%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO093+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 07:12:19 AM UTC 2026
% Result : Theorem 32.47s 7.76s
% Output : Refutation 27.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 26
% Syntax : Number of formulae : 144 ( 29 unt; 0 typ; 9 def)
% Number of atoms : 539 ( 98 equ; 0 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1579 ( 159 ~; 157 |; 99 &;1090 @)
% ( 9 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 301 ( 7 ^; 257 !; 28 ?; 301 :)
% ( 0 !>; 0 ?*; 0 @-; 9 @+)
% Comments :
%------------------------------------------------------------------------------
thf(open_decl,type,
open: $i > $o ).
thf(part_of_decl,type,
part_of: $i > $i > $o ).
thf(meet_decl,type,
meet: $i > $i > $i > $o ).
thf(sum_decl,type,
sum: $i > $i > $i ).
thf(incident_c_decl,type,
incident_c: $i > $i > $o ).
thf(end_point_decl,type,
end_point: $i > $i > $o ).
thf(inner_point_decl,type,
inner_point: $i > $i > $o ).
thf(closed_decl,type,
closed: $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 > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ? [D: $i] : ( C @ ( B @ ( D @ meet ) ) )
& ( A @ ( C @ part_of ) )
& ( A @ ( B @ part_of ) )
& ( A @ open ) )
=> ( C @ ( B @ sum ) @ open ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ? [C: $i] : ( B @ ( A @ ( C @ meet ) ) )
& ( sk1 @ ( B @ part_of ) )
& ( sk1 @ ( A @ part_of ) )
& ( sk1 @ open ) )
=> ( B @ ( A @ sum ) @ open ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ? [B: $i] : ( A @ ( sk2 @ ( B @ meet ) ) )
& ( sk1 @ ( A @ part_of ) )
& ( sk1 @ ( sk2 @ part_of ) )
& ( sk1 @ open ) )
=> ( A @ ( sk2 @ sum ) @ open ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] : ( sk3 @ ( sk2 @ ( A @ meet ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ incident_c ) )
=> ( A @ ( C @ incident_c ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ incident_c ) )
=> ( B @ ( C @ incident_c ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ end_point ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ inner_point ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ end_point ) ) ) ) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ end_point ) )
<=> ( ! [C: $i,D: $i] :
( ( ( D @ ( A @ incident_c ) )
& ( C @ ( A @ incident_c ) )
& ( B @ ( D @ part_of ) )
& ( B @ ( C @ part_of ) ) )
=> ( ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) ) ) )
& ( B @ ( A @ incident_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn) ).
thf(101,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i,D: $i] :
( ( ( D @ ( A @ incident_c ) )
& ( C @ ( A @ incident_c ) )
& ( B @ ( D @ part_of ) )
& ( B @ ( C @ part_of ) ) )
=> ( ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) ) ) )
& ( B @ ( A @ incident_c ) ) )
=> ( B @ ( A @ end_point ) ) )
& ( ( B @ ( A @ end_point ) )
=> ( ! [C: $i,D: $i] :
( ( ( D @ ( A @ incident_c ) )
& ( C @ ( A @ incident_c ) )
& ( B @ ( D @ part_of ) )
& ( B @ ( C @ part_of ) ) )
=> ( ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) ) ) )
& ( B @ ( A @ incident_c ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( D @ meet ) ) )
& ( A @ ( C @ part_of ) )
& ( A @ ( B @ part_of ) )
& ( A @ open ) )
=> ( C @ ( B @ sum ) @ open ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proposition_2_14_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( D @ meet ) ) )
& ( A @ ( C @ part_of ) )
& ( A @ ( B @ part_of ) )
& ( A @ open ) )
=> ( C @ ( B @ sum ) @ open ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( D @ meet ) ) )
& ( A @ ( C @ part_of ) )
& ( A @ ( B @ part_of ) )
& ( A @ open ) )
=> ( C @ ( B @ sum ) @ open ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] : ( C @ ( B @ ( D @ meet ) ) )
& ( A @ ( C @ part_of ) )
& ( A @ ( B @ part_of ) )
& ( A @ open ) )
=> ( C @ ( B @ sum ) @ open ) ),
inference(miniscope,[status(thm)],[19]) ).
