%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT033+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 : 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 06:55:29 AM UTC 2026
% Result : Theorem 4.96s 1.91s
% Output : Refutation 4.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 45
% Syntax : Number of formulae : 92 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 319 ( 22 equ; 0 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 985 ( 38 ~; 2 |; 145 &; 720 @)
% ( 2 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 2 con; 0-6 aty)
% Number of variables : 181 ( 0 ^; 161 !; 20 ?; 181 :)
% Comments :
%------------------------------------------------------------------------------
thf(v2_cat_1_decl,type,
v2_cat_1: $i > $o ).
thf(l1_cat_1_decl,type,
l1_cat_1: $i > $o ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(u1_cat_1_decl,type,
u1_cat_1: $i > $i ).
thf(m2_cat_1_decl,type,
m2_cat_1: $i > $i > $i > $o ).
thf(k20_ens_1_decl,type,
k20_ens_1: $i > $i > $i ).
thf(k1_yoneda_1_decl,type,
k1_yoneda_1: $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
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(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(g1_cat_1_decl,type,
g1_cat_1: $i > $i > $i > $i > $i > $i > $i ).
thf(v1_relat_1_decl,type,
v1_relat_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(k2_ens_1_decl,type,
k2_ens_1: $i > $i ).
thf(u2_cat_1_decl,type,
u2_cat_1: $i > $i ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(k17_ens_1_decl,type,
k17_ens_1: $i > $i ).
thf(u3_cat_1_decl,type,
u3_cat_1: $i > $i ).
thf(u6_cat_1_decl,type,
u6_cat_1: $i > $i ).
thf(u5_cat_1_decl,type,
u5_cat_1: $i > $i ).
thf(k12_ens_1_decl,type,
k12_ens_1: $i > $i ).
thf(u4_cat_1_decl,type,
u4_cat_1: $i > $i ).
thf(v1_cat_1_decl,type,
v1_cat_1: $i > $o ).
thf(32,axiom,
? [A: $i] : ( A @ l1_cat_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_cat_1) ).
thf(153,plain,
? [A: $i] : ( A @ l1_cat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(38,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k12_ens_1 @ l1_cat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_ens_1) ).
thf(174,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k12_ens_1 @ l1_cat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(57,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(106,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(8,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(65,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,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(53,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(23,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(124,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)],[23]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_cat_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( A @ k17_ens_1 @ k2_ens_1 @ ( A @ u2_cat_1 @ ( B @ ( A @ k20_ens_1 ) @ m2_relset_1 ) ) )
& ( A @ k17_ens_1 @ k2_ens_1 @ ( A @ u2_cat_1 @ ( B @ ( A @ k20_ens_1 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k20_ens_1 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k20_ens_1) ).
thf(128,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_cat_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( A @ k17_ens_1 @ k2_ens_1 @ ( A @ u2_cat_1 @ ( B @ ( A @ k20_ens_1 ) @ m2_relset_1 ) ) )
& ( A @ k17_ens_1 @ k2_ens_1 @ ( A @ u2_cat_1 @ ( B @ ( A @ k20_ens_1 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k20_ens_1 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(71,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( A @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( B @ ( C @ m1_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ g1_cat_1 ) ) ) ) ) )
= ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ g1_cat_1 ) ) ) ) ) ) )
=> ( ( F = L )
& ( E = K )
& ( D = J )
& ( C = I )
& ( B = H )
& ( A = G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_cat_1) ).
thf(80,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( A @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( B @ ( C @ m1_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ g1_cat_1 ) ) ) ) ) )
= ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ g1_cat_1 ) ) ) ) ) ) )
=> ( ( F = L )
& ( E = K )
& ( D = J )
& ( C = I )
& ( B = H )
& ( A = G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(112,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(7,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(63,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ( ( A @ u2_cat_1 @ ( A @ u2_cat_1 @ ( A @ u2_cat_1 @ k2_zfmisc_1 ) @ ( A @ u5_cat_1 @ m2_relset_1 ) ) )
& ( A @ u5_cat_1 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u5_cat_1) ).
