) ) )
=> ( ( ( A = k1_xboole_0 )
=> ( ( A @ k14_finseq_1 )
= k1_xboole_0 ) )
& ( ( ( A @ k14_finseq_1 )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(753,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/sandbox/benchmark/theBenchmark.p',t49_xboole_1) ).
thf(5438,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)],[753]) ).
thf(913,axiom,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( A = B )
<=> ( B @ ( A @ r2_wellord2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_card_1) ).
thf(6139,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)],[913]) ).
thf(896,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/sandbox/benchmark/theBenchmark.p',t19_group_2) ).
thf(6064,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)],[896]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 @ ( B @ r1_tarski ) )
& ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( ( A @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t161_funct_1) ).
thf(2118,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 @ ( B @ r1_tarski ) )
& ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( ( A @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(938,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/sandbox/benchmark/theBenchmark.p',t76_group_3) ).
thf(6250,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)],[938]) ).
thf(574,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/sandbox/benchmark/theBenchmark.p',fc1_group_1) ).
thf(4557,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)],[574]) ).
thf(1328,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/sandbox/benchmark/theBenchmark.p',abstractness_v1_group_1) ).
thf(8397,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)],[1328]) ).
thf(680,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_xboole_1) ).
thf(5034,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)],[680]) ).
thf(1375,axiom,
? [A: $i] : ( A @ v1_int_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_int_1) ).
thf(8613,plain,
? [A: $i] : ( A @ v1_int_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
thf(2047,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)],[47]) ).
thf(970,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/sandbox/benchmark/theBenchmark.p',t41_group_2) ).
thf(6388,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)],[970]) ).
thf(1747,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/sandbox/benchmark/theBenchmark.p',t84_group_2) ).
thf(10165,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)],[1747]) ).
thf(1801,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/sandbox/benchmark/theBenchmark.p',dt_k10_group_3) ).
thf(10374,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)],[1801]) ).
thf(765,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_xboole_1) ).
thf(5487,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(1773,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/sandbox/benchmark/theBenchmark.p',t165_group_2) ).
thf(10258,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)],[1773]) ).
thf(852,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/sandbox/benchmark/theBenchmark.p',t32_partfun1) ).
thf(5862,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)],[852]) ).
thf(1501,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/sandbox/benchmark/theBenchmark.p',t176_partfun1) ).
thf(9252,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)],[1501]) ).
thf(1104,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/sandbox/benchmark/theBenchmark.p',t48_group_6) ).
thf(7078,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)],[1104]) ).
thf(204,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/sandbox/benchmark/theBenchmark.p',t19_funct_4) ).
thf(2790,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)],[204]) ).
thf(1614,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/sandbox/benchmark/theBenchmark.p',t93_group_4) ).
thf(9688,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)],[1614]) ).
thf(1660,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/sandbox/benchmark/theBenchmark.p',symmetry_r6_group_3) ).
thf(9881,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)],[1660]) ).
thf(1217,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/sandbox/benchmark/theBenchmark.p',t119_group_2) ).
thf(7735,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)],[1217]) ).
thf(929,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/sandbox/benchmark/theBenchmark.p',t61_group_2) ).
thf(6200,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)],[929]) ).
thf(1582,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/sandbox/benchmark/theBenchmark.p',t77_group_2) ).
thf(9549,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)],[1582]) ).
thf(1633,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/sandbox/benchmark/theBenchmark.p',t78_group_6) ).
thf(9753,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)],[1633]) ).
thf(961,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/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(6343,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)],[961]) ).
thf(154,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/sandbox/benchmark/theBenchmark.p',reflexivity_r1_partfun1) ).
thf(2541,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)],[154]) ).
thf(1432,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_xboole_1) ).
thf(8888,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)],[1432]) ).
thf(638,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/sandbox/benchmark/theBenchmark.p',t172_partfun1) ).
thf(4836,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)],[638]) ).
thf(368,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/sandbox/benchmark/theBenchmark.p',t3_realset1) ).
thf(3514,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)],[368]) ).
thf(1355,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/sandbox/benchmark/theBenchmark.p',t36_group_2) ).
thf(8513,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)],[1355]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k10_finseq_1 ) @ k4_finseq_1 )
= ( np__2 @ k2_finseq_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finseq_3) ).
thf(2441,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k10_finseq_1 ) @ k4_finseq_1 )
= ( np__2 @ k2_finseq_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(187,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/sandbox/benchmark/theBenchmark.p',t14_relat_1) ).
thf(2673,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)],[187]) ).
thf(1310,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/sandbox/benchmark/theBenchmark.p',t68_xboole_1) ).
thf(8265,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)],[1310]) ).
thf(168,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/sandbox/benchmark/theBenchmark.p',t15_relat_1) ).
thf(2601,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)],[168]) ).
thf(209,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/sandbox/benchmark/theBenchmark.p',t24_partfun1) ).
thf(2805,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)],[209]) ).
thf(413,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ k2_relat_1 )
= k1_xboole_0 )
& ( ( B @ ( k1_xboole_0 @ ( A @ k4_relset_1 ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_partfun1) ).
thf(3711,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ k2_relat_1 )
= k1_xboole_0 )
& ( ( B @ ( k1_xboole_0 @ ( A @ k4_relset_1 ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(1257,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_group_6) ).
thf(7989,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)],[1257]) ).
thf(937,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(6247,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(388,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( np__1 @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 @ ( np__1 @ ( A @ k2_xcmplx_0 ) @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_finseq_1) ).
thf(3603,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( np__1 @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 @ ( np__1 @ ( A @ k2_xcmplx_0 ) @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_xboole_1) ).
thf(3867,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)],[431]) ).
thf(1548,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/sandbox/benchmark/theBenchmark.p',symmetry_r2_group_3) ).
thf(9412,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)],[1548]) ).
thf(537,axiom,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_partfun1) ).
thf(4375,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(1408,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/sandbox/benchmark/theBenchmark.p',t62_group_3) ).
thf(8756,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)],[1408]) ).
thf(1239,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/sandbox/benchmark/theBenchmark.p',t69_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 @ ( 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)],[1239]) ).
thf(738,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_partfun1) ).
thf(5349,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k10_relat_1 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t177_relat_1) ).
thf(3022,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k10_relat_1 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(511,axiom,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
thf(4252,plain,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(840,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/sandbox/benchmark/theBenchmark.p',dt_k4_group_2) ).
thf(5815,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)],[840]) ).
thf(416,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(3742,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(531,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( ( A @ k2_group_4 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_group_4) ).
thf(4344,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( ( A @ k2_group_4 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(1402,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/sandbox/benchmark/theBenchmark.p',t20_group_2) ).
thf(8724,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)],[1402]) ).
thf(418,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/sandbox/benchmark/theBenchmark.p',t57_setfam_1) ).
thf(3752,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)],[418]) ).
thf(458,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/sandbox/benchmark/theBenchmark.p',t14_binop_1) ).
thf(3989,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)],[458]) ).
thf(1657,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/sandbox/benchmark/theBenchmark.p',d1_group_3) ).
thf(9849,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)],[1657]) ).
thf(1105,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/sandbox/benchmark/theBenchmark.p',t59_group_1) ).
thf(7084,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)],[1105]) ).
thf(1689,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/sandbox/benchmark/theBenchmark.p',t19_group_3) ).
thf(9981,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)],[1689]) ).
thf(1729,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/sandbox/benchmark/theBenchmark.p',t139_group_3) ).
thf(10102,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)],[1729]) ).
thf(286,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/sandbox/benchmark/theBenchmark.p',free_g1_group_1) ).
thf(3154,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)],[286]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
<=> ! [E: $i] :
( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_2) ).
thf(3134,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ! [E: $i] :
( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( D @ ( C @ r1_partfun1 ) ) )
& ( ( D @ ( C @ r1_partfun1 ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(6,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/sandbox/benchmark/theBenchmark.p',t140_partfun1) ).
thf(1824,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)],[6]) ).
thf(1726,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/sandbox/benchmark/theBenchmark.p',d14_group_3) ).
thf(10084,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)],[1726]) ).
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 ) )
=> ( ( ( 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/sandbox/benchmark/theBenchmark.p',t62_group_2) ).
thf(9745,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)],[1630]) ).
thf(998,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/sandbox/benchmark/theBenchmark.p',t68_group_1) ).
thf(6496,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)],[998]) ).
thf(635,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( B @ ( A @ k10_finseq_1 ) @ v2_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_finseq_3) ).
thf(4821,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k10_finseq_1 ) @ v2_funct_1 )
=> ( A != B ) )
& ( ( A != B )
=> ( B @ ( A @ k10_finseq_1 ) @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(321,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/sandbox/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(3286,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)],[321]) ).
thf(1131,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/sandbox/benchmark/theBenchmark.p',t164_funct_2) ).
thf(7301,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)],[1131]) ).
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 @ ( 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/sandbox/benchmark/theBenchmark.p',t21_group_1) ).
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 @ ( 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)],[1378]) ).
thf(471,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/sandbox/benchmark/theBenchmark.p',t53_funct_2) ).
thf(4044,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)],[471]) ).
thf(865,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/sandbox/benchmark/theBenchmark.p',t115_group_3) ).
thf(5924,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)],[865]) ).
thf(1025,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/sandbox/benchmark/theBenchmark.p',d14_group_6) ).
thf(6646,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)],[1025]) ).
thf(1263,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/sandbox/benchmark/theBenchmark.p',d1_group_2) ).
thf(8026,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)],[1263]) ).
thf(815,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_xboole_1) ).
thf(5690,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)],[815]) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',t21_funct_2) ).
thf(2200,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)],[85]) ).
thf(715,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(5201,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)],[715]) ).
thf(895,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(6060,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',t73_funct_4) ).
thf(2344,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)],[115]) ).
thf(1029,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(6666,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t175_relat_1) ).
thf(2228,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(881,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/sandbox/benchmark/theBenchmark.p',t4_relset_1) ).
thf(5993,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)],[881]) ).
thf(443,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/sandbox/benchmark/theBenchmark.p',t45_funct_2) ).
thf(3931,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)],[443]) ).
thf(421,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/sandbox/benchmark/theBenchmark.p',t49_funct_2) ).
thf(3799,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)],[421]) ).
thf(448,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/sandbox/benchmark/theBenchmark.p',t59_domain_1) ).
thf(3948,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)],[448]) ).
thf(1108,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/sandbox/benchmark/theBenchmark.p',t64_group_1) ).
thf(7097,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)],[1108]) ).
thf(1256,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_2_domain_1) ).
thf(7977,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)],[1256]) ).
thf(818,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ k1_tarski ) )
=> ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_zfmisc_1) ).
thf(5702,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)],[818]) ).
thf(392,axiom,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(3618,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(1425,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(8832,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425]) ).
thf(1021,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/sandbox/benchmark/theBenchmark.p',t86_card_1) ).
thf(6629,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)],[1021]) ).
thf(1708,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/sandbox/benchmark/theBenchmark.p',t40_group_4) ).
thf(10038,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)],[1708]) ).
thf(879,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/sandbox/benchmark/theBenchmark.p',t151_funct_2) ).
thf(5983,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)],[879]) ).
thf(174,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
thf(2628,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)],[174]) ).
thf(499,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 @ ( np__1 @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 @ ( k5_numbers @ k6_subset_1 ) ) )
= ( np__1 @ ( A @ k2_xcmplx_0 ) @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_finseq_3) ).
thf(4192,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 @ ( np__1 @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 @ ( k5_numbers @ k6_subset_1 ) ) )
= ( np__1 @ ( A @ k2_xcmplx_0 ) @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ( ( C @ ( B @ k3_finseq_1 @ r1_xreal_0 ) )
=> ( ( C @ ( B @ ( A @ k16_finseq_1 ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_finseq_1) ).
thf(2670,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ( ( C @ ( B @ k3_finseq_1 @ r1_xreal_0 ) )
=> ( ( C @ ( B @ ( A @ k16_finseq_1 ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(582,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(4608,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)],[582]) ).
thf(1178,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/sandbox/benchmark/theBenchmark.p',t29_group_3) ).
thf(7576,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)],[1178]) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',t158_relat_1) ).
thf(1920,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)],[26]) ).
thf(917,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/sandbox/benchmark/theBenchmark.p',dt_k12_group_2) ).
thf(6163,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)],[917]) ).
thf(1606,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/sandbox/benchmark/theBenchmark.p',dt_m1_group_6) ).
thf(9658,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)],[1606]) ).
thf(615,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_xboole_1) ).
thf(4725,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)],[615]) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',t56_funct_1) ).
thf(2565,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)],[160]) ).
thf(1288,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/sandbox/benchmark/theBenchmark.p',t26_group_4) ).
thf(8145,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)],[1288]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= ( C @ k1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
thf(2663,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= ( C @ k1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(890,axiom,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_xboole_1) ).
thf(6043,plain,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(622,axiom,
! [A: $i] :
( ( ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( k1_xboole_0 @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finsub_1) ).
thf(4757,plain,
! [A: $i] :
( ( ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(264,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/sandbox/benchmark/theBenchmark.p',t48_relat_1) ).
thf(3065,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)],[264]) ).
thf(337,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/sandbox/benchmark/theBenchmark.p',d8_group_1) ).
thf(3349,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)],[337]) ).
thf(1404,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/sandbox/benchmark/theBenchmark.p',t58_group_6) ).
thf(8736,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)],[1404]) ).
thf(541,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_xboole_1) ).
thf(4385,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)],[541]) ).
thf(1734,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/sandbox/benchmark/theBenchmark.p',t138_group_2) ).
thf(10116,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)],[1734]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',t72_partfun1) ).
thf(1951,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)],[30]) ).
thf(1770,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/sandbox/benchmark/theBenchmark.p',t48_group_2) ).
thf(10247,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)],[1770]) ).
thf(434,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/sandbox/benchmark/theBenchmark.p',t131_zfmisc_1) ).
thf(3877,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)],[434]) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',t17_funct_1) ).
thf(2068,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)],[55]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(1819,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)],[4]) ).
thf(497,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( A @ k2_card_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_card_1) ).
thf(4187,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( A @ k2_card_1 @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(1516,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/sandbox/benchmark/theBenchmark.p',t69_group_4) ).
thf(9301,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)],[1516]) ).
thf(375,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/sandbox/benchmark/theBenchmark.p',t131_funct_2) ).
thf(3535,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)],[375]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',t47_funct_1) ).
thf(1836,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)],[9]) ).
thf(695,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(5113,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)],[695]) ).
thf(902,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/sandbox/benchmark/theBenchmark.p',t34_group_1) ).
thf(6096,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)],[902]) ).
thf(1552,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/sandbox/benchmark/theBenchmark.p',t86_group_6) ).
thf(9423,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)],[1552]) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',t154_relat_1) ).
thf(2181,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)],[79]) ).
thf(1707,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/sandbox/benchmark/theBenchmark.p',t77_group_3) ).
thf(10035,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)],[1707]) ).
thf(619,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/sandbox/benchmark/theBenchmark.p',t130_zfmisc_1) ).
thf(4740,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)],[619]) ).
thf(974,axiom,
? [A: $i] : ( A @ l1_vectsp_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_vectsp_1) ).
thf(6402,plain,
? [A: $i] : ( A @ l1_vectsp_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(1766,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/sandbox/benchmark/theBenchmark.p',t5_latsubgr) ).
thf(10235,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)],[1766]) ).
thf(386,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/sandbox/benchmark/theBenchmark.p',t39_partfun1) ).
thf(3595,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)],[386]) ).
thf(1205,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_group_4) ).
thf(7686,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)],[1205]) ).
thf(733,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/sandbox/benchmark/theBenchmark.p',dt_g1_group_1) ).
thf(5285,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)],[733]) ).
thf(1274,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/sandbox/benchmark/theBenchmark.p',t6_orders_1) ).
thf(8073,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)],[1274]) ).
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 @ m1_subset_1 ) )
=> ( ( B @ ( np__1 @ k7_binop_2 @ ( A @ k6_group_1 ) ) )
= ( B @ ( A @ k3_group_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_group_1) ).
thf(6728,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)],[1042]) ).
thf(1360,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/sandbox/benchmark/theBenchmark.p',t6_latsubgr) ).
thf(8530,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)],[1360]) ).
thf(1647,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_2) ).
thf(9804,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)],[1647]) ).
thf(1744,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/sandbox/benchmark/theBenchmark.p',dt_k6_group_6) ).
thf(10154,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)],[1744]) ).
thf(191,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/sandbox/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)],[191]) ).
thf(1558,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/sandbox/benchmark/theBenchmark.p',t94_group_2) ).
thf(9444,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)],[1558]) ).
thf(343,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/sandbox/benchmark/theBenchmark.p',t20_group_4) ).
thf(3386,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)],[343]) ).
thf(477,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/sandbox/benchmark/theBenchmark.p',t4_xboole_1) ).
thf(4109,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)],[477]) ).
thf(301,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/sandbox/benchmark/theBenchmark.p',t99_partfun1) ).
thf(3205,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)],[301]) ).
thf(1143,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/sandbox/benchmark/theBenchmark.p',t76_xboole_1) ).
thf(7346,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)],[1143]) ).
thf(1027,axiom,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
thf(6656,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(142,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i] : ( B @ ( B @ ( A @ k9_relat_1 ) @ ( A @ k10_relat_1 ) @ r1_tarski ) )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t153_funct_1) ).
thf(2498,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i] : ( B @ ( B @ ( A @ k9_relat_1 ) @ ( A @ k10_relat_1 ) @ r1_tarski ) )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(960,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/sandbox/benchmark/theBenchmark.p',t13_latsubgr) ).
thf(6339,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)],[960]) ).
thf(1316,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/sandbox/benchmark/theBenchmark.p',t43_group_6) ).
thf(8314,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)],[1316]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).
thf(2115,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(313,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(3254,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)],[313]) ).
thf(904,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/sandbox/benchmark/theBenchmark.p',dt_k9_group_4) ).
thf(6101,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)],[904]) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',t79_funct_4) ).
thf(1851,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)],[13]) ).
thf(1391,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/sandbox/benchmark/theBenchmark.p',t4_mcart_1) ).
thf(8677,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)],[1391]) ).
thf(721,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/sandbox/benchmark/theBenchmark.p',dt_k8_setfam_1) ).
thf(5238,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)],[721]) ).
thf(1090,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/sandbox/benchmark/theBenchmark.p',t120_group_2) ).
thf(6995,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)],[1090]) ).
thf(562,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/sandbox/benchmark/theBenchmark.p',t9_group_4) ).
thf(4512,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)],[562]) ).
thf(748,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/sandbox/benchmark/theBenchmark.p',t42_subset_1) ).
thf(5423,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)],[748]) ).
thf(666,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/sandbox/benchmark/theBenchmark.p',t13_binop_1) ).
thf(4974,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)],[666]) ).
thf(1365,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/sandbox/benchmark/theBenchmark.p',dt_k11_domain_1) ).
thf(8562,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)],[1365]) ).
thf(1036,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/sandbox/benchmark/theBenchmark.p',t39_group_2) ).
thf(6691,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)],[1036]) ).
thf(240,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(2973,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)],[240]) ).
thf(1663,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/sandbox/benchmark/theBenchmark.p',t89_group_6) ).
thf(9889,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)],[1663]) ).
thf(163,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/sandbox/benchmark/theBenchmark.p',t125_funct_1) ).
thf(2577,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)],[163]) ).
thf(987,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/sandbox/benchmark/theBenchmark.p',dt_k7_group_6) ).
thf(6459,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)],[987]) ).
thf(1639,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/sandbox/benchmark/theBenchmark.p',dt_k11_group_3) ).
thf(9773,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)],[1639]) ).
thf(1372,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/sandbox/benchmark/theBenchmark.p',t17_group_2) ).
thf(8604,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)],[1372]) ).
thf(1498,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(9244,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498]) ).
thf(932,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/sandbox/benchmark/theBenchmark.p',dt_k10_domain_1) ).
thf(6235,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)],[932]) ).
thf(640,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ~ ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(4845,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)],[640]) ).
thf(750,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_finset_1) ).
thf(5428,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)],[750]) ).
thf(411,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(3704,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)],[411]) ).
thf(1588,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/sandbox/benchmark/theBenchmark.p',dt_k5_group_4) ).
thf(9576,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)],[1588]) ).
thf(794,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/sandbox/benchmark/theBenchmark.p',t98_group_3) ).
thf(5583,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)],[794]) ).
thf(453,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_orders_1) ).
thf(3963,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(1743,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/sandbox/benchmark/theBenchmark.p',t36_group_1) ).
thf(10152,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)],[1743]) ).
thf(1786,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/sandbox/benchmark/theBenchmark.p',t94_group_4) ).
thf(10318,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)],[1786]) ).
thf(1297,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/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(8187,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)],[1297]) ).
thf(1782,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/sandbox/benchmark/theBenchmark.p',redefinition_r1_group_2) ).
thf(10298,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)],[1782]) ).
thf(222,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/sandbox/benchmark/theBenchmark.p',t14_funct_1) ).
thf(2858,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)],[222]) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',idempotence_k1_funct_4) ).
thf(2537,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)],[153]) ).
thf(856,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/sandbox/benchmark/theBenchmark.p',t59_funct_2) ).
thf(5889,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)],[856]) ).
thf(1462,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(9063,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462]) ).
thf(417,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/sandbox/benchmark/theBenchmark.p',t174_partfun1) ).
thf(3746,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)],[417]) ).
thf(1118,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/sandbox/benchmark/theBenchmark.p',t175_partfun1) ).
thf(7204,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)],[1118]) ).
thf(848,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(5847,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(402,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/sandbox/benchmark/theBenchmark.p',t26_funct_2) ).
thf(3650,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)],[402]) ).
thf(440,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/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(3916,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)],[440]) ).
thf(445,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/sandbox/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(3941,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)],[445]) ).
thf(1578,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/sandbox/benchmark/theBenchmark.p',t132_group_3) ).
thf(9530,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)],[1578]) ).
thf(525,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/sandbox/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(4320,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)],[525]) ).
thf(528,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/sandbox/benchmark/theBenchmark.p',t24_funct_2) ).
thf(4333,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)],[528]) ).
thf(922,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/sandbox/benchmark/theBenchmark.p',dt_k4_group_4) ).
thf(6175,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)],[922]) ).
thf(1603,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/sandbox/benchmark/theBenchmark.p',t58_group_4) ).
thf(9640,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)],[1603]) ).
thf(768,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/sandbox/benchmark/theBenchmark.p',t64_funct_2) ).
thf(5496,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)],[768]) ).
thf(1621,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/sandbox/benchmark/theBenchmark.p',dt_k9_group_3) ).
thf(9714,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)],[1621]) ).
thf(126,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/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
thf(2419,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)],[126]) ).
thf(725,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/sandbox/benchmark/theBenchmark.p',t81_card_1) ).
thf(5253,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)],[725]) ).
thf(1020,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/sandbox/benchmark/theBenchmark.p',t45_card_1) ).
thf(6625,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)],[1020]) ).
thf(1130,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/sandbox/benchmark/theBenchmark.p',t141_group_3) ).
thf(7293,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)],[1130]) ).
thf(1242,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/sandbox/benchmark/theBenchmark.p',t148_funct_2) ).
thf(7898,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)],[1242]) ).
thf(659,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/sandbox/benchmark/theBenchmark.p',fc1_setfam_1) ).
thf(4951,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)],[659]) ).
thf(1155,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/sandbox/benchmark/theBenchmark.p',t38_group_4) ).
thf(7435,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)],[1155]) ).
thf(327,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/sandbox/benchmark/theBenchmark.p',t26_subset_1) ).
thf(3311,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)],[327]) ).
thf(1731,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/sandbox/benchmark/theBenchmark.p',t93_group_6) ).
thf(10107,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)],[1731]) ).
thf(226,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/sandbox/benchmark/theBenchmark.p',t66_funct_1) ).
thf(2877,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)],[226]) ).
thf(1398,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/sandbox/benchmark/theBenchmark.p',t49_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] :
( ( ( 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)],[1398]) ).
thf(1379,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/sandbox/benchmark/theBenchmark.p',dt_k13_domain_1) ).
thf(8631,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)],[1379]) ).
thf(1426,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/sandbox/benchmark/theBenchmark.p',t6_funct_2) ).
thf(8835,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)],[1426]) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',t33_funct_1) ).
thf(2023,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)],[44]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
<=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(3326,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)],[332]) ).
thf(244,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(3000,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(579,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/sandbox/benchmark/theBenchmark.p',d4_group_4) ).
thf(4582,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)],[579]) ).
thf(1262,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(8017,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)],[1262]) ).
thf(862,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/sandbox/benchmark/theBenchmark.p',t106_group_3) ).
thf(5915,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)],[862]) ).
thf(426,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ~ ( A @ ( B @ r1_xreal_0 ) )
=> ( B @ k2_finseq_1 @ ( np__1 @ ( A @ k2_xcmplx_0 ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_finseq_3) ).
thf(3846,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ~ ( A @ ( B @ r1_xreal_0 ) )
=> ( B @ k2_finseq_1 @ ( np__1 @ ( A @ k2_xcmplx_0 ) @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(819,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/sandbox/benchmark/theBenchmark.p',d8_group_3) ).
thf(5705,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)],[819]) ).
thf(1064,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k6_lattices @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_lattices) ).
thf(6844,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)],[1064]) ).
thf(806,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/sandbox/benchmark/theBenchmark.p',dt_k7_group_1) ).
thf(5651,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)],[806]) ).
thf(1307,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/sandbox/benchmark/theBenchmark.p',dt_k10_group_1) ).
thf(8251,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)],[1307]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',t50_relat_1) ).
thf(2561,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)],[158]) ).
thf(1014,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/sandbox/benchmark/theBenchmark.p',t30_group_6) ).
thf(6593,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)],[1014]) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).
thf(2830,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)],[215]) ).
thf(1541,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/sandbox/benchmark/theBenchmark.p',t13_group_6) ).
thf(9387,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)],[1541]) ).
thf(272,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/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).
thf(3094,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)],[272]) ).
thf(613,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(4721,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(550,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_xboole_1) ).
thf(4425,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)],[550]) ).
thf(1135,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/sandbox/benchmark/theBenchmark.p',d6_group_1) ).
thf(7318,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)],[1135]) ).
thf(1553,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/sandbox/benchmark/theBenchmark.p',dt_k16_group_2) ).
thf(9426,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)],[1553]) ).
thf(801,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/sandbox/benchmark/theBenchmark.p',d5_group_2) ).
thf(5620,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)],[801]) ).
thf(523,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/sandbox/benchmark/theBenchmark.p',t25_subset_1) ).
thf(4315,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)],[523]) ).
thf(110,axiom,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(2312,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(247,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/sandbox/benchmark/theBenchmark.p',t27_relat_1) ).
thf(3010,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)],[247]) ).
thf(136,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/sandbox/benchmark/theBenchmark.p',t58_funct_1) ).
thf(2455,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)],[136]) ).
thf(1596,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/sandbox/benchmark/theBenchmark.p',t21_group_3) ).
thf(9609,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)],[1596]) ).
thf(1659,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/sandbox/benchmark/theBenchmark.p',d13_group_1) ).
thf(9878,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)],[1659]) ).
thf(545,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/sandbox/benchmark/theBenchmark.p',t24_xboole_1) ).
thf(4406,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)],[545]) ).
