%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO112+1 : TPTP v9.3.1. Released v2.4.0.
% 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 : 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 07:12:22 AM UTC 2026
% Result : Theorem 138.32s 46.08s
% Output : Refutation 140.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 35
% Syntax : Number of formulae : 538 ( 112 unt; 0 typ; 17 def)
% Number of atoms : 1970 ( 445 equ; 0 cnn)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 7506 ( 753 ~; 803 |; 142 &;5710 @)
% ( 10 <=>; 88 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 6 con; 0-4 aty)
% Number of variables : 1662 ( 27 ^;1589 !; 29 ?;1662 :)
% ( 0 !>; 0 ?*; 0 @-; 17 @+)
% Comments :
%------------------------------------------------------------------------------
thf(between_c_decl,type,
between_c: $i > $i > $i > $i > $o ).
thf(incident_c_decl,type,
incident_c: $i > $i > $o ).
thf(sum_decl,type,
sum: $i > $i > $i ).
thf(meet_decl,type,
meet: $i > $i > $i > $o ).
thf(end_point_decl,type,
end_point: $i > $i > $o ).
thf(part_of_decl,type,
part_of: $i > $i > $o ).
thf(inner_point_decl,type,
inner_point: $i > $i > $o ).
thf(open_decl,type,
open: $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(sk7_decl,type,
sk7: $i > $i > $i > $o ).
thf(sk8_decl,type,
sk8: $i > $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i > $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i > $i ).
thf(sk18_decl,type,
sk18: $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i ).
thf(sk20_decl,type,
sk20: $i > $i > $i ).
thf(sk21_decl,type,
sk21: $i > $i > $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ between_c ) ) ) )
=> ( B @ ( C @ ( D @ ( A @ between_c ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( sk1 @ between_c ) ) ) )
=> ( A @ ( B @ ( C @ ( sk1 @ between_c ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ ( sk2 @ ( sk1 @ between_c ) ) ) )
=> ( sk2 @ ( A @ ( B @ ( sk1 @ between_c ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( A @ ( sk3 @ ( sk2 @ ( sk1 @ between_c ) ) ) )
=> ( sk2 @ ( sk3 @ ( A @ ( sk1 @ between_c ) ) ) ) ) ) ) ).
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,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ incident_c ) )
=> ( ( A @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( A @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) ) )
=> ( C @ ( D @ incident_c ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( C
= ( A @ ( B @ sum ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ! [D: $i] :
( ( ( D @ ( B @ incident_c ) )
& ( C @ ( B @ incident_c ) )
& ( A @ ( D @ part_of ) )
& ( A @ ( C @ part_of ) ) )
=> ( ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( C @ ( B @ incident_c ) )
& ( B @ ( A @ sk11 ) @ ( B @ incident_c ) )
& ( A @ ( C @ part_of ) )
& ( A @ ( B @ ( A @ sk11 ) @ part_of ) ) )
=> ( ( B @ ( A @ sk11 ) @ ( C @ part_of ) )
| ( C @ ( B @ ( A @ sk11 ) @ part_of ) ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ end_point ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( A != C )
& ( B @ ( C @ end_point ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ end_point ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ inner_point ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ incident_c ) )
=> ( B @ ( C @ incident_c ) ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( ^ [A: $i,B: $i,C: $i,D: $i] :
@+[E: $i] :
( ( E @ ( B @ inner_point ) )
& ( E @ ( A @ end_point ) )
& ( E @ ( C @ end_point ) )
& ( D @ ( E @ part_of ) ) ) ) ) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',sum_defn) ).
thf(35,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)],[4]) ).
thf(36,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) ) )
=> ( A @ ( D @ incident_c ) ) )
& ! [D: $i] :
( ( A @ ( D @ incident_c ) )
=> ( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) ) ) ) )
=> ( A
= ( C @ ( B @ sum ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( A
= ( C @ ( B @ sum ) ) )
=> ( ! [D: $i] :
( ( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) ) )
=> ( A @ ( D @ incident_c ) ) )
& ! [D: $i] :
( ( A @ ( D @ incident_c ) )
=> ( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[35]) ).
thf(37,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( H @ ( G @ sum ) ) )
| ~ ( F @ ( F @ ( G @ ( H @ sk9 ) ) @ incident_c ) )
| ( F @ ( H @ ( G @ sk7 ) ) ) )
& ( ( F
= ( H @ ( G @ sum ) ) )
| ( H @ ( F @ ( G @ ( H @ sk9 ) ) @ incident_c ) )
| ( G @ ( F @ ( G @ ( H @ sk9 ) ) @ incident_c ) )
| ( F @ ( H @ ( G @ sk7 ) ) ) )
& ( ( F
= ( H @ ( G @ sum ) ) )
| ~ ( F @ ( H @ ( G @ sk7 ) ) )
| ~ ( H @ ( F @ ( G @ ( H @ sk8 ) ) @ incident_c ) ) )
& ( ( F
= ( H @ ( G @ sum ) ) )
| ~ ( F @ ( H @ ( G @ sk7 ) ) )
| ~ ( G @ ( F @ ( G @ ( H @ sk8 ) ) @ incident_c ) ) )
& ( ( F
= ( H @ ( G @ sum ) ) )
| ~ ( F @ ( H @ ( G @ sk7 ) ) )
| ( F @ ( F @ ( G @ ( H @ sk8 ) ) @ incident_c ) ) )
& ( ( A @ ( E @ incident_c ) )
| ~ ( C @ ( E @ incident_c ) )
| ( A
!= ( C @ ( B @ sum ) ) ) )
& ( ( A @ ( E @ incident_c ) )
| ~ ( B @ ( E @ incident_c ) )
| ( A
!= ( C @ ( B @ sum ) ) ) )
& ( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) )
| ~ ( A @ ( D @ incident_c ) )
| ( A
!= ( C @ ( B @ sum ) ) ) ) ),
inference(cnf,[status(esa)],[36]) ).
thf(45,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) )
| ~ ( A @ ( D @ incident_c ) )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(52,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) )
| ~ ( A @ ( D @ incident_c ) )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ incident_c ) )
| ( A @ ( C @ incident_c ) )
| ~ ( B @ ( A @ sum ) @ ( C @ incident_c ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(15,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ inner_point ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3) ).
thf(129,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ inner_point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(130,plain,
! [A: $i] : ( A @ ( A @ sk19 @ inner_point ) ),
inference(cnf,[status(esa)],[129]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ inner_point ) )
<=> ( ~ ( B @ ( A @ end_point ) )
& ( B @ ( A @ incident_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_point_defn) ).
thf(82,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)],[7]) ).
thf(83,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)],[82]) ).
thf(84,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)],[83]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ incident_c ) )
| ~ ( B @ ( A @ inner_point ) ) ),
inference(cnfConj,[status(thm)],[84]) ).
thf(4431,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk19 @ inner_point ) )
!= ( C @ ( B @ inner_point ) ) )
| ( C @ ( B @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[130,85]) ).
thf(4432,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk19 @ inner_point ) )
!= ( C @ ( B @ inner_point ) ) )
| ( C @ ( B @ incident_c ) ) ),
inference(simp,[status(thm)],[4431]) ).
thf(4433,plain,
! [A: $i] : ( A @ ( A @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[4432:[bind(A,$thf( D )),bind(B,$thf( D @ sk19 )),bind(C,$thf( D ))]]) ).
thf(4434,plain,
! [A: $i] : ( A @ ( A @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[4433]) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ incident_c ) )
| ~ ( C @ ( D @ incident_c ) )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(58,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ incident_c ) )
| ~ ( C @ ( D @ incident_c ) )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ sum ) @ ( C @ incident_c ) )
| ~ ( B @ ( C @ incident_c ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(12089,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( C @ ( D @ incident_c ) ) )
| ( C @ ( B @ sum ) @ ( D @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4434,59]) ).
thf(12090,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( C @ ( D @ incident_c ) ) )
| ( C @ ( B @ sum ) @ ( D @ incident_c ) ) ),
inference(simp,[status(thm)],[12089]) ).
thf(12091,plain,
! [B: $i,A: $i] : ( B @ ( A @ sum ) @ ( B @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[12090:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( E @ sk19 ))]]) ).
thf(12271,plain,
! [B: $i,A: $i] : ( B @ ( A @ sum ) @ ( B @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[12091]) ).
thf(44,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ incident_c ) )
| ~ ( B @ ( D @ incident_c ) )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(54,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ incident_c ) )
| ~ ( B @ ( D @ incident_c ) )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(lifteq,[status(thm)],[44]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ sum ) @ ( C @ incident_c ) )
| ~ ( A @ ( C @ incident_c ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(12410,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sum ) @ ( B @ sk19 @ incident_c ) )
!= ( C @ ( E @ incident_c ) ) )
| ( D @ ( C @ sum ) @ ( E @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12271,55]) ).
thf(12411,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sum ) @ ( B @ sk19 @ incident_c ) )
!= ( C @ ( E @ incident_c ) ) )
| ( D @ ( C @ sum ) @ ( E @ incident_c ) ) ),
inference(simp,[status(thm)],[12410]) ).
thf(12412,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[12411:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( H @ ( G @ sum ) )),bind(D,$thf( D )),bind(E,$thf( H @ sk19 ))]]) ).
thf(12491,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[12412]) ).
thf(13057,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( D @ ( F @ incident_c ) ) )
| ( E @ ( D @ sum ) @ ( F @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12491,55]) ).
thf(13058,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( D @ ( F @ incident_c ) ) )
| ( E @ ( D @ sum ) @ ( F @ incident_c ) ) ),
inference(simp,[status(thm)],[13057]) ).
thf(13059,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( C @ sum ) @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[13058:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( I @ ( K @ ( J @ sum ) @ sum ) )),bind(E,$thf( E )),bind(F,$thf( K @ sk19 ))]]) ).
thf(13115,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( C @ sum ) @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[13059]) ).
thf(18366,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ sum ) @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( F @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13115,59]) ).
thf(18367,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ sum ) @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( F @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) ) ),
inference(simp,[status(thm)],[18366]) ).
thf(18368,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( E @ ( D @ sum ) @ sum ) @ sum ) @ ( A @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[18367:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( J @ ( L @ ( N @ ( M @ sum ) @ sum ) @ sum ) )),bind(G,$thf( N @ sk19 ))]]) ).
thf(18534,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( E @ ( D @ sum ) @ sum ) @ sum ) @ ( A @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[18368]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ open )
<=> ? [B: $i] : ( A @ ( B @ end_point ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',open_defn) ).
thf(96,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)],[10]) ).
