%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL644+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n015.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 07:52:16 AM UTC 2026
% Result : Theorem 6.11s 3.20s
% Output : Refutation 7.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 39
% Syntax : Number of formulae : 48 ( 42 unt; 0 typ; 38 def)
% Number of atoms : 2402 ( 38 equ; 0 cnn)
% Maximal formula atoms : 765 ( 50 avg)
% Number of connectives : 6296 (1451 ~;1665 |; 651 &;2529 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 208 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 65 usr; 50 con; 0-2 aty)
% Number of variables : 621 ( 10 ^; 569 !; 4 ?; 621 :)
% ( 0 !>; 0 ?*; 0 @-; 38 @+)
% Comments :
%------------------------------------------------------------------------------
thf(r1_decl,type,
r1: $i > $i > $o ).
thf(p6_decl,type,
p6: $i > $o ).
thf(p5_decl,type,
p5: $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: $o ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk4_decl,type,
sk4: $o ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk6_decl,type,
sk6: $o ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $o ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: $o ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk15_decl,type,
sk15: $o ).
thf(sk16_decl,type,
sk16: $i > $i ).
thf(sk17_decl,type,
sk17: $o ).
thf(sk18_decl,type,
sk18: $i ).
thf(sk19_decl,type,
sk19: $i ).
thf(sk20_decl,type,
sk20: $o ).
thf(sk21_decl,type,
sk21: $i ).
thf(sk22_decl,type,
sk22: $i ).
thf(sk23_decl,type,
sk23: $i ).
thf(sk24_decl,type,
sk24: $o ).
thf(sk25_decl,type,
sk25: $i > $i ).
thf(sk26_decl,type,
sk26: $o ).
thf(sk27_decl,type,
sk27: $i > $i ).
thf(sk28_decl,type,
sk28: $o ).
thf(sk29_decl,type,
sk29: $i ).
thf(sk30_decl,type,
sk30: $i ).
thf(sk31_decl,type,
sk31: $o ).
thf(sk32_decl,type,
sk32: $i ).
thf(sk33_decl,type,
sk33: $i ).
thf(sk34_decl,type,
sk34: $i ).
thf(sk35_decl,type,
sk35: $o ).
thf(sk36_decl,type,
sk36: $i > $i ).
thf(sk37_decl,type,
sk37: $o ).
thf(sk38_decl,type,
sk38: $i > $i ).
thf(sk39_decl,type,
sk39: $o ).
thf(sk40_decl,type,
sk40: $i ).
thf(sk41_decl,type,
sk41: $i ).
thf(sk42_decl,type,
sk42: $o ).
thf(sk43_decl,type,
sk43: $i ).
thf(sk44_decl,type,
sk44: $i ).
thf(sk45_decl,type,
sk45: $i ).
thf(sk46_decl,type,
sk46: $i ).
thf(sk47_decl,type,
sk47: $i ).
thf(sk48_decl,type,
sk48: $o ).
thf(sk49_decl,type,
sk49: $i > $i ).
thf(sk50_decl,type,
sk50: $o ).
thf(sk51_decl,type,
sk51: $i > $i ).
thf(sk52_decl,type,
sk52: $o ).
thf(sk53_decl,type,
sk53: $i ).
thf(sk54_decl,type,
sk54: $i ).
thf(sk55_decl,type,
sk55: $o ).
thf(sk56_decl,type,
sk56: $i ).
thf(sk57_decl,type,
sk57: $i ).
thf(sk58_decl,type,
sk58: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p1 )
& ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p1 ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ! [C: $i] :
( ( C @ p1 )
| ~ ( ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p2 )
& ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 ) )
| ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p3 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p3 )
& ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p3 ) )
| ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ! [C: $i] :
( ( C @ p3 )
| ~ ( ! [D: $i] :
( ( D @ p4 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p4 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p4 )
& ! [D: $i] :
( ( D @ p4 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p4 ) )
| ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ! [C: $i] :
( ( C @ p4 )
| ~ ( ! [D: $i] :
( ( D @ p5 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p5 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p5 )
& ! [D: $i] :
( ( D @ p5 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p5 ) )
| ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ! [C: $i] :
( ( C @ p5 )
| ~ ( ! [D: $i] :
( ( D @ p6 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p6 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p6 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ~ ( ( A @ p5 )
& ! [B: $i] :
( ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p5 ) )
| ( A @ p6 )
| ! [B: $i] :
( ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( ( A @ p5 )
| ~ ( ! [B: $i] :
( ( B @ p6 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p6 ) )
| ~ ( A @ ( sk7 @ r1 ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ( ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ~ ( B @ ( A @ r1 ) ) )
| ( A @ p5 )
| ~ ( ! [B: $i] :
( ( B @ p6 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p6 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
~ ( ~ ( ( A @ p5 )
& ! [B: $i] :
( ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p5 ) )
| ( A @ p6 )
| ~ ( A @ ( sk10 @ r1 ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] :
~ ( ~ ( ( A @ p5 )
& ! [B: $i] :
( ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p5 ) )
| ( A @ p6 )
| ( A @ p5 )
| ~ ( ! [B: $i] :
( ( B @ p6 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p6 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( @+[A: $i] :
~ ( ~ ( ( A @ p4 )
& ! [B: $i] :
( ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p4 ) )
| ( A @ p5 )
| ! [B: $i] :
( ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( @+[A: $i] :
~ ( ( A @ p4 )
| ~ ( ! [B: $i] :
( ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p5 ) )
| ~ ( A @ ( sk18 @ r1 ) ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( @+[A: $i] :
~ ( ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ( A @ p4 )
| ~ ( ! [B: $i] :
( ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p5 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( @+[A: $i] :
~ ( ~ ( ( A @ p4 )
& ! [B: $i] :
( ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p4 ) )
| ( A @ p5 )
| ~ ( A @ ( sk21 @ r1 ) ) ) ) ) ).
