%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM824^5 : 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 : n026.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 : Wed Sep 30 08:18:15 AM UTC 2026
% Result : Theorem 102.19s 63.59s
% Output : Refutation 102.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 4
% Syntax : Number of formulae : 142 ( 37 unt; 0 typ; 3 def)
% Number of atoms : 553 ( 186 equ; 34 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1762 ( 271 ~; 238 |; 24 &;1202 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 75 ( 75 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 189 ( 36 ^; 150 !; 0 ?; 189 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cN_decl,type,
cN: $i > $o ).
thf(cODD_decl,type,
cODD: $i > $o ).
thf(cEVEN_decl,type,
cEVEN: $i > $o ).
thf(cS_decl,type,
cS: $i > $i ).
thf(c0_decl,type,
c0: $i ).
thf(sk1_decl,type,
sk1: ( $i > $o ) > ( $i > $o ) > $o ).
thf(sk2_decl,type,
sk2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(sk3_decl,type,
sk3: ( $i > $o ) > ( $i > $o ) > $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i > $o,B: $i > $o] :
@+[C: $i] :
~ ( ( B @ C )
=> ( A @ ( cS @ C ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i > $o,B: $i > $o] :
@+[C: $i] :
~ ( ( A @ C )
=> ( B @ ( cS @ C ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ( cEVEN @ A )
| ( cODD @ A ) )
=> ( cN @ A ) ) ) ) ).
thf(1,conjecture,
( ( ! [A: $i > $o,B: $i > $o] :
( ( ( A @ c0 )
& ! [C: $i] :
( ( A @ C )
=> ( B @ ( cS @ C ) ) )
& ! [C: $i] :
( ( B @ C )
=> ( A @ ( cS @ C ) ) ) )
=> ( ! [C: $i] :
( ( cEVEN @ C )
=> ( A @ C ) )
& ! [C: $i] :
( ( cODD @ C )
=> ( B @ C ) ) ) )
& ( cN @ c0 )
& ! [A: $i] :
( ( cN @ A )
=> ( cN @ ( cS @ A ) ) ) )
=> ! [A: $i] :
( ( ( cEVEN @ A )
| ( cODD @ A ) )
=> ( cN @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM623_pme) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i > $o,B: $i > $o] :
( ( ( A @ c0 )
& ! [C: $i] :
( ( A @ C )
=> ( B @ ( cS @ C ) ) )
& ! [C: $i] :
( ( B @ C )
=> ( A @ ( cS @ C ) ) ) )
=> ( ! [C: $i] :
( ( cEVEN @ C )
=> ( A @ C ) )
& ! [C: $i] :
( ( cODD @ C )
=> ( B @ C ) ) ) )
& ( cN @ c0 )
& ! [A: $i] :
( ( cN @ A )
=> ( cN @ ( cS @ A ) ) ) )
=> ! [A: $i] :
( ( ( cEVEN @ A )
| ( cODD @ A ) )
=> ( cN @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $i > $o,B: $i > $o] :
( ( ( A @ c0 )
& ! [C: $i] :
( ( A @ C )
=> ( B @ ( cS @ C ) ) )
& ! [C: $i] :
( ( B @ C )
=> ( A @ ( cS @ C ) ) ) )
=> ( ! [C: $i] :
( ( cEVEN @ C )
=> ( A @ C ) )
& ! [C: $i] :
( ( cODD @ C )
=> ( B @ C ) ) ) )
& ( cN @ c0 )
& ! [A: $i] :
( ( cN @ A )
=> ( cN @ ( cS @ A ) ) ) )
=> ! [A: $i] :
( ( ( cEVEN @ A )
| ( cODD @ A ) )
=> ( cN @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [E: $i,D: $i,C: $i,B: $i > $o,A: $i > $o] :
( ( ~ ( A @ c0 )
| ( A @ ( sk2 @ B @ A ) )
| ( B @ ( sk3 @ B @ A ) )
| ( sk1 @ A @ B ) )
& ( ~ ( A @ c0 )
| ( A @ ( sk2 @ B @ A ) )
| ~ ( A @ ( cS @ ( sk3 @ B @ A ) ) )
| ( sk1 @ A @ B ) )
& ( ~ ( A @ c0 )
| ~ ( B @ ( cS @ ( sk2 @ B @ A ) ) )
| ( B @ ( sk3 @ B @ A ) )
| ( sk1 @ A @ B ) )
& ( ~ ( A @ c0 )
| ~ ( B @ ( cS @ ( sk2 @ B @ A ) ) )
| ~ ( A @ ( cS @ ( sk3 @ B @ A ) ) )
| ( sk1 @ A @ B ) )
& ( ~ ( sk1 @ A @ B )
| ~ ( cEVEN @ C )
| ( A @ C ) )
& ( ~ ( sk1 @ A @ B )
| ~ ( cODD @ D )
| ( B @ D ) )
& ( cN @ c0 )
& ( ~ ( cN @ E )
| ( cN @ ( cS @ E ) ) )
& ( ( cEVEN @ sk4 )
| ( cODD @ sk4 ) )
& ~ ( cN @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ B @ A ) )
| ( B @ ( sk3 @ B @ A ) )
| ( sk1 @ A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(6,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ B @ A ) )
| ~ ( A @ ( cS @ ( sk3 @ B @ A ) ) )
| ( sk1 @ A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(1260,plain,
! [D: $i > $o,C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ B @ A ) )
| ( sk1 @ A @ B )
| ~ ( C @ c0 )
| ( C @ ( sk2 @ D @ C ) )
| ~ $true
| ( sk1 @ C @ D )
| ( ( B @ ( sk3 @ B @ A ) )
!= ( C @ ( cS @ ( sk3 @ D @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,6]) ).