thf(21,plain,
( ~ ( sk3 @ ( sk2 @ sum ) @ open )
& ( sk3 @ ( sk2 @ ( sk4 @ meet ) ) )
& ( sk1 @ ( sk3 @ part_of ) )
& ( sk1 @ ( sk2 @ part_of ) )
& ( sk1 @ open ) ),
inference(cnf,[status(esa)],[20]) ).
thf(23,plain,
sk1 @ open,
inference(cnfConj,[status(thm)],[21]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ open )
<=> ? [B: $i] : ( A @ ( B @ end_point ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_defn) ).
thf(61,plain,
! [A: $i] :
( ( ? [B: $i] : ( A @ ( B @ end_point ) )
=> ( A @ open ) )
& ( ( A @ open )
=> ? [B: $i] : ( A @ ( B @ end_point ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(62,plain,
( ! [A: $i] :
( ? [B: $i] : ( A @ ( B @ end_point ) )
=> ( A @ open ) )
& ! [A: $i] :
( ( A @ open )
=> ? [B: $i] : ( A @ ( B @ end_point ) ) ) ),
inference(miniscope,[status(thm)],[61]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ open )
| ~ ( B @ ( C @ end_point ) ) )
& ( ( A @ ( A @ sk10 @ end_point ) )
| ~ ( A @ open ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(64,plain,
! [A: $i] :
( ( A @ ( A @ sk10 @ end_point ) )
| ~ ( A @ open ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(267,plain,
! [A: $i] :
( ( ( sk1 @ open )
!= ( A @ open ) )
| ( A @ ( A @ sk10 @ end_point ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,64]) ).
thf(268,plain,
! [A: $i] :
( ( ( sk1 @ open )
!= ( A @ open ) )
| ( A @ ( A @ sk10 @ end_point ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(269,plain,
sk1 @ ( sk1 @ sk10 @ end_point ),
inference(pattern_uni,[status(thm)],[268:[bind(A,$thf( sk1 ))]]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ incident_c ) )
<=> ( B @ ( C @ incident_c ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c9) ).
thf(27,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ incident_c ) )
=> ( A @ ( C @ incident_c ) ) )
& ( ( A @ ( C @ incident_c ) )
=> ( B @ ( C @ incident_c ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ incident_c ) )
=> ( A @ ( C @ incident_c ) ) )
& ! [C: $i] :
( ( A @ ( C @ incident_c ) )
=> ( B @ ( C @ incident_c ) ) ) )
=> ( A = B ) ),
inference(miniscope,[status(thm)],[27]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( ( A = B )
| ~ ( A @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ incident_c ) ) )
& ( ( A = B )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ incident_c ) ) )
& ( ( A = B )
| ~ ( A @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) )
& ( ( A = B )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ) ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(cnfConj,[status(thm)],[29]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( A @ open )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[34,23]) ).
thf(216,plain,
! [A: $i] :
( ( A @ open )
| ( sk1 @ ( A @ ( sk1 @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( sk1 @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[215:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ closed )
<=> ~ ? [B: $i] : ( A @ ( B @ end_point ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed_defn) ).
thf(53,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( A @ ( B @ end_point ) )
=> ( A @ closed ) )
& ( ( A @ closed )
=> ~ ? [B: $i] : ( A @ ( B @ end_point ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ end_point ) )
=> ? [C: $i] :
( ( B != C )
& ( A @ ( C @ end_point ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c6) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ end_point ) )
=> ? [C: $i] :
( ( B != C )
& ( A @ ( C @ end_point ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ part_of ) )
<=> ! [C: $i] :
( ( B @ ( C @ incident_c ) )
=> ( A @ ( C @ incident_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn) ).
thf(134,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ incident_c ) )
=> ( A @ ( C @ incident_c ) ) )
=> ( A @ ( B @ part_of ) ) )
& ( ( A @ ( B @ part_of ) )
=> ! [C: $i] :
( ( B @ ( C @ incident_c ) )
=> ( A @ ( C @ incident_c ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ inner_point ) )
<=> ( ~ ( B @ ( A @ end_point ) )
& ( B @ ( A @ incident_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn) ).
