TSTP Solution File: SEV260^5 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV260^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 16:02:31 EDT 2024
% Result : Theorem 0.11s 0.36s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 687 ( 338 equ; 0 cnn)
% Maximal formula atoms : 64 ( 23 avg)
% Number of connectives : 1108 ( 196 ~; 109 |; 214 &; 482 @)
% ( 0 <=>; 91 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 363 ( 363 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 5 con; 0-2 aty)
% ( 0 !!; 16 ??; 0 @@+; 0 @@-)
% Number of variables : 467 ( 178 ^ 235 !; 54 ?; 467 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_7,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_11,type,
sK0: ( b > $o ) > $o ).
thf(func_def_12,type,
sK1: a > b ).
thf(func_def_13,type,
sK2: ( a > $o ) > $o ).
thf(func_def_14,type,
sK3: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_15,type,
sK4: b > $o ).
thf(func_def_16,type,
sK5: a > $o ).
thf(func_def_17,type,
sK6: a > $o ).
thf(func_def_18,type,
sK7: ( ( b > $o ) > $o ) > b > $o ).
thf(func_def_20,type,
ph9:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK10: a ).
thf(func_def_22,type,
sK11: a ).
thf(f62,plain,
$false,
inference(subsumption_resolution,[],[f61,f37]) ).
thf(f37,plain,
( ( sK0
@ ^ [Y0: b] :
~ ( sK4 @ Y0 ) )
= $true ),
inference(equality_resolution,[],[f25]) ).
thf(f25,plain,
! [X10: b > $o] :
( ( ( sK0 @ X10 )
= $true )
| ( ( ^ [Y0: b] :
~ ( sK4 @ Y0 ) )
!= X10 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f16,plain,
( ! [X3: a > $o,X4: ( a > $o ) > $o] :
( ( ( sK2 @ X3 )
= $true )
| ( ( ( sK2 @ ( sK3 @ X4 ) )
!= $true )
& ( ( X4 @ ( sK3 @ X4 ) )
= $true ) )
| ( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X4 @ Y1 ) ) ) )
!= X3 ) )
& ! [X6: b > $o] :
( ( ( sK0 @ X6 )
= $true )
| ( ( ^ [Y0: b] : ~ $false )
!= X6 ) )
& ( ( ^ [Y0: a] : ( sK4 @ ( sK1 @ Y0 ) ) )
= sK5 )
& ( sK6
= ( ^ [Y0: a] :
~ ( sK5 @ Y0 ) ) )
& ( ( sK2 @ sK6 )
!= $true )
& ! [X10: b > $o] :
( ( ( sK0 @ X10 )
= $true )
| ( ( ^ [Y0: b] :
~ ( sK4 @ Y0 ) )
!= X10 ) )
& ! [X11: b > $o] :
( ( ( sK0 @ X11 )
= $true )
| ( ( ^ [Y0: b] : $false )
!= X11 ) )
& ! [X12: b > $o] :
( ( ( sK0 @ X12 )
!= $true )
| ! [X13: a > $o] :
( ( ( ^ [Y0: a] : ( X12 @ ( sK1 @ Y0 ) ) )
!= X13 )
| ( ( sK2 @ X13 )
= $true ) ) )
& ! [X14: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= X14 )
| ( ( sK2 @ X14 )
= $true ) )
& ! [X15: b > $o,X16: ( b > $o ) > $o] :
( ( ( sK0 @ X15 )
= $true )
| ( ( ^ [Y0: b] :
( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( X16 @ Y1 ) ) ) )
!= X15 )
| ( ( ( sK0 @ ( sK7 @ X16 ) )
!= $true )
& ( ( X16 @ ( sK7 @ X16 ) )
= $true ) ) )
& ! [X18: a > $o,X19: a > $o,X20: a > $o] :
( ( ( sK2 @ X19 )
= $true )
| ( ( sK2 @ X18 )
!= $true )
| ( ( ^ [Y0: a] :
( ( X20 @ Y0 )
& ( X18 @ Y0 ) ) )
!= X19 )
| ( ( sK2 @ X20 )
!= $true ) )
& ! [X21: a > $o] :
( ( ( sK2 @ X21 )
= $true )
| ( ( ^ [Y0: a] : ~ $false )
!= X21 ) )
& ! [X22: b > $o,X23: b > $o,X24: b > $o] :
( ( ( sK0 @ X23 )
!= $true )
| ( ( ^ [Y0: b] :
( ( X22 @ Y0 )
