TSTP Solution File: SYO664-1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SYO664-1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -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 : Wed Aug 31 19:48:53 EDT 2022
% Result : Unsatisfiable 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 105 ( 3 unt; 0 def)
% Number of atoms : 519 ( 0 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 846 ( 432 ~; 402 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 16 ( 15 usr; 13 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 84 ( 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f179,plain,
$false,
inference(avatar_sat_refutation,[],[f23,f32,f38,f55,f89,f97,f101,f107,f117,f146,f156,f163,f171,f178]) ).
fof(f178,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f177]) ).
fof(f177,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(subsumption_resolution,[],[f176,f54]) ).
fof(f54,plain,
( 'E'(s('0'),f(suc(suc(z))))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f52,plain,
( spl0_7
<=> 'E'(s('0'),f(suc(suc(z)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f176,plain,
( ~ 'E'(s('0'),f(suc(suc(z))))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(subsumption_resolution,[],[f175,f31]) ).
fof(f31,plain,
( 'E'(s('0'),f(suc(z)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f29,plain,
( spl0_3
<=> 'E'(s('0'),f(suc(z))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f175,plain,
( ~ 'E'(s('0'),f(suc(z)))
| ~ 'E'(s('0'),f(suc(suc(z))))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(resolution,[],[f174,f88]) ).
fof(f88,plain,
( iLEQ(suc(suc(z)),suc(suc(z)))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f86,plain,
( spl0_12
<=> iLEQ(suc(suc(z)),suc(suc(z))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f174,plain,
( ! [X0] :
( ~ iLEQ(suc(X0),suc(suc(z)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0))) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(subsumption_resolution,[],[f173,f31]) ).
fof(f173,plain,
( ! [X0] :
( ~ iLEQ(suc(X0),suc(suc(z)))
| ~ 'E'(s('0'),f(suc(z)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0))) )
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(subsumption_resolution,[],[f172,f54]) ).
fof(f172,plain,
( ! [X0] :
( ~ iLEQ(suc(X0),suc(suc(z)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(suc(z))))
| ~ 'E'(s('0'),f(suc(z)))
| ~ 'E'(s('0'),f(X0)) )
| ~ spl0_11
| ~ spl0_12 ),
inference(resolution,[],[f83,f88]) ).
fof(f83,plain,
( ! [X3,X1] :
( ~ iLEQ(suc(X1),suc(suc(z)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ iLEQ(suc(X3),suc(X1)) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f82,plain,
( spl0_11
<=> ! [X1,X3] :
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(suc(z)))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ iLEQ(suc(X3),suc(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f171,plain,
( spl0_11
| spl0_10
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f170,f52,f29,f79,f82]) ).
fof(f79,plain,
( spl0_10
<=> ! [X2,X0] :
( ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(suc(z)),suc(X2))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f170,plain,
( ! [X2,X3,X0,X1] :
( ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ iLEQ(suc(X1),suc(suc(z)))
| ~ iLEQ(suc(suc(z)),suc(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s('0'),f(suc(X1))) )
| ~ spl0_3
| ~ spl0_7 ),
inference(subsumption_resolution,[],[f168,f31]) ).
fof(f168,plain,
( ! [X2,X3,X0,X1] :
( ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ iLEQ(suc(suc(z)),suc(X2))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(suc(z)))
| ~ 'E'(s('0'),f(suc(z)))
| ~ 'E'(s('0'),f(suc(X0))) )
| ~ spl0_7 ),
inference(resolution,[],[f54,f1]) ).
fof(f1,axiom,
! [X2,X3,X0,X1,X4] :
( ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X3))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X4))
| ~ iLEQ(suc(X2),suc(X4))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(X3),suc(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_37) ).
fof(f163,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f162]) ).
fof(f162,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(subsumption_resolution,[],[f161,f49]) ).
fof(f49,plain,
( iLEQ(suc(z),suc(z))
| ~ spl0_2
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f40,f22]) ).
fof(f22,plain,
( 'E'(s('0'),f(z))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f20,plain,
( spl0_2
<=> 'E'(s('0'),f(z)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f40,plain,
( ~ 'E'(s('0'),f(z))
| iLEQ(suc(z),suc(z))
| ~ spl0_3 ),
inference(resolution,[],[f31,f9]) ).
fof(f9,axiom,
! [X3] :
( ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X3))
| iLEQ(suc(X3),suc(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_50) ).
fof(f161,plain,
( ~ iLEQ(suc(z),suc(z))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(subsumption_resolution,[],[f160,f22]) ).