thf(sk23_def,definition,
( sk23
= ( @+[A: $i] :
~ ( ~ ( ( A @ p4 )
& ! [B: $i] :
( ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p4 ) )
| ( A @ p5 )
| ( A @ p4 )
| ~ ( ! [B: $i] :
( ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p5 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk29_def,definition,
( sk29
= ( @+[A: $i] :
~ ( ~ ( ( A @ p3 )
& ! [B: $i] :
( ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p3 ) )
| ( A @ p4 )
| ! [B: $i] :
( ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk30_def,definition,
( sk30
= ( @+[A: $i] :
~ ( ( A @ p3 )
| ~ ( ! [B: $i] :
( ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p4 ) )
| ~ ( A @ ( sk29 @ r1 ) ) ) ) ) ).
thf(sk32_def,definition,
( sk32
= ( @+[A: $i] :
~ ( ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) )
| ( A @ p3 )
| ~ ( ! [B: $i] :
( ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p4 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk33_def,definition,
( sk33
= ( @+[A: $i] :
~ ( ~ ( ( A @ p3 )
& ! [B: $i] :
( ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p3 ) )
| ( A @ p4 )
| ~ ( A @ ( sk32 @ r1 ) ) ) ) ) ).
thf(sk34_def,definition,
( sk34
= ( @+[A: $i] :
~ ( ~ ( ( A @ p3 )
& ! [B: $i] :
( ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p3 ) )
| ( A @ p4 )
| ( A @ p3 )
| ~ ( ! [B: $i] :
( ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p4 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk36_def,definition,
( sk36
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk38_def,definition,
( sk38
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk40_def,definition,
( sk40
= ( @+[A: $i] :
~ ( ~ ( ( A @ p2 )
& ! [B: $i] :
( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p2 ) )
| ( A @ p3 )
| ! [B: $i] :
( ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk41_def,definition,
( sk41
= ( @+[A: $i] :
~ ( ( A @ p2 )
| ~ ( ! [B: $i] :
( ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p3 ) )
| ~ ( A @ ( sk40 @ r1 ) ) ) ) ) ).
thf(sk43_def,definition,
( sk43
= ( @+[A: $i] :
~ ( ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
| ( A @ p2 )
| ~ ( ! [B: $i] :
( ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p3 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk44_def,definition,
( sk44
= ( @+[A: $i] :
~ ( ~ ( ( A @ p2 )
& ! [B: $i] :
( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p2 ) )
| ( A @ p3 )
| ~ ( A @ ( sk43 @ r1 ) ) ) ) ) ).
thf(sk45_def,definition,
( sk45
= ( @+[A: $i] :
~ ( ~ ( ( A @ p2 )
& ! [B: $i] :
( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p2 ) )
| ( A @ p3 )
| ( A @ p2 )
| ~ ( ! [B: $i] :
( ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p3 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk46_def,definition,
( sk46
= ( @+[A: $i] :
~ ( ~ ( ( A @ p5 )
& ! [B: $i] :
( ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) ) )
| ( A @ p5 )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk47_def,definition,
( sk47
= ( @+[A: $i] :
~ ( ~ ( ( A @ p5 )
& ! [B: $i] :
( ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) ) )
| ( A @ p5 )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk49_def,definition,
( sk49
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk51_def,definition,
( sk51
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk53_def,definition,
( sk53
= ( @+[A: $i] :
~ ( ~ ( ( A @ p1 )
& ! [B: $i] :
( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p1 ) )
| ( A @ p2 )
| ! [B: $i] :
( ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk54_def,definition,
( sk54
= ( @+[A: $i] :
~ ( ( A @ p1 )
| ~ ( ! [B: $i] :
( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p2 ) )
| ~ ( A @ ( sk53 @ r1 ) ) ) ) ) ).
