%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL688+1.001 : TPTP v9.3.1. Released v4.0.0.
% 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 : n019.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 07:52:34 AM UTC 2026
% Result : Theorem 98.92s 25.11s
% Output : Refutation 100.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 235 ( 33 unt; 0 typ; 13 def)
% Number of atoms : 1228 ( 258 equ; 0 cnn)
% Maximal formula atoms : 83 ( 5 avg)
% Number of connectives : 3244 ( 905 ~; 709 |; 57 &;1571 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 46 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 9 con; 0-3 aty)
% Number of variables : 375 ( 13 ^; 345 !; 4 ?; 375 :)
% ( 0 !>; 0 ?*; 0 @-; 13 @+)
% Comments :
%------------------------------------------------------------------------------
thf(r1_decl,type,
r1: $i > $i > $o ).
thf(p4_decl,type,
p4: $i > $o ).
thf(p3_decl,type,
p3: $i > $o ).
thf(p2_decl,type,
p2: $i > $o ).
thf(p1_decl,type,
p1: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $o ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i > $i ).
thf(sk7_decl,type,
sk7: $o ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( ( C @ p1 )
& ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
& ~ ! [B: $i] :
( ~ ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
& ~ ( A @ p1 ) )
| ~ ! [B: $i] :
( ~ ( ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( A @ r1 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C @ p3 )
| ~ ( C @ ( B @ ( A @ sk2 ) @ r1 ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( D @ p3 )
| ~ ( D @ ( A @ r1 ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( A @ r1 ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ( ~ ! [B: $i] :
( ~ ( ( B @ p1 )
& ~ ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( A @ p1 )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ( ! [B: $i] :
( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
~ ( ~ ! [B: $i] :
( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( sk10 @ r1 ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] :
~ ( ( A @ p1 )
| ~ ( A @ ( sk10 @ r1 ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ~ ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(1,conjecture,
~ ? [A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( ( C @ p1 )
& ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
& ~ ! [B: $i] :
( ~ ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
& ~ ( A @ p1 ) )
| ~ ! [B: $i] :
( ~ ( ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
thf(2,negated_conjecture,
~ ~ ? [A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( ( C @ p1 )
& ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
& ~ ! [B: $i] :
( ~ ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
& ~ ( A @ p1 ) )
| ~ ! [B: $i] :
( ~ ( ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ~ ? [A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( ( C @ p1 )
& ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
& ~ ! [B: $i] :
( ~ ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
& ~ ( A @ p1 ) )
| ~ ! [B: $i] :
( ~ ( ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
? [A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( ( C @ p1 )
& ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
& ~ ! [B: $i] :
( ~ ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
& ~ ( A @ p1 ) )
| ~ ! [B: $i] :
( ~ ( ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
~ ! [A: $i] :
( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( ( C @ p1 )
& ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
& ~ ! [B: $i] :
( ~ ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
& ~ ( A @ p1 ) )
| ~ ! [B: $i] :
( ~ ( ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(miniscope,[status(thm)],[6]) ).
thf(8,plain,
! [O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( M @ sk15 @ p1 )
| ~ ( O @ p1 )
| ~ ( O @ ( N @ r1 ) )
| ~ ( N @ ( M @ r1 ) )
| ~ ( M @ ( sk1 @ r1 ) ) )
& ( ( M @ sk15 @ ( M @ r1 ) )
| ~ ( O @ p1 )
| ~ ( O @ ( N @ r1 ) )
| ~ ( N @ ( M @ r1 ) )
| ~ ( M @ ( sk1 @ r1 ) ) )
& ( ~ ( L @ sk14 @ p2 )
| ~ ( L @ ( sk13 @ r1 ) ) )
& ( ( L @ sk14 @ ( L @ r1 ) )
| ~ ( L @ ( sk13 @ r1 ) ) )
& ( sk13 @ ( sk1 @ r1 ) )
& ~ ( sk12 @ p1 )
& ( sk12 @ ( sk10 @ r1 ) )
& ( ( K @ p1 )
| ~ ( K @ ( sk11 @ r1 ) ) )
& ( sk11 @ ( sk10 @ r1 ) )
& ( sk10 @ ( sk1 @ r1 ) )
& ( ~ ( I @ p1 )
| ( J @ p1 )
| ~ ( J @ ( I @ r1 ) )
| ~ ( I @ ( sk9 @ r1 ) )
| sk7
| ( sk1 @ p1 ) )
& ( ~ ( sk9 @ p1 )
| sk7
| ( sk1 @ p1 ) )
& ( ( sk9 @ ( sk1 @ r1 ) )
| sk7
| ( sk1 @ p1 ) )
& ( ~ sk7
| ~ ( H @ sk8 @ p1 )
| ~ ( H @ ( sk1 @ r1 ) )
| ( sk1 @ p1 ) )
& ( ~ sk7
| ( H @ sk8 @ ( H @ r1 ) )
| ~ ( H @ ( sk1 @ r1 ) )
| ( sk1 @ p1 ) )
& ( ~ ( G @ p2 )
| ~ ( G @ ( B @ ( D @ ( F @ sk6 ) ) @ r1 ) )
| ~ ( F @ ( D @ r1 ) )
| ~ ( D @ p2 )
| ( D @ sk4 )
| ~ ( D @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ( B @ ( D @ ( F @ sk6 ) ) @ ( F @ r1 ) )
| ~ ( F @ ( D @ r1 ) )
| ~ ( D @ p2 )
| ( D @ sk4 )
| ~ ( D @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( D @ sk4 )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) )
| ~ ( D @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( D @ sk4 )
| ~ ( B @ ( D @ ( E @ sk5 ) ) @ p3 )
| ~ ( E @ ( D @ r1 ) )
| ~ ( D @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( D @ sk4 )
| ( B @ ( D @ ( E @ sk5 ) ) @ ( E @ r1 ) )
| ~ ( E @ ( D @ r1 ) )
| ~ ( D @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ( B @ ( C @ sk2 ) @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( B @ ( C @ sk3 ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ( B @ ( C @ sk3 ) @ ( B @ ( C @ sk2 ) @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ( B @ ( C @ sk2 ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( A @ p4 )
| ~ ( A @ ( sk1 @ r1 ) ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(20,plain,
sk11 @ ( sk10 @ r1 ),
inference(cnfConj,[status(thm)],[8]) ).
