TSTP Solution File: SEV223^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV223^5 : TPTP v8.2.0. 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n006.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 : Tue May 21 04:12:27 EDT 2024
% Result : Theorem 0.23s 0.42s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 35
% Syntax : Number of formulae : 177 ( 9 unt; 20 typ; 0 def)
% Number of atoms : 1179 ( 403 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 1520 ( 194 ~; 287 |; 177 &; 724 @)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 181 ( 181 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 30 usr; 22 con; 0-2 aty)
% ( 0 !!; 124 ??; 0 @@+; 0 @@-)
% Number of variables : 312 ( 206 ^ 90 !; 15 ?; 312 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
f: b > a ).
thf(func_def_3,type,
w: ( b > $o ) > $o ).
thf(func_def_15,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK2: a ).
thf(func_def_18,type,
sK3: a > $o ).
thf(func_def_19,type,
sK4: b ).
thf(func_def_20,type,
sK5: b > $o ).
thf(func_def_21,type,
sK6: b > $o ).
thf(func_def_22,type,
sK7: b > $o ).
thf(func_def_23,type,
sK8: b > $o ).
thf(func_def_24,type,
sK9: b > $o ).
thf(func_def_25,type,
sK10: a > b ).
thf(func_def_26,type,
sK11: a > b ).
thf(func_def_27,type,
sK12: a ).
thf(func_def_28,type,
sK13: a ).
thf(func_def_29,type,
sK14: b ).
thf(f331,plain,
$false,
inference(avatar_sat_refutation,[],[f69,f74,f83,f88,f97,f102,f111,f116,f117,f124,f156,f178,f214,f223,f271,f330]) ).
thf(f330,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f329]) ).
thf(f329,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_11
| ~ spl0_13 ),
inference(subsumption_resolution,[],[f325,f110]) ).
thf(f110,plain,
( ( ( f @ sK4 )
= sK2 )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f108]) ).
thf(f108,plain,
( spl0_11
<=> ( ( f @ sK4 )
= sK2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f325,plain,
( ( ( f @ sK4 )
!= sK2 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f323]) ).
thf(f323,plain,
( ( ( f @ sK4 )
!= sK2 )
| ( $false = $true )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f283,f73]) ).
thf(f73,plain,
( ( $true
= ( sK9 @ sK4 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f71]) ).
thf(f71,plain,
( spl0_3
<=> ( $true
= ( sK9 @ sK4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f283,plain,
( ! [X0: b] :
( ( $false
= ( sK9 @ X0 ) )
| ( sK2
!= ( f @ X0 ) ) )
| ~ spl0_1
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f281]) ).
thf(f281,plain,
( ! [X0: b] :
( ( $false
= ( sK9 @ X0 ) )
| ( sK2
!= ( f @ X0 ) )
| ( $false = $true ) )
| ~ spl0_1
| ~ spl0_13 ),
inference(superposition,[],[f120,f64]) ).
thf(f64,plain,
( ( $true
= ( w @ sK9 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f62,plain,
( spl0_1
<=> ( $true
= ( w @ sK9 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f120,plain,
( ! [X2: b,X3: b > $o] :
( ( $false
= ( w @ X3 ) )
| ( $false
= ( X3 @ X2 ) )
| ( ( f @ X2 )
!= sK2 ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f119]) ).
thf(f119,plain,
( spl0_13
<=> ! [X2: b,X3: b > $o] :
( ( ( f @ X2 )
!= sK2 )
| ( $false
= ( w @ X3 ) )
| ( $false
= ( X3 @ X2 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f271,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f270]) ).
thf(f270,plain,
( $false
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_13 ),
inference(subsumption_resolution,[],[f266,f110]) ).
thf(f266,plain,
( ( ( f @ sK4 )
!= sK2 )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f265]) ).
thf(f265,plain,
( ( ( f @ sK4 )
!= sK2 )
| ( $false = $true )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f101,f242]) ).
thf(f242,plain,
( ! [X0: b] :
( ( $false
= ( sK6 @ X0 ) )
| ( sK2
!= ( f @ X0 ) ) )
| ~ spl0_8
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f239]) ).
thf(f239,plain,
( ! [X0: b] :
( ( $false
= ( sK6 @ X0 ) )
| ( sK2
!= ( f @ X0 ) )
| ( $false = $true ) )
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f96,f120]) ).
