%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT025+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:55:26 AM UTC 2026
% Result : Theorem 51.34s 11.23s
% Output : Refutation 47.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 149
% Syntax : Number of formulae : 300 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 2046 ( 80 equ; 0 cnn)
% Maximal formula atoms : 31 ( 6 avg)
% Number of connectives : 7025 ( 54 ~; 2 |;1045 &;5225 @)
% ( 18 <=>; 681 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 64 usr; 1 con; 0-9 aty)
% Number of variables : 1085 ( 0 ^;1015 !; 70 ?;1085 :)
% 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(m3_cat_2_decl,type,
m3_cat_2: $i > $i > $o ).
thf(v10_cat_1_decl,type,
v10_cat_1: $i > $i > $i > $o ).
thf(k8_cat_2_decl,type,
k8_cat_2: $i > $i > $i ).
thf(m2_cat_1_decl,type,
m2_cat_1: $i > $i > $i > $o ).
thf(r1_nattra_1_decl,type,
r1_nattra_1: $i > $i > $i > $i > $o ).
thf(m1_nattra_1_decl,type,
m1_nattra_1: $i > $i > $i > $i > $i > $o ).
thf(k6_nattra_1_decl,type,
k6_nattra_1: $i > $i > $i > $i > $i > $i > $i > $i ).
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(m1_subset_1_decl,type,
m1_subset_1: $i > $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(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
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(k4_nattra_1_decl,type,
k4_nattra_1: $i > $i > $i > $i ).
thf(k7_nattra_1_decl,type,
k7_nattra_1: $i > $i > $i > $i ).
thf(m3_nattra_1_decl,type,
m3_nattra_1: $i > $i > $i > $i > $i > $o ).
thf(m1_isocat_1_decl,type,
m1_isocat_1: $i > $i > $i > $o ).
thf(k8_nattra_1_decl,type,
k8_nattra_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k11_nattra_1_decl,type,
k11_nattra_1: $i > $i > $i ).
thf(k10_nattra_1_decl,type,
k10_nattra_1: $i > $i > $i > $i > $i > $i ).
thf(k9_nattra_1_decl,type,
k9_nattra_1: $i > $i > $i > $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(v1_cat_1_decl,type,
v1_cat_1: $i > $o ).
thf(v2_nattra_1_decl,type,
v2_nattra_1: $i > $o ).
thf(k13_nattra_1_decl,type,
k13_nattra_1: $i > $i ).
thf(v8_cat_1_decl,type,
v8_cat_1: $i > $i > $i > $o ).
thf(k10_isocat_2_decl,type,
k10_isocat_2: $i > $i > $i > $i > $i > $i ).
thf(k13_funct_3_decl,type,
k13_funct_3: $i > $i > $i ).
thf(k8_cat_1_decl,type,
k8_cat_1: $i > $i > $i ).
thf(k15_cat_1_decl,type,
k15_cat_1: $i > $i ).
thf(k3_isocat_1_decl,type,
k3_isocat_1: $i > $i > $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(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(k2_funct_1_decl,type,
k2_funct_1: $i > $i ).
thf(k7_isocat_2_decl,type,
k7_isocat_2: $i > $i > $i > $i ).
thf(k1_funct_1_decl,type,
k1_funct_1: $i > $i > $i ).
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(k17_cat_2_decl,type,
k17_cat_2: $i > $i > $i ).
thf(k7_cat_2_decl,type,
k7_cat_2: $i > $i > $i ).
thf(k15_isocat_2_decl,type,
k15_isocat_2: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k16_isocat_2_decl,type,
k16_isocat_2: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k8_isocat_2_decl,type,
k8_isocat_2: $i > $i > $i ).
thf(k14_isocat_2_decl,type,
k14_isocat_2: $i > $i > $i > $i > $i > $i > $i ).
thf(k12_isocat_2_decl,type,
k12_isocat_2: $i > $i > $i > $i > $i ).
thf(k13_isocat_2_decl,type,
k13_isocat_2: $i > $i > $i > $i > $i > $i > $i ).