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 ) )
=> ! [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/sandbox/benchmark/theBenchmark.p',t4_latsubgr) ).
thf(8407,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)],[1331]) ).
thf(1234,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/sandbox/benchmark/theBenchmark.p',t113_funct_2) ).
thf(7841,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)],[1234]) ).
thf(785,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/sandbox/benchmark/theBenchmark.p',t16_funct_2) ).
thf(5547,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)],[785]) ).
thf(1269,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/sandbox/benchmark/theBenchmark.p',t48_subset_1) ).
thf(8053,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)],[1269]) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',t55_partfun1) ).
thf(3032,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)],[256]) ).
thf(1352,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_group_3) ).
thf(8499,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)],[1352]) ).
thf(1444,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_3_group_3) ).
thf(8968,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)],[1444]) ).
thf(297,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_orders_1 @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_orders_1) ).
thf(3194,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_orders_1 @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',t123_funct_1) ).
thf(2349,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)],[117]) ).
thf(157,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/sandbox/benchmark/theBenchmark.p',t15_funct_1) ).
thf(2551,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)],[157]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
=> ( A @ ( B @ k9_relat_1 ) @ ( B @ k10_relat_1 ) @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_1) ).
thf(2085,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
=> ( A @ ( B @ k9_relat_1 ) @ ( B @ k10_relat_1 ) @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1150,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/sandbox/benchmark/theBenchmark.p',t151_group_3) ).
thf(7404,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)],[1150]) ).
thf(1767,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/sandbox/benchmark/theBenchmark.p',t92_group_4) ).
thf(10239,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)],[1767]) ).
thf(185,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/sandbox/benchmark/theBenchmark.p',t33_partfun1) ).
thf(2666,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)],[185]) ).
thf(242,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(2978,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(1543,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/sandbox/benchmark/theBenchmark.p',t14_group_1) ).
thf(9392,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)],[1543]) ).
thf(1797,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/sandbox/benchmark/theBenchmark.p',t98_group_4) ).
thf(10353,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)],[1797]) ).
thf(1168,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_setfam_1 ) )
<=> ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( A @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_setfam_1) ).
thf(7523,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r1_setfam_1 ) ) )
& ( ( B @ ( A @ r1_setfam_1 ) )
=> ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( A @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(1203,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/sandbox/benchmark/theBenchmark.p',t60_group_3) ).
thf(7682,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)],[1203]) ).
thf(111,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/sandbox/benchmark/theBenchmark.p',t28_relat_1) ).
thf(2317,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)],[111]) ).
thf(1230,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_group_2) ).
thf(7821,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)],[1230]) ).
thf(1574,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/sandbox/benchmark/theBenchmark.p',t67_group_2) ).
thf(9513,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)],[1574]) ).
thf(568,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/sandbox/benchmark/theBenchmark.p',t33_subset_1) ).
thf(4530,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)],[568]) ).
thf(1504,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/sandbox/benchmark/theBenchmark.p',t75_group_1) ).
thf(9260,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)],[1504]) ).
thf(1652,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/sandbox/benchmark/theBenchmark.p',t145_group_3) ).
thf(9825,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)],[1652]) ).
thf(1433,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/sandbox/benchmark/theBenchmark.p',t61_group_6) ).
thf(8891,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)],[1433]) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t154_funct_1) ).
thf(2836,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(720,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/sandbox/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(5234,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)],[720]) ).
thf(1413,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/sandbox/benchmark/theBenchmark.p',t15_group_1) ).
thf(8775,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)],[1413]) ).
thf(1752,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/sandbox/benchmark/theBenchmark.p',d9_group_2) ).
thf(10180,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)],[1752]) ).
thf(1616,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/sandbox/benchmark/theBenchmark.p',rc4_group_1) ).
thf(9694,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)],[1616]) ).
thf(309,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 )
!= ( np__1 @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finseq_3) ).
thf(3242,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 )
!= ( np__1 @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(1486,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_zfmisc_1) ).
thf(9200,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1486]) ).
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 @ ( 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/sandbox/benchmark/theBenchmark.p',d18_group_2) ).
thf(7668,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)],[1202]) ).
thf(962,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/sandbox/benchmark/theBenchmark.p',t43_group_3) ).
thf(6349,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)],[962]) ).
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 @ ( 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/sandbox/benchmark/theBenchmark.p',t134_group_3) ).
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 ) )
& ( 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)],[1761]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m3_realset1) ).
thf(2285,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(145,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/sandbox/benchmark/theBenchmark.p',t151_relat_1) ).
thf(2504,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)],[145]) ).
thf(849,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/sandbox/benchmark/theBenchmark.p',t4_group_6) ).
thf(5850,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)],[849]) ).
thf(390,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/sandbox/benchmark/theBenchmark.p',dt_k3_funct_2) ).
thf(3611,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)],[390]) ).
thf(1389,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/sandbox/benchmark/theBenchmark.p',dt_k8_domain_1) ).
thf(8673,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)],[1389]) ).
thf(702,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m1_orders_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_orders_1) ).
thf(5149,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m1_orders_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( A @ ( A @ ( B @ k9_relat_1 ) @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t152_funct_1) ).
thf(2304,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( A @ ( A @ ( B @ k9_relat_1 ) @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(1093,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(7014,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)],[1093]) ).
thf(262,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/sandbox/benchmark/theBenchmark.p',t17_funct_4) ).
thf(3059,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)],[262]) ).
thf(959,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/sandbox/benchmark/theBenchmark.p',d9_group_3) ).
thf(6331,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)],[959]) ).
thf(1252,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/sandbox/benchmark/theBenchmark.p',dt_k14_group_2) ).
thf(7966,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)],[1252]) ).
thf(1569,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/sandbox/benchmark/theBenchmark.p',t35_group_1) ).
thf(9498,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)],[1569]) ).
thf(804,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_finset_1 )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( B @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_card_1) ).
thf(5639,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)],[804]) ).
thf(698,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_xboole_1) ).
thf(5134,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)],[698]) ).
thf(979,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/sandbox/benchmark/theBenchmark.p',t52_domain_1) ).
thf(6433,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)],[979]) ).
thf(993,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/sandbox/benchmark/theBenchmark.p',dt_k5_group_1) ).
thf(6475,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)],[993]) ).
thf(1218,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/sandbox/benchmark/theBenchmark.p',t28_group_6) ).
thf(7738,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)],[1218]) ).
thf(509,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/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(4244,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)],[509]) ).
thf(1600,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/sandbox/benchmark/theBenchmark.p',t64_group_4) ).
thf(9630,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)],[1600]) ).
thf(1165,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/sandbox/benchmark/theBenchmark.p',t60_group_1) ).
thf(7495,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)],[1165]) ).
thf(636,axiom,
! [A: $i] :
( ( ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( B @ v4_finsub_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v4_finsub_1 )
& ~ ( B @ ( A @ k3_xboole_0 ) @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_finsub_1) ).
thf(4829,plain,
! [A: $i] :
( ( ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( B @ v4_finsub_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v4_finsub_1 )
& ~ ( B @ ( A @ k3_xboole_0 ) @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(305,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/sandbox/benchmark/theBenchmark.p',t20_int_1) ).
thf(3222,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)],[305]) ).
thf(376,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/sandbox/benchmark/theBenchmark.p',fc3_lattices) ).
thf(3540,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)],[376]) ).
thf(934,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/sandbox/benchmark/theBenchmark.p',t47_subset_1) ).
thf(6239,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)],[934]) ).
thf(1473,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/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
thf(9112,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)],[1473]) ).
thf(611,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/sandbox/benchmark/theBenchmark.p',t9_setfam_1) ).
thf(4717,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)],[611]) ).
thf(1184,axiom,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( A @ u1_struct_0 @ ( A @ u1_vectsp_1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_vectsp_1) ).
thf(7597,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)],[1184]) ).
thf(1562,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/sandbox/benchmark/theBenchmark.p',t178_group_2) ).
thf(9461,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)],[1562]) ).
thf(1435,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/sandbox/benchmark/theBenchmark.p',t154_group_3) ).
thf(8896,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)],[1435]) ).
thf(1735,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/sandbox/benchmark/theBenchmark.p',fc1_group_3) ).
thf(10122,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)],[1735]) ).
thf(1207,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(7702,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(1692,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/sandbox/benchmark/theBenchmark.p',t75_group_6) ).
thf(9990,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)],[1692]) ).
thf(211,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/sandbox/benchmark/theBenchmark.p',d12_binop_1) ).
thf(2813,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)],[211]) ).
thf(532,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/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(4347,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)],[532]) ).
thf(1449,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/sandbox/benchmark/theBenchmark.p',t70_group_1) ).
thf(8995,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)],[1449]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',t135_partfun1) ).
thf(2052,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)],[49]) ).
thf(977,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/sandbox/benchmark/theBenchmark.p',t3_group_4) ).
thf(6418,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)],[977]) ).
thf(1278,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/sandbox/benchmark/theBenchmark.p',t31_finset_1) ).
thf(8090,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)],[1278]) ).
thf(660,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_zfmisc_1) ).
thf(4953,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)],[660]) ).
thf(1313,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ u1_struct_0 @ ( A @ u2_struct_0 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_struct_0) ).
thf(8307,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)],[1313]) ).
thf(277,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/sandbox/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)],[277]) ).
thf(1287,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/sandbox/benchmark/theBenchmark.p',t41_group_6) ).
thf(8142,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)],[1287]) ).
thf(605,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/sandbox/benchmark/theBenchmark.p',t186_partfun1) ).
thf(4689,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)],[605]) ).
thf(1138,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/sandbox/benchmark/theBenchmark.p',t6_group_3) ).
thf(7333,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)],[1138]) ).
thf(1088,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/sandbox/benchmark/theBenchmark.p',t44_group_1) ).
thf(6988,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)],[1088]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ v1_funct_1 )
& ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_4) ).
thf(2756,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ v1_funct_1 )
& ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(1419,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/sandbox/benchmark/theBenchmark.p',t55_group_1) ).
thf(8803,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)],[1419]) ).
thf(270,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/sandbox/benchmark/theBenchmark.p',t4_funct_2) ).
thf(3083,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)],[270]) ).
thf(288,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/sandbox/benchmark/theBenchmark.p',t21_int_1) ).
thf(3162,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)],[288]) ).
thf(1772,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/sandbox/benchmark/theBenchmark.p',t144_group_2) ).
thf(10252,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)],[1772]) ).
thf(1538,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/sandbox/benchmark/theBenchmark.p',redefinition_m1_group_6) ).
thf(9372,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)],[1538]) ).
thf(1464,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k3_finsub_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_finsub_1) ).
thf(9068,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k3_finsub_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464]) ).
thf(763,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_wellord2 ) )
=> ( ( A @ k2_card_1 )
= ( B @ k2_card_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_card_1) ).
thf(5479,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)],[763]) ).
thf(357,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/sandbox/benchmark/theBenchmark.p',t126_zfmisc_1) ).
thf(3476,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)],[357]) ).
thf(86,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(2203,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)],[86]) ).
thf(1101,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/sandbox/benchmark/theBenchmark.p',t43_group_2) ).
thf(7052,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)],[1101]) ).
thf(87,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/sandbox/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(2208,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)],[87]) ).
thf(1453,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_group_6) ).
thf(9008,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)],[1453]) ).
thf(745,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/sandbox/benchmark/theBenchmark.p',t53_setfam_1) ).
thf(5415,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)],[745]) ).
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 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k6_group_6 ) @ k8_group_1 )
= ( B @ ( A @ k16_group_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_group_6) ).
thf(9750,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)],[1632]) ).
thf(1198,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/sandbox/benchmark/theBenchmark.p',d14_group_2) ).
thf(7656,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)],[1198]) ).
thf(366,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/sandbox/benchmark/theBenchmark.p',t44_zfmisc_1) ).
thf(3508,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)],[366]) ).
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 ) )
=> ! [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/sandbox/benchmark/theBenchmark.p',t102_group_2) ).
thf(10349,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)],[1795]) ).
thf(921,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/sandbox/benchmark/theBenchmark.p',dt_k12_group_6) ).
thf(6171,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)],[921]) ).
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 @ ( 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/sandbox/benchmark/theBenchmark.p',t127_group_2) ).
thf(8796,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)],[1417]) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',t153_relat_1) ).
thf(2634,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)],[177]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',t5_funct_2) ).
thf(1857,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)],[14]) ).
thf(828,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_domain_1) ).
thf(5747,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)],[828]) ).
thf(1094,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/sandbox/benchmark/theBenchmark.p',t62_group_4) ).
thf(7020,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)],[1094]) ).
thf(424,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(3834,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(1669,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/sandbox/benchmark/theBenchmark.p',t53_group_2) ).
thf(9913,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)],[1669]) ).
thf(1082,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/sandbox/benchmark/theBenchmark.p',t7_latsubgr) ).
thf(6963,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)],[1082]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v4_finsub_1 )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ m1_subset_1 ) )
& ( C @ ( A @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ k3_xboole_0 ) @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finsub_1) ).
thf(4195,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v4_finsub_1 )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ m1_subset_1 ) )
& ( C @ ( A @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ k3_xboole_0 ) @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1305,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/sandbox/benchmark/theBenchmark.p',dt_k5_group_3) ).
thf(8247,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)],[1305]) ).
thf(1686,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/sandbox/benchmark/theBenchmark.p',t74_group_3) ).
thf(9964,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)],[1686]) ).
thf(384,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ k2_relat_1 )
= k1_xboole_0 )
& ( ( B @ ( A @ ( k1_xboole_0 @ k4_relset_1 ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_partfun1) ).
thf(3587,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ k2_relat_1 )
= k1_xboole_0 )
& ( ( B @ ( A @ ( k1_xboole_0 @ k4_relset_1 ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(996,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/sandbox/benchmark/theBenchmark.p',d16_group_1) ).
thf(6486,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)],[996]) ).
thf(1483,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_7_domain_1) ).
thf(9176,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)],[1483]) ).
thf(1276,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/sandbox/benchmark/theBenchmark.p',d10_group_6) ).
thf(8080,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)],[1276]) ).
thf(292,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/sandbox/benchmark/theBenchmark.p',cc3_vectsp_1) ).
thf(3173,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)],[292]) ).
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 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k6_group_6 ) @ u1_group_1 )
= ( B @ ( A @ k5_group_6 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_group_6) ).
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 ) )
& ( 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)],[1622]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k10_relat_1 ) )
= ( A @ ( C @ k10_relat_1 ) @ ( B @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t181_relat_1) ).
thf(2057,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k10_relat_1 ) )
= ( A @ ( C @ k10_relat_1 ) @ ( B @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(1268,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/sandbox/benchmark/theBenchmark.p',t140_group_2) ).
thf(8049,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)],[1268]) ).
thf(325,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/sandbox/benchmark/theBenchmark.p',t31_group_4) ).
thf(3306,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)],[325]) ).
thf(1058,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/sandbox/benchmark/theBenchmark.p',t8_group_3) ).
thf(6812,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)],[1058]) ).
thf(873,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(5964,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)],[873]) ).
thf(899,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/sandbox/benchmark/theBenchmark.p',t66_group_3) ).
thf(6070,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)],[899]) ).
thf(1259,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/sandbox/benchmark/theBenchmark.p',t159_funct_2) ).
thf(8004,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)],[1259]) ).
thf(399,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/sandbox/benchmark/theBenchmark.p',t1_partfun1) ).
thf(3639,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)],[399]) ).
thf(122,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/sandbox/benchmark/theBenchmark.p',t22_relat_1) ).
thf(2408,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)],[122]) ).
thf(716,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/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
thf(5209,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)],[716]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',d10_setfam_1) ).
thf(2089,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)],[60]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',t11_funct_4) ).
thf(2189,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)],[83]) ).
thf(973,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/sandbox/benchmark/theBenchmark.p',t18_group_2) ).
thf(6400,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)],[973]) ).
thf(954,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/sandbox/benchmark/theBenchmark.p',t74_group_1) ).
thf(6311,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)],[954]) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(2617,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)],[172]) ).
thf(724,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/sandbox/benchmark/theBenchmark.p',t52_setfam_1) ).
thf(5249,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)],[724]) ).
thf(1070,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k3_finsub_1 ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_finsub_1) ).
thf(6869,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k3_finsub_1 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(1111,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/sandbox/benchmark/theBenchmark.p',t47_group_3) ).
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 @ 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)],[1111]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',t55_funct_2) ).
thf(1996,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)],[39]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_partfun1) ).
thf(4308,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(1194,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/sandbox/benchmark/theBenchmark.p',t77_group_1) ).
thf(7646,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)],[1194]) ).
thf(1303,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/sandbox/benchmark/theBenchmark.p',t46_group_1) ).
thf(8234,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)],[1303]) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',t157_relat_1) ).
thf(2677,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)],[189]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
thf(2292,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)],[105]) ).
thf(1180,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/sandbox/benchmark/theBenchmark.p',t149_group_2) ).
thf(7582,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)],[1180]) ).
thf(584,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ v4_finsub_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finsub_1) ).
thf(4613,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ v4_finsub_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(1005,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(6561,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(1232,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/sandbox/benchmark/theBenchmark.p',t17_funct_2) ).
thf(7831,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)],[1232]) ).
thf(900,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/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(6084,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)],[900]) ).
thf(1710,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/sandbox/benchmark/theBenchmark.p',t81_group_4) ).
thf(10043,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)],[1710]) ).
thf(1780,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/sandbox/benchmark/theBenchmark.p',t99_group_2) ).
thf(10289,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)],[1780]) ).
thf(1176,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_card_1) ).
thf(7567,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(65,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/sandbox/benchmark/theBenchmark.p',t26_relat_1) ).
thf(2121,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)],[65]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_relat_1) ).
thf(2235,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)],[94]) ).
thf(813,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/sandbox/benchmark/theBenchmark.p',t125_group_2) ).
thf(5679,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)],[813]) ).
thf(231,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/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
thf(2936,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)],[231]) ).
thf(412,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_zfmisc_1) ).
thf(3707,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(810,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/sandbox/benchmark/theBenchmark.p',t51_group_1) ).
thf(5666,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)],[810]) ).
thf(955,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/sandbox/benchmark/theBenchmark.p',dt_k1_group_1) ).
thf(6314,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)],[955]) ).
thf(124,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/sandbox/benchmark/theBenchmark.p',t28_binop_1) ).
thf(2413,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)],[124]) ).
thf(281,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/sandbox/benchmark/theBenchmark.p',t19_group_4) ).
thf(3130,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)],[281]) ).
thf(893,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( ( A @ k2_finseq_1 @ k1_card_1 )
= ( A @ k1_card_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_finseq_1) ).
thf(6053,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( ( A @ k2_finseq_1 @ k1_card_1 )
= ( A @ k1_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(1100,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
<=> ( A @ k1_zfmisc_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_finset_1) ).
thf(7046,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)],[1100]) ).
thf(1571,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/sandbox/benchmark/theBenchmark.p',t53_group_4) ).
thf(9502,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)],[1571]) ).
thf(1755,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/sandbox/benchmark/theBenchmark.p',t89_group_3) ).
thf(10202,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)],[1755]) ).
thf(437,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/sandbox/benchmark/theBenchmark.p',t34_funct_2) ).
thf(3890,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)],[437]) ).
thf(1487,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/sandbox/benchmark/theBenchmark.p',t15_group_2) ).
thf(9203,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)],[1487]) ).
thf(1400,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/sandbox/benchmark/theBenchmark.p',reflexivity_r4_group_3) ).
thf(8713,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)],[1400]) ).
thf(268,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(3079,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)],[268]) ).
thf(1209,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/sandbox/benchmark/theBenchmark.p',t85_funct_2) ).
thf(7706,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)],[1209]) ).
thf(513,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/sandbox/benchmark/theBenchmark.p',t101_zfmisc_1) ).
thf(4256,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)],[513]) ).
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 ) )
=> ( ( B @ ( B @ ( A @ k7_group_1 ) @ ( A @ k6_group_1 ) ) )
= ( A @ k2_group_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_group_1) ).
thf(8906,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)],[1436]) ).
thf(1055,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/sandbox/benchmark/theBenchmark.p',t104_group_3) ).
thf(6792,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)],[1055]) ).
thf(1185,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/sandbox/benchmark/theBenchmark.p',t12_funct_2) ).
thf(7599,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)],[1185]) ).
thf(1788,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/sandbox/benchmark/theBenchmark.p',existence_m1_group_6) ).
thf(10327,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)],[1788]) ).
thf(1787,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/sandbox/benchmark/theBenchmark.p',t8_group_6) ).
thf(10321,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)],[1787]) ).
thf(798,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/sandbox/benchmark/theBenchmark.p',dt_k1_group_2) ).
thf(5608,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)],[798]) ).
thf(991,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/sandbox/benchmark/theBenchmark.p',t73_group_6) ).
thf(6469,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)],[991]) ).
thf(1190,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/sandbox/benchmark/theBenchmark.p',t35_group_2) ).
thf(7636,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)],[1190]) ).
thf(436,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( B @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 @ ( A @ k2_finseq_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finseq_3) ).
thf(3888,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( B @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 @ ( A @ k2_finseq_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(985,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/sandbox/benchmark/theBenchmark.p',t48_group_4) ).
thf(6454,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)],[985]) ).
thf(674,axiom,
! [A: $i] :
( ( ( A @ l1_rlvect_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( ( ( B @ k3_finseq_1 )
= D )
& ( D @ k2_finseq_1 @ ( C @ r2_hidden ) ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ k1_funct_1 ) @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_rlvect_1) ).
thf(5016,plain,
! [A: $i] :
( ( ( A @ l1_rlvect_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( ( ( B @ k3_finseq_1 )
= D )
& ( D @ k2_finseq_1 @ ( C @ r2_hidden ) ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ k1_funct_1 ) @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(1776,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/sandbox/benchmark/theBenchmark.p',t75_group_4) ).
thf(10274,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)],[1776]) ).
thf(1243,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/sandbox/benchmark/theBenchmark.p',d6_group_4) ).
thf(7920,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)],[1243]) ).
thf(779,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/sandbox/benchmark/theBenchmark.p',redefinition_r4_group_3) ).
thf(5525,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)],[779]) ).
thf(1223,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/sandbox/benchmark/theBenchmark.p',t26_group_6) ).
thf(7785,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)],[1223]) ).
thf(1605,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/sandbox/benchmark/theBenchmark.p',fc1_group_6) ).
thf(9650,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)],[1605]) ).
thf(821,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/sandbox/benchmark/theBenchmark.p',t2_group_6) ).
thf(5715,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)],[821]) ).
thf(557,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(4489,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(1429,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/sandbox/benchmark/theBenchmark.p',existence_m2_subset_1) ).
thf(8874,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)],[1429]) ).
thf(978,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/sandbox/benchmark/theBenchmark.p',t140_group_3) ).
thf(6422,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)],[978]) ).
thf(1121,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_partfun1) ).
thf(7212,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)],[1121]) ).
thf(627,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/sandbox/benchmark/theBenchmark.p',t35_funct_2) ).
thf(4786,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)],[627]) ).
thf(1210,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/sandbox/benchmark/theBenchmark.p',dt_k8_group_3) ).
thf(7709,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)],[1210]) ).
thf(758,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/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
thf(5456,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)],[758]) ).
thf(1437,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(8909,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)],[1437]) ).
thf(559,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/sandbox/benchmark/theBenchmark.p',t51_subset_1) ).
thf(4494,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)],[559]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k1_finsub_1 ) ) )
= ( B @ ( C @ ( A @ k1_finsub_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k1_finsub_1) ).
thf(3519,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k1_finsub_1 ) ) )
= ( B @ ( C @ ( A @ k1_finsub_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(1286,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/sandbox/benchmark/theBenchmark.p',t59_group_3) ).
thf(8139,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)],[1286]) ).
thf(480,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_zfmisc_1) ).
thf(4122,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)],[480]) ).
thf(1768,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/sandbox/benchmark/theBenchmark.p',dt_k10_group_2) ).
thf(10242,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)],[1768]) ).
thf(1528,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/sandbox/benchmark/theBenchmark.p',t149_group_3) ).
thf(9339,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)],[1528]) ).
thf(770,axiom,
k1_numbers @ ( k5_numbers @ r1_tarski ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_numbers) ).
thf(5503,plain,
k1_numbers @ ( k5_numbers @ r1_tarski ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(1682,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/sandbox/benchmark/theBenchmark.p',dt_k5_group_2) ).
thf(9952,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)],[1682]) ).
thf(1261,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/sandbox/benchmark/theBenchmark.p',dt_k9_domain_1) ).
thf(8015,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)],[1261]) ).
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 ) )
=> ! [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/sandbox/benchmark/theBenchmark.p',t108_group_2) ).
thf(10068,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)],[1719]) ).
thf(1645,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/sandbox/benchmark/theBenchmark.p',symmetry_r2_group_6) ).
thf(9798,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)],[1645]) ).
thf(1212,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/sandbox/benchmark/theBenchmark.p',t59_group_6) ).
thf(7714,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)],[1212]) ).
thf(530,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/sandbox/benchmark/theBenchmark.p',t121_zfmisc_1) ).
thf(4341,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)],[530]) ).
thf(515,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/sandbox/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(4268,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)],[515]) ).
thf(1253,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k3_finsub_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_finsub_1) ).
thf(7968,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k3_finsub_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(266,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/sandbox/benchmark/theBenchmark.p',t63_partfun1) ).
thf(3070,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)],[266]) ).
thf(1191,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/sandbox/benchmark/theBenchmark.p',t116_group_3) ).
thf(7639,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)],[1191]) ).
thf(1410,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/sandbox/benchmark/theBenchmark.p',d13_vectsp_1) ).
thf(8762,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)],[1410]) ).
thf(762,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/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(5474,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)],[762]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',t2_partfun1) ).
thf(1884,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)],[21]) ).
thf(423,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/sandbox/benchmark/theBenchmark.p',t22_funct_2) ).
thf(3811,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)],[423]) ).
thf(742,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/sandbox/benchmark/theBenchmark.p',dt_k1_partfun1) ).
thf(5395,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)],[742]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( B @ ( C @ ( D @ ( B @ ( A @ ( C @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_relset_1) ).
thf(3240,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( B @ ( C @ ( D @ ( B @ ( A @ ( C @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(847,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/sandbox/benchmark/theBenchmark.p',redefinition_k18_group_2) ).
thf(5844,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)],[847]) ).
thf(491,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/sandbox/benchmark/theBenchmark.p',t43_zfmisc_1) ).
thf(4159,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)],[491]) ).
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 ) )
=> ( ( B @ ( A @ k6_group_2 @ ( A @ k7_group_2 ) @ ( A @ k5_group_3 ) ) )
= ( B @ ( A @ a_2_0_group_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_group_3) ).
thf(8580,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)],[1369]) ).
thf(1695,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/sandbox/benchmark/theBenchmark.p',t75_group_2) ).
thf(9996,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)],[1695]) ).
thf(1163,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/sandbox/benchmark/theBenchmark.p',dt_k2_group_2) ).
thf(7487,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)],[1163]) ).
thf(696,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
<=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(5121,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)],[696]) ).
thf(356,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/sandbox/benchmark/theBenchmark.p',t106_xboole_1) ).
thf(3472,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)],[356]) ).
thf(269,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/sandbox/benchmark/theBenchmark.p',t25_funct_1) ).
thf(3081,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)],[269]) ).
thf(869,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/sandbox/benchmark/theBenchmark.p',t20_group_3) ).
thf(5940,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)],[869]) ).
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 ) )
& ( B @ v1_group_1 ) )
=> ( B @ ( B @ ( A @ r5_group_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_group_3) ).
thf(9706,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)],[1618]) ).
thf(320,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_zfmisc_1) ).
thf(3283,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)],[320]) ).
thf(601,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/sandbox/benchmark/theBenchmark.p',t168_partfun1) ).
thf(4677,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)],[601]) ).
thf(802,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/sandbox/benchmark/theBenchmark.p',t28_group_1) ).
thf(5627,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)],[802]) ).
thf(1789,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/sandbox/benchmark/theBenchmark.p',t137_group_3) ).
thf(10329,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)],[1789]) ).
thf(1392,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(8684,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392]) ).
thf(1623,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/sandbox/benchmark/theBenchmark.p',dt_k1_group_6) ).
thf(9719,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)],[1623]) ).
thf(609,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/sandbox/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(4709,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)],[609]) ).
thf(683,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/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).
thf(5050,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)],[683]) ).
thf(1208,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(7704,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(1321,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/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(8332,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)],[1321]) ).
thf(693,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/sandbox/benchmark/theBenchmark.p',t53_subset_1) ).
thf(5097,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)],[693]) ).
