%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT379+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n011.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 07:47:36 AM UTC 2026
% Result : Theorem 24.15s 6.19s
% Output : Refutation 21.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 75
% Syntax : Number of formulae : 152 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 621 ( 12 equ; 0 cnn)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 1712 ( 76 ~; 2 |; 289 &;1167 @)
% ( 5 <=>; 173 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 41 usr; 2 con; 0-4 aty)
% Number of variables : 285 ( 0 ^; 249 !; 36 ?; 285 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(l1_orders_2_decl,type,
l1_orders_2: $i > $o ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(v4_waybel34_decl,type,
v4_waybel34: $i > $i > $i > $o ).
thf(v20_waybel_0_decl,type,
v20_waybel_0: $i > $i > $i > $o ).
thf(v5_waybel34_decl,type,
v5_waybel34: $i > $i > $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(k2_tarski_decl,type,
k2_tarski: $i > $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(v1_setfam_1_decl,type,
v1_setfam_1: $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(v5_membered_decl,type,
v5_membered: $i > $o ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(v1_xcmplx_0_decl,type,
v1_xcmplx_0: $i > $o ).
thf(v4_ordinal2_decl,type,
v4_ordinal2: $i > $o ).
thf(v1_xreal_0_decl,type,
v1_xreal_0: $i > $o ).
thf(v1_int_1_decl,type,
v1_int_1: $i > $o ).
thf(v1_rat_1_decl,type,
v1_rat_1: $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(v3_membered_decl,type,
v3_membered: $i > $o ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(v2_membered_decl,type,
v2_membered: $i > $o ).
thf(v1_membered_decl,type,
v1_membered: $i > $o ).
thf(v4_membered_decl,type,
v4_membered: $i > $o ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(k1_pre_topc_decl,type,
k1_pre_topc: $i > $i ).
thf(k2_struct_0_decl,type,
k2_struct_0: $i > $i > $i > $i ).
thf(v12_waybel_0_decl,type,
v12_waybel_0: $i > $i > $o ).
thf(v13_waybel_0_decl,type,
v13_waybel_0: $i > $i > $o ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(r4_waybel_0_decl,type,
r4_waybel_0: $i > $i > $i > $i > $o ).
thf(v5_orders_2_decl,type,
v5_orders_2: $i > $i > $o ).
thf(v1_waybel_0_decl,type,
v1_waybel_0: $i > $i > $o ).
thf(v2_waybel_0_decl,type,
v2_waybel_0: $i > $i > $o ).
thf(19,axiom,
! [A: $i] :
( ( A @ v4_membered )
=> ( A @ v3_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_membered) ).
thf(142,plain,
! [A: $i] :
( ( A @ v4_membered )
=> ( A @ v3_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_int_1 )
& ( B @ v1_xreal_0 )
& ( B @ v4_ordinal2 )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_membered) ).
thf(102,plain,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_int_1 )
& ( B @ v1_xreal_0 )
& ( B @ v4_ordinal2 )
& ( B @ v1_xcmplx_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(24,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(165,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(63,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_orders_2 )
& ~ ( 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 @ v5_waybel34 ) ) )
<=> ( A @ k1_pre_topc @ ( C @ ( B @ ( A @ r4_waybel_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_waybel34) ).
thf(317,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_orders_2 )
& ~ ( 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 ) )
=> ( ( ( A @ k1_pre_topc @ ( C @ ( B @ ( A @ r4_waybel_0 ) ) ) )
=> ( B @ ( A @ ( C @ v5_waybel34 ) ) ) )
& ( ( B @ ( A @ ( C @ v5_waybel34 ) ) )
=> ( A @ k1_pre_topc @ ( C @ ( B @ ( A @ r4_waybel_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc17_membered) ).
thf(123,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_tarski ) @ v1_setfam_1 )
& ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_setfam_1) ).
