%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU909^5 : 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 : n020.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 08:29:34 AM UTC 2026
% Result : Theorem 82.55s 20.24s
% Output : Refutation 68.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 11
% Syntax : Number of formulae : 250 ( 25 unt; 0 typ; 10 def)
% Number of atoms : 1592 ( 341 equ; 84 cnn)
% Maximal formula atoms : 70 ( 6 avg)
% Number of connectives : 2459 ( 371 ~; 526 |; 75 &;1399 @)
% ( 0 <=>; 88 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 278 ( 278 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 10 con; 0-2 aty)
% Number of variables : 630 ( 334 ^; 277 !; 9 ?; 630 :)
% ( 0 !>; 0 ?*; 0 @-; 10 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(cA_decl,type,
cA: ( a > $o ) > $o ).
thf(sk1_decl,type,
sk1: a > $o ).
thf(sk2_decl,type,
sk2: ( ( a > $o ) > $o ) > a > $o ).
thf(sk3_decl,type,
sk3: ( ( a > $o ) > $o ) > a ).
thf(sk4_decl,type,
sk4: a > a > $o ).
thf(sk5_decl,type,
sk5: $o ).
thf(sk6_decl,type,
sk6: a > $o ).
thf(sk7_decl,type,
sk7: a > $o ).
thf(sk8_decl,type,
sk8: ( a > $o ) > $o ).
thf(sk9_decl,type,
sk9: ( a > $o ) > ( a > $o ) > $o ).
thf(sk10_decl,type,
sk10: ( a > $o ) > $o ).
thf(sk11_decl,type,
sk11: ( a > $o ) > a ).
thf(sk12_decl,type,
sk12: ( a > $o ) > a > $o ).
thf(sk13_decl,type,
sk13: ( a > $o ) > a ).
thf(sk16_decl,type,
sk16: a ).
thf(sk17_decl,type,
sk17: a ).
thf(sk20_decl,type,
sk20: a ).
thf(sk21_decl,type,
sk21: a ).
thf(sk22_decl,type,
sk22: a ).
thf(sk23_decl,type,
sk23: a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > $o] :
~ ( ( ! [B: ( a > $o ) > $o] :
( ( ( B
@ ^ [C: a] : $false )
& ! [C: a > $o] :
( ( B @ C )
=> ! [D: a] :
( ( A @ D )
=> ( B
@ ^ [E: a] :
( ( C @ E )
| ( D = E ) ) ) ) ) )
=> ( B @ A ) )
& ! [B: a] :
( ( A @ B )
=> ? [C: a > $o] :
( ( cA @ C )
& ( C @ B ) ) ) )
=> ( ! [B: a > $o] :
( ( ( cA @ B )
& ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) )
=> ( cA @ B ) )
& ! [B: a > $o] :
( ( ( cA @ B )
& ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) )
=> ? [C: a > $o] :
( ! [D: ( a > $o ) > $o] :
( ( ( D
@ ^ [E: a] : $false )
& ! [E: a > $o] :
( ( D @ E )
=> ! [F: a] :
( ( C @ F )
=> ( D
@ ^ [G: a] :
( ( E @ G )
| ( F = G ) ) ) ) ) )
=> ( D @ C ) )
& ! [D: a] :
( ( C @ D )
=> ( B @ D ) )
& ! [D: a > $o] :
( ( ( cA @ D )
& ! [E: a] :
( ( C @ E )
=> ( D @ E ) ) )
=> ( ( cA @ D )
& ! [E: a] :
( ( A @ E )
=> ( D @ E ) ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: ( a > $o ) > $o] :
@+[B: a > $o] :
~ ( ( A @ B )
=> ! [C: a] :
( ( sk1 @ C )
=> ( A
@ ^ [D: a] :
( ( B @ D )
| ( C = D ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: ( a > $o ) > $o] :
@+[B: a] :
~ ( ( sk1 @ B )
=> ( A
@ ^ [C: a] :
( ( sk2 @ A @ C )
| ( B = C ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: a] :
@+[B: a > $o] :
( ( cA @ B )
& ( B @ A ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: a > $o] :
~ ( ( ( cA @ A )
& ! [B: a] :
( ( sk1 @ B )
=> ( A @ B ) ) )
=> ( cA @ A ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: a > $o] :
~ ( ( ( cA @ A )
& ! [B: a] :
( ( sk1 @ B )
=> ( A @ B ) ) )
=> ? [B: a > $o] :
( ! [C: ( a > $o ) > $o] :
( ( ( C
@ ^ [D: a] : $false )
& ! [D: a > $o] :
( ( C @ D )
=> ! [E: a] :
( ( B @ E )
=> ( C
@ ^ [F: a] :
( ( D @ F )
| ( E = F ) ) ) ) ) )
=> ( C @ B ) )
& ! [C: a] :
( ( B @ C )
=> ( A @ C ) )
& ! [C: a > $o] :
( ( ( cA @ C )
& ! [D: a] :
( ( B @ D )
=> ( C @ D ) ) )
=> ( ( cA @ C )
& ! [D: a] :
( ( sk1 @ D )
=> ( C @ D ) ) ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: a > $o] :
@+[B: ( a > $o ) > $o] :
~ ( ( ( B
@ ^ [C: a] : $false )
& ! [C: a > $o] :
( ( B @ C )
=> ! [D: a] :
( ( A @ D )
=> ( B
@ ^ [E: a] :
( ( C @ E )
| ( D = E ) ) ) ) ) )
=> ( B @ A ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: a > $o] :
@+[B: a] :
~ ( ( A @ B )
=> ( sk7 @ B ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: a > $o] :
@+[B: a > $o] :
~ ( ( ( cA @ B )
& ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) )
=> ( ( cA @ B )
& ! [C: a] :
( ( sk1 @ C )
=> ( B @ C ) ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: a > $o] :
@+[B: a] :
~ ( ( sk1 @ B )
=> ( sk12 @ A @ B ) ) ) ) ).
