%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT032+4 : 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 : n012.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 06:55:28 AM UTC 2026
% Result : Theorem 54.68s 21.91s
% Output : Refutation 55.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 188
% Syntax : Number of formulae : 378 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 2720 ( 102 equ; 0 cnn)
% Maximal formula atoms : 31 ( 7 avg)
% Number of connectives : 11067 ( 62 ~; 2 |;1259 &;8663 @)
% ( 20 <=>;1061 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 68 usr; 1 con; 0-9 aty)
% Number of variables : 1454 ( 0 ^;1378 !; 76 ?;1454 :)
% Comments :
%------------------------------------------------------------------------------
thf(v2_cat_1_decl,type,
v2_cat_1: $i > $o ).
thf(l1_cat_1_decl,type,
l1_cat_1: $i > $o ).
thf(r1_isocat_1_decl,type,
r1_isocat_1: $i > $i > $o ).
thf(k12_nattra_1_decl,type,
k12_nattra_1: $i > $i > $i ).
thf(k11_cat_2_decl,type,
k11_cat_2: $i > $i > $i ).
thf(m2_cat_1_decl,type,
m2_cat_1: $i > $i > $i > $o ).
thf(r3_nattra_1_decl,type,
r3_nattra_1: $i > $i > $i > $i > $o ).
thf(r2_nattra_1_decl,type,
r2_nattra_1: $i > $i > $i > $i > $o ).
thf(m2_nattra_1_decl,type,
m2_nattra_1: $i > $i > $i > $i > $i > $o ).
thf(v1_nattra_1_decl,type,
v1_nattra_1: $i > $i > $i > $i > $i > $o ).
thf(m3_cat_2_decl,type,
m3_cat_2: $i > $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(k8_cat_1_decl,type,
k8_cat_1: $i > $i > $i ).
thf(m1_nattra_1_decl,type,
m1_nattra_1: $i > $i > $i > $i > $i > $o ).
thf(k15_isocat_2_decl,type,
k15_isocat_2: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k10_isocat_2_decl,type,
k10_isocat_2: $i > $i > $i > $i > $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(u2_cat_1_decl,type,
u2_cat_1: $i > $i ).
thf(k4_cat_1_decl,type,
k4_cat_1: $i > $i > $i > $i ).
thf(v1_cat_1_decl,type,
v1_cat_1: $i > $o ).
thf(r2_isocat_1_decl,type,
r2_isocat_1: $i > $i > $o ).
thf(k2_isocat_1_decl,type,
k2_isocat_1: $i > $i > $i > $i > $i > $i ).
thf(k1_isocat_1_decl,type,
k1_isocat_1: $i > $i ).
thf(m4_nattra_1_decl,type,
m4_nattra_1: $i > $i > $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k4_tarski_decl,type,
k4_tarski: $i > $i > $i ).
thf(r4_nattra_1_decl,type,
r4_nattra_1: $i > $i > $i > $i > $i > $i > $o ).
thf(k5_isocat_2_decl,type,
k5_isocat_2: $i > $i > $i > $i > $i ).
thf(k6_isocat_2_decl,type,
k6_isocat_2: $i > $i > $i > $i > $i > $i > $i ).
thf(k8_nattra_1_decl,type,
k8_nattra_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k6_isocat_1_decl,type,
k6_isocat_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k7_nattra_1_decl,type,
k7_nattra_1: $i > $i > $i > $i ).
thf(k11_isocat_2_decl,type,
k11_isocat_2: $i > $i > $i > $i > $i ).
thf(k13_isocat_2_decl,type,
k13_isocat_2: $i > $i > $i > $i > $i > $i > $i ).
thf(k12_isocat_2_decl,type,
k12_isocat_2: $i > $i > $i > $i > $i ).
thf(k14_isocat_2_decl,type,
k14_isocat_2: $i > $i > $i > $i > $i > $i > $i ).
thf(v2_nattra_1_decl,type,
v2_nattra_1: $i > $o ).
thf(m3_nattra_1_decl,type,
m3_nattra_1: $i > $i > $i > $i > $i > $o ).
thf(r1_nattra_1_decl,type,
r1_nattra_1: $i > $i > $i > $i > $o ).
thf(k16_isocat_2_decl,type,
k16_isocat_2: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(m1_isocat_1_decl,type,
m1_isocat_1: $i > $i > $i > $o ).
thf(v8_cat_1_decl,type,
v8_cat_1: $i > $i > $i > $o ).
thf(k3_isocat_1_decl,type,
k3_isocat_1: $i > $i > $i > $i ).
thf(k11_nattra_1_decl,type,
k11_nattra_1: $i > $i > $i ).
thf(k17_isocat_2_decl,type,
k17_isocat_2: $i > $i > $i > $i ).
thf(k1_funct_1_decl,type,
k1_funct_1: $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(m1_cat_2_decl,type,
m1_cat_2: $i > $i > $i > $o ).
thf(m2_cat_2_decl,type,
m2_cat_2: $i > $i > $i > $i > $o ).
thf(k13_nattra_1_decl,type,
k13_nattra_1: $i > $i ).
thf(k13_funct_3_decl,type,
k13_funct_3: $i > $i > $i ).
thf(k10_nattra_1_decl,type,
k10_nattra_1: $i > $i > $i > $i > $i > $i ).
thf(k15_cat_1_decl,type,
k15_cat_1: $i > $i ).
thf(k18_cat_2_decl,type,
k18_cat_2: $i > $i > $i > $i > $i > $i ).
thf(k5_cat_2_decl,type,
k5_cat_2: $i > $i > $i ).
thf(k17_ens_1_decl,type,
k17_ens_1: $i > $i ).
thf(k19_cat_2_decl,type,
k19_cat_2: $i > $i > $i > $i > $i > $i > $i ).
thf(k15_funct_3_decl,type,
k15_funct_3: $i > $i > $i ).
thf(k7_isocat_2_decl,type,
k7_isocat_2: $i > $i > $i > $i ).
thf(k7_commacat_decl,type,
k7_commacat: $i > $i > $i > $i > $i > $i ).
thf(k8_cat_2_decl,type,
k8_cat_2: $i > $i > $i ).
thf(k17_cat_2_decl,type,
k17_cat_2: $i > $i > $i ).
thf(k7_cat_2_decl,type,
k7_cat_2: $i > $i > $i ).
thf(m1_oppcat_1_decl,type,
m1_oppcat_1: $i > $i > $i > $o ).
thf(k16_cat_2_decl,type,
k16_cat_2: $i > $i > $i ).
thf(a_1_3_ens_1_decl,type,
a_1_3_ens_1: $i > $i ).
thf(113,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 @ k12_nattra_1 ) @ ( A @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k11_cat_2 ) @ k12_nattra_1 ) @ ( D @ m2_cat_1 ) ) )
=> ( ( D
= ( C @ ( B @ ( A @ k7_isocat_2 ) ) ) )
<=> ! [E: $i] :
( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( F @ m2_cat_1 ) ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( A @ k11_cat_2 ) @ r2_nattra_1 ) ) ) )
=> ! [G: $i] :
( ( F @ ( E @ ( C @ ( B @ ( A @ k11_cat_2 ) @ ( G @ m2_nattra_1 ) ) ) ) )
=> ( ( G @ ( F @ ( E @ k4_tarski ) @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ k4_tarski ) @ k4_tarski ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_isocat_2) ).
thf(629,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 @ k12_nattra_1 ) @ ( A @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k11_cat_2 ) @ k12_nattra_1 ) @ ( D @ m2_cat_1 ) ) )
=> ( ( ! [E: $i] :
( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( F @ m2_cat_1 ) ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( A @ k11_cat_2 ) @ r2_nattra_1 ) ) ) )
=> ! [G: $i] :
( ( F @ ( E @ ( C @ ( B @ ( A @ k11_cat_2 ) @ ( G @ m2_nattra_1 ) ) ) ) )
=> ( ( G @ ( F @ ( E @ k4_tarski ) @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ k4_tarski ) @ k4_tarski ) ) ) ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k7_isocat_2 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k7_isocat_2 ) ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( F @ m2_cat_1 ) ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( A @ k11_cat_2 ) @ r2_nattra_1 ) ) ) )
=> ! [G: $i] :
( ( F @ ( E @ ( C @ ( B @ ( A @ k11_cat_2 ) @ ( G @ m2_nattra_1 ) ) ) ) )
=> ( ( G @ ( F @ ( E @ k4_tarski ) @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ k4_tarski ) @ k4_tarski ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(45,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( ( E @ ( D @ ( B @ ( A @ r3_nattra_1 ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r3_nattra_1 ) ) ) ) )
=> ( E @ ( C @ ( B @ ( A @ r3_nattra_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_nattra_1) ).
thf(365,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( ( E @ ( D @ ( B @ ( A @ r3_nattra_1 ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r3_nattra_1 ) ) ) ) )
=> ( E @ ( C @ ( B @ ( A @ r3_nattra_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) )
& ( 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 @ ( D @ ( B @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_nattra_1 ) ) ) ) @ m2_nattra_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_nattra_1) ).
thf(555,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) )
& ( 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 @ ( D @ ( B @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_nattra_1 ) ) ) ) @ m2_nattra_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(41,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 @ ( A @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( C @ ( A @ ( G @ m2_cat_1 ) ) )
=> ( ( ( G @ ( F @ ( C @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
=> ! [H: $i] :
( ( E @ ( D @ ( B @ ( A @ ( H @ m2_nattra_1 ) ) ) ) )
=> ! [I: $i] :
( ( G @ ( F @ ( C @ ( A @ ( I @ m2_nattra_1 ) ) ) ) )
=> ( ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_isocat_2 ) ) ) ) ) ) ) ) )
= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k15_isocat_2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_isocat_2) ).
thf(352,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 @ ( A @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( C @ ( A @ ( G @ m2_cat_1 ) ) )
=> ( ( ( G @ ( F @ ( C @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
=> ! [H: $i] :
( ( E @ ( D @ ( B @ ( A @ ( H @ m2_nattra_1 ) ) ) ) )
=> ! [I: $i] :
( ( G @ ( F @ ( C @ ( A @ ( I @ m2_nattra_1 ) ) ) ) )
=> ( ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_isocat_2 ) ) ) ) ) ) ) ) )
= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k15_isocat_2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(63,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 @ r3_nattra_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_nattra_1) ).
thf(440,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 @ r3_nattra_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m3_cat_2 ) )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( B @ ( B @ ( A @ k8_cat_2 ) @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_cat_2) ).
thf(677,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m3_cat_2 ) )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( B @ ( B @ ( A @ k8_cat_2 ) @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(141,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(730,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)],[141]) ).
thf(23,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( ( E @ ( D @ ( B @ ( A @ r2_nattra_1 ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
=> ( E @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_nattra_1) ).
thf(276,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( ( E @ ( D @ ( B @ ( A @ r2_nattra_1 ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
=> ( E @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(49,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 @ ( A @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( C @ ( A @ ( G @ m2_cat_1 ) ) )
=> ( ( ( G @ ( F @ ( C @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
=> ! [H: $i] :
( ( E @ ( D @ ( B @ ( A @ ( H @ m2_nattra_1 ) ) ) ) )
=> ! [I: $i] :
( ( G @ ( F @ ( C @ ( A @ ( I @ m2_nattra_1 ) ) ) ) )
=> ( ( I @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_isocat_2 ) ) ) ) ) ) ) ) @ ( G @ ( E @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( H @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_isocat_2 ) ) ) ) ) ) ) ) @ ( G @ ( E @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_isocat_2) ).