thf(k11_isocat_2_decl,type,
k11_isocat_2: $i > $i > $i > $i > $i ).
thf(k17_isocat_2_decl,type,
k17_isocat_2: $i > $i > $i > $i ).
thf(k16_cat_2_decl,type,
k16_cat_2: $i > $i > $i ).
thf(k9_isocat_2_decl,type,
k9_isocat_2: $i > $i > $i ).
thf(76,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/sandbox2/benchmark/theBenchmark.p',dt_m1_isocat_1) ).
thf(479,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)],[76]) ).
thf(85,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k8_cat_1 ) @ v2_nattra_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_nattra_1) ).
thf(518,plain,
! [A: $i,B: $i] : ( B @ ( A @ k8_cat_1 ) @ v2_nattra_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(21,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 ) ) )
=> ( ( A @ k1_isocat_1 @ ( D @ ( C @ ( A @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( A @ ( A @ r3_nattra_1 ) ) ) )
=> ( B @ ( A @ ( C @ v10_cat_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_isocat_1) ).
thf(234,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 ) ) )
=> ( ( A @ k1_isocat_1 @ ( D @ ( C @ ( A @ ( B @ ( A @ k2_isocat_1 ) ) ) ) @ ( A @ ( A @ r3_nattra_1 ) ) ) )
=> ( B @ ( A @ ( C @ v10_cat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(77,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/sandbox2/benchmark/theBenchmark.p',d6_isocat_2) ).
thf(481,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)],[77]) ).
thf(56,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/sandbox2/benchmark/theBenchmark.p',dt_m1_cat_2) ).
thf(408,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)],[56]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',dt_m3_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 ) )
=> ! [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)],[67]) ).
thf(83,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/sandbox2/benchmark/theBenchmark.p',dt_k8_cat_2) ).
thf(511,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)],[83]) ).
thf(48,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/sandbox2/benchmark/theBenchmark.p',dt_m2_cat_2) ).
thf(385,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)],[48]) ).
thf(90,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/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_isocat_1) ).
thf(533,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)],[90]) ).
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] :
( ~ ( 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/sandbox2/benchmark/theBenchmark.p',d15_nattra_1) ).
thf(185,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)],[10]) ).
thf(101,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/sandbox2/benchmark/theBenchmark.p',dt_k8_isocat_2) ).
thf(565,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)],[101]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',t19_nattra_1) ).
thf(174,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)],[7]) ).
thf(54,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/sandbox2/benchmark/theBenchmark.p',dt_k7_nattra_1) ).
thf(404,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)],[54]) ).
thf(136,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/sandbox2/benchmark/theBenchmark.p',dt_k18_cat_2) ).
thf(651,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)],[136]) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_nattra_1) ).
thf(257,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)],[28]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(357,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)],[41]) ).
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_cat_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_cat_2) ).
thf(587,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)],[112]) ).
thf(125,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/sandbox2/benchmark/theBenchmark.p',redefinition_k8_isocat_2) ).
thf(619,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)],[125]) ).
thf(98,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/sandbox2/benchmark/theBenchmark.p',dt_k15_isocat_2) ).
thf(559,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)],[98]) ).
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] :
( ( 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/sandbox2/benchmark/theBenchmark.p',t34_nattra_1) ).
thf(284,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)],[34]) ).
thf(118,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/sandbox2/benchmark/theBenchmark.p',dt_m4_nattra_1) ).
thf(602,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)],[118]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(221,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)],[15]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(243,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)],[24]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(248,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(30,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/sandbox2/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(270,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)],[30]) ).
thf(140,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/sandbox2/benchmark/theBenchmark.p',existence_m1_isocat_1) ).
thf(661,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)],[140]) ).
thf(46,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/sandbox2/benchmark/theBenchmark.p',dt_k8_nattra_1) ).
thf(381,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)],[46]) ).
thf(39,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(334,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k4_tarski ) )
= ( D @ ( C @ k4_tarski ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(260,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)],[29]) ).
thf(99,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/sandbox2/benchmark/theBenchmark.p',dt_k16_isocat_2) ).
thf(561,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)],[99]) ).