thf(1,conjecture,
( ! [A: a > $o] :
( ( cA @ A )
=> ( cA @ A ) )
& ! [A: a > $o] :
( ( ! [B: ( a > $o ) > $o] :
( ( ( B
@ ^ [C: a] : $false )
& ! [C: a > $o] :
( ( B @ C )
=> ! [D: a] :
( ( A @ D )
=> ( B
@ ^ [E: a] :
( ( C @ E )
| ( D = E ) ) ) ) ) )
=> ( B @ A ) )
& ! [B: a] :
( ( A @ B )
=> ? [C: a > $o] :
( ( cA @ C )
& ( C @ B ) ) ) )
=> ( ! [B: a > $o] :
( ( ( cA @ B )
& ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) )
=> ( cA @ B ) )
& ! [B: a > $o] :
( ( ( cA @ B )
& ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) )
=> ? [C: a > $o] :
( ! [D: ( a > $o ) > $o] :
( ( ( D
@ ^ [E: a] : $false )
& ! [E: a > $o] :
( ( D @ E )
=> ! [F: a] :
( ( C @ F )
=> ( D
@ ^ [G: a] :
( ( E @ G )
| ( F = G ) ) ) ) ) )
=> ( D @ C ) )
& ! [D: a] :
( ( C @ D )
=> ( B @ D ) )
& ! [D: a > $o] :
( ( ( cA @ D )
& ! [E: a] :
( ( C @ E )
=> ( D @ E ) ) )
=> ( ( cA @ D )
& ! [E: a] :
( ( A @ E )
=> ( D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cDOMTHM8_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: a > $o] :
( ( cA @ A )
=> ( cA @ A ) )
& ! [A: a > $o] :
( ( ! [B: ( a > $o ) > $o] :
( ( ( B
@ ^ [C: a] : $false )
& ! [C: a > $o] :
( ( B @ C )
=> ! [D: a] :
( ( A @ D )
=> ( B
@ ^ [E: a] :
( ( C @ E )
| ( D = E ) ) ) ) ) )
=> ( B @ A ) )
& ! [B: a] :
( ( A @ B )
=> ? [C: a > $o] :
( ( cA @ C )
& ( C @ B ) ) ) )
=> ( ! [B: a > $o] :
( ( ( cA @ B )
& ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) )
=> ( cA @ B ) )
& ! [B: a > $o] :
( ( ( cA @ B )
& ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) )
=> ? [C: a > $o] :
( ! [D: ( a > $o ) > $o] :
( ( ( D
@ ^ [E: a] : $false )
& ! [E: a > $o] :
( ( D @ E )
=> ! [F: a] :
( ( C @ F )
=> ( D
@ ^ [G: a] :
( ( E @ G )
| ( F = G ) ) ) ) ) )
=> ( D @ C ) )
& ! [D: a] :
( ( C @ D )
=> ( B @ D ) )
& ! [D: a > $o] :
( ( ( cA @ D )
& ! [E: a] :
( ( C @ E )
=> ( D @ E ) ) )
=> ( ( cA @ D )
& ! [E: a] :
( ( A @ E )
=> ( D @ E ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o] :
( ( ! [B: ( a > $o ) > $o] :
( ( ( B
@ ^ [C: a] : $false )
& ! [C: a > $o] :
( ( B @ C )
=> ! [D: a] :
( ( A @ D )
=> ( B
@ ^ [E: a] :
( ( C @ E )
| ( D = E ) ) ) ) ) )
=> ( B @ A ) )
& ! [B: a] :
( ( A @ B )
=> ? [C: a > $o] :
( ( cA @ C )
& ( C @ B ) ) ) )
=> ( ! [B: a > $o] :
( ( ( cA @ B )
& ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) )
=> ( cA @ B ) )
& ! [B: a > $o] :
( ( ( cA @ B )
& ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) )
=> ? [C: a > $o] :
( ! [D: ( a > $o ) > $o] :
( ( ( D
@ ^ [E: a] : $false )
& ! [E: a > $o] :
( ( D @ E )
=> ! [F: a] :
( ( C @ F )
=> ( D
@ ^ [G: a] :
( ( E @ G )
| ( F = G ) ) ) ) ) )
=> ( D @ C ) )
& ! [D: a] :
( ( C @ D )
=> ( B @ D ) )
& ! [D: a > $o] :
( ( ( cA @ D )
& ! [E: a] :
( ( C @ E )
=> ( D @ E ) ) )
=> ( ( cA @ D )
& ! [E: a] :
( ( A @ E )
=> ( D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [H: a,G: a,F: a > $o,E: a > $o,D: a,C: a,B: a,A: ( a > $o ) > $o] :
( ( ~ ( A
@ ^ [I: a] : $false )
| ( A @ ( sk2 @ A ) )
| ( A @ sk1 ) )
& ( ~ ( A
@ ^ [I: a] : $false )
| ( sk1 @ ( sk3 @ A ) )
| ( A @ sk1 ) )
& ( ~ ( A
@ ^ [I: a] : $false )
| ~ ( A
@ ^ [I: a] :
( ( sk2 @ A @ I )
| ( ( sk3 @ A )
= I ) ) )
| ( A @ sk1 ) )
& ( ~ ( sk1 @ B )
| ( cA @ ( sk4 @ B ) ) )
& ( ~ ( sk1 @ B )
| ( sk4 @ B @ B ) )
& ( ( cA @ sk6 )
| ~ sk5 )
& ( ~ ( sk1 @ C )
| ( sk6 @ C )
| ~ sk5 )
& ( ~ ( cA @ sk6 )
| ~ sk5 )
& ( sk5
| ( cA @ sk7 ) )
& ( sk5
| ~ ( sk1 @ D )
| ( sk7 @ D ) )
& ( sk5
| ( sk9 @ E
@ ^ [I: a] : $false )
| ~ ( sk8 @ E ) )
& ( sk5
| ~ ( sk9 @ E @ F )
| ~ ( E @ G )
| ( sk9 @ E
@ ^ [I: a] :
( ( F @ I )
| ( G = I ) ) )
| ~ ( sk8 @ E ) )
& ( sk5
| ~ ( sk9 @ E @ E )
| ~ ( sk8 @ E ) )
& ( sk5
| ( sk8 @ E )
| ( E @ ( sk11 @ E ) )
| ~ ( sk10 @ E ) )
& ( sk5
| ( sk8 @ E )
| ~ ( sk7 @ ( sk11 @ E ) )
| ~ ( sk10 @ E ) )
& ( sk5
| ( sk8 @ E )
| ( sk10 @ E )
| ( cA @ ( sk12 @ E ) ) )
& ( sk5
| ( sk8 @ E )
| ( sk10 @ E )
| ~ ( E @ H )
| ( sk12 @ E @ H ) )
& ( sk5
| ( sk8 @ E )
| ( sk10 @ E )
| ~ ( cA @ ( sk12 @ E ) )
| ( sk1 @ ( sk13 @ E ) ) )
& ( sk5
| ( sk8 @ E )
| ( sk10 @ E )
| ~ ( cA @ ( sk12 @ E ) )
| ~ ( sk12 @ E @ ( sk13 @ E ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
! [A: a > $o] :
( sk5
| ( sk8 @ A )
| ( sk10 @ A )
| ( cA @ ( sk12 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(28,plain,
! [A: a > $o] :
( sk5
| ( sk8 @ A )
| ( sk10 @ A )
| ( cA @ ( sk12 @ A ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(13,plain,
( ( cA @ sk6 )
| ~ sk5 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(6,plain,
( ~ ( cA @ sk6 )
| ~ sk5 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(48,plain,
( ~ sk5
| ~ $true
| ~ sk5
| ( ( cA @ sk6 )
!= ( cA @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[13,6]) ).
thf(49,plain,
( ~ sk5
| ( ( cA @ sk6 )
!= ( cA @ sk6 ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(50,plain,
~ sk5,
inference(pattern_uni,[status(thm)],[49:[]]) ).
thf(209,plain,
! [A: a > $o] :
( $false
| ( sk8 @ A )
| ( sk10 @ A )
| ( cA @ ( sk12 @ A ) ) ),
inference(rewrite,[status(thm)],[28,50]) ).
thf(210,plain,
! [A: a > $o] :
( ( sk8 @ A )
| ( sk10 @ A )
| ( cA @ ( sk12 @ A ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(9,plain,
! [A: a > $o] :
( sk5
| ( sk8 @ A )
| ( A @ ( sk11 @ A ) )
| ~ ( sk10 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(32,plain,
! [A: a > $o] :
( sk5
| ( sk8 @ A )
| ( A @ ( sk11 @ A ) )
| ~ ( sk10 @ A ) ),
inference(simp,[status(thm)],[9]) ).
thf(3722,plain,
! [A: a > $o] :
( $false
| ( sk8 @ A )
| ( A @ ( sk11 @ A ) )
| ~ ( sk10 @ A ) ),
inference(rewrite,[status(thm)],[32,50]) ).
thf(3723,plain,
! [A: a > $o] :
( ( sk8 @ A )
| ( A @ ( sk11 @ A ) )
| ~ ( sk10 @ A ) ),
inference(simp,[status(thm)],[3722]) ).
thf(12,plain,
! [A: a > $o] :
( sk5
| ( sk8 @ A )
| ~ ( sk7 @ ( sk11 @ A ) )
| ~ ( sk10 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(34,plain,
! [A: a > $o] :
( sk5
| ( sk8 @ A )
| ~ ( sk7 @ ( sk11 @ A ) )
| ~ ( sk10 @ A ) ),
inference(simp,[status(thm)],[12]) ).
thf(4172,plain,
! [A: a > $o] :
( $false
| ( sk8 @ A )
| ~ ( sk7 @ ( sk11 @ A ) )
| ~ ( sk10 @ A ) ),
inference(rewrite,[status(thm)],[34,50]) ).
thf(4173,plain,
! [A: a > $o] :
( ( sk8 @ A )
| ~ ( sk7 @ ( sk11 @ A ) )
| ~ ( sk10 @ A ) ),
inference(simp,[status(thm)],[4172]) ).
thf(4174,plain,
! [B: a > $o,A: a > $o] :
( ( sk8 @ A )
| ~ ( sk10 @ A )
| ( sk8 @ B )
| ~ $true
| ~ ( sk10 @ B )
| ( ( A @ ( sk11 @ A ) )
!= ( sk7 @ ( sk11 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[3723,4173]) ).
