TSTP Solution File: SEV087^5 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV087^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n018.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 16:01:45 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 72 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 607 ( 253 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 605 ( 97 ~; 79 |; 62 &; 345 @)
% ( 7 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 334 ( 334 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 292 ( 194 ^ 58 !; 40 ?; 292 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_4,type,
sP0: ( ( $i > $o ) > ( $i > $o ) > $o ) > $o ).
thf(func_def_5,type,
sP1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $o ).
thf(func_def_6,type,
sK2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_7,type,
sK3: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_8,type,
sK4: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_9,type,
sK5: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_10,type,
sK6: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_11,type,
sK7: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_13,type,
ph9:
!>[X0: $tType] : X0 ).
thf(f125,plain,
$false,
inference(avatar_sat_refutation,[],[f63,f81,f86,f91,f92,f97,f123,f124]) ).
thf(f124,plain,
( ~ spl8_8
| ~ spl8_3 ),
inference(avatar_split_clause,[],[f111,f60,f119]) ).
thf(f119,plain,
( spl8_8
<=> ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
thf(f60,plain,
( spl8_3
<=> ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
thf(f111,plain,
( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f108]) ).
thf(f108,plain,
( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true != $true )
| ~ spl8_3 ),
inference(superposition,[],[f26,f62]) ).
thf(f62,plain,
( ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f26,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP0 @ X0 )
!= $true )
| ( ( sK5 @ X0 )
!= ( sK6 @ X0 ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f20,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( $true
= ( X0 @ ( sK5 @ X0 ) @ ( sK6 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) ) )
& ( ( sK5 @ X0 )
!= ( sK6 @ X0 ) ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f18,f19]) ).
thf(f19,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 @ X2 )
= $true )
& ( $true
= ( X0 @ X2 @ X1 ) )
& ( X1 != X2 ) )
=> ( ( $true
= ( X0 @ ( sK5 @ X0 ) @ ( sK6 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) ) )
& ( ( sK5 @ X0 )
!= ( sK6 @ X0 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f18,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 @ X2 )
= $true )
& ( $true
= ( X0 @ X2 @ X1 ) )
& ( X1 != X2 ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(rectify,[],[f17]) ).
thf(f17,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X2 @ X3 )
= $true )
& ( $true
= ( X0 @ X3 @ X2 ) )
& ( X2 != X3 ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(nnf_transformation,[],[f10]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X2 @ X3 )
= $true )
& ( $true
= ( X0 @ X3 @ X2 ) )
& ( X2 != X3 ) )
| ( ( sP0 @ X0 )
!= $true ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f123,plain,
( spl8_8
| ~ spl8_3 ),
inference(avatar_split_clause,[],[f114,f60,f119]) ).
thf(f114,plain,
( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_3 ),
inference(equality_proxy_clausification,[],[f113]) ).
thf(f113,plain,
( ( $true
= ( ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl8_3 ),
inference(beta_eta_normalization,[],[f112]) ).
thf(f112,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f110]) ).
thf(f110,plain,
( ( $true != $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl8_3 ),
inference(superposition,[],[f28,f62]) ).
thf(f28,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( X0 @ ( sK5 @ X0 ) @ ( sK6 @ X0 ) ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f97,plain,
~ spl8_1,
inference(avatar_contradiction_clause,[],[f96]) ).
thf(f96,plain,
( $false
| ~ spl8_1 ),
inference(trivial_inequality_removal,[],[f95]) ).
thf(f95,plain,
( ( $true = $false )
| ~ spl8_1 ),
inference(beta_eta_normalization,[],[f94]) ).
thf(f94,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : $true
@ X1 )
= ( ^ [Y0: $i] : $false
@ X1 ) )
| ~ spl8_1 ),
inference(argument_congruence,[],[f54]) ).
thf(f54,plain,
( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f52,plain,
( spl8_1
<=> ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
thf(f92,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(theory_tautology_sat_conflict,[]) ).
thf(f91,plain,
( spl8_6
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f70,f56,f88]) ).
thf(f88,plain,
( spl8_6
<=> ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
thf(f56,plain,
( spl8_2
<=> ( ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
thf(f70,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_2 ),
inference(equality_proxy_clausification,[],[f69]) ).
thf(f69,plain,
( ( $true
= ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl8_2 ),
inference(beta_eta_normalization,[],[f68]) ).
thf(f68,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f67,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ( $true != $true )
| ~ spl8_2 ),
inference(superposition,[],[f23,f58]) ).
thf(f58,plain,
( ( ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f56]) ).
