TSTP Solution File: SEV087^5 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV087^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n025.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 : Sun May 5 09:41:17 EDT 2024
% Result : Theorem 0.22s 0.42s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 23
% Syntax : Number of formulae : 81 ( 2 unt; 9 typ; 0 def)
% Number of atoms : 602 ( 249 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 592 ( 96 ~; 82 |; 57 &; 337 @)
% ( 7 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 375 ( 375 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 288 ( 194 ^ 53 !; 40 ?; 288 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% 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(f124,plain,
$false,
inference(avatar_sat_refutation,[],[f63,f81,f86,f91,f92,f96,f121,f123]) ).
thf(f123,plain,
( spl8_8
| ~ spl8_3 ),
inference(avatar_split_clause,[],[f112,f60,f118]) ).
thf(f118,plain,
( spl8_8
<=> ( ( 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_8])]) ).
thf(f60,plain,
( spl8_3
<=> ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
thf(f112,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_3 ),
inference(equality_proxy_clausification,[],[f111]) ).
thf(f111,plain,
( ( $true
= ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl8_3 ),
inference(beta_eta_normalization,[],[f110]) ).
thf(f110,plain,
( ( $true
= ( ^ [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 ) ) ) )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f109,plain,
( ( $true != $true )
| ( $true
= ( ^ [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 ) ) ) )
| ~ spl8_3 ),
inference(superposition,[],[f24,f62]) ).
thf(f62,plain,
( ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f24,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
!= ( sP1 @ X0 ) )
| ( $true
= ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( ( sK2 @ X0 )
!= ( sK3 @ X0 ) )
& ( $true
= ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK3 @ X0 ) @ ( sK2 @ X0 ) ) ) )
| ( $true
!= ( sP1 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f13,f14]) ).
thf(f14,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] :
( ( X1 != X2 )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( $true
= ( X0 @ X2 @ X1 ) ) )
=> ( ( ( sK2 @ X0 )
!= ( sK3 @ X0 ) )
& ( $true
= ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK3 @ X0 ) @ ( sK2 @ X0 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] :
( ( X1 != X2 )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( $true
= ( X0 @ X2 @ X1 ) ) )
| ( $true
!= ( sP1 @ X0 ) ) ),
inference(rectify,[],[f12]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X2: $i > $o,X1: $i > $o] :
( ( X1 != X2 )
& ( $true
= ( X0 @ X2 @ X1 ) )
& ( ( X0 @ X1 @ X2 )
= $true ) )
| ( $true
!= ( sP1 @ X0 ) ) ),
inference(nnf_transformation,[],[f10]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X2: $i > $o,X1: $i > $o] :
( ( X1 != X2 )
& ( $true
= ( X0 @ X2 @ X1 ) )
& ( ( X0 @ X1 @ X2 )
= $true ) )
| ( $true
!= ( sP1 @ X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f121,plain,
( ~ spl8_8
| ~ spl8_3 ),
inference(avatar_split_clause,[],[f116,f60,f118]) ).
thf(f116,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f107]) ).
thf(f107,plain,
( ( $true != $true )
| ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_3 ),
inference(superposition,[],[f25,f62]) ).
thf(f25,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sK2 @ X0 )
!= ( sK3 @ X0 ) )
| ( $true
!= ( sP1 @ X0 ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f96,plain,
~ spl8_1,
inference(avatar_contradiction_clause,[],[f95]) ).
thf(f95,plain,
( $false
| ~ spl8_1 ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f94,plain,
( ( $true = $false )
| ~ spl8_1 ),
inference(beta_eta_normalization,[],[f93]) ).
thf(f93,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : $true
@ X1 )
= ( ^ [Y0: $i] : $false
@ X1 ) )
| ~ spl8_1 ),
inference(argument_congruence,[],[f54]) ).
thf(f54,plain,
( ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f52,plain,
( spl8_1
<=> ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
thf(f92,plain,
( ( ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( sK4
@ ^ [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 ) )
= ( sK4
@ ^ [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
<=> ( ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
thf(f56,plain,
( spl8_2
<=> ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
thf(f70,plain,
( ( ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_2 ),
inference(equality_proxy_clausification,[],[f69]) ).
thf(f69,plain,
( ( $true
= ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl8_2 ),
inference(beta_eta_normalization,[],[f68]) ).
thf(f68,plain,
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK5
@ ^ [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 )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true != $true )
| ~ spl8_2 ),
inference(superposition,[],[f28,f58]) ).
thf(f58,plain,
( ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f56]) ).
