%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT026+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n010.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 06:55:26 AM UTC 2026
% Result : Theorem 7.43s 3.18s
% Output : Refutation 7.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 42
% Syntax : Number of formulae : 86 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 368 ( 14 equ; 0 cnn)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 1174 ( 28 ~; 2 |; 175 &; 864 @)
% ( 1 <=>; 104 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 2 con; 0-5 aty)
% Number of variables : 223 ( 0 ^; 205 !; 18 ?; 223 :)
% Comments :
%------------------------------------------------------------------------------
thf(v2_cat_1_decl,type,
v2_cat_1: $i > $o ).
thf(l1_cat_1_decl,type,
l1_cat_1: $i > $o ).
thf(m2_cat_1_decl,type,
m2_cat_1: $i > $i > $i > $o ).
thf(k11_cat_2_decl,type,
k11_cat_2: $i > $i > $i ).
thf(r2_nattra_1_decl,type,
r2_nattra_1: $i > $i > $i > $i > $o ).
thf(k11_isocat_2_decl,type,
k11_isocat_2: $i > $i > $i > $i > $i ).
thf(k12_isocat_2_decl,type,
k12_isocat_2: $i > $i > $i > $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(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k5_relat_1_decl,type,
k5_relat_1: $i > $i > $i ).
thf(u2_cat_1_decl,type,
u2_cat_1: $i > $i ).
thf(k17_cat_2_decl,type,
k17_cat_2: $i > $i > $i ).
thf(k2_isocat_1_decl,type,
k2_isocat_1: $i > $i > $i > $i > $i > $i ).
thf(k8_isocat_2_decl,type,
k8_isocat_2: $i > $i > $i ).
thf(k9_isocat_2_decl,type,
k9_isocat_2: $i > $i > $i ).
thf(k16_cat_2_decl,type,
k16_cat_2: $i > $i > $i ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(3,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(56,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_cat_1 )
& ( C @ v2_cat_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( D @ m2_cat_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) )
= ( C @ ( B @ k8_isocat_2 ) @ ( D @ ( B @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k2_isocat_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_isocat_2) ).
thf(121,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_cat_1 )
& ( C @ v2_cat_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( D @ m2_cat_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) )
= ( C @ ( B @ k8_isocat_2 ) @ ( D @ ( B @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k2_isocat_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(20,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(102,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(70,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)],[8]) ).
thf(37,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_cat_1 )
& ( C @ v2_cat_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( D @ m2_cat_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) )
= ( C @ ( B @ k9_isocat_2 ) @ ( D @ ( C @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k2_isocat_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_isocat_2) ).
thf(141,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_cat_1 )
& ( C @ v2_cat_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( D @ m2_cat_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) )
= ( C @ ( B @ k9_isocat_2 ) @ ( D @ ( C @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k2_isocat_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(104,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(4,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(58,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)],[4]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(62,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)],[5]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( B @ ( A @ k11_cat_2 ) @ ( B @ ( A @ k16_cat_2 ) @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_cat_2) ).
thf(152,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( B @ ( A @ k11_cat_2 ) @ ( B @ ( A @ k16_cat_2 ) @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(78,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)],[12]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( B @ ( A @ k9_isocat_2 ) )
= ( B @ ( A @ k17_cat_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_isocat_2) ).
thf(147,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( B @ ( A @ k9_isocat_2 ) )
= ( B @ ( A @ k17_cat_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( B @ ( A @ k11_cat_2 ) @ ( B @ ( A @ k8_isocat_2 ) @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_isocat_2) ).
thf(132,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( B @ ( A @ k11_cat_2 ) @ ( B @ ( A @ k8_isocat_2 ) @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(89,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)],[15]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( B @ ( B @ ( A @ k11_cat_2 ) @ ( B @ ( A @ k17_cat_2 ) @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_cat_2) ).
thf(116,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( B @ ( B @ ( A @ k11_cat_2 ) @ ( B @ ( A @ k17_cat_2 ) @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(74,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(109,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m2_cat_1 ) ) )
& ( B @ ( A @ ( D @ m2_cat_1 ) ) )
& ( C @ l1_cat_1 )
& ( C @ v2_cat_1 )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_isocat_1) ).
thf(124,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m2_cat_1 ) ) )
& ( B @ ( A @ ( D @ m2_cat_1 ) ) )
& ( C @ l1_cat_1 )
& ( C @ v2_cat_1 )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_cat_1) ).
thf(134,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( D @ m2_cat_1 ) ) )
& ( C @ l1_cat_1 )
& ( C @ v2_cat_1 )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( C @ ( A @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_isocat_2) ).
thf(128,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( D @ m2_cat_1 ) ) )
& ( C @ l1_cat_1 )
& ( C @ v2_cat_1 )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( C @ ( A @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_cat_1 )
& ( C @ v2_cat_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ ( A @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_isocat_2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_cat_1 )
& ( C @ v2_cat_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ ( A @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(44,plain,
~ ! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_cat_1 )
& ( C @ v2_cat_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ ( A @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m2_cat_1 ) ) )
& ( B @ ( A @ ( D @ m2_cat_1 ) ) )
& ( C @ l1_cat_1 )
& ( C @ v2_cat_1 )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_isocat_1) ).