thf(46,plain,
! [A: $i,B: $i] :
( ( ( ~ ( B @ ( A @ end_point ) )
& ( B @ ( A @ incident_c ) ) )
=> ( B @ ( A @ inner_point ) ) )
& ( ( B @ ( A @ inner_point ) )
=> ( ~ ( B @ ( A @ end_point ) )
& ( B @ ( A @ incident_c ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(47,plain,
( ! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ end_point ) )
& ( B @ ( A @ incident_c ) ) )
=> ( B @ ( A @ inner_point ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ inner_point ) )
=> ( ~ ( B @ ( A @ end_point ) )
& ( B @ ( A @ incident_c ) ) ) ) ),
inference(miniscope,[status(thm)],[46]) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ inner_point ) )
| ( D @ ( C @ end_point ) )
| ~ ( D @ ( C @ incident_c ) ) )
& ( ~ ( B @ ( A @ end_point ) )
| ~ ( B @ ( A @ inner_point ) ) )
& ( ( B @ ( A @ incident_c ) )
| ~ ( B @ ( A @ inner_point ) ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ incident_c ) )
| ~ ( B @ ( A @ inner_point ) ) ),
inference(cnfConj,[status(thm)],[48]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( A @ open )
| ~ ( A @ ( B @ end_point ) ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( A @ open )
| ~ ( A @ ( B @ end_point ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(8,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ inner_point ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c3) ).
thf(59,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ inner_point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(60,plain,
! [A: $i] : ( A @ ( A @ sk9 @ inner_point ) ),
inference(cnf,[status(esa)],[59]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ end_point ) )
| ~ ( B @ ( A @ inner_point ) ) ),
inference(cnfConj,[status(thm)],[48]) ).
thf(697,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk10 @ end_point ) )
!= ( B @ ( A @ end_point ) ) )
| ~ $true
| ~ ( B @ ( A @ inner_point ) ) ),
inference(paramod_ordered,[status(thm)],[269,50]) ).
thf(698,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk10 @ end_point ) )
!= ( B @ ( A @ end_point ) ) )
| ~ ( B @ ( A @ inner_point ) ) ),
inference(simp,[status(thm)],[697]) ).
thf(699,plain,
~ ( sk1 @ ( sk1 @ sk10 @ inner_point ) ),
inference(pattern_uni,[status(thm)],[698:[bind(A,$thf( sk1 @ sk10 )),bind(B,$thf( sk1 ))]]) ).
thf(724,plain,
! [A: $i] :
( ( ( A @ ( A @ sk9 @ inner_point ) )
!= ( sk1 @ ( sk1 @ sk10 @ inner_point ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[60,699]) ).
thf(725,plain,
! [A: $i] :
( ( A @ ( A @ sk9 @ inner_point ) )
!= ( sk1 @ ( sk1 @ sk10 @ inner_point ) ) ),
inference(simp,[status(thm)],[724]) ).
thf(738,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( A @ sk9 )
!= ( sk1 @ sk10 ) ) ),
inference(simp,[status(thm)],[725]) ).
thf(739,plain,
( ( sk1 @ sk10 )
!= ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[738]) ).
thf(54,plain,
( ! [A: $i] :
( ~ ? [B: $i] : ( A @ ( B @ end_point ) )
=> ( A @ closed ) )
& ! [A: $i] :
( ( A @ closed )
=> ~ ? [B: $i] : ( A @ ( B @ end_point ) ) ) ),
inference(miniscope,[status(thm)],[53]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ closed )
| ( C @ ( C @ sk8 @ end_point ) ) )
& ( ~ ( A @ ( B @ end_point ) )
| ~ ( A @ closed ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(57,plain,
! [A: $i] :
( ( A @ closed )
| ( A @ ( A @ sk8 @ end_point ) ) ),
inference(cnfConj,[status(thm)],[55]) ).
thf(58,plain,
! [A: $i] :
( ( A @ closed )
| ( A @ ( A @ sk8 @ end_point ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( D @ ( E @ end_point ) )
& ( C @ ( E @ end_point ) )
& ( B @ ( E @ end_point ) ) )
& ( A @ ( D @ part_of ) )
& ( A @ ( C @ part_of ) )
& ( A @ ( B @ part_of ) ) )
=> ( ( B @ ( D @ part_of ) )
| ( D @ ( B @ part_of ) )
| ( B @ ( C @ part_of ) )
| ( C @ ( B @ part_of ) )
| ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2) ).