thf(f96,plain,
( ( $true
= ( w @ sK6 ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f94]) ).
thf(f94,plain,
( spl0_8
<=> ( $true
= ( w @ sK6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f101,plain,
( ( ( sK6 @ sK4 )
= $true )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f99]) ).
thf(f99,plain,
( spl0_9
<=> ( ( sK6 @ sK4 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f223,plain,
( spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f222,f122,f119]) ).
thf(f122,plain,
( spl0_14
<=> ! [X4: b > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X4 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= X1 )
| ( $false
= ( w @ X4 ) )
| ( $false
= ( X1 @ sK2 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f222,plain,
( ! [X0: b > $o,X1: b] :
( ( $false
= ( X0 @ X1 ) )
| ( ( w @ X0 )
= $false )
| ( ( f @ X1 )
!= sK2 ) )
| ~ spl0_14 ),
inference(equality_proxy_clausification,[],[f221]) ).
thf(f221,plain,
( ! [X0: b > $o,X1: b] :
( ( $false
= ( X0 @ X1 ) )
| ( ( w @ X0 )
= $false )
| ( $false
= ( ( f @ X1 )
= sK2 ) ) )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f220]) ).
thf(f220,plain,
( ! [X0: b > $o,X1: b] :
( ( ( w @ X0 )
= $false )
| ( $false
= ( ( X0 @ X1 )
& ( ( f @ X1 )
= sK2 ) ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f219]) ).
thf(f219,plain,
( ! [X0: b > $o,X1: b] :
( ( ( w @ X0 )
= $false )
| ( $false
= ( ^ [Y0: b] :
( ( X0 @ Y0 )
& ( ( f @ Y0 )
= sK2 ) )
@ X1 ) ) )
| ~ spl0_14 ),
inference(pi_clausification,[],[f218]) ).
thf(f218,plain,
( ! [X0: b > $o] :
( ( ( w @ X0 )
= $false )
| ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( X0 @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f217]) ).
thf(f217,plain,
( ! [X0: b > $o] :
( ( $false
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X0 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
@ sK2 ) )
| ( ( w @ X0 )
= $false ) )
| ~ spl0_14 ),
inference(equality_resolution,[],[f123]) ).
thf(f123,plain,
( ! [X1: a > $o,X4: b > $o] :
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X4 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= X1 )
| ( $false
= ( w @ X4 ) )
| ( $false
= ( X1 @ sK2 ) ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f122]) ).
thf(f214,plain,
( ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f213]) ).
thf(f213,plain,
( $false
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f202]) ).
thf(f202,plain,
( ( sK2 != sK2 )
| ( $false = $true )
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f201,f92]) ).
thf(f92,plain,
( ( ( sK3 @ sK2 )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f90]) ).
thf(f90,plain,
( spl0_7
<=> ( ( sK3 @ sK2 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f201,plain,
( ! [X0: a] :
( ( $false
= ( sK3 @ X0 ) )
| ( sK2 != X0 ) )
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(duplicate_literal_removal,[],[f200]) ).
thf(f200,plain,
( ! [X0: a] :
( ( $false
= ( sK3 @ X0 ) )
| ( $false
= ( sK3 @ X0 ) )
| ( sK2 != X0 ) )
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f199,f195]) ).
thf(f195,plain,
( ! [X1: a] :
( ( ( f @ ( sK11 @ X1 ) )
= X1 )
| ( $false
= ( sK3 @ X1 ) ) )
| ~ spl0_10 ),
inference(equality_proxy_clausification,[],[f193]) ).
thf(f193,plain,
( ! [X1: a] :
( ( $false
= ( sK3 @ X1 ) )
| ( $true
= ( ( f @ ( sK11 @ X1 ) )
= X1 ) ) )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f192]) ).
thf(f192,plain,
( ! [X1: a] :
( ( ( ( sK5 @ ( sK11 @ X1 ) )
& ( ( f @ ( sK11 @ X1 ) )
= X1 ) )
= $true )
| ( $false
= ( sK3 @ X1 ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f191]) ).
thf(f191,plain,
( ! [X1: a] :
( ( $true
= ( ^ [Y0: b] :
( ( sK5 @ Y0 )
& ( ( f @ Y0 )
= X1 ) )
@ ( sK11 @ X1 ) ) )
| ( $false
= ( sK3 @ X1 ) ) )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f185]) ).