& ( X23 @ Y0 ) ) )
!= X24 )
| ( ( sK0 @ X24 )
= $true )
| ( ( sK0 @ X22 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f9,f15,f14,f13,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: ( b > $o ) > $o,X1: a > b,X2: ( a > $o ) > $o] :
( ! [X3: a > $o,X4: ( a > $o ) > $o] :
( ( ( X2 @ X3 )
= $true )
| ? [X5: a > $o] :
( ( ( X2 @ X5 )
!= $true )
& ( ( X4 @ X5 )
= $true ) )
| ( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X4 @ Y1 ) ) ) )
!= X3 ) )
& ! [X6: b > $o] :
( ( ( X0 @ X6 )
= $true )
| ( ( ^ [Y0: b] : ~ $false )
!= X6 ) )
& ? [X7: b > $o] :
( ? [X8: a > $o] :
( ( ( ^ [Y0: a] : ( X7 @ ( X1 @ Y0 ) ) )
= X8 )
& ? [X9: a > $o] :
( ( ( ^ [Y0: a] :
~ ( X8 @ Y0 ) )
= X9 )
& ( ( X2 @ X9 )
!= $true ) ) )
& ! [X10: b > $o] :
( ( ( X0 @ X10 )
= $true )
| ( ( ^ [Y0: b] :
~ ( X7 @ Y0 ) )
!= X10 ) ) )
& ! [X11: b > $o] :
( ( ( X0 @ X11 )
= $true )
| ( ( ^ [Y0: b] : $false )
!= X11 ) )
& ! [X12: b > $o] :
( ( ( X0 @ X12 )
!= $true )
| ! [X13: a > $o] :
( ( ( ^ [Y0: a] : ( X12 @ ( X1 @ Y0 ) ) )
!= X13 )
| ( ( X2 @ X13 )
= $true ) ) )
& ! [X14: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= X14 )
| ( ( X2 @ X14 )
= $true ) )
& ! [X15: b > $o,X16: ( b > $o ) > $o] :
( ( ( X0 @ X15 )
= $true )
| ( ( ^ [Y0: b] :
( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( X16 @ Y1 ) ) ) )
!= X15 )
| ? [X17: b > $o] :
( ( ( X0 @ X17 )
!= $true )
& ( ( X16 @ X17 )
= $true ) ) )
& ! [X18: a > $o,X19: a > $o,X20: a > $o] :
( ( ( X2 @ X19 )
= $true )
| ( ( X2 @ X18 )
!= $true )
| ( ( ^ [Y0: a] :
( ( X20 @ Y0 )
& ( X18 @ Y0 ) ) )
!= X19 )
| ( ( X2 @ X20 )
!= $true ) )
& ! [X21: a > $o] :
( ( ( X2 @ X21 )
= $true )
| ( ( ^ [Y0: a] : ~ $false )
!= X21 ) )
& ! [X22: b > $o,X23: b > $o,X24: b > $o] :
( ( ( X0 @ X23 )
!= $true )
| ( ( ^ [Y0: b] :
( ( X22 @ Y0 )
& ( X23 @ Y0 ) ) )
!= X24 )
| ( ( X0 @ X24 )
= $true )
| ( ( X0 @ X22 )
!= $true ) ) )
=> ( ! [X4: ( a > $o ) > $o,X3: a > $o] :
( ( ( sK2 @ X3 )
= $true )
| ? [X5: a > $o] :
( ( ( sK2 @ X5 )
!= $true )
& ( ( X4 @ X5 )
= $true ) )
| ( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X4 @ Y1 ) ) ) )
!= X3 ) )
& ! [X6: b > $o] :
( ( ( sK0 @ X6 )
= $true )
| ( ( ^ [Y0: b] : ~ $false )
!= X6 ) )
& ? [X7: b > $o] :
( ? [X8: a > $o] :
( ( ( ^ [Y0: a] : ( X7 @ ( sK1 @ Y0 ) ) )
= X8 )
& ? [X9: a > $o] :
( ( ( ^ [Y0: a] :
~ ( X8 @ Y0 ) )
= X9 )
& ( ( sK2 @ X9 )
!= $true ) ) )
& ! [X10: b > $o] :
( ( ( sK0 @ X10 )
= $true )
| ( ( ^ [Y0: b] :
~ ( X7 @ Y0 ) )
!= X10 ) ) )
& ! [X11: b > $o] :
( ( ( sK0 @ X11 )
= $true )
| ( ( ^ [Y0: b] : $false )
!= X11 ) )
& ! [X12: b > $o] :
( ( ( sK0 @ X12 )
!= $true )
| ! [X13: a > $o] :
( ( ( ^ [Y0: a] : ( X12 @ ( sK1 @ Y0 ) ) )
!= X13 )
| ( ( sK2 @ X13 )
= $true ) ) )
& ! [X14: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= X14 )
| ( ( sK2 @ X14 )
= $true ) )
& ! [X16: ( b > $o ) > $o,X15: b > $o] :
( ( ( sK0 @ X15 )
= $true )
| ( ( ^ [Y0: b] :
( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( X16 @ Y1 ) ) ) )
!= X15 )
| ? [X17: b > $o] :
( ( ( sK0 @ X17 )
!= $true )
& ( ( X16 @ X17 )
= $true ) ) )