thf(31,plain,
! [A: $i] :
( ( A @ sk14 @ ( A @ r1 ) )
| ~ ( A @ ( sk13 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(47,plain,
! [A: $i] :
( ( A @ sk14 @ ( A @ r1 ) )
| ~ ( A @ ( sk13 @ r1 ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(198,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk11 @ ( sk10 @ r1 ) ) )
| ( A @ sk14 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,47]) ).
thf(199,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk11 @ ( sk10 @ r1 ) ) )
| ( A @ sk14 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[198]) ).
thf(216,plain,
! [A: $i] :
( ( A != sk11 )
| ( sk13 != sk10 )
| ( A @ sk14 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[199]) ).
thf(221,plain,
( ( sk13 != sk10 )
| ( sk11 @ sk14 @ ( sk11 @ r1 ) ) ),
inference(simp,[status(thm)],[216]) ).
thf(27,plain,
sk12 @ ( sk10 @ r1 ),
inference(cnfConj,[status(thm)],[8]) ).
thf(11,plain,
! [A: $i] :
( ~ ( A @ p4 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(60,plain,
! [A: $i] :
( ( ( sk12 @ ( sk10 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27,11]) ).
thf(61,plain,
! [A: $i] :
( ( ( sk12 @ ( sk10 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[60]) ).
thf(63,plain,
! [A: $i] :
( ( sk12 != A )
| ( sk10 != sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[61]) ).
thf(65,plain,
( ( sk10 != sk1 )
| ~ ( sk12 @ p4 ) ),
inference(simp,[status(thm)],[63]) ).
thf(3,axiom,
! [A: $i] : ( A @ ( A @ r1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(51,plain,
! [A: $i] : ( A @ ( A @ r1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(52,plain,
! [A: $i] : ( A @ ( A @ r1 ) ),
inference(cnf,[status(esa)],[51]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( B @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52,11]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( B @ p4 ) ),
inference(simp,[status(thm)],[69]) ).
thf(71,plain,
~ ( sk1 @ p4 ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(12,plain,
! [A: $i] :
( ~ ( A @ sk14 @ p2 )
| ~ ( A @ ( sk13 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(37,plain,
! [A: $i] :
( ~ ( A @ sk14 @ p2 )
| ~ ( A @ ( sk13 @ r1 ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(91,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk12 @ ( sk10 @ r1 ) ) )
| ~ ( A @ sk14 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27,37]) ).
thf(92,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk12 @ ( sk10 @ r1 ) ) )
| ~ ( A @ sk14 @ p2 ) ),
inference(simp,[status(thm)],[91]) ).
thf(104,plain,
! [A: $i] :
( ( A != sk12 )
| ( sk13 != sk10 )
| ~ ( A @ sk14 @ p2 ) ),
inference(simp,[status(thm)],[92]) ).
thf(108,plain,
( ( sk13 != sk10 )
| ~ ( sk12 @ sk14 @ p2 ) ),
inference(simp,[status(thm)],[104]) ).
thf(29,plain,
sk13 @ ( sk1 @ r1 ),
inference(cnfConj,[status(thm)],[8]) ).
thf(17,plain,
! [A: $i] :
( ( A @ p1 )
| ~ ( A @ ( sk11 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(45,plain,
! [A: $i] :
( ( A @ p1 )
| ~ ( A @ ( sk11 @ r1 ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(81,plain,
! [A: $i] :
( ( ( A @ ( sk11 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,45]) ).
thf(82,plain,
! [A: $i] :
( ( ( A @ ( sk11 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[81]) ).
thf(86,plain,
! [A: $i] :
( ( A != sk13 )
| ( sk11 != sk1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[82]) ).
thf(90,plain,
( ( sk11 != sk1 )
| ( sk13 @ p1 ) ),
inference(simp,[status(thm)],[86]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk11 @ r1 ) ) )
| ( B @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52,45]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk11 @ r1 ) ) )
| ( B @ p1 ) ),
inference(simp,[status(thm)],[74]) ).