thf(f28,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
!= ( sP0 @ X0 ) )
| ( $true
= ( X0 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f19,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( $true
= ( X0 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) ) )
& ( $true
!= ( X0 @ ( sK6 @ X0 ) @ ( sK4 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) ) ) )
| ( $true
!= ( sP0 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f17,f18]) ).
thf(f18,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( $true
= ( X0 @ X3 @ X2 ) )
& ( ( X0 @ X3 @ X1 )
!= $true )
& ( $true
= ( X0 @ X2 @ X1 ) ) )
=> ( ( $true
= ( X0 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) ) )
& ( $true
!= ( X0 @ ( sK6 @ X0 ) @ ( sK4 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f17,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( $true
= ( X0 @ X3 @ X2 ) )
& ( ( X0 @ X3 @ X1 )
!= $true )
& ( $true
= ( X0 @ X2 @ X1 ) ) )
| ( $true
!= ( sP0 @ X0 ) ) ),
inference(rectify,[],[f16]) ).
thf(f16,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( $true
= ( X0 @ X6 @ X5 ) )
& ( $true
!= ( X0 @ X6 @ X4 ) )
& ( ( X0 @ X5 @ X4 )
= $true ) )
| ( $true
!= ( sP0 @ X0 ) ) ),
inference(nnf_transformation,[],[f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( $true
= ( X0 @ X6 @ X5 ) )
& ( $true
!= ( X0 @ X6 @ X4 ) )
& ( ( X0 @ X5 @ X4 )
= $true ) )
| ( $true
!= ( sP0 @ X0 ) ) ),
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 ) )
= ( sK5
@ ^ [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 ) )
= ( sK5
@ ^ [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 ) )
= ( sK5
@ ^ [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 )
@ ( sK5
@ ^ [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 != $true )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl8_2 ),
inference(superposition,[],[f26,f58]) ).
thf(f26,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
!= ( sP0 @ X0 ) )
| ( $true
= ( X0 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f81,plain,
( ~ spl8_4
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f76,f56,f78]) ).
thf(f78,plain,
( spl8_4
<=> ( ( sK6
@ ^ [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,
( ( ( sK6
@ ^ [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 ) )
= ( sK6
@ ^ [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 )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f67,plain,
( ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true != $true )
| ~ spl8_2 ),
inference(superposition,[],[f27,f58]) ).
thf(f27,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
!= ( X0 @ ( sK6 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( $true
!= ( sP0 @ X0 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f63,plain,
( spl8_1
| spl8_2
| spl8_3 ),
inference(avatar_split_clause,[],[f43,f60,f56,f52]) ).
thf(f43,plain,
( ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(equality_proxy_clausification,[],[f42]) ).
thf(f42,plain,
( ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) ) ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f41,plain,
( ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( $true != $true )
| ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(boolean_simplification,[],[f40]) ).
thf(f40,plain,
( ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
!= ( ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) ) ),
inference(beta_eta_normalization,[],[f31]) ).
thf(f31,plain,
( ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( ^ [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 )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(primitive_instantiation,[],[f29]) ).
thf(f29,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
!= ( X0 @ ( sK7 @ X0 ) @ ( sK7 @ X0 ) ) )
| ( $true
= ( sP1 @ X0 ) )
| ( $true
= ( sP0 @ X0 ) )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f22,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
| ( $true
= ( sP1 @ X0 ) )
| ( $true
= ( sP0 @ X0 ) )
| ( $true
!= ( X0 @ ( sK7 @ X0 ) @ ( sK7 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f20,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(f20,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
| ( $true
= ( sP1 @ X0 ) )
| ( $true
= ( sP0 @ X0 ) )
| ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true ) ),
inference(rectify,[],[f11]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
| ( $true
= ( sP1 @ X0 ) )
| ( $true
= ( sP0 @ X0 ) )
| ? [X3: $i > $o] :
( $true
!= ( X0 @ X3 @ X3 ) ) ),
inference(definition_folding,[],[f8,f10,f9]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
| ? [X2: $i > $o,X1: $i > $o] :