& ! [X20: a > $o,X19: a > $o,X18: a > $o] :
( ( ( sK2 @ X19 )
= $true )
| ( ( sK2 @ X18 )
!= $true )
| ( ( ^ [Y0: a] :
( ( X20 @ Y0 )
& ( X18 @ Y0 ) ) )
!= X19 )
| ( ( sK2 @ X20 )
!= $true ) )
& ! [X21: a > $o] :
( ( ( sK2 @ X21 )
= $true )
| ( ( ^ [Y0: a] : ~ $false )
!= X21 ) )
& ! [X24: b > $o,X23: b > $o,X22: b > $o] :
( ( ( sK0 @ X23 )
!= $true )
| ( ( ^ [Y0: b] :
( ( X22 @ Y0 )
& ( X23 @ Y0 ) ) )
!= X24 )
| ( ( sK0 @ X24 )
= $true )
| ( ( sK0 @ X22 )
!= $true ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f11,plain,
! [X4: ( a > $o ) > $o] :
( ? [X5: a > $o] :
( ( ( sK2 @ X5 )
!= $true )
& ( ( X4 @ X5 )
= $true ) )
=> ( ( ( sK2 @ ( sK3 @ X4 ) )
!= $true )
& ( ( X4 @ ( sK3 @ X4 ) )
= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
( ? [X7: b > $o] :
( ? [X8: a > $o] :
( ( ( ^ [Y0: a] : ( X7 @ ( sK1 @ Y0 ) ) )
= X8 )
& ? [X9: a > $o] :
( ( ( ^ [Y0: a] :
~ ( X8 @ Y0 ) )
= X9 )
& ( ( sK2 @ X9 )
!= $true ) ) )
& ! [X10: b > $o] :
( ( ( sK0 @ X10 )
= $true )
| ( ( ^ [Y0: b] :
~ ( X7 @ Y0 ) )
!= X10 ) ) )
=> ( ? [X8: a > $o] :
( ( ( ^ [Y0: a] : ( sK4 @ ( sK1 @ Y0 ) ) )
= X8 )
& ? [X9: a > $o] :
( ( ( ^ [Y0: a] :
~ ( X8 @ Y0 ) )
= X9 )
& ( ( sK2 @ X9 )
!= $true ) ) )
& ! [X10: b > $o] :
( ( ( sK0 @ X10 )
= $true )
| ( ( ^ [Y0: b] :
~ ( sK4 @ Y0 ) )
!= X10 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
( ? [X8: a > $o] :
( ( ( ^ [Y0: a] : ( sK4 @ ( sK1 @ Y0 ) ) )
= X8 )
& ? [X9: a > $o] :
( ( ( ^ [Y0: a] :
~ ( X8 @ Y0 ) )
= X9 )
& ( ( sK2 @ X9 )
!= $true ) ) )
=> ( ( ( ^ [Y0: a] : ( sK4 @ ( sK1 @ Y0 ) ) )
= sK5 )
& ? [X9: a > $o] :
( ( ( ^ [Y0: a] :
~ ( sK5 @ Y0 ) )
= X9 )
& ( ( sK2 @ X9 )
!= $true ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f14,plain,
( ? [X9: a > $o] :
( ( ( ^ [Y0: a] :
~ ( sK5 @ Y0 ) )
= X9 )
& ( ( sK2 @ X9 )
!= $true ) )
=> ( ( sK6
= ( ^ [Y0: a] :
~ ( sK5 @ Y0 ) ) )
& ( ( sK2 @ sK6 )
!= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f15,plain,
! [X16: ( b > $o ) > $o] :
( ? [X17: b > $o] :
( ( ( sK0 @ X17 )
!= $true )
& ( ( X16 @ X17 )
= $true ) )
=> ( ( ( sK0 @ ( sK7 @ X16 ) )
!= $true )
& ( ( X16 @ ( sK7 @ X16 ) )
= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f9,plain,
? [X0: ( b > $o ) > $o,X1: a > b,X2: ( a > $o ) > $o] :
( ! [X3: a > $o,X4: ( a > $o ) > $o] :
( ( ( X2 @ X3 )
= $true )
| ? [X5: a > $o] :
( ( ( X2 @ X5 )
!= $true )
& ( ( X4 @ X5 )
= $true ) )
| ( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X4 @ Y1 ) ) ) )
!= X3 ) )
& ! [X6: b > $o] :
( ( ( X0 @ X6 )
= $true )
| ( ( ^ [Y0: b] : ~ $false )
!= X6 ) )
& ? [X7: b > $o] :
( ? [X8: a > $o] :
( ( ( ^ [Y0: a] : ( X7 @ ( X1 @ Y0 ) ) )
= X8 )
& ? [X9: a > $o] :
( ( ( ^ [Y0: a] :
~ ( X8 @ Y0 ) )
= X9 )
& ( ( X2 @ X9 )
!= $true ) ) )
& ! [X10: b > $o] :
( ( ( X0 @ X10 )
= $true )
| ( ( ^ [Y0: b] :
~ ( X7 @ Y0 ) )
!= X10 ) ) )
& ! [X11: b > $o] :
( ( ( X0 @ X11 )
= $true )
| ( ( ^ [Y0: b] : $false )
!= X11 ) )
& ! [X12: b > $o] :
( ( ( X0 @ X12 )
!= $true )
| ! [X13: a > $o] :
( ( ( ^ [Y0: a] : ( X12 @ ( X1 @ Y0 ) ) )
!= X13 )
| ( ( X2 @ X13 )
= $true ) ) )
