%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT347+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 : n007.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 07:47:26 AM UTC 2026
% Result : Theorem 8.15s 3.51s
% Output : Refutation 8.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 97
% Syntax : Number of formulae : 196 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 925 ( 39 equ; 0 cnn)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 2439 ( 147 ~; 2 |; 534 &;1563 @)
% ( 5 <=>; 188 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 2 con; 0-3 aty)
% Number of variables : 297 ( 0 ^; 243 !; 54 ?; 297 :)
% Comments :
%------------------------------------------------------------------------------
thf(v2_orders_2_decl,type,
v2_orders_2: $i > $o ).
thf(v3_orders_2_decl,type,
v3_orders_2: $i > $o ).
thf(v4_orders_2_decl,type,
v4_orders_2: $i > $o ).
thf(v2_yellow_0_decl,type,
v2_yellow_0: $i > $o ).
thf(v2_lattice3_decl,type,
v2_lattice3: $i > $o ).
thf(l1_orders_2_decl,type,
l1_orders_2: $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(v1_waybel_0_decl,type,
v1_waybel_0: $i > $i > $o ).
thf(k2_yellow_1_decl,type,
k2_yellow_1: $i > $i ).
thf(k9_waybel_0_decl,type,
k9_waybel_0: $i > $i ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(k1_yellow_0_decl,type,
k1_yellow_0: $i > $i > $i ).
thf(k3_tarski_decl,type,
k3_tarski: $i > $i ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(g1_orders_2_decl,type,
g1_orders_2: $i > $i > $i ).
thf(k6_relset_1_decl,type,
k6_relset_1: $i > $i > $i > $i ).
thf(k4_relat_1_decl,type,
k4_relat_1: $i > $i ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(v1_orders_2_decl,type,
v1_orders_2: $i > $o ).
thf(u1_orders_2_decl,type,
u1_orders_2: $i > $i ).
thf(v1_lattice3_decl,type,
v1_lattice3: $i > $o ).
thf(v3_lattice3_decl,type,
v3_lattice3: $i > $o ).
thf(k7_lattice3_decl,type,
k7_lattice3: $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(v12_waybel_0_decl,type,
v12_waybel_0: $i > $i > $o ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(v1_yellow_0_decl,type,
v1_yellow_0: $i > $o ).
thf(v3_yellow_0_decl,type,
v3_yellow_0: $i > $o ).
thf(k8_waybel_0_decl,type,
k8_waybel_0: $i > $i ).
thf(a_1_0_waybel_0_decl,type,
a_1_0_waybel_0: $i > $i ).
thf(v24_waybel_0_decl,type,
v24_waybel_0: $i > $o ).
thf(v25_waybel_0_decl,type,
v25_waybel_0: $i > $o ).
thf(v13_waybel_0_decl,type,
v13_waybel_0: $i > $i > $o ).
thf(a_1_1_waybel_0_decl,type,
a_1_1_waybel_0: $i > $i ).
thf(v2_waybel_0_decl,type,
v2_waybel_0: $i > $i > $o ).
thf(33,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_lattice3 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k7_lattice3 @ v3_yellow_0 )
& ( A @ k7_lattice3 @ v2_yellow_0 )
& ( A @ k7_lattice3 @ v1_yellow_0 )
& ( A @ k7_lattice3 @ v3_lattice3 )
& ( A @ k7_lattice3 @ v2_lattice3 )
& ( A @ k7_lattice3 @ v1_lattice3 )
& ( A @ k7_lattice3 @ v1_orders_2 )
& ~ ( A @ k7_lattice3 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_yellow_7) ).
thf(234,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_lattice3 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k7_lattice3 @ v3_yellow_0 )
& ( A @ k7_lattice3 @ v2_yellow_0 )
& ( A @ k7_lattice3 @ v1_yellow_0 )
& ( A @ k7_lattice3 @ v3_lattice3 )
& ( A @ k7_lattice3 @ v2_lattice3 )
& ( A @ k7_lattice3 @ v1_lattice3 )
& ( A @ k7_lattice3 @ v1_orders_2 )
& ~ ( A @ k7_lattice3 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v24_waybel_0 )
& ( A @ v1_yellow_0 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_yellow_0 )
& ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_waybel_0) ).