thf(63,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/sandbox2/benchmark/theBenchmark.p',t13_isocat_1) ).
thf(424,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)],[63]) ).
thf(129,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/sandbox2/benchmark/theBenchmark.p',dt_k9_isocat_2) ).
thf(630,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)],[129]) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',d11_isocat_1) ).
thf(429,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)],[65]) ).
thf(32,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/sandbox2/benchmark/theBenchmark.p',t26_nattra_1) ).
thf(275,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)],[32]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',d11_nattra_1) ).
thf(165,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)],[5]) ).
thf(116,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/sandbox2/benchmark/theBenchmark.p',dt_k11_isocat_2) ).
thf(598,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)],[116]) ).
thf(3,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_cat_2 ) )
=> ( A @ ( B @ ( B @ ( A @ k8_cat_2 ) @ v10_cat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_cat_2) ).
thf(160,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_cat_2 ) )
=> ( A @ ( B @ ( B @ ( A @ k8_cat_2 ) @ v10_cat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( B @ ( A @ ( E @ m1_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 @ k9_nattra_1 ) ) ) ) @ m1_nattra_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_nattra_1) ).
thf(467,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( B @ ( A @ ( E @ m1_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 @ k9_nattra_1 ) ) ) ) @ m1_nattra_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',d3_cat_2) ).
thf(435,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)],[66]) ).
thf(142,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ ( A @ k1_isocat_1 @ m1_isocat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_isocat_1) ).
thf(665,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)],[142]) ).
thf(110,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/sandbox2/benchmark/theBenchmark.p',t21_isocat_1) ).
thf(583,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)],[110]) ).
thf(148,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/sandbox2/benchmark/theBenchmark.p',dt_k7_isocat_2) ).
thf(682,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)],[148]) ).
thf(36,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(324,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(123,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/sandbox2/benchmark/theBenchmark.p',dt_k3_isocat_1) ).
thf(615,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)],[123]) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',dt_k12_isocat_2) ).
thf(593,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)],[114]) ).
thf(61,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(420,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(79,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/sandbox2/benchmark/theBenchmark.p',t19_cat_2) ).
thf(499,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)],[79]) ).
thf(73,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/sandbox2/benchmark/theBenchmark.p',redefinition_k19_cat_2) ).
thf(471,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)],[73]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',dt_k2_isocat_1) ).
thf(225,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)],[17]) ).
thf(97,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/sandbox2/benchmark/theBenchmark.p',dt_k12_nattra_1) ).
thf(554,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)],[97]) ).
thf(144,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/sandbox2/benchmark/theBenchmark.p',dt_k10_isocat_2) ).
thf(669,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)],[144]) ).
thf(132,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ ( A @ k15_cat_1 @ v8_cat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_cat_1) ).
thf(642,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)],[132]) ).
thf(87,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/sandbox2/benchmark/theBenchmark.p',dt_k17_cat_2) ).
thf(526,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)],[87]) ).
thf(95,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/sandbox2/benchmark/theBenchmark.p',d4_isocat_1) ).
thf(547,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)],[95]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(212,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)],[13]) ).
thf(126,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ? [B: $i] : ( A @ ( B @ m3_cat_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_cat_2) ).
thf(622,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)],[126]) ).
thf(51,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/sandbox2/benchmark/theBenchmark.p',rc2_nattra_1) ).
thf(393,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)],[51]) ).
thf(134,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/sandbox2/benchmark/theBenchmark.p',t51_nattra_1) ).
thf(647,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)],[134]) ).