thf(97,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)],[96]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ open )
| ~ ( B @ ( C @ end_point ) ) )
& ( ( A @ ( A @ sk15 @ end_point ) )
| ~ ( A @ open ) ) ),
inference(cnf,[status(esa)],[97]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( A @ open )
| ~ ( A @ ( B @ end_point ) ) ),
inference(cnfConj,[status(thm)],[98]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( A @ open )
| ~ ( A @ ( B @ end_point ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ closed )
<=> ~ ? [B: $i] : ( A @ ( B @ end_point ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closed_defn) ).
thf(123,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)],[14]) ).
thf(124,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)],[123]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ closed )
| ( C @ ( C @ sk18 @ end_point ) ) )
& ( ~ ( A @ ( B @ end_point ) )
| ~ ( A @ closed ) ) ),
inference(cnf,[status(esa)],[124]) ).
thf(127,plain,
! [A: $i] :
( ( A @ closed )
| ( A @ ( A @ sk18 @ end_point ) ) ),
inference(cnfConj,[status(thm)],[125]) ).
thf(128,plain,
! [A: $i] :
( ( A @ closed )
| ( A @ ( A @ sk18 @ end_point ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ end_point ) )
| ~ ( B @ ( A @ inner_point ) ) ),
inference(cnfConj,[status(thm)],[84]) ).
thf(312,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk19 @ inner_point ) )
!= ( C @ ( B @ inner_point ) ) )
| ~ ( C @ ( B @ end_point ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[130,86]) ).
thf(313,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk19 @ inner_point ) )
!= ( C @ ( B @ inner_point ) ) )
| ~ ( C @ ( B @ end_point ) ) ),
inference(simp,[status(thm)],[312]) ).
thf(314,plain,
! [A: $i] :
~ ( A @ ( A @ sk19 @ end_point ) ),
inference(pattern_uni,[status(thm)],[313:[bind(A,$thf( D )),bind(B,$thf( D @ sk19 )),bind(C,$thf( D ))]]) ).
thf(319,plain,
! [A: $i] :
~ ( A @ ( A @ sk19 @ end_point ) ),
inference(simp,[status(thm)],[314]) ).
thf(321,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk18 @ end_point ) )
!= ( B @ ( B @ sk19 @ end_point ) ) )
| ~ $true
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[128,319]) ).
thf(322,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk18 @ end_point ) )
!= ( B @ ( B @ sk19 @ end_point ) ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[321]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( A @ sk18 )
!= ( B @ sk19 ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[322]) ).
thf(333,plain,
! [A: $i] :
( ( ( A @ sk19 )
!= ( A @ sk18 ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[329]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ incident_c ) )
<=> ( B @ ( C @ incident_c ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c9) ).
thf(24,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(25,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)],[24]) ).
thf(26,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)],[25]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(cnfConj,[status(thm)],[26]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ incident_c ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ between_c ) ) ) )
=> ( B @ ( C @ ( D @ ( A @ between_c ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem_3_8_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ between_c ) ) ) )
=> ( B @ ( C @ ( D @ ( A @ between_c ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(20,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ between_c ) ) ) )
=> ( B @ ( C @ ( D @ ( A @ between_c ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,plain,
( ~ ( sk2 @ ( sk3 @ ( sk4 @ ( sk1 @ between_c ) ) ) )
& ( sk4 @ ( sk3 @ ( sk2 @ ( sk1 @ between_c ) ) ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(22,plain,
sk4 @ ( sk3 @ ( sk2 @ ( sk1 @ between_c ) ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(23,plain,
~ ( sk2 @ ( sk3 @ ( sk4 @ ( sk1 @ between_c ) ) ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(160,plain,
( ( ( sk2 @ ( sk3 @ ( sk4 @ ( sk1 @ between_c ) ) ) )
!= ( sk4 @ ( sk3 @ ( sk2 @ ( sk1 @ between_c ) ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,23]) ).
thf(161,plain,
( ( sk2 @ ( sk3 @ ( sk4 @ ( sk1 @ between_c ) ) ) )
!= ( sk4 @ ( sk3 @ ( sk2 @ ( sk1 @ between_c ) ) ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(162,plain,
( ( sk4 != sk2 )
| ( sk3 != sk3 )
| ( sk4 != sk2 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[161]) ).
thf(163,plain,
sk4 != sk2,
inference(simp,[status(thm)],[162]) ).
thf(1621,plain,
! [B: $i,A: $i] :
( ( B != sk4 )
| ( A != sk2 )
| ~ ( A @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[34,163]) ).
thf(1622,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( A @ ( A @ ( sk4 @ sk6 ) @ incident_c ) )
| ~ ( sk4 @ ( A @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[1621:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(1840,plain,
( ~ ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[1622]) ).
thf(2291,plain,
( ~ $true
| ( ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(eqfactor_ordered,[status(thm)],[1840]) ).
thf(2295,plain,
( ( ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[2291]) ).
thf(6795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( B @ ( D @ incident_c ) ) )
| ( C @ ( B @ sum ) @ ( D @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4434,55]) ).
thf(6796,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( B @ ( D @ incident_c ) ) )
| ( C @ ( B @ sum ) @ ( D @ incident_c ) ) ),
inference(simp,[status(thm)],[6795]) ).
thf(6797,plain,
! [B: $i,A: $i] : ( A @ ( B @ sum ) @ ( B @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[6796:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( E @ sk19 ))]]) ).
thf(6937,plain,
! [B: $i,A: $i] : ( A @ ( B @ sum ) @ ( B @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[6797]) ).
thf(7059,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sum ) @ ( B @ sk19 @ incident_c ) )
!= ( C @ ( E @ incident_c ) ) )
| ( D @ ( C @ sum ) @ ( E @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6937,55]) ).
thf(7060,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sum ) @ ( B @ sk19 @ incident_c ) )
!= ( C @ ( E @ incident_c ) ) )
| ( D @ ( C @ sum ) @ ( E @ incident_c ) ) ),
inference(simp,[status(thm)],[7059]) ).
thf(7061,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ sum ) @ sum ) @ ( B @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[7060:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ sum ) )),bind(D,$thf( D )),bind(E,$thf( G @ sk19 ))]]) ).
thf(7109,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ sum ) @ sum ) @ ( B @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[7061]) ).
thf(7233,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ sum ) @ sum ) @ ( B @ sk19 @ incident_c ) )
!= ( D @ ( F @ incident_c ) ) )
| ( E @ ( D @ sum ) @ ( F @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7109,55]) ).
thf(7234,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ sum ) @ sum ) @ ( B @ sk19 @ incident_c ) )
!= ( D @ ( F @ incident_c ) ) )
| ( E @ ( D @ sum ) @ ( F @ incident_c ) ) ),
inference(simp,[status(thm)],[7233]) ).
thf(7235,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( C @ sum ) @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[7234:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( I @ ( K @ ( J @ sum ) @ sum ) )),bind(E,$thf( E )),bind(F,$thf( J @ sk19 ))]]) ).
thf(7309,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( C @ sum ) @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[7235]) ).
thf(7449,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ sum ) @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( E @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7309,55]) ).
thf(7450,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ sum ) @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( E @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) ) ),
inference(simp,[status(thm)],[7449]) ).
thf(7451,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( E @ ( D @ sum ) @ sum ) @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[7450:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( J @ ( L @ ( N @ ( M @ sum ) @ sum ) @ sum ) )),bind(F,$thf( F )),bind(G,$thf( M @ sk19 ))]]) ).
thf(7519,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( E @ ( D @ sum ) @ sum ) @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[7451]) ).
thf(7707,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( E @ ( D @ sum ) @ sum ) @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( F @ ( H @ incident_c ) ) )
| ( G @ ( F @ sum ) @ ( H @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7519,55]) ).
thf(7708,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( E @ ( D @ sum ) @ sum ) @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( F @ ( H @ incident_c ) ) )
| ( G @ ( F @ sum ) @ ( H @ incident_c ) ) ),
inference(simp,[status(thm)],[7707]) ).
thf(7709,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( F @ ( E @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[7708:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( Q )),bind(F,$thf( K @ ( M @ ( O @ ( Q @ ( P @ sum ) @ sum ) @ sum ) @ sum ) )),bind(G,$thf( G )),bind(H,$thf( P @ sk19 ))]]) ).
thf(7788,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( F @ ( E @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[7709]) ).
thf(9317,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( F @ ( E @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) )
!= ( G @ ( I @ incident_c ) ) )
| ( H @ ( G @ sum ) @ ( I @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7788,55]) ).
thf(9318,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( F @ ( E @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) )
!= ( G @ ( I @ incident_c ) ) )
| ( H @ ( G @ sum ) @ ( I @ incident_c ) ) ),
inference(simp,[status(thm)],[9317]) ).
thf(9319,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( G @ ( F @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ ( F @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[9318:[bind(A,$thf( L )),bind(B,$thf( N )),bind(C,$thf( P )),bind(D,$thf( R )),bind(E,$thf( S )),bind(F,$thf( T )),bind(G,$thf( L @ ( N @ ( P @ ( R @ ( T @ ( S @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) )),bind(H,$thf( H )),bind(I,$thf( S @ sk19 ))]]) ).
thf(9438,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( G @ ( F @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ ( F @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[9319]) ).
thf(9699,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( G @ ( F @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ ( F @ sk19 @ incident_c ) )
!= ( H @ ( J @ incident_c ) ) )
| ( I @ ( H @ sum ) @ ( J @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9438,55]) ).
thf(9700,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( G @ ( F @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ ( F @ sk19 @ incident_c ) )
!= ( H @ ( J @ incident_c ) ) )
| ( I @ ( H @ sum ) @ ( J @ incident_c ) ) ),
inference(simp,[status(thm)],[9699]) ).
thf(9701,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( H @ ( G @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ ( G @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[9700:[bind(A,$thf( M )),bind(B,$thf( O )),bind(C,$thf( Q )),bind(D,$thf( S )),bind(E,$thf( U )),bind(F,$thf( V )),bind(G,$thf( W )),bind(H,$thf( M @ ( O @ ( Q @ ( S @ ( U @ ( W @ ( V @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) )),bind(I,$thf( I )),bind(J,$thf( V @ sk19 ))]]) ).
thf(9886,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( H @ ( G @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ ( G @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[9701]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(cnfConj,[status(thm)],[26]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( B != sk4 )
| ( A != sk2 )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[31,163]) ).
thf(226,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk4 @ ( A @ ( sk4 @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[225:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(239,plain,
( ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[226]) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',end_point_defn) ).
thf(65,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)],[6]) ).
thf(66,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 ) ) )
& ! [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 ) ) ) ) ),
inference(miniscope,[status(thm)],[65]) ).