thf(533,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v24_waybel_0 )
& ( A @ v1_yellow_0 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_yellow_0 )
& ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(45,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_waybel_8) ).
thf(288,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v3_lattice3 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v25_waybel_0 )
& ( A @ v24_waybel_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_waybel_0) ).
thf(316,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v3_lattice3 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v25_waybel_0 )
& ( A @ v24_waybel_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k4_relat_1 @ k4_relat_1 )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(169,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k4_relat_1 @ k4_relat_1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ k7_lattice3 )
= ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k6_relset_1 ) ) @ ( A @ u1_struct_0 @ g1_orders_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_lattice3) ).
thf(373,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ k7_lattice3 )
= ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k6_relset_1 ) ) @ ( A @ u1_struct_0 @ g1_orders_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ k2_yellow_1 @ l1_orders_2 )
& ( A @ k2_yellow_1 @ v1_orders_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_yellow_1) ).
thf(217,plain,
! [A: $i] :
( ( A @ k2_yellow_1 @ l1_orders_2 )
& ( A @ k2_yellow_1 @ v1_orders_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(35,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_lattice3 ) )
=> ( ( A @ k7_lattice3 @ v1_lattice3 )
& ( A @ k7_lattice3 @ v1_orders_2 )
& ~ ( A @ k7_lattice3 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_yellow_7) ).
thf(247,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_lattice3 ) )
=> ( ( A @ k7_lattice3 @ v1_lattice3 )
& ( A @ k7_lattice3 @ v1_orders_2 )
& ~ ( A @ k7_lattice3 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(91,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ k9_waybel_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_waybel16) ).
thf(511,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ k9_waybel_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(202,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(61,axiom,
? [A: $i] :
( ( A @ v25_waybel_0 )
& ( A @ v24_waybel_0 )
& ( A @ v3_yellow_0 )
& ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ( A @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_waybel_0) ).
thf(357,plain,
? [A: $i] :
( ( A @ v25_waybel_0 )
& ( A @ v24_waybel_0 )
& ( A @ v3_yellow_0 )
& ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ( A @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(25,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( A @ k7_lattice3 @ v4_orders_2 )
& ( A @ k7_lattice3 @ v3_orders_2 )
& ( A @ k7_lattice3 @ v2_orders_2 )
& ( A @ k7_lattice3 @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_lattice3) ).
thf(196,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( A @ k7_lattice3 @ v4_orders_2 )
& ( A @ k7_lattice3 @ v3_orders_2 )
& ( A @ k7_lattice3 @ v2_orders_2 )
& ( A @ k7_lattice3 @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(14,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(157,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(63,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(376,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)],[63]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v2_lattice3 )
=> ~ ( A @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(348,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v2_lattice3 )
=> ~ ( A @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ ( B @ ( C @ ( B @ ( A @ k6_relset_1 ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relset_1) ).
thf(133,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ ( B @ ( C @ ( B @ ( A @ k6_relset_1 ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,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(116,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(46,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(292,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(76,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v13_waybel_0 ) )
& ( A @ ( B @ v2_waybel_0 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc10_waybel_0) ).
thf(439,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v13_waybel_0 ) )
& ( A @ ( B @ v2_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)],[76]) ).
thf(39,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(270,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)],[39]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m1_relset_1 ) ) )
=> ( ( B @ ( A @ g1_orders_2 ) @ l1_orders_2 )
& ( B @ ( A @ g1_orders_2 ) @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(334,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m1_relset_1 ) ) )
=> ( ( B @ ( A @ g1_orders_2 ) @ l1_orders_2 )
& ( B @ ( A @ g1_orders_2 ) @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(23,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(192,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)],[23]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(275,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(17,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(165,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(36,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(252,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v3_lattice3 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_yellow_0 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_yellow_0) ).
thf(435,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v3_lattice3 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_yellow_0 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(95,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ? [B: $i] :
( ( A @ ( B @ v13_waybel_0 ) )
& ( A @ ( B @ v12_waybel_0 ) )
& ( A @ ( B @ v2_waybel_0 ) )
& ( A @ ( B @ v1_waybel_0 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc11_waybel_0) ).