thf(143,plain,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ( ( A @ u2_cat_1 @ ( A @ u2_cat_1 @ ( A @ u2_cat_1 @ k2_zfmisc_1 ) @ ( A @ u5_cat_1 @ m2_relset_1 ) ) )
& ( A @ u5_cat_1 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(15,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(99,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(34,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ u1_cat_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ k17_ens_1 @ r1_tarski ) )
=> ( A @ k12_ens_1 @ ( B @ ( C @ ( B @ k20_ens_1 ) @ m2_cat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_ens_1) ).
thf(158,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ u1_cat_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ k17_ens_1 @ r1_tarski ) )
=> ( A @ k12_ens_1 @ ( B @ ( C @ ( B @ k20_ens_1 ) @ m2_cat_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ u1_cat_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_yoneda_1 @ ( A @ ( B @ ( A @ k20_ens_1 ) @ m2_cat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_yoneda_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ u1_cat_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_yoneda_1 @ ( A @ ( B @ ( A @ k20_ens_1 ) @ m2_cat_1 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(47,plain,
~ ! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ u1_cat_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_yoneda_1 @ ( A @ ( B @ ( A @ k20_ens_1 ) @ m2_cat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(122,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ( ( A @ u2_cat_1 @ ( A @ u1_cat_1 @ ( A @ u6_cat_1 @ m2_relset_1 ) ) )
& ( A @ u2_cat_1 @ ( A @ u1_cat_1 @ ( A @ u6_cat_1 @ v1_funct_2 ) ) )
& ( A @ u6_cat_1 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u6_cat_1) ).
thf(138,plain,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ( ( A @ u2_cat_1 @ ( A @ u1_cat_1 @ ( A @ u6_cat_1 @ m2_relset_1 ) ) )
& ( A @ u2_cat_1 @ ( A @ u1_cat_1 @ ( A @ u6_cat_1 @ v1_funct_2 ) ) )
& ( A @ u6_cat_1 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(16,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(101,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)],[16]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( A @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( B @ ( C @ m1_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ g1_cat_1 ) ) ) ) ) @ l1_cat_1 )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ g1_cat_1 ) ) ) ) ) @ v1_cat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_cat_1) ).
thf(170,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( A @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( B @ ( C @ m1_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ g1_cat_1 ) ) ) ) ) @ l1_cat_1 )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ g1_cat_1 ) ) ) ) ) @ v1_cat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(20,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(115,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(21,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(120,plain,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ~ ( A @ u2_cat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(184,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)],[42]) ).
thf(18,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k2_ens_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ens_1) ).
thf(110,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k2_ens_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(29,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(147,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)],[29]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(61,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ( ( A @ u1_cat_1 @ ( A @ u2_cat_1 @ ( A @ u3_cat_1 @ m2_relset_1 ) ) )
& ( A @ u1_cat_1 @ ( A @ u2_cat_1 @ ( A @ u3_cat_1 @ v1_funct_2 ) ) )
& ( A @ u3_cat_1 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u3_cat_1) ).
thf(133,plain,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ( ( A @ u1_cat_1 @ ( A @ u2_cat_1 @ ( A @ u3_cat_1 @ m2_relset_1 ) ) )
& ( A @ u1_cat_1 @ ( A @ u2_cat_1 @ ( A @ u3_cat_1 @ v1_funct_2 ) ) )
& ( A @ u3_cat_1 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(12,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(74,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)],[12]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ( ( A @ u1_cat_1 @ ( A @ u2_cat_1 @ ( A @ u4_cat_1 @ m2_relset_1 ) ) )
& ( A @ u1_cat_1 @ ( A @ u2_cat_1 @ ( A @ u4_cat_1 @ v1_funct_2 ) ) )
& ( A @ u4_cat_1 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u4_cat_1) ).
thf(160,plain,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ( ( A @ u1_cat_1 @ ( A @ u2_cat_1 @ ( A @ u4_cat_1 @ m2_relset_1 ) ) )
& ( A @ u1_cat_1 @ ( A @ u2_cat_1 @ ( A @ u4_cat_1 @ v1_funct_2 ) ) )
& ( A @ u4_cat_1 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(10,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(70,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(44,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(192,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)],[44]) ).
thf(36,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(165,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)],[36]) ).
thf(40,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(180,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)],[40]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(149,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(39,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k12_ens_1 @ v2_cat_1 )
& ( A @ k12_ens_1 @ v1_cat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_ens_1) ).