thf(384,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 @ ( A @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( C @ ( A @ ( G @ m2_cat_1 ) ) )
=> ( ( ( G @ ( F @ ( C @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
=> ! [H: $i] :
( ( E @ ( D @ ( B @ ( A @ ( H @ m2_nattra_1 ) ) ) ) )
=> ! [I: $i] :
( ( G @ ( F @ ( C @ ( A @ ( I @ m2_nattra_1 ) ) ) ) )
=> ( ( I @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_isocat_2 ) ) ) ) ) ) ) ) @ ( G @ ( E @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( H @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_isocat_2 ) ) ) ) ) ) ) ) @ ( G @ ( E @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( G @ ( F @ ( C @ ( A @ ( I @ m2_nattra_1 ) ) ) ) )
& ( E @ ( D @ ( B @ ( A @ ( H @ m2_nattra_1 ) ) ) ) )
& ( C @ ( A @ ( G @ m2_cat_1 ) ) )
& ( C @ ( A @ ( F @ m2_cat_1 ) ) )
& ( B @ ( A @ ( 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 ) )
=> ( G @ ( E @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_isocat_2 ) ) ) ) ) ) ) ) @ m2_nattra_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_isocat_2) ).
thf(533,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( G @ ( F @ ( C @ ( A @ ( I @ m2_nattra_1 ) ) ) ) )
& ( E @ ( D @ ( B @ ( A @ ( H @ m2_nattra_1 ) ) ) ) )
& ( C @ ( A @ ( G @ m2_cat_1 ) ) )
& ( C @ ( A @ ( F @ m2_cat_1 ) ) )
& ( B @ ( A @ ( 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 ) )
=> ( G @ ( E @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_isocat_2 ) ) ) ) ) ) ) ) @ m2_nattra_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(90,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 @ m1_cat_2 ) ) )
=> ~ ( C @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_cat_2) ).
thf(550,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 @ m1_cat_2 ) ) )
=> ~ ( C @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(72,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 @ ( A @ k11_cat_2 ) @ ( D @ m2_cat_1 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ k7_nattra_1 ) ) @ ( D @ ( D @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( C @ ( B @ k12_nattra_1 ) @ ( A @ k7_nattra_1 ) ) @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_isocat_2) ).
thf(500,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 @ ( A @ k11_cat_2 ) @ ( D @ m2_cat_1 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ k7_nattra_1 ) ) @ ( D @ ( D @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( C @ ( B @ k12_nattra_1 ) @ ( A @ k7_nattra_1 ) ) @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_cat_2 ) ) )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m2_cat_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_cat_2) ).
thf(797,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_cat_2 ) ) )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m2_cat_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ ( F @ m2_nattra_1 ) ) ) ) )
& ( C @ ( B @ ( A @ k11_cat_2 ) @ ( E @ m2_cat_1 ) ) )
& ( C @ ( B @ ( A @ k11_cat_2 ) @ ( 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 @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( C @ ( B @ k12_nattra_1 ) @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ m2_nattra_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_isocat_2) ).
thf(829,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ ( F @ m2_nattra_1 ) ) ) ) )
& ( C @ ( B @ ( A @ k11_cat_2 ) @ ( E @ m2_cat_1 ) ) )
& ( C @ ( B @ ( A @ k11_cat_2 ) @ ( 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 @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( C @ ( B @ k12_nattra_1 ) @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ m2_nattra_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(134,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( ( B @ ( A @ k11_cat_2 ) @ k13_nattra_1 )
= ( B @ k13_nattra_1 @ ( A @ k13_nattra_1 @ k11_cat_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_nattra_1) ).
thf(709,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( ( B @ ( A @ k11_cat_2 ) @ k13_nattra_1 )
= ( B @ k13_nattra_1 @ ( A @ k13_nattra_1 @ k11_cat_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(417,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
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 @ k12_nattra_1 ) @ ( A @ ( D @ m2_cat_1 ) ) )
=> ? [E: $i] :
( ( E @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u2_cat_1 @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( C @ ( B @ ( A @ k11_cat_2 ) @ ( E @ m2_cat_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_isocat_2) ).
thf(288,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 @ k12_nattra_1 ) @ ( A @ ( D @ m2_cat_1 ) ) )
=> ? [E: $i] :
( ( E @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u2_cat_1 @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( C @ ( B @ ( A @ k11_cat_2 ) @ ( E @ m2_cat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(98,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ( ( B @ ( A @ ( C @ v8_cat_1 ) ) )
=> ( A @ ( B @ ( C @ ( B @ ( A @ k3_isocat_1 ) ) @ v8_cat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_isocat_1) ).
thf(570,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ( ( B @ ( A @ ( C @ v8_cat_1 ) ) )
=> ( A @ ( B @ ( C @ ( B @ ( A @ k3_isocat_1 ) ) @ v8_cat_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(165,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 ) )
=> ( C @ ( B @ k12_nattra_1 ) @ ( A @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k11_cat_2 ) @ k12_nattra_1 ) @ r1_isocat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_isocat_2) ).
thf(785,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 ) )
=> ( C @ ( B @ k12_nattra_1 ) @ ( A @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k11_cat_2 ) @ k12_nattra_1 ) @ r1_isocat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k8_cat_1 ) @ u2_cat_1 @ ( C @ m1_subset_1 ) )
=> ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_cat_1) ).
thf(504,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k8_cat_1 ) @ u2_cat_1 @ ( C @ m1_subset_1 ) )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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 @ k12_nattra_1 ) @ ( B @ ( A @ k12_nattra_1 ) @ k11_cat_2 ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k17_isocat_2 ) ) @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_isocat_2) ).
thf(770,plain,
! [A: $i,B: $i,C: $i] :
( ( ( 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 @ k12_nattra_1 ) @ ( B @ ( A @ k12_nattra_1 ) @ k11_cat_2 ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k17_isocat_2 ) ) @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(17,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 @ ( A @ k11_cat_2 ) @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( E @ m2_cat_1 ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u2_cat_1 @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) )
=> ( E @ ( D @ ( C @ u2_cat_1 @ ( B @ ( A @ k11_cat_2 ) @ u2_cat_1 @ ( C @ u2_cat_1 @ ( B @ ( A @ k11_cat_2 ) @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_isocat_2) ).
thf(261,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 @ ( A @ k11_cat_2 ) @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( E @ m2_cat_1 ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u2_cat_1 @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) )
=> ( E @ ( D @ ( C @ u2_cat_1 @ ( B @ ( A @ k11_cat_2 ) @ u2_cat_1 @ ( C @ u2_cat_1 @ ( B @ ( A @ k11_cat_2 ) @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u2_cat_1 @ ( C @ m1_subset_1 ) )
& ( A @ u2_cat_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_cat_1 ) )
=> ( A @ u2_cat_1 @ ( C @ ( B @ ( A @ k4_cat_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_cat_1) ).
thf(216,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u2_cat_1 @ ( C @ m1_subset_1 ) )
& ( A @ u2_cat_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_cat_1 ) )
=> ( A @ u2_cat_1 @ ( C @ ( B @ ( A @ k4_cat_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(69,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( D @ ( C @ ( B @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
=> ! [G: $i] :
( ( E @ ( D @ ( B @ ( A @ ( G @ m2_nattra_1 ) ) ) ) )
=> ! [H: $i] :
( ( B @ ( A @ k12_nattra_1 ) @ u2_cat_1 @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( B @ ( A @ k12_nattra_1 ) @ u2_cat_1 @ ( I @ m1_subset_1 ) )
=> ( ( ( I
= ( G @ ( E @ ( D @ k4_tarski ) @ k4_tarski ) ) )
& ( H
= ( F @ ( D @ ( C @ k4_tarski ) @ k4_tarski ) ) ) )
=> ( ( I @ ( H @ ( B @ ( A @ k12_nattra_1 ) @ k4_cat_1 ) ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ ( E @ ( C @ k4_tarski ) @ k4_tarski ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_nattra_1) ).
thf(492,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( D @ ( C @ ( B @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
=> ! [G: $i] :
( ( E @ ( D @ ( B @ ( A @ ( G @ m2_nattra_1 ) ) ) ) )
=> ! [H: $i] :
( ( B @ ( A @ k12_nattra_1 ) @ u2_cat_1 @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( B @ ( A @ k12_nattra_1 ) @ u2_cat_1 @ ( I @ m1_subset_1 ) )
=> ( ( ( I
= ( G @ ( E @ ( D @ k4_tarski ) @ k4_tarski ) ) )
& ( H
= ( F @ ( D @ ( C @ k4_tarski ) @ k4_tarski ) ) ) )
=> ( ( I @ ( H @ ( B @ ( A @ k12_nattra_1 ) @ k4_cat_1 ) ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ ( E @ ( C @ k4_tarski ) @ k4_tarski ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(153,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(756,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)],[153]) ).
thf(167,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(789,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)],[167]) ).
thf(64,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] :
( ( C @ ( B @ ( E @ m2_cat_1 ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( C @ ( A @ k7_nattra_1 ) ) @ ( E @ ( D @ ( B @ ( A @ k7_nattra_1 ) ) @ ( D @ ( D @ ( C @ ( B @ ( A @ k6_isocat_1 ) ) ) ) ) ) @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_isocat_1) ).
thf(443,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] :
( ( C @ ( B @ ( E @ m2_cat_1 ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( C @ ( A @ k7_nattra_1 ) ) @ ( E @ ( D @ ( B @ ( A @ k7_nattra_1 ) ) @ ( D @ ( D @ ( C @ ( B @ ( A @ k6_isocat_1 ) ) ) ) ) ) @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(15,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m4_nattra_1 ) ) )
<=> ! [D: $i] :
~ ( ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( B @ ( A @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( F @ ( E @ ( B @ ( A @ ( G @ m2_nattra_1 ) ) ) ) )
=> ~ ( ( F @ ( E @ ( B @ ( A @ r2_nattra_1 ) ) ) )
& ( D
= ( G @ ( F @ ( E @ k4_tarski ) @ k4_tarski ) ) ) ) ) ) )
& ( C @ ( D @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_nattra_1) ).
thf(238,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ( ( ! [D: $i] :
~ ( ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( B @ ( A @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( F @ ( E @ ( B @ ( A @ ( G @ m2_nattra_1 ) ) ) ) )
=> ~ ( ( F @ ( E @ ( B @ ( A @ r2_nattra_1 ) ) ) )
& ( D
= ( G @ ( F @ ( E @ k4_tarski ) @ k4_tarski ) ) ) ) ) ) )
& ( C @ ( D @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m4_nattra_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m4_nattra_1 ) ) )
=> ! [D: $i] :
~ ( ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( B @ ( A @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( F @ ( E @ ( B @ ( A @ ( G @ m2_nattra_1 ) ) ) ) )
=> ~ ( ( F @ ( E @ ( B @ ( A @ r2_nattra_1 ) ) ) )
& ( D
= ( G @ ( F @ ( E @ k4_tarski ) @ k4_tarski ) ) ) ) ) ) )
& ( C @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(174,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(806,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)],[174]) ).
thf(180,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i,C: $i] : ( A @ ( A @ ( C @ ( B @ k8_cat_1 ) @ k12_nattra_1 ) @ r1_isocat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_isocat_2) ).
thf(821,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i,C: $i] : ( A @ ( A @ ( C @ ( B @ k8_cat_1 ) @ k12_nattra_1 ) @ r1_isocat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(54,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) )
<=> ( B @ ( A @ k11_nattra_1 ) @ ( E @ ( D @ ( C @ k4_tarski ) @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_nattra_1) ).
thf(397,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) )
=> ( ( ( B @ ( A @ k11_nattra_1 ) @ ( E @ ( D @ ( C @ k4_tarski ) @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) )
=> ( B @ ( A @ k11_nattra_1 ) @ ( E @ ( D @ ( C @ k4_tarski ) @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(25,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(280,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)],[25]) ).
thf(143,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(734,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)],[143]) ).
thf(160,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 ) )
=> ? [E: $i] : ( D @ ( C @ ( B @ ( A @ ( E @ m3_nattra_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_nattra_1) ).
thf(774,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 ) )
=> ? [E: $i] : ( D @ ( C @ ( B @ ( A @ ( E @ m3_nattra_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(117,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_cat_2 ) )
=> ( A @ ( B @ ( B @ k15_cat_1 @ m2_cat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_cat_2) ).