thf(f185,plain,
( ! [X1: a] :
( ( $false
= ( sK3 @ X1 ) )
| ( $true
= ( ?? @ b
@ ^ [Y0: b] :
( ( sK5 @ Y0 )
& ( ( f @ Y0 )
= X1 ) ) ) ) )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f184]) ).
thf(f184,plain,
( ! [X1: a] :
( ( ?? @ b
@ ^ [Y0: b] :
( ( sK5 @ Y0 )
& ( ( f @ Y0 )
= X1 ) ) )
= ( sK3 @ X1 ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f183]) ).
thf(f183,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
@ X1 )
= ( sK3 @ X1 ) )
| ~ spl0_10 ),
inference(argument_congruence,[],[f106]) ).
thf(f106,plain,
( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f104]) ).
thf(f104,plain,
( spl0_10
<=> ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f199,plain,
( ! [X0: a] :
( ( ( f @ ( sK11 @ X0 ) )
!= sK2 )
| ( $false
= ( sK3 @ X0 ) ) )
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f196]) ).
thf(f196,plain,
( ! [X0: a] :
( ( $false = $true )
| ( ( f @ ( sK11 @ X0 ) )
!= sK2 )
| ( $false
= ( sK3 @ X0 ) ) )
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f194,f182]) ).
thf(f182,plain,
( ! [X0: b] :
( ( $false
= ( sK5 @ X0 ) )
| ( sK2
!= ( f @ X0 ) ) )
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f180]) ).
thf(f180,plain,
( ! [X0: b] :
( ( $false = $true )
| ( sK2
!= ( f @ X0 ) )
| ( $false
= ( sK5 @ X0 ) ) )
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f120,f115]) ).
thf(f115,plain,
( ( $true
= ( w @ sK5 ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f113]) ).
thf(f113,plain,
( spl0_12
<=> ( $true
= ( w @ sK5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f194,plain,
( ! [X1: a] :
( ( ( sK5 @ ( sK11 @ X1 ) )
= $true )
| ( $false
= ( sK3 @ X1 ) ) )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f192]) ).
thf(f178,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f177]) ).
thf(f177,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_13 ),
inference(subsumption_resolution,[],[f173,f110]) ).
thf(f173,plain,
( ( ( f @ sK4 )
!= sK2 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f172]) ).
thf(f172,plain,
( ( $false = $true )
| ( ( f @ sK4 )
!= sK2 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13 ),
inference(superposition,[],[f87,f170]) ).
thf(f170,plain,
( ! [X0: b] :
( ( $false
= ( sK8 @ X0 ) )
| ( sK2
!= ( f @ X0 ) ) )
| ~ spl0_5
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f167]) ).
thf(f167,plain,
( ! [X0: b] :
( ( sK2
!= ( f @ X0 ) )
| ( $false = $true )
| ( $false
= ( sK8 @ X0 ) ) )
| ~ spl0_5
| ~ spl0_13 ),
inference(superposition,[],[f82,f120]) ).
thf(f82,plain,
( ( $true
= ( w @ sK8 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f80]) ).
thf(f80,plain,
( spl0_5
<=> ( $true
= ( w @ sK8 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f87,plain,
( ( $true
= ( sK8 @ sK4 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
thf(f85,plain,
( spl0_6
<=> ( $true
= ( sK8 @ sK4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f156,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f155]) ).
thf(f155,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f150]) ).
thf(f150,plain,
( ( $false = $true )
| ( sK2 != sK2 )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13 ),
inference(superposition,[],[f92,f147]) ).
thf(f147,plain,
( ! [X0: a] :
( ( $false
= ( sK3 @ X0 ) )
| ( sK2 != X0 ) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_13 ),
inference(duplicate_literal_removal,[],[f146]) ).
thf(f146,plain,
( ! [X0: a] :
( ( $false
= ( sK3 @ X0 ) )
| ( sK2 != X0 )
| ( $false
= ( sK3 @ X0 ) ) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_13 ),
inference(superposition,[],[f145,f141]) ).
thf(f141,plain,
( ! [X1: a] :
( ( ( f @ ( sK10 @ X1 ) )
= X1 )
| ( $false
= ( sK3 @ X1 ) ) )
| ~ spl0_2 ),
inference(equality_proxy_clausification,[],[f139]) ).