thf(sk56_def,definition,
( sk56
= ( @+[A: $i] :
~ ( ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ( A @ p1 )
| ~ ( ! [B: $i] :
( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p2 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk57_def,definition,
( sk57
= ( @+[A: $i] :
~ ( ~ ( ( A @ p1 )
& ! [B: $i] :
( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p1 ) )
| ( A @ p2 )
| ~ ( A @ ( sk56 @ r1 ) ) ) ) ) ).
thf(sk58_def,definition,
( sk58
= ( @+[A: $i] :
~ ( ~ ( ( A @ p1 )
& ! [B: $i] :
( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p1 ) )
| ( A @ p2 )
| ( A @ p1 )
| ~ ( ! [B: $i] :
( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
& ( A @ p2 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(1,conjecture,
~ ? [A: $i] :
~ ( ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p1 )
& ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p1 ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ! [C: $i] :
( ( C @ p1 )
| ~ ( ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p2 )
& ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 ) )
| ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p3 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p3 )
& ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p3 ) )
| ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ! [C: $i] :
( ( C @ p3 )
| ~ ( ! [D: $i] :
( ( D @ p4 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p4 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p4 )
& ! [D: $i] :
( ( D @ p4 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p4 ) )
| ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ! [C: $i] :
( ( C @ p4 )
| ~ ( ! [D: $i] :
( ( D @ p5 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p5 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p5 )
& ! [D: $i] :
( ( D @ p5 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p5 ) )
| ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ! [C: $i] :
( ( C @ p5 )
| ~ ( ! [D: $i] :
( ( D @ p6 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p6 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
thf(2,negated_conjecture,
~ ~ ? [A: $i] :
~ ( ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p1 )
& ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p1 ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ! [C: $i] :
( ( C @ p1 )
| ~ ( ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p2 )
& ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 ) )
| ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p3 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p3 )
& ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p3 ) )
| ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ! [C: $i] :
( ( C @ p3 )
| ~ ( ! [D: $i] :
( ( D @ p4 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p4 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p4 )
& ! [D: $i] :
( ( D @ p4 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p4 ) )
| ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ! [C: $i] :
( ( C @ p4 )
| ~ ( ! [D: $i] :
( ( D @ p5 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p5 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p5 )
& ! [D: $i] :
( ( D @ p5 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p5 ) )
| ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ! [C: $i] :
( ( C @ p5 )
| ~ ( ! [D: $i] :
( ( D @ p6 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p6 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ? [A: $i] :
~ ( ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p1 )
& ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p1 ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ! [C: $i] :
( ( C @ p1 )
| ~ ( ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p2 )
& ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 ) )
| ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p3 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p3 )
& ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p3 ) )
| ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ! [C: $i] :
( ( C @ p3 )
| ~ ( ! [D: $i] :
( ( D @ p4 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p4 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p4 )
& ! [D: $i] :
( ( D @ p4 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p4 ) )
| ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ! [C: $i] :
( ( C @ p4 )
| ~ ( ! [D: $i] :
( ( D @ p5 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p5 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p5 )
& ! [D: $i] :
( ( D @ p5 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p5 ) )
| ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ! [C: $i] :
( ( C @ p5 )
| ~ ( ! [D: $i] :
( ( D @ p6 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p6 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
? [A: $i] :
~ ( ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p1 )
& ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p1 ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ! [C: $i] :
( ( C @ p1 )
| ~ ( ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p2 )
& ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 ) )
| ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p3 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p3 )
& ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p3 ) )
| ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ! [C: $i] :
( ( C @ p3 )
| ~ ( ! [D: $i] :
( ( D @ p4 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p4 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p4 )
& ! [D: $i] :
( ( D @ p4 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p4 ) )
| ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ! [C: $i] :
( ( C @ p4 )
| ~ ( ! [D: $i] :
( ( D @ p5 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p5 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p5 )
& ! [D: $i] :
( ( D @ p5 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p5 ) )
| ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ! [C: $i] :
( ( C @ p5 )
| ~ ( ! [D: $i] :
( ( D @ p6 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p6 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
~ ! [A: $i] :
( ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p1 )
& ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p1 ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ! [C: $i] :
( ( C @ p1 )
| ~ ( ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p1 )
& ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p1 )
| ~ ( ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p2 )
& ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 ) )
| ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p3 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p2 )
& ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p2 ) )
| ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p2 )
| ~ ( ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p3 )
& ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p3 ) )
| ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ! [C: $i] :
( ( C @ p3 )
| ~ ( ! [D: $i] :
( ( D @ p4 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p4 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p3 )
& ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p3 ) )
| ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p3 )
| ~ ( ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p4 )
& ! [D: $i] :
( ( D @ p4 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p4 ) )
| ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ! [C: $i] :
( ( C @ p4 )
| ~ ( ! [D: $i] :
( ( D @ p5 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p5 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p4 )
& ! [C: $i] :
( ( C @ p4 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p4 ) )
| ( B @ p5 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p4 )
| ~ ( ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ( ~ ( ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ! [C: $i] :
( ~ ( ( C @ p5 )
& ! [D: $i] :
( ( D @ p5 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p5 ) )
| ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ! [C: $i] :
( ( C @ p5 )
| ~ ( ! [D: $i] :
( ( D @ p6 )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p6 ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ! [B: $i] :
( ~ ( ( B @ p5 )
& ! [C: $i] :
( ( C @ p5 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p5 ) )
| ( B @ p6 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p5 )
| ~ ( ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
& ( B @ p6 ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ),
inference(miniscope,[status(thm)],[4]) ).