thf(95,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_tarski ) @ v1_setfam_1 )
& ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(76,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(386,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_int_1 )
& ( A @ v1_int_1 ) )
=> ( ( B @ ( A @ k2_tarski ) @ v4_membered )
& ( B @ ( A @ k2_tarski ) @ v3_membered )
& ( B @ ( A @ k2_tarski ) @ v2_membered )
& ( B @ ( A @ k2_tarski ) @ v1_membered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc15_membered) ).
thf(151,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_int_1 )
& ( A @ v1_int_1 ) )
=> ( ( B @ ( A @ k2_tarski ) @ v4_membered )
& ( B @ ( A @ k2_tarski ) @ v3_membered )
& ( B @ ( A @ k2_tarski ) @ v2_membered )
& ( B @ ( A @ k2_tarski ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(365,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)],[70]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(276,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_membered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).
thf(269,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_int_1 )
& ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_membered) ).
thf(202,plain,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_int_1 )
& ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(68,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(357,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)],[68]) ).
thf(22,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(157,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(189,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)],[30]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ ( A @ k1_pre_topc @ v13_waybel_0 ) )
& ( A @ ( A @ k1_pre_topc @ v12_waybel_0 ) )
& ( A @ ( A @ k1_pre_topc @ v2_waybel_0 ) )
& ( A @ ( A @ k1_pre_topc @ v1_waybel_0 ) )
& ( A @ k1_pre_topc @ v5_membered )
& ( A @ k1_pre_topc @ v4_membered )
& ( A @ k1_pre_topc @ v3_membered )
& ( A @ k1_pre_topc @ v2_membered )
& ( A @ k1_pre_topc @ v1_membered )
& ( A @ ( A @ k1_pre_topc @ v5_orders_2 ) )
& ( A @ k1_pre_topc @ v1_finset_1 )
& ( A @ k1_pre_topc @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_waybel11) ).
thf(325,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ ( A @ k1_pre_topc @ v13_waybel_0 ) )
& ( A @ ( A @ k1_pre_topc @ v12_waybel_0 ) )
& ( A @ ( A @ k1_pre_topc @ v2_waybel_0 ) )
& ( A @ ( A @ k1_pre_topc @ v1_waybel_0 ) )
& ( A @ k1_pre_topc @ v5_membered )
& ( A @ k1_pre_topc @ v4_membered )
& ( A @ k1_pre_topc @ v3_membered )
& ( A @ k1_pre_topc @ v2_membered )
& ( A @ k1_pre_topc @ v1_membered )
& ( A @ ( A @ k1_pre_topc @ v5_orders_2 ) )
& ( A @ k1_pre_topc @ v1_finset_1 )
& ( A @ k1_pre_topc @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(56,axiom,
? [A: $i] : ( A @ l1_orders_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(289,plain,
? [A: $i] : ( A @ l1_orders_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ( B @ v4_ordinal2 )
& ( A @ v4_ordinal2 ) )
=> ( ( B @ ( A @ k2_tarski ) @ v5_membered )
& ( B @ ( A @ k2_tarski ) @ v4_membered )
& ( B @ ( A @ k2_tarski ) @ v3_membered )
& ( B @ ( A @ k2_tarski ) @ v2_membered )
& ( B @ ( A @ k2_tarski ) @ v1_membered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc16_membered) ).
thf(216,plain,
! [A: $i,B: $i] :
( ( ( B @ v4_ordinal2 )
& ( A @ v4_ordinal2 ) )
=> ( ( B @ ( A @ k2_tarski ) @ v5_membered )
& ( B @ ( A @ k2_tarski ) @ v4_membered )
& ( B @ ( A @ k2_tarski ) @ v3_membered )
& ( B @ ( A @ k2_tarski ) @ v2_membered )
& ( B @ ( A @ k2_tarski ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(27,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(179,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(64,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(321,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k2_struct_0 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_struct_0) ).
thf(376,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k2_struct_0 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(121,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)],[12]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_struct_0 ) ) )
= ( C @ ( B @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_struct_0) ).
thf(280,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_struct_0 ) ) )
= ( C @ ( B @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_membered) ).