thf(660,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_cat_2 ) )
=> ( A @ ( B @ ( B @ k15_cat_1 @ m2_cat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( E @ ( D @ ( B @ ( A @ ( G @ m2_nattra_1 ) ) ) ) )
& ( D @ ( C @ ( B @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
& ( B @ ( A @ ( E @ m2_cat_1 ) ) )
& ( 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 ) )
=> ( E @ ( C @ ( B @ ( A @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ m2_nattra_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_nattra_1) ).
thf(507,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( E @ ( D @ ( B @ ( A @ ( G @ m2_nattra_1 ) ) ) ) )
& ( D @ ( C @ ( B @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
& ( B @ ( A @ ( E @ m2_cat_1 ) ) )
& ( 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 ) )
=> ( E @ ( C @ ( B @ ( A @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ m2_nattra_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_cat_2 ) ) )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m2_cat_2 ) ) ) )
=> ( B @ ( A @ ( D @ m2_cat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_cat_2) ).
thf(527,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_cat_2 ) ) )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m2_cat_2 ) ) ) )
=> ( B @ ( A @ ( D @ m2_cat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(292,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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 @ ( C @ ( B @ ( A @ k7_nattra_1 ) ) @ m2_nattra_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_nattra_1) ).
thf(546,plain,
! [A: $i,B: $i,C: $i] :
( ( ( 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 @ ( C @ ( B @ ( A @ k7_nattra_1 ) ) @ m2_nattra_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(155,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(761,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)],[155]) ).
thf(176,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( ( B @ ( A @ r1_isocat_1 ) )
=> ( B @ ( A @ r2_isocat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_isocat_1) ).
thf(810,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( ( B @ ( A @ r1_isocat_1 ) )
=> ( B @ ( A @ r2_isocat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( 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 @ ( B @ k12_nattra_1 ) @ ( A @ ( D @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_isocat_2) ).
thf(714,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( 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 @ ( B @ k12_nattra_1 ) @ ( A @ ( D @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(20,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 @ ( A @ k11_cat_2 ) @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( F @ m2_cat_1 ) ) )
=> ( ( ( F @ ( E @ ( C @ ( B @ ( A @ k11_cat_2 ) @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ r2_nattra_1 ) ) ) ) )
=> ! [G: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ ( G @ m2_nattra_1 ) ) ) ) )
=> ! [H: $i] :
( ( F @ ( E @ ( C @ ( B @ ( A @ k11_cat_2 ) @ ( H @ m2_nattra_1 ) ) ) ) )
=> ( H @ ( F @ ( E @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( C @ ( B @ k12_nattra_1 ) @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ k8_nattra_1 ) ) ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_isocat_2) ).
thf(270,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 @ ( A @ k11_cat_2 ) @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( F @ m2_cat_1 ) ) )
=> ( ( ( F @ ( E @ ( C @ ( B @ ( A @ k11_cat_2 ) @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ r2_nattra_1 ) ) ) ) )
=> ! [G: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ ( G @ m2_nattra_1 ) ) ) ) )
=> ! [H: $i] :
( ( F @ ( E @ ( C @ ( B @ ( A @ k11_cat_2 ) @ ( H @ m2_nattra_1 ) ) ) ) )
=> ( H @ ( F @ ( E @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( C @ ( B @ k12_nattra_1 ) @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ k8_nattra_1 ) ) ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(83,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(529,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(149,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 ) )
=> ( C @ ( A @ k12_nattra_1 ) @ ( B @ ( A @ k12_nattra_1 ) @ k11_cat_2 ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k17_isocat_2 ) ) @ v8_cat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_isocat_2) ).
thf(746,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 ) )
=> ( C @ ( A @ k12_nattra_1 ) @ ( B @ ( A @ k12_nattra_1 ) @ k11_cat_2 ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k17_isocat_2 ) ) @ v8_cat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(182,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 ) )
=> ( C @ ( B @ k12_nattra_1 ) @ ( A @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k11_cat_2 ) @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k7_isocat_2 ) ) @ v8_cat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_isocat_2) ).
thf(825,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 ) )
=> ( C @ ( B @ k12_nattra_1 ) @ ( A @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k11_cat_2 ) @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k7_isocat_2 ) ) @ v8_cat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ~ ( B @ ( A @ k5_cat_2 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_cat_2) ).
thf(778,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ~ ( B @ ( A @ k5_cat_2 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_zfmisc_1) ).
thf(302,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(31,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(297,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_cat_2 ) ) )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m2_cat_2 ) ) ) )
<=> ( C @ ( D @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_cat_2) ).
thf(693,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_cat_2 ) ) )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [D: $i] :
( ( ( C @ ( D @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ ( D @ m2_cat_2 ) ) ) ) )
& ( ( C @ ( B @ ( A @ ( D @ m2_cat_2 ) ) ) )
=> ( C @ ( D @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(178,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(815,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)],[178]) ).
thf(13,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(229,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(111,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 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ u2_cat_1 @ ( A @ u2_cat_1 @ ( C @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( E @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ u2_cat_1 @ ( A @ u2_cat_1 @ ( C @ ( B @ k11_cat_2 ) @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_isocat_2) ).
thf(625,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 @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ u2_cat_1 @ ( A @ u2_cat_1 @ ( C @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( E @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ u2_cat_1 @ ( A @ u2_cat_1 @ ( C @ ( B @ k11_cat_2 ) @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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 @ ( B @ k12_nattra_1 ) @ ( A @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k11_cat_2 ) @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k7_isocat_2 ) ) @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_isocat_2) ).
thf(842,plain,
! [A: $i,B: $i,C: $i] :
( ( ( 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 @ ( B @ k12_nattra_1 ) @ ( A @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k11_cat_2 ) @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k7_isocat_2 ) ) @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(35,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 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( F @ m2_cat_1 ) ) )
=> ( ( ( F @ ( E @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) ) )
=> ! [G: $i] :
( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( G @ m2_nattra_1 ) ) ) ) )
=> ! [H: $i] :
( ( F @ ( E @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( H @ m2_nattra_1 ) ) ) ) )
=> ( ( H @ ( F @ ( E @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( H @ ( F @ ( E @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_isocat_2) ).
thf(324,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 ) ) )
=> ! [F: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( F @ m2_cat_1 ) ) )
=> ( ( ( F @ ( E @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) ) )
=> ! [G: $i] :
( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( G @ m2_nattra_1 ) ) ) ) )
=> ! [H: $i] :
( ( F @ ( E @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( H @ m2_nattra_1 ) ) ) ) )
=> ( ( H @ ( F @ ( E @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( H @ ( F @ ( E @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 )
& ( A @ v1_cat_1 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m3_cat_2 ) )
& ( B @ v1_cat_1 ) )
=> ( ( ( ( B @ u2_cat_1 )
= ( A @ u2_cat_1 ) )
& ( ( B @ u1_cat_1 )
= ( A @ u1_cat_1 ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_nattra_1) ).
thf(224,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 )
& ( A @ v1_cat_1 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m3_cat_2 ) )
& ( B @ v1_cat_1 ) )
=> ( ( ( ( B @ u2_cat_1 )
= ( A @ u2_cat_1 ) )
& ( ( B @ u1_cat_1 )
= ( A @ u1_cat_1 ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(107,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 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) )
= ( C @ ( B @ k8_isocat_2 ) @ ( F @ ( E @ ( D @ ( B @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k6_isocat_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_isocat_2) ).
thf(615,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 ) ) )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) )
= ( C @ ( B @ k8_isocat_2 ) @ ( F @ ( E @ ( D @ ( B @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k6_isocat_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k8_cat_1 ) @ u2_cat_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k8_cat_1 ) @ u2_cat_1 @ ( D @ m1_subset_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_nattra_1) ).
thf(403,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k8_cat_1 ) @ u2_cat_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k8_cat_1 ) @ u2_cat_1 @ ( D @ m1_subset_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(388,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(79,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 @ ( A @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( C @ ( A @ ( G @ m2_cat_1 ) ) )
=> ( ( ( G @ ( F @ ( C @ ( A @ r1_nattra_1 ) ) ) )
& ( E @ ( D @ ( B @ ( A @ r1_nattra_1 ) ) ) ) )
=> ( G @ ( E @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r1_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_isocat_2) ).
thf(519,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 @ ( A @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( C @ ( A @ ( G @ m2_cat_1 ) ) )
=> ( ( ( G @ ( F @ ( C @ ( A @ r1_nattra_1 ) ) ) )
& ( E @ ( D @ ( B @ ( A @ r1_nattra_1 ) ) ) ) )
=> ( G @ ( E @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r1_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(147,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( B @ ( A @ r2_isocat_1 ) )
=> ( A @ ( B @ r2_isocat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r2_isocat_1) ).
thf(742,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( B @ ( A @ r2_isocat_1 ) )
=> ( A @ ( B @ r2_isocat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( B @ ( A @ ( B @ ( A @ k11_nattra_1 ) @ m4_nattra_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_nattra_1) ).
thf(783,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( B @ ( A @ ( B @ ( A @ k11_nattra_1 ) @ m4_nattra_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(60,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( ( E @ ( D @ ( B @ ( A @ r3_nattra_1 ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r3_nattra_1 ) ) ) ) )
=> ! [F: $i] :
( ( D @ ( C @ ( B @ ( A @ ( F @ m3_nattra_1 ) ) ) ) )
=> ! [G: $i] :
( ( E @ ( D @ ( B @ ( A @ ( G @ m3_nattra_1 ) ) ) ) )
=> ( E @ ( C @ ( B @ ( A @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ m3_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_nattra_1) ).
thf(420,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( ( E @ ( D @ ( B @ ( A @ r3_nattra_1 ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r3_nattra_1 ) ) ) ) )
=> ! [F: $i] :
( ( D @ ( C @ ( B @ ( A @ ( F @ m3_nattra_1 ) ) ) ) )
=> ! [G: $i] :
( ( E @ ( D @ ( B @ ( A @ ( G @ m3_nattra_1 ) ) ) ) )
=> ( E @ ( C @ ( B @ ( A @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ m3_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(328,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r2_hidden ) ) )
& ( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
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 @ ( A @ k11_cat_2 ) @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( E @ m2_cat_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ r2_nattra_1 ) ) ) )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ ( F @ m2_nattra_1 ) ) ) ) )
=> ! [G: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ ( G @ m2_nattra_1 ) ) ) ) )
=> ( ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) )
=> ( G @ ( F @ ( C @ u2_cat_1 @ ( B @ ( A @ k11_cat_2 ) @ u1_cat_1 @ ( C @ u2_cat_1 @ ( B @ ( A @ k11_cat_2 ) @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_isocat_2) ).
thf(339,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 @ ( A @ k11_cat_2 ) @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( E @ m2_cat_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ r2_nattra_1 ) ) ) )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ ( F @ m2_nattra_1 ) ) ) ) )
=> ! [G: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ ( G @ m2_nattra_1 ) ) ) ) )
=> ( ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) )
=> ( G @ ( F @ ( C @ u2_cat_1 @ ( B @ ( A @ k11_cat_2 ) @ u1_cat_1 @ ( C @ u2_cat_1 @ ( B @ ( A @ k11_cat_2 ) @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(86,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ? [B: $i] :
( ( B @ v2_nattra_1 )
& ( B @ v2_cat_1 )
& ( B @ v1_cat_1 )
& ( A @ ( B @ m3_cat_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_nattra_1) ).
thf(537,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ? [B: $i] :
( ( B @ v2_nattra_1 )
& ( B @ v2_cat_1 )
& ( B @ v1_cat_1 )
& ( A @ ( B @ m3_cat_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(121,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( A @ ( A @ k13_nattra_1 @ m3_cat_2 ) )
& ( A @ k13_nattra_1 @ v2_nattra_1 )
& ( A @ k13_nattra_1 @ v1_cat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_nattra_1) ).
thf(669,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( A @ ( A @ k13_nattra_1 @ m3_cat_2 ) )
& ( A @ k13_nattra_1 @ v2_nattra_1 )
& ( A @ k13_nattra_1 @ v1_cat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(126,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 ) )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ m3_nattra_1 ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m3_nattra_1) ).
