%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT362+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 : n019.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 07:47:30 AM UTC 2026
% Result : Theorem 5.98s 3.02s
% Output : Refutation 6.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 54
% Syntax : Number of formulae : 110 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 605 ( 4 equ; 0 cnn)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1662 ( 123 ~; 2 |; 371 &;1044 @)
% ( 1 <=>; 121 =>; 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 : 42 ( 40 usr; 2 con; 0-3 aty)
% Number of variables : 202 ( 0 ^; 159 !; 43 ?; 202 :)
% Comments :
%------------------------------------------------------------------------------
thf(v2_setfam_1_decl,type,
v2_setfam_1: $i > $o ).
thf(r2_functor0_decl,type,
r2_functor0: $i > $i > $o ).
thf(k4_waybel34_decl,type,
k4_waybel34: $i > $i ).
thf(k5_waybel34_decl,type,
k5_waybel34: $i > $i ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(l1_altcat_1_decl,type,
l1_altcat_1: $i > $o ).
thf(l2_functor0_decl,type,
l2_functor0: $i > $i > $i > $o ).
thf(l1_functor0_decl,type,
l1_functor0: $i > $i > $i > $o ).
thf(v9_functor0_decl,type,
v9_functor0: $i > $i > $i > $o ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(v11_functor0_decl,type,
v11_functor0: $i > $i > $i > $o ).
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(v2_altcat_1_decl,type,
v2_altcat_1: $i > $o ).
thf(v12_altcat_1_decl,type,
v12_altcat_1: $i > $o ).
thf(l2_altcat_1_decl,type,
l2_altcat_1: $i > $o ).
thf(m2_functor0_decl,type,
m2_functor0: $i > $i > $i > $o ).
thf(v16_functor0_decl,type,
v16_functor0: $i > $i > $i > $o ).
thf(v6_functor0_decl,type,
v6_functor0: $i > $i > $i > $o ).
thf(v8_functor0_decl,type,
v8_functor0: $i > $i > $i > $o ).
thf(v12_functor0_decl,type,
v12_functor0: $i > $i > $i > $o ).
thf(v14_functor0_decl,type,
v14_functor0: $i > $i > $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(v6_altcat_1_decl,type,
v6_altcat_1: $i > $o ).
thf(v9_altcat_1_decl,type,
v9_altcat_1: $i > $o ).
thf(v11_altcat_1_decl,type,
v11_altcat_1: $i > $o ).
thf(v1_altcat_2_decl,type,
v1_altcat_2: $i > $o ).
thf(v2_yellow18_decl,type,
v2_yellow18: $i > $o ).
thf(v3_yellow18_decl,type,
v3_yellow18: $i > $o ).
thf(v4_yellow18_decl,type,
v4_yellow18: $i > $o ).
thf(v1_yellow21_decl,type,
v1_yellow21: $i > $o ).
thf(v2_yellow21_decl,type,
v2_yellow21: $i > $o ).
thf(v3_yellow21_decl,type,
v3_yellow21: $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k6_waybel34_decl,type,
k6_waybel34: $i > $i ).
thf(v21_functor0_decl,type,
v21_functor0: $i > $i > $i > $o ).
thf(44,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(217,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1,conjecture,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ r2_functor0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_waybel34) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ r2_functor0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(56,plain,
~ ! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ r2_functor0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(36,axiom,
? [A: $i] :
( ( A @ v1_altcat_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_altcat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_functor0) ).
thf(174,plain,
? [A: $i] :
( ( A @ v1_altcat_2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_altcat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(32,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(157,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)],[32]) ).
