%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT026+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 : n004.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 112.60s 27.45s
% Output : Refutation 89.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 20 unt; 0 typ; 6 def)
% Number of atoms : 182 ( 71 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 660 ( 38 ~; 27 |; 39 &; 504 @)
% ( 2 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 8 con; 0-4 aty)
% Number of variables : 92 ( 0 ^; 85 !; 1 ?; 92 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v2_cat_1_decl,type,
v2_cat_1: $i > $o ).
thf(l1_cat_1_decl,type,
l1_cat_1: $i > $o ).
thf(m2_cat_1_decl,type,
m2_cat_1: $i > $i > $i > $o ).
thf(k11_cat_2_decl,type,
k11_cat_2: $i > $i > $i ).
thf(r2_nattra_1_decl,type,
r2_nattra_1: $i > $i > $i > $i > $o ).
thf(k11_isocat_2_decl,type,
k11_isocat_2: $i > $i > $i > $i > $i ).
thf(k12_isocat_2_decl,type,
k12_isocat_2: $i > $i > $i > $i > $i ).
thf(u1_cat_1_decl,type,
u1_cat_1: $i > $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_cat_1 )
& ( C @ v2_cat_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ ( A @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ k11_cat_2 ) @ ( sk1 @ ( C @ m2_cat_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ k11_cat_2 ) @ ( sk1 @ ( D @ m2_cat_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k11_cat_2 ) @ ( sk1 @ r2_nattra_1 ) ) ) )
=> ( ( D @ ( B @ ( A @ ( sk1 @ k12_isocat_2 ) ) ) @ ( C @ ( B @ ( A @ ( sk1 @ k12_isocat_2 ) ) ) @ ( B @ ( sk1 @ r2_nattra_1 ) ) ) )
& ( D @ ( B @ ( A @ ( sk1 @ k11_isocat_2 ) ) ) @ ( C @ ( B @ ( A @ ( sk1 @ k11_isocat_2 ) ) ) @ ( A @ ( sk1 @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( A @ ( sk2 @ k11_cat_2 ) @ ( sk1 @ ( B @ m2_cat_1 ) ) )
=> ! [C: $i] :
( ( A @ ( sk2 @ k11_cat_2 ) @ ( sk1 @ ( C @ m2_cat_1 ) ) )
=> ( ( C @ ( B @ ( A @ ( sk2 @ k11_cat_2 ) @ ( sk1 @ r2_nattra_1 ) ) ) )
=> ( ( C @ ( A @ ( sk2 @ ( sk1 @ k12_isocat_2 ) ) ) @ ( B @ ( A @ ( sk2 @ ( sk1 @ k12_isocat_2 ) ) ) @ ( A @ ( sk1 @ r2_nattra_1 ) ) ) )
& ( C @ ( A @ ( sk2 @ ( sk1 @ k11_isocat_2 ) ) ) @ ( B @ ( A @ ( sk2 @ ( sk1 @ k11_isocat_2 ) ) ) @ ( sk2 @ ( sk1 @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( sk3 @ ( sk2 @ k11_cat_2 ) @ ( sk1 @ ( A @ m2_cat_1 ) ) )
=> ! [B: $i] :
( ( sk3 @ ( sk2 @ k11_cat_2 ) @ ( sk1 @ ( B @ m2_cat_1 ) ) )
=> ( ( B @ ( A @ ( sk3 @ ( sk2 @ k11_cat_2 ) @ ( sk1 @ r2_nattra_1 ) ) ) )
=> ( ( B @ ( sk3 @ ( sk2 @ ( sk1 @ k12_isocat_2 ) ) ) @ ( A @ ( sk3 @ ( sk2 @ ( sk1 @ k12_isocat_2 ) ) ) @ ( sk3 @ ( sk1 @ r2_nattra_1 ) ) ) )
& ( B @ ( sk3 @ ( sk2 @ ( sk1 @ k11_isocat_2 ) ) ) @ ( A @ ( sk3 @ ( sk2 @ ( sk1 @ k11_isocat_2 ) ) ) @ ( sk2 @ ( sk1 @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( sk3 @ ( sk2 @ k11_cat_2 ) @ ( sk1 @ ( A @ m2_cat_1 ) ) )
=> ( ( A @ ( sk4 @ ( sk3 @ ( sk2 @ k11_cat_2 ) @ ( sk1 @ r2_nattra_1 ) ) ) )
=> ( ( A @ ( sk3 @ ( sk2 @ ( sk1 @ k12_isocat_2 ) ) ) @ ( sk4 @ ( sk3 @ ( sk2 @ ( sk1 @ k12_isocat_2 ) ) ) @ ( sk3 @ ( sk1 @ r2_nattra_1 ) ) ) )
& ( A @ ( sk3 @ ( sk2 @ ( sk1 @ k11_isocat_2 ) ) ) @ ( sk4 @ ( sk3 @ ( sk2 @ ( sk1 @ k11_isocat_2 ) ) ) @ ( sk2 @ ( sk1 @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ) ) ) ).