thf(686,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 ) )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ m3_nattra_1 ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(104,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( C
= ( B @ ( A @ k5_cat_2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( B @ ( A @ ( D @ m2_cat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_cat_2) ).
thf(590,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( A @ ( D @ m2_cat_1 ) ) ) ) )
=> ( C
= ( B @ ( A @ k5_cat_2 ) ) ) )
& ( ( C
= ( B @ ( A @ k5_cat_2 ) ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( A @ ( D @ m2_cat_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
& ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
& ( 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 ) )
=> ( E @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ m2_nattra_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_isocat_2) ).
thf(679,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
& ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
& ( 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 ) )
=> ( E @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ m2_nattra_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( G @ ( F @ ( C @ ( A @ ( I @ m1_nattra_1 ) ) ) ) )
& ( E @ ( D @ ( B @ ( A @ ( H @ m1_nattra_1 ) ) ) ) )
& ( C @ ( A @ ( G @ m2_cat_1 ) ) )
& ( C @ ( A @ ( F @ m2_cat_1 ) ) )
& ( B @ ( A @ ( 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 ) )
=> ( G @ ( E @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k15_isocat_2 ) ) ) ) ) ) ) ) @ m1_nattra_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_isocat_2) ).
thf(212,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( G @ ( F @ ( C @ ( A @ ( I @ m1_nattra_1 ) ) ) ) )
& ( E @ ( D @ ( B @ ( A @ ( H @ m1_nattra_1 ) ) ) ) )
& ( C @ ( A @ ( G @ m2_cat_1 ) ) )
& ( C @ ( A @ ( F @ m2_cat_1 ) ) )
& ( B @ ( A @ ( 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 ) )
=> ( G @ ( E @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k15_isocat_2 ) ) ) ) ) ) ) ) @ m1_nattra_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ r1_isocat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_isocat_1) ).
thf(706,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ r1_isocat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(52,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_cat_2 ) )
=> ! [C: $i] :
( ( B @ u2_cat_1 @ ( C @ m1_subset_1 ) )
=> ( A @ u2_cat_1 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_cat_2) ).
thf(393,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_cat_2 ) )
=> ! [C: $i] :
( ( B @ u2_cat_1 @ ( C @ m1_subset_1 ) )
=> ( A @ u2_cat_1 @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m2_cat_1 ) ) )
& ( C @ ( 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 @ k7_commacat ) ) ) ) @ l1_cat_1 )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_commacat ) ) ) ) @ v2_cat_1 )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_commacat ) ) ) ) @ v1_cat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_commacat) ).
thf(647,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m2_cat_1 ) ) )
& ( C @ ( 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 @ k7_commacat ) ) ) ) @ l1_cat_1 )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_commacat ) ) ) ) @ v2_cat_1 )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_commacat ) ) ) ) @ v1_cat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( B @ ( A @ ( B @ ( A @ k7_cat_2 ) @ m1_cat_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_cat_2) ).
thf(701,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( B @ ( A @ ( B @ ( A @ k7_cat_2 ) @ m1_cat_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(78,axiom,
? [A: $i] :
( ( A @ v1_cat_1 )
& ( A @ l1_cat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_cat_1) ).
thf(515,plain,
? [A: $i] :
( ( A @ v1_cat_1 )
& ( A @ l1_cat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(145,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( ( ( B @ v2_nattra_1 )
& ( A @ v2_nattra_1 ) )
=> ( B @ ( A @ k11_cat_2 ) @ v2_nattra_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_nattra_1) ).
thf(738,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( ( ( B @ v2_nattra_1 )
& ( A @ v2_nattra_1 ) )
=> ( B @ ( A @ k11_cat_2 ) @ v2_nattra_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(138,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 ) )
=> ( ( ( C @ ( B @ r2_isocat_1 ) )
& ( B @ ( A @ r2_isocat_1 ) ) )
=> ( C @ ( A @ r2_isocat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_isocat_1) ).
thf(721,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 ) )
=> ( ( ( C @ ( B @ r2_isocat_1 ) )
& ( B @ ( A @ r2_isocat_1 ) ) )
=> ( C @ ( A @ r2_isocat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(47,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(371,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)],[47]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m2_cat_1 ) ) )
& ( C @ ( A @ ( E @ m2_cat_1 ) ) )
& ( D @ l1_cat_1 )
& ( D @ v2_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 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k19_cat_2 ) ) ) ) ) )
= ( F @ ( E @ k15_funct_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k19_cat_2) ).
thf(622,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m2_cat_1 ) ) )
& ( C @ ( A @ ( E @ m2_cat_1 ) ) )
& ( D @ l1_cat_1 )
& ( D @ v2_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 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k19_cat_2 ) ) ) ) ) )
= ( F @ ( E @ k15_funct_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(187,axiom,
? [A: $i] :
( ( A @ v2_cat_1 )
& ( A @ v1_cat_1 )
& ( A @ l1_cat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_cat_1) ).
thf(837,plain,
? [A: $i] :
( ( A @ v2_cat_1 )
& ( A @ v1_cat_1 )
& ( A @ l1_cat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(168,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( A @ k1_isocat_1 )
= ( A @ k15_cat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_isocat_1) ).
thf(792,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( A @ k1_isocat_1 )
= ( A @ k15_cat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(44,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( ( B @ ( A @ r2_isocat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_isocat_1 ) ) )
=> ? [D: $i] :
( ( B @ k1_isocat_1 @ ( C @ ( D @ ( B @ ( A @ ( B @ k2_isocat_1 ) ) ) ) @ ( B @ ( B @ r3_nattra_1 ) ) ) )
& ( A @ k1_isocat_1 @ ( D @ ( C @ ( A @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( A @ ( A @ r3_nattra_1 ) ) ) )
& ( A @ ( B @ ( D @ m1_isocat_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_isocat_1) ).
thf(360,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( ( B @ ( A @ r2_isocat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_isocat_1 ) ) )
=> ? [D: $i] :
( ( B @ k1_isocat_1 @ ( C @ ( D @ ( B @ ( A @ ( B @ k2_isocat_1 ) ) ) ) @ ( B @ ( B @ r3_nattra_1 ) ) ) )
& ( A @ k1_isocat_1 @ ( D @ ( C @ ( A @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( A @ ( A @ r3_nattra_1 ) ) ) )
& ( A @ ( B @ ( D @ m1_isocat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(4,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_cat_2 ) )
=> ! [C: $i] :
( ( B @ u1_cat_1 @ ( C @ m1_subset_1 ) )
=> ( A @ u1_cat_1 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_cat_2) ).
thf(205,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_cat_2 ) )
=> ! [C: $i] :
( ( B @ u1_cat_1 @ ( C @ m1_subset_1 ) )
=> ( A @ u1_cat_1 @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(157,axiom,
? [A: $i] :
( ( A @ v2_nattra_1 )
& ( A @ v2_cat_1 )
& ( A @ l1_cat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_nattra_1) ).
thf(765,plain,
? [A: $i] :
( ( A @ v2_nattra_1 )
& ( A @ v2_cat_1 )
& ( A @ l1_cat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(122,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_cat_2 ) )
=> ( ( B @ ( A @ k8_cat_2 ) )
= ( B @ k15_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_cat_2) ).
thf(674,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_cat_2 ) )
=> ( ( B @ ( A @ k8_cat_2 ) )
= ( B @ k15_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(102,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 ) )
=> ? [E: $i] : ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_nattra_1) ).
thf(586,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 ) )
=> ? [E: $i] : ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(118,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 ) )
=> ( ( ( C @ ( B @ r2_isocat_1 ) )
& ( B @ ( A @ r2_isocat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m1_isocat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( E @ m1_isocat_1 ) ) )
=> ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ m1_isocat_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_isocat_1) ).
thf(662,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 ) )
=> ( ( ( C @ ( B @ r2_isocat_1 ) )
& ( B @ ( A @ r2_isocat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m1_isocat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( E @ m1_isocat_1 ) ) )
=> ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ m1_isocat_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(58,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 @ ( A @ k11_cat_2 ) @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( E @ m2_cat_1 ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( C @ ( B @ k12_nattra_1 ) @ ( A @ r2_nattra_1 ) ) ) )
=> ! [F: $i] :
( ( E @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( C @ ( B @ k12_nattra_1 ) @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
=> ( ? [G: $i] :
( ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ ( G @ m2_nattra_1 ) ) ) ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_isocat_2) ).
thf(412,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 @ ( A @ k11_cat_2 ) @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k11_cat_2 ) @ ( E @ m2_cat_1 ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( C @ ( B @ k12_nattra_1 ) @ ( A @ r2_nattra_1 ) ) ) )
=> ! [F: $i] :
( ( E @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k5_isocat_2 ) ) ) @ ( C @ ( B @ k12_nattra_1 ) @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
=> ( ? [G: $i] :
( ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ ( B @ k12_nattra_1 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ ( G @ m2_nattra_1 ) ) ) ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(151,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 @ m1_cat_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_cat_2) ).
thf(750,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 @ m1_cat_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( B @ ( C @ ( B @ ( A @ k3_isocat_1 ) ) @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_isocat_1) ).
thf(618,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
& ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( B @ ( C @ ( B @ ( A @ k3_isocat_1 ) ) @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(77,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ ( A @ k1_isocat_1 @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_isocat_1) ).
thf(513,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ ( A @ k1_isocat_1 @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(179,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 @ m4_nattra_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m4_nattra_1) ).
thf(819,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 @ m4_nattra_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(95,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ ( A @ k15_cat_1 @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_cat_1) ).
thf(562,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ ( A @ k15_cat_1 @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(142,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 ) )
=> ( ( ( C @ ( B @ r1_isocat_1 ) )
& ( B @ ( A @ r1_isocat_1 ) ) )
=> ( C @ ( A @ r1_isocat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_isocat_1) ).
thf(732,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 ) )
=> ( ( ( C @ ( B @ r1_isocat_1 ) )
& ( B @ ( A @ r1_isocat_1 ) ) )
=> ( C @ ( A @ r1_isocat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(159,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 @ m1_oppcat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_oppcat_1) ).
thf(772,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 @ m1_oppcat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(286,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(51,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ r3_nattra_1 ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ r3_nattra_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_nattra_1) ).
thf(391,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ r3_nattra_1 ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ r3_nattra_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(65,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m4_nattra_1 ) ) )
=> ( ( C
= ( B @ ( A @ k11_nattra_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( F @ ( E @ ( B @ ( A @ r2_nattra_1 ) ) ) )
& ( D
= ( G @ ( F @ ( E @ k4_tarski ) @ k4_tarski ) ) )
& ( F @ ( E @ ( B @ ( A @ ( G @ m2_nattra_1 ) ) ) ) ) )
& ( B @ ( A @ ( F @ m2_cat_1 ) ) ) )
& ( B @ ( A @ ( E @ m2_cat_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_nattra_1) ).
thf(445,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m4_nattra_1 ) ) )
=> ( ( ! [D: $i] :
( ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( F @ ( E @ ( B @ ( A @ r2_nattra_1 ) ) ) )
& ( D
= ( G @ ( F @ ( E @ k4_tarski ) @ k4_tarski ) ) )
& ( F @ ( E @ ( B @ ( A @ ( G @ m2_nattra_1 ) ) ) ) ) )
& ( B @ ( A @ ( F @ m2_cat_1 ) ) ) )
& ( B @ ( A @ ( E @ m2_cat_1 ) ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( F @ ( E @ ( B @ ( A @ r2_nattra_1 ) ) ) )
& ( D
= ( G @ ( F @ ( E @ k4_tarski ) @ k4_tarski ) ) )
& ( F @ ( E @ ( B @ ( A @ ( G @ m2_nattra_1 ) ) ) ) ) )
& ( B @ ( A @ ( F @ m2_cat_1 ) ) ) )
& ( B @ ( A @ ( E @ m2_cat_1 ) ) ) ) ) )
=> ( C
= ( B @ ( A @ k11_nattra_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k11_nattra_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( F @ ( E @ ( B @ ( A @ r2_nattra_1 ) ) ) )
& ( D
= ( G @ ( F @ ( E @ k4_tarski ) @ k4_tarski ) ) )
& ( F @ ( E @ ( B @ ( A @ ( G @ m2_nattra_1 ) ) ) ) ) )
& ( B @ ( A @ ( F @ m2_cat_1 ) ) ) )
& ( B @ ( A @ ( E @ m2_cat_1 ) ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( F @ ( E @ ( B @ ( A @ r2_nattra_1 ) ) ) )
& ( D
= ( G @ ( F @ ( E @ k4_tarski ) @ k4_tarski ) ) )
& ( F @ ( E @ ( B @ ( A @ ( G @ m2_nattra_1 ) ) ) ) ) )
& ( B @ ( A @ ( F @ m2_cat_1 ) ) ) )
& ( B @ ( A @ ( E @ m2_cat_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( 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 @ k18_cat_2 ) ) ) ) )
= ( E @ ( D @ k13_funct_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k18_cat_2) ).