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(60,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( A @ l1_altcat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_altcat_1) ).
thf(109,plain,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( A @ l1_altcat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_struct_0 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ l1_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v11_functor0 ) ) )
=> ( B @ ( A @ ( C @ v6_functor0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_functor0) ).
thf(129,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_struct_0 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ l1_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v11_functor0 ) ) )
=> ( B @ ( A @ ( C @ v6_functor0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( A @ l1_altcat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ l2_functor0 ) ) )
=> ( B @ ( A @ ( C @ l1_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_functor0) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( A @ l1_altcat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ l2_functor0 ) ) )
=> ( B @ ( A @ ( C @ l1_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ r2_functor0 ) )
=> ( A @ ( B @ r2_functor0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r2_functor0) ).
thf(291,plain,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ r2_functor0 ) )
=> ( A @ ( B @ r2_functor0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(48,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v21_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v16_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v14_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v12_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v11_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v9_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v8_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v6_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_waybel34) ).
thf(258,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v21_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v16_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v14_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v12_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v11_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v9_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v8_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v6_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(111,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_functor0) ).
thf(138,plain,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(101,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v16_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v14_functor0 ) ) )
& ( B @ ( A @ ( C @ v12_functor0 ) ) )
& ( B @ ( A @ ( C @ v11_functor0 ) ) )
& ( B @ ( A @ ( C @ v8_functor0 ) ) )
& ( B @ ( A @ ( C @ v6_functor0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_functor2) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v16_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v14_functor0 ) ) )
& ( B @ ( A @ ( C @ v12_functor0 ) ) )
& ( B @ ( A @ ( C @ v11_functor0 ) ) )
& ( B @ ( A @ ( C @ v8_functor0 ) ) )
& ( B @ ( A @ ( C @ v6_functor0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( ( ( A @ v3_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_yellow21 )
& ( A @ v1_altcat_2 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow21) ).
thf(189,plain,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( ( ( A @ v3_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_yellow21 )
& ( A @ v1_altcat_2 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(46,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k5_waybel34 @ v3_yellow21 )
& ( A @ k5_waybel34 @ v2_yellow21 )
& ( A @ k5_waybel34 @ v1_yellow21 )
& ( A @ k5_waybel34 @ v4_yellow18 )
& ( A @ k5_waybel34 @ v3_yellow18 )
& ( A @ k5_waybel34 @ v2_yellow18 )
& ( A @ k5_waybel34 @ v1_altcat_2 )
& ( A @ k5_waybel34 @ v12_altcat_1 )
& ( A @ k5_waybel34 @ v11_altcat_1 )
& ( A @ k5_waybel34 @ v9_altcat_1 )
& ( A @ k5_waybel34 @ v6_altcat_1 )
& ( A @ k5_waybel34 @ v2_altcat_1 )
& ~ ( A @ k5_waybel34 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_waybel34) ).
thf(228,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k5_waybel34 @ v3_yellow21 )
& ( A @ k5_waybel34 @ v2_yellow21 )
& ( A @ k5_waybel34 @ v1_yellow21 )
& ( A @ k5_waybel34 @ v4_yellow18 )
& ( A @ k5_waybel34 @ v3_yellow18 )
& ( A @ k5_waybel34 @ v2_yellow18 )
& ( A @ k5_waybel34 @ v1_altcat_2 )
& ( A @ k5_waybel34 @ v12_altcat_1 )
& ( A @ k5_waybel34 @ v11_altcat_1 )
& ( A @ k5_waybel34 @ v9_altcat_1 )
& ( A @ k5_waybel34 @ v6_altcat_1 )
& ( A @ k5_waybel34 @ v2_altcat_1 )
& ~ ( A @ k5_waybel34 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(37,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(179,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(13,axiom,
? [A: $i] : ( A @ l1_altcat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_altcat_1) ).
thf(84,plain,
? [A: $i] : ( A @ l1_altcat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(55,axiom,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ ( A @ r2_functor0 ) )
<=> ? [C: $i] :
( ( B @ ( A @ ( C @ v16_functor0 ) ) )
& ( B @ ( A @ ( C @ v21_functor0 ) ) )
& ( B @ ( A @ ( C @ m2_functor0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d41_functor0) ).