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 ) )
& ( 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/sandbox/benchmark/theBenchmark.p',t146_group_3) ).
thf(9663,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)],[1608]) ).
thf(1440,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/sandbox/benchmark/theBenchmark.p',t148_group_2) ).
thf(8941,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)],[1440]) ).
thf(526,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k1_finsub_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_finsub_1) ).
thf(4328,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k1_finsub_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(1017,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/sandbox/benchmark/theBenchmark.p',t24_group_3) ).
thf(6606,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)],[1017]) ).
thf(886,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/sandbox/benchmark/theBenchmark.p',t56_group_1) ).
thf(6019,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)],[886]) ).
thf(1591,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/sandbox/benchmark/theBenchmark.p',t79_group_1) ).
thf(9585,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)],[1591]) ).
thf(214,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/sandbox/benchmark/theBenchmark.p',t13_relat_1) ).
thf(2827,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)],[214]) ).
thf(1229,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/sandbox/benchmark/theBenchmark.p',dt_k10_group_6) ).
thf(7815,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)],[1229]) ).
thf(1599,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/sandbox/benchmark/theBenchmark.p',t84_group_1) ).
thf(9627,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)],[1599]) ).
thf(387,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/sandbox/benchmark/theBenchmark.p',t41_funct_4) ).
thf(3599,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)],[387]) ).
thf(236,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( k1_xboole_0 @ k1_funct_4 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_4) ).
thf(2959,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)],[236]) ).
thf(782,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/sandbox/benchmark/theBenchmark.p',t155_group_2) ).
thf(5535,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)],[782]) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',d4_binop_1) ).
thf(2193,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)],[84]) ).
thf(1513,axiom,
! [A: $i,B: $i] :
( k1_xboole_0
!= ( B @ ( A @ k10_finseq_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_finseq_3) ).
thf(9285,plain,
! [A: $i,B: $i] :
( k1_xboole_0
!= ( B @ ( A @ k10_finseq_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1513]) ).
thf(195,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v1_finset_1 )
=> ( ( A @ k2_finseq_1 @ ( B @ r1_tarski ) )
=> ( ( B @ k14_finseq_1 @ k3_finseq_1 )
= ( B @ k4_card_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_finseq_3) ).
thf(2753,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v1_finset_1 )
=> ( ( A @ k2_finseq_1 @ ( B @ r1_tarski ) )
=> ( ( B @ k14_finseq_1 @ k3_finseq_1 )
= ( B @ k4_card_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(361,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/sandbox/benchmark/theBenchmark.p',t84_xboole_1) ).
thf(3487,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)],[361]) ).
thf(1532,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/sandbox/benchmark/theBenchmark.p',t78_group_4) ).
thf(9354,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)],[1532]) ).
thf(1557,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/sandbox/benchmark/theBenchmark.p',t24_group_1) ).
thf(9439,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)],[1557]) ).
thf(1272,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/sandbox/benchmark/theBenchmark.p',d13_group_6) ).
thf(8064,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)],[1272]) ).
thf(1225,axiom,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(7795,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(1592,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/sandbox/benchmark/theBenchmark.p',t9_group_6) ).
thf(9587,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)],[1592]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',t19_funct_1) ).
thf(2220,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)],[89]) ).
thf(789,axiom,
! [A: $i] :
~ ( ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ~ ( B @ ( A @ r2_wellord2 ) ) )
& ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_card_1) ).
thf(5567,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)],[789]) ).
thf(969,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_partfun1) ).
thf(6385,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)],[969]) ).
thf(261,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/sandbox/benchmark/theBenchmark.p',t111_finseq_3) ).
thf(3051,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)],[261]) ).
thf(761,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( ( np__1 @ ( A @ k2_xcmplx_0 ) @ k1_tarski @ ( A @ k2_finseq_1 @ k2_xboole_0 ) )
= ( np__1 @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_finseq_1) ).
thf(5471,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( ( np__1 @ ( A @ k2_xcmplx_0 ) @ k1_tarski @ ( A @ k2_finseq_1 @ k2_xboole_0 ) )
= ( np__1 @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(629,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/sandbox/benchmark/theBenchmark.p',t55_xboole_1) ).
thf(4796,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)],[629]) ).
thf(672,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_relset_1) ).
thf(5011,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(267,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/sandbox/benchmark/theBenchmark.p',t30_funct_4) ).
thf(3077,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)],[267]) ).
thf(1312,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_zfmisc_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(8286,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)],[1312]) ).
thf(478,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/sandbox/benchmark/theBenchmark.p',t39_funct_4) ).
thf(4112,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)],[478]) ).
thf(1031,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/sandbox/benchmark/theBenchmark.p',t61_group_4) ).
thf(6673,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)],[1031]) ).
thf(1753,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/sandbox/benchmark/theBenchmark.p',d7_group_4) ).
thf(10183,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)],[1753]) ).
thf(1428,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/sandbox/benchmark/theBenchmark.p',d1_int_1) ).
thf(8841,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)],[1428]) ).
thf(860,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/sandbox/benchmark/theBenchmark.p',t74_group_6) ).
thf(5908,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)],[860]) ).
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 @ 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/sandbox/benchmark/theBenchmark.p',t15_group_3) ).
thf(5859,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)],[851]) ).
thf(408,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/sandbox/benchmark/theBenchmark.p',commutativity_k7_domain_1) ).
thf(3695,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)],[408]) ).
thf(1306,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/sandbox/benchmark/theBenchmark.p',t79_group_6) ).
thf(8249,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)],[1306]) ).
thf(1367,axiom,
( ! [A: $i] :
( ( f1_s2_funct_2 @ ( A @ r2_hidden ) )
=> ( f2_s2_funct_2 @ ( A @ f3_s2_funct_2 @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s2_funct_2 @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f3_s2_funct_2 ) ) )
& ( f2_s2_funct_2 @ ( f1_s2_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s2_funct_2 @ ( f1_s2_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_2) ).
thf(8566,plain,
( ! [A: $i] :
( ( f1_s2_funct_2 @ ( A @ r2_hidden ) )
=> ( f2_s2_funct_2 @ ( A @ f3_s2_funct_2 @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s2_funct_2 @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f3_s2_funct_2 ) ) )
& ( f2_s2_funct_2 @ ( f1_s2_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s2_funct_2 @ ( f1_s2_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).
thf(732,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/sandbox/benchmark/theBenchmark.p',t8_group_4) ).
thf(5282,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)],[732]) ).
thf(403,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/sandbox/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(3663,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)],[403]) ).
thf(599,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(4672,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(1089,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/sandbox/benchmark/theBenchmark.p',t5_group_3) ).
thf(6991,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)],[1089]) ).
thf(1713,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/sandbox/benchmark/theBenchmark.p',t161_group_3) ).
thf(10051,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)],[1713]) ).
thf(951,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/sandbox/benchmark/theBenchmark.p',t85_group_1) ).
thf(6302,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)],[951]) ).
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 @ 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/sandbox/benchmark/theBenchmark.p',t33_group_3) ).
thf(7109,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)],[1112]) ).
thf(691,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/sandbox/benchmark/theBenchmark.p',d8_binop_1) ).
thf(5086,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)],[691]) ).
thf(1406,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/sandbox/benchmark/theBenchmark.p',t62_group_6) ).
thf(8745,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)],[1406]) ).
thf(625,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/sandbox/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(4764,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)],[625]) ).
thf(1738,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_setfam_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_setfam_1) ).
thf(10130,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_setfam_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1738]) ).
thf(1107,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/sandbox/benchmark/theBenchmark.p',t13_group_3) ).
thf(7094,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)],[1107]) ).
thf(1114,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/sandbox/benchmark/theBenchmark.p',t26_group_2) ).
thf(7145,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)],[1114]) ).
thf(1170,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/sandbox/benchmark/theBenchmark.p',t8_realset1) ).
thf(7536,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)],[1170]) ).
thf(400,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/sandbox/benchmark/theBenchmark.p',t71_xboole_1) ).
thf(3641,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)],[400]) ).
thf(909,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/sandbox/benchmark/theBenchmark.p',t91_group_6) ).
thf(6123,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)],[909]) ).
thf(516,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/sandbox/benchmark/theBenchmark.p',t177_orders_1) ).
thf(4273,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)],[516]) ).
thf(1357,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(8524,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).
thf(838,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/sandbox/benchmark/theBenchmark.p',d4_group_6) ).
thf(5784,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)],[838]) ).
thf(1179,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(7579,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(1134,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/sandbox/benchmark/theBenchmark.p',t24_group_2) ).
thf(7315,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)],[1134]) ).
thf(1750,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/sandbox/benchmark/theBenchmark.p',dt_k8_group_1) ).
thf(10176,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)],[1750]) ).
thf(1469,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/sandbox/benchmark/theBenchmark.p',t115_funct_2) ).
thf(9089,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)],[1469]) ).
thf(1503,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k5_lattices @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattices) ).
thf(9258,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)],[1503]) ).
thf(1518,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/sandbox/benchmark/theBenchmark.p',t79_group_2) ).
thf(9307,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)],[1518]) ).
thf(792,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/sandbox/benchmark/theBenchmark.p',d1_group_1) ).
thf(5578,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)],[792]) ).
thf(112,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/sandbox/benchmark/theBenchmark.p',t16_funct_1) ).
thf(2319,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)],[112]) ).
thf(1715,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/sandbox/benchmark/theBenchmark.p',t177_group_2) ).
thf(10056,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)],[1715]) ).
thf(787,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/sandbox/benchmark/theBenchmark.p',t63_group_6) ).
thf(5556,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)],[787]) ).
thf(1494,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/sandbox/benchmark/theBenchmark.p',t11_group_4) ).
thf(9224,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)],[1494]) ).
thf(1542,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/sandbox/benchmark/theBenchmark.p',dt_k15_group_2) ).
thf(9390,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)],[1542]) ).
thf(1654,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/sandbox/benchmark/theBenchmark.p',t72_group_4) ).
thf(9835,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)],[1654]) ).
thf(374,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/sandbox/benchmark/theBenchmark.p',redefinition_k9_group_6) ).
thf(3532,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)],[374]) ).
thf(146,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_finseq_1) ).
thf(2510,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)],[146]) ).
thf(1335,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/sandbox/benchmark/theBenchmark.p',dt_k7_group_3) ).
thf(8419,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)],[1335]) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
thf(2361,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)],[119]) ).
thf(1152,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/sandbox/benchmark/theBenchmark.p',d7_group_1) ).
thf(7415,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)],[1152]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
thf(2679,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)],[190]) ).
thf(1059,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/sandbox/benchmark/theBenchmark.p',t42_group_3) ).
thf(6815,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)],[1059]) ).
thf(1460,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(9047,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460]) ).
thf(1643,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/sandbox/benchmark/theBenchmark.p',t14_group_6) ).
thf(9789,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)],[1643]) ).
thf(927,axiom,
~ ( k1_numbers @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_numbers) ).
thf(6196,plain,
~ ( k1_numbers @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(561,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( B @ ( A @ r1_xreal_0 ) )
=> ( ( A @ k2_finseq_1 )
= ( A @ k2_finseq_1 @ ( B @ k2_finseq_1 @ ( k5_numbers @ k5_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_finseq_1) ).
thf(4509,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( B @ ( A @ r1_xreal_0 ) )
=> ( ( A @ k2_finseq_1 )
= ( A @ k2_finseq_1 @ ( B @ k2_finseq_1 @ ( k5_numbers @ k5_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(542,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/sandbox/benchmark/theBenchmark.p',t20_funct_2) ).
thf(4388,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)],[542]) ).
thf(688,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 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_rlvect_1 ) ) ) )
= ( D @ ( C @ ( B @ k11_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_rlvect_1) ).
thf(5071,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 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_rlvect_1 ) ) ) )
= ( D @ ( C @ ( B @ k11_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(1800,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/sandbox/benchmark/theBenchmark.p',dt_k6_group_4) ).
thf(10370,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)],[1800]) ).
thf(1009,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/sandbox/benchmark/theBenchmark.p',t40_group_3) ).
thf(6572,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)],[1009]) ).
thf(1246,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/sandbox/benchmark/theBenchmark.p',t15_group_4) ).
thf(7933,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)],[1246]) ).
thf(1183,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/sandbox/benchmark/theBenchmark.p',t30_group_4) ).
thf(7594,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)],[1183]) ).
thf(460,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/sandbox/benchmark/theBenchmark.p',t15_subset_1) ).
thf(3996,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)],[460]) ).
thf(953,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/sandbox/benchmark/theBenchmark.p',d1_group_6) ).
thf(6308,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)],[953]) ).
thf(312,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i,C: $i] :
( ( B @ ( C @ m2_finseq_1 ) )
=> ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( A @ ( D @ r1_xreal_0 ) )
=> ( ( D @ ( A @ ( C @ ( B @ k16_finseq_1 ) ) @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_finseq_3) ).
thf(3251,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i,C: $i] :
( ( B @ ( C @ m2_finseq_1 ) )
=> ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( A @ ( D @ r1_xreal_0 ) )
=> ( ( D @ ( A @ ( C @ ( B @ k16_finseq_1 ) ) @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
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 ) )
=> ! [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/sandbox/benchmark/theBenchmark.p',t80_group_4) ).
thf(9349,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)],[1530]) ).
thf(772,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/sandbox/benchmark/theBenchmark.p',t65_funct_2) ).
thf(5506,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)],[772]) ).
thf(88,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/sandbox/benchmark/theBenchmark.p',t31_funct_4) ).
thf(2214,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)],[88]) ).
thf(1418,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/sandbox/benchmark/theBenchmark.p',t67_xboole_1) ).
thf(8799,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)],[1418]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_funct_1) ).
thf(2493,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(178,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t171_relat_1) ).
thf(2637,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(1756,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/sandbox/benchmark/theBenchmark.p',t101_group_2) ).
thf(10204,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)],[1756]) ).
thf(1665,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/sandbox/benchmark/theBenchmark.p',t92_group_6) ).
thf(9903,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)],[1665]) ).
thf(127,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(2422,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(1718,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/sandbox/benchmark/theBenchmark.p',t80_group_6) ).
thf(10066,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)],[1718]) ).
thf(587,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/sandbox/benchmark/theBenchmark.p',d13_binop_1) ).
thf(4620,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)],[587]) ).
thf(988,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/sandbox/benchmark/theBenchmark.p',dt_m2_subset_1) ).
thf(6461,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)],[988]) ).
thf(1304,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_3_domain_1) ).
thf(8237,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)],[1304]) ).
thf(906,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/sandbox/benchmark/theBenchmark.p',t6_group_4) ).
thf(6112,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)],[906]) ).
thf(653,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/sandbox/benchmark/theBenchmark.p',t111_xboole_1) ).
thf(4914,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)],[653]) ).
thf(1136,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/sandbox/benchmark/theBenchmark.p',t6_group_2) ).
thf(7328,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)],[1136]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',t11_relset_1) ).
thf(2246,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)],[98]) ).
thf(1396,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/sandbox/benchmark/theBenchmark.p',d15_group_6) ).
thf(8693,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)],[1396]) ).
thf(1344,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/sandbox/benchmark/theBenchmark.p',d3_group_3) ).
thf(8461,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)],[1344]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_partfun1) ).
thf(3468,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(855,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/sandbox/benchmark/theBenchmark.p',t70_group_3) ).
thf(5880,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)],[855]) ).
thf(1475,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/sandbox/benchmark/theBenchmark.p',s2_group_4) ).
thf(9118,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)],[1475]) ).
thf(1672,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/sandbox/benchmark/theBenchmark.p',t105_group_2) ).
thf(9920,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)],[1672]) ).
thf(217,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/sandbox/benchmark/theBenchmark.p',t51_relat_1) ).
thf(2839,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)],[217]) ).
thf(799,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/sandbox/benchmark/theBenchmark.p',t122_group_2) ).
thf(5610,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)],[799]) ).
thf(662,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(4958,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(1127,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/sandbox/benchmark/theBenchmark.p',t80_group_3) ).
thf(7265,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)],[1127]) ).
thf(1147,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/sandbox/benchmark/theBenchmark.p',t67_group_3) ).
thf(7360,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)],[1147]) ).
thf(737,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( A @ k1_setfam_1 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_setfam_1) ).
thf(5346,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( A @ k1_setfam_1 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(475,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/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(4073,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)],[475]) ).
thf(692,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_xboole_1) ).
thf(5093,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)],[692]) ).
thf(597,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 @ ( B @ ( A @ k2_xcmplx_0 ) @ r2_hidden ) )
=> ( B = np__0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_finseq_3) ).
thf(4667,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 @ ( B @ ( A @ k2_xcmplx_0 ) @ r2_hidden ) )
=> ( B = np__0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(915,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/sandbox/benchmark/theBenchmark.p',t40_subset_1) ).
thf(6154,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)],[915]) ).
thf(1189,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/sandbox/benchmark/theBenchmark.p',t16_group_6) ).
thf(7632,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)],[1189]) ).
thf(1016,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( ( A @ ( np__0 @ r1_xreal_0 ) )
=> ( k5_numbers @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_int_1) ).
thf(6604,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)],[1016]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',t67_relat_1) ).
thf(1969,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)],[34]) ).
thf(729,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/sandbox/benchmark/theBenchmark.p',d18_binop_1) ).
thf(5267,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)],[729]) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_setfam_1 ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_setfam_1) ).
thf(3160,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_setfam_1 ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ k10_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t168_relat_1) ).
thf(2824,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ k10_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(637,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_relat_1) ).
thf(4833,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(858,axiom,
! [A: $i,B: $i] :
( ( A @ k1_tarski @ ( B @ r1_setfam_1 ) )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_setfam_1) ).
thf(5894,plain,
! [A: $i,B: $i] :
( ( A @ k1_tarski @ ( B @ r1_setfam_1 ) )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(1505,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/sandbox/benchmark/theBenchmark.p',t71_card_1) ).
thf(9263,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)],[1505]) ).
thf(495,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(4181,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(225,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t182_relat_1) ).
thf(2874,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(1175,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/sandbox/benchmark/theBenchmark.p',t26_group_3) ).
thf(7561,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)],[1175]) ).
thf(1083,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/sandbox/benchmark/theBenchmark.p',dt_k13_group_2) ).
thf(6969,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)],[1083]) ).
thf(1676,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/sandbox/benchmark/theBenchmark.p',t87_group_2) ).
thf(9931,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)],[1676]) ).
thf(591,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_partfun1) ).
thf(4635,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)],[591]) ).
thf(774,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/sandbox/benchmark/theBenchmark.p',t54_group_3) ).
thf(5511,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)],[774]) ).
thf(1488,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/sandbox/benchmark/theBenchmark.p',t33_relset_1) ).
thf(9206,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)],[1488]) ).
thf(552,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/sandbox/benchmark/theBenchmark.p',d7_partfun1) ).
thf(4430,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)],[552]) ).
thf(1477,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/sandbox/benchmark/theBenchmark.p',dt_k6_domain_1) ).
thf(9129,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)],[1477]) ).
thf(918,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(6165,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(1423,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/sandbox/benchmark/theBenchmark.p',t58_partfun1) ).
thf(8826,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)],[1423]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',t10_relset_1) ).
thf(1877,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)],[18]) ).
thf(1442,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/sandbox/benchmark/theBenchmark.p',t25_group_1) ).
thf(8958,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)],[1442]) ).
thf(808,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/sandbox/benchmark/theBenchmark.p',redefinition_r2_group_3) ).
thf(5657,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)],[808]) ).
thf(176,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( k1_xboole_0 @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_partfun1) ).
thf(2632,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)],[176]) ).
thf(548,axiom,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(4420,plain,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(254,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/sandbox/benchmark/theBenchmark.p',t70_funct_2) ).
thf(3027,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)],[254]) ).
thf(1380,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(8633,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)],[1380]) ).
thf(1206,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(7699,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(1280,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_group_3) ).
thf(8103,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)],[1280]) ).
thf(1386,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/sandbox/benchmark/theBenchmark.p',t11_group_3) ).
thf(8661,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)],[1386]) ).
thf(473,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/sandbox/benchmark/theBenchmark.p',t65_group_6) ).
thf(4064,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)],[473]) ).
thf(1615,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/sandbox/benchmark/theBenchmark.p',t82_group_2) ).
thf(9691,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)],[1615]) ).
thf(201,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v1_finset_1 )
=> ( ( A @ k2_finseq_1 @ ( B @ r1_tarski ) )
=> ( ( B @ k14_finseq_1 @ k4_finseq_1 )
= ( B @ k4_card_1 @ k2_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_finseq_3) ).
thf(2780,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v1_finset_1 )
=> ( ( A @ k2_finseq_1 @ ( B @ r1_tarski ) )
=> ( ( B @ k14_finseq_1 @ k4_finseq_1 )
= ( B @ k4_card_1 @ k2_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(1056,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/sandbox/benchmark/theBenchmark.p',t44_group_3) ).
thf(6800,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)],[1056]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
thf(1821,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)],[5]) ).
thf(1085,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/sandbox/benchmark/theBenchmark.p',t73_group_1) ).
thf(6974,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)],[1085]) ).
thf(976,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/sandbox/benchmark/theBenchmark.p',t167_funct_2) ).
thf(6414,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)],[976]) ).
thf(296,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/sandbox/benchmark/theBenchmark.p',t44_xboole_1) ).
thf(3192,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)],[296]) ).
thf(10,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relat_1) ).
thf(1838,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(391,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( B @ ( A @ r1_xreal_0 ) )
<=> ( B @ k2_finseq_1 @ ( A @ k2_finseq_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_finseq_1) ).
thf(3614,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( ( B @ k2_finseq_1 @ ( A @ k2_finseq_1 @ r1_tarski ) )
=> ( B @ ( A @ r1_xreal_0 ) ) )
& ( ( B @ ( A @ r1_xreal_0 ) )
=> ( B @ k2_finseq_1 @ ( A @ k2_finseq_1 @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k1_finsub_1 ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k1_finsub_1) ).
thf(3977,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k1_finsub_1 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(1741,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/sandbox/benchmark/theBenchmark.p',t39_group_3) ).
thf(10136,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)],[1741]) ).
thf(1450,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/sandbox/benchmark/theBenchmark.p',t37_group_2) ).
thf(8998,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)],[1450]) ).
thf(1265,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/sandbox/benchmark/theBenchmark.p',t143_group_3) ).
thf(8032,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)],[1265]) ).
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 @ ( 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/sandbox/benchmark/theBenchmark.p',t156_group_2) ).
thf(7869,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)],[1238]) ).
thf(359,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/sandbox/benchmark/theBenchmark.p',t61_card_1) ).
thf(3483,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)],[359]) ).
thf(383,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/sandbox/benchmark/theBenchmark.p',t5_orders_1) ).
thf(3583,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)],[383]) ).
thf(1466,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_2_group_3) ).
thf(9074,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)],[1466]) ).
thf(1095,axiom,
~ ( k4_numbers @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_numbers) ).
thf(7023,plain,
~ ( k4_numbers @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(137,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/sandbox/benchmark/theBenchmark.p',t18_funct_1) ).
thf(2461,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)],[137]) ).
thf(1698,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/sandbox/benchmark/theBenchmark.p',t8_group_2) ).
thf(10004,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)],[1698]) ).
thf(759,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/sandbox/benchmark/theBenchmark.p',t24_binop_1) ).
thf(5459,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)],[759]) ).
thf(603,axiom,
np__0 = k1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_card_1) ).
thf(4684,plain,
np__0 = k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(218,axiom,
! [A: $i] : ( k5_numbers @ ( A @ k14_finseq_1 @ m2_finseq_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_finseq_1) ).
thf(2842,plain,
! [A: $i] : ( k5_numbers @ ( A @ k14_finseq_1 @ m2_finseq_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(845,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/sandbox/benchmark/theBenchmark.p',t23_group_2) ).
thf(5838,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)],[845]) ).
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] :
( ( 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/sandbox/benchmark/theBenchmark.p',t11_latsubgr) ).
thf(8413,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)],[1333]) ).
thf(1525,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/sandbox/benchmark/theBenchmark.p',t27_group_4) ).
thf(9327,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)],[1525]) ).
thf(670,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/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(4990,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)],[670]) ).
thf(1454,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(9018,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454]) ).
thf(940,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/sandbox/benchmark/theBenchmark.p',d12_group_4) ).
thf(6255,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)],[940]) ).
thf(1598,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/sandbox/benchmark/theBenchmark.p',rc3_group_1) ).
thf(9619,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)],[1598]) ).
thf(1018,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/sandbox/benchmark/theBenchmark.p',dt_k1_latsubgr) ).
thf(6609,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)],[1018]) ).
thf(1053,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/sandbox/benchmark/theBenchmark.p',t32_group_3) ).
thf(6783,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)],[1053]) ).
thf(841,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/sandbox/benchmark/theBenchmark.p',d5_group_3) ).
thf(5817,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)],[841]) ).
thf(1140,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(7339,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(1447,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/sandbox/benchmark/theBenchmark.p',t44_group_4) ).
thf(8990,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)],[1447]) ).
thf(664,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
<=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_partfun1) ).
thf(4965,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A )
=> ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(1762,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/sandbox/benchmark/theBenchmark.p',t138_group_3) ).
thf(10226,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)],[1762]) ).
thf(1010,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/sandbox/benchmark/theBenchmark.p',t34_relset_1) ).
thf(6574,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)],[1010]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k10_relat_1 ) @ v1_finset_1 )
& ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finset_1) ).
thf(2439,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k10_relat_1 ) @ v1_finset_1 )
& ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(827,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/sandbox/benchmark/theBenchmark.p',d1_realset1) ).
thf(5742,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)],[827]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_funct_1) ).
thf(2962,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1343,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_partfun1) ).
thf(8456,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)],[1343]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
<=> ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).
thf(3627,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)],[395]) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',t3_partfun1) ).
thf(2171,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)],[76]) ).
thf(713,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/sandbox/benchmark/theBenchmark.p',t169_partfun1) ).
thf(5197,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)],[713]) ).
thf(198,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/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
thf(2765,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)],[198]) ).
thf(971,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/sandbox/benchmark/theBenchmark.p',t55_setfam_1) ).
thf(6394,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)],[971]) ).
thf(1244,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/sandbox/benchmark/theBenchmark.p',t119_group_3) ).
thf(7929,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)],[1244]) ).
thf(805,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/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(5641,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)],[805]) ).
thf(1629,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_struct_0) ).
thf(9741,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1629]) ).
thf(764,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/sandbox/benchmark/theBenchmark.p',dt_k7_funct_2) ).
thf(5482,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)],[764]) ).
thf(1567,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/sandbox/benchmark/theBenchmark.p',t83_group_4) ).
thf(9492,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)],[1567]) ).
thf(1723,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/sandbox/benchmark/theBenchmark.p',t50_group_2) ).
thf(10076,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)],[1723]) ).
thf(946,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/sandbox/benchmark/theBenchmark.p',t17_relset_1) ).
thf(6288,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)],[946]) ).
thf(1656,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/sandbox/benchmark/theBenchmark.p',fc2_group_6) ).
thf(9841,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)],[1656]) ).
thf(1227,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/sandbox/benchmark/theBenchmark.p',t142_funct_2) ).
thf(7805,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)],[1227]) ).
thf(1251,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/sandbox/benchmark/theBenchmark.p',t47_group_1) ).
thf(7960,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)],[1251]) ).
thf(229,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/sandbox/benchmark/theBenchmark.p',t32_funct_4) ).
thf(2931,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)],[229]) ).
thf(791,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/sandbox/benchmark/theBenchmark.p',t121_group_2) ).
thf(5575,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)],[791]) ).
thf(1670,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/sandbox/benchmark/theBenchmark.p',t109_group_2) ).
thf(9916,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)],[1670]) ).
thf(1485,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/sandbox/benchmark/theBenchmark.p',t62_funct_2) ).
thf(9197,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)],[1485]) ).
thf(450,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( ( ( A @ k2_finseq_1 )
= k1_xboole_0 )
<=> ~ ( A @ k2_finseq_1 @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_finseq_3) ).
thf(3953,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( ( ~ ( A @ k2_finseq_1 @ ( A @ r2_hidden ) )
=> ( ( A @ k2_finseq_1 )
= k1_xboole_0 ) )
& ( ( ( A @ k2_finseq_1 )
= k1_xboole_0 )
=> ~ ( A @ k2_finseq_1 @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
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 @ 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/sandbox/benchmark/theBenchmark.p',t66_group_6) ).
thf(8175,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)],[1293]) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( C @ ( B @ k5_relat_1 ) @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_funct_1) ).
thf(2797,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( C @ ( B @ k5_relat_1 ) @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(1775,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/sandbox/benchmark/theBenchmark.p',t2_latsubgr) ).
thf(10264,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)],[1775]) ).
thf(166,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/sandbox/benchmark/theBenchmark.p',d6_partfun1) ).
thf(2592,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)],[166]) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',t33_funct_4) ).
thf(2244,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)],[97]) ).
thf(1536,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/sandbox/benchmark/theBenchmark.p',t170_group_2) ).
thf(9366,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)],[1536]) ).
thf(1717,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/sandbox/benchmark/theBenchmark.p',redefinition_k3_group_6) ).
thf(10063,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)],[1717]) ).
thf(338,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ v6_group_1 )
<=> ( A @ u1_struct_0 @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_group_1) ).
thf(3363,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)],[338]) ).
thf(1117,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/sandbox/benchmark/theBenchmark.p',t30_partfun1) ).
thf(7200,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)],[1117]) ).
thf(823,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/sandbox/benchmark/theBenchmark.p',d10_group_4) ).
thf(5725,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)],[823]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t179_relat_1) ).
thf(2535,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(518,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/sandbox/benchmark/theBenchmark.p',t35_xboole_1) ).
thf(4304,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)],[518]) ).
thf(367,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/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(3512,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)],[367]) ).
thf(293,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_xboole_1) ).
thf(3178,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)],[293]) ).
thf(1019,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ r1_tarski ) )
<=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(6614,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)],[1019]) ).
thf(924,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/sandbox/benchmark/theBenchmark.p',t54_group_6) ).