thf(1261,plain,
! [D: $i > $o,C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ B @ A ) )
| ( sk1 @ A @ B )
| ~ ( C @ c0 )
| ( C @ ( sk2 @ D @ C ) )
| ( sk1 @ C @ D )
| ( ( B @ ( sk3 @ B @ A ) )
!= ( C @ ( cS @ ( sk3 @ D @ C ) ) ) ) ),
inference(simp,[status(thm)],[1260]) ).
thf(1418,plain,
! [B: $i > $o,A: $i > $o] :
( ( c0 != c0 )
| ( c0
= ( sk2 @ A @ ( (=) @ $i @ c0 ) ) )
| ( sk1 @ ( (=) @ $i @ c0 ) @ A )
| ( c0 != c0 )
| ( c0
= ( sk2 @ B @ ( (=) @ $i @ c0 ) ) )
| ( sk1 @ ( (=) @ $i @ c0 ) @ B )
| ( ( A @ ( sk3 @ A @ ( (=) @ $i @ c0 ) ) )
!= ( c0
= ( cS @ ( sk3 @ B @ ( (=) @ $i @ c0 ) ) ) ) ) ),
inference(replace_leibeq,[status(thm)],[1261:[bind(A,$thf( (=) @ $i @ c0 )),bind(B,$thf( B )),bind(C,$thf( (=) @ $i @ c0 ))]]) ).
thf(1433,plain,
! [B: $i > $o,A: $i > $o] :
( ( c0 != c0 )
| ( ( sk2 @ A @ ( (=) @ $i @ c0 ) )
= c0 )
| ( c0 != c0 )
| ( ( sk2 @ B @ ( (=) @ $i @ c0 ) )
= c0 )
| ( sk1 @ ( (=) @ $i @ c0 ) @ A )
| ( sk1 @ ( (=) @ $i @ c0 ) @ B )
| ( ( A @ ( sk3 @ A @ ( (=) @ $i @ c0 ) ) )
!= ( c0
= ( cS @ ( sk3 @ B @ ( (=) @ $i @ c0 ) ) ) ) ) ),
inference(lifteq,[status(thm)],[1418]) ).
thf(1497,plain,
( ( sk1 @ ( (=) @ $i @ c0 )
@ ^ [A: $i] :
( c0
= ( cS @ A ) ) )
| ( sk1 @ ( (=) @ $i @ c0 )
@ ^ [A: $i] :
( c0
= ( cS @ A ) ) )
| ( ( sk2
@ ^ [A: $i] :
( c0
= ( cS @ A ) )
@ ( (=) @ $i @ c0 ) )
= c0 )
| ( ( sk2
@ ^ [A: $i] :
( c0
= ( cS @ A ) )
@ ( (=) @ $i @ c0 ) )
= c0 ) ),
inference(pre_uni,[status(thm)],[1433:[bind(A,$thf( ^ [C: $i] : ( c0 = ( cS @ C ) ) )),bind(B,$thf( ^ [C: $i] : ( c0 = ( cS @ C ) ) ))]]) ).
thf(1640,plain,
( ( sk1 @ ( (=) @ $i @ c0 )
@ ^ [A: $i] :
( c0
= ( cS @ A ) ) )
| ( ( sk2
@ ^ [A: $i] :
( c0
= ( cS @ A ) )
@ ( (=) @ $i @ c0 ) )
= c0 ) ),
inference(simp,[status(thm)],[1497]) ).