thf(293,plain,
! [A: $i] :
( ( ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ( B @ v2_altcat_1 )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ( B @ ( A @ ( C @ v16_functor0 ) ) )
& ( B @ ( A @ ( C @ v21_functor0 ) ) )
& ( B @ ( A @ ( C @ m2_functor0 ) ) ) )
=> ( B @ ( A @ r2_functor0 ) ) )
& ( ( B @ ( A @ r2_functor0 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v16_functor0 ) ) )
& ( B @ ( A @ ( C @ v21_functor0 ) ) )
& ( B @ ( A @ ( C @ m2_functor0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(47,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k4_waybel34 @ v3_yellow21 )
& ( A @ k4_waybel34 @ v2_yellow21 )
& ( A @ k4_waybel34 @ v1_yellow21 )
& ( A @ k4_waybel34 @ v4_yellow18 )
& ( A @ k4_waybel34 @ v3_yellow18 )
& ( A @ k4_waybel34 @ v2_yellow18 )
& ( A @ k4_waybel34 @ v1_altcat_2 )
& ( A @ k4_waybel34 @ v12_altcat_1 )
& ( A @ k4_waybel34 @ v11_altcat_1 )
& ( A @ k4_waybel34 @ v9_altcat_1 )
& ( A @ k4_waybel34 @ v6_altcat_1 )
& ( A @ k4_waybel34 @ v2_altcat_1 )
& ~ ( A @ k4_waybel34 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_waybel34) ).
thf(243,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k4_waybel34 @ v3_yellow21 )
& ( A @ k4_waybel34 @ v2_yellow21 )
& ( A @ k4_waybel34 @ v1_yellow21 )
& ( A @ k4_waybel34 @ v4_yellow18 )
& ( A @ k4_waybel34 @ v3_yellow18 )
& ( A @ k4_waybel34 @ v2_yellow18 )
& ( A @ k4_waybel34 @ v1_altcat_2 )
& ( A @ k4_waybel34 @ v12_altcat_1 )
& ( A @ k4_waybel34 @ v11_altcat_1 )
& ( A @ k4_waybel34 @ v9_altcat_1 )
& ( A @ k4_waybel34 @ v6_altcat_1 )
& ( A @ k4_waybel34 @ v2_altcat_1 )
& ~ ( A @ k4_waybel34 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(9,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(74,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ l1_altcat_1 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_altcat_1) ).
thf(70,plain,
! [A: $i] :
( ( A @ l1_altcat_1 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(51,axiom,
? [A: $i] :
~ ( A @ v2_setfam_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_setfam_1) ).
thf(275,plain,
? [A: $i] :
~ ( A @ v2_setfam_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( ( ( A @ v2_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_yellow21 )
& ( A @ v4_yellow18 )
& ( A @ v3_yellow18 )
& ( A @ v2_yellow18 )
& ( A @ v1_altcat_2 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v9_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_yellow21) ).
thf(197,plain,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( ( ( A @ v2_yellow21 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_yellow21 )
& ( A @ v4_yellow18 )
& ( A @ v3_yellow18 )
& ( A @ v2_yellow18 )
& ( A @ v1_altcat_2 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v9_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(17,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(97,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(86,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(159,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_functor0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_functor0) ).
thf(187,plain,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_functor0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(23,axiom,
? [A: $i] :
( ( A @ v3_yellow21 )
& ( A @ v2_yellow21 )
& ( A @ v1_yellow21 )
& ( A @ v4_yellow18 )
& ( A @ v3_yellow18 )
& ( A @ v2_yellow18 )
& ( A @ v1_altcat_2 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v9_altcat_1 )
& ( A @ v6_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_altcat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_yellow21) ).
thf(113,plain,
? [A: $i] :
( ( A @ v3_yellow21 )
& ( A @ v2_yellow21 )
& ( A @ v1_yellow21 )
& ( A @ v4_yellow18 )
& ( A @ v3_yellow18 )
& ( A @ v2_yellow18 )
& ( A @ v1_altcat_2 )
& ( A @ v12_altcat_1 )
& ( A @ v11_altcat_1 )
& ( A @ v9_altcat_1 )
& ( A @ v6_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_altcat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(45,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k4_waybel34 @ l2_altcat_1 )
& ( A @ k4_waybel34 @ v2_yellow21 )
& ( A @ k4_waybel34 @ v12_altcat_1 )
& ( A @ k4_waybel34 @ v11_altcat_1 )
& ( A @ k4_waybel34 @ v6_altcat_1 )
& ( A @ k4_waybel34 @ v2_altcat_1 )
& ~ ( A @ k4_waybel34 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_waybel34) ).