thf(67,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ end_point ) )
| ~ ( E @ ( F @ sk11 ) @ ( E @ ( F @ sk12 ) @ part_of ) )
| ~ ( F @ ( E @ incident_c ) ) )
& ( ( F @ ( E @ end_point ) )
| ~ ( E @ ( F @ sk12 ) @ ( E @ ( F @ sk11 ) @ part_of ) )
| ~ ( F @ ( E @ incident_c ) ) )
& ( ( F @ ( E @ end_point ) )
| ( E @ ( F @ sk12 ) @ ( E @ incident_c ) )
| ~ ( F @ ( E @ incident_c ) ) )
& ( ( F @ ( E @ end_point ) )
| ( E @ ( F @ sk11 ) @ ( E @ incident_c ) )
| ~ ( F @ ( E @ incident_c ) ) )
& ( ( F @ ( E @ end_point ) )
| ( F @ ( E @ ( F @ sk12 ) @ part_of ) )
| ~ ( F @ ( E @ incident_c ) ) )
& ( ( F @ ( E @ end_point ) )
| ( F @ ( E @ ( F @ sk11 ) @ part_of ) )
| ~ ( F @ ( E @ incident_c ) ) )
& ( ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) )
| ~ ( D @ ( A @ incident_c ) )
| ~ ( C @ ( A @ incident_c ) )
| ~ ( B @ ( D @ part_of ) )
| ~ ( B @ ( C @ part_of ) )
| ~ ( B @ ( A @ end_point ) ) )
& ( ( B @ ( A @ incident_c ) )
| ~ ( B @ ( A @ end_point ) ) ) ),
inference(cnf,[status(esa)],[66]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ( B @ ( A @ ( B @ sk12 ) @ part_of ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(cnfConj,[status(thm)],[67]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ( B @ ( A @ ( B @ sk12 ) @ part_of ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(22715,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
!= ( B @ ( A @ incident_c ) ) )
| ( B @ ( A @ end_point ) )
| ( B @ ( A @ ( B @ sk12 ) @ part_of ) )
| ~ $true
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[239,76]) ).
thf(22716,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
!= ( B @ ( A @ incident_c ) ) )
| ( B @ ( A @ end_point ) )
| ( B @ ( A @ ( B @ sk12 ) @ part_of ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[22715]) ).
thf(22717,plain,
( ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ end_point ) )
| ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ ( sk4 @ sk12 ) @ part_of ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[22716:[bind(A,$thf( sk2 @ ( sk4 @ sk6 ) )),bind(B,$thf( sk4 ))]]) ).
thf(18411,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ sum ) @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( E @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13115,55]) ).
thf(18412,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ sum ) @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( E @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) ) ),
inference(simp,[status(thm)],[18411]) ).
thf(18413,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( E @ ( D @ sum ) @ sum ) @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[18412:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( J @ ( L @ ( N @ ( M @ sum ) @ sum ) @ sum ) )),bind(F,$thf( F )),bind(G,$thf( N @ sk19 ))]]) ).
thf(18549,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( E @ ( D @ sum ) @ sum ) @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[18413]) ).
thf(12381,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sum ) @ ( B @ sk19 @ incident_c ) )
!= ( D @ ( E @ incident_c ) ) )
| ( D @ ( C @ sum ) @ ( E @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12271,59]) ).
thf(12382,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sum ) @ ( B @ sk19 @ incident_c ) )
!= ( D @ ( E @ incident_c ) ) )
| ( D @ ( C @ sum ) @ ( E @ incident_c ) ) ),
inference(simp,[status(thm)],[12381]) ).
thf(12383,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[12382:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ sum ) )),bind(E,$thf( H @ sk19 ))]]) ).
thf(12484,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[12383]) ).
thf(12797,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( E @ ( F @ incident_c ) ) )
| ( E @ ( D @ sum ) @ ( F @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12484,59]) ).
thf(12798,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( E @ ( F @ incident_c ) ) )
| ( E @ ( D @ sum ) @ ( F @ incident_c ) ) ),
inference(simp,[status(thm)],[12797]) ).
thf(12799,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[12798:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ sum ) @ ( H @ sum ) )),bind(F,$thf( K @ sk19 ))]]) ).
thf(12939,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[12799]) ).
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/sandbox2/benchmark/theBenchmark.p',c7) ).
thf(142,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(99,plain,
! [A: $i] :
( ( A @ ( A @ sk15 @ end_point ) )
| ~ ( A @ open ) ),
inference(cnfConj,[status(thm)],[98]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ incident_c ) )
| ~ ( B @ ( A @ end_point ) ) ),
inference(cnfConj,[status(thm)],[67]) ).
thf(3777,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk15 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ( C @ ( B @ incident_c ) )
| ~ $true
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[99,71]) ).
thf(3778,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk15 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ( C @ ( B @ incident_c ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[3777]) ).
thf(3779,plain,
! [A: $i] :
( ( A @ ( A @ sk15 @ incident_c ) )
| ~ ( A @ open ) ),
inference(pattern_uni,[status(thm)],[3778:[bind(A,$thf( D )),bind(B,$thf( D @ sk15 )),bind(C,$thf( D ))]]) ).
thf(3781,plain,
! [A: $i] :
( ( A @ ( A @ sk15 @ incident_c ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[3779]) ).
thf(12834,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( D @ ( F @ incident_c ) ) )
| ( E @ ( D @ sum ) @ ( F @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12484,55]) ).
thf(12835,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( D @ ( F @ incident_c ) ) )
| ( E @ ( D @ sum ) @ ( F @ incident_c ) ) ),
inference(simp,[status(thm)],[12834]) ).
thf(12836,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[12835:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( K @ ( J @ sum ) @ ( H @ sum ) )),bind(E,$thf( E )),bind(F,$thf( K @ sk19 ))]]) ).
thf(12901,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[12836]) ).
thf(16434,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( E @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12901,55]) ).
thf(16435,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( E @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) ) ),
inference(simp,[status(thm)],[16434]) ).
thf(16436,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( E @ ( D @ sum ) @ ( C @ sum ) @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[16435:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( J @ ( N @ ( M @ sum ) @ ( K @ sum ) @ sum ) )),bind(F,$thf( F )),bind(G,$thf( N @ sk19 ))]]) ).
thf(16520,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( E @ ( D @ sum ) @ ( C @ sum ) @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[16436]) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk18 @ end_point ) )
!= ( B @ ( C @ end_point ) ) )
| ( B @ open )
| ~ $true
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[128,101]) ).
thf(172,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk18 @ end_point ) )
!= ( B @ ( C @ end_point ) ) )
| ( B @ open )
| ( A @ closed ) ),
inference(simp,[status(thm)],[171]) ).
thf(173,plain,
! [A: $i] :
( ( A @ open )
| ( A @ closed ) ),
inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk18 ))]]) ).
thf(174,plain,
! [A: $i] :
( ( A @ open )
| ( A @ closed ) ),
inference(simp,[status(thm)],[173]) ).
thf(315,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk15 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ~ $true
| ~ ( C @ ( B @ inner_point ) )
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[99,86]) ).
thf(316,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk15 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ~ ( C @ ( B @ inner_point ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[315]) ).
thf(317,plain,
! [A: $i] :
( ~ ( A @ ( A @ sk15 @ inner_point ) )
| ~ ( A @ open ) ),
inference(pattern_uni,[status(thm)],[316:[bind(A,$thf( D )),bind(B,$thf( D @ sk15 )),bind(C,$thf( D ))]]) ).
thf(320,plain,
! [A: $i] :
( ~ ( A @ ( A @ sk15 @ inner_point ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[317]) ).
thf(4448,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[4434,2295]) ).
thf(4449,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4448]) ).
thf(4505,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ sk19 )
!= ( sk2 @ ( sk4 @ sk6 ) ) )
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4449]) ).
thf(4527,plain,
( ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ sk19 ) )
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4505]) ).
thf(5036,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ sk19 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4434,4527]) ).
thf(5037,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ sk19 ) ) ),
inference(simp,[status(thm)],[5036]) ).
thf(5167,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( A @ sk19 )
!= ( sk2 @ ( sk4 @ sk5 ) ) )
| ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ sk19 ) ) ),
inference(simp,[status(thm)],[5037]) ).
thf(5195,plain,
( ( ( sk2 @ ( sk4 @ sk5 ) )
!= ( sk4 @ sk19 ) )
| ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ sk19 ) ) ),
inference(simp,[status(thm)],[5167]) ).
thf(10129,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( H @ ( G @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ ( G @ sk19 @ incident_c ) )
!= ( I @ ( K @ incident_c ) ) )
| ( J @ ( I @ sum ) @ ( K @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9886,55]) ).
thf(10130,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( H @ ( G @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ ( G @ sk19 @ incident_c ) )
!= ( I @ ( K @ incident_c ) ) )
| ( J @ ( I @ sum ) @ ( K @ incident_c ) ) ),
inference(simp,[status(thm)],[10129]) ).
thf(10131,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( I @ ( H @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ ( H @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[10130:[bind(A,$thf( N )),bind(B,$thf( P )),bind(C,$thf( R )),bind(D,$thf( T )),bind(E,$thf( V )),bind(F,$thf( X )),bind(G,$thf( Y )),bind(H,$thf( Z )),bind(I,$thf( N @ ( P @ ( R @ ( T @ ( V @ ( X @ ( Z @ ( Y @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) )),bind(J,$thf( J )),bind(K,$thf( Y @ sk19 ))]]) ).
thf(10286,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( I @ ( H @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ sum ) @ ( H @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[10131]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(cnfConj,[status(thm)],[26]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(410,plain,
! [B: $i,A: $i] :
( ( B != sk4 )
| ( A != sk2 )
| ~ ( A @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[32,163]) ).
thf(411,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( A @ ( A @ ( sk4 @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[410:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(462,plain,
( ~ ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[411]) ).
thf(4483,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ~ $true
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[4434,462]) ).
thf(4484,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4483]) ).
thf(4503,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ sk19 )
!= ( sk2 @ ( sk4 @ sk6 ) ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4484]) ).
thf(4524,plain,
( ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ sk19 ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4503]) ).
thf(4337,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ~ ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ~ $true
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[3781,1840]) ).
thf(4338,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ~ ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[4337]) ).
thf(4388,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( A @ sk15 )
!= ( sk2 @ ( sk4 @ sk5 ) ) )
| ~ ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[4338]) ).
thf(4415,plain,
( ( ( sk2 @ ( sk4 @ sk5 ) )
!= ( sk4 @ sk15 ) )
| ~ ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ~ ( sk4 @ open ) ),
inference(simp,[status(thm)],[4388]) ).
thf(13,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/sandbox2/benchmark/theBenchmark.p',meet_defn) ).
thf(110,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)],[13]) ).
thf(195,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( sk4 @ ( sk3 @ ( sk2 @ ( A @ between_c ) ) ) )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[31,22]) ).