thf(4175,plain,
! [B: a > $o,A: a > $o] :
( ( sk8 @ A )
| ~ ( sk10 @ A )
| ( sk8 @ B )
| ~ ( sk10 @ B )
| ( ( A @ ( sk11 @ A ) )
!= ( sk7 @ ( sk11 @ B ) ) ) ),
inference(simp,[status(thm)],[4174]) ).
thf(4217,plain,
( ( sk8 @ sk7 )
| ~ ( sk10 @ sk7 )
| ( sk8 @ sk7 )
| ~ ( sk10 @ sk7 ) ),
inference(pre_uni,[status(thm)],[4175:[bind(A,$thf( sk7 )),bind(B,$thf( sk7 ))]]) ).
thf(4227,plain,
( ( sk8 @ sk7 )
| ~ ( sk10 @ sk7 ) ),
inference(simp,[status(thm)],[4217]) ).
thf(4234,plain,
! [A: a > $o] :
( ( sk8 @ A )
| ( cA @ ( sk12 @ A ) )
| ( sk8 @ sk7 )
| ~ $true
| ( ( sk10 @ A )
!= ( sk10 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[210,4227]) ).
thf(4235,plain,
! [A: a > $o] :
( ( sk8 @ A )
| ( cA @ ( sk12 @ A ) )
| ( sk8 @ sk7 )
| ( ( sk10 @ A )
!= ( sk10 @ sk7 ) ) ),
inference(simp,[status(thm)],[4234]) ).
thf(4236,plain,
( ( sk8 @ sk7 )
| ( cA @ ( sk12 @ sk7 ) )
| ( sk8 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[4235:[bind(A,$thf( sk7 ))]]) ).
thf(4247,plain,
( ( sk8 @ sk7 )
| ( cA @ ( sk12 @ sk7 ) ) ),
inference(simp,[status(thm)],[4236]) ).
thf(8,plain,
( sk5
| ( cA @ sk7 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(51,plain,
( $false
| ( cA @ sk7 ) ),
inference(rewrite,[status(thm)],[8,50]) ).
thf(52,plain,
cA @ sk7,
inference(simp,[status(thm)],[51]) ).
thf(15,plain,
! [A: a > $o] :
( sk5
| ( sk8 @ A )
| ( sk10 @ A )
| ~ ( cA @ ( sk12 @ A ) )
| ( sk1 @ ( sk13 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(38,plain,
! [A: a > $o] :
( sk5
| ( sk8 @ A )
| ( sk10 @ A )
| ~ ( cA @ ( sk12 @ A ) )
| ( sk1 @ ( sk13 @ A ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(5578,plain,
! [A: a > $o] :
( $false
| ( sk8 @ A )
| ( sk10 @ A )
| ~ ( cA @ ( sk12 @ A ) )
| ( sk1 @ ( sk13 @ A ) ) ),
inference(rewrite,[status(thm)],[38,50]) ).
thf(5579,plain,
! [A: a > $o] :
( ( sk8 @ A )
| ( sk10 @ A )
| ~ ( cA @ ( sk12 @ A ) )
| ( sk1 @ ( sk13 @ A ) ) ),
inference(simp,[status(thm)],[5578]) ).
thf(3842,plain,
! [A: a > $o] :
( ( sk8 @ A )
| ~ ( sk10 @ A )
| ~ $true
| ( ( A @ ( sk11 @ A ) )
!= sk5 ) ),
inference(paramod_ordered,[status(thm)],[3723,50]) ).
thf(3843,plain,
! [A: a > $o] :
( ( sk8 @ A )
| ~ ( sk10 @ A )
| ( ( A @ ( sk11 @ A ) )
!= sk5 ) ),
inference(simp,[status(thm)],[3842]) ).
thf(3975,plain,
( ( sk8
@ ^ [A: a] : sk5 )
| ~ ( sk10
@ ^ [A: a] : sk5 ) ),
inference(pre_uni,[status(thm)],[3843:[bind(A,$thf( ^ [B: a] : sk5 ))]]) ).
thf(4044,plain,
( ( sk8
@ ^ [A: a] : $false )
| ~ ( sk10
@ ^ [A: a] : $false ) ),
inference(rewrite,[status(thm)],[3975,50]) ).
thf(4053,plain,
! [A: a > $o] :
( ( sk8 @ A )
| ( cA @ ( sk12 @ A ) )
| ( sk8
@ ^ [B: a] : $false )
| ~ $true
| ( ( sk10 @ A )
!= ( sk10
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[210,4044]) ).
thf(4054,plain,
! [A: a > $o] :
( ( sk8 @ A )
| ( cA @ ( sk12 @ A ) )
| ( sk8
@ ^ [B: a] : $false )
| ( ( sk10 @ A )
!= ( sk10
@ ^ [B: a] : $false ) ) ),
inference(simp,[status(thm)],[4053]) ).
thf(4055,plain,
( ( sk8
@ ^ [A: a] : $false )
| ( cA
@ ( sk12
@ ^ [A: a] : $false ) )
| ( sk8
@ ^ [A: a] : $false ) ),
inference(pattern_uni,[status(thm)],[4054:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(4079,plain,
( ( sk8
@ ^ [A: a] : $false )
| ( cA
@ ( sk12
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[4055]) ).
thf(14,plain,
! [A: a > $o] :
( sk5
| ( sk9 @ A
@ ^ [B: a] : $false )
| ~ ( sk8 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(29,plain,
! [A: a > $o] :
( sk5
| ( sk9 @ A
@ ^ [B: a] : $false )
| ~ ( sk8 @ A ) ),
inference(simp,[status(thm)],[14]) ).
thf(2402,plain,
! [A: a > $o] :
( $false
| ( sk9 @ A
@ ^ [B: a] : $false )
| ~ ( sk8 @ A ) ),
inference(rewrite,[status(thm)],[29,50]) ).
thf(2403,plain,
! [A: a > $o] :
( ( sk9 @ A
@ ^ [B: a] : $false )
| ~ ( sk8 @ A ) ),
inference(simp,[status(thm)],[2402]) ).
thf(19,plain,
! [A: a > $o] :
( sk5
| ~ ( sk9 @ A @ A )
| ~ ( sk8 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(37,plain,
! [A: a > $o] :
( sk5
| ~ ( sk9 @ A @ A )
| ~ ( sk8 @ A ) ),
inference(simp,[status(thm)],[19]) ).
thf(54,plain,
! [A: a > $o] :
( $false
| ~ ( sk9 @ A @ A )
| ~ ( sk8 @ A ) ),
inference(rewrite,[status(thm)],[37,50]) ).
thf(55,plain,
! [A: a > $o] :
( ~ ( sk9 @ A @ A )
| ~ ( sk8 @ A ) ),
inference(simp,[status(thm)],[54]) ).
thf(2430,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk8 @ A )
| ~ $true
| ~ ( sk8 @ B )
| ( ( sk9 @ A
@ ^ [C: a] : $false )
!= ( sk9 @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2403,55]) ).
thf(2431,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk8 @ A )
| ~ ( sk8 @ B )
| ( ( sk9 @ A
@ ^ [C: a] : $false )
!= ( sk9 @ B @ B ) ) ),
inference(simp,[status(thm)],[2430]) ).
thf(2432,plain,
( ~ ( sk8
@ ^ [A: a] : $false )
| ~ ( sk8
@ ^ [A: a] : $false ) ),
inference(pattern_uni,[status(thm)],[2431:[bind(A,$thf( ^ [C: a] : $false )),bind(B,$thf( ^ [C: a] : $false ))]]) ).
thf(2470,plain,
~ ( sk8
@ ^ [A: a] : $false ),
inference(simp,[status(thm)],[2432]) ).
thf(4112,plain,
( $false
| ( cA
@ ( sk12
@ ^ [A: a] : $false ) ) ),
inference(rewrite,[status(thm)],[4079,2470]) ).
thf(4113,plain,
( cA
@ ( sk12
@ ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[4112]) ).
thf(5684,plain,
! [A: a > $o] :
( ( sk8 @ A )
| ( sk10 @ A )
| ~ $true
| ( sk1 @ ( sk13 @ A ) )
| ( ( cA
@ ( sk12
@ ^ [B: a] : $false ) )
!= ( cA @ ( sk12 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[4113,5579]) ).