thf(572,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( 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 @ k18_cat_2 ) ) ) ) )
= ( E @ ( D @ k13_funct_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(71,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 ) )
=> ? [E: $i] : ( D @ ( C @ ( B @ ( A @ ( E @ m1_nattra_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_nattra_1) ).
thf(498,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 ) )
=> ? [E: $i] : ( D @ ( C @ ( B @ ( A @ ( E @ m1_nattra_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(173,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( ( A @ v2_nattra_1 )
=> ( A @ ( B @ k12_nattra_1 ) @ v2_nattra_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_nattra_1) ).
thf(804,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( ( A @ v2_nattra_1 )
=> ( A @ ( B @ k12_nattra_1 ) @ v2_nattra_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(40,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_nattra_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( A @ ( B @ ( D @ m2_cat_1 ) ) )
=> ( ( D @ ( C @ ( A @ ( B @ r1_nattra_1 ) ) ) )
=> ( D @ ( C @ ( A @ u2_cat_1 @ ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ ( B @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_nattra_1) ).
thf(350,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_nattra_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( A @ ( B @ ( D @ m2_cat_1 ) ) )
=> ( ( D @ ( C @ ( A @ ( B @ r1_nattra_1 ) ) ) )
=> ( D @ ( C @ ( A @ u2_cat_1 @ ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ ( B @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(105,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(611,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)],[105]) ).
thf(166,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ? [B: $i] : ( A @ ( B @ m3_cat_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_cat_2) ).
thf(787,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ? [B: $i] : ( A @ ( B @ m3_cat_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(57,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ k7_nattra_1 ) ) @ ( D @ ( C @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) )
= E )
& ( ( D @ ( B @ ( A @ k7_nattra_1 ) ) @ ( E @ ( D @ ( D @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) )
= E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_nattra_1) ).
thf(406,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ k7_nattra_1 ) ) @ ( D @ ( C @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) )
= E )
& ( ( D @ ( B @ ( A @ k7_nattra_1 ) ) @ ( E @ ( D @ ( D @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) )
= E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( 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 @ ( B @ k11_cat_2 ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_isocat_2) ).
thf(831,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( 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 @ ( B @ k11_cat_2 ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(125,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ? [B: $i] :
( ( B @ v2_cat_1 )
& ( B @ v1_cat_1 )
& ( A @ ( B @ m3_cat_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_cat_2) ).
thf(681,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ? [B: $i] :
( ( B @ v2_cat_1 )
& ( B @ v1_cat_1 )
& ( A @ ( B @ m3_cat_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(22,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] :
( ( ( D @ l1_cat_1 )
& ( D @ v2_cat_1 ) )
=> ! [E: $i] :
( ( D @ ( C @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( D @ ( C @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( A @ ( D @ ( G @ m2_cat_1 ) ) )
=> ! [H: $i] :
( ( B @ ( A @ ( H @ m2_cat_1 ) ) )
=> ! [I: $i] :
( ( F @ ( E @ ( D @ ( C @ ( I @ m2_nattra_1 ) ) ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ r2_nattra_1 ) ) ) )
=> ( H @ ( G @ ( I @ ( F @ ( E @ ( A @ ( D @ ( C @ k6_isocat_1 ) ) ) ) ) ) @ ( G @ ( F @ ( A @ ( D @ ( C @ k2_isocat_1 ) ) ) ) @ ( G @ ( E @ ( A @ ( D @ ( C @ k2_isocat_1 ) ) ) ) @ ( B @ ( A @ ( C @ k6_isocat_1 ) ) ) ) ) ) @ ( H @ ( G @ ( B @ ( A @ ( D @ k2_isocat_1 ) ) ) ) @ ( I @ ( F @ ( E @ ( B @ ( D @ ( C @ k6_isocat_1 ) ) ) ) ) ) @ ( B @ u2_cat_1 @ ( C @ u1_cat_1 @ ( B @ u2_cat_1 @ ( C @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_isocat_1) ).
thf(274,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] :
( ( ( D @ l1_cat_1 )
& ( D @ v2_cat_1 ) )
=> ! [E: $i] :
( ( D @ ( C @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( D @ ( C @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( A @ ( D @ ( G @ m2_cat_1 ) ) )
=> ! [H: $i] :
( ( B @ ( A @ ( H @ m2_cat_1 ) ) )
=> ! [I: $i] :
( ( F @ ( E @ ( D @ ( C @ ( I @ m2_nattra_1 ) ) ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ r2_nattra_1 ) ) ) )
=> ( H @ ( G @ ( I @ ( F @ ( E @ ( A @ ( D @ ( C @ k6_isocat_1 ) ) ) ) ) ) @ ( G @ ( F @ ( A @ ( D @ ( C @ k2_isocat_1 ) ) ) ) @ ( G @ ( E @ ( A @ ( D @ ( C @ k2_isocat_1 ) ) ) ) @ ( B @ ( A @ ( C @ k6_isocat_1 ) ) ) ) ) ) @ ( H @ ( G @ ( B @ ( A @ ( D @ k2_isocat_1 ) ) ) ) @ ( I @ ( F @ ( E @ ( B @ ( D @ ( C @ k6_isocat_1 ) ) ) ) ) ) @ ( B @ u2_cat_1 @ ( C @ u1_cat_1 @ ( B @ u2_cat_1 @ ( C @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(144,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( A @ ( B @ k11_cat_2 ) @ ( B @ ( A @ k11_cat_2 ) @ r1_isocat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_isocat_1) ).
thf(736,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( A @ ( B @ k11_cat_2 ) @ ( B @ ( A @ k11_cat_2 ) @ r1_isocat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(76,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 ) ) )
=> ! [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(509,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)],[76]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( B @ ( A @ k7_cat_2 ) )
= ( B @ ( A @ k5_cat_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_cat_2) ).
thf(758,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( B @ ( A @ k7_cat_2 ) )
= ( B @ ( A @ k5_cat_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(85,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ( C @ ( C @ ( B @ ( A @ ( C @ ( B @ ( A @ k7_nattra_1 ) ) @ m3_nattra_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_nattra_1) ).
thf(535,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ( C @ ( C @ ( B @ ( A @ ( C @ ( B @ ( A @ k7_nattra_1 ) ) @ m3_nattra_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(171,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ ( A @ k15_cat_1 @ v8_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_cat_1) ).
thf(799,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ ( A @ k15_cat_1 @ v8_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(66,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(483,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( B @ v1_xboole_0 ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( A @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(251,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xboole_0 ) ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( ( A @ ( B @ r2_hidden ) )
=> ( A @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(39,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
thf(345,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(46,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_cat_1 ) ) )
=> ( ( A @ ( B @ ( C @ v8_cat_1 ) ) )
=> ( ( B @ k1_isocat_1 @ ( C @ ( A @ ( B @ k3_isocat_1 ) ) @ ( C @ ( B @ ( A @ ( B @ k2_isocat_1 ) ) ) ) @ ( B @ u2_cat_1 @ ( B @ u2_cat_1 @ ( B @ u2_cat_1 @ ( B @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( A @ k1_isocat_1 @ ( C @ ( C @ ( A @ ( B @ k3_isocat_1 ) ) @ ( A @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( A @ u2_cat_1 @ ( A @ u2_cat_1 @ ( A @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_isocat_1) ).
thf(367,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_cat_1 ) ) )
=> ( ( A @ ( B @ ( C @ v8_cat_1 ) ) )
=> ( ( B @ k1_isocat_1 @ ( C @ ( A @ ( B @ k3_isocat_1 ) ) @ ( C @ ( B @ ( A @ ( B @ k2_isocat_1 ) ) ) ) @ ( B @ u2_cat_1 @ ( B @ u2_cat_1 @ ( B @ u2_cat_1 @ ( B @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( A @ k1_isocat_1 @ ( C @ ( C @ ( A @ ( B @ k3_isocat_1 ) ) @ ( A @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( A @ u2_cat_1 @ ( A @ u2_cat_1 @ ( A @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( 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 @ k10_isocat_2 ) ) ) ) )
= ( E @ ( D @ k13_funct_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_isocat_2) ).
thf(552,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( 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 @ k10_isocat_2 ) ) ) ) )
= ( E @ ( D @ k13_funct_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(80,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(521,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)],[80]) ).
thf(183,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ ( A @ k1_isocat_1 @ m1_isocat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_isocat_1) ).
thf(827,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ ( A @ k1_isocat_1 @ m1_isocat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(24,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(278,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)],[24]) ).
thf(163,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(780,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)],[163]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(267,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(68,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( ( E @ ( D @ ( B @ ( A @ r1_nattra_1 ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r1_nattra_1 ) ) ) ) )
=> ( E @ ( C @ ( B @ ( A @ r1_nattra_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_nattra_1) ).
thf(490,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( ( E @ ( D @ ( B @ ( A @ r1_nattra_1 ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r1_nattra_1 ) ) ) ) )
=> ( E @ ( C @ ( B @ ( A @ r1_nattra_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(169,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(795,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)],[169]) ).
thf(89,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] :
( ( C @ ( B @ ( E @ m2_cat_1 ) ) )
=> ( ( ( C @ ( B @ ( E @ v8_cat_1 ) ) )
& ( B @ ( A @ ( D @ v8_cat_1 ) ) ) )
=> ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ v8_cat_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_isocat_1) ).
thf(548,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] :
( ( C @ ( B @ ( E @ m2_cat_1 ) ) )
=> ( ( ( C @ ( B @ ( E @ v8_cat_1 ) ) )
& ( B @ ( A @ ( D @ v8_cat_1 ) ) ) )
=> ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ v8_cat_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k4_tarski ) )
= ( D @ ( C @ k4_tarski ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(374,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k4_tarski ) )
= ( D @ ( C @ k4_tarski ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(177,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( A @ k17_ens_1 )
= ( A @ a_1_3_ens_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d19_ens_1) ).
thf(812,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( A @ k17_ens_1 )
= ( A @ a_1_3_ens_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(42,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( B @ ( A @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( D @ ( C @ ( B @ ( A @ ( G @ m2_nattra_1 ) ) ) ) )
=> ! [H: $i] :
( ( E @ ( D @ ( B @ ( A @ ( H @ m2_nattra_1 ) ) ) ) )
=> ( ( ( F @ ( E @ ( B @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( B @ ( A @ r2_nattra_1 ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
=> ! [I: $i] :
( ( F @ ( E @ ( B @ ( A @ ( I @ m2_nattra_1 ) ) ) ) )
=> ( ( I @ ( H @ ( F @ ( E @ ( D @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) )
= ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ ( F @ ( E @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_nattra_1) ).
thf(355,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( B @ ( A @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( D @ ( C @ ( B @ ( A @ ( G @ m2_nattra_1 ) ) ) ) )
=> ! [H: $i] :
( ( E @ ( D @ ( B @ ( A @ ( H @ m2_nattra_1 ) ) ) ) )
=> ( ( ( F @ ( E @ ( B @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( B @ ( A @ r2_nattra_1 ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
=> ! [I: $i] :
( ( F @ ( E @ ( B @ ( A @ ( I @ m2_nattra_1 ) ) ) ) )
=> ( ( I @ ( H @ ( F @ ( E @ ( D @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) )
= ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) @ ( F @ ( E @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(181,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 @ m1_isocat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_isocat_1) ).