thf(196,plain,
! [A: $i] :
( ( sk4 @ ( sk3 @ ( sk2 @ ( A @ between_c ) ) ) )
| ( sk1 @ ( A @ ( sk1 @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( sk1 @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ between_c ) ) ) )
<=> ( ? [E: $i] :
( ( E @ ( C @ inner_point ) )
& ( E @ ( D @ end_point ) )
& ( E @ ( B @ end_point ) )
& ( A @ ( E @ part_of ) ) )
& ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',between_c_defn) ).
thf(147,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ? [E: $i] :
( ( E @ ( C @ inner_point ) )
& ( E @ ( D @ end_point ) )
& ( E @ ( B @ end_point ) )
& ( A @ ( E @ part_of ) ) )
& ( B != D ) )
=> ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ between_c ) ) ) )
=> ( ? [E: $i] :
( ( E @ ( C @ inner_point ) )
& ( E @ ( D @ end_point ) )
& ( E @ ( B @ end_point ) )
& ( A @ ( E @ part_of ) ) )
& ( B != D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(148,plain,
( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ ( C @ inner_point ) )
& ( E @ ( D @ end_point ) )
& ( E @ ( B @ end_point ) )
& ( A @ ( E @ part_of ) ) )
& ( B != D ) )
=> ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ between_c ) ) ) )
=> ( ? [E: $i] :
( ( E @ ( C @ inner_point ) )
& ( E @ ( D @ end_point ) )
& ( E @ ( B @ end_point ) )
& ( A @ ( E @ part_of ) ) )
& ( B != D ) ) ) ),
inference(miniscope,[status(thm)],[147]) ).
thf(149,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( G @ ( F @ ( E @ between_c ) ) ) )
| ~ ( I @ ( G @ inner_point ) )
| ~ ( I @ ( H @ end_point ) )
| ~ ( I @ ( F @ end_point ) )
| ~ ( E @ ( I @ part_of ) )
| ( F = H ) )
& ( ( A @ ( B @ ( C @ ( D @ sk21 ) ) ) @ ( C @ inner_point ) )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ sk21 ) ) ) @ ( D @ end_point ) )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ sk21 ) ) ) @ ( B @ end_point ) )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) )
& ( ( A @ ( A @ ( B @ ( C @ ( D @ sk21 ) ) ) @ part_of ) )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) )
& ( ( B != D )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) ) ),
inference(cnf,[status(esa)],[148]) ).
thf(154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != D )
| ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) ) ),
inference(cnfConj,[status(thm)],[149]) ).
thf(156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ between_c ) ) ) )
| ( B != D ) ),
inference(lifteq,[status(thm)],[154]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ ( C @ ( A @ between_c ) ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ sum ) ) )
| ~ ( A @ ( C @ ( B @ sk7 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk8 ) ) @ incident_c ) ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ sk7 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk8 ) ) @ incident_c ) )
| ( A
= ( C @ ( B @ sum ) ) ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ sk7 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk8 ) ) @ incident_c ) )
| ( A
= ( C @ ( B @ sum ) ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ~ ( A @ ( B @ sk11 ) @ ( A @ ( B @ sk12 ) @ part_of ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(cnfConj,[status(thm)],[67]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ~ ( A @ ( B @ sk11 ) @ ( A @ ( B @ sk12 ) @ part_of ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(simp,[status(thm)],[70]) ).
thf(1619,plain,
! [B: $i,A: $i] :
( ( A != sk4 )
| ( B != sk2 )
| ~ ( A @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[34,163]) ).
thf(1620,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( sk4 @ ( sk4 @ ( A @ sk6 ) @ incident_c ) )
| ~ ( A @ ( sk4 @ ( A @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[1619:[bind(A,$thf( sk4 ))]]) ).
thf(1839,plain,
( ~ ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[1620]) ).
thf(4372,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) )
| ~ ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ~ $true
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[3781,1839]) ).
thf(4373,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) )
| ~ ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[4372]) ).
thf(4384,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ sk15 )
!= ( sk4 @ ( sk2 @ sk5 ) ) )
| ~ ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[4373]) ).
thf(4411,plain,
( ( ( sk4 @ ( sk2 @ sk5 ) )
!= ( sk2 @ sk15 ) )
| ~ ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ~ ( sk2 @ open ) ),
inference(simp,[status(thm)],[4384]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( A != sk4 )
| ( B != sk2 )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[31,163]) ).
thf(224,plain,
! [A: $i] :
( ( A != sk2 )
| ( A @ ( sk4 @ ( A @ sk6 ) @ incident_c ) )
| ( sk4 @ ( sk4 @ ( A @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[223:[bind(A,$thf( sk4 ))]]) ).
thf(238,plain,
( ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ sum ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ sk9 ) ) @ incident_c ) )
| ( A @ ( C @ ( B @ sk7 ) ) ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ sk9 ) ) @ incident_c ) )
| ( A @ ( C @ ( B @ sk7 ) ) )
| ( A
= ( C @ ( B @ sum ) ) ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ sk9 ) ) @ incident_c ) )
| ( A @ ( C @ ( B @ sk7 ) ) )
| ( A
= ( C @ ( B @ sum ) ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',c2) ).
thf(89,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)],[8]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( sk4 @ ( sk3 @ ( B @ ( sk1 @ between_c ) ) ) )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[31,22]) ).
thf(184,plain,
! [A: $i] :
( ( sk4 @ ( sk3 @ ( A @ ( sk1 @ between_c ) ) ) )
| ( A @ ( sk2 @ ( A @ sk6 ) @ incident_c ) )
| ( sk2 @ ( sk2 @ ( A @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( sk2 ))]]) ).
thf(243,plain,
! [A: $i] :
( ( sk4 @ ( sk3 @ ( A @ ( sk1 @ between_c ) ) ) )
| ( A @ ( sk2 @ ( A @ sk6 ) @ incident_c ) )
| ( sk2 @ ( sk2 @ ( A @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(3774,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk18 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ( C @ ( B @ incident_c ) )
| ~ $true
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[128,71]) ).
thf(3775,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk18 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ( C @ ( B @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3774]) ).
thf(3776,plain,
! [A: $i] :
( ( A @ ( A @ sk18 @ incident_c ) )
| ( A @ closed ) ),
inference(pattern_uni,[status(thm)],[3775:[bind(A,$thf( D )),bind(B,$thf( D @ sk18 )),bind(C,$thf( D ))]]) ).
thf(3780,plain,
! [A: $i] :
( ( A @ ( A @ sk18 @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3776]) ).
thf(3828,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ~ $true
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[3780,462]) ).
thf(3829,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3828]) ).
thf(3852,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ sk18 )
!= ( sk2 @ ( sk4 @ sk6 ) ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3829]) ).
thf(3870,plain,
( ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ sk18 ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ( sk2 @ closed ) ),
inference(simp,[status(thm)],[3852]) ).
thf(4485,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) )
| ~ ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4434,1839]) ).
thf(4486,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) )
| ~ ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4485]) ).
thf(4500,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ sk19 )
!= ( sk4 @ ( sk2 @ sk5 ) ) )
| ~ ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4486]) ).
thf(4521,plain,
( ( ( sk4 @ ( sk2 @ sk5 ) )
!= ( sk2 @ sk19 ) )
| ~ ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4500]) ).
thf(4591,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ( ( sk4 @ ( sk2 @ sk5 ) )
!= ( sk2 @ sk19 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4434,4521]) ).
thf(4592,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ( ( sk4 @ ( sk2 @ sk5 ) )
!= ( sk2 @ sk19 ) ) ),
inference(simp,[status(thm)],[4591]) ).
thf(4709,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( A @ sk19 )
!= ( sk4 @ ( sk2 @ sk6 ) ) )
| ( ( sk4 @ ( sk2 @ sk5 ) )
!= ( sk2 @ sk19 ) ) ),
inference(simp,[status(thm)],[4592]) ).
thf(4753,plain,
( ( ( sk4 @ ( sk2 @ sk6 ) )
!= ( sk4 @ sk19 ) )
| ( ( sk4 @ ( sk2 @ sk5 ) )
!= ( sk2 @ sk19 ) ) ),
inference(simp,[status(thm)],[4709]) ).
thf(4370,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ~ $true
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[3781,462]) ).
thf(4371,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[4370]) ).
thf(4380,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ sk15 )
!= ( sk2 @ ( sk4 @ sk6 ) ) )
| ~ ( A @ open )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4371]) ).
thf(4407,plain,
( ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ sk15 ) )
| ~ ( sk2 @ open )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4380]) ).
thf(12138,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ sum ) @ sum ) @ ( B @ sk19 @ incident_c ) )
!= ( E @ ( F @ incident_c ) ) )
| ( E @ ( D @ sum ) @ ( F @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7109,59]) ).
thf(12139,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ sum ) @ sum ) @ ( B @ sk19 @ incident_c ) )
!= ( E @ ( F @ incident_c ) ) )
| ( E @ ( D @ sum ) @ ( F @ incident_c ) ) ),
inference(simp,[status(thm)],[12138]) ).
thf(12140,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[12139:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( I @ ( K @ ( J @ sum ) @ sum ) )),bind(F,$thf( J @ sk19 ))]]) ).
thf(12310,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[12140]) ).
thf(15492,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( F @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12310,59]) ).
thf(15493,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( F @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) ) ),
inference(simp,[status(thm)],[15492]) ).
thf(15494,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( C @ ( E @ ( D @ sum ) @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[15493:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( L @ ( N @ ( M @ sum ) @ sum ) @ ( I @ sum ) )),bind(G,$thf( M @ sk19 ))]]) ).
thf(15642,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( C @ ( E @ ( D @ sum ) @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[15494]) ).
thf(22576,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
!= ( B @ ( A @ incident_c ) ) )
| ( B @ ( A @ end_point ) )
| ( B @ ( A @ ( B @ sk12 ) @ part_of ) )
| ~ $true
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[238,76]) ).
thf(22577,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
!= ( B @ ( A @ incident_c ) ) )
| ( B @ ( A @ end_point ) )
| ( B @ ( A @ ( B @ sk12 ) @ part_of ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[22576]) ).
thf(22578,plain,
( ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ end_point ) )
| ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ ( sk2 @ sk12 ) @ part_of ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[22577:[bind(A,$thf( sk4 @ ( sk2 @ sk6 ) )),bind(B,$thf( sk2 ))]]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',c5) ).
thf(102,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)],[11]) ).
thf(408,plain,
! [B: $i,A: $i] :
( ( A != sk4 )
| ( B != sk2 )
| ~ ( A @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[32,163]) ).
thf(409,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( sk4 @ ( sk4 @ ( A @ sk6 ) @ incident_c ) )
| ( sk4 @ ( sk4 @ ( A @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[408:[bind(A,$thf( sk4 ))]]) ).
thf(461,plain,
( ~ ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[409]) ).
thf(4435,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ~ $true
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[4434,461]) ).