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 @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_cat_1) ).
thf(569,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)],[103]) ).
thf(43,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/sandbox2/benchmark/theBenchmark.p',t35_nattra_1) ).
thf(371,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)],[43]) ).
thf(81,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/sandbox2/benchmark/theBenchmark.p',dt_k13_nattra_1) ).
thf(503,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)],[81]) ).
thf(82,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/sandbox2/benchmark/theBenchmark.p',d5_cat_2) ).
thf(508,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)],[82]) ).
thf(138,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/sandbox2/benchmark/theBenchmark.p',existence_m4_nattra_1) ).
thf(657,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)],[138]) ).
thf(89,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/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_isocat_1) ).
thf(530,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)],[89]) ).
thf(84,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/sandbox2/benchmark/theBenchmark.p',rc1_cat_2) ).
thf(513,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)],[84]) ).
thf(105,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/sandbox2/benchmark/theBenchmark.p',t22_isocat_1) ).
thf(573,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)],[105]) ).
thf(69,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/sandbox2/benchmark/theBenchmark.p',existence_m2_nattra_1) ).
thf(444,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)],[69]) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_nattra_1) ).
thf(375,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)],[44]) ).
thf(8,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(176,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( E @ ( D @ ( B @ ( A @ ( G @ m1_nattra_1 ) ) ) ) )
& ( D @ ( C @ ( B @ ( A @ ( F @ m1_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 @ k6_nattra_1 ) ) ) ) ) ) @ m1_nattra_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_nattra_1) ).
thf(402,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( E @ ( D @ ( B @ ( A @ ( G @ m1_nattra_1 ) ) ) ) )
& ( D @ ( C @ ( B @ ( A @ ( F @ m1_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 @ k6_nattra_1 ) ) ) ) ) ) @ m1_nattra_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
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] :
( ( 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/sandbox2/benchmark/theBenchmark.p',d16_nattra_1) ).
thf(286,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)],[35]) ).
thf(107,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/sandbox2/benchmark/theBenchmark.p',dt_k19_cat_2) ).
thf(577,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)],[107]) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',symmetry_r2_isocat_1) ).
thf(579,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)],[108]) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(281,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)],[33]) ).
thf(94,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/sandbox2/benchmark/theBenchmark.p',dt_k5_isocat_2) ).
thf(545,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)],[94]) ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',dt_k10_nattra_1) ).
thf(413,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)],[58]) ).
thf(50,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/sandbox2/benchmark/theBenchmark.p',t33_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 ) ) )
=> ( C @ ( C @ ( B @ ( A @ ( C @ ( B @ ( A @ k7_nattra_1 ) ) @ m3_nattra_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',dt_k17_isocat_2) ).
thf(611,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)],[121]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(236,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)],[22]) ).
thf(92,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/sandbox2/benchmark/theBenchmark.p',t55_nattra_1) ).
thf(540,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)],[92]) ).
thf(119,axiom,
? [A: $i] :
( ( A @ v2_nattra_1 )
& ( A @ v2_cat_1 )
& ( A @ l1_cat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_nattra_1) ).
thf(604,plain,
? [A: $i] :
( ( A @ v2_nattra_1 )
& ( A @ v2_cat_1 )
& ( A @ l1_cat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
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] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',t17_isocat_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] :
( ( ( 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)],[55]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',t27_isocat_1) ).
thf(230,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)],[19]) ).
thf(102,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/sandbox2/benchmark/theBenchmark.p',t20_isocat_1) ).
thf(567,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)],[102]) ).
thf(135,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/sandbox2/benchmark/theBenchmark.p',dt_k16_cat_2) ).
thf(649,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)],[135]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',t49_isocat_1) ).
thf(208,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)],[12]) ).
thf(75,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/sandbox2/benchmark/theBenchmark.p',t47_nattra_1) ).
thf(477,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)],[75]) ).
thf(49,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(387,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
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 ) )
=> ( ( ( C @ ( B @ r2_isocat_1 ) )
& ( B @ ( A @ r2_isocat_1 ) ) )
=> ( C @ ( A @ r2_isocat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_isocat_1) ).
thf(552,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)],[96]) ).
thf(120,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/sandbox2/benchmark/theBenchmark.p',existence_m3_nattra_1) ).
thf(609,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)],[120]) ).
thf(86,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/sandbox2/benchmark/theBenchmark.p',redefinition_m2_cat_2) ).
thf(520,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)],[86]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(198,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)],[11]) ).
thf(52,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/sandbox2/benchmark/theBenchmark.p',t52_nattra_1) ).
thf(399,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)],[52]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',t25_nattra_1) ).
thf(223,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)],[16]) ).