thf(823,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 @ m1_isocat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(161,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ m3_cat_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_cat_2) ).
thf(776,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ m3_cat_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(30,axiom,
! [A: $i,B: $i] : ( A @ ( B @ k8_cat_1 ) @ u2_cat_1 @ ( A @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_cat_1) ).
thf(295,plain,
! [A: $i,B: $i] : ( A @ ( B @ k8_cat_1 ) @ u2_cat_1 @ ( A @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(26,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 @ k11_cat_2 ) @ ( A @ k7_nattra_1 ) ) @ ( D @ ( D @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ ( A @ k7_nattra_1 ) ) @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k7_nattra_1 ) ) @ ( D @ ( D @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ ( A @ k7_nattra_1 ) ) @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_isocat_2) ).
thf(282,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 @ k11_cat_2 ) @ ( A @ k7_nattra_1 ) ) @ ( D @ ( D @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ ( A @ k7_nattra_1 ) ) @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k7_nattra_1 ) ) @ ( D @ ( D @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ ( A @ k7_nattra_1 ) ) @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(18,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( A @ ( B @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( A @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( A @ k1_isocat_1 @ ( E @ ( A @ ( A @ r3_nattra_1 ) ) ) )
=> ( ( D @ ( E @ ( D @ ( A @ ( A @ ( B @ k2_isocat_1 ) ) ) ) @ ( A @ ( B @ r3_nattra_1 ) ) ) )
& ( C @ ( C @ ( E @ ( B @ ( A @ ( A @ k2_isocat_1 ) ) ) ) @ ( B @ ( A @ r3_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_isocat_1) ).
thf(263,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( A @ ( B @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( A @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( A @ k1_isocat_1 @ ( E @ ( A @ ( A @ r3_nattra_1 ) ) ) )
=> ( ( D @ ( E @ ( D @ ( A @ ( A @ ( B @ k2_isocat_1 ) ) ) ) @ ( A @ ( B @ r3_nattra_1 ) ) ) )
& ( C @ ( C @ ( E @ ( B @ ( A @ ( A @ k2_isocat_1 ) ) ) ) @ ( B @ ( A @ r3_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(135,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( B @ ( A @ r1_isocat_1 ) )
=> ( A @ ( B @ r1_isocat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_isocat_1) ).
thf(712,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( B @ ( A @ r1_isocat_1 ) )
=> ( A @ ( B @ r1_isocat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k8_cat_1 ) @ k13_nattra_1 )
= ( B @ ( A @ k8_cat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_nattra_1) ).
thf(557,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k8_cat_1 ) @ k13_nattra_1 )
= ( B @ ( A @ k8_cat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(3,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ r3_nattra_1 ) ) ) )
<=> ( ? [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ v1_nattra_1 ) ) ) ) )
& ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_nattra_1) ).
thf(199,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ( ( ( ? [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ v1_nattra_1 ) ) ) ) )
& ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ r3_nattra_1 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ r3_nattra_1 ) ) ) )
=> ( ? [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ v1_nattra_1 ) ) ) ) )
& ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(73,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 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( G @ m2_cat_1 ) ) )
=> ( ( ( G @ ( F @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) ) )
=> ! [H: $i] :
( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( H @ m2_nattra_1 ) ) ) ) )
=> ! [I: $i] :
( ( G @ ( F @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( I @ m2_nattra_1 ) ) ) ) )
=> ( ( ( I @ ( G @ ( F @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( H @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( I @ ( G @ ( F @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( H @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) )
=> ( I @ ( H @ ( C @ ( B @ k11_cat_2 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ ( B @ k11_cat_2 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_isocat_2) ).
thf(502,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 ) ) )
=> ! [F: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( G @ m2_cat_1 ) ) )
=> ( ( ( G @ ( F @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) ) )
=> ! [H: $i] :
( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( H @ m2_nattra_1 ) ) ) ) )
=> ! [I: $i] :
( ( G @ ( F @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( I @ m2_nattra_1 ) ) ) ) )
=> ( ( ( I @ ( G @ ( F @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( H @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( I @ ( G @ ( F @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( H @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) )
=> ( I @ ( H @ ( C @ ( B @ k11_cat_2 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ ( C @ ( B @ k11_cat_2 ) @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( 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 @ ( B @ k11_cat_2 ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k18_cat_2 ) ) ) ) @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k18_cat_2) ).
thf(808,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( 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 @ ( B @ k11_cat_2 ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k18_cat_2 ) ) ) ) @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(148,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] :
( ( ( D @ l1_cat_1 )
& ( D @ v2_cat_1 ) )
=> ( ( ( D @ ( C @ r1_isocat_1 ) )
& ( B @ ( A @ r1_isocat_1 ) ) )
=> ( D @ ( B @ k11_cat_2 ) @ ( C @ ( A @ k11_cat_2 ) @ r1_isocat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_isocat_1) ).
thf(744,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] :
( ( ( D @ l1_cat_1 )
& ( D @ v2_cat_1 ) )
=> ( ( ( D @ ( C @ r1_isocat_1 ) )
& ( B @ ( A @ r1_isocat_1 ) ) )
=> ( D @ ( B @ k11_cat_2 ) @ ( C @ ( A @ k11_cat_2 ) @ r1_isocat_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ r2_isocat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r2_isocat_1) ).
thf(703,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ r2_isocat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(106,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k8_cat_1 ) @ v2_nattra_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_nattra_1) ).
thf(613,plain,
! [A: $i,B: $i] : ( B @ ( A @ k8_cat_1 ) @ v2_nattra_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(14,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( ( B @ ( A @ r2_isocat_1 ) )
<=> ? [C: $i] :
( ? [D: $i] :
( ( B @ k1_isocat_1 @ ( C @ ( D @ ( B @ ( A @ ( B @ k2_isocat_1 ) ) ) ) @ ( B @ ( B @ r3_nattra_1 ) ) ) )
& ( A @ k1_isocat_1 @ ( D @ ( C @ ( A @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( A @ ( A @ r3_nattra_1 ) ) ) )
& ( A @ ( B @ ( D @ m2_cat_1 ) ) ) )
& ( B @ ( A @ ( C @ m2_cat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_isocat_1) ).
thf(231,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( ( ? [C: $i] :
( ? [D: $i] :
( ( B @ k1_isocat_1 @ ( C @ ( D @ ( B @ ( A @ ( B @ k2_isocat_1 ) ) ) ) @ ( B @ ( B @ r3_nattra_1 ) ) ) )
& ( A @ k1_isocat_1 @ ( D @ ( C @ ( A @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( A @ ( A @ r3_nattra_1 ) ) ) )
& ( A @ ( B @ ( D @ m2_cat_1 ) ) ) )
& ( B @ ( A @ ( C @ m2_cat_1 ) ) ) )
=> ( B @ ( A @ r2_isocat_1 ) ) )
& ( ( B @ ( A @ r2_isocat_1 ) )
=> ? [C: $i] :
( ? [D: $i] :
( ( B @ k1_isocat_1 @ ( C @ ( D @ ( B @ ( A @ ( B @ k2_isocat_1 ) ) ) ) @ ( B @ ( B @ r3_nattra_1 ) ) ) )
& ( A @ k1_isocat_1 @ ( D @ ( C @ ( A @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( A @ ( A @ r3_nattra_1 ) ) ) )
& ( A @ ( B @ ( D @ m2_cat_1 ) ) ) )
& ( B @ ( A @ ( C @ m2_cat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(112,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 @ m1_isocat_1 ) ) )
=> ( B @ ( A @ ( C @ m2_cat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_isocat_1) ).
thf(627,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 @ m1_isocat_1 ) ) )
=> ( B @ ( A @ ( C @ m2_cat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(127,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(688,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)],[127]) ).
thf(10,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ k12_nattra_1 ) @ u1_cat_1 @ ( C @ m1_subset_1 ) )
<=> ( B @ ( A @ ( C @ m2_cat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_isocat_2) ).
thf(218,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ( B @ ( A @ k12_nattra_1 ) @ u1_cat_1 @ ( C @ m1_subset_1 ) ) )
& ( ( B @ ( A @ k12_nattra_1 ) @ u1_cat_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ ( C @ m2_cat_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(189,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_cat_2 ) )
=> ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m3_cat_2) ).
thf(844,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_cat_2 ) )
=> ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(81,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 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) )
= ( C @ ( B @ k9_isocat_2 ) @ ( F @ ( E @ ( D @ ( C @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k6_isocat_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_isocat_2) ).
thf(524,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 ) ) )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) )
= ( C @ ( B @ k9_isocat_2 ) @ ( F @ ( E @ ( D @ ( C @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k6_isocat_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(101,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m1_cat_2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ m1_subset_1 ) )
=> ( B @ ( A @ ( D @ m2_cat_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_cat_2) ).
thf(581,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ( ( ! [D: $i] :
( ( C @ ( D @ m1_subset_1 ) )
=> ( B @ ( A @ ( D @ m2_cat_1 ) ) ) )
=> ( B @ ( A @ ( C @ m1_cat_2 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_cat_2 ) ) )
=> ! [D: $i] :
( ( C @ ( D @ m1_subset_1 ) )
=> ( B @ ( A @ ( D @ m2_cat_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(150,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i,C: $i] : ( A @ ( A @ ( C @ ( B @ k8_cat_1 ) @ k11_cat_2 ) @ r1_isocat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_isocat_1) ).
thf(748,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i,C: $i] : ( A @ ( A @ ( C @ ( B @ k8_cat_1 ) @ k11_cat_2 ) @ r1_isocat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k8_cat_1 ) @ l1_cat_1 )
& ( B @ ( A @ k8_cat_1 ) @ v2_cat_1 )
& ( B @ ( A @ k8_cat_1 ) @ v1_cat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_cat_1) ).
thf(652,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k8_cat_1 ) @ l1_cat_1 )
& ( B @ ( A @ k8_cat_1 ) @ v2_cat_1 )
& ( B @ ( A @ k8_cat_1 ) @ v1_cat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(55,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ( ( B @ ( A @ ( C @ v8_cat_1 ) ) )
=> ( C @ ( C @ ( B @ ( A @ k3_isocat_1 ) ) @ ( A @ ( B @ k3_isocat_1 ) ) @ ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_isocat_1) ).
thf(401,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ( ( B @ ( A @ ( C @ v8_cat_1 ) ) )
=> ( C @ ( C @ ( B @ ( A @ k3_isocat_1 ) ) @ ( A @ ( B @ k3_isocat_1 ) ) @ ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(103,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 @ m4_nattra_1 ) ) )
=> ~ ( C @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m4_nattra_1) ).
thf(588,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 @ m4_nattra_1 ) ) )
=> ~ ( C @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(130,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(699,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)],[130]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
& ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
& ( 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 ) )
=> ( E @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ m2_nattra_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_isocat_2) ).
thf(568,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
& ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
& ( 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 ) )
=> ( E @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ m2_nattra_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k8_cat_1 ) @ u1_cat_1 @ ( C @ m1_subset_1 ) )
=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_cat_1) ).
thf(207,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k8_cat_1 ) @ u1_cat_1 @ ( C @ m1_subset_1 ) )
=> ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(120,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 @ ( A @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( C @ ( A @ ( G @ m2_cat_1 ) ) )
=> ( ( ( G @ ( F @ ( C @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
=> ( G @ ( E @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_isocat_2) ).
thf(667,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 @ ( A @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( C @ ( A @ ( G @ m2_cat_1 ) ) )
=> ( ( ( G @ ( F @ ( C @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
=> ( G @ ( E @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(156,axiom,
? [A: $i] : ( A @ l1_cat_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_cat_1) ).