thf(4436,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4435]) ).
thf(4508,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( A @ sk19 )
!= ( sk4 @ ( sk2 @ sk6 ) ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4436]) ).
thf(4531,plain,
( ( ( sk4 @ ( sk2 @ sk6 ) )
!= ( sk4 @ sk19 ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4508]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk15 @ end_point ) )
!= ( B @ ( B @ sk19 @ end_point ) ) )
| ~ $true
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[99,319]) ).
thf(328,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk15 @ end_point ) )
!= ( B @ ( B @ sk19 @ end_point ) ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[327]) ).
thf(330,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( A @ sk15 )
!= ( B @ sk19 ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[328]) ).
thf(334,plain,
! [A: $i] :
( ( ( A @ sk19 )
!= ( A @ sk15 ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[330]) ).
thf(12132,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sum ) @ ( B @ sk19 @ incident_c ) )
!= ( D @ ( E @ incident_c ) ) )
| ( D @ ( C @ sum ) @ ( E @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6937,59]) ).
thf(12133,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sum ) @ ( B @ sk19 @ incident_c ) )
!= ( D @ ( E @ incident_c ) ) )
| ( D @ ( C @ sum ) @ ( E @ incident_c ) ) ),
inference(simp,[status(thm)],[12132]) ).
thf(12134,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ sum ) @ ( A @ sum ) @ ( B @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[12133:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ sum ) )),bind(E,$thf( G @ sk19 ))]]) ).
thf(12309,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ sum ) @ ( A @ sum ) @ ( B @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[12134]) ).
thf(12610,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ sum ) @ ( A @ sum ) @ ( B @ sk19 @ incident_c ) )
!= ( D @ ( F @ incident_c ) ) )
| ( E @ ( D @ sum ) @ ( F @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12309,55]) ).
thf(12611,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ sum ) @ ( A @ sum ) @ ( B @ sk19 @ incident_c ) )
!= ( D @ ( F @ incident_c ) ) )
| ( E @ ( D @ sum ) @ ( F @ incident_c ) ) ),
inference(simp,[status(thm)],[12610]) ).
thf(12612,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[12611:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( K @ ( J @ sum ) @ ( H @ sum ) )),bind(E,$thf( E )),bind(F,$thf( J @ sk19 ))]]) ).
thf(12690,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[12612]) ).
thf(16135,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( E @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12690,55]) ).
thf(16136,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( E @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) ) ),
inference(simp,[status(thm)],[16135]) ).
thf(16137,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( E @ ( D @ sum ) @ ( C @ sum ) @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[16136:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( J @ ( N @ ( M @ sum ) @ ( K @ sum ) @ sum ) )),bind(F,$thf( F )),bind(G,$thf( M @ sk19 ))]]) ).
thf(16205,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( E @ ( D @ sum ) @ ( C @ sum ) @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[16137]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( sk4 @ ( sk3 @ ( A @ ( sk1 @ between_c ) ) ) )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[31,22]) ).
thf(192,plain,
! [A: $i] :
( ( sk4 @ ( sk3 @ ( A @ ( sk1 @ between_c ) ) ) )
| ( sk2 @ ( A @ ( sk2 @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[191:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ part_of ) )
<=> ! [C: $i] :
( ( B @ ( C @ incident_c ) )
=> ( A @ ( C @ incident_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_defn) ).
thf(131,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(132,plain,
( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ incident_c ) )
=> ( A @ ( C @ incident_c ) ) )
=> ( A @ ( B @ part_of ) ) )
& ! [A: $i,B: $i] :
( ( A @ ( B @ part_of ) )
=> ! [C: $i] :
( ( B @ ( C @ incident_c ) )
=> ( A @ ( C @ incident_c ) ) ) ) ),
inference(miniscope,[status(thm)],[131]) ).
thf(133,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( E @ part_of ) )
| ~ ( D @ ( D @ ( E @ sk20 ) @ incident_c ) ) )
& ( ( D @ ( E @ part_of ) )
| ( E @ ( D @ ( E @ sk20 ) @ incident_c ) ) )
& ( ( A @ ( C @ incident_c ) )
| ~ ( B @ ( C @ incident_c ) )
| ~ ( A @ ( B @ part_of ) ) ) ),
inference(cnf,[status(esa)],[132]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ part_of ) )
| ( B @ ( A @ ( B @ sk20 ) @ incident_c ) ) ),
inference(cnfConj,[status(thm)],[133]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ part_of ) )
| ( B @ ( A @ ( B @ sk20 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(cnfConj,[status(thm)],[26]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ incident_c ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(20337,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( E @ ( D @ sum ) @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( G @ ( H @ incident_c ) ) )
| ( G @ ( F @ sum ) @ ( H @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15642,59]) ).
thf(20338,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( E @ ( D @ sum ) @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( G @ ( H @ incident_c ) ) )
| ( G @ ( F @ sum ) @ ( H @ incident_c ) ) ),
inference(simp,[status(thm)],[20337]) ).
thf(20339,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ ( F @ ( E @ sum ) @ sum ) @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[20338:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( Q )),bind(F,$thf( F )),bind(G,$thf( O @ ( Q @ ( P @ sum ) @ sum ) @ ( L @ sum ) @ ( J @ sum ) )),bind(H,$thf( P @ sk19 ))]]) ).
thf(20521,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ ( F @ ( E @ sum ) @ sum ) @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[20339]) ).
thf(820,plain,
! [B: $i,A: $i] :
( ( A != sk4 )
| ( B != sk2 )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[33,163]) ).
thf(821,plain,
! [A: $i] :
( ( A != sk2 )
| ( A @ ( sk4 @ ( A @ sk6 ) @ incident_c ) )
| ~ ( A @ ( sk4 @ ( A @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[820:[bind(A,$thf( sk4 ))]]) ).
thf(954,plain,
( ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[821]) ).
thf(3784,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ incident_c ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) )
| ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ~ $true
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[3780,954]) ).
thf(3785,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ incident_c ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) )
| ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3784]) ).
thf(3858,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ sk18 )
!= ( sk4 @ ( sk2 @ sk5 ) ) )
| ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3785]) ).
thf(3877,plain,
( ( ( sk4 @ ( sk2 @ sk5 ) )
!= ( sk2 @ sk18 ) )
| ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ( sk2 @ closed ) ),
inference(simp,[status(thm)],[3858]) ).
thf(13020,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( E @ ( F @ incident_c ) ) )
| ( E @ ( D @ sum ) @ ( F @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12491,59]) ).
thf(13021,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( E @ ( F @ incident_c ) ) )
| ( E @ ( D @ sum ) @ ( F @ incident_c ) ) ),
inference(simp,[status(thm)],[13020]) ).
thf(13022,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[13021:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( I @ ( K @ ( J @ sum ) @ sum ) )),bind(F,$thf( K @ sk19 ))]]) ).
thf(13153,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[13022]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ end_point ) )
=> ? [C: $i] :
( ( B != C )
& ( A @ ( C @ end_point ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c6) ).
thf(105,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)],[12]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ( ( B
!= ( A @ ( B @ sk16 ) ) )
| ~ ( A @ ( B @ end_point ) ) )
& ( ( A @ ( A @ ( B @ sk16 ) @ end_point ) )
| ~ ( A @ ( B @ end_point ) ) ) ),
inference(cnf,[status(esa)],[105]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( B
!= ( A @ ( B @ sk16 ) ) )
| ~ ( A @ ( B @ end_point ) ) ),
inference(cnfConj,[status(thm)],[106]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ end_point ) )
| ( ( A @ ( B @ sk16 ) )
!= B ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ~ ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk11 ) @ part_of ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(cnfConj,[status(thm)],[67]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ~ ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk11 ) @ part_of ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(simp,[status(thm)],[74]) ).
thf(4339,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ~ $true
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[3781,1840]) ).
thf(4340,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[4339]) ).
thf(4397,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ sk15 )
!= ( sk2 @ ( sk4 @ sk6 ) ) )
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[4340]) ).
thf(4425,plain,
( ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ sk15 ) )
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ~ ( sk2 @ open ) ),
inference(simp,[status(thm)],[4397]) ).
thf(12148,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( E @ ( D @ sum ) @ sum ) @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( G @ ( H @ incident_c ) ) )
| ( G @ ( F @ sum ) @ ( H @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7519,59]) ).
thf(12149,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( E @ ( D @ sum ) @ sum ) @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( G @ ( H @ incident_c ) ) )
| ( G @ ( F @ sum ) @ ( H @ incident_c ) ) ),
inference(simp,[status(thm)],[12148]) ).
thf(12150,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ ( F @ ( E @ sum ) @ sum ) @ sum ) @ sum ) @ ( A @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[12149:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( Q )),bind(F,$thf( F )),bind(G,$thf( K @ ( M @ ( O @ ( Q @ ( P @ sum ) @ sum ) @ sum ) @ sum ) )),bind(H,$thf( P @ sk19 ))]]) ).
thf(12314,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ ( F @ ( E @ sum ) @ sum ) @ sum ) @ sum ) @ ( A @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[12150]) ).
thf(2074,plain,
( ~ $true
| ( ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(eqfactor_ordered,[status(thm)],[1839]) ).
thf(2089,plain,
( ( ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[2074]) ).
thf(4349,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[3781,2089]) ).
thf(4350,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[4349]) ).
thf(4389,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( A @ sk15 )
!= ( sk4 @ ( sk2 @ sk6 ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[4350]) ).
thf(4416,plain,
( ( ( sk4 @ ( sk2 @ sk6 ) )
!= ( sk4 @ sk15 ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ~ ( sk4 @ open ) ),
inference(simp,[status(thm)],[4389]) ).
thf(12081,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ sum ) @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( F @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7309,59]) ).
thf(12082,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ sum ) @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( F @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) ) ),
inference(simp,[status(thm)],[12081]) ).
thf(12083,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( E @ ( D @ sum ) @ sum ) @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[12082:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( J @ ( L @ ( N @ ( M @ sum ) @ sum ) @ sum ) )),bind(G,$thf( M @ sk19 ))]]) ).
thf(12270,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( E @ ( D @ sum ) @ sum ) @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[12083]) ).
thf(18061,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( F @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12939,59]) ).
thf(18062,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( F @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) ) ),
inference(simp,[status(thm)],[18061]) ).
thf(18063,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ sum ) @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[18062:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( N @ ( M @ sum ) @ ( K @ sum ) @ ( I @ sum ) )),bind(G,$thf( N @ sk19 ))]]) ).
thf(18216,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ sum ) @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[18063]) ).
thf(18996,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( E @ ( D @ sum ) @ sum ) @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( G @ ( H @ incident_c ) ) )
| ( G @ ( F @ sum ) @ ( H @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12270,59]) ).