thf(5685,plain,
! [A: a > $o] :
( ( sk8 @ A )
| ( sk10 @ A )
| ( sk1 @ ( sk13 @ A ) )
| ( ( cA
@ ( sk12
@ ^ [B: a] : $false ) )
!= ( cA @ ( sk12 @ A ) ) ) ),
inference(simp,[status(thm)],[5684]) ).
thf(5686,plain,
( ( sk8
@ ^ [A: a] : $false )
| ( sk10
@ ^ [A: a] : $false )
| ( sk1
@ ( sk13
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[5685:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(3861,plain,
( ( sk8
@ ^ [A: a] : $false )
| $false
| ~ ( sk10
@ ^ [A: a] : $false ) ),
inference(prim_subst,[status(thm)],[3723:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(3981,plain,
( ( sk8
@ ^ [A: a] : $false )
| ~ ( sk10
@ ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[3861]) ).
thf(4080,plain,
( $false
| ~ ( sk10
@ ^ [A: a] : $false ) ),
inference(rewrite,[status(thm)],[3981,2470]) ).
thf(4081,plain,
~ ( sk10
@ ^ [A: a] : $false ),
inference(simp,[status(thm)],[4080]) ).
thf(6206,plain,
( $false
| $false
| ( sk1
@ ( sk13
@ ^ [A: a] : $false ) ) ),
inference(rewrite,[status(thm)],[5686,4081,2470]) ).
thf(6207,plain,
( sk1
@ ( sk13
@ ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[6206]) ).
thf(11,plain,
! [A: ( a > $o ) > $o] :
( ~ ( A
@ ^ [B: a] : $false )
| ( sk1 @ ( sk3 @ A ) )
| ( A @ sk1 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(26,plain,
( ( ( ^ [A: a] : $false )
!= ( ^ [A: a] : $false ) )
| ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) ) )
| ( ( ^ [A: a] : $false )
= sk1 ) ),
inference(replace_leibeq,[status(thm)],[11:[bind(A,$thf( (=) @ ( a > $o ) @ ^ [B: a] : $false ))]]) ).
thf(43,plain,
( ( ( ^ [A: a] : $false )
!= ( ^ [A: a] : $false ) )
| ( sk1
= ( ^ [A: a] : $false ) )
| ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(44,plain,
( ( sk1
= ( ^ [A: a] : $false ) )
| ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(57,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) ) ),
inference(func_ext,[status(esa)],[44]) ).
thf(21,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( cA @ ( sk4 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(31,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( cA @ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(143,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ~ $true
| ( cA @ ( sk4 @ B ) )
| ( ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [C: a] : $false ) ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57,31]) ).
thf(144,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ( cA @ ( sk4 @ B ) )
| ( ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [C: a] : $false ) ) )
!= ( sk1 @ B ) ) ),
inference(simp,[status(thm)],[143]) ).
thf(145,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( cA
@ ( sk4
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) ) ) ),
inference(pattern_uni,[status(thm)],[144:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( (=) @ ( a > $o ) @ ^ [C: a] : $false ) ))]]) ).
thf(6265,plain,
! [A: a] :
( ~ $true
| ( cA
@ ( sk4
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) ) )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6207,145]) ).
thf(6266,plain,
! [A: a] :
( ( cA
@ ( sk4
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) ) )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[6265]) ).
thf(6267,plain,
( cA
@ ( sk4
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) ) ) ),
inference(pattern_uni,[status(thm)],[6266:[bind(A,$thf( sk13 @ ^ [B: a] : $false ))]]) ).
thf(17,plain,
! [A: ( a > $o ) > $o] :
( ~ ( A
@ ^ [B: a] : $false )
| ( A @ ( sk2 @ A ) )
| ( A @ sk1 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(1032,plain,
! [A: ( a > $o ) > $o] :
( ~ ( A
@ ^ [B: a] : $false )
| ( A @ sk1 )
| ( ( A @ ( sk2 @ A ) )
!= ( A @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[17]) ).
thf(1061,plain,
( ( ( ^ [A: a] : $false )
!= ( ^ [A: a] : $false ) )
| ( ( ^ [A: a] : $false )
= sk1 )
| ( ( ( ^ [A: a] : $false )
= ( sk2
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) ) )
!= ( ( ^ [A: a] : $false )
= sk1 ) )
| ~ $true ),
inference(replace_leibeq,[status(thm)],[1032:[bind(A,$thf( (=) @ ( a > $o ) @ ^ [B: a] : $false ))]]) ).
thf(1120,plain,
( ( ( ^ [A: a] : $false )
!= ( ^ [A: a] : $false ) )
| ( sk1
= ( ^ [A: a] : $false ) )
| ( ( ( ^ [A: a] : $false )
= ( sk2
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) ) )
!= ( ( ^ [A: a] : $false )
= sk1 ) )
| ~ $true ),
inference(lifteq,[status(thm)],[1061]) ).
thf(1263,plain,
( ( sk1
= ( ^ [A: a] : $false ) )
| ( ( ( ^ [A: a] : $false )
= ( sk2
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) ) )
!= ( ( ^ [A: a] : $false )
= sk1 ) ) ),
inference(simp,[status(thm)],[1120]) ).
thf(1950,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( ( ( ^ [B: a] : $false )
= ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) )
!= ( ( ^ [B: a] : $false )
= sk1 ) ) ),
inference(func_ext,[status(esa)],[1263]) ).
thf(2124,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( ( ^ [B: a] : $false )
!= ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) )
| ( ( ^ [B: a] : $false )
!= sk1 ) ),
inference(bool_ext,[status(thm)],[1950]) ).
thf(2168,plain,
! [A: a] :
( ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) )
!= ( ^ [B: a] : $false ) )
| ( sk1
!= ( ^ [B: a] : $false ) )
| ~ ( sk1 @ A ) ),
inference(lifteq,[status(thm)],[2124]) ).
thf(6236,plain,
! [A: a] :
( ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) )
!= ( ^ [B: a] : $false ) )
| ( sk1
!= ( ^ [B: a] : $false ) )
| ~ $true
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6207,2168]) ).
thf(6237,plain,
! [A: a] :
( ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) )
!= ( ^ [B: a] : $false ) )
| ( sk1
!= ( ^ [B: a] : $false ) )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[6236]) ).
thf(6238,plain,
( ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) )
!= ( ^ [A: a] : $false ) )
| ( sk1
!= ( ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[6237:[bind(A,$thf( sk13 @ ^ [B: a] : $false ))]]) ).
thf(24,plain,
( ( ( ^ [A: a] : $false )
!= ( ^ [A: a] : $false ) )
| ( ( ^ [A: a] : $false )
= ( sk2
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) ) )
| ( ( ^ [A: a] : $false )
= sk1 ) ),
inference(replace_leibeq,[status(thm)],[17:[bind(A,$thf( (=) @ ( a > $o ) @ ^ [B: a] : $false ))]]) ).
thf(39,plain,
( ( ( ^ [A: a] : $false )
!= ( ^ [A: a] : $false ) )
| ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) )
= ( ^ [A: a] : $false ) )
| ( sk1
= ( ^ [A: a] : $false ) ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(40,plain,
( ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) )
= ( ^ [A: a] : $false ) )
| ( sk1
= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(56,plain,
! [B: a,A: a] :
( ~ ( sk2
@ ( (=) @ ( a > $o )
@ ^ [C: a] : $false )
@ A )
| ~ ( sk1 @ B ) ),
inference(func_ext,[status(esa)],[40]) ).
thf(6233,plain,
! [B: a,A: a] :
( ~ ( sk2
@ ( (=) @ ( a > $o )
@ ^ [C: a] : $false )
@ A )
| ~ $true
| ( ( sk1
@ ( sk13
@ ^ [C: a] : $false ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6207,56]) ).
thf(6234,plain,
! [B: a,A: a] :
( ~ ( sk2
@ ( (=) @ ( a > $o )
@ ^ [C: a] : $false )
@ A )
| ( ( sk1
@ ( sk13
@ ^ [C: a] : $false ) )
!= ( sk1 @ B ) ) ),
inference(simp,[status(thm)],[6233]) ).