thf(13,plain,
cN @ c0,
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
! [A: $i] :
( ~ ( cN @ A )
| ( cN @ ( cS @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(22,plain,
! [A: $i] :
( ~ ( cN @ A )
| ( cN @ ( cS @ A ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(552,plain,
! [A: $i] :
( ~ $true
| ( cN @ ( cS @ A ) )
| ( ( cN @ c0 )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13,22]) ).
thf(553,plain,
! [A: $i] :
( ( cN @ ( cS @ A ) )
| ( ( cN @ c0 )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[552]) ).
thf(554,plain,
cN @ ( cS @ c0 ),
inference(pattern_uni,[status(thm)],[553:[bind(A,$thf( c0 ))]]) ).
thf(1014,plain,
! [A: $i] :
( ~ $true
| ( cN @ ( cS @ A ) )
| ( ( cN @ ( cS @ c0 ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[554,22]) ).
thf(1015,plain,
! [A: $i] :
( ( cN @ ( cS @ A ) )
| ( ( cN @ ( cS @ c0 ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[1014]) ).
thf(1016,plain,
cN @ ( cS @ ( cS @ c0 ) ),
inference(pattern_uni,[status(thm)],[1015:[bind(A,$thf( cS @ c0 ))]]) ).
thf(1070,plain,
! [A: $i] :
( ~ $true
| ( cN @ ( cS @ A ) )
| ( ( cN @ ( cS @ ( cS @ c0 ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1016,22]) ).
thf(1071,plain,
! [A: $i] :
( ( cN @ ( cS @ A ) )
| ( ( cN @ ( cS @ ( cS @ c0 ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[1070]) ).
thf(1072,plain,
cN @ ( cS @ ( cS @ ( cS @ c0 ) ) ),
inference(pattern_uni,[status(thm)],[1071:[bind(A,$thf( cS @ ( cS @ c0 ) ))]]) ).
thf(1153,plain,
! [A: $i] :
( ~ $true
| ( cN @ ( cS @ A ) )
| ( ( cN @ ( cS @ ( cS @ ( cS @ c0 ) ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1072,22]) ).
thf(1154,plain,
! [A: $i] :
( ( cN @ ( cS @ A ) )
| ( ( cN @ ( cS @ ( cS @ ( cS @ c0 ) ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[1153]) ).
thf(1155,plain,
cN @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ),
inference(pattern_uni,[status(thm)],[1154:[bind(A,$thf( cS @ ( cS @ ( cS @ c0 ) ) ))]]) ).
thf(1206,plain,
! [A: $i] :
( ~ $true
| ( cN @ ( cS @ A ) )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1155,22]) ).
thf(1207,plain,
! [A: $i] :
( ( cN @ ( cS @ A ) )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[1206]) ).
thf(1208,plain,
cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1207:[bind(A,$thf( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ))]]) ).
thf(1675,plain,
! [A: $i] :
( ~ $true
| ( cN @ ( cS @ A ) )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1208,22]) ).
thf(1676,plain,
! [A: $i] :
( ( cN @ ( cS @ A ) )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[1675]) ).
thf(1677,plain,
cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1676:[bind(A,$thf( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ))]]) ).
thf(1749,plain,
! [A: $i] :
( ~ $true
| ( cN @ ( cS @ A ) )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1677,22]) ).
thf(1750,plain,
! [A: $i] :
( ( cN @ ( cS @ A ) )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[1749]) ).
thf(1751,plain,
cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1750:[bind(A,$thf( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ))]]) ).
thf(2320,plain,
! [A: $i] :
( ~ $true
| ( cN @ ( cS @ A ) )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1751,22]) ).
thf(2321,plain,
! [A: $i] :
( ( cN @ ( cS @ A ) )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[2320]) ).
thf(2322,plain,
cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2321:[bind(A,$thf( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ))]]) ).
thf(2369,plain,
! [A: $i] :
( ~ $true
| ( cN @ ( cS @ A ) )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2322,22]) ).
thf(2370,plain,
! [A: $i] :
( ( cN @ ( cS @ A ) )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[2369]) ).
thf(2371,plain,
cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2370:[bind(A,$thf( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ))]]) ).
thf(569,plain,
! [B: $i,A: $i] :
( ~ ( cN @ A )
| ~ $true
| ( cN @ ( cS @ B ) )
| ( ( cN @ ( cS @ A ) )
!= ( cN @ B ) ) ),
inference(paramod_ordered,[status(thm)],[22,22]) ).