& ! [X14: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= X14 )
| ( ( X2 @ X14 )
= $true ) )
& ! [X15: b > $o,X16: ( b > $o ) > $o] :
( ( ( X0 @ X15 )
= $true )
| ( ( ^ [Y0: b] :
( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( X16 @ Y1 ) ) ) )
!= X15 )
| ? [X17: b > $o] :
( ( ( X0 @ X17 )
!= $true )
& ( ( X16 @ X17 )
= $true ) ) )
& ! [X18: a > $o,X19: a > $o,X20: a > $o] :
( ( ( X2 @ X19 )
= $true )
| ( ( X2 @ X18 )
!= $true )
| ( ( ^ [Y0: a] :
( ( X20 @ Y0 )
& ( X18 @ Y0 ) ) )
!= X19 )
| ( ( X2 @ X20 )
!= $true ) )
& ! [X21: a > $o] :
( ( ( X2 @ X21 )
= $true )
| ( ( ^ [Y0: a] : ~ $false )
!= X21 ) )
& ! [X22: b > $o,X23: b > $o,X24: b > $o] :
( ( ( X0 @ X23 )
!= $true )
| ( ( ^ [Y0: b] :
( ( X22 @ Y0 )
& ( X23 @ Y0 ) ) )
!= X24 )
| ( ( X0 @ X24 )
= $true )
| ( ( X0 @ X22 )
!= $true ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,plain,
? [X0: ( b > $o ) > $o,X1: a > b,X2: ( a > $o ) > $o] :
( ! [X18: a > $o,X19: ( a > $o ) > $o] :
( ( ( X2 @ X18 )
= $true )
| ? [X20: a > $o] :
( ( ( X2 @ X20 )
!= $true )
& ( ( X19 @ X20 )
= $true ) )
| ( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X19 @ Y1 ) ) ) )
!= X18 ) )
& ! [X14: b > $o] :
( ( ( X0 @ X14 )
= $true )
| ( ( ^ [Y0: b] : ~ $false )
!= X14 ) )
& ? [X21: b > $o] :
( ? [X23: a > $o] :
( ( ( ^ [Y0: a] : ( X21 @ ( X1 @ Y0 ) ) )
= X23 )
& ? [X24: a > $o] :
( ( ( ^ [Y0: a] :
~ ( X23 @ Y0 ) )
= X24 )
& ( ( X2 @ X24 )
!= $true ) ) )
& ! [X22: b > $o] :
( ( ( X0 @ X22 )
= $true )
| ( ( ^ [Y0: b] :
~ ( X21 @ Y0 ) )
!= X22 ) ) )
& ! [X17: b > $o] :
( ( ( X0 @ X17 )
= $true )
| ( ( ^ [Y0: b] : $false )
!= X17 ) )
& ! [X6: b > $o] :
( ( ( X0 @ X6 )
!= $true )
| ! [X7: a > $o] :
( ( ( ^ [Y0: a] : ( X6 @ ( X1 @ Y0 ) ) )
!= X7 )
| ( ( X2 @ X7 )
= $true ) ) )
& ! [X15: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= X15 )
| ( ( X2 @ X15 )
= $true ) )
& ! [X8: b > $o,X9: ( b > $o ) > $o] :
( ( ( X0 @ X8 )
= $true )
| ( ( ^ [Y0: b] :
( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( X9 @ Y1 ) ) ) )
!= X8 )
| ? [X10: b > $o] :
( ( ( X0 @ X10 )
!= $true )
& ( ( X9 @ X10 )
= $true ) ) )
& ! [X3: a > $o,X4: a > $o,X5: a > $o] :
( ( ( X2 @ X4 )
= $true )
| ( ( X2 @ X3 )
!= $true )
| ( ( ^ [Y0: a] :
( ( X5 @ Y0 )
& ( X3 @ Y0 ) ) )
!= X4 )
| ( ( X2 @ X5 )
!= $true ) )
& ! [X16: a > $o] :
( ( ( X2 @ X16 )
= $true )
| ( ( ^ [Y0: a] : ~ $false )
!= X16 ) )
& ! [X11: b > $o,X12: b > $o,X13: b > $o] :
( ( ( X0 @ X12 )
!= $true )
| ( ( ^ [Y0: b] :
( ( X11 @ Y0 )
& ( X12 @ Y0 ) ) )
!= X13 )
| ( ( X0 @ X13 )
= $true )
| ( ( X0 @ X11 )
!= $true ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
? [X0: ( b > $o ) > $o,X1: a > b,X2: ( a > $o ) > $o] :
( ? [X21: b > $o] :
( ? [X23: a > $o] :
( ( ( ^ [Y0: a] : ( X21 @ ( X1 @ Y0 ) ) )
= X23 )
& ? [X24: a > $o] :
( ( ( ^ [Y0: a] :
~ ( X23 @ Y0 ) )
= X24 )
& ( ( X2 @ X24 )
!= $true ) ) )
& ! [X22: b > $o] :
( ( ( X0 @ X22 )
= $true )
| ( ( ^ [Y0: b] :
~ ( X21 @ Y0 ) )
!= X22 ) ) )
& ! [X16: a > $o] :
( ( ( X2 @ X16 )
= $true )
| ( ( ^ [Y0: a] : ~ $false )
!= X16 ) )
& ! [X11: b > $o,X12: b > $o,X13: b > $o] :