thf(522,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ? [B: $i] :
( ( A @ ( B @ v13_waybel_0 ) )
& ( A @ ( B @ v12_waybel_0 ) )
& ( A @ ( B @ v2_waybel_0 ) )
& ( A @ ( B @ v1_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)],[95]) ).
thf(79,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v25_waybel_0 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_waybel_0) ).
thf(456,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v25_waybel_0 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_relset_1 ) ) )
= ( C @ k4_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_relset_1) ).
thf(124,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_relset_1 ) ) )
= ( C @ k4_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(53,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( A @ k7_lattice3 @ v2_orders_2 )
& ( A @ k7_lattice3 @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_yellow_7) ).
thf(328,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( A @ k7_lattice3 @ v2_orders_2 )
& ( A @ k7_lattice3 @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(82,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(471,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(37,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_yellow_0 )
& ( A @ v2_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( A @ k9_waybel_0 @ k2_yellow_1 @ v25_waybel_0 )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ v24_waybel_0 )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ v1_yellow_0 )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ v3_lattice3 )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ v2_lattice3 )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ v4_orders_2 )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ v3_orders_2 )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ v2_orders_2 )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ v1_orders_2 )
& ~ ( A @ k9_waybel_0 @ k2_yellow_1 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_waybel16) ).
thf(256,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_yellow_0 )
& ( A @ v2_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ( ( A @ k9_waybel_0 @ k2_yellow_1 @ v25_waybel_0 )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ v24_waybel_0 )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ v1_yellow_0 )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ v3_lattice3 )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ v2_lattice3 )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ v4_orders_2 )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ v3_orders_2 )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ v2_orders_2 )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ v1_orders_2 )
& ~ ( A @ k9_waybel_0 @ k2_yellow_1 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(68,axiom,
? [A: $i] :
( ( A @ v3_yellow_0 )
& ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_yellow_0) ).
thf(393,plain,
? [A: $i] :
( ( A @ v3_yellow_0 )
& ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 )
& ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(93,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(515,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(34,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k8_waybel_0 )
= ( A @ a_1_0_waybel_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d23_waybel_0) ).
thf(244,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k8_waybel_0 )
= ( A @ a_1_0_waybel_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(27,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(205,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)],[27]) ).
thf(96,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_yellow_0 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ! [B: $i] :
( ( ( A @ k8_waybel_0 @ k2_yellow_1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ k8_waybel_0 @ k2_yellow_1 @ ( B @ v1_waybel_0 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k8_waybel_0 @ k2_yellow_1 @ k1_yellow_0 ) )
= ( B @ k3_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_waybel13) ).
thf(530,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_yellow_0 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ! [B: $i] :
( ( ( A @ k8_waybel_0 @ k2_yellow_1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ k8_waybel_0 @ k2_yellow_1 @ ( B @ v1_waybel_0 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k8_waybel_0 @ k2_yellow_1 @ k1_yellow_0 ) )
= ( B @ k3_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(72,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_orders_2 @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(425,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_orders_2 @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(513,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)],[92]) ).
thf(74,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v2_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_waybel_8) ).
thf(430,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v2_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m1_relset_1 ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_orders_2 ) )
= ( D @ ( C @ g1_orders_2 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(118,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m1_relset_1 ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_orders_2 ) )
= ( D @ ( C @ g1_orders_2 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(43,axiom,
? [A: $i] : ( A @ l1_orders_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(281,plain,
? [A: $i] : ( A @ l1_orders_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(98,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(545,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)],[98]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v3_lattice3 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_0) ).
thf(445,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v3_lattice3 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(65,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_waybel_8) ).
thf(382,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(144,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)],[12]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ k7_lattice3 @ l1_orders_2 )
& ( A @ k7_lattice3 @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_lattice3) ).
thf(498,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ k7_lattice3 @ l1_orders_2 )
& ( A @ k7_lattice3 @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(81,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_lattice3 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v2_lattice3 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_waybel_8) ).
thf(466,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_lattice3 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v2_lattice3 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(22,axiom,
? [A: $i] :
( ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ( A @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_lattice3) ).