thf(18997,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( E @ ( D @ sum ) @ sum ) @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( G @ ( H @ incident_c ) ) )
| ( G @ ( F @ sum ) @ ( H @ incident_c ) ) ),
inference(simp,[status(thm)],[18996]) ).
thf(18998,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( F @ ( E @ sum ) @ sum ) @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[18997:[bind(A,$thf( J )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( Q )),bind(F,$thf( F )),bind(G,$thf( M @ ( O @ ( Q @ ( P @ sum ) @ sum ) @ sum ) @ ( J @ sum ) )),bind(H,$thf( P @ sk19 ))]]) ).
thf(19149,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( F @ ( E @ sum ) @ sum ) @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[18998]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ( A != sk3 )
| ( sk4 @ ( B @ ( sk2 @ ( sk1 @ between_c ) ) ) )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[31,22]) ).
thf(186,plain,
! [A: $i] :
( ( sk4 @ ( A @ ( sk2 @ ( sk1 @ between_c ) ) ) )
| ( A @ ( sk3 @ ( A @ sk6 ) @ incident_c ) )
| ( sk3 @ ( sk3 @ ( A @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[185:[bind(A,$thf( sk3 ))]]) ).
thf(244,plain,
! [A: $i] :
( ( sk4 @ ( A @ ( sk2 @ ( sk1 @ between_c ) ) ) )
| ( A @ ( sk3 @ ( A @ sk6 ) @ incident_c ) )
| ( sk3 @ ( sk3 @ ( A @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(16389,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( F @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12901,59]) ).
thf(16390,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( F @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) ) ),
inference(simp,[status(thm)],[16389]) ).
thf(16391,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( E @ ( D @ sum ) @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[16390:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( J @ ( N @ ( M @ sum ) @ ( K @ sum ) @ sum ) )),bind(G,$thf( N @ sk19 ))]]) ).
thf(16505,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( E @ ( D @ sum ) @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[16391]) ).
thf(263,plain,
( ~ $true
| ( ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(eqfactor_ordered,[status(thm)],[238]) ).
thf(264,plain,
( ( ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[263]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( B @ ( A @ ( C @ meet ) ) )
=> ? [C: $i] :
( C
= ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c8) ).
thf(62,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)],[5]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk10 ) )
= ( B @ ( A @ sum ) ) )
| ~ ( B @ ( A @ ( C @ meet ) ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ meet ) ) )
| ( ( A @ ( B @ sk10 ) )
= ( B @ ( A @ sum ) ) ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(15537,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( E @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12310,55]) ).
thf(15538,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( E @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) ) ),
inference(simp,[status(thm)],[15537]) ).
thf(15539,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( E @ ( D @ sum ) @ sum ) @ ( B @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[15538:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( L @ ( N @ ( M @ sum ) @ sum ) @ ( I @ sum ) )),bind(F,$thf( F )),bind(G,$thf( M @ sk19 ))]]) ).
thf(15657,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( E @ ( D @ sum ) @ sum ) @ ( B @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[15539]) ).
thf(20707,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( E @ ( D @ sum ) @ sum ) @ ( B @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( G @ ( H @ incident_c ) ) )
| ( G @ ( F @ sum ) @ ( H @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15657,59]) ).
thf(20708,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( E @ ( D @ sum ) @ sum ) @ ( B @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( G @ ( H @ incident_c ) ) )
| ( G @ ( F @ sum ) @ ( H @ incident_c ) ) ),
inference(simp,[status(thm)],[20707]) ).
thf(20709,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( F @ ( E @ sum ) @ sum ) @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[20708:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( Q )),bind(F,$thf( F )),bind(G,$thf( K @ ( O @ ( Q @ ( P @ sum ) @ sum ) @ ( L @ sum ) @ sum ) )),bind(H,$thf( P @ sk19 ))]]) ).
thf(20932,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( F @ ( E @ sum ) @ sum ) @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[20709]) ).
thf(4462,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[4434,2089]) ).
thf(4463,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4462]) ).
thf(4502,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( A @ sk19 )
!= ( sk4 @ ( sk2 @ sk6 ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4463]) ).
thf(4523,plain,
( ( ( sk4 @ ( sk2 @ sk6 ) )
!= ( sk4 @ sk19 ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4502]) ).
thf(4773,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) )
| ( ( sk4 @ ( sk2 @ sk6 ) )
!= ( sk4 @ sk19 ) )
| ~ $true
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[3781,4523]) ).
thf(4774,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) )
| ( ( sk4 @ ( sk2 @ sk6 ) )
!= ( sk4 @ sk19 ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[4773]) ).
thf(4939,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ sk15 )
!= ( sk4 @ ( sk2 @ sk5 ) ) )
| ( ( sk4 @ ( sk2 @ sk6 ) )
!= ( sk4 @ sk19 ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[4774]) ).
thf(4975,plain,
( ( ( sk4 @ ( sk2 @ sk5 ) )
!= ( sk2 @ sk15 ) )
| ( ( sk4 @ ( sk2 @ sk6 ) )
!= ( sk4 @ sk19 ) )
| ~ ( sk2 @ open ) ),
inference(simp,[status(thm)],[4939]) ).
thf(6888,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
!= ( A @ ( C @ incident_c ) ) )
| ( B @ ( A @ sum ) @ ( C @ incident_c ) )
| ~ $true
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[239,55]) ).
thf(6889,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
!= ( A @ ( C @ incident_c ) ) )
| ( B @ ( A @ sum ) @ ( C @ incident_c ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[6888]) ).
thf(6890,plain,
! [A: $i] :
( ( A @ ( sk4 @ sum ) @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[6889:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( sk2 @ ( sk4 @ sk6 ) ))]]) ).
thf(6966,plain,
! [A: $i] :
( ( A @ ( sk4 @ sum ) @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[6890]) ).
thf(8107,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ sum ) @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ~ $true
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[6966,462]) ).
thf(8108,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ sum ) @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[8107]) ).
thf(8189,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ sum ) )
!= sk2 )
| ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ ( sk4 @ sk6 ) ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[8108]) ).
thf(8249,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ sum ) )
!= sk2 )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[8189]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ sum ) ) )
| ~ ( A @ ( C @ ( B @ sk7 ) ) )
| ~ ( C @ ( A @ ( B @ ( C @ sk8 ) ) @ incident_c ) ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ sk7 ) ) )
| ~ ( C @ ( A @ ( B @ ( C @ sk8 ) ) @ incident_c ) )
| ( A
= ( C @ ( B @ sum ) ) ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ sk7 ) ) )
| ~ ( C @ ( A @ ( B @ ( C @ sk8 ) ) @ incident_c ) )
| ( A
= ( C @ ( B @ sum ) ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(12212,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
!= ( B @ ( C @ incident_c ) ) )
| ( B @ ( A @ sum ) @ ( C @ incident_c ) )
| ~ $true
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[239,59]) ).
thf(12213,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
!= ( B @ ( C @ incident_c ) ) )
| ( B @ ( A @ sum ) @ ( C @ incident_c ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[12212]) ).
thf(12214,plain,
! [A: $i] :
( ( sk4 @ ( A @ sum ) @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[12213:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( sk2 @ ( sk4 @ sk6 ) ))]]) ).
thf(309,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk18 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ~ $true
| ~ ( C @ ( B @ inner_point ) )
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[128,86]) ).
thf(310,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk18 @ end_point ) )
!= ( C @ ( B @ end_point ) ) )
| ~ ( C @ ( B @ inner_point ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[309]) ).
thf(311,plain,
! [A: $i] :
( ~ ( A @ ( A @ sk18 @ inner_point ) )
| ( A @ closed ) ),
inference(pattern_uni,[status(thm)],[310:[bind(A,$thf( D )),bind(B,$thf( D @ sk18 )),bind(C,$thf( D ))]]) ).
thf(318,plain,
! [A: $i] :
( ~ ( A @ ( A @ sk18 @ inner_point ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[311]) ).
thf(5000,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ sk19 ) )
| ~ $true
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[3781,4527]) ).
thf(5001,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ sk19 ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[5000]) ).
thf(5173,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( A @ sk15 )
!= ( sk2 @ ( sk4 @ sk5 ) ) )
| ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ sk19 ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[5001]) ).
thf(5202,plain,
( ( ( sk2 @ ( sk4 @ sk5 ) )
!= ( sk4 @ sk15 ) )
| ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ sk19 ) )
| ~ ( sk4 @ open ) ),
inference(simp,[status(thm)],[5173]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ inner_point ) )
=> ? [C: $i,D: $i] :
( ( A
= ( D @ ( C @ sum ) ) )
& ( D @ ( C @ ( B @ meet ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c4) ).
thf(91,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)],[9]) ).
thf(3830,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ incident_c ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) )
| ~ ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ~ $true
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[3780,1839]) ).
thf(3831,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ incident_c ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) )
| ~ ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3830]) ).
thf(3842,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ sk18 )
!= ( sk4 @ ( sk2 @ sk5 ) ) )
| ~ ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3831]) ).
thf(3861,plain,
( ( ( sk4 @ ( sk2 @ sk5 ) )
!= ( sk2 @ sk18 ) )
| ~ ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ( sk2 @ closed ) ),
inference(simp,[status(thm)],[3842]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( B != sk4 )
| ( A @ ( sk3 @ ( sk2 @ ( sk1 @ between_c ) ) ) )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[31,22]) ).
thf(198,plain,
! [A: $i] :
( ( A @ ( sk3 @ ( sk2 @ ( sk1 @ between_c ) ) ) )
| ( sk4 @ ( A @ ( sk4 @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[197:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(4450,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ~ ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4434,1840]) ).
thf(4451,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ~ ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4450]) ).
thf(4510,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( A @ sk19 )
!= ( sk2 @ ( sk4 @ sk5 ) ) )
| ~ ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4451]) ).
thf(4534,plain,
( ( ( sk2 @ ( sk4 @ sk5 ) )
!= ( sk4 @ sk19 ) )
| ~ ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4510]) ).
thf(6100,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ( ( sk2 @ ( sk4 @ sk5 ) )
!= ( sk4 @ sk19 ) )
| ~ $true
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[3781,4534]) ).
thf(6101,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ( ( sk2 @ ( sk4 @ sk5 ) )
!= ( sk4 @ sk19 ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[6100]) ).
thf(6278,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ sk15 )
!= ( sk2 @ ( sk4 @ sk6 ) ) )
| ( ( sk2 @ ( sk4 @ sk5 ) )
!= ( sk4 @ sk19 ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[6101]) ).
thf(6293,plain,
( ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ sk15 ) )
| ( ( sk2 @ ( sk4 @ sk5 ) )
!= ( sk4 @ sk19 ) )
| ~ ( sk2 @ open ) ),
inference(simp,[status(thm)],[6278]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ( B @ ( A @ ( B @ sk11 ) @ part_of ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(cnfConj,[status(thm)],[67]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ( B @ ( A @ ( B @ sk11 ) @ part_of ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(simp,[status(thm)],[72]) ).