( ( ( X0 @ X13 )
= $true )
| ( ( X0 @ X12 )
!= $true )
| ( ( ^ [Y0: b] :
( ( X11 @ Y0 )
& ( X12 @ Y0 ) ) )
!= X13 )
| ( ( X0 @ X11 )
!= $true ) )
& ! [X18: a > $o,X19: ( a > $o ) > $o] :
( ( ( X2 @ X18 )
= $true )
| ( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X19 @ Y1 ) ) ) )
!= X18 )
| ? [X20: a > $o] :
( ( ( X2 @ X20 )
!= $true )
& ( ( X19 @ X20 )
= $true ) ) )
& ! [X17: b > $o] :
( ( ( X0 @ X17 )
= $true )
| ( ( ^ [Y0: b] : $false )
!= X17 ) )
& ! [X8: b > $o,X9: ( b > $o ) > $o] :
( ( ( X0 @ X8 )
= $true )
| ? [X10: b > $o] :
( ( ( X0 @ X10 )
!= $true )
& ( ( X9 @ X10 )
= $true ) )
| ( ( ^ [Y0: b] :
( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( X9 @ Y1 ) ) ) )
!= X8 ) )
& ! [X3: a > $o,X4: a > $o,X5: a > $o] :
( ( ( X2 @ X4 )
= $true )
| ( ( ^ [Y0: a] :
( ( X5 @ Y0 )
& ( X3 @ Y0 ) ) )
!= X4 )
| ( ( X2 @ X5 )
!= $true )
| ( ( X2 @ X3 )
!= $true ) )
& ! [X15: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= X15 )
| ( ( X2 @ X15 )
= $true ) )
& ! [X6: b > $o] :
( ( ( X0 @ X6 )
!= $true )
| ! [X7: a > $o] :
( ( ( ^ [Y0: a] : ( X6 @ ( X1 @ Y0 ) ) )
!= X7 )
| ( ( X2 @ X7 )
= $true ) ) )
& ! [X14: b > $o] :
( ( ( X0 @ X14 )
= $true )
| ( ( ^ [Y0: b] : ~ $false )
!= X14 ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ! [X0: ( b > $o ) > $o,X1: a > b,X2: ( a > $o ) > $o] :
( ( ! [X16: a > $o] :
( ( ( ^ [Y0: a] : ~ $false )
= X16 )
=> ( ( X2 @ X16 )
= $true ) )
& ! [X11: b > $o,X12: b > $o,X13: b > $o] :
( ( ( ( X0 @ X12 )
= $true )
& ( ( ^ [Y0: b] :
( ( X11 @ Y0 )
& ( X12 @ Y0 ) ) )
= X13 )
& ( ( X0 @ X11 )
= $true ) )
=> ( ( X0 @ X13 )
= $true ) )
& ! [X18: a > $o,X19: ( a > $o ) > $o] :
( ( ( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X19 @ Y1 ) ) ) )
= X18 )
& ! [X20: a > $o] :
( ( ( X19 @ X20 )
= $true )
=> ( ( X2 @ X20 )
= $true ) ) )
=> ( ( X2 @ X18 )
= $true ) )
& ! [X17: b > $o] :
( ( ( ^ [Y0: b] : $false )
= X17 )
=> ( ( X0 @ X17 )
= $true ) )
& ! [X8: b > $o,X9: ( b > $o ) > $o] :
( ( ! [X10: b > $o] :
( ( ( X9 @ X10 )
= $true )
=> ( ( X0 @ X10 )
= $true ) )
& ( ( ^ [Y0: b] :
( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( X9 @ Y1 ) ) ) )
= X8 ) )
=> ( ( X0 @ X8 )
= $true ) )
& ! [X3: a > $o,X4: a > $o,X5: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X5 @ Y0 )
& ( X3 @ Y0 ) ) )
= X4 )
& ( ( X2 @ X5 )
= $true )
& ( ( X2 @ X3 )
= $true ) )
=> ( ( X2 @ X4 )
= $true ) )
& ! [X15: a > $o] :
( ( ( ^ [Y0: a] : $false )
= X15 )
=> ( ( X2 @ X15 )
= $true ) )
& ! [X6: b > $o] :
( ( ( X0 @ X6 )
= $true )
=> ! [X7: a > $o] :
( ( ( ^ [Y0: a] : ( X6 @ ( X1 @ Y0 ) ) )
= X7 )
=> ( ( X2 @ X7 )
= $true ) ) )
& ! [X14: b > $o] :
( ( ( ^ [Y0: b] : ~ $false )
= X14 )
=> ( ( X0 @ X14 )
= $true ) ) )
=> ! [X21: b > $o] :
( ! [X22: b > $o] :
( ( ( ^ [Y0: b] :
~ ( X21 @ Y0 ) )
= X22 )
=> ( ( X0 @ X22 )
= $true ) )
=> ! [X23: a > $o] :
( ( ( ^ [Y0: a] : ( X21 @ ( X1 @ Y0 ) ) )
= X23 )
=> ! [X24: a > $o] :
( ( ( ^ [Y0: a] :
~ ( X23 @ Y0 ) )
= X24 )
=> ( ( X2 @ X24 )
= $true ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f5,plain,