fof(f160,plain,
( ~ 'E'(s('0'),f(z))
| ~ iLEQ(suc(z),suc(z))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(resolution,[],[f159,f31]) ).
fof(f159,plain,
( ! [X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ iLEQ(suc(z),suc(X0))
| ~ 'E'(s('0'),f(X0)) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(subsumption_resolution,[],[f158,f22]) ).
fof(f158,plain,
( ! [X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ iLEQ(suc(z),suc(X0))
| ~ 'E'(s('0'),f(z))
| ~ 'E'(s('0'),f(X0)) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(subsumption_resolution,[],[f157,f49]) ).
fof(f157,plain,
( ! [X0] :
( ~ iLEQ(suc(z),suc(z))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(z),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(z)) )
| ~ spl0_3
| ~ spl0_6 ),
inference(resolution,[],[f47,f31]) ).
fof(f47,plain,
( ! [X2,X0] :
( ~ 'E'(s('0'),f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(z),suc(X2))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X2)) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f46,plain,
( spl0_6
<=> ! [X2,X0] :
( ~ iLEQ(suc(z),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f156,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f155,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f154,f49]) ).
fof(f154,plain,
( ~ iLEQ(suc(z),suc(z))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f153,f22]) ).
fof(f153,plain,
( ~ 'E'(s('0'),f(z))
| ~ iLEQ(suc(z),suc(z))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(duplicate_literal_removal,[],[f152]) ).
fof(f152,plain,
( ~ 'E'(s('0'),f(z))
| ~ iLEQ(suc(z),suc(z))
| ~ iLEQ(suc(z),suc(z))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(resolution,[],[f138,f31]) ).
fof(f138,plain,
( ! [X1] :
( ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| ~ iLEQ(suc(z),suc(X1))
| ~ iLEQ(suc(X1),suc(z)) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f137,f22]) ).
fof(f137,plain,
( ! [X1] :
( ~ iLEQ(suc(z),suc(X1))
| ~ 'E'(s('0'),f(z))
| ~ 'E'(s('0'),f(X1))
| ~ iLEQ(suc(X1),suc(z))
| ~ 'E'(s('0'),f(suc(X1))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(resolution,[],[f44,f31]) ).
fof(f44,plain,
( ! [X3,X1] :
( ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(z))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s('0'),f(X1)) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f43,plain,
( spl0_5
<=> ! [X1,X3] :
( ~ 'E'(s('0'),f(suc(X3)))
| ~ iLEQ(suc(X1),suc(z))
| ~ 'E'(s('0'),f(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f146,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f145]) ).
fof(f145,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10 ),
inference(subsumption_resolution,[],[f144,f31]) ).
fof(f144,plain,
( ~ 'E'(s('0'),f(suc(z)))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10 ),
inference(subsumption_resolution,[],[f143,f54]) ).
fof(f143,plain,
( ~ 'E'(s('0'),f(suc(suc(z))))
| ~ 'E'(s('0'),f(suc(z)))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10 ),
inference(resolution,[],[f142,f76]) ).
fof(f76,plain,
( iLEQ(suc(suc(z)),suc(suc(z)))
| ~ spl0_3
| ~ spl0_7 ),
inference(subsumption_resolution,[],[f75,f31]) ).
fof(f75,plain,
( iLEQ(suc(suc(z)),suc(suc(z)))
| ~ 'E'(s('0'),f(suc(z)))
| ~ spl0_7 ),
inference(resolution,[],[f54,f9]) ).
fof(f142,plain,
( ! [X0] :
( ~ iLEQ(suc(suc(z)),suc(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0))) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10 ),
inference(subsumption_resolution,[],[f141,f31]) ).
fof(f141,plain,
( ! [X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(suc(z)),suc(X0))
| ~ 'E'(s('0'),f(suc(z))) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10 ),
inference(subsumption_resolution,[],[f140,f54]) ).
fof(f140,plain,
( ! [X0] :
( ~ 'E'(s('0'),f(suc(suc(z))))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(z)))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(suc(z)),suc(X0)) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10 ),
inference(resolution,[],[f80,f76]) ).
fof(f80,plain,
( ! [X2,X0] :
( ~ iLEQ(suc(suc(z)),suc(X2))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(X2),suc(X0)) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f117,plain,
( spl0_5
| spl0_6
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f116,f29,f20,f46,f43]) ).