thf(100,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/sandbox2/benchmark/theBenchmark.p',t23_isocat_1) ).
thf(563,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)],[100]) ).
thf(137,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/sandbox2/benchmark/theBenchmark.p',dt_k11_cat_2) ).
thf(653,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)],[137]) ).
thf(146,axiom,
? [A: $i] :
( ( A @ v2_cat_1 )
& ( A @ v1_cat_1 )
& ( A @ l1_cat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_cat_1) ).
thf(675,plain,
? [A: $i] :
( ( A @ v2_cat_1 )
& ( A @ v1_cat_1 )
& ( A @ l1_cat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(64,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/sandbox2/benchmark/theBenchmark.p',redefinition_k18_cat_2) ).
thf(426,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)],[64]) ).
thf(113,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/sandbox2/benchmark/theBenchmark.p',fc2_cat_2) ).
thf(589,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)],[113]) ).
thf(4,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 ) ) )
=> ( ( ( F @ ( E @ ( B @ ( A @ r1_nattra_1 ) ) ) )
& ( E @ ( D @ ( B @ ( A @ r1_nattra_1 ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r1_nattra_1 ) ) ) ) )
=> ! [G: $i] :
( ( D @ ( C @ ( B @ ( A @ ( G @ m1_nattra_1 ) ) ) ) )
=> ! [H: $i] :
( ( E @ ( D @ ( B @ ( A @ ( H @ m1_nattra_1 ) ) ) ) )
=> ! [I: $i] :
( ( F @ ( E @ ( B @ ( A @ ( I @ m1_nattra_1 ) ) ) ) )
=> ( ( I @ ( H @ ( F @ ( E @ ( D @ ( B @ ( A @ k6_nattra_1 ) ) ) ) ) ) @ ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ k6_nattra_1 ) ) ) ) ) ) )
= ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_nattra_1 ) ) ) ) ) ) @ ( F @ ( E @ ( C @ ( B @ ( A @ k6_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_nattra_1) ).
thf(162,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 ) ) )
=> ( ( ( F @ ( E @ ( B @ ( A @ r1_nattra_1 ) ) ) )
& ( E @ ( D @ ( B @ ( A @ r1_nattra_1 ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r1_nattra_1 ) ) ) ) )
=> ! [G: $i] :
( ( D @ ( C @ ( B @ ( A @ ( G @ m1_nattra_1 ) ) ) ) )
=> ! [H: $i] :
( ( E @ ( D @ ( B @ ( A @ ( H @ m1_nattra_1 ) ) ) ) )
=> ! [I: $i] :
( ( F @ ( E @ ( B @ ( A @ ( I @ m1_nattra_1 ) ) ) ) )
=> ( ( I @ ( H @ ( F @ ( E @ ( D @ ( B @ ( A @ k6_nattra_1 ) ) ) ) ) ) @ ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ k6_nattra_1 ) ) ) ) ) ) )
= ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_nattra_1 ) ) ) ) ) ) @ ( F @ ( E @ ( C @ ( B @ ( A @ k6_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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 @ ( B @ ( A @ k11_nattra_1 ) @ m4_nattra_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_nattra_1) ).
thf(680,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)],[147]) ).
thf(141,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/sandbox2/benchmark/theBenchmark.p',t33_isocat_2) ).
thf(663,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)],[141]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',t32_nattra_1) ).
thf(255,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)],[27]) ).
thf(124,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ m3_cat_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_cat_2) ).
thf(617,plain,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ m3_cat_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',existence_m2_cat_2) ).
thf(640,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)],[131]) ).
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] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',t48_isocat_1) ).
thf(327,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)],[37]) ).