thf(4437,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) )
| ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4434,954]) ).
thf(4438,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) )
| ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4437]) ).
thf(4506,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ sk19 )
!= ( sk4 @ ( sk2 @ sk5 ) ) )
| ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4438]) ).
thf(4529,plain,
( ( ( sk4 @ ( sk2 @ sk5 ) )
!= ( sk2 @ sk19 ) )
| ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4506]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( B != sk3 )
| ( sk4 @ ( A @ ( sk2 @ ( sk1 @ between_c ) ) ) )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[31,22]) ).
thf(194,plain,
! [A: $i] :
( ( sk4 @ ( A @ ( sk2 @ ( sk1 @ between_c ) ) ) )
| ( sk3 @ ( A @ ( sk3 @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( sk3 @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[193:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(17071,plain,
! [A: $i] :
( ( ( sk4 @ ( A @ sum ) @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ~ $true
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[12214,462]) ).
thf(17072,plain,
! [A: $i] :
( ( ( sk4 @ ( A @ sum ) @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[17071]) ).
thf(17135,plain,
! [A: $i] :
( ( ( sk4 @ ( A @ sum ) )
!= sk2 )
| ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ ( sk4 @ sk6 ) ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[17072]) ).
thf(17217,plain,
! [A: $i] :
( ( ( sk4 @ ( A @ sum ) )
!= sk2 )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[17135]) ).
thf(12086,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
!= ( B @ ( C @ incident_c ) ) )
| ( B @ ( A @ sum ) @ ( C @ incident_c ) )
| ~ $true
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[238,59]) ).
thf(12087,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
!= ( B @ ( C @ incident_c ) ) )
| ( B @ ( A @ sum ) @ ( C @ incident_c ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[12086]) ).
thf(12088,plain,
! [A: $i] :
( ( sk2 @ ( A @ sum ) @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[12087:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk4 @ ( sk2 @ sk6 ) ))]]) ).
thf(18671,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( F @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13153,59]) ).
thf(18672,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( F @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) ) ),
inference(simp,[status(thm)],[18671]) ).
thf(18673,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( C @ ( E @ ( D @ sum ) @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[18672:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( L @ ( N @ ( M @ sum ) @ sum ) @ ( I @ sum ) )),bind(G,$thf( N @ sk19 ))]]) ).
thf(18854,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( C @ ( E @ ( D @ sum ) @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[18673]) ).
thf(822,plain,
! [B: $i,A: $i] :
( ( B != sk4 )
| ( A != sk2 )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[33,163]) ).
thf(823,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk4 @ ( A @ ( sk4 @ sk6 ) @ incident_c ) )
| ~ ( sk4 @ ( A @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[822:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(955,plain,
( ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[823]) ).
thf(4489,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4434,955]) ).
thf(4490,plain,
! [A: $i] :
( ( ( A @ ( A @ sk19 @ incident_c ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4489]) ).
thf(4501,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( A @ sk19 )
!= ( sk2 @ ( sk4 @ sk5 ) ) )
| ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4490]) ).
thf(4522,plain,
( ( ( sk2 @ ( sk4 @ sk5 ) )
!= ( sk4 @ sk19 ) )
| ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[4501]) ).
thf(5450,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ ( sk4 @ sk5 ) ) )
| ( B
!= ( sk4 @ sk19 ) )
| ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ( B @ ( A @ ( B @ sk6 ) @ incident_c ) )
| ( A @ ( A @ ( B @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[31,4522]) ).
thf(5451,plain,
! [A: $i] :
( ( A
!= ( sk4 @ sk19 ) )
| ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ( A @ ( sk2 @ ( sk4 @ sk5 ) @ ( A @ sk6 ) @ incident_c ) )
| ( sk2 @ ( sk4 @ sk5 ) @ ( sk2 @ ( sk4 @ sk5 ) @ ( A @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[5450:[bind(A,$thf( sk2 @ ( sk4 @ sk5 ) )),bind(B,$thf( B ))]]) ).
thf(5555,plain,
( ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ( sk4 @ sk19 @ ( sk2 @ ( sk4 @ sk5 ) @ ( sk4 @ sk19 @ sk6 ) @ incident_c ) )
| ( sk2 @ ( sk4 @ sk5 ) @ ( sk2 @ ( sk4 @ sk5 ) @ ( sk4 @ sk19 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[5451]) ).
thf(16090,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( F @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12690,59]) ).
thf(16091,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( F @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) ) ),
inference(simp,[status(thm)],[16090]) ).
thf(16092,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( E @ ( D @ sum ) @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[16091:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( J @ ( N @ ( M @ sum ) @ ( K @ sum ) @ sum ) )),bind(G,$thf( M @ sk19 ))]]) ).
thf(16262,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( E @ ( D @ sum ) @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[16092]) ).
thf(6778,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
!= ( A @ ( C @ incident_c ) ) )
| ( B @ ( A @ sum ) @ ( C @ incident_c ) )
| ~ $true
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[238,55]) ).
thf(6779,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
!= ( A @ ( C @ incident_c ) ) )
| ( B @ ( A @ sum ) @ ( C @ incident_c ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[6778]) ).
thf(6780,plain,
! [A: $i] :
( ( A @ ( sk2 @ sum ) @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[6779:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk4 @ ( sk2 @ sk6 ) ))]]) ).
thf(6975,plain,
! [A: $i] :
( ( A @ ( sk2 @ sum ) @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[6780]) ).
thf(18716,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( E @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13153,55]) ).
thf(18717,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( C @ sum ) @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( E @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) ) ),
inference(simp,[status(thm)],[18716]) ).
thf(18718,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( E @ ( D @ sum ) @ sum ) @ ( B @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[18717:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( L @ ( N @ ( M @ sum ) @ sum ) @ ( I @ sum ) )),bind(F,$thf( F )),bind(G,$thf( N @ sk19 ))]]) ).
thf(18797,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( E @ ( D @ sum ) @ sum ) @ ( B @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[18718]) ).
thf(3795,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ incident_c ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ~ ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ~ $true
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[3780,1840]) ).
thf(3796,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ incident_c ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ~ ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3795]) ).
thf(3855,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( A @ sk18 )
!= ( sk2 @ ( sk4 @ sk5 ) ) )
| ~ ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3796]) ).
thf(3874,plain,
( ( ( sk2 @ ( sk4 @ sk5 ) )
!= ( sk4 @ sk18 ) )
| ~ ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ( sk4 @ closed ) ),
inference(simp,[status(thm)],[3855]) ).
thf(13494,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ sum ) @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ~ $true
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[12088,461]) ).
thf(13495,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ sum ) @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[13494]) ).
thf(13687,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ sum ) )
!= sk4 )
| ( ( sk4 @ ( sk2 @ sk6 ) )
!= ( sk4 @ ( sk2 @ sk6 ) ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[13495]) ).
thf(13756,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ sum ) )
!= sk4 )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[13687]) ).
thf(12573,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ sum ) @ ( A @ sum ) @ ( B @ sk19 @ incident_c ) )
!= ( E @ ( F @ incident_c ) ) )
| ( E @ ( D @ sum ) @ ( F @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12309,59]) ).
thf(12574,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ sum ) @ ( A @ sum ) @ ( B @ sk19 @ incident_c ) )
!= ( E @ ( F @ incident_c ) ) )
| ( E @ ( D @ sum ) @ ( F @ incident_c ) ) ),
inference(simp,[status(thm)],[12573]) ).
thf(12575,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[12574:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ sum ) @ ( H @ sum ) )),bind(F,$thf( J @ sk19 ))]]) ).
thf(12679,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[12575]) ).
thf(15836,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( E @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12679,55]) ).
thf(15837,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( E @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) ) ),
inference(simp,[status(thm)],[15836]) ).
thf(15838,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( E @ ( D @ sum ) @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[15837:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( N @ ( M @ sum ) @ ( K @ sum ) @ ( I @ sum ) )),bind(F,$thf( F )),bind(G,$thf( M @ sk19 ))]]) ).
thf(15964,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( E @ ( D @ sum ) @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[15838]) ).
thf(20392,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( E @ ( D @ sum ) @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( F @ ( H @ incident_c ) ) )
| ( G @ ( F @ sum ) @ ( H @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15642,55]) ).
thf(20393,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( E @ ( D @ sum ) @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( F @ ( H @ incident_c ) ) )
| ( G @ ( F @ sum ) @ ( H @ incident_c ) ) ),
inference(simp,[status(thm)],[20392]) ).
thf(20394,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( F @ ( E @ sum ) @ sum ) @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[20393:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( Q )),bind(F,$thf( O @ ( Q @ ( P @ sum ) @ sum ) @ ( L @ sum ) @ ( J @ sum ) )),bind(G,$thf( G )),bind(H,$thf( P @ sk19 ))]]) ).
thf(20540,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( F @ ( E @ sum ) @ sum ) @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[20394]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( B != A )
& ( A @ ( B @ part_of ) ) )
=> ( B @ open ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c1) ).
thf(139,plain,
! [A: $i,B: $i] :
( ( ( B != A )
& ( A @ ( B @ part_of ) ) )
=> ( B @ open ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3834,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ incident_c ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ~ $true
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[3780,955]) ).
thf(3835,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ incident_c ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3834]) ).
thf(3840,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( A @ sk18 )
!= ( sk2 @ ( sk4 @ sk5 ) ) )
| ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3835]) ).
thf(3859,plain,
( ( ( sk2 @ ( sk4 @ sk5 ) )
!= ( sk4 @ sk18 ) )
| ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
| ( sk4 @ closed ) ),
inference(simp,[status(thm)],[3840]) ).
thf(75,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) )
| ~ ( D @ ( A @ incident_c ) )
| ~ ( C @ ( A @ incident_c ) )
| ~ ( B @ ( D @ part_of ) )
| ~ ( B @ ( C @ part_of ) )
| ~ ( B @ ( A @ end_point ) ) ),
inference(cnfConj,[status(thm)],[67]) ).
thf(286,plain,
( ~ $true
| ( ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(eqfactor_ordered,[status(thm)],[239]) ).
thf(287,plain,
( ( ( sk4 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) )
| ( sk2 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[286]) ).
thf(18106,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( E @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12939,55]) ).
thf(18107,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( E @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) ) ),
inference(simp,[status(thm)],[18106]) ).
thf(18108,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( E @ ( D @ sum ) @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[18107:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( N @ ( M @ sum ) @ ( K @ sum ) @ ( I @ sum ) )),bind(F,$thf( F )),bind(G,$thf( N @ sk19 ))]]) ).
thf(18231,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( E @ ( D @ sum ) @ ( C @ sum ) @ ( B @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[18108]) ).