thf(570,plain,
! [B: $i,A: $i] :
( ~ ( cN @ A )
| ( cN @ ( cS @ B ) )
| ( ( cN @ ( cS @ A ) )
!= ( cN @ B ) ) ),
inference(simp,[status(thm)],[569]) ).
thf(571,plain,
! [A: $i] :
( ~ ( cN @ A )
| ( cN @ ( cS @ ( cS @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[570:[bind(A,$thf( C )),bind(B,$thf( cS @ C ))]]) ).
thf(605,plain,
! [A: $i] :
( ~ ( cN @ A )
| ( cN @ ( cS @ ( cS @ A ) ) ) ),
inference(simp,[status(thm)],[571]) ).
thf(2855,plain,
! [A: $i] :
( ~ $true
| ( cN @ ( cS @ ( cS @ A ) ) )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2371,605]) ).
thf(2856,plain,
! [A: $i] :
( ( cN @ ( cS @ ( cS @ A ) ) )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[2855]) ).
thf(2857,plain,
cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2856:[bind(A,$thf( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) ))]]) ).
thf(9,plain,
~ ( cN @ sk4 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( B @ ( cS @ ( sk2 @ B @ A ) ) )
| ( B @ ( sk3 @ B @ A ) )
| ( sk1 @ A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ~ ( sk1 @ A @ B )
| ~ ( cODD @ C )
| ( B @ C ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(18,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ~ ( sk1 @ A @ B )
| ~ ( cODD @ C )
| ( B @ C ) ),
inference(simp,[status(thm)],[10]) ).
thf(7,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( B @ ( cS @ ( sk2 @ B @ A ) ) )
| ~ ( A @ ( cS @ ( sk3 @ B @ A ) ) )
| ( sk1 @ A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(34,plain,
! [D: $i > $o,C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( B @ ( cS @ ( sk2 @ B @ A ) ) )
| ~ ( A @ ( cS @ ( sk3 @ B @ A ) ) )
| ~ $true
| ~ ( D @ ( cS @ ( sk2 @ D @ C ) ) )
| ~ ( C @ ( cS @ ( sk3 @ D @ C ) ) )
| ( sk1 @ C @ D )
| ( ( sk1 @ A @ B )
!= ( C @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(35,plain,
! [D: $i > $o,C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( B @ ( cS @ ( sk2 @ B @ A ) ) )
| ~ ( A @ ( cS @ ( sk3 @ B @ A ) ) )
| ~ ( D @ ( cS @ ( sk2 @ D @ C ) ) )
| ~ ( C @ ( cS @ ( sk3 @ D @ C ) ) )
| ( sk1 @ C @ D )
| ( ( sk1 @ A @ B )
!= ( C @ c0 ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(77,plain,
! [C: $i > $i > $o,B: $i > $i > $o,A: $i > $o] :
( ~ ( B @ c0 @ c0 )
| ~ ( C @ c0 @ ( cS @ ( sk2 @ ( C @ c0 ) @ ( B @ c0 ) ) ) )
| ~ ( B @ c0 @ ( cS @ ( sk3 @ ( C @ c0 ) @ ( B @ c0 ) ) ) )
| ~ ( A
@ ( cS
@ ( sk2 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) ) )
| ~ ( sk1
@ ( B
@ ( cS
@ ( sk3 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) ) )
@ ( C
@ ( cS
@ ( sk3 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) ) ) )
| ( sk1
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) )
@ A ) ),
inference(pre_uni,[status(thm)],[35:[bind(A,$thf( E @ c0 )),bind(B,$thf( F @ c0 )),bind(C,$thf( ^ [G: $i] : ( sk1 @ ( E @ G ) @ ( F @ G ) ) ))]]) ).
thf(104,plain,
! [C: $i > $i > $o,B: $i > $i > $o,A: $i > $o] :
( ~ ( B @ c0 @ c0 )
| ~ ( C @ c0 @ ( cS @ ( sk2 @ ( C @ c0 ) @ ( B @ c0 ) ) ) )
| ~ ( B @ c0 @ ( cS @ ( sk3 @ ( C @ c0 ) @ ( B @ c0 ) ) ) )
| ~ ( A
@ ( cS
@ ( sk2 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) ) )
| ~ ( sk1
@ ( B
@ ( cS
@ ( sk3 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) ) )
@ ( C
@ ( cS
@ ( sk3 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) ) ) )
| ( sk1
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) )
@ A ) ),
inference(simp,[status(thm)],[77]) ).