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 ) ) )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ m2_nattra_1 ) ) ) ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ ( E @ v1_nattra_1 ) ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k10_nattra_1 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ k9_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_nattra_1) ).
thf(331,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 @ ( E @ v1_nattra_1 ) ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k10_nattra_1 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ k9_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(111,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/sandbox2/benchmark/theBenchmark.p',dt_k13_isocat_2) ).
thf(585,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)],[111]) ).
thf(122,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/sandbox2/benchmark/theBenchmark.p',fc1_cat_2) ).
thf(613,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)],[122]) ).
thf(117,axiom,
? [A: $i] : ( A @ l1_cat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_cat_1) ).
thf(600,plain,
? [A: $i] : ( A @ l1_cat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(115,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/sandbox2/benchmark/theBenchmark.p',redefinition_k7_cat_2) ).
thf(595,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)],[115]) ).
thf(70,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/sandbox2/benchmark/theBenchmark.p',d2_cat_2) ).
thf(446,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)],[70]) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',dt_k14_isocat_2) ).
thf(571,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)],[104]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',t56_isocat_1) ).
thf(250,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)],[26]) ).
thf(128,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( ( A @ k1_isocat_1 )
= ( A @ k15_cat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_isocat_1) ).
thf(627,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)],[128]) ).
thf(145,axiom,
? [A: $i] :
( ( A @ v2_cat_1 )
& ( A @ l1_cat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_cat_1) ).
thf(671,plain,
? [A: $i] :
( ( A @ v2_cat_1 )
& ( A @ l1_cat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(150,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/sandbox2/benchmark/theBenchmark.p',t50_isocat_1) ).
thf(688,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)],[150]) ).
thf(109,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/sandbox2/benchmark/theBenchmark.p',t24_isocat_1) ).
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 @ 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)],[109]) ).
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/sandbox2/benchmark/theBenchmark.p',t28_nattra_1) ).
thf(368,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(130,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/sandbox2/benchmark/theBenchmark.p',dt_k8_cat_1) ).
thf(632,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)],[130]) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_nattra_1) ).
thf(171,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)],[6]) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',existence_m1_nattra_1) ).
thf(418,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)],[60]) ).
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 @ r2_nattra_1 ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r2_nattra_1 ) ) ) ) )
=> ! [F: $i] :
( ( D @ ( C @ ( B @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
=> ! [G: $i] :
( ( E @ ( D @ ( B @ ( A @ ( G @ m2_nattra_1 ) ) ) ) )
=> ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_nattra_1) ).
thf(378,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 ) ) ) ) )
=> ! [F: $i] :
( ( D @ ( C @ ( B @ ( A @ ( F @ m2_nattra_1 ) ) ) ) )
=> ! [G: $i] :
( ( E @ ( D @ ( B @ ( A @ ( G @ m2_nattra_1 ) ) ) ) )
=> ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_nattra_1 ) ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(143,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/sandbox2/benchmark/theBenchmark.p',dt_k6_isocat_2) ).
thf(667,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)],[143]) ).
thf(47,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ ( A @ k1_isocat_1 @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_isocat_1) ).
thf(383,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)],[47]) ).
thf(149,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/sandbox2/benchmark/theBenchmark.p',dt_m3_cat_2) ).
thf(684,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)],[149]) ).
thf(91,axiom,
? [A: $i] :
( ( A @ v1_cat_1 )
& ( A @ l1_cat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_cat_1) ).
thf(536,plain,
? [A: $i] :
( ( A @ v1_cat_1 )
& ( A @ l1_cat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
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 @ ( B @ k12_nattra_1 ) @ ( A @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k11_cat_2 ) @ k12_nattra_1 ) @ r1_isocat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_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 @ ( B @ k12_nattra_1 ) @ ( A @ k12_nattra_1 ) @ ( C @ ( B @ ( A @ k11_cat_2 ) @ k12_nattra_1 ) @ r1_isocat_1 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(151,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)],[2]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',redefinition_k10_isocat_2) ).
thf(410,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)],[57]) ).
thf(62,axiom,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ( A @ ( A @ ( A @ k15_cat_1 @ m2_cat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_cat_1) ).
thf(422,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)],[62]) ).
thf(31,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/sandbox2/benchmark/theBenchmark.p',t31_nattra_1) ).
thf(273,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)],[31]) ).