thf(6,plain,
! [ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,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] :
( ( ( sk58 @ p1 )
| sk55
| sk52
| ~ sk50
| ~ sk48 )
& ( ( ZP @ p1 )
| ~ ( ZP @ ( sk58 @ r1 ) )
| sk55
| sk52
| ~ sk50
| ~ sk48 )
& ( ( sk58 @ p1 )
| sk55
| sk52
| ~ sk50
| ~ sk48 )
& ( ~ ( sk58 @ p2 )
| sk55
| sk52
| ~ sk50
| ~ sk48 )
& ( ~ ( sk58 @ p1 )
| sk55
| sk52
| ~ sk50
| ~ sk48 )
& ( ( ZO @ p2 )
| ~ ( ZO @ ( sk58 @ r1 ) )
| sk55
| sk52
| ~ sk50
| ~ sk48 )
& ( ( sk58 @ p2 )
| sk55
| sk52
| ~ sk50
| ~ sk48 )
& ( ( sk58 @ ( sk1 @ r1 ) )
| sk55
| sk52
| ~ sk50
| ~ sk48 )
& ( ~ sk55
| ( sk57 @ p1 )
| sk52
| ~ sk50
| ~ sk48 )
& ( ~ sk55
| ( ZN @ p1 )
| ~ ( ZN @ ( sk57 @ r1 ) )
| sk52
| ~ sk50
| ~ sk48 )
& ( ~ sk55
| ( sk57 @ p1 )
| sk52
| ~ sk50
| ~ sk48 )
& ( ~ sk55
| ~ ( sk57 @ p2 )
| sk52
| ~ sk50
| ~ sk48 )
& ( ~ sk55
| ( sk57 @ ( sk56 @ r1 ) )
| sk52
| ~ sk50
| ~ sk48 )
& ( ~ sk55
| ~ ( sk56 @ p1 )
| sk52
| ~ sk50
| ~ sk48 )
& ( ~ sk55
| ( ZM @ p2 )
| ~ ( ZM @ ( sk56 @ r1 ) )
| sk52
| ~ sk50
| ~ sk48 )
& ( ~ sk55
| ( sk56 @ p2 )
| sk52
| ~ sk50
| ~ sk48 )
& ( ~ sk55
| ( sk56 @ ( sk1 @ r1 ) )
| sk52
| ~ sk50
| ~ sk48 )
& ( ~ sk52
| ( sk53 @ p1 )
| ~ sk50
| ~ sk48 )
& ( ~ sk52
| ( ZL @ p1 )
| ~ ( ZL @ ( sk53 @ r1 ) )
| ~ sk50
| ~ sk48 )
& ( ~ sk52
| ( sk53 @ p1 )
| ~ sk50
| ~ sk48 )
& ( ~ sk52
| ~ ( sk53 @ p2 )
| ~ sk50
| ~ sk48 )
& ( ~ sk52
| ~ ( sk54 @ p1 )
| ~ sk50
| ~ sk48 )
& ( ~ sk52
| ( ZK @ p2 )
| ~ ( ZK @ ( sk54 @ r1 ) )
| ~ sk50
| ~ sk48 )
& ( ~ sk52
| ( sk54 @ p2 )
| ~ sk50
| ~ sk48 )
& ( ~ sk52
| ( sk54 @ ( sk53 @ r1 ) )
| ~ sk50
| ~ sk48 )
& ( ~ sk52
| ( sk53 @ ( sk1 @ r1 ) )
| ~ sk50
| ~ sk48 )
& ( sk50
| ~ ( ZJ @ p1 )
| ~ ( ZJ @ sk51 @ p1 )
| ~ ( ZJ @ p1 )
| ( ZJ @ p2 )
| ~ ( ZJ @ ( sk1 @ r1 ) )
| ~ sk48 )
& ( sk50
| ~ ( ZJ @ p1 )
| ( ZJ @ sk51 @ ( ZJ @ r1 ) )
| ~ ( ZJ @ p1 )
| ( ZJ @ p2 )
| ~ ( ZJ @ ( sk1 @ r1 ) )
| ~ sk48 )
& ( sk48
| ( ZI @ p1 )
| ~ ( ZI @ sk49 @ p2 )
| ~ ( ZI @ p2 )
| ~ ( ZI @ ( sk1 @ r1 ) ) )
& ( sk48
| ( ZI @ p1 )
| ( ZI @ sk49 @ ( ZI @ r1 ) )
| ~ ( ZI @ p2 )
| ~ ( ZI @ ( sk1 @ r1 ) ) )
& ( sk47 @ p5 )
& ( ( ZH @ p5 )
| ~ ( ZH @ ( sk47 @ r1 ) ) )
& ~ ( sk47 @ p5 )
& ( sk47 @ ( sk1 @ r1 ) )
& ( sk46 @ p5 )
& ( ( ZG @ p5 )
| ~ ( ZG @ ( sk46 @ r1 ) ) )
& ~ ( sk46 @ p5 )
& ( sk46 @ ( sk1 @ r1 ) )