thf(8,plain,
( ( cEVEN @ sk4 )
| ( cODD @ sk4 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(550,plain,
! [A: $i] :
( ~ ( cN @ A )
| ~ $true
| ( ( cN @ ( cS @ A ) )
!= ( cN @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[22,9]) ).
thf(551,plain,
! [A: $i] :
( ~ ( cN @ A )
| ( ( cN @ ( cS @ A ) )
!= ( cN @ sk4 ) ) ),
inference(simp,[status(thm)],[550]) ).
thf(589,plain,
! [A: $i] :
( ~ ( cN @ A )
| ( ( cS @ A )
!= sk4 ) ),
inference(simp,[status(thm)],[551]) ).
thf(1195,plain,
! [A: $i] :
( ~ $true
| ( ( cS @ A )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1155,589]) ).
thf(1196,plain,
! [A: $i] :
( ( ( cS @ A )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[1195]) ).
thf(1197,plain,
( ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) )
!= sk4 ),
inference(pattern_uni,[status(thm)],[1196:[bind(A,$thf( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ))]]) ).
thf(2329,plain,
! [A: $i] :
( ~ $true
| ( ( cS @ A )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1751,589]) ).
thf(2330,plain,
! [A: $i] :
( ( ( cS @ A )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[2329]) ).
thf(2331,plain,
( ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) )
!= sk4 ),
inference(pattern_uni,[status(thm)],[2330:[bind(A,$thf( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ))]]) ).
thf(1684,plain,
! [A: $i] :
( ~ $true
| ( ( cS @ A )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1208,589]) ).
thf(1685,plain,
! [A: $i] :
( ( ( cS @ A )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[1684]) ).
thf(1686,plain,
( ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) )
!= sk4 ),
inference(pattern_uni,[status(thm)],[1685:[bind(A,$thf( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ))]]) ).
thf(51,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( B @ ( cS @ ( sk2 @ B @ A ) ) )
| ( sk1 @ A @ B )
| ~ ( A @ ( cS @ ( sk3 @ B @ A ) ) )
| ~ ( B @ ( cS @ ( sk2 @ B @ A ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[7]) ).
thf(78,plain,
( ~ $true
| ~ $true
| ( sk1
@ ^ [A: $i] : $true
@ ^ [A: $i] : $true ) ),
inference(pre_uni,[status(thm)],[51:[bind(A,$thf( ^ [C: $i] : $true )),bind(B,$thf( ^ [C: $i] : $true ))]]) ).
thf(105,plain,
( sk1
@ ^ [A: $i] : $true
@ ^ [A: $i] : $true ),
inference(simp,[status(thm)],[78]) ).
thf(14,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ~ ( sk1 @ A @ B )
| ~ ( cEVEN @ C )
| ( A @ C ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(2599,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ~ ( sk1 @ A @ B )
| ~ ( cEVEN @ C )
| ~ $true
| ( ( A @ C )
!= ( cN @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[14,9]) ).
thf(2600,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ~ ( sk1 @ A @ B )
| ~ ( cEVEN @ C )
| ( ( A @ C )
!= ( cN @ sk4 ) ) ),
inference(simp,[status(thm)],[2599]) ).
thf(2774,plain,
! [A: $i > $o] :
( ~ ( sk1 @ cN @ A )
| ~ ( cEVEN @ sk4 ) ),
inference(pre_uni,[status(thm)],[2600:[bind(A,$thf( cN )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(2820,plain,
! [A: $i > $o] :
( ~ ( sk1 @ cN @ A )
| ~ ( cEVEN @ sk4 ) ),
inference(simp,[status(thm)],[2774]) ).
thf(2977,plain,
! [A: $i > $o] :
( ~ $true
| ~ ( cEVEN @ sk4 )
| ( ( sk1 @ cN @ A )
!= ( sk1
@ ^ [B: $i] : $true
@ ^ [B: $i] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[105,2820]) ).
thf(2978,plain,
! [A: $i > $o] :
( ~ ( cEVEN @ sk4 )
| ( ( sk1 @ cN @ A )
!= ( sk1
@ ^ [B: $i] : $true
@ ^ [B: $i] : $true ) ) ),
inference(simp,[status(thm)],[2977]) ).
thf(2992,plain,
! [A: $i > $o] :
( ~ ( cEVEN @ sk4 )
| ( cN
!= ( ^ [B: $i] : $true ) )
| ( A
!= ( ^ [B: $i] : $true ) ) ),
inference(simp,[status(thm)],[2978]) ).