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 ) ) )
=> ( ( 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/sandbox2/benchmark/theBenchmark.p',d14_nattra_1) ).
thf(239,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)],[23]) ).
thf(74,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 @ ( B @ ( A @ k3_isocat_1 ) ) )
= ( C @ k2_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_isocat_1) ).
thf(474,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 @ ( B @ ( A @ k3_isocat_1 ) ) )
= ( C @ k2_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k8_cat_1 ) @ k13_nattra_1 )
= ( B @ ( A @ k8_cat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_nattra_1) ).
thf(415,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)],[59]) ).
thf(127,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/sandbox2/benchmark/theBenchmark.p',redefinition_k9_isocat_2) ).
thf(624,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)],[127]) ).
thf(106,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/sandbox2/benchmark/theBenchmark.p',t48_nattra_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 @ v2_nattra_1 )
& ( A @ v2_nattra_1 ) )
=> ( B @ ( A @ k11_cat_2 ) @ v2_nattra_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',dt_k7_cat_2) ).
thf(528,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)],[88]) ).
thf(133,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/sandbox2/benchmark/theBenchmark.p',t53_nattra_1) ).
thf(644,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)],[133]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',d10_isocat_1) ).
thf(178,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)],[9]) ).
thf(68,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 @ k4_nattra_1 ) ) @ m1_nattra_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_nattra_1) ).
thf(442,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 @ k4_nattra_1 ) ) @ m1_nattra_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
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 ) )
=> ( ( ( 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/sandbox2/benchmark/theBenchmark.p',t55_isocat_1) ).
thf(501,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)],[80]) ).
thf(18,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 @ ( B @ ( A @ k7_nattra_1 ) ) )
= ( C @ ( B @ ( A @ k4_nattra_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_nattra_1) ).
thf(227,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 @ ( B @ ( A @ k7_nattra_1 ) ) )
= ( C @ ( B @ ( A @ k4_nattra_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(40,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/sandbox2/benchmark/theBenchmark.p',t112_zfmisc_1) ).
thf(337,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)],[40]) ).
thf(72,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/sandbox2/benchmark/theBenchmark.p',dt_m2_nattra_1) ).
thf(469,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)],[72]) ).
thf(139,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/sandbox2/benchmark/theBenchmark.p',t11_isocat_2) ).
thf(659,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)],[139]) ).
thf(93,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/sandbox2/benchmark/theBenchmark.p',symmetry_r1_isocat_1) ).
thf(543,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)],[93]) ).
thf(14,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 @ r1_nattra_1 ) ) ) )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ m1_nattra_1 ) ) ) ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ k4_nattra_1 ) ) @ ( D @ ( C @ ( C @ ( B @ ( A @ k6_nattra_1 ) ) ) ) ) ) )
= E )
& ( ( D @ ( B @ ( A @ k4_nattra_1 ) ) @ ( E @ ( D @ ( D @ ( C @ ( B @ ( A @ k6_nattra_1 ) ) ) ) ) ) )
= E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_nattra_1) ).
thf(215,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 @ r1_nattra_1 ) ) ) )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ ( E @ m1_nattra_1 ) ) ) ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ k4_nattra_1 ) ) @ ( D @ ( C @ ( C @ ( B @ ( A @ k6_nattra_1 ) ) ) ) ) ) )
= E )
& ( ( D @ ( B @ ( A @ k4_nattra_1 ) ) @ ( E @ ( D @ ( D @ ( C @ ( B @ ( A @ k6_nattra_1 ) ) ) ) ) ) )
= E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(78,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(496,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(232,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5230,plain,
$false,
inference(e,[status(thm)],[479,518,234,481,408,440,511,385,533,185,565,174,404,651,257,357,587,619,559,284,602,221,243,248,270,661,381,334,260,561,424,630,429,275,165,598,160,467,435,665,583,682,324,615,593,420,499,471,225,554,669,642,526,547,212,622,393,647,569,371,503,508,657,530,513,573,444,375,176,402,286,577,579,281,545,413,391,611,236,540,604,406,230,567,649,208,477,387,552,609,520,198,399,223,563,653,675,426,589,162,680,663,255,617,640,327,331,585,613,600,595,446,571,250,627,671,688,581,368,632,171,418,378,667,383,684,536,151,410,422,273,239,474,415,624,575,528,644,178,442,501,227,337,469,659,543,215,496,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT025+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 22:53:33 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.91/0.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 4.26/1.80 % [INFO] Parsing done (859ms).