thf(6235,plain,
! [A: a] :
~ ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false )
@ A ),
inference(pattern_uni,[status(thm)],[6234:[bind(A,$thf( A )),bind(B,$thf( sk13 @ ^ [C: a] : $false ))]]) ).
thf(7107,plain,
( ( ( ^ [A: a] : $false )
!= ( ^ [A: a] : $false ) )
| ( sk1
!= ( ^ [A: a] : $false ) ) ),
inference(rewrite,[status(thm)],[6238,6235]) ).
thf(7108,plain,
( sk1
!= ( ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[7107]) ).
thf(7151,plain,
sk1 @ sk23,
inference(func_ext,[status(esa)],[7108]) ).
thf(7221,plain,
! [A: a] :
( ~ $true
| ( cA @ ( sk4 @ A ) )
| ( ( sk1 @ sk23 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7151,31]) ).
thf(7222,plain,
! [A: a] :
( ( cA @ ( sk4 @ A ) )
| ( ( sk1 @ sk23 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[7221]) ).
thf(7223,plain,
cA @ ( sk4 @ sk23 ),
inference(pattern_uni,[status(thm)],[7222:[bind(A,$thf( sk23 ))]]) ).
thf(2123,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( ( ^ [B: a] : $false )
!= ( ^ [B: a] : $false ) )
| ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) )
!= sk1 ) ),
inference(simp,[status(thm)],[1950]) ).
thf(2190,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) )
!= sk1 ) ),
inference(simp,[status(thm)],[2123]) ).
thf(6245,plain,
! [A: a] :
( ~ $true
| ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) )
!= sk1 )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6207,2190]) ).
thf(6246,plain,
! [A: a] :
( ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) )
!= sk1 )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[6245]) ).
thf(6247,plain,
( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[6246:[bind(A,$thf( sk13 @ ^ [B: a] : $false ))]]) ).
thf(6675,plain,
( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false )
@ sk20 )
!= ( sk1 @ sk20 ) ),
inference(func_ext,[status(esa)],[6247]) ).
thf(7109,plain,
sk1 @ sk20,
inference(rewrite,[status(thm)],[6675,6235]) ).
thf(4287,plain,
! [A: a > $o] :
( ( cA @ ( sk12 @ sk7 ) )
| ~ ( sk9 @ A @ A )
| ~ $true
| ( ( sk8 @ sk7 )
!= ( sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4247,55]) ).
thf(4288,plain,
! [A: a > $o] :
( ( cA @ ( sk12 @ sk7 ) )
| ~ ( sk9 @ A @ A )
| ( ( sk8 @ sk7 )
!= ( sk8 @ A ) ) ),
inference(simp,[status(thm)],[4287]) ).
thf(4289,plain,
( ( cA @ ( sk12 @ sk7 ) )
| ~ ( sk9 @ sk7 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[4288:[bind(A,$thf( sk7 ))]]) ).
thf(16,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk4 @ A @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(36,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk4 @ A @ A ) ),
inference(simp,[status(thm)],[16]) ).
thf(379,plain,
( ~ ( cA
@ ^ [A: a] : $false )
| ( sk1 @ ( sk3 @ cA ) )
| ( cA @ sk1 ) ),
inference(prim_subst,[status(thm)],[11:[bind(A,$thf( cA ))]]) ).
thf(18,plain,
! [B: a,A: a > $o] :
( sk5
| ( sk8 @ A )
| ( sk10 @ A )
| ~ ( A @ B )
| ( sk12 @ A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(35,plain,
! [B: a,A: a > $o] :
( sk5
| ( sk8 @ A )
| ( sk10 @ A )
| ~ ( A @ B )
| ( sk12 @ A @ B ) ),
inference(simp,[status(thm)],[18]) ).
thf(4613,plain,
! [B: a,A: a > $o] :
( $false
| ( sk8 @ A )
| ( sk10 @ A )
| ~ ( A @ B )
| ( sk12 @ A @ B ) ),
inference(rewrite,[status(thm)],[35,50]) ).
thf(4614,plain,
! [B: a,A: a > $o] :
( ( sk8 @ A )
| ( sk10 @ A )
| ~ ( A @ B )
| ( sk12 @ A @ B ) ),
inference(simp,[status(thm)],[4613]) ).
thf(4290,plain,
( ( cA @ ( sk12 @ sk7 ) )
| ~ $true
| ( ( sk8 @ sk7 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[4247,2470]) ).
thf(4291,plain,
( ( cA @ ( sk12 @ sk7 ) )
| ( ( sk8 @ sk7 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[4290]) ).
thf(4303,plain,
( ( cA @ ( sk12 @ sk7 ) )
| ( sk7
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[4291]) ).
thf(4326,plain,
( ( sk7 @ sk17 )
| ( cA @ ( sk12 @ sk7 ) ) ),
inference(func_ext,[status(esa)],[4303]) ).
thf(7180,plain,
! [A: a] :
( ~ $true
| ( cA @ ( sk4 @ A ) )
| ( ( sk1 @ sk20 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7109,31]) ).
thf(7181,plain,
! [A: a] :
( ( cA @ ( sk4 @ A ) )
| ( ( sk1 @ sk20 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[7180]) ).
thf(7182,plain,
cA @ ( sk4 @ sk20 ),
inference(pattern_uni,[status(thm)],[7181:[bind(A,$thf( sk20 ))]]) ).
thf(1949,plain,
( ( sk1
= ( ^ [A: a] : $false ) )
| ( ( ^ [A: a] : $false )
!= ( ^ [A: a] : $false ) )
| ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) )
!= sk1 ) ),
inference(simp,[status(thm)],[1263]) ).
thf(2047,plain,
( ( sk1
= ( ^ [A: a] : $false ) )
| ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) )
!= sk1 ) ),
inference(simp,[status(thm)],[1949]) ).
thf(2049,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false )
@ sk16 )
!= ( sk1 @ sk16 ) ) ),
inference(func_ext,[status(esa)],[2047]) ).
thf(2072,plain,
! [A: a] :
( ( sk1
= ( ^ [B: a] : $false ) )
| ~ $true
| ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false )
@ sk16 )
!= ( sk1 @ sk16 ) )
| ( ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44,2049]) ).
thf(2073,plain,
! [A: a] :
( ( sk1
= ( ^ [B: a] : $false ) )
| ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false )
@ sk16 )
!= ( sk1 @ sk16 ) )
| ( ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[2072]) ).
thf(2074,plain,
( ( sk1
= ( ^ [A: a] : $false ) )
| ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false )
@ sk16 )
!= ( sk1 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[2073:[bind(A,$thf( sk3 @ ( (=) @ ( a > $o ) @ ^ [B: a] : $false ) ))]]) ).
thf(2519,plain,
( ( sk1
= ( ^ [A: a] : $false ) )
| ( sk2
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false )
@ sk16 )
| ( sk1 @ sk16 ) ),
inference(bool_ext,[status(thm)],[2074]) ).
thf(198,plain,
! [B: a,A: a] :
( ( sk1
= ( ^ [C: a] : $false ) )
| ~ ( sk2
@ ( (=) @ ( a > $o )
@ ^ [C: a] : $false )
@ A )
| ~ $true
| ( ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [C: a] : $false ) ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44,56]) ).
thf(199,plain,
! [B: a,A: a] :
( ( sk1
= ( ^ [C: a] : $false ) )
| ~ ( sk2
@ ( (=) @ ( a > $o )
@ ^ [C: a] : $false )
@ A )
| ( ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [C: a] : $false ) ) )
!= ( sk1 @ B ) ) ),
inference(simp,[status(thm)],[198]) ).
thf(200,plain,
! [A: a] :
( ( sk1
= ( ^ [B: a] : $false ) )
| ~ ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false )
@ A ) ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( (=) @ ( a > $o ) @ ^ [C: a] : $false ) ))]]) ).
thf(2691,plain,
! [A: a] :
( ( sk1
= ( ^ [B: a] : $false ) )
| ( sk1 @ sk16 )
| ( sk1
= ( ^ [B: a] : $false ) )
| ~ $true
| ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false )
@ sk16 )
!= ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false )
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[2519,200]) ).