thf(219,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k4_waybel34 @ l2_altcat_1 )
& ( A @ k4_waybel34 @ v2_yellow21 )
& ( A @ k4_waybel34 @ v12_altcat_1 )
& ( A @ k4_waybel34 @ v11_altcat_1 )
& ( A @ k4_waybel34 @ v6_altcat_1 )
& ( A @ k4_waybel34 @ v2_altcat_1 )
& ~ ( A @ k4_waybel34 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( A @ l1_altcat_1 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v11_functor0 ) ) )
& ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_functor0) ).
thf(76,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( A @ l1_altcat_1 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v11_functor0 ) ) )
& ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,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(103,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)],[19]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( ( ( B @ ( A @ ( C @ v14_functor0 ) ) )
& ( B @ ( A @ ( C @ v11_functor0 ) ) ) )
=> ( ( B @ ( A @ ( C @ v16_functor0 ) ) )
& ( B @ ( A @ ( C @ v12_functor0 ) ) )
& ( B @ ( A @ ( C @ v8_functor0 ) ) )
& ( B @ ( A @ ( C @ v6_functor0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_functor2) ).
thf(140,plain,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( ( ( B @ ( A @ ( C @ v14_functor0 ) ) )
& ( B @ ( A @ ( C @ v11_functor0 ) ) ) )
=> ( ( B @ ( A @ ( C @ v16_functor0 ) ) )
& ( B @ ( A @ ( C @ v12_functor0 ) ) )
& ( B @ ( A @ ( C @ v8_functor0 ) ) )
& ( B @ ( A @ ( C @ v6_functor0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( A @ l1_altcat_1 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v9_functor0 ) ) )
& ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_functor0) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( A @ l1_altcat_1 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v9_functor0 ) ) )
& ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(52,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_setfam_1) ).
thf(278,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(11,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(80,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)],[11]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v12_functor0 ) ) )
& ( B @ ( A @ ( C @ v9_functor0 ) ) )
& ( B @ ( A @ ( C @ v8_functor0 ) ) )
& ( B @ ( A @ ( C @ v6_functor0 ) ) )
& ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc9_functor0) ).
thf(167,plain,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v12_functor0 ) ) )
& ( B @ ( A @ ( C @ v9_functor0 ) ) )
& ( B @ ( A @ ( C @ v8_functor0 ) ) )
& ( B @ ( A @ ( C @ v6_functor0 ) ) )
& ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(34,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(162,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)],[34]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( B @ v1_altcat_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v8_functor0 ) ) )
& ( B @ ( A @ ( C @ v6_functor0 ) ) )
& ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc8_functor0) ).
thf(209,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( B @ v1_altcat_2 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v8_functor0 ) ) )
& ( B @ ( A @ ( C @ v6_functor0 ) ) )
& ( B @ ( A @ ( C @ l2_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(53,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k5_waybel34 @ l2_altcat_1 )
& ( A @ k5_waybel34 @ v2_yellow21 )
& ( A @ k5_waybel34 @ v12_altcat_1 )
& ( A @ k5_waybel34 @ v11_altcat_1 )
& ( A @ k5_waybel34 @ v6_altcat_1 )
& ( A @ k5_waybel34 @ v2_altcat_1 )
& ~ ( A @ k5_waybel34 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_waybel34) ).
thf(282,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k5_waybel34 @ l2_altcat_1 )
& ( A @ k5_waybel34 @ v2_yellow21 )
& ( A @ k5_waybel34 @ v12_altcat_1 )
& ( A @ k5_waybel34 @ v11_altcat_1 )
& ( A @ k5_waybel34 @ v6_altcat_1 )
& ( A @ k5_waybel34 @ v2_altcat_1 )
& ~ ( A @ k5_waybel34 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v12_functor0 ) ) )
& ( B @ ( A @ ( C @ v8_functor0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_functor2) ).
thf(150,plain,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v12_functor0 ) ) )
& ( B @ ( A @ ( C @ v8_functor0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(16,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(95,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)],[16]) ).
thf(31,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(154,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)],[31]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( A @ l1_altcat_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ l2_functor0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_functor0) ).
thf(72,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_altcat_1 )
& ( A @ l1_altcat_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ l2_functor0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_struct_0 )
& ( A @ l1_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ l1_functor0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_functor0) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_struct_0 )
& ( A @ l1_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ l1_functor0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(43,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(214,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( ( ( A @ v12_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_altcat_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_functor0) ).