thf(3012,plain,
( ~ ( cEVEN @ sk4 )
| ( cN
!= ( ^ [A: $i] : $true ) ) ),
inference(simp,[status(thm)],[2992]) ).
thf(2378,plain,
! [A: $i] :
( ~ $true
| ( ( cS @ A )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2322,589]) ).
thf(2379,plain,
! [A: $i] :
( ( ( cS @ A )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[2378]) ).
thf(2380,plain,
( ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) )
!= sk4 ),
inference(pattern_uni,[status(thm)],[2379:[bind(A,$thf( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ))]]) ).
thf(1758,plain,
! [A: $i] :
( ~ $true
| ( ( cS @ A )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1677,589]) ).
thf(1759,plain,
! [A: $i] :
( ( ( cS @ A )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[1758]) ).
thf(1760,plain,
( ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) )
!= sk4 ),
inference(pattern_uni,[status(thm)],[1759:[bind(A,$thf( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ))]]) ).
thf(686,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ B @ A ) )
| ( sk1 @ A @ B )
| ( ( B @ ( sk3 @ B @ A ) )
!= ( ~ ( A @ c0 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[5]) ).
thf(728,plain,
! [A: $i > $o] :
( ( c0 != c0 )
| ( c0
= ( sk2 @ A @ ( (=) @ $i @ c0 ) ) )
| ( sk1 @ ( (=) @ $i @ c0 ) @ A )
| ( ( A @ ( sk3 @ A @ ( (=) @ $i @ c0 ) ) )
!= ( c0 != c0 ) )
| ~ $true ),
inference(replace_leibeq,[status(thm)],[686:[bind(A,$thf( (=) @ $i @ c0 ))]]) ).
thf(805,plain,
! [A: $i > $o] :
( ( c0 != c0 )
| ( ( sk2 @ A @ ( (=) @ $i @ c0 ) )
= c0 )
| ( sk1 @ ( (=) @ $i @ c0 ) @ A )
| ( ( A @ ( sk3 @ A @ ( (=) @ $i @ c0 ) ) )
!= ( c0 != c0 ) )
| ~ $true ),
inference(lifteq,[status(thm)],[728]) ).
thf(850,plain,
( ~ $true
| ( sk1 @ ( (=) @ $i @ c0 )
@ ^ [A: $i] : ( c0 != c0 ) )
| ( ( sk2
@ ^ [A: $i] : ( c0 != c0 )
@ ( (=) @ $i @ c0 ) )
= c0 ) ),
inference(pre_uni,[status(thm)],[805:[bind(A,$thf( ^ [B: $i] : ( c0 != c0 ) ))]]) ).
thf(942,plain,
( ( sk1 @ ( (=) @ $i @ c0 )
@ ^ [A: $i] : $false )
| ( ( sk2
@ ^ [A: $i] : $false
@ ( (=) @ $i @ c0 ) )
= c0 ) ),
inference(simp,[status(thm)],[850]) ).
thf(1121,plain,
! [B: $i,A: $i] :
( ~ ( cN @ A )
| ~ $true
| ( ( cS @ B )
!= sk4 )
| ( ( cN @ ( cS @ A ) )
!= ( cN @ B ) ) ),
inference(paramod_ordered,[status(thm)],[22,589]) ).
thf(1122,plain,
! [B: $i,A: $i] :
( ~ ( cN @ A )
| ( ( cS @ B )
!= sk4 )
| ( ( cN @ ( cS @ A ) )
!= ( cN @ B ) ) ),
inference(simp,[status(thm)],[1121]) ).
thf(1123,plain,
! [A: $i] :
( ~ ( cN @ A )
| ( ( cS @ ( cS @ A ) )
!= sk4 ) ),
inference(pattern_uni,[status(thm)],[1122:[bind(A,$thf( C )),bind(B,$thf( cS @ C ))]]) ).
thf(1128,plain,
! [A: $i] :
( ~ ( cN @ A )
| ( ( cS @ ( cS @ A ) )
!= sk4 ) ),
inference(simp,[status(thm)],[1123]) ).
thf(2412,plain,
! [A: $i] :
( ~ $true
| ( ( cS @ ( cS @ A ) )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2322,1128]) ).
thf(2413,plain,
! [A: $i] :
( ( ( cS @ ( cS @ A ) )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[2412]) ).
thf(2414,plain,
( ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) ) )
!= sk4 ),
inference(pattern_uni,[status(thm)],[2413:[bind(A,$thf( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ))]]) ).