thf(59,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(822,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(823,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[822]) ).
thf(824,plain,
! [B: $i,A: $i] :
( ( ( B @ v1_xboole_0 )
| ( B != k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[823]) ).
thf(826,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[824]) ).
thf(828,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[826]) ).
thf(829,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[828]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_cat_1 )
& ( C @ v2_cat_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ ( A @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_isocat_2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_cat_1 )
& ( C @ v2_cat_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ ( A @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(490,plain,
~ ! [A: $i] :
( ( ( A @ l1_cat_1 )
& ( A @ v2_cat_1 ) )
=> ! [B: $i] :
( ( ( B @ l1_cat_1 )
& ( B @ v2_cat_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_cat_1 )
& ( C @ v2_cat_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( D @ m2_cat_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ k11_cat_2 ) @ ( A @ ( E @ m2_cat_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ k11_cat_2 ) @ ( A @ r2_nattra_1 ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_isocat_2 ) ) ) @ ( C @ ( A @ r2_nattra_1 ) ) ) )
& ( E @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k11_isocat_2 ) ) ) @ ( B @ ( A @ r2_nattra_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(491,plain,
( ( ~ ( sk5 @ ( sk3 @ ( sk2 @ ( sk1 @ k12_isocat_2 ) ) ) @ ( sk4 @ ( sk3 @ ( sk2 @ ( sk1 @ k12_isocat_2 ) ) ) @ ( sk3 @ ( sk1 @ r2_nattra_1 ) ) ) )
| ~ ( sk5 @ ( sk3 @ ( sk2 @ ( sk1 @ k11_isocat_2 ) ) ) @ ( sk4 @ ( sk3 @ ( sk2 @ ( sk1 @ k11_isocat_2 ) ) ) @ ( sk2 @ ( sk1 @ r2_nattra_1 ) ) ) ) )
& ( sk5 @ ( sk4 @ ( sk3 @ ( sk2 @ k11_cat_2 ) @ ( sk1 @ r2_nattra_1 ) ) ) )
& ( sk3 @ ( sk2 @ k11_cat_2 ) @ ( sk1 @ ( sk5 @ m2_cat_1 ) ) )
& ( sk3 @ ( sk2 @ k11_cat_2 ) @ ( sk1 @ ( sk4 @ m2_cat_1 ) ) )
& ( sk3 @ l1_cat_1 )
& ( sk3 @ v2_cat_1 )
& ( sk2 @ l1_cat_1 )
& ( sk2 @ v2_cat_1 )
& ( sk1 @ l1_cat_1 )
& ( sk1 @ v2_cat_1 ) ),
inference(cnf,[status(esa)],[490]) ).
thf(494,plain,
sk3 @ l1_cat_1,
inference(cnfConj,[status(thm)],[491]) ).