thf(2692,plain,
! [A: a] :
( ( sk1
= ( ^ [B: a] : $false ) )
| ( sk1 @ sk16 )
| ( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false )
@ sk16 )
!= ( sk2
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false )
@ A ) ) ),
inference(simp,[status(thm)],[2691]) ).
thf(2693,plain,
( ( sk1
= ( ^ [A: a] : $false ) )
| ( sk1 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[2692:[bind(A,$thf( sk16 ))]]) ).
thf(23,plain,
! [A: a] :
( sk5
| ~ ( sk1 @ A )
| ( sk7 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(45,plain,
! [A: a] :
( sk5
| ~ ( sk1 @ A )
| ( sk7 @ A ) ),
inference(simp,[status(thm)],[23]) ).
thf(239,plain,
! [A: a] :
( $false
| ~ ( sk1 @ A )
| ( sk7 @ A ) ),
inference(rewrite,[status(thm)],[45,50]) ).
thf(240,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk7 @ A ) ),
inference(simp,[status(thm)],[239]) ).
thf(2865,plain,
! [A: a] :
( ( sk1
= ( ^ [B: a] : $false ) )
| ~ $true
| ( sk7 @ A )
| ( ( sk1 @ sk16 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2693,240]) ).
thf(2866,plain,
! [A: a] :
( ( sk1
= ( ^ [B: a] : $false ) )
| ( sk7 @ A )
| ( ( sk1 @ sk16 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[2865]) ).
thf(2867,plain,
( ( sk1
= ( ^ [A: a] : $false ) )
| ( sk7 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[2866:[bind(A,$thf( sk16 ))]]) ).
thf(2926,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk7 @ sk16 ) ),
inference(func_ext,[status(esa)],[2867]) ).
thf(6251,plain,
! [A: a] :
( ~ $true
| ( sk7 @ sk16 )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6207,2926]) ).
thf(6252,plain,
! [A: a] :
( ( sk7 @ sk16 )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[6251]) ).
thf(6253,plain,
sk7 @ sk16,
inference(pattern_uni,[status(thm)],[6252:[bind(A,$thf( sk13 @ ^ [B: a] : $false ))]]) ).
thf(7213,plain,
! [A: a] :
( ~ $true
| ( sk7 @ A )
| ( ( sk1 @ sk23 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7151,240]) ).
thf(7214,plain,
! [A: a] :
( ( sk7 @ A )
| ( ( sk1 @ sk23 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[7213]) ).
thf(7215,plain,
sk7 @ sk23,
inference(pattern_uni,[status(thm)],[7214:[bind(A,$thf( sk23 ))]]) ).
thf(6257,plain,
! [A: a] :
( ~ $true
| ( sk7 @ A )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6207,240]) ).
thf(6258,plain,
! [A: a] :
( ( sk7 @ A )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[6257]) ).
thf(6259,plain,
( sk7
@ ( sk13
@ ^ [A: a] : $false ) ),
inference(pattern_uni,[status(thm)],[6258:[bind(A,$thf( sk13 @ ^ [B: a] : $false ))]]) ).
thf(370,plain,
! [B: a > $o,A: ( a > $o ) > $o] :
( ~ ( A
@ ^ [C: a] : $false )
| ( sk1 @ ( sk3 @ A ) )
| ~ $true
| ~ ( sk8 @ B )
| ( ( A @ sk1 )
!= ( sk9 @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11,55]) ).
thf(371,plain,
! [B: a > $o,A: ( a > $o ) > $o] :
( ~ ( A
@ ^ [C: a] : $false )
| ( sk1 @ ( sk3 @ A ) )
| ~ ( sk8 @ B )
| ( ( A @ sk1 )
!= ( sk9 @ B @ B ) ) ),
inference(simp,[status(thm)],[370]) ).
thf(438,plain,
! [B: ( a > $o ) > a > $o,A: ( a > $o ) > a > $o] :
( ~ ( sk9
@ ( A
@ ^ [C: a] : $false )
@ ( B
@ ^ [C: a] : $false ) )
| ( sk1
@ ( sk3
@ ^ [C: a > $o] : ( sk9 @ ( A @ C ) @ ( B @ C ) ) ) )
| ~ ( sk8 @ ( A @ sk1 ) )
| ( ( B @ sk1 )
!= ( A @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[371:[bind(A,$thf( ^ [E: a > $o] : ( sk9 @ ( C @ E ) @ ( D @ E ) ) )),bind(B,$thf( C @ sk1 ))]]) ).
thf(439,plain,
! [B: ( a > $o ) > a > $o,A: ( a > $o ) > a > $o] :
( ~ ( sk8 @ ( A @ sk1 ) )
| ( sk1
@ ( sk3
@ ^ [C: a > $o] : ( sk9 @ ( A @ C ) @ ( B @ C ) ) ) )
| ~ ( sk9
@ ( A
@ ^ [C: a] : $false )
@ ( B
@ ^ [C: a] : $false ) )
| ( ( B @ sk1 )
!= ( A @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[438:[]]) ).
thf(514,plain,
! [B: ( a > $o ) > a > $o,A: ( a > $o ) > a > $o] :
( ~ ( sk8 @ ( A @ sk1 ) )
| ( sk1
@ ( sk3
@ ^ [C: a > $o] : ( sk9 @ ( A @ C ) @ ( B @ C ) ) ) )
| ~ ( sk9
@ ( A
@ ^ [C: a] : $false )
@ ( B
@ ^ [C: a] : $false ) )
| ( ( B @ sk1 )
!= ( A @ sk1 ) ) ),
inference(simp,[status(thm)],[439]) ).
thf(20,plain,
! [A: a > $o] :
( sk5
| ( sk8 @ A )
| ( sk10 @ A )
| ~ ( cA @ ( sk12 @ A ) )
| ~ ( sk12 @ A @ ( sk13 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(30,plain,
! [A: a > $o] :
( sk5
| ( sk8 @ A )
| ( sk10 @ A )
| ~ ( cA @ ( sk12 @ A ) )
| ~ ( sk12 @ A @ ( sk13 @ A ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(3035,plain,
! [A: a > $o] :
( $false
| ( sk8 @ A )
| ( sk10 @ A )
| ~ ( cA @ ( sk12 @ A ) )
| ~ ( sk12 @ A @ ( sk13 @ A ) ) ),
inference(rewrite,[status(thm)],[30,50]) ).
thf(3036,plain,
! [A: a > $o] :
( ( sk8 @ A )
| ( sk10 @ A )
| ~ ( cA @ ( sk12 @ A ) )
| ~ ( sk12 @ A @ ( sk13 @ A ) ) ),
inference(simp,[status(thm)],[3035]) ).
thf(7,plain,
! [A: ( a > $o ) > $o] :
( ~ ( A
@ ^ [B: a] : $false )
| ~ ( A
@ ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
| ( A @ sk1 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(74,plain,
( ~ ( cA
@ ^ [A: a] : $false )
| ~ ( cA
@ ^ [A: a] :
( ( sk2 @ cA @ A )
| ( ( sk3 @ cA )
= A ) ) )
| ( cA @ sk1 ) ),
inference(prim_subst,[status(thm)],[7:[bind(A,$thf( cA ))]]) ).
thf(241,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ~ $true
| ( sk7 @ B )
| ( ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [C: a] : $false ) ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57,240]) ).
thf(242,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ( sk7 @ B )
| ( ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [C: a] : $false ) ) )
!= ( sk1 @ B ) ) ),
inference(simp,[status(thm)],[241]) ).
thf(243,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk7
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) ) ),
inference(pattern_uni,[status(thm)],[242:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( (=) @ ( a > $o ) @ ^ [C: a] : $false ) ))]]) ).
thf(6248,plain,
! [A: a] :
( ~ $true
| ( sk7
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6207,243]) ).
thf(6249,plain,
! [A: a] :
( ( sk7
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[6248]) ).
thf(6250,plain,
( sk7
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[6249:[bind(A,$thf( sk13 @ ^ [B: a] : $false ))]]) ).
thf(66,plain,
! [A: ( a > $o ) > $o] :
( ~ ( A
@ ^ [B: a] : $false )
| ( A @ sk1 )
| ( ( A
@ ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
!= ( A
@ ^ [B: a] : $false ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[7]) ).