( ( X1 != X2 )
& ( $true
= ( X0 @ X2 @ X1 ) )
& ( ( X0 @ X1 @ X2 )
= $true ) )
| ? [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( $true
= ( X0 @ X6 @ X5 ) )
& ( $true
!= ( X0 @ X6 @ X4 ) )
& ( ( X0 @ X5 @ X4 )
= $true ) )
| ? [X3: $i > $o] :
( $true
!= ( X0 @ X3 @ X3 ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X3: $i > $o] :
( $true
!= ( X0 @ X3 @ X3 ) )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
| ? [X2: $i > $o,X1: $i > $o] :
( ( X1 != X2 )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( $true
= ( X0 @ X2 @ X1 ) ) )
| ? [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( $true
!= ( X0 @ X6 @ X4 ) )
& ( ( X0 @ X5 @ X4 )
= $true )
& ( $true
= ( X0 @ X6 @ X5 ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X3: $i > $o] :
( $true
= ( X0 @ X3 @ X3 ) )
& ( $true
!= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
& ! [X2: $i > $o,X1: $i > $o] :
( ( ( ( X0 @ X1 @ X2 )
= $true )
& ( $true
= ( X0 @ X2 @ X1 ) ) )
=> ( X1 = X2 ) )
& ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ( ( X0 @ X5 @ X4 )
= $true )
& ( $true
= ( X0 @ X6 @ X5 ) ) )
=> ( $true
= ( X0 @ X6 @ X4 ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X2: $i > $o,X1: $i > $o] :
( ( ( ( X0 @ X1 @ X2 )
= $true )
& ( $true
= ( X0 @ X2 @ X1 ) ) )
=> ( X1 = X2 ) )
& ! [X3: $i > $o] :
( $true
= ( X0 @ X3 @ X3 ) )
& ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ( ( X0 @ X5 @ X4 )
= $true )
& ( $true
= ( X0 @ X6 @ X5 ) ) )
=> ( $true
= ( X0 @ X6 @ X4 ) ) )
& ( $true
!= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X1 @ X2 ) )
=> ( X1 = X2 ) )
& ! [X3: $i > $o] : ( X0 @ X3 @ X3 )
& ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ( X0 @ X5 @ X4 )
& ( X0 @ X6 @ X5 ) )
=> ( X0 @ X6 @ X4 ) )
& ~ ( X0
@ ^ [X7: $i] : $true
@ ^ [X8: $i] : $false ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X5: $i > $o,X4: $i > $o] :
( ( ( X0 @ X4 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X4 = X5 ) )
& ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
& ! [X3: $i > $o,X2: $i > $o,X1: $i > $o] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) )
& ~ ( X0
@ ^ [X1: $i] : $true
@ ^ [X1: $i] : $false ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X5: $i > $o,X4: $i > $o] :
( ( ( X0 @ X4 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X4 = X5 ) )
& ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
& ! [X3: $i > $o,X2: $i > $o,X1: $i > $o] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) )
& ~ ( X0
@ ^ [X1: $i] : $true
@ ^ [X1: $i] : $false ) ),
file('/export/starexec/sandbox2/tmp/tmp.MRPBNrCvvy/Vampire---4.8_15918',cTHM120H_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEV087^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36 % Computer : n025.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 12:17:29 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.MRPBNrCvvy/Vampire---4.8_15918
% 0.15/0.39 % (16111)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.39 % (16113)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.39 % (16110)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.39 % (16107)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.15/0.39 % (16109)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 Vampire---4 for (2999ds/27Mi)
% 0.15/0.39 % (16108)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 Vampire---4 for (2999ds/4Mi)
% 0.15/0.39 % (16112)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.15/0.39 % (16111)Instruction limit reached!
% 0.15/0.39 % (16111)------------------------------
% 0.15/0.39 % (16111)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (16111)Termination reason: Unknown
% 0.15/0.39 % (16111)Termination phase: Property scanning
% 0.15/0.39
% 0.15/0.39 % (16111)Memory used [KB]: 895
% 0.15/0.39 % (16111)Time elapsed: 0.004 s
% 0.15/0.39 % (16111)Instructions burned: 2 (million)
% 0.15/0.39 % (16111)------------------------------
% 0.15/0.39 % (16111)------------------------------
% 0.15/0.39 % (16114)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.39 % (16110)Instruction limit reached!
% 0.15/0.39 % (16110)------------------------------
% 0.15/0.39 % (16110)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (16110)Termination reason: Unknown
% 0.15/0.39 % (16110)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (16110)Memory used [KB]: 5500
% 0.15/0.39 % (16110)Time elapsed: 0.004 s
% 0.15/0.39 % (16110)Instructions burned: 2 (million)
% 0.15/0.39 % (16110)------------------------------
% 0.15/0.39 % (16110)------------------------------
% 0.15/0.40 % (16108)Instruction limit reached!