thf(6180,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)],[924]) ).
thf(1705,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/sandbox/benchmark/theBenchmark.p',t133_group_3) ).
thf(10031,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)],[1705]) ).
thf(816,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) )
= ( F @ ( E @ ( B @ ( A @ k4_funct_4 ) ) ) ) )
=> ( ( ( D = F )
& ( C = E ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_4) ).
thf(5693,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k4_funct_4 ) ) ) )
= ( F @ ( E @ ( B @ ( A @ k4_funct_4 ) ) ) ) )
=> ( ( ( D = F )
& ( C = E ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(1544,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/sandbox/benchmark/theBenchmark.p',t86_group_4) ).
thf(9398,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)],[1544]) ).
thf(700,axiom,
( ( k1_xboole_0 @ k1_setfam_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_setfam_1) ).
thf(5139,plain,
( ( k1_xboole_0 @ k1_setfam_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(648,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/sandbox/benchmark/theBenchmark.p',t60_partfun1) ).
thf(4890,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)],[648]) ).
thf(1045,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/sandbox/benchmark/theBenchmark.p',t154_group_2) ).
thf(6736,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)],[1045]) ).
thf(554,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( ( A @ k2_finseq_1 )
= ( B @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 ) )
=> ( B = np__0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finseq_3) ).
thf(4481,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( ( A @ k2_finseq_1 )
= ( B @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 ) )
=> ( B = np__0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(1590,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/sandbox/benchmark/theBenchmark.p',t171_group_2) ).
thf(9582,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)],[1590]) ).
thf(362,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ v3_struct_0 )
<=> ( A @ u1_struct_0 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_struct_0) ).
thf(3490,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)],[362]) ).
thf(1394,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/sandbox/benchmark/theBenchmark.p',dt_k9_group_1) ).
thf(8689,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)],[1394]) ).
thf(1451,axiom,
! [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 @ ( A @ r1_ordinal1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_card_1) ).
thf(9001,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( ( B @ ( A @ r1_ordinal1 ) )
=> ( B @ ( A @ r1_xreal_0 ) ) )
& ( ( B @ ( A @ r1_xreal_0 ) )
=> ( B @ ( A @ r1_ordinal1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).
thf(814,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/sandbox/benchmark/theBenchmark.p',t18_int_1) ).
thf(5688,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)],[814]) ).
thf(1495,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/sandbox/benchmark/theBenchmark.p',t176_group_2) ).
thf(9227,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)],[1495]) ).
thf(1148,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/sandbox/benchmark/theBenchmark.p',d12_group_1) ).
thf(7371,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)],[1148]) ).
thf(66,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/sandbox/benchmark/theBenchmark.p',t138_partfun1) ).
thf(2124,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)],[66]) ).
thf(517,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/sandbox/benchmark/theBenchmark.p',t67_group_4) ).
thf(4292,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)],[517]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k3_realset1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k3_realset1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k3_realset1 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_realset1) ).
thf(3278,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k3_realset1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k3_realset1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k3_realset1 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(40,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/sandbox/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(2005,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)],[40]) ).
thf(809,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/sandbox/benchmark/theBenchmark.p',d2_realset1) ).
thf(5661,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)],[809]) ).
thf(1051,axiom,
! [A: $i,B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( B @ a_1_0_finseq_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( B @ ( C @ r1_xreal_0 ) )
& ( C @ ( np__1 @ r1_xreal_0 ) )
& ( A = C )
& ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_finseq_1) ).
thf(6768,plain,
! [A: $i,B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( ? [C: $i] :
( ( B @ ( C @ r1_xreal_0 ) )
& ( C @ ( np__1 @ r1_xreal_0 ) )
& ( A = C )
& ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) ) )
=> ( B @ a_1_0_finseq_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_finseq_1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( B @ ( C @ r1_xreal_0 ) )
& ( C @ ( np__1 @ r1_xreal_0 ) )
& ( A = C )
& ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(370,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_xboole_1) ).
thf(3522,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',t36_funct_4) ).
thf(2054,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)],[50]) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',t55_relat_1) ).
thf(1948,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)],[29]) ).
thf(1785,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/sandbox/benchmark/theBenchmark.p',t52_group_4) ).
thf(10311,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)],[1785]) ).
thf(1482,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/sandbox/benchmark/theBenchmark.p',t27_group_3) ).
thf(9170,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)],[1482]) ).
thf(483,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_orders_1) ).
thf(4136,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(171,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_relat_1) ).
thf(2614,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)],[171]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',t60_funct_1) ).
thf(2096,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)],[61]) ).
thf(1086,axiom,
( ( k1_xboole_0 @ k1_card_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_card_1) ).
thf(6977,plain,
( ( k1_xboole_0 @ k1_card_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(462,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/sandbox/benchmark/theBenchmark.p',t12_binop_1) ).
thf(4013,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)],[462]) ).
thf(652,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/sandbox/benchmark/theBenchmark.p',t3_lattice4) ).
thf(4901,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)],[652]) ).
thf(1241,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/sandbox/benchmark/theBenchmark.p',dt_k3_group_2) ).
thf(7896,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)],[1241]) ).
thf(1625,axiom,
? [A: $i] :
( ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_group_1) ).
thf(9727,plain,
? [A: $i] :
( ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1625]) ).
thf(643,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/sandbox/benchmark/theBenchmark.p',t31_funct_2) ).
thf(4868,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)],[643]) ).
thf(578,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/sandbox/benchmark/theBenchmark.p',t158_partfun1) ).
thf(4580,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)],[578]) ).
thf(1527,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/sandbox/benchmark/theBenchmark.p',dt_k2_group_6) ).
thf(9334,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)],[1527]) ).
thf(677,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ? [C: $i] :
( ( ( C @ k3_finseq_1 )
= A )
& ( B @ ( C @ m2_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_finseq_1) ).
thf(5025,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ? [C: $i] :
( ( ( C @ k3_finseq_1 )
= A )
& ( B @ ( C @ m2_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(1771,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/sandbox/benchmark/theBenchmark.p',t17_group_1) ).
thf(10249,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)],[1771]) ).
thf(1291,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/sandbox/benchmark/theBenchmark.p',d2_group_1) ).
thf(8160,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)],[1291]) ).
thf(1727,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/sandbox/benchmark/theBenchmark.p',t18_latsubgr) ).
thf(10091,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)],[1727]) ).
thf(1028,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/sandbox/benchmark/theBenchmark.p',t92_group_1) ).
thf(6659,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)],[1028]) ).
thf(456,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/sandbox/benchmark/theBenchmark.p',d9_group_1) ).
thf(3981,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)],[456]) ).
thf(901,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
<=> ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(6088,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)],[901]) ).
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 ) )
=> ! [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/sandbox/benchmark/theBenchmark.p',t3_group_6) ).
thf(9777,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)],[1640]) ).
thf(283,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/sandbox/benchmark/theBenchmark.p',t30_subset_1) ).
thf(3146,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)],[283]) ).
thf(644,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ m2_finseq_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finseq_1) ).
thf(4879,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ m2_finseq_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(894,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/sandbox/benchmark/theBenchmark.p',t135_group_2) ).
thf(6056,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)],[894]) ).
thf(1739,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/sandbox/benchmark/theBenchmark.p',t18_group_3) ).
thf(10132,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)],[1739]) ).
thf(493,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/sandbox/benchmark/theBenchmark.p',dt_k9_group_6) ).
thf(4177,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)],[493]) ).
thf(1319,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/sandbox/benchmark/theBenchmark.p',t15_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,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)],[1319]) ).
thf(577,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/sandbox/benchmark/theBenchmark.p',t30_funct_2) ).
thf(4566,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)],[577]) ).
thf(708,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) )
=> ( ( A @ k2_card_1 )
= ( B @ k2_card_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_card_1) ).
thf(5165,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)],[708]) ).
thf(1581,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/sandbox/benchmark/theBenchmark.p',d5_group_6) ).
thf(9546,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)],[1581]) ).
thf(1110,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/sandbox/benchmark/theBenchmark.p',t7_group_1) ).
thf(7102,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)],[1110]) ).
thf(1006,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/sandbox/benchmark/theBenchmark.p',t69_partfun1) ).
thf(6564,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)],[1006]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_1) ).
thf(2256,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(1572,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/sandbox/benchmark/theBenchmark.p',t182_group_2) ).
thf(9507,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)],[1572]) ).
thf(534,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/sandbox/benchmark/theBenchmark.p',t47_setfam_1) ).
thf(4355,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)],[534]) ).
thf(832,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/sandbox/benchmark/theBenchmark.p',t90_group_1) ).
thf(5763,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)],[832]) ).
thf(1091,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/sandbox/benchmark/theBenchmark.p',t19_funct_2) ).
thf(6998,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)],[1091]) ).
thf(1298,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/sandbox/benchmark/theBenchmark.p',t41_group_3) ).
thf(8194,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)],[1298]) ).
thf(632,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/sandbox/benchmark/theBenchmark.p',t49_setfam_1) ).
thf(4812,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)],[632]) ).
thf(1040,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/sandbox/benchmark/theBenchmark.p',t98_group_2) ).
thf(6719,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)],[1040]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k2_realset1 ) ) @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k2_realset1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k2_realset1 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_realset1) ).
thf(4336,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k2_realset1 ) ) @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k2_realset1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k2_realset1 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(910,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/sandbox/benchmark/theBenchmark.p',t86_group_1) ).
thf(6132,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)],[910]) ).
thf(1023,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_xboole_1) ).
thf(6641,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)],[1023]) ).
thf(1072,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/sandbox/benchmark/theBenchmark.p',t56_group_4) ).
thf(6875,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)],[1072]) ).
thf(1522,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/sandbox/benchmark/theBenchmark.p',t35_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 ) )
& ( 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)],[1522]) ).
thf(232,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/sandbox/benchmark/theBenchmark.p',d9_binop_1) ).
thf(2942,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)],[232]) ).
thf(718,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/sandbox/benchmark/theBenchmark.p',t41_subset_1) ).
thf(5229,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)],[718]) ).
thf(775,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_zfmisc_1) ).
thf(5514,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(656,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/sandbox/benchmark/theBenchmark.p',t78_xboole_1) ).
thf(4937,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)],[656]) ).
thf(1015,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/sandbox/benchmark/theBenchmark.p',t101_group_3) ).
thf(6597,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)],[1015]) ).
thf(1716,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/sandbox/benchmark/theBenchmark.p',t88_group_2) ).
thf(10059,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)],[1716]) ).
thf(1076,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/sandbox/benchmark/theBenchmark.p',t48_funct_2) ).
thf(6921,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)],[1076]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',dt_k8_finseq_1) ).
thf(2175,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)],[77]) ).
thf(663,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/sandbox/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(4961,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)],[663]) ).
thf(1324,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_domain_1) ).
thf(8350,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)],[1324]) ).
thf(755,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_partfun1) ).
thf(5446,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(965,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/sandbox/benchmark/theBenchmark.p',t57_group_4) ).
thf(6362,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)],[965]) ).
thf(1011,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/sandbox/benchmark/theBenchmark.p',t38_funct_2) ).
thf(6577,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)],[1011]) ).
thf(682,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( A != np__0 )
=> ( B @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_finseq_3) ).
thf(5047,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( A != np__0 )
=> ( B @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(908,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k5_funct_4 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ k4_funct_4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_funct_4) ).
thf(6120,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k5_funct_4 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ k4_funct_4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(1412,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/sandbox/benchmark/theBenchmark.p',t16_group_2) ).
thf(8772,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)],[1412]) ).
thf(1102,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/sandbox/benchmark/theBenchmark.p',t3_group_2) ).
thf(7058,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)],[1102]) ).
thf(439,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/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(3913,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)],[439]) ).
thf(1226,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/sandbox/benchmark/theBenchmark.p',t72_card_1) ).
thf(7801,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)],[1226]) ).
thf(1079,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/sandbox/benchmark/theBenchmark.p',t45_group_6) ).
thf(6945,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)],[1079]) ).
thf(1315,axiom,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_card_1 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_card_1) ).
thf(8312,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)],[1315]) ).
thf(1733,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/sandbox/benchmark/theBenchmark.p',redefinition_r6_group_3) ).
thf(10112,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)],[1733]) ).
thf(892,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(6051,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)],[892]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t155_funct_1) ).
thf(2060,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(743,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C != A )
& ( B != C )
& ( A != B ) )
<=> ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v2_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_finseq_3) ).
thf(5399,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v2_funct_1 )
=> ( ( C != A )
& ( B != C )
& ( A != B ) ) )
& ( ( ( C != A )
& ( B != C )
& ( A != B ) )
=> ( C @ ( B @ ( A @ k11_finseq_1 ) ) @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(536,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
thf(4366,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)],[536]) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',t16_binop_1) ).
thf(2588,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)],[165]) ).
thf(1458,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/sandbox/benchmark/theBenchmark.p',t55_group_6) ).
thf(9037,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)],[1458]) ).
thf(769,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/sandbox/benchmark/theBenchmark.p',t29_group_2) ).
thf(5499,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)],[769]) ).
thf(1397,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/sandbox/benchmark/theBenchmark.p',t52_group_1) ).
thf(8701,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)],[1397]) ).
thf(353,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_zfmisc_1) ).
thf(3462,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)],[353]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) )
=> ( C @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_partfun1) ).
thf(5074,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) )
=> ( C @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(1284,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/sandbox/benchmark/theBenchmark.p',t16_relset_1) ).
thf(8128,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)],[1284]) ).
thf(148,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ k1_tarski @ ( A @ k10_relat_1 ) )
!= ( C @ k1_tarski ) )
& ( A @ k2_relat_1 @ ( B @ r2_hidden ) ) )
<=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_funct_1) ).
thf(2518,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ v2_funct_1 )
=> ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ k1_tarski @ ( A @ k10_relat_1 ) )
!= ( C @ k1_tarski ) )
& ( A @ k2_relat_1 @ ( B @ r2_hidden ) ) ) )
& ( ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ k1_tarski @ ( A @ k10_relat_1 ) )
!= ( C @ k1_tarski ) )
& ( A @ k2_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ v2_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1160,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_group_2) ).
thf(7462,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)],[1160]) ).
thf(212,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/sandbox/benchmark/theBenchmark.p',t18_relat_1) ).
thf(2821,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)],[212]) ).
thf(302,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/sandbox/benchmark/theBenchmark.p',t2_binop_1) ).
thf(3209,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)],[302]) ).
thf(1636,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/sandbox/benchmark/theBenchmark.p',t166_group_2) ).
thf(9766,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)],[1636]) ).
thf(1452,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/sandbox/benchmark/theBenchmark.p',t157_group_3) ).
thf(9005,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)],[1452]) ).
thf(665,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(4971,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)],[665]) ).
thf(538,axiom,
! [A: $i] :
( ( A @ v1_card_1 )
=> ( A @ k2_card_1 @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_card_1) ).
thf(4377,plain,
! [A: $i] :
( ( A @ v1_card_1 )
=> ( A @ k2_card_1 @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(1790,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/sandbox/benchmark/theBenchmark.p',t111_group_2) ).
thf(10333,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)],[1790]) ).
thf(1681,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/sandbox/benchmark/theBenchmark.p',cc2_group_2) ).
thf(9948,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)],[1681]) ).
thf(221,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/sandbox/benchmark/theBenchmark.p',d2_binop_1) ).
thf(2850,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)],[221]) ).
thf(1763,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_setfam_1 ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_setfam_1) ).
thf(10228,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_setfam_1 ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1763]) ).
thf(74,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/sandbox/benchmark/theBenchmark.p',dt_k1_funct_4) ).
thf(2160,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)],[74]) ).
thf(1703,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/sandbox/benchmark/theBenchmark.p',dt_k3_group_1) ).
thf(10027,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)],[1703]) ).
thf(914,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_wellord2 ) )
<=> ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_card_1) ).
thf(6146,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)],[914]) ).
thf(317,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/sandbox/benchmark/theBenchmark.p',t165_funct_2) ).
thf(3273,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)],[317]) ).
thf(1003,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(6545,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)],[1003]) ).
thf(1461,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_group_4) ).
thf(9050,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)],[1461]) ).
thf(730,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/sandbox/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(5276,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)],[730]) ).
thf(1200,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/sandbox/benchmark/theBenchmark.p',t64_card_1) ).
thf(7662,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)],[1200]) ).
thf(882,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ ( A @ r2_wellord2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_card_1) ).
thf(5995,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ ( A @ r2_wellord2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(784,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/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
thf(5543,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)],[784]) ).
thf(546,axiom,
! [A: $i,B: $i] : ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_xboole_1) ).
thf(4409,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)],[546]) ).
thf(1784,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/sandbox/benchmark/theBenchmark.p',t57_group_2) ).
thf(10307,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)],[1784]) ).
thf(1759,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/sandbox/benchmark/theBenchmark.p',t151_group_2) ).
thf(10218,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)],[1759]) ).
thf(350,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/sandbox/benchmark/theBenchmark.p',t8_setfam_1) ).
thf(3448,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)],[350]) ).
thf(565,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/sandbox/benchmark/theBenchmark.p',dt_k8_rlvect_1) ).
thf(4522,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)],[565]) ).
thf(943,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/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(6280,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)],[943]) ).
thf(1712,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/sandbox/benchmark/theBenchmark.p',t70_group_2) ).
thf(10048,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)],[1712]) ).
thf(834,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(5767,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(751,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ~ ( A @ k2_finseq_1 @ ( np__1 @ ( A @ k2_xcmplx_0 ) @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_finseq_3) ).
thf(5431,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ~ ( A @ k2_finseq_1 @ ( np__1 @ ( A @ k2_xcmplx_0 ) @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(1049,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/sandbox/benchmark/theBenchmark.p',t63_group_1) ).
thf(6762,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)],[1049]) ).
thf(575,axiom,
! [A: $i,B: $i] :
( ( B @ k6_partfun1 @ ( A @ k6_partfun1 @ k1_funct_4 ) )
= ( B @ ( A @ k2_xboole_0 ) @ k6_partfun1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_4) ).
thf(4561,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)],[575]) ).
thf(936,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(6244,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(747,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/sandbox/benchmark/theBenchmark.p',t5_xboole_1) ).
thf(5420,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)],[747]) ).
thf(1197,axiom,
k1_numbers @ ( k4_numbers @ r1_tarski ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_numbers) ).
thf(7655,plain,
k1_numbers @ ( k4_numbers @ r1_tarski ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(746,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_eqrel_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(5418,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_eqrel_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(1511,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/sandbox/benchmark/theBenchmark.p',dt_k11_group_2) ).
thf(9281,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)],[1511]) ).
thf(435,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/sandbox/benchmark/theBenchmark.p',t73_xboole_1) ).
thf(3885,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)],[435]) ).
thf(888,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/sandbox/benchmark/theBenchmark.p',t45_group_1) ).
thf(6037,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)],[888]) ).
thf(1746,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/sandbox/benchmark/theBenchmark.p',t76_group_2) ).
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 ) )
=> ( ( B @ k5_group_2 )
= ( C @ k5_group_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1746]) ).
thf(1594,axiom,
? [A: $i] :
( ( A @ v7_group_1 )
& ( A @ v4_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc8_vectsp_1) ).
thf(9599,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)],[1594]) ).
thf(415,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/sandbox/benchmark/theBenchmark.p',t27_funct_2) ).
thf(3722,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)],[415]) ).
thf(463,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/sandbox/benchmark/theBenchmark.p',t72_xboole_1) ).
thf(4020,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)],[463]) ).
thf(1728,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/sandbox/benchmark/theBenchmark.p',d10_group_2) ).
thf(10095,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)],[1728]) ).
thf(1302,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/sandbox/benchmark/theBenchmark.p',t61_group_3) ).
thf(8231,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)],[1302]) ).
thf(1351,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/sandbox/benchmark/theBenchmark.p',t46_group_3) ).
thf(8496,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)],[1351]) ).
thf(300,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/sandbox/benchmark/theBenchmark.p',t32_subset_1) ).
thf(3202,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)],[300]) ).
thf(505,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_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 @ k2_finseq_1 @ ( A @ r2_hidden ) )
& ( D @ k2_finseq_1 @ ( B @ r2_hidden ) )
& ( D
= ( np__1 @ ( C @ k1_nat_1 ) ) ) )
=> ( ( ( ( C @ ( A @ r1_xreal_0 ) )
& ( A @ ( B @ r1_xreal_0 ) ) )
=> ( ( A @ ( B @ k1_tarski @ ( D @ k2_finseq_1 @ k4_xboole_0 ) @ k14_finseq_1 @ k1_funct_1 ) )
= ( np__1 @ ( A @ k1_nat_1 ) ) ) )
& ( ( A @ ( np__1 @ r1_xreal_0 ) )
=> ( ( ( A @ ( B @ k1_tarski @ ( D @ k2_finseq_1 @ k4_xboole_0 ) @ k14_finseq_1 @ k1_funct_1 ) )
= A )
| ( A @ ( B @ r1_xreal_0 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_finseq_3) ).
thf(4222,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_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 @ k2_finseq_1 @ ( A @ r2_hidden ) )
& ( D @ k2_finseq_1 @ ( B @ r2_hidden ) )
& ( D
= ( np__1 @ ( C @ k1_nat_1 ) ) ) )
=> ( ( ( ( C @ ( A @ r1_xreal_0 ) )
& ( A @ ( B @ r1_xreal_0 ) ) )
=> ( ( A @ ( B @ k1_tarski @ ( D @ k2_finseq_1 @ k4_xboole_0 ) @ k14_finseq_1 @ k1_funct_1 ) )
= ( np__1 @ ( A @ k1_nat_1 ) ) ) )
& ( ( A @ ( np__1 @ r1_xreal_0 ) )
=> ( ( ( A @ ( B @ k1_tarski @ ( D @ k2_finseq_1 @ k4_xboole_0 ) @ k14_finseq_1 @ k1_funct_1 ) )
= A )
| ( A @ ( B @ r1_xreal_0 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(1575,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/sandbox/benchmark/theBenchmark.p',t34_group_6) ).
thf(9518,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)],[1575]) ).
thf(129,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/sandbox/benchmark/theBenchmark.p',t159_relat_1) ).
thf(2429,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)],[129]) ).
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 @ 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/sandbox/benchmark/theBenchmark.p',rc1_group_3) ).
thf(9567,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)],[1587]) ).
thf(1649,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/sandbox/benchmark/theBenchmark.p',t130_group_3) ).
thf(9809,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)],[1649]) ).
thf(1533,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/sandbox/benchmark/theBenchmark.p',t91_group_2) ).
thf(9358,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)],[1533]) ).
thf(1248,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/sandbox/benchmark/theBenchmark.p',t27_group_6) ).
thf(7947,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)],[1248]) ).
thf(678,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_xboole_1) ).
thf(5030,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)],[678]) ).
thf(704,axiom,
! [A: $i] :
( ( A @ k1_orders_1 )
= ( k1_xboole_0 @ k1_tarski @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_orders_1) ).
thf(5154,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)],[704]) ).
thf(1359,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/sandbox/benchmark/theBenchmark.p',t59_group_2) ).
thf(8528,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)],[1359]) ).
thf(963,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/sandbox/benchmark/theBenchmark.p',d11_group_6) ).
thf(6352,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)],[963]) ).
thf(1612,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/sandbox/benchmark/theBenchmark.p',t82_group_6) ).
thf(9683,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)],[1612]) ).
thf(377,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/sandbox/benchmark/theBenchmark.p',t175_orders_1) ).
thf(3544,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)],[377]) ).
thf(980,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/sandbox/benchmark/theBenchmark.p',t158_funct_2) ).
thf(6436,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)],[980]) ).
thf(1521,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/sandbox/benchmark/theBenchmark.p',t77_group_4) ).
thf(9313,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)],[1521]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',t12_funct_1) ).
thf(2599,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)],[167]) ).
thf(1383,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_ordinal1 ) )
=> ( B @ ( C @ m1_ordinal1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_ordinal1) ).
thf(8644,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_ordinal1 ) )
=> ( B @ ( C @ m1_ordinal1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ~ ( ( C
= ( E @ ( D @ k1_funct_1 ) ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( D @ k2_relat_1 @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_partfun1) ).
thf(3564,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ~ ( ( C
= ( E @ ( D @ k1_funct_1 ) ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( D @ k2_relat_1 @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(1701,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/sandbox/benchmark/theBenchmark.p',t6_group_1) ).
thf(10012,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)],[1701]) ).