thf(176,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k12_ens_1 @ v2_cat_1 )
& ( A @ k12_ens_1 @ v1_cat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(5,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(59,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(33,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( A @ k1_yoneda_1 )
= ( A @ k17_ens_1 @ k12_ens_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_yoneda_1) ).
thf(155,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( A @ k1_yoneda_1 )
= ( A @ k17_ens_1 @ k12_ens_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(46,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( A @ k1_yoneda_1 @ l1_cat_1 )
& ( A @ k1_yoneda_1 @ v2_cat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yoneda_1) ).
thf(198,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( A @ k1_yoneda_1 @ l1_cat_1 )
& ( A @ k1_yoneda_1 @ v2_cat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(67,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ~ ( A @ u1_cat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_cat_1) ).
thf(182,plain,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ~ ( A @ u1_cat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(31,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(151,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)],[31]) ).
thf(43,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ~ ( A @ k17_ens_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_ens_1) ).
thf(190,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ~ ( A @ k17_ens_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(24,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(126,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)],[24]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ( ( A @ v1_cat_1 )
=> ( A
= ( A @ u6_cat_1 @ ( A @ u5_cat_1 @ ( A @ u4_cat_1 @ ( A @ u3_cat_1 @ ( A @ u2_cat_1 @ ( A @ u1_cat_1 @ g1_cat_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_cat_1) ).
thf(195,plain,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ( ( A @ v1_cat_1 )
=> ( A
= ( A @ u6_cat_1 @ ( A @ u5_cat_1 @ ( A @ u4_cat_1 @ ( A @ u3_cat_1 @ ( A @ u2_cat_1 @ ( A @ u1_cat_1 @ g1_cat_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(14,axiom,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(94,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(306,plain,
$false,
inference(e,[status(thm)],[153,174,57,106,65,53,124,128,71,80,112,63,143,99,158,47,122,138,101,170,115,120,184,110,147,61,133,74,160,70,192,165,180,149,176,59,155,198,67,182,151,190,126,195,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT033+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
% 0.13/0.40 % Computer : n019.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 22:58:50 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 0.59/0.69 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.99/0.81 % [INFO] Parsing done (120ms).
% 0.99/0.82 % [INFO] Running in sequential loop mode.
% 1.35/1.02 % [INFO] eprover registered as external prover.
% 1.35/1.02 % [INFO] Scanning for conjecture ...
% 1.68/1.08 % [INFO] Found a conjecture (or negated_conjecture) and 52 axioms. Running axiom selection ...
% 1.68/1.12 % [INFO] Axiom selection finished. Selected 44 axioms (removed 8 axioms).
% 1.95/1.18 % [INFO] Problem is first-order (TPTP FOF).
% 1.95/1.19 % [INFO] Type checking passed.
% 1.95/1.19 % [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 ...
% 4.96/1.91 % External prover 'e' found a proof!
% 4.96/1.91 % [INFO] Killing All external provers ...
% 4.96/1.91 % Time passed: 1420ms (effective reasoning time: 1088ms)
% 4.96/1.91 % 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)>
% 4.96/1.91 % Axioms used in derivation (44): redefinition_m2_relset_1, existence_l1_cat_1, dt_m2_relset_1, rc1_funct_1, d1_yoneda_1, t5_subset, existence_m2_cat_1, rc2_funct_1, existence_m2_relset_1, dt_u4_cat_1, reflexivity_r1_tarski, dt_u2_cat_1, t2_subset, fc2_ens_1, abstractness_v1_cat_1, rc2_xboole_0, fc1_xboole_0, t1_subset, fc4_ens_1, dt_m2_cat_1, rc3_funct_1, t49_ens_1, fc5_ens_1, dt_g1_cat_1, dt_u5_cat_1, t6_boole, free_g1_cat_1, existence_m1_relset_1, dt_k20_ens_1, t4_subset, dt_u6_cat_1, dt_u3_cat_1, t7_boole, cc1_funct_1, cc2_funct_1, t3_subset, cc1_relset_1, existence_m1_subset_1, dt_u1_cat_1, dt_k1_yoneda_1, t8_boole, rc1_xboole_0, dt_k12_ens_1, antisymmetry_r2_hidden
% 4.96/1.91 % No. of inferences in proof: 92
% 4.96/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1420 ms resp. 1088 ms w/o parsing
% 4.96/1.96 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.96/1.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------