thf(76,plain,
sk11 @ p1,
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( sk11 )),bind(B,$thf( sk11 ))]]) ).
thf(24,plain,
~ ( sk12 @ p1 ),
inference(cnfConj,[status(thm)],[8]) ).
thf(112,plain,
( ( ( sk12 @ p1 )
!= ( sk11 @ p1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,24]) ).
thf(113,plain,
( ( sk12 @ p1 )
!= ( sk11 @ p1 ) ),
inference(simp,[status(thm)],[112]) ).
thf(115,plain,
sk12 != sk11,
inference(simp,[status(thm)],[113]) ).
thf(693,plain,
! [A: $i] :
( ( ( sk11 @ sk14 @ ( sk11 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk13 != sk10 ) ),
inference(paramod_ordered,[status(thm)],[221,11]) ).
thf(694,plain,
! [A: $i] :
( ( ( sk11 @ sk14 @ ( sk11 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk13 != sk10 ) ),
inference(simp,[status(thm)],[693]) ).
thf(724,plain,
! [A: $i] :
( ( ( sk11 @ sk14 )
!= A )
| ( sk11 != sk1 )
| ~ ( A @ p4 )
| ( sk13 != sk10 ) ),
inference(simp,[status(thm)],[694]) ).
thf(730,plain,
( ( sk11 != sk1 )
| ~ ( sk11 @ sk14 @ p4 )
| ( sk13 != sk10 ) ),
inference(simp,[status(thm)],[724]) ).
thf(184,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk12 @ ( sk10 @ r1 ) ) )
| ( A @ sk14 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27,47]) ).
thf(185,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk12 @ ( sk10 @ r1 ) ) )
| ( A @ sk14 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(212,plain,
! [A: $i] :
( ( A != sk12 )
| ( sk13 != sk10 )
| ( A @ sk14 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(217,plain,
( ( sk13 != sk10 )
| ( sk12 @ sk14 @ ( sk12 @ r1 ) ) ),
inference(simp,[status(thm)],[212]) ).
thf(707,plain,
! [A: $i] :
( ( ( sk11 @ sk14 @ ( sk11 @ r1 ) )
!= ( A @ ( sk11 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk13 != sk10 ) ),
inference(paramod_ordered,[status(thm)],[221,45]) ).
thf(708,plain,
! [A: $i] :
( ( ( sk11 @ sk14 @ ( sk11 @ r1 ) )
!= ( A @ ( sk11 @ r1 ) ) )
| ( A @ p1 )
| ( sk13 != sk10 ) ),
inference(simp,[status(thm)],[707]) ).
thf(709,plain,
( ( sk11 @ sk14 @ p1 )
| ( sk13 != sk10 ) ),
inference(pattern_uni,[status(thm)],[708:[bind(A,$thf( sk11 @ sk14 ))]]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk13 @ r1 ) ) )
| ( B @ sk14 @ ( B @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52,47]) ).
thf(194,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk13 @ r1 ) ) )
| ( B @ sk14 @ ( B @ r1 ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(195,plain,
sk13 @ sk14 @ ( sk13 @ r1 ),
inference(pattern_uni,[status(thm)],[194:[bind(A,$thf( sk13 )),bind(B,$thf( sk13 ))]]) ).
thf(231,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ ( sk13 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ sk14 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,47]) ).
thf(232,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ ( sk13 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ sk14 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(233,plain,
sk13 @ sk14 @ sk14 @ ( sk13 @ sk14 @ r1 ),
inference(pattern_uni,[status(thm)],[232:[bind(A,$thf( sk13 @ sk14 ))]]) ).
thf(250,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ sk14 @ ( sk13 @ sk14 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ sk14 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,47]) ).
thf(251,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ sk14 @ ( sk13 @ sk14 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ sk14 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[250]) ).
thf(256,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ sk14 )
!= A )
| ( ( sk13 @ sk14 )
!= sk13 )
| ( A @ sk14 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[251]) ).
thf(257,plain,
( ( ( sk13 @ sk14 )
!= sk13 )
| ( sk13 @ sk14 @ sk14 @ sk14 @ ( sk13 @ sk14 @ sk14 @ r1 ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(14,plain,
sk10 @ ( sk1 @ r1 ),
inference(cnfConj,[status(thm)],[8]) ).
thf(431,plain,
! [A: $i] :
( ( ( sk12 @ sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk13 != sk10 ) ),
inference(paramod_ordered,[status(thm)],[217,11]) ).
thf(432,plain,
! [A: $i] :
( ( ( sk12 @ sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk13 != sk10 ) ),
inference(simp,[status(thm)],[431]) ).
thf(454,plain,
! [A: $i] :
( ( ( sk12 @ sk14 )
!= A )
| ( sk12 != sk1 )
| ~ ( A @ p4 )
| ( sk13 != sk10 ) ),
inference(simp,[status(thm)],[432]) ).
thf(460,plain,
( ( sk12 != sk1 )
| ~ ( sk12 @ sk14 @ p4 )
| ( sk13 != sk10 ) ),
inference(simp,[status(thm)],[454]) ).