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 ) )
=> ( C @ ( B @ ( A @ k7_group_4 ) ) @ ( A @ k5_group_4 ) @ ( C @ ( B @ ( A @ k8_group_4 ) ) @ ( A @ r1_group_2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_group_4) ).
thf(9911,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)],[1668]) ).
thf(618,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/sandbox/benchmark/theBenchmark.p',d3_group_4) ).
thf(4737,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)],[618]) ).
thf(1235,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/sandbox/benchmark/theBenchmark.p',t72_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 @ 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)],[1235]) ).
thf(1648,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/sandbox/benchmark/theBenchmark.p',t91_group_3) ).
thf(9807,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)],[1648]) ).
thf(756,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/sandbox/benchmark/theBenchmark.p',t54_setfam_1) ).
thf(5450,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)],[756]) ).
thf(1556,axiom,
? [A: $i] :
( ( A @ v1_group_1 )
& ( A @ l1_group_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_group_1) ).
thf(9435,plain,
? [A: $i] :
( ( A @ v1_group_1 )
& ( A @ l1_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1556]) ).
thf(871,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/sandbox/benchmark/theBenchmark.p',t13_card_1) ).
thf(5949,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)],[871]) ).
thf(276,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/sandbox/benchmark/theBenchmark.p',t36_subset_1) ).
thf(3107,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)],[276]) ).
thf(1137,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/sandbox/benchmark/theBenchmark.p',t44_funct_2) ).
thf(7331,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)],[1137]) ).
thf(825,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/sandbox/benchmark/theBenchmark.p',t38_group_2) ).
thf(5736,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)],[825]) ).
thf(1119,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/sandbox/benchmark/theBenchmark.p',t139_group_2) ).
thf(7207,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)],[1119]) ).
thf(241,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/sandbox/benchmark/theBenchmark.p',t160_relat_1) ).
thf(2975,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)],[241]) ).
thf(1296,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(8185,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).
thf(1690,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/sandbox/benchmark/theBenchmark.p',dt_k3_group_6) ).
thf(9983,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)],[1690]) ).
thf(1764,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/sandbox/benchmark/theBenchmark.p',t11_group_6) ).
thf(10231,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)],[1764]) ).
thf(1602,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/sandbox/benchmark/theBenchmark.p',t64_group_2) ).
thf(9637,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)],[1602]) ).
thf(1266,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( B @ k2_finseq_1 @ ( A @ k2_finseq_1 @ r2_wellord2 ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_finseq_1) ).
thf(8043,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( B @ k2_finseq_1 @ ( A @ k2_finseq_1 @ r2_wellord2 ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(452,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_finseq_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_finseq_1) ).
thf(3961,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_finseq_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(188,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/sandbox/benchmark/theBenchmark.p',t18_funct_4) ).
thf(2675,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)],[188]) ).
thf(1345,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/sandbox/benchmark/theBenchmark.p',dt_k3_latsubgr) ).
thf(8464,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)],[1345]) ).
thf(736,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/sandbox/benchmark/theBenchmark.p',t162_partfun1) ).
thf(5319,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)],[736]) ).
thf(1434,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/sandbox/benchmark/theBenchmark.p',t45_group_3) ).
thf(8893,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)],[1434]) ).
thf(986,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/sandbox/benchmark/theBenchmark.p',t31_group_1) ).
thf(6457,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)],[986]) ).
thf(925,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/sandbox/benchmark/theBenchmark.p',t49_group_1) ).
thf(6188,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)],[925]) ).
thf(123,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/sandbox/benchmark/theBenchmark.p',t155_relat_1) ).
thf(2411,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)],[123]) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',t17_finset_1) ).
thf(2500,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)],[143]) ).
thf(1061,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/sandbox/benchmark/theBenchmark.p',t114_group_2) ).
thf(6825,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)],[1061]) ).
thf(472,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/sandbox/benchmark/theBenchmark.p',t70_group_6) ).
thf(4057,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)],[472]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( B @ k6_partfun1 @ ( A @ k6_partfun1 @ r1_tarski ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funct_4) ).
thf(3124,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)],[280]) ).
thf(128,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/sandbox/benchmark/theBenchmark.p',t65_funct_1) ).
thf(2426,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)],[128]) ).
thf(482,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k1_setfam_1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_setfam_1) ).
thf(4133,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_setfam_1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(1057,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/sandbox/benchmark/theBenchmark.p',t51_group_3) ).
thf(6803,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)],[1057]) ).
thf(1366,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( A @ ( A @ k2_finseq_1 @ r2_wellord2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_finseq_1) ).
thf(8564,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( A @ ( A @ k2_finseq_1 @ r2_wellord2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).
thf(1570,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/sandbox/benchmark/theBenchmark.p',cc1_group_2) ).
thf(9500,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)],[1570]) ).
thf(1737,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/sandbox/benchmark/theBenchmark.p',t73_group_4) ).
thf(10128,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)],[1737]) ).
thf(583,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/sandbox/benchmark/theBenchmark.p',t112_partfun1) ).
thf(4611,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)],[583]) ).
thf(883,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/sandbox/benchmark/theBenchmark.p',d5_group_1) ).
thf(5998,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)],[883]) ).
thf(722,axiom,
! [A: $i] : ( A @ k2_card_1 @ v1_card_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_card_1) ).
thf(5240,plain,
! [A: $i] : ( A @ k2_card_1 @ v1_card_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(1499,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/sandbox/benchmark/theBenchmark.p',t33_group_1) ).
thf(9247,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)],[1499]) ).
thf(1188,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/sandbox/benchmark/theBenchmark.p',t38_group_3) ).
thf(7621,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)],[1188]) ).
thf(620,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/sandbox/benchmark/theBenchmark.p',t37_funct_4) ).
thf(4748,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)],[620]) ).
thf(771,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_2) ).
thf(5504,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)],[771]) ).
thf(1181,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/sandbox/benchmark/theBenchmark.p',t4_group_4) ).
thf(7585,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)],[1181]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v4_ordinal2 )
=> ! [D: $i] :
( ( D @ v4_ordinal2 )
=> ( ( ( D @ k2_finseq_1 @ ( B @ r1_tarski ) )
& ( C @ k2_finseq_1 @ ( A @ r1_tarski ) ) )
=> ( ! [E: $i] :
( ( k5_numbers @ ( k1_numbers @ ( E @ m2_subset_1 ) ) )
=> ! [F: $i] :
( ( k5_numbers @ ( k1_numbers @ ( F @ m2_subset_1 ) ) )
=> ~ ( ( E @ ( F @ r1_xreal_0 ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) )
<=> ( ( B @ ( A @ k2_xboole_0 ) @ k14_finseq_1 )
= ( B @ k14_finseq_1 @ ( A @ k14_finseq_1 @ ( k5_numbers @ k8_finseq_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_finseq_3) ).
thf(1972,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v4_ordinal2 )
=> ! [D: $i] :
( ( D @ v4_ordinal2 )
=> ( ( ( D @ k2_finseq_1 @ ( B @ r1_tarski ) )
& ( C @ k2_finseq_1 @ ( A @ r1_tarski ) ) )
=> ( ( ( ( B @ ( A @ k2_xboole_0 ) @ k14_finseq_1 )
= ( B @ k14_finseq_1 @ ( A @ k14_finseq_1 @ ( k5_numbers @ k8_finseq_1 ) ) ) )
=> ! [E: $i] :
( ( k5_numbers @ ( k1_numbers @ ( E @ m2_subset_1 ) ) )
=> ! [F: $i] :
( ( k5_numbers @ ( k1_numbers @ ( F @ m2_subset_1 ) ) )
=> ~ ( ( E @ ( F @ r1_xreal_0 ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) )
& ( ! [E: $i] :
( ( k5_numbers @ ( k1_numbers @ ( E @ m2_subset_1 ) ) )
=> ! [F: $i] :
( ( k5_numbers @ ( k1_numbers @ ( F @ m2_subset_1 ) ) )
=> ~ ( ( E @ ( F @ r1_xreal_0 ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k14_finseq_1 )
= ( B @ k14_finseq_1 @ ( A @ k14_finseq_1 @ ( k5_numbers @ k8_finseq_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_xboole_1) ).
thf(4106,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)],[476]) ).
thf(1271,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/sandbox/benchmark/theBenchmark.p',t40_group_2) ).
thf(8061,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)],[1271]) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',d10_binop_1) ).
thf(2579,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)],[164]) ).
thf(803,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/sandbox/benchmark/theBenchmark.p',t137_group_2) ).
thf(5633,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)],[803]) ).
thf(1317,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/sandbox/benchmark/theBenchmark.p',d12_group_2) ).
thf(8317,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)],[1317]) ).
thf(757,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/sandbox/benchmark/theBenchmark.p',redefinition_k8_group_6) ).
thf(5453,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)],[757]) ).
thf(486,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 @ k7_rlvect_1 ) ) )
= ( C @ ( B @ k10_finseq_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_rlvect_1) ).
thf(4143,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 @ k7_rlvect_1 ) ) )
= ( C @ ( B @ k10_finseq_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(306,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/sandbox/benchmark/theBenchmark.p',t122_zfmisc_1) ).
thf(3224,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)],[306]) ).
thf(1187,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/sandbox/benchmark/theBenchmark.p',t2_group_3) ).
thf(7612,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)],[1187]) ).
thf(1455,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ r2_wellord2 ) )
<=> ? [C: $i] :
( A
= ( C @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_card_1) ).
thf(9019,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)],[1455]) ).
thf(253,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/sandbox/benchmark/theBenchmark.p',t16_funct_4) ).
thf(3024,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)],[253]) ).
thf(1509,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/sandbox/benchmark/theBenchmark.p',t79_group_4) ).
thf(9274,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)],[1509]) ).
thf(1277,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/sandbox/benchmark/theBenchmark.p',t183_group_2) ).
thf(8087,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)],[1277]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k1_finsub_1 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_finsub_1) ).
thf(3256,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k1_finsub_1 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
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 @ 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/sandbox/benchmark/theBenchmark.p',d8_group_4) ).
thf(6511,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)],[1000]) ).
thf(1166,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_6_domain_1) ).
thf(7498,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)],[1166]) ).
thf(1751,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/sandbox/benchmark/theBenchmark.p',t81_group_3) ).
thf(10178,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)],[1751]) ).
thf(1626,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/sandbox/benchmark/theBenchmark.p',t57_group_6) ).
thf(9732,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)],[1626]) ).
thf(246,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/sandbox/benchmark/theBenchmark.p',t15_funct_4) ).
thf(3007,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)],[246]) ).
thf(488,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k4_card_1 )
= ( A @ k1_card_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_card_1) ).
thf(4150,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k4_card_1 )
= ( A @ k1_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(1559,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/sandbox/benchmark/theBenchmark.p',dt_k2_latsubgr) ).
thf(9453,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)],[1559]) ).
thf(846,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/sandbox/benchmark/theBenchmark.p',t64_xboole_1) ).
thf(5841,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)],[846]) ).
thf(634,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_eqrel_1) ).
thf(4819,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)],[634]) ).
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 @ ( C @ m1_group_2 ) )
=> ( ( C @ v6_group_1 )
=> ( ( C @ k9_group_1 )
= ( B @ ( C @ ( A @ k6_group_3 ) ) @ k9_group_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_group_3) ).
thf(8431,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)],[1337]) ).
thf(543,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/sandbox/benchmark/theBenchmark.p',t23_xboole_1) ).
thf(4392,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)],[543]) ).
thf(322,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/sandbox/benchmark/theBenchmark.p',t82_funct_2) ).
thf(3288,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)],[322]) ).
thf(503,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/sandbox/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(4217,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)],[503]) ).
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 ) )
=> ( B @ ( B @ ( A @ r6_group_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r6_group_3) ).
thf(9770,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)],[1638]) ).
thf(863,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/sandbox/benchmark/theBenchmark.p',t44_group_2) ).
thf(5917,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)],[863]) ).
thf(1658,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/sandbox/benchmark/theBenchmark.p',t56_group_6) ).
thf(9876,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)],[1658]) ).
thf(1550,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/sandbox/benchmark/theBenchmark.p',reflexivity_r2_group_6) ).
thf(9417,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)],[1550]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m3_realset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_realset1) ).
thf(2347,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m3_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(394,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m2_finseq_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_finseq_1) ).
thf(3625,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m2_finseq_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(257,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/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(3039,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)],[257]) ).
thf(385,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/sandbox/benchmark/theBenchmark.p',t84_zfmisc_1) ).
thf(3593,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)],[385]) ).
thf(1421,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/sandbox/benchmark/theBenchmark.p',t43_funct_2) ).
thf(8812,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)],[1421]) ).
thf(1758,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/sandbox/benchmark/theBenchmark.p',t76_group_4) ).
thf(10214,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)],[1758]) ).
thf(1325,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/sandbox/benchmark/theBenchmark.p',t89_group_2) ).
thf(8360,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)],[1325]) ).
thf(593,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A )
<=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(4639,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)],[593]) ).
thf(1038,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/sandbox/benchmark/theBenchmark.p',t115_group_2) ).
thf(6706,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)],[1038]) ).
thf(1077,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(6928,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)],[1077]) ).
thf(447,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/sandbox/benchmark/theBenchmark.p',t13_xboole_1) ).
thf(3946,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)],[447]) ).
thf(572,axiom,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( ( A @ k2_vectsp_1 )
= ( A @ u1_vectsp_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_vectsp_1) ).
thf(4548,plain,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( ( A @ k2_vectsp_1 )
= ( A @ u1_vectsp_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
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 @ 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/sandbox/benchmark/theBenchmark.p',t155_group_3) ).
thf(7659,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)],[1199]) ).
thf(1066,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/sandbox/benchmark/theBenchmark.p',t3_latsubgr) ).
thf(6850,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)],[1066]) ).
thf(766,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/sandbox/benchmark/theBenchmark.p',t48_group_1) ).
thf(5490,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)],[766]) ).
thf(878,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/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(5981,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)],[878]) ).
thf(484,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/sandbox/benchmark/theBenchmark.p',t141_zfmisc_1) ).
thf(4138,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)],[484]) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(3457,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)],[352]) ).
thf(118,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/sandbox/benchmark/theBenchmark.p',t130_partfun1) ).
thf(2352,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)],[118]) ).
thf(1065,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/sandbox/benchmark/theBenchmark.p',t96_group_3) ).
thf(6846,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)],[1065]) ).
thf(607,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/sandbox/benchmark/theBenchmark.p',t42_xboole_1) ).
thf(4698,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)],[607]) ).
thf(1441,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/sandbox/benchmark/theBenchmark.p',d15_group_1) ).
thf(8944,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)],[1441]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(2045,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)],[46]) ).
thf(807,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/sandbox/benchmark/theBenchmark.p',t113_group_3) ).
thf(5653,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)],[807]) ).
thf(265,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/sandbox/benchmark/theBenchmark.p',redefinition_k1_partfun1) ).
thf(3067,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)],[265]) ).
thf(1799,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/sandbox/benchmark/theBenchmark.p',t175_group_2) ).
thf(10364,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)],[1799]) ).
thf(626,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/sandbox/benchmark/theBenchmark.p',t176_orders_1) ).
thf(4770,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)],[626]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',t136_partfun1) ).
thf(1966,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)],[33]) ).
thf(1115,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/sandbox/benchmark/theBenchmark.p',d3_group_1) ).
thf(7177,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)],[1115]) ).
thf(224,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(2870,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(1641,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/sandbox/benchmark/theBenchmark.p',t70_group_4) ).
thf(9780,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)],[1641]) ).
thf(3,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/sandbox/benchmark/theBenchmark.p',fc17_finseq_1) ).
thf(1817,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)],[3]) ).
thf(885,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/sandbox/benchmark/theBenchmark.p',t117_group_3) ).
thf(6013,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)],[885]) ).
thf(291,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/sandbox/benchmark/theBenchmark.p',t21_group_4) ).
thf(3171,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)],[291]) ).
thf(898,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(6068,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(1706,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/sandbox/benchmark/theBenchmark.p',t3_group_3) ).
thf(10033,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)],[1706]) ).
thf(912,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/sandbox/benchmark/theBenchmark.p',t17_group_6) ).
thf(6137,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)],[912]) ).
thf(1182,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/sandbox/benchmark/theBenchmark.p',dt_k4_group_1) ).
thf(7589,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)],[1182]) ).
thf(1295,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/sandbox/benchmark/theBenchmark.p',t71_partfun1) ).
thf(8183,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)],[1295]) ).
thf(1754,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/sandbox/benchmark/theBenchmark.p',t59_group_4) ).
thf(10199,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)],[1754]) ).
thf(1745,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/sandbox/benchmark/theBenchmark.p',t109_group_3) ).
thf(10156,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)],[1745]) ).
thf(139,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/sandbox/benchmark/theBenchmark.p',t145_relat_1) ).
thf(2490,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)],[139]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',t28_funct_4) ).
thf(2187,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)],[82]) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',t169_funct_2) ).
thf(2110,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)],[62]) ).
thf(330,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ( ( ( A @ k2_finseq_1 @ ( C @ r2_hidden ) )
& ( A
= ( np__1 @ ( B @ k2_xcmplx_0 ) ) ) )
=> ( ( C @ k1_tarski @ ( A @ k2_finseq_1 @ k4_xboole_0 ) @ k14_finseq_1 @ k3_finseq_1 )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_finseq_3) ).
thf(3320,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ( ( ( A @ k2_finseq_1 @ ( C @ r2_hidden ) )
& ( A
= ( np__1 @ ( B @ k2_xcmplx_0 ) ) ) )
=> ( ( C @ k1_tarski @ ( A @ k2_finseq_1 @ k4_xboole_0 ) @ k14_finseq_1 @ k3_finseq_1 )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(1290,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_mcart_1) ).
thf(8153,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)],[1290]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).
thf(2342,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)],[114]) ).
thf(1047,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/sandbox/benchmark/theBenchmark.p',t9_funct_2) ).
thf(6743,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)],[1047]) ).
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 @ ( 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/sandbox/benchmark/theBenchmark.p',t129_group_2) ).
thf(7974,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)],[1255]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',t157_funct_1) ).
thf(2226,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)],[90]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ( ( B @ k3_finseq_1 @ ( C @ r1_xreal_0 ) )
=> ( ( C @ ( B @ ( A @ k16_finseq_1 ) ) @ k3_finseq_1 )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_finseq_1) ).
thf(2071,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ( ( B @ k3_finseq_1 @ ( C @ r1_xreal_0 ) )
=> ( ( C @ ( B @ ( A @ k16_finseq_1 ) ) @ k3_finseq_1 )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',d11_binop_1) ).
thf(2658,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)],[183]) ).
thf(442,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/sandbox/benchmark/theBenchmark.p',t81_zfmisc_1) ).
thf(3929,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)],[442]) ).
thf(199,axiom,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k2_relat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(2775,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)],[199]) ).
thf(687,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/sandbox/benchmark/theBenchmark.p',t29_subset_1) ).
thf(5068,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)],[687]) ).
thf(205,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/sandbox/benchmark/theBenchmark.p',t49_relat_1) ).
thf(2792,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)],[205]) ).
thf(1,conjecture,
! [A: $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/sandbox/benchmark/theBenchmark.p',t20_latsubgr) ).
thf(2,negated_conjecture,
~ ! [A: $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(neg_conjecture,[status(cth)],[1]) ).
thf(1807,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)],[2]) ).
thf(1346,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/sandbox/benchmark/theBenchmark.p',d4_group_2) ).
thf(8469,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)],[1346]) ).
thf(710,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/sandbox/benchmark/theBenchmark.p',t10_group_4) ).
thf(5184,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)],[710]) ).
thf(438,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/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(3911,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)],[438]) ).
thf(1099,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/sandbox/benchmark/theBenchmark.p',t4_group_3) ).
thf(7044,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)],[1099]) ).
thf(342,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/sandbox/benchmark/theBenchmark.p',t143_funct_2) ).
thf(3383,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)],[342]) ).
thf(997,axiom,
! [A: $i] :
( ( k4_numbers @ ( A @ m1_subset_1 ) )
=> ( A @ v1_int_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_int_1) ).
thf(6494,plain,
! [A: $i] :
( ( k4_numbers @ ( A @ m1_subset_1 ) )
=> ( A @ v1_int_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(645,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/sandbox/benchmark/theBenchmark.p',t98_zfmisc_1) ).
thf(4881,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)],[645]) ).
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 ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) )
& ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= ( D @ ( B @ ( A @ k4_relset_1 ) ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_partfun1) ).
thf(5600,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) )
& ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= ( D @ ( B @ ( A @ k4_relset_1 ) ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(685,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/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(5055,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)],[685]) ).
thf(354,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/sandbox/benchmark/theBenchmark.p',t46_subset_1) ).
thf(3465,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)],[354]) ).
thf(1634,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/sandbox/benchmark/theBenchmark.p',t144_group_3) ).
thf(9755,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)],[1634]) ).
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 @ k8_group_1 @ ( B @ k8_group_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_group_2) ).
thf(10072,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)],[1721]) ).
thf(1760,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/sandbox/benchmark/theBenchmark.p',fc3_group_6) ).
thf(10220,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)],[1760]) ).
thf(1624,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/sandbox/benchmark/theBenchmark.p',t99_group_4) ).
thf(9724,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)],[1624]) ).
thf(930,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/sandbox/benchmark/theBenchmark.p',t7_group_2) ).
thf(6230,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)],[930]) ).
thf(1048,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/sandbox/benchmark/theBenchmark.p',t33_group_2) ).
thf(6753,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)],[1048]) ).
thf(631,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/sandbox/benchmark/theBenchmark.p',dt_k8_group_6) ).
thf(4806,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)],[631]) ).
thf(1060,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/sandbox/benchmark/theBenchmark.p',t6_mcart_1) ).
thf(6818,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)],[1060]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t180_relat_1) ).
thf(2290,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(585,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/sandbox/benchmark/theBenchmark.p',t25_group_4) ).
thf(4615,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)],[585]) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',t13_funct_4) ).
thf(2251,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)],[100]) ).
thf(1035,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(6689,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(1472,axiom,
( ! [A: $i] :
~ ( ! [B: $i] :
~ ( ( B @ ( A @ p1_s1_funct_2 ) )
& ( f2_s1_funct_2 @ ( B @ r2_hidden ) ) )
& ( f1_s1_funct_2 @ ( A @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_funct_2 @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( B @ p1_s1_funct_2 ) ) )
& ( f2_s1_funct_2 @ ( f1_s1_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s1_funct_2 @ ( f1_s1_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_2) ).
thf(9102,plain,
( ! [A: $i] :
~ ( ! [B: $i] :
~ ( ( B @ ( A @ p1_s1_funct_2 ) )
& ( f2_s1_funct_2 @ ( B @ r2_hidden ) ) )
& ( f1_s1_funct_2 @ ( A @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_funct_2 @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( B @ p1_s1_funct_2 ) ) )
& ( f2_s1_funct_2 @ ( f1_s1_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s1_funct_2 @ ( f1_s1_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472]) ).
thf(1142,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/sandbox/benchmark/theBenchmark.p',t90_group_2) ).
thf(7344,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)],[1142]) ).
thf(602,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( ( A @ k2_finseq_1 )
= ( B @ k2_finseq_1 @ ( A @ k2_finseq_1 @ ( k5_numbers @ k5_subset_1 ) ) ) )
=> ( B @ ( A @ r1_xreal_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_finseq_1) ).
thf(4681,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( ( A @ k2_finseq_1 )
= ( B @ k2_finseq_1 @ ( A @ k2_finseq_1 @ ( k5_numbers @ k5_subset_1 ) ) ) )
=> ( B @ ( A @ r1_xreal_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(697,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 @ ( B @ r2_hidden ) )
=> ( C @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 @ ( C @ ( B @ k2_xcmplx_0 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_finseq_1) ).
thf(5132,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 @ ( B @ r2_hidden ) )
=> ( C @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 @ ( C @ ( B @ k2_xcmplx_0 ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(3336,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)],[334]) ).
thf(1233,axiom,
k1_numbers @ k1_zfmisc_1 @ ( k5_numbers @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_numbers) ).
thf(7840,plain,
k1_numbers @ k1_zfmisc_1 @ ( k5_numbers @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(481,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
<=> ! [D: $i] :
( ( B @ ( A @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_2) ).
thf(4126,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( B @ ( A @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
=> ( C @ ( B @ r1_partfun1 ) ) )
& ( ( C @ ( B @ r1_partfun1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(304,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( A @ ( B @ k1_setfam_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_setfam_1) ).
thf(3220,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( A @ ( B @ k1_setfam_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(470,axiom,
! [A: $i] : ( A @ k2_card_1 @ ( k1_xboole_0 @ k1_card_1 @ r2_hidden ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_card_1) ).
thf(4042,plain,
! [A: $i] : ( A @ k2_card_1 @ ( k1_xboole_0 @ k1_card_1 @ r2_hidden ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(571,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( B @ ( A @ r1_rlvect_1 ) )
<=> ( A @ u1_struct_0 @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_rlvect_1) ).
thf(4542,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)],[571]) ).
thf(1677,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/sandbox/benchmark/theBenchmark.p',t16_group_1) ).
thf(9934,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)],[1677]) ).
thf(275,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/sandbox/benchmark/theBenchmark.p',t37_funct_2) ).
thf(3104,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)],[275]) ).
thf(1561,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ m1_ordinal1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_ordinal1) ).
thf(9459,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ m1_ordinal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1561]) ).
thf(239,axiom,
? [A: $i] : ( A @ l1_rlvect_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_rlvect_1) ).
thf(2971,plain,
? [A: $i] : ( A @ l1_rlvect_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1593,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/sandbox/benchmark/theBenchmark.p',t36_group_6) ).
thf(9591,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)],[1593]) ).
thf(829,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/sandbox/benchmark/theBenchmark.p',t128_group_2) ).
thf(5756,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)],[829]) ).
thf(461,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/sandbox/benchmark/theBenchmark.p',t57_domain_1) ).
thf(4010,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)],[461]) ).
thf(1414,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/sandbox/benchmark/theBenchmark.p',t116_group_2) ).
thf(8781,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)],[1414]) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',t35_funct_4) ).
thf(2130,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)],[68]) ).
thf(1401,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) )
<=> ? [C: $i] :
( A
= ( C @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_card_1) ).
thf(8716,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)],[1401]) ).
thf(1037,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ? [E: $i] :
( ( ( E @ ( D @ k1_funct_1 ) )
!= ( E @ ( C @ k1_funct_1 ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_funct_2) ).
thf(6694,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ? [E: $i] :
( ( ( E @ ( D @ k1_funct_1 ) )
!= ( E @ ( C @ k1_funct_1 ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(1377,axiom,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
& ( A @ k1_subset_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_subset_1) ).
thf(8617,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)],[1377]) ).
thf(567,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_zfmisc_1) ).
thf(4527,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)],[567]) ).
thf(1803,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/sandbox/benchmark/theBenchmark.p',t60_group_2) ).
thf(10386,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)],[1803]) ).
thf(230,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/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
thf(2934,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)],[230]) ).
thf(1156,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).
thf(7437,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)],[1156]) ).
thf(1696,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/sandbox/benchmark/theBenchmark.p',t174_group_2) ).
thf(9999,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)],[1696]) ).
thf(707,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k2_realset1 ) ) )
= ( C @ ( B @ k1_realset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_realset1) ).
thf(5162,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k2_realset1 ) ) )
= ( C @ ( B @ k1_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(1067,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/sandbox/benchmark/theBenchmark.p',t60_funct_2) ).
thf(6854,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)],[1067]) ).
thf(45,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/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
thf(2041,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)],[45]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_relat_1) ).
thf(2066,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(942,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( A
= ( A @ k1_card_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_card_1) ).
thf(6277,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( A
= ( A @ k1_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(826,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/sandbox/benchmark/theBenchmark.p',t58_zfmisc_1) ).
thf(5739,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)],[826]) ).
thf(1607,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/sandbox/benchmark/theBenchmark.p',t148_group_3) ).
thf(9660,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)],[1607]) ).
thf(1580,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/sandbox/benchmark/theBenchmark.p',t104_group_2) ).
thf(9542,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)],[1580]) ).
thf(1474,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/sandbox/benchmark/theBenchmark.p',t46_group_6) ).
thf(9115,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)],[1474]) ).
thf(134,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( A @ k1_relat_1 )
= k1_xboole_0 )
<=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
thf(2447,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)],[134]) ).
thf(1292,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/sandbox/benchmark/theBenchmark.p',t44_group_6) ).
thf(8172,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)],[1292]) ).
thf(235,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/sandbox/benchmark/theBenchmark.p',dt_k1_group_4) ).
thf(2956,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)],[235]) ).
thf(1308,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/sandbox/benchmark/theBenchmark.p',t55_group_3) ).
thf(8253,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)],[1308]) ).
thf(294,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/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(3181,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)],[294]) ).
thf(203,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/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
thf(2786,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)],[203]) ).
thf(1688,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_1_group_4) ).
thf(9972,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)],[1688]) ).
thf(501,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/sandbox/benchmark/theBenchmark.p',t17_subset_1) ).
thf(4197,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)],[501]) ).
thf(331,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( A @ v1_int_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_int_1) ).
thf(3324,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( A @ v1_int_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(1709,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/sandbox/benchmark/theBenchmark.p',t58_group_2) ).
thf(10040,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)],[1709]) ).
thf(952,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_partfun1) ).
thf(6305,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(489,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/sandbox/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(4153,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)],[489]) ).
thf(1685,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/sandbox/benchmark/theBenchmark.p',t83_group_6) ).
thf(9962,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)],[1685]) ).
thf(947,axiom,
k4_numbers @ ( k5_numbers @ r1_tarski ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_numbers) ).
thf(6290,plain,
k4_numbers @ ( k5_numbers @ r1_tarski ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(1573,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/sandbox/benchmark/theBenchmark.p',d9_group_4) ).
thf(9510,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)],[1573]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k2_relat_1 @ ( A @ r2_hidden ) )
<=> ( ( A @ k1_tarski @ ( B @ k10_relat_1 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_funct_1) ).
thf(2648,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( A @ k1_tarski @ ( B @ k10_relat_1 ) )
!= k1_xboole_0 )
=> ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k10_relat_1 ) )
!= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(837,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/sandbox/benchmark/theBenchmark.p',t63_group_4) ).
thf(5781,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)],[837]) ).
thf(623,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(4759,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)],[623]) ).
thf(1382,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/sandbox/benchmark/theBenchmark.p',t10_realset1) ).
thf(8638,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)],[1382]) ).
thf(316,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/sandbox/benchmark/theBenchmark.p',t6_setfam_1) ).
thf(3267,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)],[316]) ).
thf(891,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/sandbox/benchmark/theBenchmark.p',t78_int_1) ).
thf(6045,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)],[891]) ).
thf(676,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ k3_tarski @ r1_tarski ) ) )
=> ( B @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_setfam_1) ).
thf(5023,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)],[676]) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_finset_1) ).
thf(3149,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)],[284]) ).
thf(373,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/sandbox/benchmark/theBenchmark.p',t124_zfmisc_1) ).
thf(3529,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)],[373]) ).
thf(817,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/sandbox/benchmark/theBenchmark.p',t42_group_1) ).
thf(5699,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)],[817]) ).
thf(1416,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/sandbox/benchmark/theBenchmark.p',t95_group_1) ).
thf(8793,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)],[1416]) ).
thf(80,axiom,
( ( k1_xboole_0 @ k14_finseq_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_finseq_3) ).
thf(2183,plain,
( ( k1_xboole_0 @ k14_finseq_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1001,axiom,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( A @ u1_struct_0 @ ( A @ k2_vectsp_1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_vectsp_1) ).
thf(6536,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)],[1001]) ).
thf(1584,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/sandbox/benchmark/theBenchmark.p',dt_k7_group_4) ).
thf(9559,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)],[1584]) ).
thf(939,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/sandbox/benchmark/theBenchmark.p',t27_relset_1) ).
thf(6252,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)],[939]) ).
thf(459,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/sandbox/benchmark/theBenchmark.p',t148_partfun1) ).
thf(3993,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)],[459]) ).
thf(1490,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/sandbox/benchmark/theBenchmark.p',t44_card_1) ).
thf(9211,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)],[1490]) ).
thf(1008,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/sandbox/benchmark/theBenchmark.p',t28_group_3) ).
thf(6569,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)],[1008]) ).
thf(776,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/sandbox/benchmark/theBenchmark.p',t27_xboole_1) ).
thf(5517,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)],[776]) ).
thf(1311,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/sandbox/benchmark/theBenchmark.p',d11_group_4) ).
thf(8267,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)],[1311]) ).
thf(812,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/sandbox/benchmark/theBenchmark.p',t116_funct_2) ).
thf(5672,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)],[812]) ).
thf(1514,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/sandbox/benchmark/theBenchmark.p',d6_group_2) ).
thf(9289,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)],[1514]) ).
thf(1520,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/sandbox/benchmark/theBenchmark.p',t69_group_6) ).
thf(9311,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)],[1520]) ).
thf(1732,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/sandbox/benchmark/theBenchmark.p',t29_group_6) ).
thf(10109,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)],[1732]) ).
thf(1193,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_partfun1) ).
thf(7644,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(1748,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/sandbox/benchmark/theBenchmark.p',t132_group_2) ).
thf(10167,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)],[1748]) ).
thf(982,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ k10_finseq_1 ) )
!= ( E @ ( D @ ( C @ k11_finseq_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_finseq_3) ).
thf(6444,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ k10_finseq_1 ) )
!= ( E @ ( D @ ( C @ k11_finseq_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(1604,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/sandbox/benchmark/theBenchmark.p',fc5_group_6) ).
thf(9643,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)],[1604]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t176_relat_1) ).
thf(1994,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(519,axiom,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(4306,plain,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(712,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/sandbox/benchmark/theBenchmark.p',t13_group_4) ).
thf(5194,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)],[712]) ).
thf(999,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/sandbox/benchmark/theBenchmark.p',t158_group_3) ).
thf(6499,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)],[999]) ).
thf(1655,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/sandbox/benchmark/theBenchmark.p',t52_group_6) ).
thf(9839,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)],[1655]) ).
thf(1399,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/sandbox/benchmark/theBenchmark.p',t65_group_1) ).
thf(8710,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)],[1399]) ).
thf(928,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(6198,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)],[928]) ).
thf(1523,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/sandbox/benchmark/theBenchmark.p',symmetry_r1_group_2) ).
thf(9321,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)],[1523]) ).
thf(1539,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/sandbox/benchmark/theBenchmark.p',d7_group_2) ).
thf(9378,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)],[1539]) ).
thf(1281,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_subset_1 )
= ( A @ a_1_1_domain_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_domain_1) ).
thf(8115,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)],[1281]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k10_finseq_1 ) @ v1_funct_1 )
& ( B @ ( A @ k10_finseq_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_finseq_1) ).
thf(1957,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k10_finseq_1 ) @ v1_funct_1 )
& ( B @ ( A @ k10_finseq_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( C @ ( D @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_funct_2) ).
thf(4670,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( C @ ( D @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(512,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/sandbox/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(4254,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)],[512]) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',t139_partfun1) ).
thf(2233,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)],[93]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( C @ ( B @ ( A @ k3_realset1 ) ) )
= ( B @ ( C @ k1_realset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_realset1) ).
thf(2951,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( C @ ( B @ ( A @ k3_realset1 ) ) )
= ( B @ ( C @ k1_realset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(933,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/sandbox/benchmark/theBenchmark.p',t42_group_4) ).
thf(6237,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)],[933]) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(1986,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)],[36]) ).
thf(1778,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/sandbox/benchmark/theBenchmark.p',d6_group_3) ).
thf(10280,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)],[1778]) ).
thf(289,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/sandbox/benchmark/theBenchmark.p',t18_binop_1) ).
thf(3164,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)],[289]) ).
thf(1534,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/sandbox/benchmark/theBenchmark.p',t184_group_2) ).