thf(94,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( D @ ( E @ end_point ) )
& ( C @ ( E @ end_point ) )
& ( B @ ( E @ end_point ) ) )
& ( A @ ( D @ part_of ) )
& ( A @ ( C @ part_of ) )
& ( A @ ( B @ part_of ) ) )
=> ( ( B @ ( D @ part_of ) )
| ( D @ ( B @ part_of ) )
| ( B @ ( C @ part_of ) )
| ( C @ ( B @ part_of ) )
| ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ end_point ) )
| ~ ( A @ closed ) ),
inference(cnfConj,[status(thm)],[55]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( B != A )
& ( A @ ( B @ part_of ) ) )
=> ( B @ open ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c1) ).
thf(142,plain,
! [A: $i,B: $i] :
( ( ( B != A )
& ( A @ ( B @ part_of ) ) )
=> ( B @ open ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(703,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk9 @ inner_point ) )
!= ( C @ ( B @ inner_point ) ) )
| ~ ( C @ ( B @ end_point ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[60,50]) ).
thf(704,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk9 @ inner_point ) )
!= ( C @ ( B @ inner_point ) ) )
| ~ ( C @ ( B @ end_point ) ) ),
inference(simp,[status(thm)],[703]) ).
thf(705,plain,
! [A: $i] :
~ ( A @ ( A @ sk9 @ end_point ) ),
inference(pattern_uni,[status(thm)],[704:[bind(A,$thf( D )),bind(B,$thf( D @ sk9 )),bind(C,$thf( D ))]]) ).
thf(709,plain,
! [A: $i] :
~ ( A @ ( A @ sk9 @ end_point ) ),
inference(simp,[status(thm)],[705]) ).
thf(24,plain,
~ ( sk3 @ ( sk2 @ sum ) @ open ),
inference(cnfConj,[status(thm)],[21]) ).
thf(25,plain,
sk1 @ ( sk2 @ part_of ),
inference(cnfConj,[status(thm)],[21]) ).
thf(150,plain,
( ( ( sk3 @ ( sk2 @ sum ) @ open )
!= ( sk1 @ open ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,24]) ).
thf(151,plain,
( ( sk3 @ ( sk2 @ sum ) @ open )
!= ( sk1 @ open ) ),
inference(simp,[status(thm)],[150]) ).
thf(152,plain,
( ( sk3 @ ( sk2 @ sum ) )
!= sk1 ),
inference(simp,[status(thm)],[151]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(cnfConj,[status(thm)],[29]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ incident_c ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(871,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk3 @ ( sk2 @ sum ) ) )
| ( B != sk1 )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[36,152]) ).
thf(872,plain,
! [A: $i] :
( ( A != sk1 )
| ( A @ ( sk3 @ ( sk2 @ sum ) @ ( A @ sk6 ) @ incident_c ) )
| ~ ( A @ ( sk3 @ ( sk2 @ sum ) @ ( A @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[871:[bind(A,$thf( sk3 @ ( sk2 @ sum ) )),bind(B,$thf( B ))]]) ).
thf(1169,plain,
( ( sk1 @ ( sk3 @ ( sk2 @ sum ) @ ( sk1 @ sk6 ) @ incident_c ) )
| ~ ( sk1 @ ( sk3 @ ( sk2 @ sum ) @ ( sk1 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[872]) ).
thf(257,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk10 @ end_point ) )
!= ( B @ ( C @ end_point ) ) )
| ~ $true
| ~ ( B @ closed )
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[64,56]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk10 @ end_point ) )
!= ( B @ ( C @ end_point ) ) )
| ~ ( B @ closed )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[257]) ).
thf(259,plain,
! [A: $i] :
( ~ ( A @ closed )
| ~ ( A @ open ) ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk10 ))]]) ).
thf(270,plain,
! [A: $i] :
( ~ ( A @ closed )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[259]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ end_point ) )
& ( A @ ( C @ end_point ) )
& ( A @ ( B @ end_point ) ) )
=> ( ( C = D )
| ( B = D )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c5) ).
thf(38,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ end_point ) )
& ( A @ ( C @ end_point ) )
& ( A @ ( B @ end_point ) ) )
=> ( ( C = D )
| ( B = D )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk10 @ end_point ) )
!= ( A @ ( B @ end_point ) ) )
| ~ $true
| ~ ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[269,56]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk10 @ end_point ) )
!= ( A @ ( B @ end_point ) ) )
| ~ ( A @ closed ) ),
inference(simp,[status(thm)],[273]) ).