& ( ( sk45 @ p2 )
| sk42
| sk39
| ~ sk37
| ~ sk35 )
& ( ( ZF @ p2 )
| ~ ( ZF @ ( sk45 @ r1 ) )
| sk42
| sk39
| ~ sk37
| ~ sk35 )
& ( ( sk45 @ p2 )
| sk42
| sk39
| ~ sk37
| ~ sk35 )
& ( ~ ( sk45 @ p3 )
| sk42
| sk39
| ~ sk37
| ~ sk35 )
& ( ~ ( sk45 @ p2 )
| sk42
| sk39
| ~ sk37
| ~ sk35 )
& ( ( ZE @ p3 )
| ~ ( ZE @ ( sk45 @ r1 ) )
| sk42
| sk39
| ~ sk37
| ~ sk35 )
& ( ( sk45 @ p3 )
| sk42
| sk39
| ~ sk37
| ~ sk35 )
& ( ( sk45 @ ( sk1 @ r1 ) )
| sk42
| sk39
| ~ sk37
| ~ sk35 )
& ( ~ sk42
| ( sk44 @ p2 )
| sk39
| ~ sk37
| ~ sk35 )
& ( ~ sk42
| ( ZD @ p2 )
| ~ ( ZD @ ( sk44 @ r1 ) )
| sk39
| ~ sk37
| ~ sk35 )
& ( ~ sk42
| ( sk44 @ p2 )
| sk39
| ~ sk37
| ~ sk35 )
& ( ~ sk42
| ~ ( sk44 @ p3 )
| sk39
| ~ sk37
| ~ sk35 )
& ( ~ sk42
| ( sk44 @ ( sk43 @ r1 ) )
| sk39
| ~ sk37
| ~ sk35 )
& ( ~ sk42
| ~ ( sk43 @ p2 )
| sk39
| ~ sk37
| ~ sk35 )
& ( ~ sk42
| ( ZC @ p3 )
| ~ ( ZC @ ( sk43 @ r1 ) )
| sk39
| ~ sk37
| ~ sk35 )
& ( ~ sk42
| ( sk43 @ p3 )
| sk39
| ~ sk37
| ~ sk35 )
& ( ~ sk42
| ( sk43 @ ( sk1 @ r1 ) )
| sk39
| ~ sk37
| ~ sk35 )
& ( ~ sk39
| ( sk40 @ p2 )
| ~ sk37
| ~ sk35 )
& ( ~ sk39
| ( ZB @ p2 )
| ~ ( ZB @ ( sk40 @ r1 ) )
| ~ sk37
| ~ sk35 )
& ( ~ sk39
| ( sk40 @ p2 )
| ~ sk37
| ~ sk35 )
& ( ~ sk39
| ~ ( sk40 @ p3 )
| ~ sk37
| ~ sk35 )
& ( ~ sk39
| ~ ( sk41 @ p2 )
| ~ sk37
| ~ sk35 )
& ( ~ sk39
| ( ZA @ p3 )
| ~ ( ZA @ ( sk41 @ r1 ) )
| ~ sk37
| ~ sk35 )
& ( ~ sk39
| ( sk41 @ p3 )
| ~ sk37
| ~ sk35 )
& ( ~ sk39
| ( sk41 @ ( sk40 @ r1 ) )
| ~ sk37
| ~ sk35 )
& ( ~ sk39
| ( sk40 @ ( sk1 @ r1 ) )
| ~ sk37
| ~ sk35 )
& ( sk37
| ~ ( Z @ p2 )
| ~ ( Z @ sk38 @ p2 )
| ~ ( Z @ p2 )
| ( Z @ p3 )
| ~ ( Z @ ( sk1 @ r1 ) )
| ~ sk35 )
& ( sk37
| ~ ( Z @ p2 )
| ( Z @ sk38 @ ( Z @ r1 ) )
| ~ ( Z @ p2 )
| ( Z @ p3 )
| ~ ( Z @ ( sk1 @ r1 ) )
| ~ sk35 )
& ( sk35
| ( Y @ p2 )
| ~ ( Y @ sk36 @ p3 )
| ~ ( Y @ p3 )
| ~ ( Y @ ( sk1 @ r1 ) ) )
& ( sk35
| ( Y @ p2 )
| ( Y @ sk36 @ ( Y @ r1 ) )
| ~ ( Y @ p3 )
| ~ ( Y @ ( sk1 @ r1 ) ) )
& ( ( sk34 @ p3 )
| sk31
| sk28
| ~ sk26
| ~ sk24 )
& ( ( X @ p3 )
| ~ ( X @ ( sk34 @ r1 ) )
| sk31
| sk28
| ~ sk26
| ~ sk24 )
& ( ( sk34 @ p3 )
| sk31
| sk28
| ~ sk26
| ~ sk24 )
& ( ~ ( sk34 @ p4 )
| sk31
| sk28
| ~ sk26
| ~ sk24 )
& ( ~ ( sk34 @ p3 )
| sk31
| sk28
| ~ sk26
| ~ sk24 )
& ( ( W @ p4 )
| ~ ( W @ ( sk34 @ r1 ) )
| sk31
| sk28
| ~ sk26
| ~ sk24 )
& ( ( sk34 @ p4 )