thf(55,plain,
! [A: $i] :
( ( ( sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,11]) ).
thf(56,plain,
! [A: $i] :
( ( ( sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[55]) ).
thf(57,plain,
~ ( sk10 @ p4 ),
inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( sk10 ))]]) ).
thf(244,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ sk14 @ ( sk13 @ sk14 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ~ ( A @ sk14 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,37]) ).
thf(245,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ sk14 @ ( sk13 @ sk14 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ~ ( A @ sk14 @ p2 ) ),
inference(simp,[status(thm)],[244]) ).
thf(255,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ sk14 )
!= A )
| ( ( sk13 @ sk14 )
!= sk13 )
| ~ ( A @ sk14 @ p2 ) ),
inference(simp,[status(thm)],[245]) ).
thf(261,plain,
( ( ( sk13 @ sk14 )
!= sk13 )
| ~ ( sk13 @ sk14 @ sk14 @ sk14 @ p2 ) ),
inference(simp,[status(thm)],[255]) ).
thf(229,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ ( sk13 @ r1 ) )
!= ( A @ ( sk11 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,45]) ).
thf(230,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ ( sk13 @ r1 ) )
!= ( A @ ( sk11 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[229]) ).
thf(235,plain,
! [A: $i] :
( ( ( sk13 @ sk14 )
!= A )
| ( sk13 != sk11 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[230]) ).
thf(238,plain,
( ( sk13 != sk11 )
| ( sk13 @ sk14 @ p1 ) ),
inference(simp,[status(thm)],[235]) ).
thf(77,plain,
! [A: $i] :
( ( ( A @ ( sk11 @ r1 ) )
!= ( sk10 @ ( sk1 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,45]) ).
thf(78,plain,
! [A: $i] :
( ( ( A @ ( sk11 @ r1 ) )
!= ( sk10 @ ( sk1 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[77]) ).
thf(83,plain,
! [A: $i] :
( ( A != sk10 )
| ( sk11 != sk1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[78]) ).
thf(87,plain,
( ( sk11 != sk1 )
| ( sk10 @ p1 ) ),
inference(simp,[status(thm)],[83]) ).
thf(118,plain,
( ( ( sk12 @ p1 )
!= ( sk10 @ p1 ) )
| ~ $true
| ( sk11 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[87,24]) ).
thf(119,plain,
( ( ( sk12 @ p1 )
!= ( sk10 @ p1 ) )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[118]) ).
thf(121,plain,
( ( sk12 != sk10 )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[119]) ).
thf(196,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk10 @ ( sk1 @ r1 ) ) )
| ( A @ sk14 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,47]) ).
thf(197,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk10 @ ( sk1 @ r1 ) ) )
| ( A @ sk14 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(215,plain,
! [A: $i] :
( ( A != sk10 )
| ( sk13 != sk1 )
| ( A @ sk14 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[197]) ).
thf(220,plain,
( ( sk13 != sk1 )
| ( sk10 @ sk14 @ ( sk10 @ r1 ) ) ),
inference(simp,[status(thm)],[215]) ).
thf(242,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ sk14 @ ( sk13 @ sk14 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,11]) ).
thf(243,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ sk14 @ ( sk13 @ sk14 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[242]) ).
thf(254,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ sk14 )
!= A )
| ( ( sk13 @ sk14 )
!= sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[243]) ).
thf(260,plain,
( ( ( sk13 @ sk14 )
!= sk1 )
| ~ ( sk13 @ sk14 @ sk14 @ p4 ) ),
inference(simp,[status(thm)],[254]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk15 @ ( A @ r1 ) )
| ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk15 @ ( A @ r1 ) )
| ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(10,plain,
! [A: $i] :
( ~ sk7
| ( A @ sk8 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk1 @ p1 ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(34,plain,
! [A: $i] :
( ~ sk7
| ( A @ sk8 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[10]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ sk7
| ( B @ sk8 @ ( B @ r1 ) )
| ~ $true
| ( sk1 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[52,34]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ sk7
| ( B @ sk8 @ ( B @ r1 ) )
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[163]) ).
thf(165,plain,
( ~ sk7
| ( sk1 @ sk8 @ ( sk1 @ r1 ) )
| ( sk1 @ p1 ) ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(740,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ~ sk7
| ( sk1 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[165,11]) ).
thf(741,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ sk7
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[740]) ).
thf(742,plain,
( ~ ( sk1 @ sk8 @ p4 )
| ~ sk7
| ( sk1 @ p1 ) ),
inference(pattern_uni,[status(thm)],[741:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1 ) )
& ( B @ ( A @ r1 ) ) )
=> ( C @ ( A @ r1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(53,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1 ) )
& ( B @ ( A @ r1 ) ) )
=> ( C @ ( A @ r1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
! [A: $i] :
( ~ sk7
| ~ ( A @ sk8 @ p1 )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk1 @ p1 ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(39,plain,
! [A: $i] :
( ~ sk7
| ~ ( A @ sk8 @ p1 )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[15]) ).
thf(1136,plain,
! [A: $i] :
( ( ( sk13 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ sk7
| ~ ( A @ sk8 @ p1 )
| ~ $true
| ( sk1 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[29,39]) ).