% 4.26/1.81 % [INFO] Running in sequential loop mode.
% 4.66/2.01 % [INFO] eprover registered as external prover.
% 4.66/2.02 % [INFO] Scanning for conjecture ...
% 6.91/2.45 % [INFO] Found a conjecture (or negated_conjecture) and 4055 axioms. Running axiom selection ...
% 8.89/3.02 % [INFO] Axiom selection finished. Selected 148 axioms (removed 3907 axioms).
% 9.56/3.26 % [INFO] Problem is first-order (TPTP FOF).
% 9.56/3.29 % [INFO] Type checking passed.
% 9.56/3.29 % [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 ...
% 51.34/11.22 % External prover 'e' found a proof!
% 51.34/11.22 % [INFO] Killing All external provers ...
% 51.34/11.23 % Time passed: 10716ms (effective reasoning time: 9411ms)
% 51.34/11.23 % 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)>
% 51.34/11.23 % Axioms used in derivation (148): t2_tarski, dt_k3_isocat_1, t57_isocat_1, dt_k9_nattra_1, dt_k13_isocat_2, dt_k7_isocat_2, dt_k16_cat_2, dt_m3_cat_2, t48_nattra_1, fc1_zfmisc_1, dt_k7_cat_2, t46_nattra_1, t13_isocat_1, t51_nattra_1, t24_cat_2, existence_l1_cat_1, t23_isocat_1, reflexivity_r1_isocat_1, t17_isocat_1, existence_m4_nattra_1, dt_m1_cat_2, t4_ordinal1, redefinition_k7_nattra_1, d10_isocat_1, t27_isocat_1, t1_subset, existence_m3_nattra_1, fc2_cat_2, dt_m3_nattra_1, dt_k10_nattra_1, redefinition_k9_isocat_2, t31_nattra_1, t33_isocat_2, dt_k8_cat_1, t19_cat_2, rc2_nattra_1, t55_isocat_1, t47_nattra_1, redefinition_k10_isocat_2, t54_nattra_1, dt_k15_isocat_2, dt_k2_isocat_1, t18_cat_2, d14_nattra_1, symmetry_r2_isocat_1, dt_k19_cat_2, dt_k12_isocat_2, t56_isocat_1, t52_nattra_1, t21_isocat_1, redefinition_k18_cat_2, dt_k15_cat_1, dt_k5_isocat_2, t54_isocat_1, d15_nattra_1, reflexivity_r3_nattra_1, existence_m3_cat_2, d13_nattra_1, 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, dt_k4_nattra_1, reflexivity_r2_isocat_1, dt_k8_cat_2, t23_nattra_1, t22_isocat_1, existence_m2_cat_1, d6_isocat_2, t7_boole, t50_isocat_1, t122_cat_1, d2_subset_1, t33_zfmisc_1, t3_ordinal1, 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, dt_m4_nattra_1, t35_nattra_1, rc1_nattra_1, t20_isocat_1, dt_m2_nattra_1, existence_m1_subset_1, d3_cat_2, reflexivity_r1_nattra_1, d2_isocat_1, t19_nattra_1, rc3_cat_1, t53_isocat_1, t33_nattra_1, dt_k16_isocat_2, d11_nattra_1, dt_k6_nattra_1, redefinition_k19_cat_2, t26_nattra_1, existence_m2_cat_2, dt_k10_isocat_2, dt_k11_cat_2, redefinition_k8_isocat_2, t22_nattra_1, redefinition_k7_cat_2, dt_k13_nattra_1, dt_k11_nattra_1, existence_m1_isocat_1, rc1_cat_2, d11_isocat_1, d9_nattra_1, d16_nattra_1, 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, 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, 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_k18_cat_2, dt_k17_cat_2, antisymmetry_r2_hidden
% 51.34/11.23 % No. of inferences in proof: 300
% 51.34/11.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10716 ms resp. 9411 ms w/o parsing
% 47.55/11.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 47.55/11.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------