% 0.15/0.40 % (16108)------------------------------
% 0.15/0.40 % (16108)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (16108)Termination reason: Unknown
% 0.15/0.40 % (16108)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (16108)Memory used [KB]: 5500
% 0.15/0.40 % (16108)Time elapsed: 0.006 s
% 0.15/0.40 % (16108)Instructions burned: 4 (million)
% 0.15/0.40 % (16108)------------------------------
% 0.15/0.40 % (16108)------------------------------
% 0.22/0.40 % (16114)Instruction limit reached!
% 0.22/0.40 % (16114)------------------------------
% 0.22/0.40 % (16114)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (16114)Termination reason: Unknown
% 0.22/0.40 % (16114)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.40 % (16114)Memory used [KB]: 5500
% 0.22/0.40 % (16114)Time elapsed: 0.006 s
% 0.22/0.40 % (16114)Instructions burned: 3 (million)
% 0.22/0.40 % (16114)------------------------------
% 0.22/0.40 % (16114)------------------------------
% 0.22/0.40 % (16109)Refutation not found, incomplete strategy
% 0.22/0.40 % (16109)------------------------------
% 0.22/0.40 % (16109)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (16109)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.40
% 0.22/0.40
% 0.22/0.40 % (16109)Memory used [KB]: 5500
% 0.22/0.40 % (16109)Time elapsed: 0.007 s
% 0.22/0.40 % (16109)Instructions burned: 5 (million)
% 0.22/0.40 % (16109)------------------------------
% 0.22/0.40 % (16109)------------------------------
% 0.22/0.40 % (16113)Instruction limit reached!
% 0.22/0.40 % (16113)------------------------------
% 0.22/0.40 % (16113)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (16113)Termination reason: Unknown
% 0.22/0.40 % (16113)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.40 % (16113)Memory used [KB]: 5628
% 0.22/0.40 % (16113)Time elapsed: 0.013 s
% 0.22/0.40 % (16113)Instructions burned: 18 (million)
% 0.22/0.40 % (16113)------------------------------
% 0.22/0.40 % (16113)------------------------------
% 0.22/0.41 % (16117)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 Vampire---4 for (2999ds/37Mi)
% 0.22/0.41 % (16112)Refutation not found, incomplete strategy
% 0.22/0.41 % (16112)------------------------------
% 0.22/0.41 % (16112)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (16112)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.41
% 0.22/0.41
% 0.22/0.41 % (16112)Memory used [KB]: 5628
% 0.22/0.41 % (16112)Time elapsed: 0.020 s
% 0.22/0.41 % (16112)Instructions burned: 26 (million)
% 0.22/0.41 % (16112)------------------------------
% 0.22/0.41 % (16112)------------------------------
% 0.22/0.41 % (16120)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.41 % (16118)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 Vampire---4 for (2999ds/15Mi)
% 0.22/0.41 % (16122)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.22/0.42 % (16120)Instruction limit reached!
% 0.22/0.42 % (16120)------------------------------
% 0.22/0.42 % (16120)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (16120)Termination reason: Unknown
% 0.22/0.42 % (16120)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (16120)Memory used [KB]: 5500
% 0.22/0.42 % (16120)Time elapsed: 0.004 s
% 0.22/0.42 % (16120)Instructions burned: 4 (million)
% 0.22/0.42 % (16120)------------------------------
% 0.22/0.42 % (16120)------------------------------
% 0.22/0.42 % (16121)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on Vampire---4 for (2999ds/1041Mi)
% 0.22/0.42 % (16123)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.22/0.42 % (16122)Instruction limit reached!
% 0.22/0.42 % (16122)------------------------------
% 0.22/0.42 % (16122)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (16122)Termination reason: Unknown
% 0.22/0.42 % (16122)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (16122)Memory used [KB]: 1023
% 0.22/0.42 % (16122)Time elapsed: 0.006 s
% 0.22/0.42 % (16122)Instructions burned: 7 (million)
% 0.22/0.42 % (16122)------------------------------
% 0.22/0.42 % (16122)------------------------------
% 0.22/0.42 % (16118)First to succeed.
% 0.22/0.42 % (16118)Refutation found. Thanks to Tanya!
% 0.22/0.42 % SZS status Theorem for Vampire---4
% 0.22/0.42 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.42 % (16118)------------------------------
% 0.22/0.42 % (16118)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (16118)Termination reason: Refutation
% 0.22/0.42
% 0.22/0.42 % (16118)Memory used [KB]: 5628
% 0.22/0.42 % (16118)Time elapsed: 0.010 s
% 0.22/0.42 % (16118)Instructions burned: 8 (million)
% 0.22/0.42 % (16118)------------------------------
% 0.22/0.42 % (16118)------------------------------
% 0.22/0.42 % (16104)Success in time 0.049 s
% 0.22/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------