fof(f116,plain,
( ! [X2,X3,X0,X1] :
( ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(X1),suc(z))
| ~ iLEQ(suc(z),suc(X2))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X1)) )
| ~ spl0_2
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f113,f22]) ).
fof(f113,plain,
( ! [X2,X3,X0,X1] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(z),suc(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(z))
| ~ iLEQ(suc(X1),suc(z))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X2)) )
| ~ spl0_3 ),
inference(resolution,[],[f31,f1]) ).
fof(f107,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f106]) ).
fof(f106,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f105,f18]) ).
fof(f18,plain,
( 'E'('0',f(z))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f16,plain,
( spl0_1
<=> 'E'('0',f(z)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f105,plain,
( ~ 'E'('0',f(z))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f104,f37]) ).
fof(f37,plain,
( 'E'('0',f(suc(z)))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f35,plain,
( spl0_4
<=> 'E'('0',f(suc(z))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f104,plain,
( ~ 'E'('0',f(suc(z)))
| ~ 'E'('0',f(z))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f103,f57]) ).
fof(f57,plain,
( iLEQ(suc(z),suc(z))
| ~ spl0_1
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f56,f18]) ).
fof(f56,plain,
( iLEQ(suc(z),suc(z))
| ~ 'E'('0',f(z))
| ~ spl0_4 ),
inference(resolution,[],[f37,f6]) ).
fof(f6,axiom,
! [X8] :
( ~ 'E'('0',f(suc(X8)))
| iLEQ(suc(X8),suc(X8))
| ~ 'E'('0',f(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
fof(f103,plain,
( ~ iLEQ(suc(z),suc(z))
| ~ 'E'('0',f(z))
| ~ 'E'('0',f(suc(z)))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(duplicate_literal_removal,[],[f102]) ).
fof(f102,plain,
( ~ 'E'('0',f(z))
| ~ 'E'('0',f(suc(z)))
| ~ 'E'('0',f(z))
| ~ iLEQ(suc(z),suc(z))
| ~ 'E'('0',f(suc(z)))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(resolution,[],[f67,f57]) ).
fof(f67,plain,
( ! [X2,X1] :
( ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X1),suc(z))
| ~ 'E'('0',f(suc(X2))) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f66,plain,
( spl0_9
<=> ! [X2,X1] :
( ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X1),suc(z)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f101,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f100]) ).
fof(f100,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(subsumption_resolution,[],[f99,f37]) ).
fof(f99,plain,
( ~ 'E'('0',f(suc(z)))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(subsumption_resolution,[],[f98,f18]) ).
fof(f98,plain,
( ~ 'E'('0',f(z))
| ~ 'E'('0',f(suc(z)))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(resolution,[],[f64,f57]) ).
fof(f64,plain,
( ! [X0] :
( ~ iLEQ(suc(z),suc(X0))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0))) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f63,plain,
( spl0_8
<=> ! [X0] :
( ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(z),suc(X0))
| ~ 'E'('0',f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f97,plain,
( spl0_8
| spl0_9
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f96,f35,f16,f66,f63]) ).
fof(f96,plain,
( ! [X2,X0,X1] :
( ~ iLEQ(suc(X1),suc(z))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(z),suc(X0))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X0))) )
| ~ spl0_1
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f95,f18]) ).
fof(f95,plain,
( ! [X2,X0,X1] :
( ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X2)))
| ~ iLEQ(suc(z),suc(X0))
| ~ 'E'('0',f(z))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(z))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X0))) )
| ~ spl0_1
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f94,f37]) ).
fof(f94,plain,
( ! [X2,X0,X1] :
( ~ 'E'('0',f(suc(z)))
| ~ iLEQ(suc(X1),suc(z))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(z),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(z))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X2))) )
| ~ spl0_1
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f93]) ).
fof(f93,plain,
( ! [X2,X0,X1] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(z))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(z),suc(X0))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(z))
| ~ 'E'('0',f(suc(z)))
| ~ 'E'('0',f(suc(z)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X1),suc(z))
| ~ 'E'('0',f(suc(X2))) )
| ~ spl0_1
| ~ spl0_4 ),
inference(resolution,[],[f57,f4]) ).