thf(763,plain,
? [A: $i] : ( A @ l1_cat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(21,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(272,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)],[21]) ).
thf(137,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( ( B @ ( A @ r1_isocat_1 ) )
<=> ? [C: $i] :
( ( B @ ( A @ ( C @ v8_cat_1 ) ) )
& ( B @ ( A @ ( C @ m2_cat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_isocat_1) ).
thf(716,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( ( ? [C: $i] :
( ( B @ ( A @ ( C @ v8_cat_1 ) ) )
& ( B @ ( A @ ( C @ m2_cat_1 ) ) ) )
=> ( B @ ( A @ r1_isocat_1 ) ) )
& ( ( B @ ( A @ r1_isocat_1 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v8_cat_1 ) ) )
& ( B @ ( A @ ( C @ m2_cat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(8,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(214,plain,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ~ ( A @ u1_cat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(32,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_nattra_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( C @ ( C @ ( A @ ( B @ ( D @ m1_nattra_1 ) ) ) ) )
=> ( C @ ( A @ ( B @ k7_nattra_1 ) ) @ ( D @ ( A @ u2_cat_1 @ ( B @ u1_cat_1 @ ( A @ u2_cat_1 @ ( B @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_nattra_1) ).
thf(300,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_nattra_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( C @ ( C @ ( A @ ( B @ ( D @ m1_nattra_1 ) ) ) ) )
=> ( C @ ( A @ ( B @ k7_nattra_1 ) ) @ ( D @ ( A @ u2_cat_1 @ ( B @ u1_cat_1 @ ( A @ u2_cat_1 @ ( B @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(109,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 ) )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ ( E @ m1_nattra_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_nattra_1) ).
thf(620,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 ) )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ ( E @ m1_nattra_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(152,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 ) @ v2_cat_1 )
& ( B @ ( A @ k11_cat_2 ) @ v1_cat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_cat_2) ).
thf(752,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 ) @ v2_cat_1 )
& ( B @ ( A @ k11_cat_2 ) @ v1_cat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(186,axiom,
? [A: $i] :
( ( A @ v2_cat_1 )
& ( A @ l1_cat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_cat_1) ).
thf(833,plain,
? [A: $i] :
( ( A @ v2_cat_1 )
& ( A @ l1_cat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
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 ) )
=> ( C @ ( A @ k12_nattra_1 ) @ ( B @ ( A @ k12_nattra_1 ) @ k11_cat_2 ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k12_nattra_1 ) @ r1_isocat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_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 ) )
=> ( C @ ( A @ k12_nattra_1 ) @ ( B @ ( A @ k12_nattra_1 ) @ k11_cat_2 ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k12_nattra_1 ) @ r1_isocat_1 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(190,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 ) )
=> ( C @ ( A @ k12_nattra_1 ) @ ( B @ ( A @ k12_nattra_1 ) @ k11_cat_2 ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k12_nattra_1 ) @ r1_isocat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(61,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 @ ( A @ k12_nattra_1 ) @ ( B @ ( A @ k12_nattra_1 ) @ k11_cat_2 ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k12_nattra_1 ) @ ( D @ m2_cat_1 ) ) )
=> ( ( D
= ( C @ ( B @ ( A @ k17_isocat_2 ) ) ) )
<=> ! [E: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( F @ m2_cat_1 ) ) )
=> ( ( F @ ( E @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) )
=> ! [G: $i] :
( ( F @ ( E @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( G @ m2_nattra_1 ) ) ) ) )
=> ( ( G @ ( F @ ( E @ k4_tarski ) @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ k4_tarski ) @ k4_tarski ) @ ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ k4_tarski ) @ k4_tarski ) @ k4_tarski ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_isocat_2) ).
thf(422,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 @ ( A @ k12_nattra_1 ) @ ( B @ ( A @ k12_nattra_1 ) @ k11_cat_2 ) @ ( C @ ( B @ k11_cat_2 ) @ ( A @ k12_nattra_1 ) @ ( D @ m2_cat_1 ) ) )
=> ( ( ! [E: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( F @ m2_cat_1 ) ) )
=> ( ( F @ ( E @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) )
=> ! [G: $i] :
( ( F @ ( E @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( G @ m2_nattra_1 ) ) ) ) )
=> ( ( G @ ( F @ ( E @ k4_tarski ) @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ k4_tarski ) @ k4_tarski ) @ ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ k4_tarski ) @ k4_tarski ) @ k4_tarski ) ) ) ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k17_isocat_2 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k17_isocat_2 ) ) ) )
=> ! [E: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( F @ m2_cat_1 ) ) )
=> ( ( F @ ( E @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) )
=> ! [G: $i] :
( ( F @ ( E @ ( C @ ( B @ k11_cat_2 ) @ ( A @ ( G @ m2_nattra_1 ) ) ) ) )
=> ( ( G @ ( F @ ( E @ k4_tarski ) @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k14_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ k4_tarski ) @ k4_tarski ) @ ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k13_isocat_2 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ k4_tarski ) @ k4_tarski ) @ k4_tarski ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(96,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] :
( ( C @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( E @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ u2_cat_1 @ ( A @ u2_cat_1 @ ( C @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_isocat_2) ).
thf(564,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] :
( ( C @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( E @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ u2_cat_1 @ ( A @ u2_cat_1 @ ( C @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) )
& ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_isocat_2 ) ) ) ) @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ ( B @ u2_cat_1 @ ( A @ u2_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(6,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k8_cat_1 ) @ u1_cat_1 @ ( A @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_cat_1) ).
thf(210,plain,
! [A: $i,B: $i] : ( B @ ( A @ k8_cat_1 ) @ u1_cat_1 @ ( A @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(172,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( A @ k13_nattra_1 @ k13_nattra_1 )
= ( A @ k13_nattra_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_nattra_1) ).
thf(801,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( A @ k13_nattra_1 @ k13_nattra_1 )
= ( A @ k13_nattra_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(38,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ r3_nattra_1 ) ) ) )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ ( E @ m3_nattra_1 ) ) ) ) )
<=> ( D @ ( C @ ( B @ ( A @ ( E @ v1_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_nattra_1) ).
thf(341,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ r3_nattra_1 ) ) ) )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ ( E @ v1_nattra_1 ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ ( E @ m3_nattra_1 ) ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ ( E @ m3_nattra_1 ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ ( E @ v1_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(358,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(62,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 @ r1_nattra_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_nattra_1) ).
thf(437,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 @ r1_nattra_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(119,axiom,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_gate_1) ).
thf(664,plain,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(53,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) )
=> ( E @ ( B @ k1_isocat_1 @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k6_isocat_1 ) ) ) ) ) ) @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_isocat_1) ).
thf(395,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) )
=> ( E @ ( B @ k1_isocat_1 @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k6_isocat_1 ) ) ) ) ) ) @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ ( B @ u2_cat_1 @ ( A @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(100,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( ( B @ ( A @ r2_isocat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ( ( B @ ( A @ ( C @ m1_isocat_1 ) ) )
<=> ? [D: $i] :
( ( B @ k1_isocat_1 @ ( C @ ( D @ ( B @ ( A @ ( B @ k2_isocat_1 ) ) ) ) @ ( B @ ( B @ r3_nattra_1 ) ) ) )
& ( A @ k1_isocat_1 @ ( D @ ( C @ ( A @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( A @ ( A @ r3_nattra_1 ) ) ) )
& ( A @ ( B @ ( D @ m2_cat_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_isocat_1) ).
thf(575,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ( ( B @ ( A @ r2_isocat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_cat_1 ) ) )
=> ( ( ? [D: $i] :
( ( B @ k1_isocat_1 @ ( C @ ( D @ ( B @ ( A @ ( B @ k2_isocat_1 ) ) ) ) @ ( B @ ( B @ r3_nattra_1 ) ) ) )
& ( A @ k1_isocat_1 @ ( D @ ( C @ ( A @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( A @ ( A @ r3_nattra_1 ) ) ) )
& ( A @ ( B @ ( D @ m2_cat_1 ) ) ) )
=> ( B @ ( A @ ( C @ m1_isocat_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_isocat_1 ) ) )
=> ? [D: $i] :
( ( B @ k1_isocat_1 @ ( C @ ( D @ ( B @ ( A @ ( B @ k2_isocat_1 ) ) ) ) @ ( B @ ( B @ r3_nattra_1 ) ) ) )
& ( A @ k1_isocat_1 @ ( D @ ( C @ ( A @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( A @ ( A @ r3_nattra_1 ) ) ) )
& ( A @ ( B @ ( D @ m2_cat_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(114,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(644,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( B @ ( A @ k12_nattra_1 ) @ l1_cat_1 )
& ( B @ ( A @ k12_nattra_1 ) @ v2_cat_1 )
& ( B @ ( A @ k12_nattra_1 ) @ v1_cat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_nattra_1) ).
thf(723,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 )
& ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( B @ ( A @ k12_nattra_1 ) @ l1_cat_1 )
& ( B @ ( A @ k12_nattra_1 ) @ v2_cat_1 )
& ( B @ ( A @ k12_nattra_1 ) @ v1_cat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(128,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_nattra_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_cat_2 ) )
=> ( B @ v2_nattra_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_nattra_1) ).
thf(691,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_nattra_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_cat_2 ) )
=> ( B @ v2_nattra_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(140,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 ) )
=> ( C @ ( B @ k11_cat_2 ) @ ( A @ k11_cat_2 ) @ ( C @ ( B @ ( A @ k11_cat_2 ) @ k11_cat_2 ) @ r1_isocat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_isocat_1) ).
thf(728,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 ) )
=> ( C @ ( B @ k11_cat_2 ) @ ( A @ k11_cat_2 ) @ ( C @ ( B @ ( A @ k11_cat_2 ) @ k11_cat_2 ) @ r1_isocat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m2_cat_1 ) ) )
& ( C @ ( A @ ( E @ m2_cat_1 ) ) )
& ( D @ l1_cat_1 )
& ( D @ v2_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 ) )
=> ( D @ ( C @ k11_cat_2 ) @ ( B @ ( A @ k11_cat_2 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k19_cat_2 ) ) ) ) ) @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k19_cat_2) ).
thf(740,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m2_cat_1 ) ) )
& ( C @ ( A @ ( E @ m2_cat_1 ) ) )
& ( D @ l1_cat_1 )
& ( D @ v2_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 ) )
=> ( D @ ( C @ k11_cat_2 ) @ ( B @ ( A @ k11_cat_2 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k19_cat_2 ) ) ) ) ) @ m2_cat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(12,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(227,plain,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ~ ( A @ u2_cat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(34,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 @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( C @ ( B @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( A @ ( C @ ( G @ m2_cat_1 ) ) )
=> ! [H: $i] :
( ( E @ ( D @ ( C @ ( B @ ( H @ m2_nattra_1 ) ) ) ) )
=> ! [I: $i] :
( ( F @ ( E @ ( C @ ( B @ ( I @ m2_nattra_1 ) ) ) ) )
=> ( ( ( F @ ( E @ ( C @ ( B @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( C @ ( B @ r2_nattra_1 ) ) ) ) )
=> ( G @ ( I @ ( F @ ( E @ ( A @ ( C @ ( B @ k6_isocat_1 ) ) ) ) ) ) @ ( G @ ( H @ ( E @ ( D @ ( A @ ( C @ ( B @ k6_isocat_1 ) ) ) ) ) ) @ ( G @ ( F @ ( A @ ( C @ ( B @ k2_isocat_1 ) ) ) ) @ ( G @ ( E @ ( A @ ( C @ ( B @ k2_isocat_1 ) ) ) ) @ ( G @ ( D @ ( A @ ( C @ ( B @ k2_isocat_1 ) ) ) ) @ ( A @ ( B @ k8_nattra_1 ) ) ) ) ) ) @ ( G @ ( I @ ( H @ ( F @ ( E @ ( D @ ( C @ ( B @ k8_nattra_1 ) ) ) ) ) ) @ ( F @ ( D @ ( A @ ( C @ ( B @ k6_isocat_1 ) ) ) ) ) ) @ ( A @ u2_cat_1 @ ( B @ u1_cat_1 @ ( A @ u2_cat_1 @ ( B @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_isocat_1) ).