thf(f139,plain,
( ! [X1: a] :
( ( ( ( f @ ( sK10 @ X1 ) )
= X1 )
= $true )
| ( $false
= ( sK3 @ X1 ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f138]) ).
thf(f138,plain,
( ! [X1: a] :
( ( $true
= ( ( sK7 @ ( sK10 @ X1 ) )
& ( ( f @ ( sK10 @ X1 ) )
= X1 ) ) )
| ( $false
= ( sK3 @ X1 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f137]) ).
thf(f137,plain,
( ! [X1: a] :
( ( $false
= ( sK3 @ X1 ) )
| ( ( ^ [Y0: b] :
( ( sK7 @ Y0 )
& ( ( f @ Y0 )
= X1 ) )
@ ( sK10 @ X1 ) )
= $true ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f131]) ).
thf(f131,plain,
( ! [X1: a] :
( ( $true
= ( ?? @ b
@ ^ [Y0: b] :
( ( sK7 @ Y0 )
& ( ( f @ Y0 )
= X1 ) ) ) )
| ( $false
= ( sK3 @ X1 ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f130]) ).
thf(f130,plain,
( ! [X1: a] :
( ( ?? @ b
@ ^ [Y0: b] :
( ( sK7 @ Y0 )
& ( ( f @ Y0 )
= X1 ) ) )
= ( sK3 @ X1 ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f129]) ).
thf(f129,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK7 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
@ X1 )
= ( sK3 @ X1 ) )
| ~ spl0_2 ),
inference(argument_congruence,[],[f68]) ).
thf(f68,plain,
( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK7 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f66]) ).
thf(f66,plain,
( spl0_2
<=> ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK7 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f145,plain,
( ! [X0: a] :
( ( ( f @ ( sK10 @ X0 ) )
!= sK2 )
| ( $false
= ( sK3 @ X0 ) ) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f142]) ).
thf(f142,plain,
( ! [X0: a] :
( ( $false = $true )
| ( ( f @ ( sK10 @ X0 ) )
!= sK2 )
| ( $false
= ( sK3 @ X0 ) ) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_13 ),
inference(superposition,[],[f140,f128]) ).
thf(f128,plain,
( ! [X0: b] :
( ( $false
= ( sK7 @ X0 ) )
| ( sK2
!= ( f @ X0 ) ) )
| ~ spl0_4
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f126]) ).
thf(f126,plain,
( ! [X0: b] :
( ( $false = $true )
| ( $false
= ( sK7 @ X0 ) )
| ( sK2
!= ( f @ X0 ) ) )
| ~ spl0_4
| ~ spl0_13 ),
inference(superposition,[],[f120,f78]) ).
thf(f78,plain,
( ( $true
= ( w @ sK7 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f76]) ).
thf(f76,plain,
( spl0_4
<=> ( $true
= ( w @ sK7 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f140,plain,
( ! [X1: a] :
( ( ( sK7 @ ( sK10 @ X1 ) )
= $true )
| ( $false
= ( sK3 @ X1 ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f138]) ).
thf(f124,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f25,f122,f119]) ).
thf(f25,plain,
! [X2: b,X3: b > $o,X1: a > $o,X4: b > $o] :
( ( ( f @ X2 )
!= sK2 )
| ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X4 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= X1 )
| ( $false
= ( w @ X3 ) )
| ( $false
= ( X3 @ X2 ) )
| ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( w @ X4 ) ) ),
inference(equality_proxy_clausification,[],[f24]) ).
thf(f24,plain,
! [X2: b,X3: b > $o,X1: a > $o,X4: b > $o] :
( ( $false
= ( w @ X4 ) )
| ( $false
= ( X1 @ sK2 ) )
| ( ( f @ X2 )
!= sK2 )
| ( $false
= ( w @ X3 ) )
| ( $false
= ( X3 @ X2 ) )
| ( ( X1
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X4 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f23,plain,
! [X2: b,X3: b > $o,X1: a > $o,X4: b > $o] :
( ( $false
= ( X3 @ X2 ) )
| ( ( f @ X2 )
!= sK2 )
| ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( w @ X3 ) )
| ( $false
= ( ( w @ X4 )
& ( X1
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X4 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f22]) ).
thf(f22,plain,
! [X2: b,X3: b > $o,X1: a > $o,X4: b > $o] :
( ( $false
= ( ( X3 @ X2 )
& ( w @ X3 ) ) )
| ( $false
= ( X1 @ sK2 ) )
| ( ( f @ X2 )
!= sK2 )
| ( $false
= ( ( w @ X4 )
& ( X1
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X4 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f21]) ).