thf(181,plain,
? [A: $i] :
( ( A @ v3_lattice3 )
& ( A @ v2_lattice3 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ( A @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v25_waybel_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_yellow_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_waybel_0) ).
thf(350,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v25_waybel_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_yellow_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(15,axiom,
! [A: $i] :
( ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k4_relat_1 @ v1_funct_1 )
& ( A @ k4_relat_1 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_funct_1) ).
thf(159,plain,
! [A: $i] :
( ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k4_relat_1 @ v1_funct_1 )
& ( A @ k4_relat_1 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v1_orders_2 )
=> ( A
= ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(406,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v1_orders_2 )
=> ( A
= ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_relset_1 ) ) @ ( B @ ( A @ k6_relset_1 ) ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k6_relset_1) ).
thf(172,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_relset_1 ) ) @ ( B @ ( A @ k6_relset_1 ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(84,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(477,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(13,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(155,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(80,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_yellow_0 ) )
=> ( ( A @ k7_lattice3 @ v1_yellow_0 )
& ( A @ k7_lattice3 @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_yellow_7) ).
thf(462,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_yellow_0 ) )
=> ( ( A @ k7_lattice3 @ v1_yellow_0 )
& ( A @ k7_lattice3 @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(31,axiom,
? [A: $i] :
( ( A @ v3_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ( A @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice3) ).
thf(223,plain,
? [A: $i] :
( ( A @ v3_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ( A @ v1_orders_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_orders_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(10,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(135,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v24_waybel_0 )
& ( A @ v1_lattice3 )
& ( A @ v2_orders_2 ) )
=> ( ( A @ v2_yellow_0 )
& ( A @ v1_lattice3 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc9_waybel_0) ).
thf(299,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v24_waybel_0 )
& ( A @ v1_lattice3 )
& ( A @ v2_orders_2 ) )
=> ( ( A @ v2_yellow_0 )
& ( A @ v1_lattice3 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(89,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(505,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(3,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(112,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(57,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(342,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)],[57]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(355,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(194,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(28,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v12_waybel_0 ) )
& ( A @ ( B @ v1_waybel_0 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc9_waybel_0) ).
thf(209,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v12_waybel_0 ) )
& ( A @ ( B @ v1_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)],[28]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ a_1_0_waybel_0 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ ( C @ v12_waybel_0 ) )
& ( B @ ( C @ v1_waybel_0 ) )
& ~ ( C @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_waybel_0) ).
thf(487,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ ( C @ v12_waybel_0 ) )
& ( B @ ( C @ v1_waybel_0 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( B @ a_1_0_waybel_0 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_waybel_0 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ ( C @ v12_waybel_0 ) )
& ( B @ ( C @ v1_waybel_0 ) )
& ~ ( C @ v1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v3_yellow_0 )
=> ( ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_yellow_0) ).
thf(295,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v3_yellow_0 )
=> ( ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ a_1_1_waybel_0 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ ( C @ v13_waybel_0 ) )
& ( B @ ( C @ v2_waybel_0 ) )
& ~ ( C @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_1_waybel_0) ).
thf(414,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( B @ v3_orders_2 )
& ( B @ v2_orders_2 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ ( C @ v13_waybel_0 ) )
& ( B @ ( C @ v2_waybel_0 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( B @ a_1_1_waybel_0 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_1_waybel_0 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ ( C @ v13_waybel_0 ) )
& ( B @ ( C @ v2_waybel_0 ) )
& ~ ( C @ v1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(70,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(409,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)],[70]) ).
thf(21,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v4_orders_2 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v4_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_waybel_8) ).
thf(177,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v4_orders_2 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v4_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(88,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(502,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(8,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(127,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)],[8]) ).
thf(56,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k7_lattice3 @ v1_orders_2 )
& ~ ( A @ k7_lattice3 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_lattice3) ).
thf(338,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k7_lattice3 @ v1_orders_2 )
& ~ ( A @ k7_lattice3 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(20,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(175,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(66,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v4_orders_2 ) )
=> ( ( A @ k7_lattice3 @ v4_orders_2 )
& ( A @ k7_lattice3 @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_yellow_7) ).