thf(1137,plain,
! [A: $i] :
( ( ( sk13 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ sk7
| ~ ( A @ sk8 @ p1 )
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[1136]) ).
thf(1138,plain,
( ~ sk7
| ~ ( sk13 @ sk8 @ p1 )
| ( sk1 @ p1 ) ),
inference(pattern_uni,[status(thm)],[1137:[bind(A,$thf( sk13 ))]]) ).
thf(138,plain,
( ( ( sk13 @ p1 )
!= ( sk12 @ p1 ) )
| ~ $true
| ( sk11 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[90,24]) ).
thf(139,plain,
( ( ( sk13 @ p1 )
!= ( sk12 @ p1 ) )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[138]) ).
thf(141,plain,
( ( sk13 != sk12 )
| ( sk11 != sk1 ) ),
inference(simp,[status(thm)],[139]) ).
thf(96,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk10 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk14 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,37]) ).
thf(97,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk10 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk14 @ p2 ) ),
inference(simp,[status(thm)],[96]) ).
thf(105,plain,
! [A: $i] :
( ( A != sk10 )
| ( sk13 != sk1 )
| ~ ( A @ sk14 @ p2 ) ),
inference(simp,[status(thm)],[97]) ).
thf(109,plain,
( ( sk13 != sk1 )
| ~ ( sk10 @ sk14 @ p2 ) ),
inference(simp,[status(thm)],[105]) ).
thf(26,plain,
( ( sk9 @ ( sk1 @ r1 ) )
| sk7
| ( sk1 @ p1 ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(122,plain,
! [A: $i] :
( ( ( sk9 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| sk7
| ( sk1 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[26,11]) ).
thf(123,plain,
! [A: $i] :
( ( ( sk9 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| sk7
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[122]) ).
thf(124,plain,
( ~ ( sk9 @ p4 )
| sk7
| ( sk1 @ p1 ) ),
inference(pattern_uni,[status(thm)],[123:[bind(A,$thf( sk9 ))]]) ).
thf(72,plain,
! [A: $i] :
( ( ( A @ ( sk11 @ r1 ) )
!= ( sk12 @ ( sk10 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27,45]) ).
thf(73,plain,
! [A: $i] :
( ( ( A @ ( sk11 @ r1 ) )
!= ( sk12 @ ( sk10 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[72]) ).
thf(84,plain,
! [A: $i] :
( ( A != sk12 )
| ( sk11 != sk10 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[73]) ).
thf(88,plain,
( ( sk11 != sk10 )
| ( sk12 @ p1 ) ),
inference(simp,[status(thm)],[84]) ).
thf(133,plain,
( ( sk11 != sk10 )
| $false ),
inference(rewrite,[status(thm)],[88,24]) ).
thf(134,plain,
sk11 != sk10,
inference(simp,[status(thm)],[133]) ).
thf(248,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ sk14 @ ( sk13 @ sk14 @ r1 ) )
!= ( A @ ( sk11 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,45]) ).
thf(249,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ sk14 @ ( sk13 @ sk14 @ r1 ) )
!= ( A @ ( sk11 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[248]) ).
thf(252,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ sk14 )
!= A )
| ( ( sk13 @ sk14 )
!= sk11 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[249]) ).
thf(258,plain,
( ( ( sk13 @ sk14 )
!= sk11 )
| ( sk13 @ sk14 @ sk14 @ p1 ) ),
inference(simp,[status(thm)],[252]) ).
thf(1048,plain,
( ( ( sk13 @ sk14 @ sk14 @ p1 )
!= ( sk12 @ p1 ) )
| ~ $true
| ( ( sk13 @ sk14 )
!= sk11 ) ),
inference(paramod_ordered,[status(thm)],[258,24]) ).
thf(1049,plain,
( ( ( sk13 @ sk14 @ sk14 @ p1 )
!= ( sk12 @ p1 ) )
| ( ( sk13 @ sk14 )
!= sk11 ) ),
inference(simp,[status(thm)],[1048]) ).
thf(1054,plain,
( ( ( sk13 @ sk14 @ sk14 )
!= sk12 )
| ( ( sk13 @ sk14 )
!= sk11 ) ),
inference(simp,[status(thm)],[1049]) ).
thf(427,plain,
( ( ( sk13 @ sk14 @ p1 )
!= ( sk12 @ p1 ) )
| ~ $true
| ( sk13 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[238,24]) ).
thf(428,plain,
( ( ( sk13 @ sk14 @ p1 )
!= ( sk12 @ p1 ) )
| ( sk13 != sk11 ) ),
inference(simp,[status(thm)],[427]) ).
thf(430,plain,
( ( ( sk13 @ sk14 )
!= sk12 )
| ( sk13 != sk11 ) ),
inference(simp,[status(thm)],[428]) ).
thf(58,plain,
! [A: $i] :
( ( ( sk11 @ ( sk10 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,11]) ).
thf(59,plain,
! [A: $i] :
( ( ( sk11 @ ( sk10 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[58]) ).
thf(62,plain,
! [A: $i] :
( ( sk11 != A )
| ( sk10 != sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[59]) ).