thf(f23,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP1 @ X0 )
!= $true )
| ( $true
= ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f16,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( $true
= ( X0 @ ( sK3 @ X0 ) @ ( sK4 @ X0 ) ) )
& ( ( X0 @ ( sK2 @ X0 ) @ ( sK4 @ X0 ) )
!= $true )
& ( $true
= ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f14,f15]) ).
thf(f15,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X2 @ X3 )
= $true )
& ( ( X0 @ X1 @ X3 )
!= $true )
& ( ( X0 @ X1 @ X2 )
= $true ) )
=> ( ( $true
= ( X0 @ ( sK3 @ X0 ) @ ( sK4 @ X0 ) ) )
& ( ( X0 @ ( sK2 @ X0 ) @ ( sK4 @ X0 ) )
!= $true )
& ( $true
= ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f14,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X2 @ X3 )
= $true )
& ( ( X0 @ X1 @ X3 )
!= $true )
& ( ( X0 @ X1 @ X2 )
= $true ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(rectify,[],[f13]) ).
thf(f13,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X6: $i > $o,X5: $i > $o,X4: $i > $o] :
( ( ( X0 @ X5 @ X4 )
= $true )
& ( ( X0 @ X6 @ X4 )
!= $true )
& ( $true
= ( X0 @ X6 @ X5 ) ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(nnf_transformation,[],[f11]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X6: $i > $o,X5: $i > $o,X4: $i > $o] :
( ( ( X0 @ X5 @ X4 )
= $true )
& ( ( X0 @ X6 @ X4 )
!= $true )
& ( $true
= ( X0 @ X6 @ X5 ) ) )
| ( ( sP1 @ X0 )
!= $true ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f86,plain,
( ~ spl8_5
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f73,f56,f83]) ).
thf(f83,plain,
( spl8_5
<=> ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
thf(f73,plain,
( ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_2 ),
inference(equality_proxy_clausification,[],[f72]) ).
thf(f72,plain,
( ( $true
!= ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl8_2 ),
inference(beta_eta_normalization,[],[f71]) ).
thf(f71,plain,
( ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[],[f66]) ).
thf(f66,plain,
( ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true != $true )
| ~ spl8_2 ),
inference(superposition,[],[f24,f58]) ).
thf(f24,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP1 @ X0 )
!= $true )
| ( ( X0 @ ( sK2 @ X0 ) @ ( sK4 @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f81,plain,
( spl8_4
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f76,f56,f78]) ).
thf(f78,plain,
( spl8_4
<=> ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
thf(f76,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_2 ),
inference(equality_proxy_clausification,[],[f75]) ).
thf(f75,plain,
( ( ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl8_2 ),
inference(beta_eta_normalization,[],[f74]) ).
thf(f74,plain,
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[],[f65]) ).
thf(f65,plain,
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true != $true )
| ~ spl8_2 ),
inference(superposition,[],[f25,f58]) ).
thf(f25,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( X0 @ ( sK3 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f63,plain,
( spl8_1
| spl8_2
| spl8_3 ),
inference(avatar_split_clause,[],[f40,f60,f56,f52]) ).
thf(f40,plain,
( ( ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(equality_proxy_clausification,[],[f39]) ).
thf(f39,plain,
( ( ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) ) ),
inference(trivial_inequality_removal,[],[f38]) ).
thf(f38,plain,
( ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( $true != $true )
| ( ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(boolean_simplification,[],[f37]) ).
thf(f37,plain,
( ( $true
!= ( ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true ) ),
inference(beta_eta_normalization,[],[f31]) ).
thf(f31,plain,
( ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true ) ),
inference(primitive_instantiation,[],[f29]) ).
thf(f29,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
!= ( X0 @ ( sK7 @ X0 ) @ ( sK7 @ X0 ) ) )
| ( ( sP1 @ X0 )
= $true )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
| ( ( sP0 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f22,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP1 @ X0 )
= $true )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
| ( $true
!= ( X0 @ ( sK7 @ X0 ) @ ( sK7 @ X0 ) ) )
| ( ( sP0 @ X0 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f12,f21]) ).