thf(386,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v4_orders_2 ) )
=> ( ( A @ k7_lattice3 @ v4_orders_2 )
& ( A @ k7_lattice3 @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(78,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(450,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)],[78]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v2_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ! [B: $i] :
( ( ( A @ k9_waybel_0 @ k2_yellow_1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ ( B @ v1_waybel_0 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k9_waybel_0 @ k2_yellow_1 @ k1_yellow_0 ) )
= ( B @ k3_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_waybel22) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v2_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ! [B: $i] :
( ( ( A @ k9_waybel_0 @ k2_yellow_1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ ( B @ v1_waybel_0 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k9_waybel_0 @ k2_yellow_1 @ k1_yellow_0 ) )
= ( B @ k3_tarski ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(99,plain,
~ ! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v2_lattice3 )
& ( A @ v2_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 ) )
=> ! [B: $i] :
( ( ( A @ k9_waybel_0 @ k2_yellow_1 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ k9_waybel_0 @ k2_yellow_1 @ ( B @ v1_waybel_0 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k9_waybel_0 @ k2_yellow_1 @ k1_yellow_0 ) )
= ( B @ k3_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(85,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_lattice3 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_lattice3 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_waybel_8) ).
thf(482,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_lattice3 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_lattice3 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(94,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(517,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)],[94]) ).
thf(67,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k9_waybel_0 )
= ( A @ a_1_1_waybel_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d24_waybel_0) ).
thf(390,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k9_waybel_0 )
= ( A @ a_1_1_waybel_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(114,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,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(139,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(64,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 ) )
=> ( ( A @ k7_lattice3 @ v3_orders_2 )
& ( A @ k7_lattice3 @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_yellow_7) ).
thf(378,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 ) )
=> ( ( A @ k7_lattice3 @ v3_orders_2 )
& ( A @ k7_lattice3 @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(40,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k9_waybel_0 )
= ( A @ k7_lattice3 @ k8_waybel_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_waybel16) ).
thf(272,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v3_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k9_waybel_0 )
= ( A @ k7_lattice3 @ k8_waybel_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(49,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_yellow_0 ) )
=> ( ( A @ k7_lattice3 @ v2_yellow_0 )
& ( A @ k7_lattice3 @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_yellow_7) ).
thf(305,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_yellow_0 ) )
=> ( ( A @ k7_lattice3 @ v2_yellow_0 )
& ( A @ k7_lattice3 @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( A @ l1_orders_2 )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k1_yellow_0 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
thf(474,plain,
! [A: $i,B: $i] :
( ( A @ l1_orders_2 )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k1_yellow_0 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(44,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(283,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)],[44]) ).
thf(90,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_lattice3 ) )
=> ( ( A @ k7_lattice3 @ v2_lattice3 )
& ( A @ k7_lattice3 @ v1_orders_2 )
& ~ ( A @ k7_lattice3 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_yellow_7) ).
thf(506,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v1_lattice3 ) )
=> ( ( A @ k7_lattice3 @ v2_lattice3 )
& ( A @ k7_lattice3 @ v1_orders_2 )
& ~ ( A @ k7_lattice3 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v1_lattice3 )
=> ~ ( A @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(268,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v1_lattice3 )
=> ~ ( A @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 ) )
=> ( A @ v3_yellow_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_yellow_0) ).
thf(332,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v2_yellow_0 )
& ( A @ v1_yellow_0 ) )
=> ( A @ v3_yellow_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(73,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(427,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)],[73]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k4_relat_1 @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(163,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k4_relat_1 @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(42,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(277,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)],[42]) ).
thf(52,axiom,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v24_waybel_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v24_waybel_0 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v2_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_waybel_8) ).
thf(322,plain,
! [A: $i] :
( ( ( A @ l1_orders_2 )
& ( A @ v24_waybel_0 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v24_waybel_0 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v2_orders_2 )
& ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v1_orders_2 )
& ~ ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v25_waybel_0 )
& ( A @ v2_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_yellow_0 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_waybel_0) ).
thf(309,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( ( A @ v25_waybel_0 )
& ( A @ v2_yellow_0 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_yellow_0 )
& ( A @ v1_lattice3 )
& ( A @ v4_orders_2 )
& ( A @ v2_orders_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(29,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(215,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)],[29]) ).
thf(32,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(232,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)],[32]) ).