thf(101,plain,
! [A: ( a > $o ) > $o] :
( ~ ( A
@ ^ [B: a] : $false )
| ( A @ sk1 )
| ( ( A
@ ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
!= ( A
@ ^ [B: a] : $false ) ) ),
inference(pre_uni,[status(thm)],[66:[]]) ).
thf(102,plain,
! [A: ( a > $o ) > $o] :
( ( A @ sk1 )
| ~ ( A
@ ^ [B: a] : $false )
| ( ( A
@ ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
!= ( A
@ ^ [B: a] : $false ) ) ),
inference(pre_uni,[status(thm)],[101:[]]) ).
thf(2876,plain,
! [A: a] :
( ( sk1
= ( ^ [B: a] : $false ) )
| ~ $true
| ( cA @ ( sk4 @ A ) )
| ( ( sk1 @ sk16 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2693,31]) ).
thf(2877,plain,
! [A: a] :
( ( sk1
= ( ^ [B: a] : $false ) )
| ( cA @ ( sk4 @ A ) )
| ( ( sk1 @ sk16 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[2876]) ).
thf(2878,plain,
( ( sk1
= ( ^ [A: a] : $false ) )
| ( cA @ ( sk4 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[2877:[bind(A,$thf( sk16 ))]]) ).
thf(3112,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( cA @ ( sk4 @ sk16 ) ) ),
inference(func_ext,[status(esa)],[2878]) ).
thf(6222,plain,
! [A: a] :
( ~ $true
| ( cA @ ( sk4 @ sk16 ) )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6207,3112]) ).
thf(6223,plain,
! [A: a] :
( ( cA @ ( sk4 @ sk16 ) )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[6222]) ).
thf(6224,plain,
cA @ ( sk4 @ sk16 ),
inference(pattern_uni,[status(thm)],[6223:[bind(A,$thf( sk13 @ ^ [B: a] : $false ))]]) ).
thf(7172,plain,
! [A: a] :
( ~ $true
| ( sk7 @ A )
| ( ( sk1 @ sk20 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7109,240]) ).
thf(7173,plain,
! [A: a] :
( ( sk7 @ A )
| ( ( sk1 @ sk20 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[7172]) ).
thf(7174,plain,
sk7 @ sk20,
inference(pattern_uni,[status(thm)],[7173:[bind(A,$thf( sk20 ))]]) ).
thf(1035,plain,
( ~ ( cA
@ ^ [A: a] : $false )
| ( cA @ ( sk2 @ cA ) )
| ( cA @ sk1 ) ),
inference(prim_subst,[status(thm)],[17:[bind(A,$thf( cA ))]]) ).
thf(7163,plain,
! [A: a] :
( ~ $true
| ( sk4 @ A @ A )
| ( ( sk1 @ sk20 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7109,36]) ).
thf(7164,plain,
! [A: a] :
( ( sk4 @ A @ A )
| ( ( sk1 @ sk20 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[7163]) ).
thf(7165,plain,
sk4 @ sk20 @ sk20,
inference(pattern_uni,[status(thm)],[7164:[bind(A,$thf( sk20 ))]]) ).
thf(2792,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk1 @ sk16 ) ),
inference(func_ext,[status(esa)],[2693]) ).
thf(5009,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ~ $true
| ( sk4 @ B @ B )
| ( ( sk1 @ sk16 )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2792,36]) ).
thf(5010,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ( sk4 @ B @ B )
| ( ( sk1 @ sk16 )
!= ( sk1 @ B ) ) ),
inference(simp,[status(thm)],[5009]) ).
thf(5011,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk4 @ sk16 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[5010:[bind(A,$thf( A )),bind(B,$thf( sk16 ))]]) ).
thf(6215,plain,
! [A: a] :
( ~ $true
| ( sk4 @ sk16 @ sk16 )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6207,5011]) ).
thf(6216,plain,
! [A: a] :
( ( sk4 @ sk16 @ sk16 )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[6215]) ).
thf(6217,plain,
sk4 @ sk16 @ sk16,
inference(pattern_uni,[status(thm)],[6216:[bind(A,$thf( sk13 @ ^ [B: a] : $false ))]]) ).
thf(7204,plain,
! [A: a] :
( ~ $true
| ( sk4 @ A @ A )
| ( ( sk1 @ sk23 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7151,36]) ).
thf(7205,plain,
! [A: a] :
( ( sk4 @ A @ A )
| ( ( sk1 @ sk23 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[7204]) ).
thf(7206,plain,
sk4 @ sk23 @ sk23,
inference(pattern_uni,[status(thm)],[7205:[bind(A,$thf( sk23 ))]]) ).
thf(68,plain,
! [A: ( a > $o ) > $o] :
( ~ ( A
@ ^ [B: a] : $false )
| ( A @ sk1 )
| ( ( A
@ ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
!= ( ~ ( A @ sk1 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[7]) ).
thf(98,plain,
! [A: ( a > $o ) > $o] :
( ( A @ sk1 )
| ~ ( A
@ ^ [B: a] : $false )
| ( ( A
@ ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
!= ( ~ ( A @ sk1 ) ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(5,plain,
! [C: a,B: a > $o,A: a > $o] :
( sk5
| ~ ( sk9 @ A @ B )
| ~ ( A @ C )
| ( sk9 @ A
@ ^ [D: a] :
( ( B @ D )
| ( C = D ) ) )
| ~ ( sk8 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(27,plain,
! [C: a,B: a > $o,A: a > $o] :
( sk5
| ~ ( sk9 @ A @ B )
| ~ ( A @ C )
| ( sk9 @ A
@ ^ [D: a] :
( ( B @ D )
| ( C = D ) ) )
| ~ ( sk8 @ A ) ),
inference(simp,[status(thm)],[5]) ).
thf(1730,plain,
! [C: a,B: a > $o,A: a > $o] :
( $false
| ~ ( sk9 @ A @ B )
| ~ ( A @ C )
| ( sk9 @ A
@ ^ [D: a] :
( ( B @ D )
| ( C = D ) ) )
| ~ ( sk8 @ A ) ),
inference(rewrite,[status(thm)],[27,50]) ).
thf(1731,plain,
! [C: a,B: a > $o,A: a > $o] :
( ~ ( sk9 @ A @ B )
| ~ ( A @ C )
| ( sk9 @ A
@ ^ [D: a] :
( ( B @ D )
| ( C = D ) ) )
| ~ ( sk8 @ A ) ),
inference(simp,[status(thm)],[1730]) ).
thf(4262,plain,
! [A: a > $o] :
( ( cA @ ( sk12 @ sk7 ) )
| ( sk9 @ A
@ ^ [B: a] : $false )
| ~ $true
| ( ( sk8 @ sk7 )
!= ( sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4247,2403]) ).
thf(4263,plain,
! [A: a > $o] :
( ( cA @ ( sk12 @ sk7 ) )
| ( sk9 @ A
@ ^ [B: a] : $false )
| ( ( sk8 @ sk7 )
!= ( sk8 @ A ) ) ),
inference(simp,[status(thm)],[4262]) ).
thf(4264,plain,
( ( cA @ ( sk12 @ sk7 ) )
| ( sk9 @ sk7
@ ^ [A: a] : $false ) ),
inference(pattern_uni,[status(thm)],[4263:[bind(A,$thf( sk7 ))]]) ).
thf(6268,plain,
! [A: a] :
( ~ $true
| ( cA @ ( sk4 @ A ) )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6207,31]) ).
thf(6269,plain,
! [A: a] :
( ( cA @ ( sk4 @ A ) )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[6268]) ).
thf(6270,plain,
( cA
@ ( sk4
@ ( sk13
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[6269:[bind(A,$thf( sk13 @ ^ [B: a] : $false ))]]) ).
thf(62,plain,
! [A: ( a > $o ) > $o] :
( ( sk1
= ( ^ [B: a] : $false ) )
| ~ $true
| ~ ( A
@ ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
| ( A @ sk1 )
| ( ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) )
!= ( A
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[44,7]) ).