~ ! [X0: ( b > $o ) > $o,X1: a > b,X2: ( a > $o ) > $o] :
( ( ! [X3: a > $o,X4: a > $o,X5: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X5 @ Y0 )
& ( X3 @ Y0 ) ) )
= X4 )
& ( ( X2 @ X5 )
= $true )
& ( ( X2 @ X3 )
= $true ) )
=> ( ( X2 @ X4 )
= $true ) )
& ! [X7: b > $o] :
( ( ( X0 @ X7 )
= $true )
=> ! [X8: a > $o] :
( ( ( ^ [Y0: a] : ( X7 @ ( X1 @ Y0 ) ) )
= X8 )
=> ( ( X2 @ X8 )
= $true ) ) )
& ! [X10: b > $o,X11: ( b > $o ) > $o] :
( ( ( ( ^ [Y0: b] :
( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( X11 @ Y1 ) ) ) )
= X10 )
& ! [X14: b > $o] :
( ( ( X11 @ X14 )
= $true )
=> ( ( X0 @ X14 )
= $true ) ) )
=> ( ( X0 @ X10 )
= $true ) )
& ! [X15: b > $o,X16: b > $o,X17: b > $o] :
( ( ( ( X0 @ X16 )
= $true )
& ( ( X0 @ X15 )
= $true )
& ( ( ^ [Y0: b] :
( ( X15 @ Y0 )
& ( X16 @ Y0 ) ) )
= X17 ) )
=> ( ( X0 @ X17 )
= $true ) )
& ! [X19: b > $o] :
( ( ( ^ [Y0: b] : ~ $false )
= X19 )
=> ( ( X0 @ X19 )
= $true ) )
& ! [X21: a > $o] :
( ( ( ^ [Y0: a] : $false )
= X21 )
=> ( ( X2 @ X21 )
= $true ) )
& ! [X23: a > $o] :
( ( ( ^ [Y0: a] : ~ $false )
= X23 )
=> ( ( X2 @ X23 )
= $true ) )
& ! [X25: b > $o] :
( ( ( ^ [Y0: b] : $false )
= X25 )
=> ( ( X0 @ X25 )
= $true ) )
& ! [X27: a > $o,X28: ( a > $o ) > $o] :
( ( ( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X28 @ Y1 ) ) ) )
= X27 )
& ! [X31: a > $o] :
( ( $true
= ( X28 @ X31 ) )
=> ( ( X2 @ X31 )
= $true ) ) )
=> ( ( X2 @ X27 )
= $true ) ) )
=> ! [X32: b > $o] :
( ! [X33: b > $o] :
( ( ( ^ [Y0: b] :
~ ( X32 @ Y0 ) )
= X33 )
=> ( ( X0 @ X33 )
= $true ) )
=> ! [X35: a > $o] :
( ( ( ^ [Y0: a] : ( X32 @ ( X1 @ Y0 ) ) )
= X35 )
=> ! [X37: a > $o] :
( ( ( ^ [Y0: a] :
~ ( X35 @ Y0 ) )
= X37 )
=> ( ( X2 @ X37 )
= $true ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: ( b > $o ) > $o,X1: a > b,X2: ( a > $o ) > $o] :
( ( ! [X3: a > $o,X4: a > $o,X5: a > $o] :
( ( ( ( ^ [X6: a] :
( ( X3 @ X6 )
& ( X5 @ X6 ) ) )
= X4 )
& ( X2 @ X3 )
& ( X2 @ X5 ) )
=> ( X2 @ X4 ) )
& ! [X7: b > $o] :
( ( X0 @ X7 )
=> ! [X8: a > $o] :
( ( ( ^ [X9: a] : ( X7 @ ( X1 @ X9 ) ) )
= X8 )
=> ( X2 @ X8 ) ) )
& ! [X10: b > $o,X11: ( b > $o ) > $o] :
( ( ( ( ^ [X12: b] :
? [X13: b > $o] :
( ( X11 @ X13 )
& ( X13 @ X12 ) ) )
= X10 )
& ! [X14: b > $o] :
( ( X11 @ X14 )
=> ( X0 @ X14 ) ) )
=> ( X0 @ X10 ) )
& ! [X15: b > $o,X16: b > $o,X17: b > $o] :
( ( ( X0 @ X16 )
& ( X0 @ X15 )
& ( X17
= ( ^ [X18: b] :
( ( X16 @ X18 )
& ( X15 @ X18 ) ) ) ) )
=> ( X0 @ X17 ) )
& ! [X19: b > $o] :
( ( X19
= ( ^ [X20: b] : ~ $false ) )
=> ( X0 @ X19 ) )
& ! [X21: a > $o] :
( ( ( ^ [X22: a] : $false )
= X21 )
=> ( X2 @ X21 ) )
& ! [X23: a > $o] :
( ( X23
= ( ^ [X24: a] : ~ $false ) )
=> ( X2 @ X23 ) )
& ! [X25: b > $o] :
( ( ( ^ [X26: b] : $false )
= X25 )
=> ( X0 @ X25 ) )
& ! [X27: a > $o,X28: ( a > $o ) > $o] :
( ( ( ( ^ [X29: a] :
? [X30: a > $o] :
( ( X28 @ X30 )
& ( X30 @ X29 ) ) )
= X27 )
& ! [X31: a > $o] :
( ( X28 @ X31 )
=> ( X2 @ X31 ) ) )
=> ( X2 @ X27 ) ) )
=> ! [X32: b > $o] :
( ! [X33: b > $o] :
( ( ( ^ [X34: b] :
~ ( X32 @ X34 ) )
= X33 )
=> ( X0 @ X33 ) )
=> ! [X35: a > $o] :