thf(f21,plain,
! [X2: b,X3: b > $o,X1: a > $o,X4: b > $o] :
( ( $false
= ( ( X3 @ X2 )
& ( w @ X3 ) ) )
| ( ( f @ X2 )
!= sK2 )
| ( $false
= ( ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( X1
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) )
@ X4 ) )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(pi_clausification,[],[f20]) ).
thf(f20,plain,
! [X2: b,X3: b > $o,X1: a > $o] :
( ( ( f @ X2 )
!= sK2 )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( X1
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( ( X3 @ X2 )
& ( w @ X3 ) ) )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(beta_eta_normalization,[],[f19]) ).
thf(f19,plain,
! [X2: b,X3: b > $o,X1: a > $o] :
( ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( X1
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: b > $o] :
( ( Y0 @ X2 )
& ( w @ Y0 ) )
@ X3 ) )
| ( $false
= ( X1 @ sK2 ) )
| ( ( f @ X2 )
!= sK2 ) ),
inference(pi_clausification,[],[f18]) ).
thf(f18,plain,
! [X2: b,X1: a > $o] :
( ( $false
= ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ X2 )
& ( w @ Y0 ) ) ) )
| ( ( f @ X2 )
!= sK2 )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( X1
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(equality_proxy_clausification,[],[f17]) ).
thf(f17,plain,
! [X2: b,X1: a > $o] :
( ( $false
= ( ( f @ X2 )
= sK2 ) )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( X1
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ X2 )
& ( w @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f16]) ).
thf(f16,plain,
! [X2: b,X1: a > $o] :
( ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( ( ( f @ X2 )
= sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ X2 )
& ( w @ Y0 ) ) ) ) )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( X1
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f15]) ).
thf(f15,plain,
! [X2: b,X1: a > $o] :
( ( $false
= ( ( X1 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( X1
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) ) ) )
| ( $false
= ( ( ( f @ X2 )
= sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ X2 )
& ( w @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
! [X2: b,X1: a > $o] :
( ( $false
= ( ( X1 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( X1
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) ) ) )
| ( ( ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( w @ Y1 ) ) ) )
@ X2 )
= $false ) ),
inference(pi_clausification,[],[f13]) ).
thf(f13,plain,
! [X1: a > $o] :
( ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( w @ Y1 ) ) ) ) ) )
| ( $false
= ( ( X1 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( X1
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
! [X1: a > $o] :
( ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( w @ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) ) ) ) )
@ X1 )
= $false ) ),
inference(pi_clausification,[],[f11]) ).
thf(f11,plain,
( ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( w @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f9]) ).
thf(f9,plain,
( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) ) ) ) ) )
!= ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( w @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y2 @ Y1 )
& ( w @ Y2 ) ) ) ) )
@ sK2 )
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( w @ Y2 )
& ( Y1
= ( ^ [Y3: a] :
( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( f @ Y4 )
= Y3 ) ) ) ) ) ) ) ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f7]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( w @ Y2 )
& ( Y1
= ( ^ [Y3: a] :
( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( f @ Y4 )
= Y3 ) ) ) ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y2 @ Y1 )
& ( w @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( w @ Y2 )
& ( Y1
= ( ^ [Y3: a] :
( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( f @ Y4 )
= Y3 ) ) ) ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y2 @ Y1 )
& ( w @ Y2 ) ) ) ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f5,plain,
( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( w @ Y2 )
& ( Y1
= ( ^ [Y3: a] :
( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( f @ Y4 )
= Y3 ) ) ) ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y2 @ Y1 )
& ( w @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
( ( ^ [X0: a] :
? [X1: b] :
( ? [X2: b > $o] :
( ( w @ X2 )
& ( X2 @ X1 ) )
& ( ( f @ X1 )
= X0 ) ) )
!= ( ^ [X3: a] :
? [X4: a > $o] :
( ? [X5: b > $o] :
( ( X4
= ( ^ [X6: a] :
? [X7: b] :
( ( ( f @ X7 )
= X6 )
& ( X5 @ X7 ) ) ) )
& ( w @ X5 ) )
& ( X4 @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a] :
? [X1: b] :
( ? [X2: b > $o] :
( ( w @ X2 )
& ( X2 @ X1 ) )
& ( ( f @ X1 )
= X0 ) ) )
!= ( ^ [X3: a] :
? [X2: a > $o] :
( ? [X1: b > $o] :
( ( X2
= ( ^ [X0: a] :
? [X4: b] :
( ( ( f @ X4 )
= X0 )
& ( X1 @ X4 ) ) ) )
& ( w @ X1 ) )
& ( X2 @ X3 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ( ^ [X0: a] :
? [X1: b] :
( ? [X2: b > $o] :
( ( w @ X2 )
& ( X2 @ X1 ) )
& ( ( f @ X1 )
= X0 ) ) )
= ( ^ [X3: a] :
? [X2: a > $o] :
( ? [X1: b > $o] :
( ( X2
= ( ^ [X0: a] :
? [X4: b] :
( ( ( f @ X4 )
= X0 )
& ( X1 @ X4 ) ) ) )
& ( w @ X1 ) )
& ( X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5204_pme) ).