thf(118,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m2_cat_1 ) ) )
& ( B @ ( A @ ( D @ m2_cat_1 ) ) )
& ( C @ l1_cat_1 )
& ( C @ v2_cat_1 )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( B @ ( A @ k8_isocat_2 ) )
= ( B @ ( A @ k16_cat_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_isocat_2) ).
thf(144,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( B @ ( A @ k8_isocat_2 ) )
= ( B @ ( A @ k16_cat_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( B @ ( A @ k11_cat_2 ) @ l1_cat_1 )
& ( B @ ( A @ k11_cat_2 ) @ v2_cat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_cat_2) ).
thf(159,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( B @ ( A @ k11_cat_2 ) @ l1_cat_1 )
& ( B @ ( A @ k11_cat_2 ) @ v2_cat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(11,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(76,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(98,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(91,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(66,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)],[7]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( D @ m2_cat_1 ) ) )
& ( C @ l1_cat_1 )
& ( C @ v2_cat_1 )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_isocat_2) ).
thf(130,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( D @ m2_cat_1 ) ) )
& ( C @ l1_cat_1 )
& ( C @ v2_cat_1 )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(80,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)],[13]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( B @ ( B @ ( A @ k11_cat_2 ) @ ( B @ ( A @ k9_isocat_2 ) @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_isocat_2) ).
thf(150,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( B @ ( B @ ( A @ k11_cat_2 ) @ ( B @ ( A @ k9_isocat_2 ) @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(95,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ( ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ ( C @ m2_relset_1 ) ) )
& ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_cat_1) ).
thf(154,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ( ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ ( C @ m2_relset_1 ) ) )
& ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(72,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)],[9]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ~ ( A @ u2_cat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_cat_1) ).
thf(114,plain,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ~ ( A @ u2_cat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(36,axiom,
? [A: $i] : ( A @ l1_cat_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_cat_1) ).
thf(139,plain,
? [A: $i] : ( A @ l1_cat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(22,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(107,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(17,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(94,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(30,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_cat_1 )
& ( C @ v2_cat_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( C @ ( B @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( C @ ( B @ ( G @ m2_cat_1 ) ) )
=> ( ( ( G @ ( F @ ( C @ ( B @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
=> ( G @ ( E @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( C @ ( A @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_isocat_1) ).
thf(126,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_cat_1 )
& ( C @ v2_cat_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( C @ ( B @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( C @ ( B @ ( G @ m2_cat_1 ) ) )
=> ( ( ( G @ ( F @ ( C @ ( B @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
=> ( G @ ( E @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( C @ ( A @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
& ( B @ ( A @ ( C @ m2_cat_1 ) ) )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( C @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r2_nattra_1) ).
thf(136,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
& ( B @ ( A @ ( C @ m2_cat_1 ) ) )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( C @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(24,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(111,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
<=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(83,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)],[14]) ).
thf(227,plain,
$false,
inference(e,[status(thm)],[56,121,102,70,141,64,104,58,62,152,78,147,132,89,116,74,109,124,134,128,44,118,144,159,76,98,91,66,130,80,150,95,154,72,114,139,107,94,126,136,111,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT026+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.16/0.41 % Computer : n010.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 22:53:30 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.92/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.45/1.25 % [INFO] Parsing done (244ms).
% 1.45/1.26 % [INFO] Running in sequential loop mode.
% 2.21/1.64 % [INFO] eprover registered as external prover.
% 2.21/1.64 % [INFO] Scanning for conjecture ...
% 2.53/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 49 axioms. Running axiom selection ...
% 2.53/1.77 % [INFO] Axiom selection finished. Selected 41 axioms (removed 8 axioms).
% 2.82/1.82 % [INFO] Problem is first-order (TPTP FOF).
% 2.82/1.84 % [INFO] Type checking passed.
% 2.82/1.85 % [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 ...
% 7.43/3.18 % External prover 'e' found a proof!
% 7.43/3.18 % [INFO] Killing All external provers ...
% 7.43/3.18 % Time passed: 2627ms (effective reasoning time: 1911ms)
% 7.43/3.18 % 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)>
% 7.43/3.18 % Axioms used in derivation (41): existence_l1_cat_1, dt_k12_isocat_2, t5_subset, existence_m1_relset_1, t4_subset, d7_isocat_2, existence_m2_relset_1, dt_u2_cat_1, t2_subset, dt_k11_isocat_2, redefinition_m2_relset_1, dt_k16_cat_2, fc1_xboole_0, t27_isocat_1, t1_subset, fc4_subset_1, redefinition_k9_isocat_2, dt_m2_cat_1, dt_m2_relset_1, d8_isocat_2, dt_k2_isocat_1, t6_boole, rc2_subset_1, existence_m2_cat_1, redefinition_k2_isocat_1, t7_boole, fc1_subset_1, rc1_subset_1, reflexivity_r2_nattra_1, cc1_relset_1, existence_m1_subset_1, dt_k11_cat_2, redefinition_k8_isocat_2, dt_k5_relat_1, t8_boole, rc1_xboole_0, rc2_xboole_0, dt_k9_isocat_2, dt_k8_isocat_2, dt_k17_cat_2, antisymmetry_r2_hidden
% 7.43/3.18 % No. of inferences in proof: 86
% 7.43/3.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2627 ms resp. 1911 ms w/o parsing
% 7.71/3.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.71/3.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------