| sk31
| sk28
| ~ sk26
| ~ sk24 )
& ( ( sk34 @ ( sk1 @ r1 ) )
| sk31
| sk28
| ~ sk26
| ~ sk24 )
& ( ~ sk31
| ( sk33 @ p3 )
| sk28
| ~ sk26
| ~ sk24 )
& ( ~ sk31
| ( V @ p3 )
| ~ ( V @ ( sk33 @ r1 ) )
| sk28
| ~ sk26
| ~ sk24 )
& ( ~ sk31
| ( sk33 @ p3 )
| sk28
| ~ sk26
| ~ sk24 )
& ( ~ sk31
| ~ ( sk33 @ p4 )
| sk28
| ~ sk26
| ~ sk24 )
& ( ~ sk31
| ( sk33 @ ( sk32 @ r1 ) )
| sk28
| ~ sk26
| ~ sk24 )
& ( ~ sk31
| ~ ( sk32 @ p3 )
| sk28
| ~ sk26
| ~ sk24 )
& ( ~ sk31
| ( U @ p4 )
| ~ ( U @ ( sk32 @ r1 ) )
| sk28
| ~ sk26
| ~ sk24 )
& ( ~ sk31
| ( sk32 @ p4 )
| sk28
| ~ sk26
| ~ sk24 )
& ( ~ sk31
| ( sk32 @ ( sk1 @ r1 ) )
| sk28
| ~ sk26
| ~ sk24 )
& ( ~ sk28
| ( sk29 @ p3 )
| ~ sk26
| ~ sk24 )
& ( ~ sk28
| ( T @ p3 )
| ~ ( T @ ( sk29 @ r1 ) )
| ~ sk26
| ~ sk24 )
& ( ~ sk28
| ( sk29 @ p3 )
| ~ sk26
| ~ sk24 )
& ( ~ sk28
| ~ ( sk29 @ p4 )
| ~ sk26
| ~ sk24 )
& ( ~ sk28
| ~ ( sk30 @ p3 )
| ~ sk26
| ~ sk24 )
& ( ~ sk28
| ( S @ p4 )
| ~ ( S @ ( sk30 @ r1 ) )
| ~ sk26
| ~ sk24 )
& ( ~ sk28
| ( sk30 @ p4 )
| ~ sk26
| ~ sk24 )
& ( ~ sk28
| ( sk30 @ ( sk29 @ r1 ) )
| ~ sk26
| ~ sk24 )
& ( ~ sk28
| ( sk29 @ ( sk1 @ r1 ) )
| ~ sk26
| ~ sk24 )
& ( sk26
| ~ ( R @ p3 )
| ~ ( R @ sk27 @ p3 )
| ~ ( R @ p3 )
| ( R @ p4 )
| ~ ( R @ ( sk1 @ r1 ) )
| ~ sk24 )
& ( sk26
| ~ ( R @ p3 )
| ( R @ sk27 @ ( R @ r1 ) )
| ~ ( R @ p3 )
| ( R @ p4 )
| ~ ( R @ ( sk1 @ r1 ) )
| ~ sk24 )
& ( sk24
| ( Q @ p3 )
| ~ ( Q @ sk25 @ p4 )
| ~ ( Q @ p4 )
| ~ ( Q @ ( sk1 @ r1 ) ) )
& ( sk24
| ( Q @ p3 )
| ( Q @ sk25 @ ( Q @ r1 ) )
| ~ ( Q @ p4 )
| ~ ( Q @ ( sk1 @ r1 ) ) )
& ( ( sk23 @ p4 )
| sk20
| sk17
| ~ sk15
| ~ sk13 )
& ( ( P @ p4 )
| ~ ( P @ ( sk23 @ r1 ) )
| sk20
| sk17
| ~ sk15
| ~ sk13 )
& ( ( sk23 @ p4 )
| sk20
| sk17
| ~ sk15
| ~ sk13 )
& ( ~ ( sk23 @ p5 )
| sk20
| sk17
| ~ sk15
| ~ sk13 )
& ( ~ ( sk23 @ p4 )
| sk20
| sk17
| ~ sk15
| ~ sk13 )
& ( ( O @ p5 )
| ~ ( O @ ( sk23 @ r1 ) )
| sk20
| sk17
| ~ sk15
| ~ sk13 )
& ( ( sk23 @ p5 )
| sk20
| sk17
| ~ sk15
| ~ sk13 )
& ( ( sk23 @ ( sk1 @ r1 ) )
| sk20
| sk17
| ~ sk15
| ~ sk13 )
& ( ~ sk20
| ( sk22 @ p4 )
| sk17
| ~ sk15
| ~ sk13 )
& ( ~ sk20
| ( N @ p4 )
| ~ ( N @ ( sk22 @ r1 ) )
| sk17
| ~ sk15
| ~ sk13 )
& ( ~ sk20
| ( sk22 @ p4 )
| sk17
| ~ sk15
| ~ sk13 )
& ( ~ sk20
| ~ ( sk22 @ p5 )
| sk17
| ~ sk15
| ~ sk13 )
& ( ~ sk20
| ( sk22 @ ( sk21 @ r1 ) )