thf(f117,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f34,f90,f108]) ).
thf(f34,plain,
( ( ( f @ sK4 )
= sK2 )
| ( ( sK3 @ sK2 )
= $true ) ),
inference(equality_proxy_clausification,[],[f33]) ).
thf(f33,plain,
( ( ( sK3 @ sK2 )
= $true )
| ( $true
= ( ( f @ sK4 )
= sK2 ) ) ),
inference(binary_proxy_clausification,[],[f31]) ).
thf(f31,plain,
( ( ( ( sK3 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( ( f @ sK4 )
= sK2 ) ) ),
inference(binary_proxy_clausification,[],[f29]) ).
thf(f29,plain,
( ( ( ( ( f @ sK4 )
= sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ sK4 )
& ( w @ Y0 ) ) ) )
= $true )
| ( ( ( sK3 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[],[f28]) ).
thf(f28,plain,
( ( ( ( sK3 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( w @ Y1 ) ) ) )
@ sK4 ) ) ),
inference(sigma_clausification,[],[f27]) ).
thf(f27,plain,
( ( $true
= ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( w @ Y1 ) ) ) ) ) )
| ( ( ( sK3 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[],[f26]) ).
thf(f26,plain,
( ( $true
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) ) ) ) )
@ sK3 ) )
| ( $true
= ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( w @ Y1 ) ) ) ) ) ) ),
inference(sigma_clausification,[],[f10]) ).
thf(f10,plain,
( ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( w @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f9]) ).
thf(f116,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f39,f113,f108]) ).
thf(f39,plain,
( ( ( f @ sK4 )
= sK2 )
| ( $true
= ( w @ sK5 ) ) ),
inference(equality_proxy_clausification,[],[f38]) ).
thf(f38,plain,
( ( $true
= ( ( f @ sK4 )
= sK2 ) )
| ( $true
= ( w @ sK5 ) ) ),
inference(binary_proxy_clausification,[],[f36]) ).
thf(f36,plain,
( ( $true
= ( ( w @ sK5 )
& ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ) )
| ( $true
= ( ( f @ sK4 )
= sK2 ) ) ),
inference(beta_eta_normalization,[],[f35]) ).
thf(f35,plain,
( ( $true
= ( ( f @ sK4 )
= sK2 ) )
| ( $true
= ( ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) )
@ sK5 ) ) ),
inference(sigma_clausification,[],[f32]) ).
thf(f32,plain,
( ( $true
= ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) ) )
| ( $true
= ( ( f @ sK4 )
= sK2 ) ) ),
inference(binary_proxy_clausification,[],[f31]) ).
thf(f111,plain,
( spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f41,f108,f104]) ).
thf(f41,plain,
( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
| ( ( f @ sK4 )
= sK2 ) ),
inference(equality_proxy_clausification,[],[f40]) ).
thf(f40,plain,
( ( $true
= ( ( f @ sK4 )
= sK2 ) )
| ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f37]) ).
thf(f37,plain,
( ( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
= $true )
| ( $true
= ( ( f @ sK4 )
= sK2 ) ) ),
inference(binary_proxy_clausification,[],[f36]) ).
thf(f102,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f47,f90,f99]) ).
thf(f47,plain,
( ( ( sK6 @ sK4 )
= $true )
| ( ( sK3 @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[],[f45]) ).