thf(64,plain,
( ( sk10 != sk1 )
| ~ ( sk11 @ p4 ) ),
inference(simp,[status(thm)],[62]) ).
thf(1112,plain,
( ( ( sk12 @ p1 )
!= ( sk1 @ p1 ) )
| ~ $true
| ~ ( sk1 @ sk8 @ p4 )
| ~ sk7 ),
inference(paramod_ordered,[status(thm)],[742,24]) ).
thf(1113,plain,
( ( ( sk12 @ p1 )
!= ( sk1 @ p1 ) )
| ~ ( sk1 @ sk8 @ p4 )
| ~ sk7 ),
inference(simp,[status(thm)],[1112]) ).
thf(1117,plain,
( ( sk12 != sk1 )
| ~ ( sk1 @ sk8 @ p4 )
| ~ sk7 ),
inference(simp,[status(thm)],[1113]) ).
thf(224,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ ( sk13 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ~ ( A @ sk14 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,37]) ).
thf(225,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ ( sk13 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ~ ( A @ sk14 @ p2 ) ),
inference(simp,[status(thm)],[224]) ).
thf(226,plain,
~ ( sk13 @ sk14 @ sk14 @ p2 ),
inference(pattern_uni,[status(thm)],[225:[bind(A,$thf( sk13 @ sk14 ))]]) ).
thf(16,plain,
( ~ ( sk9 @ p1 )
| sk7
| ( sk1 @ p1 ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(110,plain,
( ( ( sk11 @ p1 )
!= ( sk9 @ p1 ) )
| ~ $true
| sk7
| ( sk1 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[76,16]) ).
thf(111,plain,
( ( ( sk11 @ p1 )
!= ( sk9 @ p1 ) )
| sk7
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[110]) ).
thf(114,plain,
( ( sk11 != sk9 )
| sk7
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[111]) ).
thf(264,plain,
( ( ( sk12 @ p1 )
!= ( sk1 @ p1 ) )
| ~ $true
| ( sk11 != sk9 )
| sk7 ),
inference(paramod_ordered,[status(thm)],[114,24]) ).
thf(265,plain,
( ( ( sk12 @ p1 )
!= ( sk1 @ p1 ) )
| ( sk11 != sk9 )
| sk7 ),
inference(simp,[status(thm)],[264]) ).
thf(267,plain,
( ( sk12 != sk1 )
| ( sk11 != sk9 )
| sk7 ),
inference(simp,[status(thm)],[265]) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk4 )
| ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk4 )
| ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(433,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk12 @ sk14 @ ( sk12 @ r1 ) ) )
| ~ ( A @ sk14 @ p2 )
| ~ $true
| ( sk13 != sk10 ) ),
inference(paramod_ordered,[status(thm)],[217,37]) ).
thf(434,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk12 @ sk14 @ ( sk12 @ r1 ) ) )
| ~ ( A @ sk14 @ p2 )
| ( sk13 != sk10 ) ),
inference(simp,[status(thm)],[433]) ).
thf(452,plain,
! [A: $i] :
( ( A
!= ( sk12 @ sk14 ) )
| ( sk13 != sk12 )
| ~ ( A @ sk14 @ p2 )
| ( sk13 != sk10 ) ),
inference(simp,[status(thm)],[434]) ).
thf(458,plain,
( ( sk13 != sk12 )
| ~ ( sk12 @ sk14 @ sk14 @ p2 )
| ( sk13 != sk10 ) ),
inference(simp,[status(thm)],[452]) ).
thf(127,plain,
! [A: $i] :
( ( ( A @ ( sk11 @ r1 ) )
!= ( sk9 @ ( sk1 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| sk7
| ( sk1 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[26,45]) ).
thf(128,plain,
! [A: $i] :
( ( ( A @ ( sk11 @ r1 ) )
!= ( sk9 @ ( sk1 @ r1 ) ) )
| ( A @ p1 )
| sk7
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[127]) ).
thf(130,plain,
! [A: $i] :
( ( A != sk9 )
| ( sk11 != sk1 )
| ( A @ p1 )
| sk7
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[128]) ).
thf(132,plain,
( ( sk11 != sk1 )
| ( sk9 @ p1 )
| sk7
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[130]) ).
thf(143,plain,
( ( ( sk9 @ p1 )
!= ( sk9 @ p1 ) )
| ~ $true
| sk7
| ( sk1 @ p1 )
| ( sk11 != sk1 )
| sk7
| ( sk1 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[132,16]) ).
thf(144,plain,
( ( ( sk9 @ p1 )
!= ( sk9 @ p1 ) )
| ( sk11 != sk1 )
| sk7
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[143]) ).
thf(145,plain,
( ( sk11 != sk1 )
| sk7
| ( sk1 @ p1 ) ),
inference(pattern_uni,[status(thm)],[144:[]]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk13 @ r1 ) ) )
| ~ ( B @ sk14 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52,37]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk13 @ r1 ) ) )
| ~ ( B @ sk14 @ p2 ) ),
inference(simp,[status(thm)],[93]) ).