( ( ( ^ [X36: a] : ( X32 @ ( X1 @ X36 ) ) )
= X35 )
=> ! [X37: a > $o] :
( ( X37
= ( ^ [X38: a] :
~ ( X35 @ X38 ) ) )
=> ( X2 @ X37 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: ( b > $o ) > $o,X2: a > b,X0: ( a > $o ) > $o] :
( ( ! [X8: a > $o,X6: a > $o,X7: a > $o] :
( ( ( ( ^ [X4: a] :
( ( X8 @ X4 )
& ( X7 @ X4 ) ) )
= X6 )
& ( X0 @ X8 )
& ( X0 @ X7 ) )
=> ( X0 @ X6 ) )
& ! [X9: b > $o] :
( ( X1 @ X9 )
=> ! [X7: a > $o] :
( ( ( ^ [X10: a] : ( X9 @ ( X2 @ X10 ) ) )
= X7 )
=> ( X0 @ X7 ) ) )
& ! [X3: b > $o,X5: ( b > $o ) > $o] :
( ( ( ( ^ [X4: b] :
? [X6: b > $o] :
( ( X5 @ X6 )
& ( X6 @ X4 ) ) )
= X3 )
& ! [X4: b > $o] :
( ( X5 @ X4 )
=> ( X1 @ X4 ) ) )
=> ( X1 @ X3 ) )
& ! [X7: b > $o,X8: b > $o,X6: b > $o] :
( ( ( X1 @ X8 )
& ( X1 @ X7 )
& ( X6
= ( ^ [X4: b] :
( ( X8 @ X4 )
& ( X7 @ X4 ) ) ) ) )
=> ( X1 @ X6 ) )
& ! [X3: b > $o] :
( ( X3
= ( ^ [X4: b] : ~ $false ) )
=> ( X1 @ X3 ) )
& ! [X3: a > $o] :
( ( ( ^ [X4: a] : $false )
= X3 )
=> ( X0 @ X3 ) )
& ! [X3: a > $o] :
( ( X3
= ( ^ [X4: a] : ~ $false ) )
=> ( X0 @ X3 ) )
& ! [X3: b > $o] :
( ( ( ^ [X4: b] : $false )
= X3 )
=> ( X1 @ X3 ) )
& ! [X3: a > $o,X5: ( a > $o ) > $o] :
( ( ( ( ^ [X4: a] :
? [X6: a > $o] :
( ( X5 @ X6 )
& ( X6 @ X4 ) ) )
= X3 )
& ! [X4: a > $o] :
( ( X5 @ X4 )
=> ( X0 @ X4 ) ) )
=> ( X0 @ X3 ) ) )
=> ! [X9: b > $o] :
( ! [X3: b > $o] :
( ( ( ^ [X4: b] :
~ ( X9 @ X4 ) )
= X3 )
=> ( X1 @ X3 ) )
=> ! [X7: a > $o] :
( ( ( ^ [X10: a] : ( X9 @ ( X2 @ X10 ) ) )
= X7 )
=> ! [X3: a > $o] :
( ( X3
= ( ^ [X4: a] :
~ ( X7 @ X4 ) ) )
=> ( X0 @ X3 ) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X1: ( b > $o ) > $o,X2: a > b,X0: ( a > $o ) > $o] :
( ( ! [X8: a > $o,X6: a > $o,X7: a > $o] :
( ( ( ( ^ [X4: a] :
( ( X8 @ X4 )
& ( X7 @ X4 ) ) )
= X6 )
& ( X0 @ X8 )
& ( X0 @ X7 ) )
=> ( X0 @ X6 ) )
& ! [X9: b > $o] :
( ( X1 @ X9 )
=> ! [X7: a > $o] :
( ( ( ^ [X10: a] : ( X9 @ ( X2 @ X10 ) ) )
= X7 )
=> ( X0 @ X7 ) ) )
& ! [X3: b > $o,X5: ( b > $o ) > $o] :
( ( ( ( ^ [X4: b] :
? [X6: b > $o] :
( ( X5 @ X6 )
& ( X6 @ X4 ) ) )
= X3 )
& ! [X4: b > $o] :
( ( X5 @ X4 )
=> ( X1 @ X4 ) ) )
=> ( X1 @ X3 ) )
& ! [X7: b > $o,X8: b > $o,X6: b > $o] :
( ( ( X1 @ X8 )
& ( X1 @ X7 )
& ( X6
= ( ^ [X4: b] :
( ( X8 @ X4 )
& ( X7 @ X4 ) ) ) ) )
=> ( X1 @ X6 ) )
& ! [X3: b > $o] :
( ( X3
= ( ^ [X4: b] : ~ $false ) )
=> ( X1 @ X3 ) )
& ! [X3: a > $o] :
( ( ( ^ [X4: a] : $false )
= X3 )
=> ( X0 @ X3 ) )
& ! [X3: a > $o] :
( ( X3
= ( ^ [X4: a] : ~ $false ) )
=> ( X0 @ X3 ) )
& ! [X3: b > $o] :
( ( ( ^ [X4: b] : $false )
= X3 )
=> ( X1 @ X3 ) )
& ! [X3: a > $o,X5: ( a > $o ) > $o] :
( ( ( ( ^ [X4: a] :
? [X6: a > $o] :
( ( X5 @ X6 )
& ( X6 @ X4 ) ) )
= X3 )
& ! [X4: a > $o] :
( ( X5 @ X4 )
=> ( X0 @ X4 ) ) )
=> ( X0 @ X3 ) ) )
=> ! [X9: b > $o] :
( ! [X3: b > $o] :
( ( ( ^ [X4: b] :
~ ( X9 @ X4 ) )
= X3 )
=> ( X1 @ X3 ) )
=> ! [X7: a > $o] :
( ( ( ^ [X10: a] : ( X9 @ ( X2 @ X10 ) ) )
= X7 )
=> ! [X3: a > $o] :
( ( X3
= ( ^ [X4: a] :
~ ( X7 @ X4 ) ) )
=> ( X0 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCLOSED_THM1_pme) ).