thf(146,plain,
! [A: $i] :
( ( A @ l2_altcat_1 )
=> ( ( ( A @ v12_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_altcat_2 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(38,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(183,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(50,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_setfam_1) ).
thf(273,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(20,axiom,
? [A: $i] : ( A @ l2_altcat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_altcat_1) ).
thf(107,plain,
? [A: $i] : ( A @ l2_altcat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v16_functor0 ) ) )
=> ( B @ ( A @ ( C @ v6_functor0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_functor0) ).
thf(136,plain,
! [A: $i,B: $i] :
( ( ( B @ l2_altcat_1 )
& ( B @ v12_altcat_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ l2_altcat_1 )
& ( A @ v12_altcat_1 )
& ( A @ v2_altcat_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_functor0 ) ) )
=> ( ( B @ ( A @ ( C @ v16_functor0 ) ) )
=> ( B @ ( A @ ( C @ v6_functor0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(49,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ m2_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v16_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v9_functor0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_waybel34) ).
thf(268,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ( ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ m2_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v16_functor0 ) ) )
& ( A @ k5_waybel34 @ ( A @ k4_waybel34 @ ( A @ k6_waybel34 @ v9_functor0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(25,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(131,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)],[25]) ).
thf(4,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(62,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)],[4]) ).
thf(299,plain,
$false,
inference(e,[status(thm)],[217,56,174,157,60,109,129,64,291,258,111,138,101,88,189,228,179,84,293,243,74,70,275,197,97,86,159,187,113,219,76,103,140,66,278,80,167,162,209,282,150,95,154,72,82,214,146,183,273,107,136,268,131,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT362+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 : n019.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 21:21:03 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
% 0.84/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.41/1.24 % [INFO] Parsing done (262ms).
% 1.41/1.25 % [INFO] Running in sequential loop mode.
% 2.29/1.64 % [INFO] eprover registered as external prover.
% 2.29/1.65 % [INFO] Scanning for conjecture ...
% 2.49/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 112 axioms. Running axiom selection ...
% 2.69/1.87 % [INFO] Axiom selection finished. Selected 53 axioms (removed 59 axioms).
% 2.95/1.98 % [INFO] Problem is first-order (TPTP FOF).
% 2.95/1.99 % [INFO] Type checking passed.
% 2.95/1.99 % [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 ...
% 5.98/3.02 % External prover 'e' found a proof!
% 5.98/3.02 % [INFO] Killing All external provers ...
% 5.98/3.02 % Time passed: 2478ms (effective reasoning time: 1759ms)
% 5.98/3.02 % 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)>
% 5.98/3.02 % Axioms used in derivation (53): rc2_setfam_1, rc4_finset_1, dt_l2_altcat_1, t5_subset, rc3_setfam_1, rc9_functor0, cc2_setfam_1, cc1_functor2, rc3_finset_1, dt_l2_functor0, rc7_functor0, cc2_finset_1, cc4_functor0, symmetry_r2_functor0, dt_l1_altcat_1, cc2_yellow21, t1_subset, fc5_waybel34, existence_m2_functor0, rc8_functor0, t6_boole, d41_functor0, fc6_waybel34, existence_l2_functor0, existence_l2_altcat_1, cc2_functor0, t4_subset, t7_boole, cc1_funct_1, rc3_struct_0, cc1_yellow21, existence_m1_subset_1, cc6_functor0, existence_l1_altcat_1, rc3_functor0, dt_k4_waybel34, fc1_struct_0, rc1_yellow21, dt_k5_waybel34, dt_k6_waybel34, rc1_finset_1, cc4_functor2, cc1_finset_1, t8_boole, dt_m2_functor0, rc5_functor0, rc5_struct_0, t2_subset, cc5_functor2, existence_l1_struct_0, fc7_waybel34, antisymmetry_r2_hidden, existence_l1_functor0
% 5.98/3.02 % No. of inferences in proof: 110
% 5.98/3.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2478 ms resp. 1759 ms w/o parsing
% 6.43/3.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.72/3.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------