thf(3807,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[3780,2089]) ).
thf(3808,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3807]) ).
thf(3841,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( A @ sk18 )
!= ( sk4 @ ( sk2 @ sk6 ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3808]) ).
thf(3860,plain,
( ( ( sk4 @ ( sk2 @ sk6 ) )
!= ( sk4 @ sk18 ) )
| ~ ( sk2 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ( sk4 @ closed ) ),
inference(simp,[status(thm)],[3841]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ sum ) ) )
| ~ ( A @ ( C @ ( B @ sk7 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk8 ) ) @ incident_c ) ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ sk7 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk8 ) ) @ incident_c ) )
| ( A
= ( C @ ( B @ sum ) ) ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ sk7 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk8 ) ) @ incident_c ) )
| ( A
= ( C @ ( B @ sum ) ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(11474,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ sum ) @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ~ $true
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[6975,461]) ).
thf(11475,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ sum ) @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[11474]) ).
thf(11672,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ sum ) )
!= sk4 )
| ( ( sk4 @ ( sk2 @ sk6 ) )
!= ( sk4 @ ( sk2 @ sk6 ) ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[11475]) ).
thf(11695,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ sum ) )
!= sk4 )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[11672]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ end_point ) )
| ~ ( A @ closed ) ),
inference(cnfConj,[status(thm)],[125]) ).
thf(300,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk15 @ end_point ) )
!= ( B @ ( C @ end_point ) ) )
| ~ $true
| ~ ( B @ closed )
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[99,126]) ).
thf(301,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk15 @ end_point ) )
!= ( B @ ( C @ end_point ) ) )
| ~ ( B @ closed )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[300]) ).
thf(302,plain,
! [A: $i] :
( ~ ( A @ closed )
| ~ ( A @ open ) ),
inference(pattern_uni,[status(thm)],[301:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk15 ))]]) ).
thf(305,plain,
! [A: $i] :
( ~ ( A @ closed )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[302]) ).
thf(4544,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ( ( sk4 @ ( sk2 @ sk5 ) )
!= ( sk2 @ sk19 ) )
| ~ $true
| ~ ( A @ open ) ),
inference(paramod_ordered,[status(thm)],[3781,4521]) ).
thf(4545,plain,
! [A: $i] :
( ( ( A @ ( A @ sk15 @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ( ( sk4 @ ( sk2 @ sk5 ) )
!= ( sk2 @ sk19 ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[4544]) ).
thf(4711,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( A @ sk15 )
!= ( sk4 @ ( sk2 @ sk6 ) ) )
| ( ( sk4 @ ( sk2 @ sk5 ) )
!= ( sk2 @ sk19 ) )
| ~ ( A @ open ) ),
inference(simp,[status(thm)],[4545]) ).
thf(4755,plain,
( ( ( sk4 @ ( sk2 @ sk6 ) )
!= ( sk4 @ sk15 ) )
| ( ( sk4 @ ( sk2 @ sk5 ) )
!= ( sk2 @ sk19 ) )
| ~ ( sk4 @ open ) ),
inference(simp,[status(thm)],[4711]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ( A @ ( B @ sk12 ) @ ( A @ incident_c ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(cnfConj,[status(thm)],[67]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ end_point ) )
| ( A @ ( B @ sk12 ) @ ( A @ incident_c ) )
| ~ ( B @ ( A @ incident_c ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(3782,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ~ $true
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[3780,461]) ).
thf(3783,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ incident_c ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ sk6 ) @ incident_c ) ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3782]) ).
thf(3856,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( A @ sk18 )
!= ( sk4 @ ( sk2 @ sk6 ) ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3783]) ).
thf(3875,plain,
( ( ( sk4 @ ( sk2 @ sk6 ) )
!= ( sk4 @ sk18 ) )
| ( sk4 @ ( sk4 @ ( sk2 @ sk5 ) @ incident_c ) )
| ( sk4 @ closed ) ),
inference(simp,[status(thm)],[3856]) ).
thf(15791,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( F @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12679,59]) ).
thf(15792,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( C @ sk19 @ incident_c ) )
!= ( F @ ( G @ incident_c ) ) )
| ( F @ ( E @ sum ) @ ( G @ incident_c ) ) ),
inference(simp,[status(thm)],[15791]) ).
thf(15793,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ sum ) @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[15792:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( N @ ( M @ sum ) @ ( K @ sum ) @ ( I @ sum ) )),bind(G,$thf( M @ sk19 ))]]) ).
thf(15949,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ sum ) @ ( C @ sum ) @ ( B @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[15793]) ).
thf(20762,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( E @ ( D @ sum ) @ sum ) @ ( B @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( F @ ( H @ incident_c ) ) )
| ( G @ ( F @ sum ) @ ( H @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15657,55]) ).
thf(20763,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( E @ ( D @ sum ) @ sum ) @ ( B @ sum ) @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( F @ ( H @ incident_c ) ) )
| ( G @ ( F @ sum ) @ ( H @ incident_c ) ) ),
inference(simp,[status(thm)],[20762]) ).
thf(20764,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( F @ ( E @ sum ) @ sum ) @ ( C @ sum ) @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[20763:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( Q )),bind(F,$thf( K @ ( O @ ( Q @ ( P @ sum ) @ sum ) @ ( L @ sum ) @ sum ) )),bind(G,$thf( G )),bind(H,$thf( P @ sk19 ))]]) ).
thf(20859,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( F @ ( E @ sum ) @ sum ) @ ( C @ sum ) @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[20764]) ).
thf(3797,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ~ $true
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ( A @ closed ) ),
inference(paramod_ordered,[status(thm)],[3780,1840]) ).
thf(3798,plain,
! [A: $i] :
( ( ( A @ ( A @ sk18 @ incident_c ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ sk6 ) @ incident_c ) ) )
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3797]) ).
thf(3838,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ sk18 )
!= ( sk2 @ ( sk4 @ sk6 ) ) )
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ( A @ closed ) ),
inference(simp,[status(thm)],[3798]) ).
thf(3886,plain,
( ( ( sk2 @ ( sk4 @ sk6 ) )
!= ( sk2 @ sk18 ) )
| ~ ( sk4 @ ( sk2 @ ( sk4 @ sk5 ) @ incident_c ) )
| ( sk2 @ closed ) ),
inference(simp,[status(thm)],[3838]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ sum ) ) )
| ( C @ ( A @ ( B @ ( C @ sk9 ) ) @ incident_c ) )
| ( B @ ( A @ ( B @ ( C @ sk9 ) ) @ incident_c ) )
| ( A @ ( C @ ( B @ sk7 ) ) ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ ( C @ sk9 ) ) @ incident_c ) )
| ( B @ ( A @ ( B @ ( C @ sk9 ) ) @ incident_c ) )
| ( A @ ( C @ ( B @ sk7 ) ) )
| ( A
= ( C @ ( B @ sum ) ) ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ ( C @ sk9 ) ) @ incident_c ) )
| ( B @ ( A @ ( B @ ( C @ sk9 ) ) @ incident_c ) )
| ( A @ ( C @ ( B @ sk7 ) ) )
| ( A
= ( C @ ( B @ sum ) ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(19049,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( E @ ( D @ sum ) @ sum ) @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( F @ ( H @ incident_c ) ) )
| ( G @ ( F @ sum ) @ ( H @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12270,55]) ).
thf(19050,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( E @ ( D @ sum ) @ sum ) @ sum ) @ ( A @ sum ) @ ( D @ sk19 @ incident_c ) )
!= ( F @ ( H @ incident_c ) ) )
| ( G @ ( F @ sum ) @ ( H @ incident_c ) ) ),
inference(simp,[status(thm)],[19049]) ).
thf(19051,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ ( F @ ( E @ sum ) @ sum ) @ sum ) @ ( B @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(pattern_uni,[status(thm)],[19050:[bind(A,$thf( J )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( Q )),bind(F,$thf( M @ ( O @ ( Q @ ( P @ sum ) @ sum ) @ sum ) @ ( J @ sum ) )),bind(G,$thf( G )),bind(H,$thf( P @ sk19 ))]]) ).
thf(19168,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ ( F @ ( E @ sum ) @ sum ) @ sum ) @ ( B @ sum ) @ sum ) @ ( E @ sk19 @ incident_c ) ),
inference(simp,[status(thm)],[19051]) ).
thf(64733,plain,
$false,
inference(e,[status(thm)],[53,18534,101,333,1840,2295,9886,22717,18549,12939,142,3781,13115,16520,174,320,24,5195,10286,4524,4415,110,12901,196,157,20,57,78,7309,4411,238,147,61,89,243,3870,4753,4407,15642,22578,102,85,4531,334,4434,16205,4521,192,137,33,20521,65,3877,461,13153,109,77,4425,12314,96,129,12310,4416,12270,128,2089,18216,19149,105,244,16505,264,64,20932,32,34,22,59,4975,71,6937,8249,7109,49,86,7519,12214,76,318,5202,91,3861,198,462,130,12309,6293,80,35,7788,15657,4529,123,194,17217,12088,12271,4534,954,18854,4522,5555,6966,31,16262,6975,99,18797,12690,9438,3874,12484,1839,13756,15964,319,20540,55,139,3859,23,4527,3780,75,12491,82,287,18231,3860,51,4523,11695,305,239,126,4755,79,3875,12679,15949,955,20859,3886,163,131,47,62,19168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO112+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % 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
% 0.14/0.41 % Computer : n007.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 12:45:53 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.57/0.70 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.96/0.81 % [INFO] Parsing done (111ms).
% 0.96/0.81 % [INFO] Running in sequential loop mode.
% 1.26/1.00 % [INFO] eprover registered as external prover.
% 1.26/1.01 % [INFO] Scanning for conjecture ...
% 1.58/1.05 % [INFO] Found a conjecture (or negated_conjecture) and 17 axioms. Running axiom selection ...
% 1.58/1.09 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 1.58/1.12 % [INFO] Problem is first-order (TPTP FOF).
% 1.58/1.12 % [INFO] Type checking passed.
% 1.58/1.12 % [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 ...
% 138.32/46.07 % External prover 'e' found a proof!
% 138.32/46.07 % [INFO] Killing All external provers ...
% 138.32/46.07 % Time passed: 45572ms (effective reasoning time: 45252ms)
% 138.32/46.07 % 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)>
% 138.32/46.07 % Axioms used in derivation (17): end_point_defn, c8, meet_defn, part_of_defn, c9, sum_defn, closed_defn, inner_point_defn, c3, c4, c5, c2, c1, c6, open_defn, c7, between_c_defn
% 138.32/46.07 % No. of inferences in proof: 521
% 138.32/46.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 45572 ms resp. 45252 ms w/o parsing
% 140.02/46.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 140.02/46.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------