thf(133,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(92,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(55,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(285,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)],[55]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(109,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)],[9]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ ( A @ k1_pre_topc @ v2_waybel_0 ) )
& ( A @ ( A @ k1_pre_topc @ v1_waybel_0 ) )
& ( A @ k1_pre_topc @ v5_membered )
& ( A @ k1_pre_topc @ v4_membered )
& ( A @ k1_pre_topc @ v3_membered )
& ( A @ k1_pre_topc @ v2_membered )
& ( A @ k1_pre_topc @ v1_membered )
& ( A @ k1_pre_topc @ v1_finset_1 )
& ( A @ ( A @ k1_pre_topc @ v5_orders_2 ) )
& ( A @ k1_pre_topc @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_waybel_0) ).
thf(339,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ ( A @ k1_pre_topc @ v2_waybel_0 ) )
& ( A @ ( A @ k1_pre_topc @ v1_waybel_0 ) )
& ( A @ k1_pre_topc @ v5_membered )
& ( A @ k1_pre_topc @ v4_membered )
& ( A @ k1_pre_topc @ v3_membered )
& ( A @ k1_pre_topc @ v2_membered )
& ( A @ k1_pre_topc @ v1_membered )
& ( A @ k1_pre_topc @ v1_finset_1 )
& ( A @ ( A @ k1_pre_topc @ v5_orders_2 ) )
& ( A @ k1_pre_topc @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_orders_2 )
& ~ ( 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 @ v4_waybel34 ) ) )
=> ( ( B @ ( A @ ( C @ v5_waybel34 ) ) )
& ( B @ ( A @ ( C @ v20_waybel_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_waybel34) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_orders_2 )
& ~ ( 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 @ v4_waybel34 ) ) )
=> ( ( B @ ( A @ ( C @ v5_waybel34 ) ) )
& ( B @ ( A @ ( C @ v20_waybel_0 ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(77,plain,
~ ! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_orders_2 )
& ~ ( 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 @ v4_waybel34 ) ) )
=> ( ( B @ ( A @ ( C @ v5_waybel34 ) ) )
& ( B @ ( A @ ( C @ v20_waybel_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(32,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(193,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)],[32]) ).
thf(15,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(129,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(72,axiom,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(371,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(42,axiom,
? [A: $i] :
( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_membered) ).
thf(237,plain,
? [A: $i] :
( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(62,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_orders_2 )
& ~ ( 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 @ v20_waybel_0 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( E @ ( D @ ( A @ k2_struct_0 ) ) @ ( C @ ( B @ ( A @ r4_waybel_0 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d35_waybel_0) ).
thf(311,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_orders_2 )
& ~ ( 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 @ k2_struct_0 ) ) @ ( C @ ( B @ ( A @ r4_waybel_0 ) ) ) ) ) )
=> ( B @ ( A @ ( C @ v20_waybel_0 ) ) ) )
& ( ( B @ ( A @ ( C @ v20_waybel_0 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( E @ ( D @ ( A @ k2_struct_0 ) ) @ ( C @ ( B @ ( A @ r4_waybel_0 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(59,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(298,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)],[59]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ k1_pre_topc )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_pre_topc) ).
thf(264,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ k1_pre_topc )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_membered) ).
thf(161,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(58,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(296,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(191,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)],[31]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ? [B: $i] :
( ( A @ ( B @ v13_waybel_0 ) )
& ( A @ ( B @ v12_waybel_0 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_waybel_0) ).
thf(291,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ? [B: $i] :
( ( A @ ( B @ v13_waybel_0 ) )
& ( A @ ( B @ v12_waybel_0 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc20_membered) ).
thf(144,plain,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(181,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)],[28]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(187,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ v5_membered )
=> ( A @ v4_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_membered) ).
thf(274,plain,
! [A: $i] :
( ( A @ v5_membered )
=> ( A @ v4_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_xcmplx_0 )
& ( A @ v1_xcmplx_0 ) )
=> ( B @ ( A @ k2_tarski ) @ v1_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_membered) ).