| sk17
| ~ sk15
| ~ sk13 )
& ( ~ sk20
| ~ ( sk21 @ p4 )
| sk17
| ~ sk15
| ~ sk13 )
& ( ~ sk20
| ( M @ p5 )
| ~ ( M @ ( sk21 @ r1 ) )
| sk17
| ~ sk15
| ~ sk13 )
& ( ~ sk20
| ( sk21 @ p5 )
| sk17
| ~ sk15
| ~ sk13 )
& ( ~ sk20
| ( sk21 @ ( sk1 @ r1 ) )
| sk17
| ~ sk15
| ~ sk13 )
& ( ~ sk17
| ( sk18 @ p4 )
| ~ sk15
| ~ sk13 )
& ( ~ sk17
| ( L @ p4 )
| ~ ( L @ ( sk18 @ r1 ) )
| ~ sk15
| ~ sk13 )
& ( ~ sk17
| ( sk18 @ p4 )
| ~ sk15
| ~ sk13 )
& ( ~ sk17
| ~ ( sk18 @ p5 )
| ~ sk15
| ~ sk13 )
& ( ~ sk17
| ~ ( sk19 @ p4 )
| ~ sk15
| ~ sk13 )
& ( ~ sk17
| ( K @ p5 )
| ~ ( K @ ( sk19 @ r1 ) )
| ~ sk15
| ~ sk13 )
& ( ~ sk17
| ( sk19 @ p5 )
| ~ sk15
| ~ sk13 )
& ( ~ sk17
| ( sk19 @ ( sk18 @ r1 ) )
| ~ sk15
| ~ sk13 )
& ( ~ sk17
| ( sk18 @ ( sk1 @ r1 ) )
| ~ sk15
| ~ sk13 )
& ( sk15
| ~ ( J @ p4 )
| ~ ( J @ sk16 @ p4 )
| ~ ( J @ p4 )
| ( J @ p5 )
| ~ ( J @ ( sk1 @ r1 ) )
| ~ sk13 )
& ( sk15
| ~ ( J @ p4 )
| ( J @ sk16 @ ( J @ r1 ) )
| ~ ( J @ p4 )
| ( J @ p5 )
| ~ ( J @ ( sk1 @ r1 ) )
| ~ sk13 )
& ( sk13
| ( I @ p4 )
| ~ ( I @ sk14 @ p5 )
| ~ ( I @ p5 )
| ~ ( I @ ( sk1 @ r1 ) ) )
& ( sk13
| ( I @ p4 )
| ( I @ sk14 @ ( I @ r1 ) )
| ~ ( I @ p5 )
| ~ ( I @ ( sk1 @ r1 ) ) )
& ( ( sk12 @ p5 )
| sk9
| sk6
| ~ sk4
| ~ sk2 )
& ( ( H @ p5 )
| ~ ( H @ ( sk12 @ r1 ) )
| sk9
| sk6
| ~ sk4
| ~ sk2 )
& ( ( sk12 @ p5 )
| sk9
| sk6
| ~ sk4
| ~ sk2 )
& ( ~ ( sk12 @ p6 )
| sk9
| sk6
| ~ sk4
| ~ sk2 )
& ( ~ ( sk12 @ p5 )
| sk9
| sk6
| ~ sk4
| ~ sk2 )
& ( ( G @ p6 )
| ~ ( G @ ( sk12 @ r1 ) )
| sk9
| sk6
| ~ sk4
| ~ sk2 )
& ( ( sk12 @ p6 )
| sk9
| sk6
| ~ sk4
| ~ sk2 )
& ( ( sk12 @ ( sk1 @ r1 ) )
| sk9
| sk6
| ~ sk4
| ~ sk2 )
& ( ~ sk9
| ( sk11 @ p5 )
| sk6
| ~ sk4
| ~ sk2 )
& ( ~ sk9
| ( F @ p5 )
| ~ ( F @ ( sk11 @ r1 ) )
| sk6
| ~ sk4
| ~ sk2 )
& ( ~ sk9
| ( sk11 @ p5 )
| sk6
| ~ sk4
| ~ sk2 )
& ( ~ sk9
| ~ ( sk11 @ p6 )
| sk6
| ~ sk4
| ~ sk2 )
& ( ~ sk9
| ( sk11 @ ( sk10 @ r1 ) )
| sk6
| ~ sk4
| ~ sk2 )
& ( ~ sk9
| ~ ( sk10 @ p5 )
| sk6
| ~ sk4
| ~ sk2 )
& ( ~ sk9
| ( E @ p6 )
| ~ ( E @ ( sk10 @ r1 ) )
| sk6
| ~ sk4
| ~ sk2 )
& ( ~ sk9
| ( sk10 @ p6 )
| sk6
| ~ sk4
| ~ sk2 )
& ( ~ sk9
| ( sk10 @ ( sk1 @ r1 ) )
| sk6
| ~ sk4
| ~ sk2 )
& ( ~ sk6
| ( sk7 @ p5 )
| ~ sk4
| ~ sk2 )
& ( ~ sk6
| ( D @ p5 )
| ~ ( D @ ( sk7 @ r1 ) )
| ~ sk4
| ~ sk2 )
& ( ~ sk6
| ( sk7 @ p5 )
| ~ sk4
| ~ sk2 )
& ( ~ sk6