thf(275,plain,
~ ( sk1 @ closed ),
inference(pattern_uni,[status(thm)],[274:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk10 ))]]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk3 @ ( sk2 @ sum ) ) )
| ( A != sk1 )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[34,152]) ).
thf(160,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk3 @ ( sk2 @ sum ) @ ( A @ ( sk3 @ ( sk2 @ sum ) @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( sk3 @ ( sk2 @ sum ) @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk2 @ sum ) ))]]) ).
thf(229,plain,
( ( sk3 @ ( sk2 @ sum ) @ ( sk1 @ ( sk3 @ ( sk2 @ sum ) @ sk6 ) @ incident_c ) )
| ( sk1 @ ( sk1 @ ( sk3 @ ( sk2 @ sum ) @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(247,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ end_point ) )
!= ( B @ ( C @ end_point ) ) )
| ( B @ open )
| ~ $true
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[58,66]) ).
thf(248,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ end_point ) )
!= ( B @ ( C @ end_point ) ) )
| ( B @ open )
| ( A @ closed ) ),
inference(simp,[status(thm)],[247]) ).
thf(249,plain,
! [A: $i] :
( ( A @ open )
| ( A @ closed ) ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk8 ))]]) ).
thf(252,plain,
! [A: $i] :
( ( A @ open )
| ( A @ closed ) ),
inference(simp,[status(thm)],[249]) ).
thf(706,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk10 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ~ $true
| ~ ( C @ ( B @ inner_point ) )
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[64,50]) ).
thf(707,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk10 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ~ ( C @ ( B @ inner_point ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[706]) ).
thf(708,plain,
! [A: $i] :
( ~ ( A @ ( A @ sk10 @ inner_point ) )
| ~ ( A @ open ) ),
inference(pattern_uni,[status(thm)],[707:[bind(A,$thf( D )),bind(B,$thf( D @ sk10 )),bind(C,$thf( D ))]]) ).
thf(710,plain,
! [A: $i] :
( ~ ( A @ ( A @ sk10 @ inner_point ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[708]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk3 @ ( sk2 @ sum ) ) )
| ( B != sk1 )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[34,152]) ).
thf(154,plain,
! [A: $i] :
( ( A != sk1 )
| ( A @ ( sk3 @ ( sk2 @ sum ) @ ( A @ sk6 ) @ incident_c ) )
| ( sk3 @ ( sk2 @ sum ) @ ( sk3 @ ( sk2 @ sum ) @ ( A @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( sk3 @ ( sk2 @ sum ) )),bind(B,$thf( B ))]]) ).
thf(225,plain,
( ( sk1 @ ( sk3 @ ( sk2 @ sum ) @ ( sk1 @ sk6 ) @ incident_c ) )
| ( sk3 @ ( sk2 @ sum ) @ ( sk3 @ ( sk2 @ sum ) @ ( sk1 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ inner_point ) )
=> ? [C: $i,D: $i] :
( ( A
= ( D @ ( C @ sum ) ) )
& ( D @ ( C @ ( B @ meet ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c4) ).
thf(96,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ inner_point ) )
=> ? [C: $i,D: $i] :
( ( A
= ( D @ ( C @ sum ) ) )
& ( D @ ( C @ ( B @ meet ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1239,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk10 @ end_point ) )
!= ( B @ ( B @ sk9 @ end_point ) ) )
| ~ $true
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[64,709]) ).
thf(1240,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk10 @ end_point ) )
!= ( B @ ( B @ sk9 @ end_point ) ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[1239]) ).
thf(1243,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( A @ sk10 )
!= ( B @ sk9 ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[1240]) ).
thf(1251,plain,
! [A: $i] :
( ( ( A @ sk10 )
!= ( A @ sk9 ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[1243]) ).
thf(22,plain,
sk3 @ ( sk2 @ ( sk4 @ meet ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(700,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ~ $true
| ~ ( C @ ( B @ inner_point ) )
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[58,50]) ).
thf(701,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ~ ( C @ ( B @ inner_point ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[700]) ).