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 ) )
& ( 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)],[1534]) ).
thf(711,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/sandbox/benchmark/theBenchmark.p',t51_funct_2) ).
thf(5187,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)],[711]) ).
thf(102,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ k10_relat_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
thf(2258,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k10_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k10_relat_1 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(1496,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/sandbox/benchmark/theBenchmark.p',t52_group_3) ).
thf(9239,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)],[1496]) ).
thf(1195,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/sandbox/benchmark/theBenchmark.p',t43_group_1) ).
thf(7649,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)],[1195]) ).
thf(741,axiom,
! [A: $i] :
( ? [B: $i] :
( ( B @ k2_finseq_1 @ ( A @ r1_tarski ) )
& ( B @ v4_ordinal2 ) )
=> ! [B: $i] :
( ( k5_numbers @ ( B @ m2_finseq_1 ) )
=> ( ( B
= ( A @ k14_finseq_1 ) )
<=> ( ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ! [D: $i] :
( ( D @ v4_ordinal2 )
=> ! [E: $i] :
( ( E @ v4_ordinal2 )
=> ! [F: $i] :
( ( F @ v4_ordinal2 )
=> ~ ( ( E @ ( F @ r1_xreal_0 ) )
& ( F
= ( D @ ( B @ k1_funct_1 ) ) )
& ( E
= ( C @ ( B @ k1_funct_1 ) ) )
& ( B @ k3_finseq_1 @ ( D @ r1_xreal_0 ) )
& ~ ( C @ ( D @ r1_xreal_0 ) )
& ( C @ ( np__1 @ r1_xreal_0 ) ) ) ) ) ) )
& ( ( B @ k2_relat_1 )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_finseq_1) ).
thf(5357,plain,
! [A: $i] :
( ? [B: $i] :
( ( B @ k2_finseq_1 @ ( A @ r1_tarski ) )
& ( B @ v4_ordinal2 ) )
=> ! [B: $i] :
( ( k5_numbers @ ( B @ m2_finseq_1 ) )
=> ( ( ( ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ! [D: $i] :
( ( D @ v4_ordinal2 )
=> ! [E: $i] :
( ( E @ v4_ordinal2 )
=> ! [F: $i] :
( ( F @ v4_ordinal2 )
=> ~ ( ( E @ ( F @ r1_xreal_0 ) )
& ( F
= ( D @ ( B @ k1_funct_1 ) ) )
& ( E
= ( C @ ( B @ k1_funct_1 ) ) )
& ( B @ k3_finseq_1 @ ( D @ r1_xreal_0 ) )
& ~ ( C @ ( D @ r1_xreal_0 ) )
& ( C @ ( np__1 @ r1_xreal_0 ) ) ) ) ) ) )
& ( ( B @ k2_relat_1 )
= A ) )
=> ( B
= ( A @ k14_finseq_1 ) ) )
& ( ( B
= ( A @ k14_finseq_1 ) )
=> ( ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ! [D: $i] :
( ( D @ v4_ordinal2 )
=> ! [E: $i] :
( ( E @ v4_ordinal2 )
=> ! [F: $i] :
( ( F @ v4_ordinal2 )
=> ~ ( ( E @ ( F @ r1_xreal_0 ) )
& ( F
= ( D @ ( B @ k1_funct_1 ) ) )
& ( E
= ( C @ ( B @ k1_funct_1 ) ) )
& ( B @ k3_finseq_1 @ ( D @ r1_xreal_0 ) )
& ~ ( C @ ( D @ r1_xreal_0 ) )
& ( C @ ( np__1 @ r1_xreal_0 ) ) ) ) ) ) )
& ( ( B @ k2_relat_1 )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(1529,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/sandbox/benchmark/theBenchmark.p',t68_group_2) ).
thf(9346,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)],[1529]) ).
thf(633,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/sandbox/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(4816,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)],[633]) ).
thf(1171,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/sandbox/benchmark/theBenchmark.p',t143_group_2) ).
thf(7542,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)],[1171]) ).
thf(1583,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/sandbox/benchmark/theBenchmark.p',rc1_group_6) ).
thf(9551,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)],[1583]) ).
thf(654,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B = k1_xboole_0 )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
<=> ( C = k1_xboole_0 ) )
| ( A = k1_xboole_0 ) ) )
& ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
<=> ( A
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).
thf(4917,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B = k1_xboole_0 )
=> ( ( ( ( C = k1_xboole_0 )
=> ( B @ ( A @ ( C @ v1_funct_2 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
=> ( C = k1_xboole_0 ) ) )
| ( A = k1_xboole_0 ) ) )
& ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ( A
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) )
=> ( B @ ( A @ ( C @ v1_funct_2 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
=> ( A
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',t13_relset_1) ).
thf(2302,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)],[107]) ).
thf(628,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/sandbox/benchmark/theBenchmark.p',existence_m1_realset1) ).
thf(4794,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)],[628]) ).
thf(1481,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/sandbox/benchmark/theBenchmark.p',dt_k13_group_6) ).
thf(9166,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)],[1481]) ).
thf(824,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/sandbox/benchmark/theBenchmark.p',d7_group_6) ).
thf(5728,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)],[824]) ).
thf(1273,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/sandbox/benchmark/theBenchmark.p',d2_group_3) ).
thf(8070,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)],[1273]) ).
thf(1457,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_xboole_1) ).
thf(9034,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)],[1457]) ).
thf(1221,axiom,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( B
= ( A @ k1_card_1 ) )
<=> ( B @ ( A @ r2_wellord2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_card_1) ).
thf(7759,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)],[1221]) ).
thf(875,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/sandbox/benchmark/theBenchmark.p',t7_group_3) ).
thf(5971,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)],[875]) ).
thf(307,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/sandbox/benchmark/theBenchmark.p',t70_xboole_1) ).
thf(3232,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)],[307]) ).
thf(323,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/sandbox/benchmark/theBenchmark.p',t52_subset_1) ).
thf(3291,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)],[323]) ).
thf(1749,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/sandbox/benchmark/theBenchmark.p',t9_group_2) ).
thf(10173,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)],[1749]) ).
thf(1054,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/sandbox/benchmark/theBenchmark.p',t66_group_1) ).
thf(6786,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)],[1054]) ).
thf(243,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/sandbox/benchmark/theBenchmark.p',t20_funct_1) ).
thf(2983,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)],[243]) ).
thf(1620,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/sandbox/benchmark/theBenchmark.p',t51_group_6) ).
thf(9711,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)],[1620]) ).
thf(1678,axiom,
! [A: $i,B: $i,C: $i] :
( k1_xboole_0
!= ( C @ ( B @ ( A @ k11_finseq_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_finseq_3) ).
thf(9937,plain,
! [A: $i,B: $i,C: $i] :
( k1_xboole_0
!= ( C @ ( B @ ( A @ k11_finseq_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1678]) ).
thf(580,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/sandbox/benchmark/theBenchmark.p',t10_setfam_1) ).
thf(4596,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)],[580]) ).
thf(1411,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(8769,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411]) ).
thf(786,axiom,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(5554,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(1123,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/sandbox/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
thf(7242,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)],[1123]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relset_1) ).
thf(3987,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(612,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/sandbox/benchmark/theBenchmark.p',t80_card_1) ).
thf(4719,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)],[612]) ).
thf(274,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ( ( C @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 @ ( C @ ( B @ k2_xcmplx_0 ) @ r2_hidden ) )
=> ( ( ( C @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 @ ( B @ r2_hidden ) )
& ( A @ k2_finseq_1 @ ( B @ r2_hidden ) ) )
| ( np__0 @ ( B @ r1_xreal_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_finseq_1) ).
thf(3100,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ! [C: $i] :
( ( C @ v4_ordinal2 )
=> ( ( C @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 @ ( C @ ( B @ k2_xcmplx_0 ) @ r2_hidden ) )
=> ( ( ( C @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 @ ( B @ r2_hidden ) )
& ( A @ k2_finseq_1 @ ( B @ r2_hidden ) ) )
| ( np__0 @ ( B @ r1_xreal_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(341,axiom,
( ! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( ( ( A @ k1_card_1 @ k4_card_1 )
= A )
& ( ( A @ k4_card_1 )
= A ) ) )
& ! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 @ k4_card_1 )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_finseq_1) ).
thf(3373,plain,
( ! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( ( ( A @ k1_card_1 @ k4_card_1 )
= A )
& ( ( A @ k4_card_1 )
= A ) ) )
& ! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 @ k4_card_1 )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
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 @ 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/sandbox/benchmark/theBenchmark.p',t21_group_2) ).
thf(7489,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)],[1164]) ).
thf(425,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/sandbox/benchmark/theBenchmark.p',d14_binop_1) ).
thf(3837,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)],[425]) ).
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 @ k12_group_2 ) ) @ ( D @ ( A @ k10_group_2 ) ) )
= ( D @ ( C @ ( A @ k7_group_4 ) ) @ ( B @ ( A @ k3_group_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_group_4) ).
thf(6906,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)],[1074]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( B @ k2_finseq_1 @ ( A @ r1_tarski ) )
=> ( A @ k14_finseq_1 @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_finseq_3) ).
thf(2050,plain,
! [A: $i,B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( B @ k2_finseq_1 @ ( A @ r1_tarski ) )
=> ( A @ k14_finseq_1 @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1314,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/sandbox/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(8309,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)],[1314]) ).
thf(1125,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/sandbox/benchmark/theBenchmark.p',t13_group_2) ).
thf(7248,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)],[1125]) ).
thf(646,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/sandbox/benchmark/theBenchmark.p',t16_group_4) ).
thf(4885,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)],[646]) ).
thf(1680,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/sandbox/benchmark/theBenchmark.p',dt_k8_group_4) ).
thf(9944,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)],[1680]) ).
thf(673,axiom,
? [A: $i] : ( A @ l2_lattices ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(5014,plain,
? [A: $i] : ( A @ l2_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(407,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(3690,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)],[407]) ).
thf(1714,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/sandbox/benchmark/theBenchmark.p',t77_group_6) ).
thf(10054,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)],[1714]) ).
thf(1563,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/sandbox/benchmark/theBenchmark.p',d1_latsubgr) ).
thf(9463,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)],[1563]) ).
thf(866,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/sandbox/benchmark/theBenchmark.p',t85_group_3) ).
thf(5926,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)],[866]) ).
thf(263,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 @ k14_finseq_1 @ k3_finseq_1 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_finseq_3) ).
thf(3062,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 @ k14_finseq_1 @ k3_finseq_1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v4_ordinal2 )
& ( A @ ( B @ m1_finseq_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ k16_finseq_1 ) ) @ m2_finseq_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_finseq_1) ).
thf(3015,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v4_ordinal2 )
& ( A @ ( B @ m1_finseq_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ k16_finseq_1 ) ) @ m2_finseq_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(1730,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/sandbox/benchmark/theBenchmark.p',t49_group_2) ).
thf(10105,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)],[1730]) ).
thf(1329,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/sandbox/benchmark/theBenchmark.p',t121_funct_2) ).
thf(8400,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)],[1329]) ).
thf(1050,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/sandbox/benchmark/theBenchmark.p',d10_group_3) ).
thf(6765,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)],[1050]) ).
thf(298,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/sandbox/benchmark/theBenchmark.p',t79_funct_2) ).
thf(3196,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)],[298]) ).
thf(1500,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_setfam_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_setfam_1) ).
thf(9250,plain,
! [A: $i] : ( A @ ( A @ r1_setfam_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1500]) ).
thf(524,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/sandbox/benchmark/theBenchmark.p',t70_partfun1) ).
thf(4318,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)],[524]) ).
thf(788,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/sandbox/benchmark/theBenchmark.p',d7_group_3) ).
thf(5559,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)],[788]) ).
thf(326,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/sandbox/benchmark/theBenchmark.p',t81_xboole_1) ).
thf(3309,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)],[326]) ).
thf(1154,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/sandbox/benchmark/theBenchmark.p',dt_k4_group_3) ).
thf(7433,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)],[1154]) ).
thf(487,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/sandbox/benchmark/theBenchmark.p',t30_xboole_1) ).
thf(4146,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)],[487]) ).
thf(920,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relset_1) ).
thf(6169,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(706,axiom,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_subset_1) ).
thf(5159,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(667,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/sandbox/benchmark/theBenchmark.p',t50_xboole_1) ).
thf(4981,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)],[667]) ).
thf(949,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/sandbox/benchmark/theBenchmark.p',t49_subset_1) ).
thf(6294,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)],[949]) ).
thf(378,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/sandbox/benchmark/theBenchmark.p',dt_m1_realset1) ).
thf(3560,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)],[378]) ).
thf(650,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/sandbox/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(4895,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)],[650]) ).
thf(336,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/sandbox/benchmark/theBenchmark.p',dt_k12_finseq_1) ).
thf(3347,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)],[336]) ).
thf(907,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/sandbox/benchmark/theBenchmark.p',t26_group_1) ).
thf(6114,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)],[907]) ).
thf(1349,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/sandbox/benchmark/theBenchmark.p',t25_group_2) ).
thf(8484,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)],[1349]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( E @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( ( ( C @ ( E @ ( D @ ( B @ ( A @ k9_relset_1 ) ) ) @ k1_funct_1 ) )
= ( C @ ( E @ k1_funct_1 ) ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_funct_2) ).
thf(5990,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( E @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( ( ( C @ ( E @ ( D @ ( B @ ( A @ k9_relset_1 ) ) ) @ k1_funct_1 ) )
= ( C @ ( E @ k1_funct_1 ) ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(1508,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/sandbox/benchmark/theBenchmark.p',t164_group_3) ).
thf(9271,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)],[1508]) ).
thf(589,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/sandbox/benchmark/theBenchmark.p',t35_subset_1) ).
thf(4631,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)],[589]) ).
thf(1354,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/sandbox/benchmark/theBenchmark.p',d3_group_2) ).
thf(8510,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)],[1354]) ).
thf(1700,axiom,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_subset_1) ).
thf(10009,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1700]) ).
thf(1364,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/sandbox/benchmark/theBenchmark.p',dt_k10_group_4) ).
thf(8557,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)],[1364]) ).
thf(694,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/sandbox/benchmark/theBenchmark.p',t17_group_4) ).
thf(5105,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)],[694]) ).
thf(1024,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/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(6644,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)],[1024]) ).
thf(464,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/sandbox/benchmark/theBenchmark.p',t86_xboole_1) ).
thf(4024,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)],[464]) ).
thf(744,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/sandbox/benchmark/theBenchmark.p',t114_xboole_1) ).
thf(5413,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)],[744]) ).
thf(428,axiom,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(3850,plain,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(358,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/sandbox/benchmark/theBenchmark.p',t168_funct_2) ).
thf(3479,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)],[358]) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t170_relat_1) ).
thf(2417,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(1684,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/sandbox/benchmark/theBenchmark.p',t61_group_1) ).
thf(9959,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)],[1684]) ).
thf(1013,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/sandbox/benchmark/theBenchmark.p',t94_group_1) ).
thf(6590,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)],[1013]) ).
thf(1356,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r2_wellord2 ) )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_card_1) ).
thf(8516,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)],[1356]) ).
thf(754,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
<=> ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_realset1) ).
thf(5441,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m3_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(121,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k1_relat_1 @ v1_relat_1 )
& ( A @ k1_relat_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(2404,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)],[121]) ).
thf(1491,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/sandbox/benchmark/theBenchmark.p',t50_group_1) ).
thf(9215,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)],[1491]) ).
thf(255,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/sandbox/benchmark/theBenchmark.p',t52_relat_1) ).
thf(3030,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)],[255]) ).
thf(467,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 @ ( B @ ( A @ k6_xcmplx_0 ) @ r2_hidden ) )
<=> ~ ( B @ ( A @ r1_xreal_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finseq_3) ).
thf(4034,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ! [B: $i] :
( ( B @ v4_ordinal2 )
=> ( ( ~ ( B @ ( A @ r1_xreal_0 ) )
=> ( A @ k2_finseq_1 @ ( B @ ( A @ k6_xcmplx_0 ) @ r2_hidden ) ) )
& ( ( A @ k2_finseq_1 @ ( B @ ( A @ k6_xcmplx_0 ) @ r2_hidden ) )
=> ~ ( B @ ( A @ r1_xreal_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(1644,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/sandbox/benchmark/theBenchmark.p',t85_group_2) ).
thf(9795,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)],[1644]) ).
thf(1549,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/sandbox/benchmark/theBenchmark.p',reflexivity_r2_group_3) ).
thf(9414,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)],[1549]) ).
thf(396,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_xboole_1) ).
thf(3633,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)],[396]) ).
thf(972,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(6398,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(1661,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/sandbox/benchmark/theBenchmark.p',redefinition_k9_group_2) ).
thf(9883,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)],[1661]) ).
thf(889,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/sandbox/benchmark/theBenchmark.p',t30_group_2) ).
thf(6040,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)],[889]) ).
thf(1674,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/sandbox/benchmark/theBenchmark.p',t87_group_6) ).
thf(9927,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)],[1674]) ).
thf(1467,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/sandbox/benchmark/theBenchmark.p',t19_int_1) ).
thf(9083,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)],[1467]) ).
thf(1547,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/sandbox/benchmark/theBenchmark.p',commutativity_k9_group_2) ).
thf(9409,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)],[1547]) ).
thf(1586,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/sandbox/benchmark/theBenchmark.p',t86_group_3) ).
thf(9564,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)],[1586]) ).
thf(405,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/sandbox/benchmark/theBenchmark.p',free_g4_vectsp_1) ).
thf(3673,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)],[405]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).
thf(2063,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)],[53]) ).
thf(202,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/sandbox/benchmark/theBenchmark.p',t122_funct_1) ).
thf(2783,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)],[202]) ).
thf(1204,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_setfam_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_setfam_1) ).
thf(7684,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(1390,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/sandbox/benchmark/theBenchmark.p',t99_group_3) ).
thf(8675,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)],[1390]) ).
thf(144,axiom,
! [A: $i] :
( ( A @ l1_rlvect_1 )
=> ( A @ l2_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_rlvect_1) ).
thf(2502,plain,
! [A: $i] :
( ( A @ l1_rlvect_1 )
=> ( A @ l2_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(1651,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/sandbox/benchmark/theBenchmark.p',t163_group_3) ).
thf(9816,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)],[1651]) ).
thf(839,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/sandbox/benchmark/theBenchmark.p',t8_subset_1) ).
thf(5803,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)],[839]) ).
thf(703,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/sandbox/benchmark/theBenchmark.p',t60_domain_1) ).
thf(5151,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)],[703]) ).
thf(432,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/sandbox/benchmark/theBenchmark.p',t5_realset1) ).
thf(3869,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)],[432]) ).
thf(931,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/sandbox/benchmark/theBenchmark.p',dt_k6_group_1) ).
thf(6233,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)],[931]) ).
thf(1096,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/sandbox/benchmark/theBenchmark.p',t18_finset_1) ).
thf(7025,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)],[1096]) ).
thf(1289,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/sandbox/benchmark/theBenchmark.p',t36_group_3) ).
thf(8147,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)],[1289]) ).
thf(1145,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/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(7352,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)],[1145]) ).
thf(956,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/sandbox/benchmark/theBenchmark.p',d13_group_3) ).
thf(6316,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)],[956]) ).
thf(410,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(3701,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)],[410]) ).
thf(508,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/sandbox/benchmark/theBenchmark.p',t97_zfmisc_1) ).
thf(4242,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)],[508]) ).
thf(958,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/sandbox/benchmark/theBenchmark.p',t141_group_2) ).
thf(6329,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)],[958]) ).
thf(630,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/sandbox/benchmark/theBenchmark.p',d16_binop_1) ).
thf(4799,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)],[630]) ).
thf(220,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/sandbox/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
thf(2847,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)],[220]) ).
thf(381,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/sandbox/benchmark/theBenchmark.p',t155_funct_2) ).
thf(3570,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)],[381]) ).
thf(389,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/sandbox/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(3605,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)],[389]) ).
thf(1635,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/sandbox/benchmark/theBenchmark.p',reflexivity_r1_group_6) ).
thf(9763,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)],[1635]) ).
thf(540,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/sandbox/benchmark/theBenchmark.p',t54_xboole_1) ).
thf(4382,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)],[540]) ).
thf(1564,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/sandbox/benchmark/theBenchmark.p',t23_group_1) ).
thf(9474,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)],[1564]) ).
thf(793,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/sandbox/benchmark/theBenchmark.p',dt_k3_group_3) ).
thf(5581,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)],[793]) ).
thf(967,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/sandbox/benchmark/theBenchmark.p',t126_group_2) ).
thf(6373,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)],[967]) ).
thf(420,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/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(3772,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)],[420]) ).
thf(669,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/sandbox/benchmark/theBenchmark.p',t113_xboole_1) ).
thf(4987,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)],[669]) ).
thf(1158,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/sandbox/benchmark/theBenchmark.p',t117_group_2) ).
thf(7457,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)],[1158]) ).
thf(560,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/sandbox/benchmark/theBenchmark.p',t48_setfam_1) ).
thf(4506,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)],[560]) ).
thf(992,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( k4_numbers @ ( A @ k2_group_4 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_group_4) ).
thf(6473,plain,
! [A: $i] :
( ( A @ v1_int_1 )
=> ( k4_numbers @ ( A @ k2_group_4 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(315,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
<=> ( ( B @ ( A @ k4_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(3259,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)],[315]) ).
thf(555,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 )
= ( np__1 @ ( A @ k2_xcmplx_0 ) @ k1_tarski @ ( np__1 @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_finseq_1) ).
thf(4484,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 )
= ( np__1 @ ( A @ k2_xcmplx_0 ) @ k1_tarski @ ( np__1 @ ( A @ k2_xcmplx_0 ) @ k2_finseq_1 @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(1231,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/sandbox/benchmark/theBenchmark.p',t114_group_3) ).
thf(7829,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)],[1231]) ).
thf(454,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/sandbox/benchmark/theBenchmark.p',t37_group_4) ).
thf(3965,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)],[454]) ).
thf(310,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/sandbox/benchmark/theBenchmark.p',t51_partfun1) ).
thf(3245,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)],[310]) ).
thf(1403,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/sandbox/benchmark/theBenchmark.p',t71_group_2) ).
thf(8730,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)],[1403]) ).
thf(1545,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/sandbox/benchmark/theBenchmark.p',t25_group_3) ).
thf(9402,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)],[1545]) ).
thf(251,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/sandbox/benchmark/theBenchmark.p',t60_card_1) ).
thf(3020,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)],[251]) ).
thf(1220,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/sandbox/benchmark/theBenchmark.p',t43_partfun1) ).
thf(7755,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)],[1220]) ).
thf(1711,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/sandbox/benchmark/theBenchmark.p',t22_group_6) ).
thf(10045,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)],[1711]) ).
thf(1779,axiom,
? [A: $i] : ( A @ l1_group_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_group_1) ).
thf(10287,plain,
? [A: $i] : ( A @ l1_group_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1779]) ).
thf(610,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_xboole_1) ).
thf(4713,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)],[610]) ).
thf(1693,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/sandbox/benchmark/theBenchmark.p',t74_group_4) ).
thf(9992,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)],[1693]) ).
thf(1601,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/sandbox/benchmark/theBenchmark.p',t127_group_3) ).
thf(9633,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)],[1601]) ).
thf(1342,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/sandbox/benchmark/theBenchmark.p',t40_funct_4) ).
thf(8453,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)],[1342]) ).
thf(1106,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/sandbox/benchmark/theBenchmark.p',t185_group_2) ).
thf(7088,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)],[1106]) ).
thf(1736,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/sandbox/benchmark/theBenchmark.p',t179_group_2) ).
thf(10124,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)],[1736]) ).
thf(1742,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/sandbox/benchmark/theBenchmark.p',t167_group_2) ).
thf(10146,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)],[1742]) ).
thf(544,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/sandbox/benchmark/theBenchmark.p',t91_orders_1) ).
thf(4395,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)],[544]) ).
thf(740,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A
= ( A @ a_1_0_domain_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_domain_1) ).
thf(5354,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A
= ( A @ a_1_0_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(527,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/sandbox/benchmark/theBenchmark.p',t53_xboole_1) ).
thf(4330,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)],[527]) ).
thf(760,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finset_1) ).
thf(5468,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)],[760]) ).
thf(661,axiom,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 @ ( A @ r2_hidden ) )
| ( A = np__0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_finseq_1) ).
thf(4955,plain,
! [A: $i] :
( ( A @ v4_ordinal2 )
=> ( ( A @ k2_finseq_1 @ ( A @ r2_hidden ) )
| ( A = np__0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(1595,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/sandbox/benchmark/theBenchmark.p',t128_group_3) ).
thf(9605,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)],[1595]) ).
thf(1463,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/sandbox/benchmark/theBenchmark.p',t41_group_4) ).
thf(9066,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)],[1463]) ).