thf(230,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_xcmplx_0 )
& ( A @ v1_xcmplx_0 ) )
=> ( B @ ( A @ k2_tarski ) @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_rat_1 )
& ( A @ v1_rat_1 ) )
=> ( ( B @ ( A @ k2_tarski ) @ v3_membered )
& ( B @ ( A @ k2_tarski ) @ v2_membered )
& ( B @ ( A @ k2_tarski ) @ v1_membered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_membered) ).
thf(245,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_rat_1 )
& ( A @ v1_rat_1 ) )
=> ( ( B @ ( A @ k2_tarski ) @ v3_membered )
& ( B @ ( A @ k2_tarski ) @ v2_membered )
& ( B @ ( A @ k2_tarski ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_pre_topc @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pre_topc) ).
thf(303,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_pre_topc @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(271,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)],[49]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_finset_1 )
& ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finset_1) ).
thf(208,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_finset_1 )
& ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(71,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(367,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(140,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)],[18]) ).
thf(33,axiom,
? [A: $i] :
( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_setfam_1) ).
thf(198,plain,
? [A: $i] :
( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(278,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc15_membered) ).
thf(223,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc18_membered) ).
thf(135,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xcmplx_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_membered) ).
thf(267,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xcmplx_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_xreal_0 )
& ( A @ v1_xreal_0 ) )
=> ( ( B @ ( A @ k2_tarski ) @ v2_membered )
& ( B @ ( A @ k2_tarski ) @ v1_membered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_membered) ).
thf(167,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_xreal_0 )
& ( A @ v1_xreal_0 ) )
=> ( ( B @ ( A @ k2_tarski ) @ v2_membered )
& ( B @ ( A @ k2_tarski ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(127,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)],[14]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
<=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(359,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)],[69]) ).
thf(44,axiom,
( ( k1_xboole_0 @ v5_membered )
& ( k1_xboole_0 @ v4_membered )
& ( k1_xboole_0 @ v3_membered )
& ( k1_xboole_0 @ v2_membered )
& ( k1_xboole_0 @ v1_membered )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
thf(250,plain,
( ( k1_xboole_0 @ v5_membered )
& ( k1_xboole_0 @ v4_membered )
& ( k1_xboole_0 @ v3_membered )
& ( k1_xboole_0 @ v2_membered )
& ( k1_xboole_0 @ v1_membered )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(99,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc19_membered) ).
thf(258,plain,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(67,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_orders_2 )
& ~ ( 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 @ v4_waybel34 ) ) )
<=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( D @ v1_finset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ r4_waybel_0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_waybel34) ).
thf(351,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_orders_2 )
& ~ ( 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 @ v1_finset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ r4_waybel_0 ) ) ) ) )
=> ( B @ ( A @ ( C @ v4_waybel34 ) ) ) )
& ( ( B @ ( A @ ( C @ v4_waybel34 ) ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( D @ v1_finset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ r4_waybel_0 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_membered) ).
thf(114,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ k1_pre_topc @ v5_membered )
& ( A @ k1_pre_topc @ v4_membered )
& ( A @ k1_pre_topc @ v3_membered )
& ( A @ k1_pre_topc @ v2_membered )
& ( A @ k1_pre_topc @ v1_membered )
& ( A @ k1_pre_topc @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_pre_topc) ).
thf(171,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ k1_pre_topc @ v5_membered )
& ( A @ k1_pre_topc @ v4_membered )
& ( A @ k1_pre_topc @ v3_membered )
& ( A @ k1_pre_topc @ v2_membered )
& ( A @ k1_pre_topc @ v1_membered )
& ( A @ k1_pre_topc @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(41,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(235,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_struct_0 ) ) )
= ( B @ ( C @ ( A @ k2_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_struct_0) ).
thf(383,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_struct_0 ) ) )
= ( B @ ( C @ ( A @ k2_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_membered) ).