thf(702,plain,
! [A: $i] :
( ~ ( A @ ( A @ sk8 @ inner_point ) )
| ( A @ closed ) ),
inference(pattern_uni,[status(thm)],[701:[bind(A,$thf( D )),bind(B,$thf( D @ sk8 )),bind(C,$thf( D ))]]) ).
thf(711,plain,
! [A: $i] :
( ~ ( A @ ( A @ sk8 @ inner_point ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[702]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ meet ) ) )
<=> ( ! [D: $i] :
( ( ( C @ ( D @ incident_c ) )
& ( B @ ( D @ incident_c ) ) )
=> ( ( C @ ( D @ end_point ) )
& ( B @ ( D @ end_point ) ) ) )
& ( C @ ( A @ incident_c ) )
& ( B @ ( A @ incident_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_defn) ).
thf(118,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( ( C @ ( D @ incident_c ) )
& ( B @ ( D @ incident_c ) ) )
=> ( ( C @ ( D @ end_point ) )
& ( B @ ( D @ end_point ) ) ) )
& ( C @ ( A @ incident_c ) )
& ( B @ ( A @ incident_c ) ) )
=> ( C @ ( B @ ( A @ meet ) ) ) )
& ( ( C @ ( B @ ( A @ meet ) ) )
=> ( ! [D: $i] :
( ( ( C @ ( D @ incident_c ) )
& ( B @ ( D @ incident_c ) ) )
=> ( ( C @ ( D @ end_point ) )
& ( B @ ( D @ end_point ) ) ) )
& ( C @ ( A @ incident_c ) )
& ( B @ ( A @ incident_c ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1229,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ end_point ) )
!= ( B @ ( B @ sk9 @ end_point ) ) )
| ~ $true
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[58,709]) ).
thf(1230,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ end_point ) )
!= ( B @ ( B @ sk9 @ end_point ) ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[1229]) ).
thf(1242,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( A @ sk8 )
!= ( B @ sk9 ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[1230]) ).
thf(1250,plain,
! [A: $i] :
( ( ( A @ sk9 )
!= ( A @ sk8 ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[1242]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(cnfConj,[status(thm)],[29]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(382,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk3 @ ( sk2 @ sum ) ) )
| ( A != sk1 )
| ~ ( A @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[35,152]) ).
thf(383,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( A @ ( A @ ( sk3 @ ( sk2 @ sum ) @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( sk3 @ ( sk2 @ sum ) @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[382:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk2 @ sum ) ))]]) ).
thf(548,plain,
( ~ ( sk1 @ ( sk1 @ ( sk3 @ ( sk2 @ sum ) @ sk6 ) @ incident_c ) )
| ( sk1 @ ( sk1 @ ( sk3 @ ( sk2 @ sum ) @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[383]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A
= ( C @ ( B @ sum ) ) )
& ( C @ ( B @ ( D @ meet ) ) )
& ( A @ closed ) )
=> ! [E: $i] :
( ( B @ ( E @ end_point ) )
=> ( C @ ( B @ ( E @ meet ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c7) ).
thf(145,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A
= ( C @ ( B @ sum ) ) )
& ( C @ ( B @ ( D @ meet ) ) )
& ( A @ closed ) )
=> ! [E: $i] :
( ( B @ ( E @ end_point ) )
=> ( C @ ( B @ ( E @ meet ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( A
= ( C @ ( B @ sum ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ incident_c ) )
<=> ( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn) ).
thf(67,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) ) )
=> ( A @ ( D @ incident_c ) ) )
& ( ( A @ ( D @ incident_c ) )
=> ( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) ) ) ) )
=> ( A
= ( C @ ( B @ sum ) ) ) )
& ( ( A
= ( C @ ( B @ sum ) ) )
=> ! [D: $i] :
( ( ( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) ) )
=> ( A @ ( D @ incident_c ) ) )
& ( ( A @ ( D @ incident_c ) )
=> ( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(26,plain,
sk1 @ ( sk3 @ part_of ),
inference(cnfConj,[status(thm)],[21]) ).
thf(849,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ sk10 ) )
| ( A
!= ( sk1 @ sk9 ) )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[34,739]) ).
thf(850,plain,
! [A: $i] :
( ( A
!= ( sk1 @ sk9 ) )
| ( sk1 @ sk10 @ ( A @ ( sk1 @ sk10 @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( sk1 @ sk10 @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[849:[bind(A,$thf( A )),bind(B,$thf( sk1 @ sk10 ))]]) ).