thf(322,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 @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( C @ ( B @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( A @ ( C @ ( G @ m2_cat_1 ) ) )
=> ! [H: $i] :
( ( E @ ( D @ ( C @ ( B @ ( H @ m2_nattra_1 ) ) ) ) )
=> ! [I: $i] :
( ( F @ ( E @ ( C @ ( B @ ( I @ m2_nattra_1 ) ) ) ) )
=> ( ( ( F @ ( E @ ( C @ ( B @ r2_nattra_1 ) ) ) )
& ( E @ ( D @ ( C @ ( B @ r2_nattra_1 ) ) ) ) )
=> ( G @ ( I @ ( F @ ( E @ ( A @ ( C @ ( B @ k6_isocat_1 ) ) ) ) ) ) @ ( G @ ( H @ ( E @ ( D @ ( A @ ( C @ ( B @ k6_isocat_1 ) ) ) ) ) ) @ ( G @ ( F @ ( A @ ( C @ ( B @ k2_isocat_1 ) ) ) ) @ ( G @ ( E @ ( A @ ( C @ ( B @ k2_isocat_1 ) ) ) ) @ ( G @ ( D @ ( A @ ( C @ ( B @ k2_isocat_1 ) ) ) ) @ ( A @ ( B @ k8_nattra_1 ) ) ) ) ) ) @ ( G @ ( I @ ( H @ ( F @ ( E @ ( D @ ( C @ ( B @ k8_nattra_1 ) ) ) ) ) ) @ ( F @ ( D @ ( A @ ( C @ ( B @ k6_isocat_1 ) ) ) ) ) ) @ ( A @ u2_cat_1 @ ( B @ u1_cat_1 @ ( A @ u2_cat_1 @ ( B @ u1_cat_1 @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(67,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] :
( ( ( D @ l1_cat_1 )
& ( D @ v2_cat_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( D @ ( C @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( C @ ( B @ ( G @ m2_cat_1 ) ) )
=> ! [H: $i] :
( ( C @ ( B @ ( H @ m2_cat_1 ) ) )
=> ( ( H @ ( G @ ( C @ ( B @ r3_nattra_1 ) ) ) )
=> ( ( H @ ( E @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( G @ ( E @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( C @ ( A @ r3_nattra_1 ) ) ) )
& ( F @ ( H @ ( D @ ( C @ ( B @ k2_isocat_1 ) ) ) ) @ ( F @ ( G @ ( D @ ( C @ ( B @ k2_isocat_1 ) ) ) ) @ ( D @ ( B @ r3_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_isocat_1) ).
thf(486,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] :
( ( ( D @ l1_cat_1 )
& ( D @ v2_cat_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m2_cat_1 ) ) )
=> ! [F: $i] :
( ( D @ ( C @ ( F @ m2_cat_1 ) ) )
=> ! [G: $i] :
( ( C @ ( B @ ( G @ m2_cat_1 ) ) )
=> ! [H: $i] :
( ( C @ ( B @ ( H @ m2_cat_1 ) ) )
=> ( ( H @ ( G @ ( C @ ( B @ r3_nattra_1 ) ) ) )
=> ( ( H @ ( E @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( G @ ( E @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( C @ ( A @ r3_nattra_1 ) ) ) )
& ( F @ ( H @ ( D @ ( C @ ( B @ k2_isocat_1 ) ) ) ) @ ( F @ ( G @ ( D @ ( C @ ( B @ k2_isocat_1 ) ) ) ) @ ( D @ ( B @ r3_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(87,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 )
& ( A @ v1_cat_1 ) )
=> ( ( A @ v2_nattra_1 )
=> ( ( A @ k13_nattra_1 )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_nattra_1) ).
thf(543,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 )
& ( A @ v1_cat_1 ) )
=> ( ( A @ v2_nattra_1 )
=> ( ( A @ k13_nattra_1 )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(94,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(560,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( B @ ( G @ m2_cat_1 ) ) )
& ( E @ ( D @ ( B @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
& ( B @ ( A @ ( 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 ) )
=> ( G @ ( E @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( G @ ( D @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( C @ ( A @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_isocat_1 ) ) ) ) ) ) @ m2_nattra_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_isocat_1) ).
thf(496,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( B @ ( G @ m2_cat_1 ) ) )
& ( E @ ( D @ ( B @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
& ( B @ ( A @ ( 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 ) )
=> ( G @ ( E @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( G @ ( D @ ( C @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( C @ ( A @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_isocat_1 ) ) ) ) ) ) @ m2_nattra_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(21131,plain,
$false,
inference(e,[status(thm)],[629,365,555,352,440,677,730,276,384,533,550,500,797,829,709,417,288,570,785,504,770,261,216,492,756,789,443,238,806,821,397,280,734,774,660,507,527,292,546,761,810,714,270,529,746,825,778,302,297,693,815,229,625,842,324,224,615,403,388,519,742,783,420,328,339,537,669,686,590,679,212,706,393,647,701,515,738,721,371,622,837,792,360,205,765,674,586,662,412,750,618,513,819,562,732,772,286,391,445,572,498,804,350,611,787,406,831,681,274,736,509,758,535,799,483,251,345,367,552,521,827,278,780,267,490,795,548,374,812,355,823,776,295,282,263,712,557,199,502,808,744,703,613,231,627,688,218,844,524,581,748,652,401,588,699,568,207,667,763,272,716,214,300,620,752,833,190,422,564,210,801,341,358,437,664,395,575,644,723,691,728,740,227,322,486,543,560,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : CAT032+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % 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
% 0.05/0.32 % Computer : n012.cluster.edu
% 0.05/0.32 % Model : x86_64 x86_64
% 0.05/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.32 % Memory : 8046.5625MB
% 0.05/0.32 % OS : Linux 6.8.0-71-generic
% 0.05/0.32 % CPULimit : 300
% 0.05/0.32 % WCLimit : 300
% 0.05/0.32 % DateTime : Sat Sep 26 22:57:56 UTC 2026
% 0.05/0.33 % CPUTime :
% 0.05/0.33 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
% 0.53/0.70 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 6.08/3.62 % [INFO] Parsing done (2907ms).
% 6.08/3.64 % [INFO] Running in sequential loop mode.
% 6.44/3.91 % [INFO] eprover registered as external prover.
% 6.44/3.93 % [INFO] Scanning for conjecture ...
% 8.66/5.28 % [INFO] Found a conjecture (or negated_conjecture) and 29117 axioms. Running axiom selection ...
% 10.70/6.94 % [INFO] Axiom selection finished. Selected 187 axioms (removed 28930 axioms).
% 11.11/7.25 % [INFO] Problem is first-order (TPTP FOF).
% 11.11/7.27 % [INFO] Type checking passed.
% 11.11/7.28 % [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 ...
% 54.68/21.90 % External prover 'e' found a proof!
% 54.68/21.90 % [INFO] Killing All external provers ...
% 54.68/21.91 % Time passed: 21505ms (effective reasoning time: 18260ms)
% 54.68/21.91 % 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)>
% 54.68/21.91 % Axioms used in derivation (187): t2_tarski, dt_k3_isocat_1, t32_isocat_1, t28_isocat_2, dt_k13_isocat_2, dt_k4_cat_1, dt_k7_isocat_2, dt_k16_cat_2, t46_isocat_2, dt_m3_cat_2, t48_nattra_1, fc1_zfmisc_1, dt_k7_cat_2, t36_isocat_2, t46_nattra_1, t13_isocat_1, t26_isocat_2, t51_nattra_1, existence_l1_cat_1, t23_isocat_1, reflexivity_r1_isocat_1, t17_isocat_1, existence_m4_nattra_1, dt_m1_cat_2, t4_ordinal1, d10_isocat_1, t27_isocat_1, t1_subset, existence_m3_nattra_1, t36_isocat_1, dt_m3_nattra_1, t49_nattra_1, dt_k10_nattra_1, fc2_cat_2, t37_isocat_2, redefinition_k9_isocat_2, t31_nattra_1, t33_isocat_2, dt_k8_cat_1, t29_isocat_2, t19_cat_2, rc2_nattra_1, t55_isocat_1, t47_nattra_1, t30_isocat_2, redefinition_k10_isocat_2, t54_nattra_1, dt_k15_isocat_2, t18_cat_2, t12_cat_2, t8_isocat_2, d14_nattra_1, d8_isocat_2, t48_isocat_2, dt_k2_isocat_1, d13_isocat_2, symmetry_r2_isocat_1, dt_k6_isocat_1, dt_k19_cat_2, t15_isocat_1, dt_k12_isocat_2, t56_isocat_1, d19_ens_1, t32_isocat_2, t33_cat_1, t52_nattra_1, fc5_ens_1, t21_isocat_1, dt_k7_commacat, redefinition_k18_cat_2, dt_k15_cat_1, dt_k5_isocat_2, t54_isocat_1, t35_cat_1, d15_nattra_1, reflexivity_r3_nattra_1, existence_m3_cat_2, d12_isocat_2, t55_nattra_1, dt_k7_nattra_1, t25_nattra_1, d4_isocat_1, t48_isocat_1, symmetry_r1_isocat_1, t49_isocat_1, existence_m2_nattra_1, t5_ordinal1, reflexivity_r2_isocat_1, dt_k8_cat_2, d10_isocat_2, t22_isocat_1, existence_m2_cat_1, d6_isocat_2, t7_boole, t50_isocat_1, t122_cat_1, t31_isocat_2, d2_subset_1, t33_zfmisc_1, t3_ordinal1, d9_isocat_2, dt_m1_isocat_1, rc1_cat_1, d5_cat_2, existence_m1_cat_2, reflexivity_r2_nattra_1, rc2_cat_1, dt_k14_isocat_2, t41_isocat_2, dt_m4_nattra_1, t35_nattra_1, rc1_nattra_1, t2_gate_1, t44_isocat_2, t20_isocat_1, dt_m2_nattra_1, t39_isocat_2, existence_m1_subset_1, d3_cat_2, reflexivity_r1_nattra_1, d7_isocat_2, dt_u1_cat_1, t19_nattra_1, rc3_cat_1, d11_nattra_1, t53_isocat_1, t33_nattra_1, dt_k16_isocat_2, t47_isocat_2, redefinition_k19_cat_2, t26_nattra_1, t34_cat_1, t42_nattra_1, existence_m2_cat_2, dt_k10_isocat_2, dt_k11_cat_2, t40_isocat_2, redefinition_k8_isocat_2, t50_nattra_1, t38_isocat_2, redefinition_k7_cat_2, t10_nattra_1, dt_k13_nattra_1, dt_k11_nattra_1, t32_cat_1, dt_u2_cat_1, existence_m1_isocat_1, rc1_cat_2, d11_isocat_1, existence_m1_oppcat_1, d16_nattra_1, t14_cat_2, dt_k17_isocat_2, dt_k12_nattra_1, dt_k6_isocat_2, t32_nattra_1, t24_isocat_1, t8_boole, rc1_xboole_0, t11_isocat_2, t16_isocat_1, dt_k8_nattra_1, t2_subset, existence_m1_nattra_1, redefinition_k1_isocat_1, t34_nattra_1, dt_k1_isocat_1, dt_k11_isocat_2, dt_m2_cat_2, t40_isocat_1, t34_isocat_2, t4_nattra_1, t7_tarski, t6_ordinal1, t53_nattra_1, fc1_cat_2, rc2_xboole_0, redefinition_m2_cat_2, t28_nattra_1, dt_k9_isocat_2, dt_k8_isocat_2, d2_cat_2, t112_zfmisc_1, dt_k17_cat_2, antisymmetry_r2_hidden, dt_k18_cat_2, t38_isocat_1
% 54.68/21.91 % No. of inferences in proof: 378
% 54.68/21.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21505 ms resp. 18260 ms w/o parsing
% 55.33/22.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 55.63/22.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------