thf(63,plain,
! [A: ( a > $o ) > $o] :
( ( sk1
= ( ^ [B: a] : $false ) )
| ~ ( A
@ ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
| ( A @ sk1 )
| ( ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) )
!= ( A
@ ^ [B: a] : $false ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(83,plain,
! [A: ( a > $o ) > $o] :
( ( sk1
= ( ^ [B: a] : $false ) )
| ( ( ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
!= ( ^ [B: a] :
( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [C: a] :
( ( sk2 @ A @ C )
| ( ( sk3 @ A )
= C ) ) )
@ B )
| ( ( sk3
@ ( (=) @ ( a > $o )
@ ^ [C: a] :
( ( sk2 @ A @ C )
| ( ( sk3 @ A )
= C ) ) ) )
= B ) ) ) )
| ( ( ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
= sk1 )
| ( ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) )
!= ( ( ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
= ( ^ [B: a] : $false ) ) ) ),
inference(replace_leibeq,[status(thm)],[63:[bind(A,$thf( (=) @ ( a > $o ) @ ^ [B: a] : ( ( sk2 @ A @ B ) | ( ( sk3 @ A ) = B ) ) ))]]) ).
thf(90,plain,
! [A: ( a > $o ) > $o] :
( ( ( ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
!= ( ^ [B: a] :
( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [C: a] :
( ( sk2 @ A @ C )
| ( ( sk3 @ A )
= C ) ) )
@ B )
| ( ( sk3
@ ( (=) @ ( a > $o )
@ ^ [C: a] :
( ( sk2 @ A @ C )
| ( ( sk3 @ A )
= C ) ) ) )
= B ) ) ) )
| ( ( ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
= sk1 )
| ( sk1
= ( ^ [B: a] : $false ) )
| ( ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) )
!= ( ( ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
= ( ^ [B: a] : $false ) ) ) ),
inference(lifteq,[status(thm)],[83]) ).
thf(6242,plain,
! [A: a] :
( ~ $true
| ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6207,57]) ).
thf(6243,plain,
! [A: a] :
( ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[6242]) ).
thf(6244,plain,
( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[6243:[bind(A,$thf( sk13 @ ^ [B: a] : $false ))]]) ).
thf(7152,plain,
! [A: ( a > $o ) > $o] :
( ( ( ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
!= ( ^ [B: a] :
( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [C: a] :
( ( sk2 @ A @ C )
| ( ( sk3 @ A )
= C ) ) )
@ B )
| ( ( sk3
@ ( (=) @ ( a > $o )
@ ^ [C: a] :
( ( sk2 @ A @ C )
| ( ( sk3 @ A )
= C ) ) ) )
= B ) ) ) )
| ( ( ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
= sk1 )
| ( sk1
= ( ^ [B: a] : $false ) )
| ( ( ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
!= ( ^ [B: a] : $false ) ) ),
inference(rewrite,[status(thm)],[90,6244]) ).
thf(7153,plain,
! [A: ( a > $o ) > $o] :
( ( ( ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
!= ( ^ [B: a] :
( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [C: a] :
( ( sk2 @ A @ C )
| ( ( sk3 @ A )
= C ) ) )
@ B )
| ( ( sk3
@ ( (=) @ ( a > $o )
@ ^ [C: a] :
( ( sk2 @ A @ C )
| ( ( sk3 @ A )
= C ) ) ) )
= B ) ) ) )
| ( ( ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
= sk1 )
| ( ( ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
!= ( ^ [B: a] : $false ) ) ),
inference(simplifyReflect,[status(thm)],[7152,7108]) ).
thf(7154,plain,
! [A: ( a > $o ) > $o] :
( ( ( ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
!= ( ^ [B: a] : $false ) )
| ( ( ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
!= ( ^ [B: a] :
( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [C: a] :
( ( sk2 @ A @ C )
| ( ( sk3 @ A )
= C ) ) )
@ B )
| ( ( sk3
@ ( (=) @ ( a > $o )
@ ^ [C: a] :
( ( sk2 @ A @ C )
| ( ( sk3 @ A )
= C ) ) ) )
= B ) ) ) )
| ( ( ^ [B: a] :
( ( sk2 @ A @ B )
| ( ( sk3 @ A )
= B ) ) )
= sk1 ) ),
inference(lifteq,[status(thm)],[7153]) ).
thf(4991,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ~ $true
| ( sk4 @ B @ B )
| ( ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [C: a] : $false ) ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57,36]) ).
thf(4992,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ( sk4 @ B @ B )
| ( ( sk1
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [C: a] : $false ) ) )
!= ( sk1 @ B ) ) ),
inference(simp,[status(thm)],[4991]) ).
thf(4993,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk4
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) )
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) ) ),
inference(pattern_uni,[status(thm)],[4992:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( (=) @ ( a > $o ) @ ^ [C: a] : $false ) ))]]) ).
thf(6260,plain,
! [A: a] :
( ~ $true
| ( sk4
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) )
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6207,4993]) ).
thf(6261,plain,
! [A: a] :
( ( sk4
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) )
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [B: a] : $false ) ) )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[6260]) ).
thf(6262,plain,
( sk4
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) )
@ ( sk3
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[6261:[bind(A,$thf( sk13 @ ^ [B: a] : $false ))]]) ).
thf(6228,plain,
! [A: a] :
( ~ $true
| ( sk4 @ A @ A )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6207,36]) ).
thf(6229,plain,
! [A: a] :
( ( sk4 @ A @ A )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[6228]) ).
thf(6230,plain,
( sk4
@ ( sk13
@ ^ [A: a] : $false )
@ ( sk13
@ ^ [A: a] : $false ) ),
inference(pattern_uni,[status(thm)],[6229:[bind(A,$thf( sk13 @ ^ [B: a] : $false ))]]) ).
thf(6892,plain,
( ( sk2
@ ( (=) @ ( a > $o )
@ ^ [A: a] : $false )
@ sk21 )
| ( sk1 @ sk22 ) ),
inference(func_ext,[status(esa)],[6238]) ).
thf(8853,plain,
( $false
| ( sk1 @ sk22 ) ),
inference(rewrite,[status(thm)],[6892,6235]) ).
thf(8854,plain,
sk1 @ sk22,
inference(simp,[status(thm)],[8853]) ).
thf(6271,plain,
! [A: a] :
( ~ $true
| ( sk1 @ sk16 )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6207,2792]) ).
thf(6272,plain,
! [A: a] :
( ( sk1 @ sk16 )
| ( ( sk1
@ ( sk13
@ ^ [B: a] : $false ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[6271]) ).
thf(6273,plain,
sk1 @ sk16,
inference(pattern_uni,[status(thm)],[6272:[bind(A,$thf( sk13 @ ^ [B: a] : $false ))]]) ).
thf(9491,plain,
$false,
inference(e,[status(thm)],[4247,52,5579,6267,3723,7223,7109,4289,36,379,4614,4326,7182,6253,2403,7215,6259,4173,514,3036,74,6250,102,6235,4227,6207,6224,7174,4081,1035,7165,17,6217,7,7206,98,240,1731,4264,6270,3,7154,7151,4113,50,6244,31,6262,11,6230,8854,55,210,4303,6273,7108,2470]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU909^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.21 % Computer : n020.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 14:45:49 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.64/0.53 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.03/0.63 % [INFO] Parsing done (106ms).
% 1.03/0.64 % [INFO] Running in sequential loop mode.
% 1.40/0.84 % [INFO] eprover registered as external prover.
% 1.40/0.84 % [INFO] Scanning for conjecture ...
% 1.67/0.90 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.67/0.92 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.67/0.92 % [INFO] Problem is higher-order (TPTP THF).
% 1.67/0.93 % [INFO] Type checking passed.
% 1.67/0.93 % [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 ...
% 82.55/20.23 % External prover 'e' found a proof!
% 82.55/20.23 % [INFO] Killing All external provers ...
% 82.55/20.23 % Time passed: 19925ms (effective reasoning time: 19589ms)
% 82.55/20.23 % 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)>
% 82.55/20.24 % Axioms used in derivation (0):
% 82.55/20.24 % No. of inferences in proof: 240
% 82.55/20.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19925 ms resp. 19589 ms w/o parsing
% 68.80/20.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 68.80/20.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------