| ~ ( sk7 @ p6 )
| ~ sk4
| ~ sk2 )
& ( ~ sk6
| ~ ( sk8 @ p5 )
| ~ sk4
| ~ sk2 )
& ( ~ sk6
| ( C @ p6 )
| ~ ( C @ ( sk8 @ r1 ) )
| ~ sk4
| ~ sk2 )
& ( ~ sk6
| ( sk8 @ p6 )
| ~ sk4
| ~ sk2 )
& ( ~ sk6
| ( sk8 @ ( sk7 @ r1 ) )
| ~ sk4
| ~ sk2 )
& ( ~ sk6
| ( sk7 @ ( sk1 @ r1 ) )
| ~ sk4
| ~ sk2 )
& ( sk4
| ~ ( B @ p5 )
| ~ ( B @ sk5 @ p5 )
| ~ ( B @ p5 )
| ( B @ p6 )
| ~ ( B @ ( sk1 @ r1 ) )
| ~ sk2 )
& ( sk4
| ~ ( B @ p5 )
| ( B @ sk5 @ ( B @ r1 ) )
| ~ ( B @ p5 )
| ( B @ p6 )
| ~ ( B @ ( sk1 @ r1 ) )
| ~ sk2 )
& ( sk2
| ( A @ p5 )
| ~ ( A @ sk3 @ p6 )
| ~ ( A @ p6 )
| ~ ( A @ ( sk1 @ r1 ) ) )
& ( sk2
| ( A @ p5 )
| ( A @ sk3 @ ( A @ r1 ) )
| ~ ( A @ p6 )
| ~ ( A @ ( sk1 @ r1 ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(53,plain,
~ ( sk46 @ p5 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(16,plain,
sk46 @ p5,
inference(cnfConj,[status(thm)],[6]) ).
thf(200,plain,
~ $true,
inference(rewrite,[status(thm)],[53,16]) ).
thf(201,plain,
$false,
inference(simp,[status(thm)],[200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL644+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41 % Computer : n015.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 22:57:28 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.86/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.41/1.23 % [INFO] Parsing done (228ms).
% 1.41/1.24 % [INFO] Running in sequential loop mode.
% 2.30/1.64 % [INFO] eprover registered as external prover.
% 2.30/1.65 % [INFO] Scanning for conjecture ...
% 2.75/1.85 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.99/1.91 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.99/1.91 % [INFO] Problem is first-order (TPTP FOF).
% 2.99/1.93 % [INFO] Type checking passed.
% 2.99/1.94 % [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 ...
% 6.11/3.19 % [INFO] Killing All external provers ...
% 6.11/3.19 % Time passed: 2636ms (effective reasoning time: 1940ms)
% 6.11/3.19 % 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)>
% 6.11/3.19 % Axioms used in derivation (0):
% 6.11/3.19 % No. of inferences in proof: 10
% 6.11/3.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2636 ms resp. 1940 ms w/o parsing
% 7.16/3.44 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.16/3.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------