thf(549,plain,
$false,
inference(e,[status(thm)],[234,533,288,316,169,373,217,247,511,202,357,196,157,376,348,133,116,292,439,270,334,192,275,165,252,435,522,456,124,328,471,256,393,515,244,205,530,425,513,430,118,281,545,445,382,144,498,466,181,350,159,406,172,477,155,462,223,135,299,505,112,342,355,194,209,487,295,414,409,177,502,127,338,175,386,450,99,482,517,390,114,139,378,272,305,474,283,506,268,332,427,163,277,322,309,215,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT347+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
% 0.14/0.41 % Computer : n007.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 21:06:38 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.38/1.25 % [INFO] Parsing done (263ms).
% 1.38/1.26 % [INFO] Running in sequential loop mode.
% 2.34/1.66 % [INFO] eprover registered as external prover.
% 2.34/1.67 % [INFO] Scanning for conjecture ...
% 2.54/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 106 axioms. Running axiom selection ...
% 2.96/1.91 % [INFO] Axiom selection finished. Selected 96 axioms (removed 10 axioms).
% 3.35/2.05 % [INFO] Problem is first-order (TPTP FOF).
% 3.35/2.07 % [INFO] Type checking passed.
% 3.35/2.07 % [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 ...
% 8.15/3.50 % External prover 'e' found a proof!
% 8.15/3.50 % [INFO] Killing All external provers ...
% 8.15/3.50 % Time passed: 2957ms (effective reasoning time: 2236ms)
% 8.15/3.50 % 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)>
% 8.15/3.51 % Axioms used in derivation (96): dt_k6_relset_1, fc4_subset_1, t5_subset, dt_l1_orders_2, cc2_lattice3, fc2_waybel16, redefinition_m2_relset_1, fc9_yellow_7, fc10_waybel_8, fc1_xboole_0, t1_subset, fc3_yellow_7, rc2_yellow_0, fc6_lattice3, cc12_waybel_0, rc3_funct_1, cc1_lattice3, dt_m2_relset_1, fc1_waybel16, d5_lattice3, cc14_waybel_0, d24_waybel_0, cc11_waybel_0, rc13_waybel_0, rc1_funct_1, fc5_lattice3, redefinition_k6_relset_1, involutiveness_k6_relset_1, rc11_waybel_0, dt_u1_orders_2, rc1_lattice3, fc8_waybel_8, fc6_waybel_8, t9_waybel13, rc2_lattice3, t6_boole, rc2_subset_1, cc9_waybel_0, existence_m1_relset_1, fc7_waybel_8, fc10_yellow_7, t2_tarski, t7_waybel16, dt_k4_relat_1, t4_subset, fc9_waybel_8, involutiveness_k4_relat_1, rc8_waybel_0, t7_boole, existence_l1_orders_2, cc1_funct_1, rc3_struct_0, fc5_yellow_7, fc1_subset_1, cc13_waybel_0, rc9_waybel_0, rc2_funct_1, rc1_subset_1, dt_g1_orders_2, fc7_yellow_7, abstractness_v1_orders_2, cc4_yellow_0, cc2_funct_1, dt_k7_lattice3, t3_subset, cc1_relset_1, fc1_yellow_7, existence_m1_subset_1, dt_k2_yellow_1, existence_m2_relset_1, free_g1_orders_2, fraenkel_a_1_0_waybel_0, fc1_struct_0, reflexivity_r1_tarski, rc10_waybel_0, cc10_waybel_0, dt_k1_yellow_0, cc5_yellow_0, fc4_waybel_8, cc1_yellow_0, fc3_funct_1, t8_boole, rc1_xboole_0, fc2_yellow_7, rc5_struct_0, t2_subset, fc6_yellow_7, existence_l1_struct_0, d23_waybel_0, rc7_waybel_0, rc1_waybel_0, rc2_xboole_0, fraenkel_a_1_1_waybel_0, cc3_yellow_0, fc5_waybel_8, antisymmetry_r2_hidden
% 8.15/3.51 % No. of inferences in proof: 196
% 8.15/3.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2957 ms resp. 2236 ms w/o parsing
% 8.55/3.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.55/3.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------