thf(f45,plain,
( ( ( sK3 @ sK2 )
= $true )
| ( $true
= ( ( sK6 @ sK4 )
& ( w @ sK6 ) ) ) ),
inference(beta_eta_normalization,[],[f44]) ).
thf(f44,plain,
( ( ( sK3 @ sK2 )
= $true )
| ( $true
= ( ^ [Y0: b > $o] :
( ( Y0 @ sK4 )
& ( w @ Y0 ) )
@ sK6 ) ) ),
inference(sigma_clausification,[],[f43]) ).
thf(f43,plain,
( ( ( sK3 @ sK2 )
= $true )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ sK4 )
& ( w @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f30]) ).
thf(f30,plain,
( ( ( ( sK3 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) ) )
= $true )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ sK4 )
& ( w @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f29]) ).
thf(f97,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f46,f94,f90]) ).
thf(f46,plain,
( ( ( sK3 @ sK2 )
= $true )
| ( $true
= ( w @ sK6 ) ) ),
inference(binary_proxy_clausification,[],[f45]) ).
thf(f88,plain,
( spl0_6
| spl0_4 ),
inference(avatar_split_clause,[],[f55,f76,f85]) ).
thf(f55,plain,
( ( $true
= ( w @ sK7 ) )
| ( $true
= ( sK8 @ sK4 ) ) ),
inference(binary_proxy_clausification,[],[f53]) ).
thf(f53,plain,
( ( $true
= ( w @ sK7 ) )
| ( $true
= ( ( sK8 @ sK4 )
& ( w @ sK8 ) ) ) ),
inference(beta_eta_normalization,[],[f52]) ).
thf(f52,plain,
( ( $true
= ( w @ sK7 ) )
| ( $true
= ( ^ [Y0: b > $o] :
( ( Y0 @ sK4 )
& ( w @ Y0 ) )
@ sK8 ) ) ),
inference(sigma_clausification,[],[f51]) ).
thf(f51,plain,
( ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ sK4 )
& ( w @ Y0 ) ) )
= $true )
| ( $true
= ( w @ sK7 ) ) ),
inference(binary_proxy_clausification,[],[f49]) ).
thf(f49,plain,
( ( $true
= ( ( w @ sK7 )
& ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK7 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ) )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ sK4 )
& ( w @ Y0 ) ) )
= $true ) ),
inference(beta_eta_normalization,[],[f48]) ).
thf(f48,plain,
( ( $true
= ( ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) )
@ sK7 ) )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ sK4 )
& ( w @ Y0 ) ) )
= $true ) ),
inference(sigma_clausification,[],[f42]) ).
thf(f42,plain,
( ( $true
= ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) ) ) ) )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ sK4 )
& ( w @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f30]) ).
thf(f83,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f54,f80,f76]) ).
thf(f54,plain,
( ( $true
= ( w @ sK7 ) )
| ( $true
= ( w @ sK8 ) ) ),
inference(binary_proxy_clausification,[],[f53]) ).
thf(f74,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f60,f66,f71]) ).
thf(f60,plain,
( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK7 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
| ( $true
= ( sK9 @ sK4 ) ) ),
inference(binary_proxy_clausification,[],[f58]) ).
thf(f58,plain,
( ( $true
= ( ( sK9 @ sK4 )
& ( w @ sK9 ) ) )
| ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK7 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f57]) ).
thf(f57,plain,
( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK7 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: b > $o] :
( ( Y0 @ sK4 )
& ( w @ Y0 ) )
@ sK9 ) ) ),
inference(sigma_clausification,[],[f56]) ).
thf(f56,plain,
( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK7 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ sK4 )
& ( w @ Y0 ) ) )
= $true ) ),
inference(equality_proxy_clausification,[],[f50]) ).
thf(f50,plain,
( ( $true
= ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK7 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0 @ sK4 )
& ( w @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f49]) ).
thf(f69,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f59,f66,f62]) ).
thf(f59,plain,
( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK7 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
| ( $true
= ( w @ sK9 ) ) ),
inference(binary_proxy_clausification,[],[f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV223^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36 % Computer : n006.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 18:25:53 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 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/sandbox/benchmark/theBenchmark.p
% 0.14/0.39 % (22005)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.39 % (22002)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.39 % (22002)Instruction limit reached!