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 ) )
& ( A @ ( B @ v1_group_3 ) ) )
=> ( ( B @ ( A @ k4_group_6 ) )
= ( B @ ( A @ k14_group_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_group_6) ).
thf(9489,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)],[1566]) ).
thf(1052,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/sandbox/benchmark/theBenchmark.p',dt_u1_group_1) ).
thf(6778,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)],[1052]) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
thf(2484,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)],[138]) ).
thf(1430,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/sandbox/benchmark/theBenchmark.p',t9_group_3) ).
thf(8876,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)],[1430]) ).
thf(363,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/sandbox/benchmark/theBenchmark.p',rc2_group_6) ).
thf(3494,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)],[363]) ).
thf(1777,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/sandbox/benchmark/theBenchmark.p',t78_group_3) ).
thf(10276,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)],[1777]) ).
thf(1445,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/sandbox/benchmark/theBenchmark.p',t6_group_6) ).
thf(8978,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)],[1445]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',t27_funct_1) ).
thf(2138,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)],[70]) ).
thf(600,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/sandbox/benchmark/theBenchmark.p',t76_card_1) ).
thf(4674,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)],[600]) ).
thf(569,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/sandbox/benchmark/theBenchmark.p',t12_group_4) ).
thf(4533,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)],[569]) ).
thf(796,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_group_3) ).
thf(5591,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)],[796]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(2563,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)],[159]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',t29_finset_1) ).
thf(2177,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)],[78]) ).
thf(617,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(4734,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)],[617]) ).
thf(1172,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_subset_1) ).
thf(7548,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)],[1172]) ).
thf(179,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/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
thf(2640,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)],[179]) ).
thf(349,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/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
thf(3437,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)],[349]) ).
thf(1174,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/sandbox/benchmark/theBenchmark.p',fc6_group_6) ).
thf(7553,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)],[1174]) ).
thf(1063,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/sandbox/benchmark/theBenchmark.p',dt_k12_domain_1) ).
thf(6842,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)],[1063]) ).
thf(1579,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/sandbox/benchmark/theBenchmark.p',t150_group_2) ).
thf(9536,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)],[1579]) ).
thf(614,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/sandbox/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(4723,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)],[614]) ).
thf(1044,axiom,
k5_numbers != k4_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_numbers) ).
thf(6733,plain,
k5_numbers != k4_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(1228,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/sandbox/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(7812,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)],[1228]) ).
thf(1133,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/sandbox/benchmark/theBenchmark.p',dt_k5_group_6) ).
thf(7310,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)],[1133]) ).
thf(1793,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/sandbox/benchmark/theBenchmark.p',t51_group_2) ).
thf(10344,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)],[1793]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',t28_card_1) ).
thf(2074,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)],[57]) ).
thf(1642,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/sandbox/benchmark/theBenchmark.p',t121_group_3) ).
thf(9784,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)],[1642]) ).
thf(1294,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/sandbox/benchmark/theBenchmark.p',t31_partfun1) ).
thf(8179,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)],[1294]) ).
thf(1424,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/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(8829,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)],[1424]) ).
thf(1260,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/sandbox/benchmark/theBenchmark.p',t95_group_3) ).
thf(8006,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)],[1260]) ).
thf(1068,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/sandbox/benchmark/theBenchmark.p',t63_group_3) ).
thf(6857,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)],[1068]) ).
thf(1540,axiom,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( A @ l1_group_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_vectsp_1) ).
thf(9385,plain,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( A @ l1_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540]) ).
thf(522,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/sandbox/benchmark/theBenchmark.p',dt_k7_rlvect_1) ).
thf(4313,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)],[522]) ).
thf(1631,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/sandbox/benchmark/theBenchmark.p',t55_group_2) ).
thf(9748,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)],[1631]) ).
thf(1565,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/sandbox/benchmark/theBenchmark.p',t93_group_2) ).
thf(9479,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)],[1565]) ).
thf(1285,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/sandbox/benchmark/theBenchmark.p',d9_group_6) ).
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 ) ) )
=> ! [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)],[1285]) ).
thf(347,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(3432,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(1128,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/sandbox/benchmark/theBenchmark.p',t147_group_3) ).
thf(7267,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)],[1128]) ).
thf(1471,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(9098,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)],[1471]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',t152_relat_1) ).
thf(1917,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)],[25]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_funct_1) ).
thf(2453,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(398,axiom,
( ( k1_xboole_0 @ k4_card_1 )
= np__0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_card_1) ).
thf(3637,plain,
( ( k1_xboole_0 @ k4_card_1 )
= np__0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(975,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/sandbox/benchmark/theBenchmark.p',t77_funct_2) ).
thf(6404,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)],[975]) ).
thf(329,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/sandbox/benchmark/theBenchmark.p',t31_subset_1) ).
thf(3316,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)],[329]) ).
thf(498,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_xboole_1) ).
thf(4189,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(1468,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/sandbox/benchmark/theBenchmark.p',t59_setfam_1) ).
thf(9087,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)],[1468]) ).
thf(1697,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/sandbox/benchmark/theBenchmark.p',t153_group_2) ).
thf(10002,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)],[1697]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_relat_1) ).
thf(2087,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)],[59]) ).
thf(1240,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/sandbox/benchmark/theBenchmark.p',t18_group_1) ).
thf(7893,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)],[1240]) ).
thf(1153,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/sandbox/benchmark/theBenchmark.p',d4_group_1) ).
thf(7424,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)],[1153]) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
thf(3047,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)],[259]) ).
thf(492,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/sandbox/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(4174,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)],[492]) ).
thf(1330,axiom,
? [A: $i] : ( A @ v1_card_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_card_1) ).
thf(8405,plain,
? [A: $i] : ( A @ v1_card_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(1080,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/sandbox/benchmark/theBenchmark.p',t26_relset_1) ).
thf(6948,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)],[1080]) ).
thf(1443,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/sandbox/benchmark/theBenchmark.p',t3_mcart_1) ).
thf(8961,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)],[1443]) ).
thf(1041,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/sandbox/benchmark/theBenchmark.p',t72_group_6) ).
thf(6722,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)],[1041]) ).
thf(1254,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/sandbox/benchmark/theBenchmark.p',t35_group_3) ).
thf(7970,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)],[1254]) ).
thf(1073,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/sandbox/benchmark/theBenchmark.p',d6_eqrel_1) ).
thf(6879,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)],[1073]) ).
thf(13627,plain,
$false,
inference(e,[status(thm)],[8607,7854,4899,1840,10081,8646,9907,7396,9929,8536,5509,7304,10007,3873,9131,2630,9405,8930,7766,1879,6836,9208,3944,6979,2612,6167,2295,2306,9886,7569,5896,5260,8097,7445,6651,3434,3167,9833,6283,4183,8338,3698,7100,6285,3397,10134,8784,9685,2544,6448,9676,6566,4728,9222,4992,8077,9241,7601,8450,6463,2527,3012,5669,9191,5529,6194,6022,6587,6177,5141,5168,7517,8434,5820,1882,9163,2231,2622,9351,3858,4311,6106,4515,2495,7641,5242,9901,3959,2248,8118,9918,10262,7726,6441,2014,6323,10244,8447,3402,10294,7341,8988,5614,9364,4487,6480,9268,5037,4633,3049,6359,4026,2712,9494,4650,1988,3562,2146,3848,8320,3017,5425,9956,6971,3217,9526,3429,8335,8551,6939,8635,3004,4839,3332,4647,3367,8879,4220,8057,8747,10346,9428,8667,3338,2141,5316,9218,6634,4564,6241,3121,3313,8838,5708,6370,7716,2844,3577,9278,7748,3717,4762,10341,9672,2575,2548,4266,8816,7729,9708,2516,6483,4156,4941,10351,3370,5227,6466,5977,6909,2432,1914,2020,9735,4618,3088,9027,9096,10078,5921,9994,5825,5723,5938,5770,8472,8256,2886,4030,8487,3809,8330,2136,6291,4948,2531,4249,5352,5533,8583,5765,4422,3275,6538,5910,7349,2444,8654,10337,1832,2126,9123,4637,2654,3248,4238,8610,5585,2603,4524,3938,7277,10305,6552,3644,4070,3116,8225,6274,9432,9561,10356,9988,5759,1871,8806,1907,6066,7652,3485,1826,6676,2185,9909,5289,4984,4428,3043,6873,2745,2571,7665,5279,7011,8389,4358,10206,5052,6098,9039,6382,5231,9420,1922,6010,9800,5256,5868,7711,5866,9612,4353,6681,5521,5199,7209,6951,7060,9155,4179,4664,9941,10074,4492,3919,4551,7215,8615,8543,4141,8220,3951,2158,8126,1963,5020,5493,1875,2388,2533,7032,7112,9768,9266,1847,9580,10025,5974,4411,8029,5084,4600,9071,5856,3527,3621,9680,7258,2007,4696,5957,2237,5433,5264,9304,9298,3524,7792,5892,9283,2794,3199,9520,6670,9330,4857,7245,8416,3670,8934,6135,2880,9811,5946,6300,5541,5032,7532,9457,8526,4115,10378,5761,4686,2335,8759,6157,8479,2777,3152,6717,8196,8664,8411,9309,5834,5773,6451,9255,7954,4701,5137,4379,8992,4475,5572,5059,7473,5929,10404,10070,8438,4751,4230,4935,7931,3189,8586,6685,2861,9369,1896,8575,6740,7936,3505,3685,8686,7194,6863,8691,10388,4040,3756,10390,4536,2809,2242,2799,4038,2750,10233,7337,1943,2965,4519,9923,7460,8362,4628,4211,7354,7722,10029,9738,8742,2762,8421,7952,4853,4893,8046,4888,6731,5968,7410,5519,1868,7999,9323,2954,9703,8508,3097,7849,5157,3450,3503,7471,3303,9968,7550,2646,3852,7037,3635,2164,5438,6139,6064,2118,6250,4557,8397,5034,8613,2047,6388,10165,10374,5487,10258,5862,9252,7078,2790,9688,9881,7735,6200,9549,9753,6343,2541,8888,4836,3514,8513,2441,2673,8265,2601,2805,3711,7989,6247,3603,3867,9412,4375,8756,7881,5349,3022,4252,5815,3742,4344,8724,3752,3989,9849,7084,9981,10102,3154,3134,1824,10084,9745,6496,4821,3286,7301,8623,4044,5924,6646,8026,5690,2200,5201,6060,2344,6666,2228,5993,3931,3799,3948,7097,7977,5702,3618,8832,6629,10038,5983,2628,4192,2670,4608,7576,1920,6163,9658,4725,2565,8145,2663,6043,4757,3065,3349,8736,4385,10116,1951,10247,3877,2068,1819,4187,9301,3535,1836,5113,6096,9423,2181,10035,4740,6402,10235,3595,7686,5285,8073,6728,8530,9804,10154,2709,9444,3386,4109,3205,7346,6656,2498,6339,8314,2115,3254,6101,1851,8677,5238,6995,4512,5423,4974,8562,6691,2973,9889,2577,6459,9773,8604,9244,6235,4845,5428,3704,9576,5583,3963,10152,10318,8187,10298,2858,2537,5889,9063,3746,7204,5847,3650,3916,3941,9530,4320,4333,6175,9640,5496,9714,2419,5253,6625,7293,7898,4951,7435,3311,10107,2877,8704,8631,8835,2023,3326,3000,4582,8017,5915,3846,5705,6844,5651,8251,2561,6593,2830,9387,3094,4721,4425,7318,9426,5620,4315,2312,3010,2455,9609,9878,4406,8407,7841,5547,8053,3032,8499,8968,3194,2349,2551,2085,7404,10239,2666,2978,9392,10353,7523,7682,2317,7821,9513,4530,9260,9825,8891,2836,5234,8775,10180,9694,3242,9200,7668,6349,10222,2285,2504,5850,3611,8673,5149,2304,7014,3059,6331,7966,9498,5639,5134,6433,6475,7738,4244,9630,7495,4829,3222,3540,6239,9112,4717,7597,9461,8896,10122,7702,9990,2813,4347,8995,2052,6418,8090,4953,8307,3109,8142,4689,7333,6988,2756,8803,3083,3162,10252,9372,9068,5479,3476,2203,7052,2208,9008,5415,9750,7656,3508,10349,6171,8796,2634,1857,5747,7020,3834,9913,6963,4195,8247,9964,3587,6486,9176,8080,3173,9716,2057,8049,3306,6812,5964,6070,8004,3639,2408,5209,2089,2189,6400,6311,2617,5249,6869,7106,1996,4308,7646,8234,2677,2292,7582,4613,6561,7831,6084,10043,10289,7567,2121,2235,5679,2936,3707,5666,6314,2413,3130,6053,7046,9502,10202,3890,9203,8713,3079,7706,4256,8906,6792,7599,10327,10321,5608,6469,7636,3888,6454,5016,10274,7920,5525,7785,9650,5715,4489,8874,6422,7212,4786,7709,5456,8909,4494,3519,8139,4122,10242,9339,5503,9952,8015,10068,9798,7714,4341,4268,7968,3070,7639,8762,5474,1884,3811,5395,3240,5844,4159,8580,9996,7487,5121,3472,3081,5940,9706,3283,4677,5627,10329,8684,9719,4709,5050,7704,8332,5097,9663,8941,4328,6606,6019,9585,2827,7815,9627,3599,2959,5535,2193,9285,2753,3487,9354,9439,8064,7795,9587,2220,5567,6385,3051,5471,4796,5011,3077,8286,4112,6673,10183,8841,5908,5859,3695,8249,8566,5282,3663,4672,6991,10051,6302,7109,5086,8745,4764,10130,7094,7145,7536,3641,6123,4273,8524,5784,7579,7315,10176,9089,9258,9307,5578,2319,10056,5556,9224,9390,9835,3532,2510,8419,2361,7415,2679,6815,9047,9789,6196,4509,4388,5071,10370,6572,7933,7594,3996,6308,3251,9349,5506,2214,8799,2493,2637,10204,9903,2422,10066,4620,6461,8237,6112,4914,7328,2246,8693,8461,3468,5880,9118,9920,2839,5610,4958,7265,7360,5346,4073,5093,4667,6154,7632,6604,1969,5267,3160,2824,4833,5894,9263,4181,2874,7561,6969,9931,4635,5511,9206,4430,9129,6165,8826,1877,8958,5657,2632,4420,3027,8633,7699,8103,8661,4064,9691,2780,6800,1821,6974,6414,3192,1838,3614,3977,10136,8998,8032,7869,3483,3583,9074,7023,2461,10004,5459,4684,2842,5838,8413,9327,4990,9018,6255,9619,6609,6783,5817,7339,8990,4965,10226,6574,2439,5742,2962,8456,3627,2171,5197,2765,6394,7929,5641,9741,5482,9492,10076,6288,9841,7805,7960,2931,5575,9916,9197,3953,8175,2797,10264,2592,2244,9366,10063,3363,7200,5725,2535,4304,3512,3178,6614,6180,10031,5693,9398,5139,4890,6736,4481,9582,3490,8689,9001,5688,9227,7371,2124,4292,3278,2005,5661,6768,3522,2054,1948,10311,9170,4136,2614,2096,6977,4013,4901,7896,9727,4868,4580,9334,5025,10249,8160,10091,6659,3981,6088,9777,3146,4879,6056,10132,4177,8323,4566,5165,9546,7102,6564,2256,9507,4355,5763,6998,8194,4812,6719,4336,6132,6641,6875,9317,2942,5229,5514,4937,6597,10059,6921,2175,4961,8350,5446,6362,6577,5047,6120,8772,7058,3913,7801,6945,8312,10112,6051,2060,5399,4366,2588,9037,5499,8701,3462,5074,8128,2518,7462,2821,3209,9766,9005,4971,4377,10333,9948,2850,10228,2160,10027,6146,3273,6545,9050,5276,7662,5995,5543,4409,10307,10218,3448,4522,6280,10048,5767,5431,6762,4561,6244,5420,7655,5418,9281,3885,6037,10162,9599,3722,4020,10095,8231,8496,3202,4222,9518,2429,9567,9809,9358,7947,5030,5154,8528,6352,9683,3544,6436,9313,2599,8644,3564,10012,9911,4737,7847,9807,5450,9435,5949,3107,7331,5736,7207,2975,8185,9983,10231,9637,8043,3961,2675,8464,5319,8893,6457,6188,2411,2500,6825,4057,3124,2426,4133,6803,8564,9500,10128,4611,5998,5240,9247,7621,4748,5504,7585,1972,4106,8061,2579,5633,8317,5453,4143,3224,7612,9019,3024,9274,8087,3256,6511,7498,10178,9732,3007,4150,9453,5841,4819,8431,4392,3288,4217,9770,5917,9876,9417,2347,3625,3039,3593,8812,10214,8360,4639,6706,6928,3946,4548,7659,6850,5490,5981,4138,3457,2352,6846,4698,8944,2045,5653,3067,10364,4770,1966,7177,2870,9780,1817,6013,3171,6068,10033,6137,7589,8183,10199,10156,2490,2187,2110,3320,8153,2342,6743,7974,2226,2071,2658,3929,2775,5068,2792,1807,8469,5184,3911,7044,3383,6494,4881,5600,5055,3465,9755,10072,10220,9724,6230,6753,4806,6818,2290,4615,2251,6689,9102,7344,4681,5132,3336,7840,4126,3220,4042,4542,9934,3104,9459,2971,9591,5756,4010,8781,2130,8716,6694,8617,4527,10386,2934,7437,9999,5162,6854,2041,2066,6277,5739,9660,9542,9115,2447,8172,2956,8253,3181,2786,9972,4197,3324,10040,6305,4153,9962,6290,9510,2648,5781,4759,8638,3267,6045,5023,3149,3529,5699,8793,2183,6536,9559,6252,3993,9211,6569,5517,8267,5672,9289,9311,10109,7644,10167,6444,9643,1994,4306,5194,6499,9839,8710,6198,9321,9378,8115,1957,4670,4254,2233,2951,6237,1986,10280,3164,9361,5187,2258,9239,7649,5357,9346,4816,7542,9551,4917,2302,4794,9166,5728,8070,9034,7759,5971,3232,3291,10173,6786,2983,9711,9937,4596,8769,5554,7242,3987,4719,3100,3373,7489,3837,6906,2050,8309,7248,4885,9944,5014,3690,10054,9463,5926,3062,3015,10105,8400,6765,3196,9250,4318,5559,3309,7433,4146,6169,5159,4981,6294,3560,4895,3347,6114,8484,5990,9271,4631,8510,10009,8557,5105,6644,4024,5413,3850,3479,2417,9959,6590,8516,5441,2404,9215,3030,4034,9795,9414,3633,6398,9883,6040,9927,9083,9409,9564,3673,2063,2783,7684,8675,2502,9816,5803,5151,3869,6233,7025,8147,7352,6316,3701,4242,6329,4799,2847,3570,3605,9763,4382,9474,5581,6373,3772,4987,7457,4506,6473,3259,4484,7829,3965,3245,8730,9402,3020,7755,10045,10287,4713,9992,9633,8453,7088,10124,10146,4395,5354,4330,5468,4955,9605,9066,9489,6778,2484,8876,3494,10276,8978,2138,4674,4533,5591,2563,2177,4734,7548,2640,3437,7553,6842,9536,4723,6733,7812,7310,10344,2074,9784,8179,8829,8006,6857,9385,4313,9748,9479,8130,3432,7267,9098,1917,2453,3637,6404,3316,4189,9087,10002,2087,7893,7424,3047,4174,8405,6948,8961,6722,7970,6879]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP642+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/5.40 % Computer : n014.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.13/5.40 % CPULimit : 300
% 0.13/5.40 % WCLimit : 300
% 0.13/5.40 % DateTime : Fri Sep 25 15:19:39 UTC 2026
% 0.13/5.40 % CPUTime :
% 0.13/5.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.17/5.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.21/6.35 % [INFO] Parsing done (634ms).
% 3.21/6.36 % [INFO] Running in sequential loop mode.
% 4.06/6.56 % [INFO] eprover registered as external prover.
% 4.06/6.56 % [INFO] Scanning for conjecture ...
% 5.84/6.93 % [INFO] Found a conjecture (or negated_conjecture) and 5658 axioms. Running axiom selection ...
% 9.59/8.49 % [INFO] Axiom selection finished. Selected 1804 axioms (removed 3854 axioms).
% 13.08/9.64 % [INFO] Problem is first-order (TPTP FOF).
% 13.35/9.72 % [INFO] Type checking passed.
% 13.35/9.73 % [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 ...
% 74.94/26.37 % External prover 'e' found a proof!
% 74.94/26.37 % [INFO] Killing All external provers ...
% 74.94/26.37 % Time passed: 20867ms (effective reasoning time: 20007ms)
% 74.94/26.37 % 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)>