thf(253,axiom,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ~ ( A @ u1_cat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_cat_1) ).
thf(1826,plain,
! [A: $i] :
( ( A @ l1_cat_1 )
=> ~ ( A @ u1_cat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1827,plain,
! [A: $i] :
( ~ ( A @ u1_cat_1 @ v1_xboole_0 )
| ~ ( A @ l1_cat_1 ) ),
inference(cnf,[status(esa)],[1826]) ).
thf(5828,plain,
! [A: $i] :
( ( ( sk3 @ l1_cat_1 )
!= ( A @ l1_cat_1 ) )
| ~ ( A @ u1_cat_1 @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[494,1827]) ).
thf(5829,plain,
! [A: $i] :
( ( ( sk3 @ l1_cat_1 )
!= ( A @ l1_cat_1 ) )
| ~ ( A @ u1_cat_1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[5828]) ).
thf(5830,plain,
~ ( sk3 @ u1_cat_1 @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[5829:[bind(A,$thf( sk3 ))]]) ).
thf(5906,plain,
( ( ( sk3 @ u1_cat_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[829,5830]) ).
thf(5907,plain,
( ( sk3 @ u1_cat_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[5906]) ).
thf(5927,plain,
( ( sk3 @ u1_cat_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[5907]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
<=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(887,plain,
! [A: $i,B: $i] :
( ( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(888,plain,
( ! [A: $i,B: $i] :
( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(miniscope,[status(thm)],[887]) ).
thf(889,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( D @ ( C @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( D != k1_xboole_0 ) )
& ( ( ( D @ ( C @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( C != k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[888]) ).
thf(892,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[889]) ).
thf(896,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[892]) ).
thf(897,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[896]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(546,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(547,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(cnf,[status(esa)],[546]) ).
thf(548,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(lifteq,[status(thm)],[547]) ).
thf(549,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[548]) ).
thf(550,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk11 ) )
= A ),
inference(cnf,[status(esa)],[549]) ).
thf(11509,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk11 ) )
= A ),
inference(lifteq,[status(thm)],[550]) ).
thf(11536,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk11 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[897,11509]) ).
thf(11537,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk11 ) )
= A ),
inference(pattern_uni,[status(thm)],[11536:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(891,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[889]) ).
thf(894,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[891]) ).
thf(895,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[894]) ).
thf(11534,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk11 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[895,11509]) ).
thf(11535,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk11 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[11534:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(15113,plain,
! [A: $i] : ( k1_xboole_0 = A ),
inference(rewrite,[status(thm)],[11537,11535]) ).
thf(15138,plain,
$false,
inference(simplifyReflect,[status(thm)],[5927,15113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT026+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n004.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 22:53:07 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.92/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 6.39/2.38 % [INFO] Parsing done (1394ms).
% 6.80/2.41 % [INFO] Running in sequential loop mode.
% 8.38/2.99 % [INFO] eprover registered as external prover.
% 8.38/3.00 % [INFO] Scanning for conjecture ...
% 11.32/3.72 % [INFO] Found a conjecture (or negated_conjecture) and 4063 axioms. Running axiom selection ...
% 13.97/4.80 % [INFO] Axiom selection finished. Selected 487 axioms (removed 3576 axioms).
% 17.00/5.87 % [INFO] Problem is first-order (TPTP FOF).
% 17.17/5.97 % [INFO] Type checking passed.
% 17.17/5.98 % [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 ...
% 112.60/27.44 % [INFO] Killing All external provers ...
% 112.60/27.45 % Time passed: 26893ms (effective reasoning time: 25026ms)
% 112.60/27.45 % 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)>
% 112.60/27.45 % Axioms used in derivation (4): d5_xboole_0, dt_u1_cat_1, t113_zfmisc_1, t115_zfmisc_1
% 112.60/27.45 % No. of inferences in proof: 44
% 112.60/27.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 26893 ms resp. 25026 ms w/o parsing
% 89.21/27.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 89.21/27.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------