thf(214,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(11,axiom,
! [A: $i] :
( ( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_setfam_1) ).
thf(119,plain,
! [A: $i] :
( ( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ? [B: $i] :
( ( A @ ( B @ v2_waybel_0 ) )
& ( A @ ( B @ v1_waybel_0 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_waybel_0) ).
thf(378,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ? [B: $i] :
( ( A @ ( B @ v2_waybel_0 ) )
& ( A @ ( B @ v1_waybel_0 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(61,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v13_waybel_0 ) )
& ( A @ ( B @ v12_waybel_0 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc8_waybel_0) ).
thf(305,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v13_waybel_0 ) )
& ( A @ ( B @ v12_waybel_0 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(283,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(4,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(90,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(40,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(232,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(3992,plain,
$false,
inference(e,[status(thm)],[142,102,165,317,123,95,386,151,365,88,276,269,202,357,157,189,325,289,216,179,321,376,121,280,133,92,285,109,339,77,193,129,371,237,311,298,264,161,296,191,291,144,181,187,274,230,245,303,271,208,367,140,198,278,223,135,267,167,127,359,250,99,258,351,114,171,235,383,214,119,378,305,283,90,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT379+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.39 % Computer : n011.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Fri Sep 25 21:35:59 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.43/1.26 % [INFO] Parsing done (273ms).
% 1.43/1.28 % [INFO] Running in sequential loop mode.
% 2.36/1.66 % [INFO] eprover registered as external prover.
% 2.36/1.67 % [INFO] Scanning for conjecture ...
% 2.57/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 82 axioms. Running axiom selection ...
% 2.96/1.91 % [INFO] Axiom selection finished. Selected 74 axioms (removed 8 axioms).
% 2.96/2.02 % [INFO] Problem is first-order (TPTP FOF).
% 3.31/2.03 % [INFO] Type checking passed.
% 3.31/2.04 % [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 ...
% 24.15/6.18 % External prover 'e' found a proof!
% 24.15/6.19 % [INFO] Killing All external provers ...
% 24.15/6.19 % Time passed: 5648ms (effective reasoning time: 4904ms)
% 24.15/6.19 % 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)>
% 24.15/6.19 % Axioms used in derivation (74): redefinition_m2_relset_1, rc1_funct_1, fc1_waybel_0, fc6_membered, rc8_waybel_0, cc15_membered, dt_l1_orders_2, cc17_membered, antisymmetry_r2_hidden, cc12_membered, cc2_finset_1, d15_waybel34, rc4_finset_1, cc1_setfam_1, cc10_membered, t1_subset, rc1_membered, fc3_setfam_1, rc3_funct_1, fc1_pre_topc, dt_m2_relset_1, dt_k1_pre_topc, fc15_membered, t6_boole, fc16_membered, t5_subset, d35_waybel_0, cc19_membered, existence_m1_relset_1, cc11_membered, d2_pre_topc, t4_subset, cc20_membered, t7_boole, existence_l1_orders_2, cc1_funct_1, rc3_struct_0, commutativity_k2_struct_0, rc2_funct_1, cc4_membered, cc18_membered, dt_k2_struct_0, cc2_funct_1, t3_subset, cc1_relset_1, cc13_membered, existence_m1_subset_1, commutativity_k2_tarski, existence_m2_relset_1, fc13_membered, fc14_membered, fc1_struct_0, fc1_waybel11, reflexivity_r1_tarski, rc3_finset_1, d16_waybel34, rc1_finset_1, cc1_finset_1, redefinition_k2_struct_0, t8_boole, rc5_struct_0, t2_subset, cc1_membered, cc2_membered, fc12_membered, cc3_membered, fc2_finset_1, cc14_membered, existence_l1_struct_0, rc7_waybel_0, rc1_waybel_0, fc14_finset_1, cc16_membered, rc1_setfam_1
% 24.15/6.19 % No. of inferences in proof: 152
% 24.15/6.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5648 ms resp. 4904 ms w/o parsing
% 21.95/6.29 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.95/6.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------