thf(f21,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true )
=> ( $true
!= ( X0 @ ( sK7 @ X0 ) @ ( sK7 @ X0 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP1 @ X0 )
= $true )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
| ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true )
| ( ( sP0 @ X0 )
= $true ) ),
inference(definition_folding,[],[f9,f11,f10]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X6: $i > $o,X5: $i > $o,X4: $i > $o] :
( ( ( X0 @ X5 @ X4 )
= $true )
& ( ( X0 @ X6 @ X4 )
!= $true )
& ( $true
= ( X0 @ X6 @ X5 ) ) )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
| ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true )
| ? [X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X2 @ X3 )
= $true )
& ( $true
= ( X0 @ X3 @ X2 ) )
& ( X2 != X3 ) ) ),
inference(flattening,[],[f8]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true )
| ? [X2: $i > $o,X3: $i > $o] :
( ( X2 != X3 )
& ( ( X0 @ X2 @ X3 )
= $true )
& ( $true
= ( X0 @ X3 @ X2 ) ) )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
| ? [X6: $i > $o,X5: $i > $o,X4: $i > $o] :
( ( ( X0 @ X6 @ X4 )
!= $true )
& ( $true
= ( X0 @ X6 @ X5 ) )
& ( ( X0 @ X5 @ X4 )
= $true ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
= $true )
& ! [X2: $i > $o,X3: $i > $o] :
( ( ( ( X0 @ X2 @ X3 )
= $true )
& ( $true
= ( X0 @ X3 @ X2 ) ) )
=> ( X2 = X3 ) )
& ( $true
!= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
& ! [X6: $i > $o,X5: $i > $o,X4: $i > $o] :
( ( ( $true
= ( X0 @ X6 @ X5 ) )
& ( ( X0 @ X5 @ X4 )
= $true ) )
=> ( ( X0 @ X6 @ X4 )
= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f6,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
= $true )
& ( $true
!= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
& ! [X2: $i > $o,X3: $i > $o] :
( ( ( ( X0 @ X2 @ X3 )
= $true )
& ( $true
= ( X0 @ X3 @ X2 ) ) )
=> ( X2 = X3 ) )
& ! [X6: $i > $o,X5: $i > $o,X4: $i > $o] :
( ( ( $true
= ( X0 @ X6 @ X5 ) )
& ( ( X0 @ X5 @ X4 )
= $true ) )
=> ( ( X0 @ X6 @ X4 )
= $true ) ) ),
inference(rectify,[],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
= $true )
& ( $true
!= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
& ! [X4: $i > $o,X5: $i > $o] :
( ( ( ( X0 @ X4 @ X5 )
= $true )
& ( ( X0 @ X5 @ X4 )
= $true ) )
=> ( X4 = X5 ) )
& ! [X6: $i > $o,X7: $i > $o,X8: $i > $o] :
( ( ( ( X0 @ X8 @ X7 )
= $true )
& ( $true
= ( X0 @ X7 @ X6 ) ) )
=> ( ( X0 @ X8 @ X6 )
= $true ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
& ~ ( X0
@ ^ [X2: $i] : $true
@ ^ [X3: $i] : $false )
& ! [X4: $i > $o,X5: $i > $o] :
( ( ( X0 @ X4 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X4 = X5 ) )
& ! [X6: $i > $o,X7: $i > $o,X8: $i > $o] :
( ( ( X0 @ X8 @ X7 )
& ( X0 @ X7 @ X6 ) )
=> ( X0 @ X8 @ X6 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
& ~ ( X0
@ ^ [X1: $i] : $true
@ ^ [X1: $i] : $false )
& ! [X4: $i > $o,X5: $i > $o] :
( ( ( X0 @ X4 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X4 = X5 ) )
& ! [X3: $i > $o,X2: $i > $o,X1: $i > $o] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
& ~ ( X0
@ ^ [X1: $i] : $true
@ ^ [X1: $i] : $false )
& ! [X4: $i > $o,X5: $i > $o] :
( ( ( X0 @ X4 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X4 = X5 ) )
& ! [X3: $i > $o,X2: $i > $o,X1: $i > $o] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120H_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV087^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:17:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TH0_THM_EQU_NAR problem
% 0.12/0.35 Running higher-order theorem proving
% 0.12/0.35 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.12/0.38 % (18333)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)
% 0.12/0.38 % (18336)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)
% 0.12/0.38 % (18332)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.38 % (18334)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.12/0.38 % (18337)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.12/0.38 % (18336)Instruction limit reached!
% 0.12/0.38 % (18336)------------------------------
% 0.12/0.38 % (18336)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (18336)Termination reason: Unknown
% 0.12/0.38 % (18336)Termination phase: Saturation
% 0.12/0.38
% 0.12/0.38 % (18336)Memory used [KB]: 5500
% 0.12/0.38 % (18336)Time elapsed: 0.004 s
% 0.12/0.38 % (18336)Instructions burned: 2 (million)
% 0.12/0.38 % (18336)------------------------------
% 0.12/0.38 % (18336)------------------------------
% 0.12/0.38 % (18338)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.38 % (18333)Instruction limit reached!