thf(854,plain,
( ( sk1 @ sk10 @ ( sk1 @ sk9 @ ( sk1 @ sk10 @ sk6 ) @ incident_c ) )
| ( sk1 @ sk9 @ ( sk1 @ sk9 @ ( sk1 @ sk10 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[850]) ).
thf(621,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk9 @ inner_point ) )
!= ( C @ ( B @ inner_point ) ) )
| ( C @ ( B @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[60,49]) ).
thf(622,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk9 @ inner_point ) )
!= ( C @ ( B @ inner_point ) ) )
| ( C @ ( B @ incident_c ) ) ),
inference(simp,[status(thm)],[621]) ).
thf(623,plain,
! [A: $i] : ( A @ ( A @ sk9 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[622:[bind(A,$thf( D )),bind(B,$thf( D @ sk9 )),bind(C,$thf( D ))]]) ).
thf(624,plain,
! [A: $i] : ( A @ ( A @ sk9 @ incident_c ) ),
inference(simp,[status(thm)],[623]) ).
thf(631,plain,
! [A: $i] :
( ( ( A @ ( A @ sk9 @ incident_c ) )
!= ( sk1 @ ( sk1 @ ( sk3 @ ( sk2 @ sum ) @ sk6 ) @ incident_c ) ) )
| ~ $true
| ( sk1 @ ( sk1 @ ( sk3 @ ( sk2 @ sum ) @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[624,548]) ).
thf(632,plain,
! [A: $i] :
( ( ( A @ ( A @ sk9 @ incident_c ) )
!= ( sk1 @ ( sk1 @ ( sk3 @ ( sk2 @ sum ) @ sk6 ) @ incident_c ) ) )
| ( sk1 @ ( sk1 @ ( sk3 @ ( sk2 @ sum ) @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[631]) ).
thf(638,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( A @ sk9 )
!= ( sk1 @ ( sk3 @ ( sk2 @ sum ) @ sk6 ) ) )
| ( sk1 @ ( sk1 @ ( sk3 @ ( sk2 @ sum ) @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[632]) ).
thf(644,plain,
( ( ( sk1 @ ( sk3 @ ( sk2 @ sum ) @ sk6 ) )
!= ( sk1 @ sk9 ) )
| ( sk1 @ ( sk1 @ ( sk3 @ ( sk2 @ sum ) @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[638]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( B @ ( A @ ( C @ meet ) ) )
=> ? [C: $i] :
( C
= ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c8) ).
thf(131,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( B @ ( A @ ( C @ meet ) ) )
=> ? [C: $i] :
( C
= ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9468,plain,
$false,
inference(e,[status(thm)],[101,269,216,53,41,134,49,66,739,58,94,56,142,709,24,25,46,152,1169,61,60,270,38,275,229,252,710,225,96,1251,34,64,22,711,27,59,118,1250,35,548,145,50,67,699,26,23,36,854,19,624,644,131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO093+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n007.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 12:40:38 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.90/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.18 % [INFO] Parsing done (211ms).
% 1.29/1.19 % [INFO] Running in sequential loop mode.
% 2.16/1.61 % [INFO] eprover registered as external prover.
% 2.16/1.61 % [INFO] Scanning for conjecture ...
% 2.35/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.35/1.79 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.53/1.84 % [INFO] Problem is first-order (TPTP FOF).
% 2.53/1.85 % [INFO] Type checking passed.
% 2.53/1.86 % [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 ...
% 32.47/7.75 % External prover 'e' found a proof!
% 32.47/7.75 % [INFO] Killing All external provers ...
% 32.47/7.75 % Time passed: 7231ms (effective reasoning time: 6557ms)
% 32.47/7.75 % 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)>
% 32.47/7.76 % Axioms used in derivation (16): end_point_defn, c8, meet_defn, part_of_defn, c9, sum_defn, closed_defn, c7, inner_point_defn, c3, c4, c5, c2, c1, c6, open_defn
% 32.47/7.76 % No. of inferences in proof: 135
% 32.47/7.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7231 ms resp. 6557 ms w/o parsing
% 27.94/7.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 27.94/7.84 % [INFO] Killing All external provers ...
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