thf(3026,plain,
( ~ ( cN @ sk5 )
| ~ ( cEVEN @ sk4 ) ),
inference(func_ext,[status(esa)],[3012]) ).
thf(3091,plain,
( ~ $true
| ~ ( cEVEN @ sk4 )
| ( ( cN @ sk5 )
!= ( cN @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[13,3026]) ).
thf(3092,plain,
( ~ ( cEVEN @ sk4 )
| ( ( cN @ sk5 )
!= ( cN @ c0 ) ) ),
inference(simp,[status(thm)],[3091]) ).
thf(3115,plain,
( ~ ( cEVEN @ sk4 )
| ( sk5 != c0 ) ),
inference(simp,[status(thm)],[3092]) ).
thf(998,plain,
( ~ $true
| ( ( cN @ ( cS @ c0 ) )
!= ( cN @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[554,9]) ).
thf(999,plain,
( ( cN @ ( cS @ c0 ) )
!= ( cN @ sk4 ) ),
inference(simp,[status(thm)],[998]) ).
thf(1035,plain,
( ( cS @ c0 )
!= sk4 ),
inference(simp,[status(thm)],[999]) ).
thf(25,plain,
( ~ $true
| ( ( cN @ sk4 )
!= ( cN @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[13,9]) ).
thf(26,plain,
( ( cN @ sk4 )
!= ( cN @ c0 ) ),
inference(simp,[status(thm)],[25]) ).
thf(27,plain,
sk4 != c0,
inference(simp,[status(thm)],[26]) ).
thf(1142,plain,
! [A: $i] :
( ~ $true
| ( ( cS @ A )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ ( cS @ c0 ) ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1072,589]) ).
thf(1143,plain,
! [A: $i] :
( ( ( cS @ A )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ ( cS @ c0 ) ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[1142]) ).
thf(1144,plain,
( ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) )
!= sk4 ),
inference(pattern_uni,[status(thm)],[1143:[bind(A,$thf( cS @ ( cS @ ( cS @ c0 ) ) ))]]) ).
thf(3029,plain,
( ( cODD @ sk4 )
| ~ $true
| ( cN
!= ( ^ [A: $i] : $true ) )
| ( ( cEVEN @ sk4 )
!= ( cEVEN @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[8,3012]) ).
thf(3030,plain,
( ( cODD @ sk4 )
| ( cN
!= ( ^ [A: $i] : $true ) )
| ( ( cEVEN @ sk4 )
!= ( cEVEN @ sk4 ) ) ),
inference(simp,[status(thm)],[3029]) ).
thf(3031,plain,
( ( cODD @ sk4 )
| ( cN
!= ( ^ [A: $i] : $true ) ) ),
inference(pattern_uni,[status(thm)],[3030:[]]) ).
thf(3142,plain,
( ~ ( cN @ sk6 )
| ( cODD @ sk4 ) ),
inference(func_ext,[status(esa)],[3031]) ).
thf(2469,plain,
! [A: $i] :
( ~ $true
| ( cN @ ( cS @ ( cS @ A ) ) )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2322,605]) ).
thf(2470,plain,
! [A: $i] :
( ( cN @ ( cS @ ( cS @ A ) ) )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[2469]) ).
thf(2471,plain,
cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2470:[bind(A,$thf( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ))]]) ).
thf(17,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( A @ c0 )
| ( ( cS @ ( sk2 @ B @ A ) )
!= ( cS @ ( sk2 @ ( (=) @ $i @ ( cS @ ( sk2 @ B @ A ) ) ) @ A ) ) )
| ( ( cS @ ( sk2 @ B @ A ) )
= ( sk3 @ ( (=) @ $i @ ( cS @ ( sk2 @ B @ A ) ) ) @ A ) )
| ( sk1 @ A @ ( (=) @ $i @ ( cS @ ( sk2 @ B @ A ) ) ) ) ),
inference(replace_leibeq,[status(thm)],[12:[bind(A,$thf( A )),bind(B,$thf( (=) @ $i @ ( cS @ ( sk2 @ B @ A ) ) ))]]) ).
thf(19,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( cS @ ( sk2 @ ( (=) @ $i @ ( cS @ ( sk2 @ B @ A ) ) ) @ A ) )
!= ( cS @ ( sk2 @ B @ A ) ) )
| ( ( sk3 @ ( (=) @ $i @ ( cS @ ( sk2 @ B @ A ) ) ) @ A )
= ( cS @ ( sk2 @ B @ A ) ) )
| ~ ( A @ c0 )
| ( sk1 @ A @ ( (=) @ $i @ ( cS @ ( sk2 @ B @ A ) ) ) ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(3060,plain,
( ( cODD @ sk4 )
| ~ ( cN @ sk5 )
| ~ $true
| ( ( cEVEN @ sk4 )
!= ( cEVEN @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[8,3026]) ).