% 0.22/0.38 % (18333)------------------------------
% 0.22/0.38 % (18333)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (18333)Termination reason: Unknown
% 0.22/0.38 % (18333)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (18333)Memory used [KB]: 5500
% 0.22/0.38 % (18333)Time elapsed: 0.006 s
% 0.22/0.38 % (18333)Instructions burned: 4 (million)
% 0.22/0.38 % (18333)------------------------------
% 0.22/0.38 % (18333)------------------------------
% 0.22/0.38 % (18334)Refutation not found, incomplete strategy
% 0.22/0.38 % (18334)------------------------------
% 0.22/0.38 % (18334)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (18334)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.38
% 0.22/0.38
% 0.22/0.38 % (18334)Memory used [KB]: 5500
% 0.22/0.38 % (18334)Time elapsed: 0.006 s
% 0.22/0.38 % (18334)Instructions burned: 4 (million)
% 0.22/0.38 % (18334)------------------------------
% 0.22/0.38 % (18334)------------------------------
% 0.22/0.38 % (18335)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.38 % (18335)Instruction limit reached!
% 0.22/0.38 % (18335)------------------------------
% 0.22/0.38 % (18335)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (18335)Termination reason: Unknown
% 0.22/0.38 % (18335)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (18335)Memory used [KB]: 5500
% 0.22/0.38 % (18335)Time elapsed: 0.003 s
% 0.22/0.38 % (18335)Instructions burned: 2 (million)
% 0.22/0.38 % (18335)------------------------------
% 0.22/0.38 % (18335)------------------------------
% 0.22/0.39 % (18338)Instruction limit reached!
% 0.22/0.39 % (18338)------------------------------
% 0.22/0.39 % (18338)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (18338)Termination reason: Unknown
% 0.22/0.39 % (18338)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (18338)Memory used [KB]: 5628
% 0.22/0.39 % (18338)Time elapsed: 0.014 s
% 0.22/0.39 % (18338)Instructions burned: 19 (million)
% 0.22/0.39 % (18338)------------------------------
% 0.22/0.39 % (18338)------------------------------
% 0.22/0.39 % (18337)Refutation not found, incomplete strategy
% 0.22/0.39 % (18337)------------------------------
% 0.22/0.39 % (18337)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (18337)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.39
% 0.22/0.39
% 0.22/0.39 % (18337)Memory used [KB]: 5628
% 0.22/0.39 % (18337)Time elapsed: 0.019 s
% 0.22/0.39 % (18337)Instructions burned: 24 (million)
% 0.22/0.39 % (18337)------------------------------
% 0.22/0.39 % (18337)------------------------------
% 0.22/0.39 % (18341)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.22/0.39 % (18339)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.39 % (18340)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.22/0.40 % (18339)Instruction limit reached!
% 0.22/0.40 % (18339)------------------------------
% 0.22/0.40 % (18339)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.40 % (18339)Termination reason: Unknown
% 0.22/0.40 % (18339)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.40 % (18339)Memory used [KB]: 5500
% 0.22/0.40 % (18339)Time elapsed: 0.004 s
% 0.22/0.40 % (18339)Instructions burned: 3 (million)
% 0.22/0.40 % (18339)------------------------------
% 0.22/0.40 % (18339)------------------------------
% 0.22/0.40 % (18342)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.40 % (18341)First to succeed.
% 0.22/0.40 % (18342)Instruction limit reached!
% 0.22/0.40 % (18342)------------------------------
% 0.22/0.40 % (18342)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.40 % (18342)Termination reason: Unknown
% 0.22/0.40 % (18342)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.40 % (18342)Memory used [KB]: 5500
% 0.22/0.40 % (18342)Time elapsed: 0.005 s
% 0.22/0.40 % (18342)Instructions burned: 4 (million)
% 0.22/0.40 % (18342)------------------------------
% 0.22/0.40 % (18342)------------------------------
% 0.22/0.40 % (18341)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40 % (18341)------------------------------
% 0.22/0.40 % (18341)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.40 % (18341)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (18341)Memory used [KB]: 5628
% 0.22/0.40 % (18341)Time elapsed: 0.009 s
% 0.22/0.40 % (18341)Instructions burned: 7 (million)
% 0.22/0.40 % (18341)------------------------------
% 0.22/0.40 % (18341)------------------------------
% 0.22/0.40 % (18331)Success in time 0.047 s
%------------------------------------------------------------------------------