% 0.14/0.39 % (22002)------------------------------
% 0.14/0.39 % (22002)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (22002)Termination reason: Unknown
% 0.14/0.39 % (22002)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (22002)Memory used [KB]: 5373
% 0.14/0.39 % (22002)Time elapsed: 0.004 s
% 0.14/0.39 % (22002)Instructions burned: 2 (million)
% 0.14/0.39 % (22002)------------------------------
% 0.14/0.39 % (22002)------------------------------
% 0.14/0.39 % (22000)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)
% 0.14/0.39 % (21999)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.39 % (22004)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)
% 0.14/0.40 % (22001)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)
% 0.14/0.40 % (22003)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)
% 0.14/0.40 % (22006)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)
% 0.14/0.40 % (22003)Instruction limit reached!
% 0.14/0.40 % (22003)------------------------------
% 0.14/0.40 % (22003)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (22003)Termination reason: Unknown
% 0.14/0.40 % (22003)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (22003)Memory used [KB]: 895
% 0.14/0.40 % (22003)Time elapsed: 0.004 s
% 0.14/0.40 % (22003)Instructions burned: 2 (million)
% 0.14/0.40 % (22003)------------------------------
% 0.14/0.40 % (22003)------------------------------
% 0.14/0.40 % (22000)Instruction limit reached!
% 0.14/0.40 % (22000)------------------------------
% 0.14/0.40 % (22000)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (22000)Termination reason: Unknown
% 0.14/0.40 % (22000)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (22006)Refutation not found, incomplete strategy
% 0.14/0.40 % (22006)------------------------------
% 0.14/0.40 % (22006)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (22006)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.40
% 0.14/0.40
% 0.14/0.40 % (22006)Memory used [KB]: 5500
% 0.14/0.40 % (22006)Time elapsed: 0.004 s
% 0.14/0.40 % (22006)Instructions burned: 2 (million)
% 0.14/0.40 % (22006)------------------------------
% 0.14/0.40 % (22006)------------------------------
% 0.14/0.40 % (22000)Memory used [KB]: 5500
% 0.14/0.40 % (22000)Time elapsed: 0.005 s
% 0.14/0.40 % (22000)Instructions burned: 4 (million)
% 0.14/0.40 % (22000)------------------------------
% 0.14/0.40 % (22000)------------------------------
% 0.23/0.40 % (22005)Instruction limit reached!
% 0.23/0.40 % (22005)------------------------------
% 0.23/0.40 % (22005)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40 % (22005)Termination reason: Unknown
% 0.23/0.40 % (22005)Termination phase: Saturation
% 0.23/0.40
% 0.23/0.40 % (22005)Memory used [KB]: 5628
% 0.23/0.40 % (22005)Time elapsed: 0.015 s
% 0.23/0.40 % (22005)Instructions burned: 19 (million)
% 0.23/0.40 % (22005)------------------------------
% 0.23/0.40 % (22005)------------------------------
% 0.23/0.41 % (22007)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)
% 0.23/0.41 % (22004)First to succeed.
% 0.23/0.41 % (22009)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)
% 0.23/0.41 % (22010)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 theBenchmark for (2999ds/1041Mi)
% 0.23/0.41 % (22008)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)
% 0.23/0.41 % (22009)Refutation not found, incomplete strategy
% 0.23/0.41 % (22009)------------------------------
% 0.23/0.41 % (22009)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.41 % (22009)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.41
% 0.23/0.41
% 0.23/0.41 % (22009)Memory used [KB]: 5500
% 0.23/0.41 % (22009)Time elapsed: 0.003 s
% 0.23/0.41 % (22009)Instructions burned: 2 (million)
% 0.23/0.41 % (22009)------------------------------
% 0.23/0.41 % (22009)------------------------------
% 0.23/0.42 % (22004)Refutation found. Thanks to Tanya!
% 0.23/0.42 % SZS status Theorem for theBenchmark
% 0.23/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.42 % (22004)------------------------------
% 0.23/0.42 % (22004)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.42 % (22004)Termination reason: Refutation
% 0.23/0.42
% 0.23/0.42 % (22004)Memory used [KB]: 5628
% 0.23/0.42 % (22004)Time elapsed: 0.023 s
% 0.23/0.42 % (22004)Instructions burned: 21 (million)
% 0.23/0.42 % (22004)------------------------------
% 0.23/0.42 % (22004)------------------------------
% 0.23/0.42 % (21998)Success in time 0.043 s
% 0.23/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------