thf(3061,plain,
( ( cODD @ sk4 )
| ~ ( cN @ sk5 )
| ( ( cEVEN @ sk4 )
!= ( cEVEN @ sk4 ) ) ),
inference(simp,[status(thm)],[3060]) ).
thf(3062,plain,
( ( cODD @ sk4 )
| ~ ( cN @ sk5 ) ),
inference(pattern_uni,[status(thm)],[3061:[]]) ).
thf(3085,plain,
( ~ $true
| ~ ( cEVEN @ sk4 )
| ( ( cN @ ( cS @ c0 ) )
!= ( cN @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[554,3026]) ).
thf(3086,plain,
( ~ ( cEVEN @ sk4 )
| ( ( cN @ ( cS @ c0 ) )
!= ( cN @ sk5 ) ) ),
inference(simp,[status(thm)],[3085]) ).
thf(3128,plain,
( ~ ( cEVEN @ sk4 )
| ( ( cS @ c0 )
!= sk5 ) ),
inference(simp,[status(thm)],[3086]) ).
thf(1118,plain,
! [A: $i] :
( ~ $true
| ( ( cS @ A )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ c0 ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1016,589]) ).
thf(1119,plain,
! [A: $i] :
( ( ( cS @ A )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ c0 ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[1118]) ).
thf(1120,plain,
( ( cS @ ( cS @ ( cS @ c0 ) ) )
!= sk4 ),
inference(pattern_uni,[status(thm)],[1119:[bind(A,$thf( cS @ ( cS @ c0 ) ))]]) ).
thf(2832,plain,
! [A: $i] :
( ~ $true
| ( ( cS @ ( cS @ A ) )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2371,1128]) ).
thf(2833,plain,
! [A: $i] :
( ( ( cS @ ( cS @ A ) )
!= sk4 )
| ( ( cN @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) ) )
!= ( cN @ A ) ) ),
inference(simp,[status(thm)],[2832]) ).
thf(2834,plain,
( ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) ) ) )
!= sk4 ),
inference(pattern_uni,[status(thm)],[2833:[bind(A,$thf( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ) ) ))]]) ).
thf(1054,plain,
( ~ $true
| ( ( cN @ ( cS @ ( cS @ c0 ) ) )
!= ( cN @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[1016,9]) ).
thf(1055,plain,
( ( cN @ ( cS @ ( cS @ c0 ) ) )
!= ( cN @ sk4 ) ),
inference(simp,[status(thm)],[1054]) ).
thf(1088,plain,
( ( cS @ ( cS @ c0 ) )
!= sk4 ),
inference(simp,[status(thm)],[1055]) ).
thf(4297,plain,
$false,
inference(e,[status(thm)],[1640,2857,1677,9,12,18,104,8,1197,2331,1686,5,3012,2380,14,1760,1072,2371,6,942,1751,2414,2820,1128,554,1016,1155,13,3115,605,105,1035,22,27,7,1144,3142,3,3031,2471,1208,589,3026,2322,19,3062,3128,1120,2834,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM824^5 : 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
% 0.09/0.23 % Computer : n026.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 13:05:42 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 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
% 0.92/0.65 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/0.80 % [INFO] Parsing done (147ms).
% 1.29/0.81 % [INFO] Running in sequential loop mode.
% 1.97/1.21 % [INFO] eprover registered as external prover.
% 1.97/1.22 % [INFO] Scanning for conjecture ...
% 2.18/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.18/1.37 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.18/1.37 % [INFO] Problem is higher-order (TPTP THF).
% 2.18/1.37 % [INFO] Type checking passed.
% 2.18/1.38 % [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 ...
% 102.19/63.58 % External prover 'e' found a proof!
% 102.19/63.58 % [INFO] Killing All external provers ...
% 102.19/63.59 % Time passed: 63252ms (effective reasoning time: 62770ms)
% 102.19/63.59 % 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)>
% 102.19/63.59 % Axioms used in derivation (0):
% 102.19/63.59 % No. of inferences in proof: 139
% 102.19/63.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 63252 ms resp. 62770 ms w/o parsing
% 102.77/63.75 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 102.77/63.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------