% 74.94/26.38 % Axioms used in derivation (1804): t23_group_3, t72_xboole_1, t107_group_3, t42_xboole_1, t76_group_4, t44_xboole_1, t60_group_2, d11_group_2, t3_group_4, t106_xboole_1, d13_group_3, t15_finset_1, t8_group_3, t62_partfun1, t56_card_1, t158_relat_1, t5_group_2, t75_finseq_1, rc3_group_1, t38_funct_4, t3_finseq_1, t133_group_3, t87_group_2, t101_group_2, t26_group_4, t55_group_2, t185_group_2, redefinition_m2_relset_1, idempotence_k1_finsub_1, fraenkel_a_1_0_domain_1, t51_partfun1, t18_finseq_3, t21_zfmisc_1, t13_zfmisc_1, t30_funct_2, t13_relset_1, t181_relat_1, t175_relat_1, t131_partfun1, t44_finseq_3, t39_group_3, t11_group_6, t48_group_2, d6_group_3, t54_rlvect_1, t19_group_3, s2_group_4, t177_relat_1, free_g1_group_1, d4_group_1, t110_group_2, t42_subset_1, dt_k3_group_3, d1_tarski, t114_group_3, t147_funct_1, t154_relat_1, t7_group_3, fraenkel_a_3_2_domain_1, t80_group_2, t12_group_3, t11_finseq_1, dt_k9_group_6, d1_group_1, t19_xboole_1, t177_orders_1, t72_group_1, t69_group_6, t169_group_2, t17_xboole_1, t17_finseq_3, t23_setfam_1, t4_funct_4, t130_partfun1, t21_int_1, d6_finseq_1, t58_group_4, t43_subset_1, t74_group_3, cc2_finset_1, t20_zfmisc_1, t4_group_4, dt_k6_group_1, t35_subset_1, t165_group_3, t135_zfmisc_1, t17_zfmisc_1, t121_group_3, fc11_finseq_1, t50_group_2, t148_funct_1, t23_card_1, t25_relset_1, d20_binop_1, t53_group_3, t66_funct_2, t143_funct_1, t67_relat_1, t18_finsub_1, dt_m1_group_6, t93_group_6, t66_partfun1, t25_card_1, t64_card_1, t49_setfam_1, t70_funct_2, t14_group_4, t182_group_2, t6_setfam_1, t35_funct_2, t14_finset_1, t154_group_2, t57_group_2, t53_subset_1, t140_zfmisc_1, rc4_finset_1, t79_funct_4, t20_funct_2, t73_xboole_1, dt_k11_group_6, t79_group_1, dt_k4_relset_1, d14_binop_1, dt_k9_domain_1, t24_group_6, t59_group_1, t105_zfmisc_1, t83_group_3, t62_group_1, commutativity_k1_finsub_1, t10_finseq_3, t109_xboole_1, idempotence_k3_xboole_0, t29_group_6, t82_group_2, t32_group_1, symmetry_r1_group_2, d10_binop_1, t10_group_2, t102_group_3, t62_relat_1, t7_subset_1, t1_boole, t70_group_4, t32_funct_2, d11_binop_1, t2_realset1, t67_group_4, t56_group_1, dt_k5_group_4, t66_xboole_1, t23_xboole_1, t16_group_1, t98_group_3, existence_m1_group_6, t27_funct_2, t14_funct_4, t50_relat_1, d10_group_1, t91_group_6, t133_group_2, t195_orders_1, d1_group_3, d3_group_1, redefinition_k5_subset_1, t9_setfam_1, t23_group_2, t3_xboole_1, t3_realset1, t137_funct_1, d3_subset_1, t40_group_2, t128_group_3, t34_xboole_1, rc7_finseq_1, t34_card_1, t68_card_1, t8_subset_1, t53_funct_2, t156_funct_1, t72_funct_4, t1_subset, t74_finseq_1, redefinition_k7_funct_2, t20_setfam_1, fc1_xboole_0, t104_group_3, t25_funct_1, t16_funct_2, t73_funct_4, t175_group_2, t113_zfmisc_1, t140_partfun1, dt_k7_domain_1, t109_group_2, t25_numbers, t27_group_3, t48_domain_1, t29_finseq_3, t44_group_4, t113_xboole_1, dt_k2_subset_1, fraenkel_a_1_0_group_4, d15_group_6, t56_partfun1, existence_l1_lattices, t84_group_4, t141_group_3, reflexivity_r1_group_2, t15_funct_1, dt_k11_domain_1, fc4_relat_1, t31_group_6, d6_group_6, t37_funct_4, t50_group_6, rc4_group_1, t4_ordinal1, t1_group_6, t59_partfun1, t158_funct_1, t44_relat_1, t147_relat_1, t10_partfun1, t71_card_1, redefinition_k2_group_6, t124_group_3, t18_xboole_1, t90_group_1, t158_partfun1, t78_finseq_1, d5_xboole_0, t167_group_2, t29_subset_1, t24_group_2, t63_group_3, t15_numbers, t92_group_6, t24_setfam_1, d7_group_4, t151_funct_1, fc1_funct_4, t52_zfmisc_1, t144_relat_1, t57_domain_1, t18_setfam_1, t134_group_3, t48_finseq_3, t9_group_3, fc4_subset_1, t61_group_2, t22_funct_1, t79_group_6, t28_group_1, t117_finseq_3, fc1_numbers, dt_k3_funct_2, t65_group_4, t80_card_1, t31_funct_4, t168_funct_2, t43_xboole_1, t54_partfun1, t81_zfmisc_1, dt_k5_lattices, t7_funct_2, t8_group_2, rc1_group_2, t10_relset_1, t135_partfun1, t143_group_3, t146_funct_2, t3_mcart_1, t155_funct_1, d2_group_6, t44_group_3, fc3_relat_1, t96_zfmisc_1, t5_finseq_1, t28_group_4, t14_binop_1, dt_k1_subset_1, t73_group_1, dt_k9_relset_1, t119_group_3, t85_group_2, d5_group_6, t131_group_3, t90_group_6, t6_xboole_1, t132_group_3, d8_funct_1, t19_relat_1, t70_xboole_1, t28_binop_1, t13_finseq_3, dt_k13_domain_1, t100_group_3, t38_group_2, t41_funct_2, t2_boole, t72_card_1, t17_setfam_1, t69_group_4, t27_group_4, t28_group_6, t156_group_2, dt_m1_realset1, t166_funct_2, t40_group_6, t47_relat_1, t18_group_2, fc9_relat_1, t6_group_3, t148_partfun1, redefinition_k4_card_1, t77_group_6, t68_xboole_1, d7_binop_1, commutativity_k9_group_2, t19_finset_1, t71_group_1, t15_group_6, t25_xboole_1, t61_card_1, t117_zfmisc_1, t29_funct_4, t65_partfun1, t186_partfun1, t44_funct_2, t103_group_2, t49_group_1, t19_latsubgr, t14_card_1, t148_group_3, t117_funct_1, t92_group_3, t36_group_1, dt_k4_subset_1, t71_xboole_1, t132_partfun1, t27_xboole_1, t122_zfmisc_1, reflexivity_r1_group_6, t4_mcart_1, t33_group_6, dt_k8_relset_1, t178_group_2, t43_zfmisc_1, rc1_group_6, t60_group_3, t52_group_3, d7_group_2, dt_u2_struct_0, t29_numbers, t18_relat_1, rc3_funct_1, t86_group_4, t89_group_6, t18_group_6, t69_zfmisc_1, t95_zfmisc_1, t42_group_6, t63_partfun1, t153_funct_1, t15_relset_1, t61_group_6, t45_ordinal1, dt_k15_group_2, t79_group_2, t99_zfmisc_1, rc2_partfun1, t42_group_3, t46_group_3, t81_xboole_1, t47_setfam_1, existence_m1_finseq_1, dt_k7_group_3, t21_group_3, t99_group_2, t49_funct_2, d9_group_4, fc1_funct_1, t60_group_6, dt_k2_vectsp_1, d11_group_6, t88_group_3, t7_orders_1, t104_finseq_3, t171_relat_1, t78_group_6, t176_group_2, t162_partfun1, fraenkel_a_3_3_domain_1, t45_zfmisc_1, t56_group_4, t10_latsubgr, dt_k6_partfun1, symmetry_r2_group_3, d15_group_1, t63_group_6, t41_group_6, t50_funct_2, d1_struct_0, t97_group_2, dt_k7_funct_2, t8_group_4, t66_group_3, t43_group_4, t70_partfun1, t20_group_2, t26_funct_2, dt_k9_group_2, t37_xboole_1, dt_k10_group_1, t17_funct_1, t42_group_4, t9_xboole_1, t67_group_1, t6_group_6, dt_k2_group_3, t6_latsubgr, t111_group_3, t41_zfmisc_1, dt_k4_group_3, t34_group_2, t77_group_2, dt_m2_relset_1, t18_finset_1, redefinition_r6_group_3, cc1_relat_1, dt_u1_group_1, redefinition_k2_funct_2, t127_group_3, t131_zfmisc_1, t94_group_1, idempotence_k5_subset_1, t120_group_2, d7_partfun1, d11_card_1, t30_card_1, t36_subset_1, redefinition_k6_setfam_1, t49_zfmisc_1, t7_finseq_1, t76_card_1, commutativity_k3_xboole_0, t154_funct_1, t29_partfun1, t140_group_3, t176_partfun1, t12_binop_1, t62_funct_2, t55_funct_1, dt_k2_realset1, commutativity_k7_domain_1, t79_card_1, t93_group_2, t138_funct_1, t114_group_2, t3_setfam_1, t81_card_1, t130_funct_2, t146_group_2, t39_finseq_3, t152_funct_2, t155_group_2, d8_group_4, fc11_finset_1, t17_binop_1, t33_group_4, t64_funct_2, t64_group_4, dt_k3_group_4, t115_zfmisc_1, t55_group_1, t62_funct_1, t65_funct_2, d10_group_2, t19_funct_1, redefinition_k9_group_2, t58_group_6, d12_group_2, dt_l1_rlvect_1, dt_k10_group_3, t39_group_4, t13_funct_4, existence_m1_group_2, t24_funct_2, t29_finset_1, t85_group_3, fc6_group_6, dt_k2_binop_1, t137_zfmisc_1, t82_group_6, t14_finseq_3, fraenkel_a_2_2_domain_1, d4_subset_1, t2_binop_1, t2_partfun1, t86_xboole_1, involutiveness_k3_subset_1, t13_relat_1, t57_group_3, rc1_funct_1, t89_xboole_1, t37_group_2, s2_card_1, t23_group_6, t25_funct_2, fc2_xboole_0, dt_l1_group_1, t102_group_2, t47_group_6, t150_group_3, fraenkel_a_2_0_group_4, d13_group_2, cc3_vectsp_1, t84_group_2, t12_group_4, t15_binop_1, dt_m2_realset1, d12_group_4, t32_subset_1, t13_group_6, t155_group_3, t107_group_2, redefinition_k3_finsub_1, t168_relat_1, d6_binop_1, t32_group_6, t126_group_2, t108_xboole_1, t34_partfun1, t147_group_2, t34_group_6, t71_group_3, t75_group_4, t30_finset_1, t68_group_6, t46_funct_2, t48_group_4, t175_partfun1, t21_funct_4, t15_relat_1, t50_group_1, t154_funct_2, t98_group_2, t48_funct_2, t173_relat_1, fraenkel_a_3_7_domain_1, t12_funct_4, t172_relat_1, t27_relat_1, t121_group_2, t156_funct_2, t65_group_1, t47_ordinal1, t78_funct_4, t43_group_3, d1_xboole_0, t53_group_2, dt_m1_eqrel_1, t49_funct_1, d3_group_6, t44_card_1, t60_group_1, dt_k4_card_1, t69_card_1, d6_group_2, t32_group_3, d1_group_2, t64_relat_1, t40_group_3, rc6_finseq_1, t25_subset_1, t138_zfmisc_1, t59_group_2, t23_funct_1, fraenkel_a_1_0_group_2, t130_zfmisc_1, t51_xboole_1, t64_group_6, t74_group_4, d5_group_4, t52_group_2, t28_funct_4, t165_funct_2, t31_finset_1, dt_l1_lattices, t29_funct_2, t14_relset_1, t39_funct_4, t85_group_6, t86_group_1, t47_funct_2, t33_card_1, t27_relset_1, t52_domain_1, t118_zfmisc_1, t55_partfun1, t2_mcart_1, t8_funct_2, dt_k6_finseq_1, fc10_finset_1, t79_finseq_1, t76_group_3, t113_group_3, t60_partfun1, t163_group_3, t89_group_3, existence_m1_realset1, t26_finset_1, t36_group_6, t137_group_2, t16_relset_1, t6_mcart_1, t91_group_3, t56_domain_1, t99_finseq_3, t46_zfmisc_1, t45_group_1, t181_group_2, t31_partfun1, fraenkel_a_3_0_group_3, t171_partfun1, t164_funct_2, fc2_funct_2, t72_group_4, t56_zfmisc_1, t6_boole, t12_funct_1, dt_k1_card_1, t81_group_4, t4_orders_1, t3_funct_2, t83_group_4, d2_group_2, rc2_subset_1, fc9_finset_1, t109_group_3, t35_group_3, existence_l2_lattices, t50_xboole_1, dt_k6_subset_1, t10_relat_1, commutativity_k10_group_1, t13_group_2, t59_setfam_1, t78_int_1, t55_group_6, t185_partfun1, t1_xboole_1, dt_k1_funct_4, t18_latsubgr, t2_group_6, t3_partfun1, t52_xboole_1, t160_funct_1, commutativity_k2_xboole_0, t59_group_6, t5_subset, t138_group_2, t26_relset_1, t108_group_2, d19_vectsp_1, dt_k3_finsub_1, t64_partfun1, t52_relat_1, symmetry_r4_group_3, t77_funct_2, t59_domain_1, d13_finseq_1, t20_funct_1, t154_group_3, existence_l2_struct_0, t25_group_3, t60_card_1, t55_relat_1, t7_setfam_1, t68_partfun1, t4_setfam_1, t32_partfun1, t46_card_1, t164_group_3, d2_group_1, rc8_vectsp_1, t26_binop_1, t28_subset_1, t75_xboole_1, d4_group_2, redefinition_r2_group_6, t15_group_2, t9_group_4, t13_latsubgr, dt_m1_group_2, t82_group_3, t68_group_2, d3_group_3, t39_partfun1, t149_funct_1, t57_group_6, t129_group_2, t4_xboole_0, t65_xboole_1, d2_int_1, t5_setfam_1, t33_group_1, t63_group_2, t14_latsubgr, t142_group_3, t45_funct_2, t79_zfmisc_1, t89_group_2, t84_group_3, t37_group_1, t94_zfmisc_1, fc4_numbers, d2_realset1, t41_group_2, fc17_finseq_1, t23_binop_1, d6_partfun1, t150_relat_1, existence_m1_relset_1, t68_group_1, t35_group_6, commutativity_k5_subset_1, t14_group_1, t55_setfam_1, d8_group_1, t1_zfmisc_1, t53_group_6, d7_group_3, t46_partfun1, redefinition_k8_rlvect_1, t92_group_1, t123_zfmisc_1, fc2_subset_1, t42_group_2, t46_group_4, t25_group_4, t5_funct_2, t176_relat_1, t21_group_2, dt_k8_funct_2, t54_group_4, t99_group_3, t46_finseq_3, t24_finset_1, d14_group_3, redefinition_k3_group_6, dt_k10_group_2, t33_xboole_1, t77_group_3, t122_funct_1, t52_setfam_1, t2_zfmisc_1, d6_realset1, t143_group_2, d18_group_2, t167_funct_2, t53_partfun1, t96_group_1, fc1_orders_1, dt_l2_lattices, t97_zfmisc_1, t108_group_3, t158_group_3, t11_funct_2, d2_group_4, t28_partfun1, dt_k3_realset1, t40_funct_2, t24_binop_1, fraenkel_a_3_0_group_6, dt_k3_latsubgr, t72_partfun1, dt_k2_group_4, t81_group_3, t121_funct_1, t86_card_1, t9_relat_1, t2_tarski, t16_funct_1, t14_relat_1, t142_funct_2, d4_group_6, t82_funct_2, t16_funct_4, rc1_group_3, t114_xboole_1, t67_zfmisc_1, d1_funct_4, dt_k1_partfun1, t52_subset_1, d13_funct_1, t17_group_2, t135_group_2, t4_subset, t76_xboole_1, fc3_xboole_0, t176_orders_1, t30_xboole_1, t69_group_1, cc1_funct_2, t39_subset_1, d4_tarski, t5_ordinal1, t4_boole, t36_funct_2, t53_xboole_1, redefinition_k9_group_6, t146_funct_1, t26_group_1, d2_funct_2, t75_group_1, t49_card_1, t84_xboole_1, t77_finseq_1, t125_funct_1, t21_xboole_1, t98_zfmisc_1, commutativity_k3_finsub_1, d12_group_3, t22_group_3, t44_group_6, t73_group_6, t178_relat_1, t38_subset_1, d1_int_1, t80_group_4, t62_group_4, dt_k1_finsub_1, t169_funct_2, t166_group_2, rc2_group_6, d2_xboole_0, d10_group_4, t5_group_3, t18_group_3, dt_k8_group_6, dt_k2_funct_1, t84_group_6, dt_k8_domain_1, t32_xboole_1, d13_group_6, t94_group_2, dt_k16_finseq_1, t14_funct_1, t141_zfmisc_1, t79_int_1, t174_relat_1, t20_group_3, t52_group_6, t17_funct_2, t104_group_2, t10_group_1, t179_relat_1, t59_funct_1, t132_funct_2, t6_group_1, t61_partfun1, redefinition_r4_group_3, d3_group_2, t184_group_2, d9_group_3, t80_xboole_1, t20_finsub_1, dt_k6_group_2, t58_funct_1, t25_finset_1, t3_rlvect_1, t34_group_1, t47_group_1, t148_funct_2, t79_xboole_1, t51_funct_2, t38_finseq_3, t67_xboole_1, d12_binop_1, existence_m2_realset1, d5_group_3, t67_group_6, existence_m3_realset1, cc3_int_1, t145_group_3, dt_k4_group_4, redefinition_k5_setfam_1, t35_card_1, t61_group_3, dt_k7_group_6, t6_group_4, t58_zfmisc_1, dt_k5_group_1, t161_group_3, t74_card_1, t21_finsub_1, existence_m1_ordinal1, d4_partfun1, t29_xboole_1, t5_orders_1, fc1_realset1, t29_group_4, fc5_finseq_1, t70_group_3, cc1_funct_1, t4_funct_2, t11_group_3, fc6_finseq_1, t65_group_2, t75_group_6, t139_zfmisc_1, t32_group_4, t30_finseq_3, t7_boole, t72_group_3, redefinition_r2_group_3, d14_group_6, t115_group_3, t15_group_4, d9_group_1, t136_partfun1, t16_finseq_3, t30_group_6, t11_binop_1, t54_group_2, dt_k7_group_2, t138_partfun1, dt_k6_group_3, t42_finseq_3, rc3_struct_0, t28_card_1, t70_group_6, t66_funct_4, d10_setfam_1, d2_subset_1, t53_group_1, t66_zfmisc_1, fc1_subset_1, t29_finseq_1, t13_finset_1, dt_k1_group_4, t117_group_3, t33_funct_4, dt_k10_group_4, fraenkel_a_2_2_group_3, t22_relat_1, t48_xboole_1, dt_k6_domain_1, t157_funct_1, s1_funct_2, t3_ordinal1, t25_group_2, dt_k6_group_6, t34_group_3, t15_finseq_3, cc1_group_1, t10_group_4, t149_funct_2, t129_group_3, t48_funct_1, t21_funct_2, t11_latsubgr, t61_group_4, t164_group_2, t12_finseq_3, t15_group_1, d1_rlvect_1, fc1_group_6, t71_group_2, t16_subset_1, dt_k2_partfun1, t62_group_3, t7_group_1, d12_group_1, t173_group_2, t69_partfun1, t122_group_2, t7_ordinal1, t153_relat_1, rc2_funct_1, t49_partfun1, t125_group_2, t9_funct_2, t160_relat_1, fc10_relat_1, t31_funct_2, rc1_subset_1, t158_funct_2, t116_group_3, t32_card_1, d10_group_6, t152_funct_1, dt_u1_vectsp_1, t54_setfam_1, t47_funct_1, t42_group_1, t183_group_2, t31_xboole_1, t4_subset_1, t88_xboole_1, t19_funct_2, t18_funct_4, t51_funct_1, t30_funct_4, t103_finseq_3, t122_group_3, t85_xboole_1, t10_group_6, t22_finset_1, t38_group_4, t5_group_4, t88_group_2, t85_group_4, d2_setfam_1, dt_k9_group_4, t73_group_3, rc1_funct_2, t91_orders_1, t24_xboole_1, d7_realset1, fraenkel_a_2_0_group_3, t64_zfmisc_1, t51_setfam_1, d3_group_4, t178_orders_1, dt_k11_group_3, t151_group_2, t65_funct_1, t28_group_3, t2_latsubgr, t118_group_2, t113_funct_2, t71_partfun1, dt_k14_finseq_1, dt_k13_group_6, t69_xboole_1, t92_group_2, t116_finseq_3, t54_group_6, t30_group_3, t159_funct_2, t116_zfmisc_1, d7_xboole_0, d4_group_3, t56_group_6, fc5_relat_1, t151_relat_1, t83_xboole_1, t35_group_2, d11_group_3, t78_group_3, t45_relat_1, t14_funct_2, t155_funct_2, dt_k3_group_1, t27_binop_1, dt_k8_group_4, t20_xboole_1, t4_group_6, dt_k7_rlvect_1, t16_zfmisc_1, t101_zfmisc_1, t5_latsubgr, t30_group_2, t27_group_2, t52_finseq_3, t56_funct_1, t43_group_2, fc1_group_3, t124_zfmisc_1, fraenkel_a_3_1_domain_1, t82_finseq_1, t60_funct_2, t82_xboole_1, t35_funct_4, dt_k8_group_2, t21_card_1, t49_group_6, t20_group_4, t54_xboole_1, t10_finseq_1, t46_setfam_1, t19_finseq_3, t23_funct_4, s1_domain_1, t26_group_6, existence_m1_subset_1, t91_group_2, dt_k1_group_2, cc2_funct_1, t120_zfmisc_1, dt_k16_group_2, t169_partfun1, t51_card_1, t84_group_1, t18_funct_1, t16_group_4, t13_group_3, t55_xboole_1, t82_group_4, t5_realset1, t17_finset_1, dt_k8_setfam_1, t4_relset_1, d10_group_3, t31_subset_1, t3_subset, cc1_relset_1, cc1_eqrel_1, t25_binop_1, d2_binop_1, t75_group_2, t160_group_3, t124_funct_1, t138_group_3, t2_group_3, t58_group_2, t60_group_4, t51_group_2, t55_subset_1, t79_funct_2, t46_funct_1, idempotence_k1_funct_4, dt_k6_setfam_1, t105_group_3, t41_group_3, dt_u1_lattices, t136_funct_2, fraenkel_a_2_1_domain_1, t53_group_4, t82_card_1, t17_group_4, t27_card_1, t19_group_1, t35_group_1, t41_funct_4, t95_group_3, t3_relat_1, dt_k8_rlvect_1, t35_xboole_1, t148_group_2, redefinition_k4_subset_1, t44_zfmisc_1, fc5_group_6, dt_k13_group_2, t155_relat_1, t48_setfam_1, t17_relset_1, t9_group_2, t74_group_6, d9_binop_1, t93_group_4, existence_m2_subset_1, t49_group_2, t130_group_3, t123_group_3, s1_int_1, dt_k12_group_2, t125_zfmisc_1, t30_subset_1, d17_binop_1, dt_k2_funct_2, d1_group_6, t7_finseq_3, t14_xboole_1, t44_setfam_1, t11_relset_1, dt_k4_group_1, t74_group_1, t11_funct_4, t47_xboole_1, fc3_group_6, fc4_group_6, t78_group_2, t19_numbers, t145_funct_1, t106_group_3, fc1_finset_1, t66_group_1, t15_subset_1, t54_group_3, t66_card_1, t36_group_3, t37_funct_2, t27_group_6, d5_subset_1, t14_group_2, t92_zfmisc_1, d8_group_2, t146_relat_1, t99_partfun1, t9_realset1, t58_partfun1, d8_setfam_1, t100_zfmisc_1, t79_group_4, t3_group_6, t26_group_2, rc2_relat_1, dt_k5_subset_1, d4_binop_1, existence_l1_vectsp_1, t139_group_2, d15_group_3, t116_funct_2, t121_funct_2, t49_finseq_3, t114_zfmisc_1, t31_zfmisc_1, d1_zfmisc_1, t16_xboole_1, t26_xboole_1, t63_xboole_1, t52_group_1, t15_xboole_1, t4_latsubgr, t43_funct_2, t81_finseq_1, commutativity_k4_subset_1, dt_k5_group_2, t57_setfam_1, t72_finseq_1, t73_card_1, existence_m2_relset_1, t7_group_6, d11_group_4, t51_group_6, dt_k12_finseq_1, t78_group_4, t92_group_4, t90_group_3, t40_group_4, t168_partfun1, t157_relat_1, t179_group_2, fraenkel_a_1_0_group_6, t80_group_3, t84_zfmisc_1, symmetry_r2_group_6, t29_card_1, t6_funct_2, d2_group_3, t142_group_2, fraenkel_a_2_3_group_3, fraenkel_a_3_6_domain_1, redefinition_m1_group_6, rc2_int_1, t142_funct_1, t17_numbers, dt_k8_group_1, t26_subset_1, redefinition_k2_binop_1, t21_group_1, t87_group_6, t73_partfun1, t7_latsubgr, t1_group_3, d5_group_1, t51_subset_1, t1_latsubgr, t21_subset_1, t111_xboole_1, t8_group_6, cc5_vectsp_1, t45_finseq_3, d16_group_2, involutiveness_k7_setfam_1, t22_xboole_1, t8_setfam_1, d14_group_2, t14_group_6, t41_subset_1, redefinition_k5_funct_4, symmetry_r6_group_3, t145_group_2, t6_finseq_1, t18_binop_1, t12_group_2, dt_k5_group_6, d8_realset1, rc1_relat_1, t54_funct_1, t63_group_1, t8_xboole_1, t70_group_2, t8_realset1, t78_xboole_1, t28_xboole_1, d1_relset_1, dt_k9_group_3, d3_tarski, t74_partfun1, t69_group_2, t3_latsubgr, t37_group_4, t46_subset_1, fc1_struct_0, t29_group_3, dt_l1_vectsp_1, cc6_funct_2, t59_group_3, t71_group_6, t51_group_3, t39_zfmisc_1, d1_realset1, t5_xboole_0, reflexivity_r4_group_3, t16_int_1, t64_group_2, t131_funct_2, t119_zfmisc_1, t9_finseq_3, d6_card_1, t13_xboole_1, t60_relat_1, t44_group_1, t45_group_3, t22_group_2, t11_group_4, t40_subset_1, t83_zfmisc_1, t170_relat_1, d6_group_1, t111_group_2, t149_group_3, t54_zfmisc_1, t174_group_2, t147_group_3, fraenkel_a_3_4_domain_1, t171_group_2, t33_group_2, t19_group_4, dt_k5_relat_1, d9_group_6, t17_subset_1, reflexivity_r1_tarski, t9_funct_1, t6_orders_1, t6_zfmisc_1, t48_relat_1, d2_orders_1, t143_funct_2, t5_mcart_1, t27_finset_1, t118_group_3, dt_k9_group_1, fc6_relat_1, dt_k2_card_1, t34_funct_2, t144_group_2, dt_k11_group_2, t51_group_1, t18_funct_2, redefinition_k7_rlvect_1, t144_funct_1, t68_group_4, t121_zfmisc_1, t10_subset_1, dt_l2_struct_0, t56_setfam_1, t96_group_3, t3_group_2, redefinition_k1_partfun1, t25_group_1, dt_k1_latsubgr, t19_group_2, t1_realset1, t48_group_1, t38_group_3, t2_xboole_1, t52_group_4, t43_group_6, t4_xboole_1, t57_partfun1, t141_partfun1, d12_funct_1, t9_finseq_1, t9_relset_1, redefinition_k2_realset1, t17_funct_4, t15_group_3, t10_group_3, t1_partfun1, t111_finseq_3, t41_xboole_1, t150_funct_1, t168_group_2, t58_group_3, t59_group_4, d15_binop_1, d1_funct_2, t116_group_2, t3_lattice4, t55_group_3, free_g3_lattices, t2_setfam_1, d4_xboole_0, t39_group_2, t93_group_3, t101_group_3, cc2_group_2, t13_group_4, t151_funct_2, t90_xboole_1, t51_relat_1, t19_int_1, fraenkel_a_3_0_group_2, t46_relat_1, fc1_setfam_1, t141_group_2, t66_funct_1, t18_zfmisc_1, dt_k17_group_2, t8_card_1, t3_group_3, dt_k5_setfam_1, rc3_finset_1, t81_group_6, fraenkel_a_1_0_finseq_1, t22_group_6, d6_eqrel_1, t83_group_2, t76_finseq_1, t45_partfun1, d9_group_2, existence_m1_eqrel_1, fc18_finseq_1, t36_xboole_1, t51_zfmisc_1, t62_group_2, t12_group_6, t27_numbers, dt_k5_group_3, t128_group_2, fraenkel_a_2_0_group_2, t22_int_1, t47_subset_1, dt_k12_domain_1, t54_group_1, dt_k7_group_1, t81_group_2, t152_group_2, t12_group_1, t64_xboole_1, dt_k7_setfam_1, t21_setfam_1, t21_funct_1, dt_k1_group_1, t26_card_1, fc1_relat_1, t27_group_1, t33_relset_1, t80_zfmisc_1, t68_zfmisc_1, t98_group_4, t16_group_2, d5_binop_1, t20_group_1, dt_m2_subset_1, dt_k5_numbers, t105_group_2, redefinition_k1_finsub_1, t77_group_4, t12_funct_2, d16_binop_1, t54_subset_1, rc1_finset_1, dt_k2_latsubgr, t127_zfmisc_1, t123_funct_1, t40_funct_4, t11_setfam_1, t44_subset_1, d1_latsubgr, t49_xboole_1, t117_group_2, t43_group_1, cc1_finset_1, d15_group_2, d8_binop_1, fc12_finset_1, t99_group_4, t136_zfmisc_1, dt_k2_group_6, t65_group_6, t77_xboole_1, t10_setfam_1, t8_boole, t169_relat_1, rc1_xboole_0, t9_group_6, t1_mcart_1, t11_xboole_1, t23_finset_1, t24_partfun1, redefinition_k8_funct_2, t35_relset_1, t48_group_6, d1_orders_1, t130_group_2, t153_group_2, t121_finseq_3, reflexivity_r1_setfam_1, t67_group_3, t24_zfmisc_1, rc5_struct_0, t2_subset, d11_group_1, fc7_relat_1, t156_relat_1, t63_group_4, t162_group_3, d13_group_4, t60_domain_1, t30_group_4, t126_zfmisc_1, dt_k3_group_2, dt_m1_orders_1, t165_group_2, t182_relat_1, d5_card_1, redefinition_k3_funct_2, t59_funct_2, t12_xboole_1, t41_group_4, reflexivity_r1_partfun1, cc4_vectsp_1, t38_funct_2, t33_partfun1, t85_funct_2, t58_card_1, t64_group_1, t28_group_2, d7_group_6, t16_finset_1, t180_relat_1, t60_funct_1, reflexivity_r6_group_3, dt_k8_group_3, fc2_relat_1, t8_finseq_1, t23_group_1, redefinition_m2_finseq_1, t37_zfmisc_1, t46_group_1, t65_relat_1, t140_group_2, t21_relat_1, t152_relat_1, dt_k6_lattices, symmetry_r1_xboole_0, t7_group_2, d1_setfam_1, t134_zfmisc_1, t48_card_1, d12_group_6, t25_partfun1, t49_relat_1, t180_group_2, fc8_relat_1, t13_finsub_1, redefinition_r1_group_2, t161_funct_1, t27_funct_1, t10_realset1, t175_orders_1, fc1_group_1, t137_group_3, t25_group_6, dt_k3_binop_1, t80_group_6, t56_group_2, t16_group_6, t151_group_3, t65_group_3, dt_k2_group_1, idempotence_k3_finsub_1, t156_group_3, t146_group_3, t50_subset_1, dt_k2_group_2, fc2_realset1, t74_xboole_1, d18_binop_1, t36_group_2, t50_group_3, redefinition_k10_group_1, t58_domain_1, t115_funct_2, t11_finseq_3, idempotence_k2_xboole_0, t48_subset_1, t119_group_2, dt_k6_group_4, t44_group_2, t28_relat_1, t71_group_4, t33_group_3, t45_card_1, t44_partfun1, t34_relset_1, t23_int_1, d6_group_4, reflexivity_r2_group_6, t31_group_4, t61_group_1, t9_tarski, t24_group_1, t145_relat_1, t6_group_2, t77_group_1, t46_xboole_1, d10_xboole_0, t100_group_2, t20_int_1, cc1_int_1, existence_l1_group_1, t149_relat_1, t43_partfun1, t7_xboole_1, t29_group_2, redefinition_k18_group_2, rc1_group_1, t57_group_4, rc9_vectsp_1, t159_funct_1, t57_funct_1, t67_partfun1, redefinition_k6_subset_1, t134_group_2, t12_relset_1, dt_u2_lattices, t86_group_3, t25_relat_1, existence_l1_struct_0, t5_xboole_1, t90_group_2, t157_group_3, t49_subset_1, rc1_card_1, dt_k2_finseq_1, t7_tarski, rc2_group_1, t115_group_2, t33_funct_1, t145_funct_2, t78_card_1, rc1_partfun1, dt_k8_finseq_1, t85_group_1, t18_int_1, t66_group_6, t3_xboole_0, t27_partfun1, symmetry_r1_partfun1, d8_group_3, d13_vectsp_1, t47_card_1, d7_group_1, t3_boole, t170_group_2, t12_latsubgr, d5_funct_1, t6_ordinal1, t24_group_3, t58_setfam_1, t76_group_2, t59_card_1, dt_k12_group_6, redefinition_k4_relset_1, t46_group_6, t10_finsub_1, cc5_funct_2, dt_k1_group_6, redefinition_m2_subset_1, t22_funct_2, t94_group_4, t17_group_6, dt_k3_group_6, t13_binop_1, fraenkel_a_2_1_group_3, t149_group_2, fc2_group_6, t95_group_1, t40_zfmisc_1, existence_m1_orders_1, t26_partfun1, t40_xboole_1, dt_m3_realset1, t4_group_3, fc14_finset_1, t26_funct_4, t36_relset_1, rc4_struct_0, dt_k10_domain_1, t150_group_2, t16_binop_1, s2_funct_2, fc13_finset_1, t15_funct_4, t139_partfun1, d16_group_1, t47_group_3, t136_group_2, t139_group_3, d13_binop_1, t132_group_2, idempotence_k4_subset_1, t72_group_6, redefinition_k8_group_6, t143_partfun1, t80_finseq_1, d14_group_1, t12_finseq_1, t87_xboole_1, t22_funct_4, t177_group_2, rc2_xboole_0, t70_group_1, t67_group_2, t174_partfun1, t186_group_2, t55_funct_2, d4_group_4, fraenkel_a_3_5_domain_1, t45_xboole_1, t38_partfun1, dt_k4_group_2, d5_group_2, reflexivity_r2_group_3, t67_funct_2, t97_group_3, t172_group_2, existence_m2_finseq_1, t45_group_6, existence_l1_rlvect_1, d13_group_1, t13_card_1, cc1_group_2, d9_vectsp_1, t22_finseq_3, t26_relat_1, t127_group_2, t61_funct_2, t36_funct_4, dt_k7_group_4, t106_group_2, fc3_lattices, t10_xboole_1, d3_binop_1, t66_group_2, t28_funct_2, t26_group_3, dt_k3_subset_1, fc1_funct_2, fraenkel_a_1_1_group_4, cc1_binop_1, t6_relat_1, t22_group_1, t172_partfun1, t33_subset_1, t159_relat_1, d17_group_2, t86_group_6, free_g4_vectsp_1, t32_funct_4, t30_partfun1, t65_zfmisc_1, dt_k14_group_2, t63_subset_1, t112_partfun1, d3_xboole_0, t73_group_4, t14_group_3, t144_group_3, t38_xboole_1, t19_funct_4, dt_k10_group_6, t62_group_6, t39_xboole_1, t31_group_1, t17_group_1, t56_group_3, t83_group_6, t18_group_1, t5_group_1, t20_funct_4, antisymmetry_r2_hidden, d19_binop_1, t53_setfam_1, t79_group_3, t24_finseq_1, t55_group_4, d8_group_6, t53_relat_1, t167_relat_1, t82_group_1, t21_group_4, dt_g1_group_1, abstractness_v1_group_1, t22_subset_1, redefinition_k6_domain_1
% 74.94/26.39 % No. of inferences in proof: 3612
% 74.94/26.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 20867 ms resp. 20007 ms w/o parsing
% 81.64/27.85 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 81.64/27.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------