thf(95,plain,
~ ( sk13 @ sk14 @ p2 ),
inference(pattern_uni,[status(thm)],[94:[bind(A,$thf( sk13 )),bind(B,$thf( sk13 ))]]) ).
thf(736,plain,
( ( ( sk11 @ sk14 @ p1 )
!= ( sk12 @ p1 ) )
| ~ $true
| ( sk13 != sk10 ) ),
inference(paramod_ordered,[status(thm)],[709,24]) ).
thf(737,plain,
( ( ( sk11 @ sk14 @ p1 )
!= ( sk12 @ p1 ) )
| ( sk13 != sk10 ) ),
inference(simp,[status(thm)],[736]) ).
thf(739,plain,
( ( ( sk11 @ sk14 )
!= sk12 )
| ( sk13 != sk10 ) ),
inference(simp,[status(thm)],[737]) ).
thf(1128,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ sk7
| ~ ( B @ sk8 @ p1 )
| ~ $true
| ( sk1 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[52,39]) ).
thf(1129,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ sk7
| ~ ( B @ sk8 @ p1 )
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[1128]) ).
thf(1130,plain,
( ~ sk7
| ~ ( sk1 @ sk8 @ p1 )
| ( sk1 @ p1 ) ),
inference(pattern_uni,[status(thm)],[1129:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(703,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk11 @ sk14 @ ( sk11 @ r1 ) ) )
| ~ ( A @ sk14 @ p2 )
| ~ $true
| ( sk13 != sk10 ) ),
inference(paramod_ordered,[status(thm)],[221,37]) ).
thf(704,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk11 @ sk14 @ ( sk11 @ r1 ) ) )
| ~ ( A @ sk14 @ p2 )
| ( sk13 != sk10 ) ),
inference(simp,[status(thm)],[703]) ).
thf(721,plain,
! [A: $i] :
( ( A
!= ( sk11 @ sk14 ) )
| ( sk13 != sk11 )
| ~ ( A @ sk14 @ p2 )
| ( sk13 != sk10 ) ),
inference(simp,[status(thm)],[704]) ).
thf(727,plain,
( ( sk13 != sk11 )
| ~ ( sk11 @ sk14 @ sk14 @ p2 )
| ( sk13 != sk10 ) ),
inference(simp,[status(thm)],[721]) ).
thf(494,plain,
( ( ( sk12 @ p1 )
!= ( sk1 @ p1 ) )
| ~ $true
| ( sk11 != sk1 )
| sk7 ),
inference(paramod_ordered,[status(thm)],[145,24]) ).
thf(495,plain,
( ( ( sk12 @ p1 )
!= ( sk1 @ p1 ) )
| ( sk11 != sk1 )
| sk7 ),
inference(simp,[status(thm)],[494]) ).
thf(497,plain,
( ( sk12 != sk1 )
| ( sk11 != sk1 )
| sk7 ),
inference(simp,[status(thm)],[495]) ).
thf(651,plain,
! [A: $i] :
( ( ( sk10 @ sk14 @ ( sk10 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk13 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[220,11]) ).
thf(652,plain,
! [A: $i] :
( ( ( sk10 @ sk14 @ ( sk10 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[651]) ).
thf(680,plain,
! [A: $i] :
( ( ( sk10 @ sk14 )
!= A )
| ( sk10 != sk1 )
| ~ ( A @ p4 )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[652]) ).
thf(688,plain,
( ( sk10 != sk1 )
| ~ ( sk10 @ sk14 @ p4 )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[680]) ).
thf(188,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk9 @ ( sk1 @ r1 ) ) )
| ( A @ sk14 @ ( A @ r1 ) )
| ~ $true
| sk7
| ( sk1 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[26,47]) ).
thf(189,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk9 @ ( sk1 @ r1 ) ) )
| ( A @ sk14 @ ( A @ r1 ) )
| sk7
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[188]) ).
thf(213,plain,
! [A: $i] :
( ( A != sk9 )
| ( sk13 != sk1 )
| ( A @ sk14 @ ( A @ r1 ) )
| sk7
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[189]) ).
thf(218,plain,
( ( sk13 != sk1 )
| ( sk9 @ sk14 @ ( sk9 @ r1 ) )
| sk7
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[213]) ).
thf(1131,plain,
! [A: $i] :
( ( ( sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ sk7
| ~ ( A @ sk8 @ p1 )
| ~ $true
| ( sk1 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[14,39]) ).
thf(1132,plain,
! [A: $i] :
( ( ( sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ sk7
| ~ ( A @ sk8 @ p1 )
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[1131]) ).
thf(1133,plain,
( ~ sk7
| ~ ( sk10 @ sk8 @ p1 )
| ( sk1 @ p1 ) ),
inference(pattern_uni,[status(thm)],[1132:[bind(A,$thf( sk10 ))]]) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk4 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk4 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(166,plain,
! [A: $i] :
( ( ( sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ sk7
| ( A @ sk8 @ ( A @ r1 ) )
| ~ $true
| ( sk1 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[14,34]) ).
thf(167,plain,
! [A: $i] :
( ( ( sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ sk7
| ( A @ sk8 @ ( A @ r1 ) )
| ( sk1 @ p1 ) ),
inference(simp,[status(thm)],[166]) ).