thf(f61,plain,
( ( sK0
@ ^ [Y0: b] :
~ ( sK4 @ Y0 ) )
!= $true ),
inference(beta_eta_normalization,[],[f60]) ).
thf(f60,plain,
( ( sK0
@ ^ [Y0: b] :
~ ( ^ [Y1: b] :
( sK4
@ ( ^ [Y2: b] : Y2
@ Y1 ) )
@ Y0 ) )
!= $true ),
inference(trivial_inequality_removal,[],[f59]) ).
thf(f59,plain,
( ( ( sK0
@ ^ [Y0: b] :
~ ( ^ [Y1: b] :
( sK4
@ ( ^ [Y2: b] : Y2
@ Y1 ) )
@ Y0 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f46,f39]) ).
thf(f39,plain,
! [X12: b > $o] :
( ( ( sK2
@ ^ [Y0: a] : ( X12 @ ( sK1 @ Y0 ) ) )
= $true )
| ( ( sK0 @ X12 )
!= $true ) ),
inference(equality_resolution,[],[f23]) ).
thf(f23,plain,
! [X12: b > $o,X13: a > $o] :
( ( ( sK0 @ X12 )
!= $true )
| ( ( ^ [Y0: a] : ( X12 @ ( sK1 @ Y0 ) ) )
!= X13 )
| ( ( sK2 @ X13 )
= $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f46,plain,
( ( sK2
@ ^ [Y0: a] :
~ ( sK4 @ ( sK1 @ Y0 ) ) )
!= $true ),
inference(beta_eta_normalization,[],[f33]) ).
thf(f33,plain,
( ( sK2
@ ^ [Y0: a] :
~ ( ^ [Y1: a] : ( sK4 @ ( sK1 @ Y1 ) )
@ Y0 ) )
!= $true ),
inference(definition_unfolding,[],[f26,f32]) ).
thf(f32,plain,
( sK6
= ( ^ [Y0: a] :
~ ( ^ [Y1: a] : ( sK4 @ ( sK1 @ Y1 ) )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f27,f28]) ).
thf(f28,plain,
( ( ^ [Y0: a] : ( sK4 @ ( sK1 @ Y0 ) ) )
= sK5 ),
inference(cnf_transformation,[],[f16]) ).
thf(f27,plain,
( sK6
= ( ^ [Y0: a] :
~ ( sK5 @ Y0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f26,plain,
( ( sK2 @ sK6 )
!= $true ),
inference(cnf_transformation,[],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEV260^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.11 % Command : run_vampire %s %d THM
% 0.11/0.32 % Computer : n001.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 21 19:00:53 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.34 This is a TH0_THM_EQU_NAR problem
% 0.11/0.34 Running higher-order theorem proving
% 0.11/0.34 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.11/0.36 % (2423)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.36 % (2424)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.11/0.36 % (2427)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.36 % (2427)Instruction limit reached!
% 0.11/0.36 % (2427)------------------------------
% 0.11/0.36 % (2427)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.36 % (2427)Termination reason: Unknown
% 0.11/0.36 % (2427)Termination phase: Saturation
% 0.11/0.36
% 0.11/0.36 % (2427)Memory used [KB]: 1023
% 0.11/0.36 % (2427)Time elapsed: 0.003 s
% 0.11/0.36 % (2427)Instructions burned: 4 (million)
% 0.11/0.36 % (2427)------------------------------
% 0.11/0.36 % (2427)------------------------------
% 0.11/0.36 % (2424)Instruction limit reached!
% 0.11/0.36 % (2424)------------------------------
% 0.11/0.36 % (2424)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.36 % (2424)Termination reason: Unknown
% 0.11/0.36 % (2424)Termination phase: Saturation
% 0.11/0.36
% 0.11/0.36 % (2424)Memory used [KB]: 5500
% 0.11/0.36 % (2424)Time elapsed: 0.004 s
% 0.11/0.36 % (2424)Instructions burned: 5 (million)
% 0.11/0.36 % (2424)------------------------------
% 0.11/0.36 % (2424)------------------------------
% 0.11/0.36 % (2423)First to succeed.
% 0.11/0.36 % (2423)Refutation found. Thanks to Tanya!
% 0.11/0.36 % SZS status Theorem for theBenchmark
% 0.11/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.36 % (2423)------------------------------
% 0.11/0.36 % (2423)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.36 % (2423)Termination reason: Refutation
% 0.11/0.36
% 0.11/0.36 % (2423)Memory used [KB]: 5628
% 0.11/0.36 % (2423)Time elapsed: 0.007 s
% 0.11/0.36 % (2423)Instructions burned: 7 (million)
% 0.11/0.36 % (2423)------------------------------
% 0.11/0.36 % (2423)------------------------------
% 0.11/0.36 % (2422)Success in time 0.015 s
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