thf(168,plain,
( ~ sk7
| ( sk10 @ sk8 @ ( sk10 @ r1 ) )
| ( sk1 @ p1 ) ),
inference(pattern_uni,[status(thm)],[167:[bind(A,$thf( sk10 ))]]) ).
thf(270,plain,
( ( ( sk12 @ p1 )
!= ( sk1 @ p1 ) )
| ~ $true
| ~ ( sk9 @ p4 )
| sk7 ),
inference(paramod_ordered,[status(thm)],[124,24]) ).
thf(271,plain,
( ( ( sk12 @ p1 )
!= ( sk1 @ p1 ) )
| ~ ( sk9 @ p4 )
| sk7 ),
inference(simp,[status(thm)],[270]) ).
thf(273,plain,
( ( sk12 != sk1 )
| ~ ( sk9 @ p4 )
| sk7 ),
inference(simp,[status(thm)],[271]) ).
thf(98,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk11 @ ( sk10 @ r1 ) ) )
| ~ ( A @ sk14 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,37]) ).
thf(99,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk11 @ ( sk10 @ r1 ) ) )
| ~ ( A @ sk14 @ p2 ) ),
inference(simp,[status(thm)],[98]) ).
thf(103,plain,
! [A: $i] :
( ( A != sk11 )
| ( sk13 != sk10 )
| ~ ( A @ sk14 @ p2 ) ),
inference(simp,[status(thm)],[99]) ).
thf(107,plain,
( ( sk13 != sk10 )
| ~ ( sk11 @ sk14 @ p2 ) ),
inference(simp,[status(thm)],[103]) ).
thf(222,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ ( sk13 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,11]) ).
thf(223,plain,
! [A: $i] :
( ( ( sk13 @ sk14 @ ( sk13 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[222]) ).
thf(236,plain,
! [A: $i] :
( ( ( sk13 @ sk14 )
!= A )
| ( sk13 != sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[223]) ).
thf(239,plain,
( ( sk13 != sk1 )
| ~ ( sk13 @ sk14 @ p4 ) ),
inference(simp,[status(thm)],[236]) ).
thf(66,plain,
! [A: $i] :
( ( ( sk13 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,11]) ).
thf(67,plain,
! [A: $i] :
( ( ( sk13 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[66]) ).
thf(68,plain,
~ ( sk13 @ p4 ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( sk13 ))]]) ).
thf(661,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk10 @ sk14 @ ( sk10 @ r1 ) ) )
| ~ ( A @ sk14 @ p2 )
| ~ $true
| ( sk13 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[220,37]) ).
thf(662,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk10 @ sk14 @ ( sk10 @ r1 ) ) )
| ~ ( A @ sk14 @ p2 )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[661]) ).
thf(683,plain,
! [A: $i] :
( ( A
!= ( sk10 @ sk14 ) )
| ( sk13 != sk10 )
| ~ ( A @ sk14 @ p2 )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[662]) ).
thf(691,plain,
( ( sk13 != sk10 )
| ~ ( sk10 @ sk14 @ sk14 @ p2 )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[683]) ).
thf(22911,plain,
$false,
inference(e,[status(thm)],[221,65,27,71,108,90,115,5,730,217,709,24,37,257,52,14,460,20,57,261,29,238,121,233,220,260,38,165,742,53,1138,141,109,124,134,1054,430,34,45,64,1117,76,39,226,267,35,458,145,95,739,16,1130,11,727,497,87,688,218,26,258,114,1133,36,168,51,273,107,239,195,47,68,691]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL688+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % 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
% 0.21/5.47 % Computer : n019.cluster.edu
% 0.21/5.47 % Model : x86_64 x86_64
% 0.21/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/5.47 % Memory : 8046.5625MB
% 0.21/5.47 % OS : Linux 6.8.0-71-generic
% 0.21/5.47 % CPULimit : 300
% 0.21/5.47 % WCLimit : 300
% 0.21/5.47 % DateTime : Fri Sep 25 23:24:41 UTC 2026
% 0.21/5.48 % CPUTime :
% 0.21/5.48 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
% 1.24/6.27 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.44/6.44 % [INFO] Parsing done (165ms).
% 1.44/6.45 % [INFO] Running in sequential loop mode.
% 2.30/6.79 % [INFO] eprover registered as external prover.
% 2.30/6.80 % [INFO] Scanning for conjecture ...
% 2.88/6.91 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.88/6.95 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.88/6.96 % [INFO] Problem is first-order (TPTP FOF).
% 2.88/6.97 % [INFO] Type checking passed.
% 2.88/6.97 % [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 ...
% 98.92/25.10 % External prover 'e' found a proof!
% 98.92/25.10 % [INFO] Killing All external provers ...
% 98.92/25.11 % Time passed: 19421ms (effective reasoning time: 18652ms)
% 98.92/25.11 % 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)>
% 98.92/25.11 % Axioms used in derivation (2): reflexivity, transitivity
% 98.92/25.11 % No. of inferences in proof: 222
% 98.92/25.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19421 ms resp. 18652 ms w/o parsing
% 100.60/25.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 100.60/25.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------