fof(f4,axiom,
! [X10,X8,X6,X9,X7] :
( ~ iLEQ(suc(X9),suc(X6))
| ~ 'E'('0',f(suc(X6)))
| ~ 'E'('0',f(X9))
| ~ 'E'('0',f(X10))
| ~ iLEQ(suc(X7),suc(X9))
| ~ 'E'('0',f(X6))
| ~ 'E'('0',f(X8))
| ~ 'E'('0',f(X7))
| ~ 'E'('0',f(suc(X8)))
| ~ 'E'('0',f(suc(X7)))
| ~ 'E'('0',f(suc(X10)))
| ~ iLEQ(suc(X6),suc(X10))
| ~ iLEQ(suc(X8),suc(X7))
| ~ 'E'('0',f(suc(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_66) ).
fof(f89,plain,
( ~ spl0_3
| spl0_12
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f75,f52,f86,f29]) ).
fof(f55,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f50,f35,f52]) ).
fof(f50,plain,
( 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(suc(z)))) ),
inference(resolution,[],[f26,f2]) ).
fof(f2,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_70) ).
fof(f26,plain,
! [X1] :
( 'LE'(f(X1),'0')
| 'E'('0',f(suc(X1)))
| 'E'(s('0'),f(suc(suc(X1)))) ),
inference(resolution,[],[f24,f7]) ).
fof(f7,axiom,
! [X12] :
( ~ 'LE'(f(suc(X12)),s('0'))
| 'LE'(f(X12),'0')
| 'E'('0',f(suc(X12))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_117) ).
fof(f24,plain,
! [X5] :
( 'LE'(f(X5),s('0'))
| 'E'(s('0'),f(suc(X5))) ),
inference(subsumption_resolution,[],[f10,f5]) ).
fof(f5,axiom,
! [X11] : 'LE'(f(X11),s(s('0'))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_58) ).
fof(f10,axiom,
! [X5] :
( 'LE'(f(X5),s('0'))
| 'E'(s('0'),f(suc(X5)))
| ~ 'LE'(f(suc(X5)),s(s('0'))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_83) ).
fof(f38,plain,
( spl0_4
| spl0_3 ),
inference(avatar_split_clause,[],[f33,f29,f35]) ).
fof(f33,plain,
( 'E'(s('0'),f(suc(z)))
| 'E'('0',f(suc(z))) ),
inference(resolution,[],[f13,f2]) ).
fof(f13,plain,
! [X1] :
( 'LE'(f(X1),'0')
| 'E'(s('0'),f(suc(X1)))
| 'E'('0',f(suc(X1))) ),
inference(resolution,[],[f11,f7]) ).
fof(f11,plain,
! [X5] :
( 'LE'(f(X5),s('0'))
| 'E'(s('0'),f(X5)) ),
inference(subsumption_resolution,[],[f3,f5]) ).
fof(f3,axiom,
! [X5] :
( 'E'(s('0'),f(X5))
| ~ 'LE'(f(X5),s(s('0')))
| 'LE'(f(X5),s('0')) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20) ).
fof(f32,plain,
( spl0_3
| spl0_1 ),
inference(avatar_split_clause,[],[f27,f16,f29]) ).
fof(f27,plain,
( 'E'('0',f(z))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[],[f25,f2]) ).
fof(f25,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0))
| 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[],[f24,f8]) ).
fof(f8,axiom,
! [X12] :
( ~ 'LE'(f(X12),s('0'))
| 'E'('0',f(X12))
| 'LE'(f(X12),'0') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_94) ).
fof(f23,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f14,f20,f16]) ).
fof(f14,plain,
( 'E'(s('0'),f(z))
| 'E'('0',f(z)) ),
inference(resolution,[],[f12,f2]) ).
fof(f12,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(X0))
| 'E'('0',f(X0)) ),
inference(resolution,[],[f11,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO664-1 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 23:20:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.50 % (29169)lrs+1011_1:1_atotf=0.0306256:ep=RST:mep=off:nm=0:sos=all:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.50 % (29185)dis+10_1:1_add=large:alpa=false:anc=none:fd=off:lcm=reverse:nwc=5.0:sd=2:sgt=20:ss=included:i=46:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/46Mi)
% 0.20/0.50 % (29170)lrs+1010_1:1_bd=off:fd=off:fde=none:ins=3:sac=on:sos=on:spb=goal:to=lpo:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50 % (29170)Refutation not found, incomplete strategy% (29170)------------------------------
% 0.20/0.50 % (29170)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50 % (29170)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50 % (29170)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.50
% 0.20/0.50 % (29170)Memory used [KB]: 5756
% 0.20/0.50 % (29170)Time elapsed: 0.003 s
% 0.20/0.50 % (29170)Instructions burned: 1 (million)
% 0.20/0.50 % (29170)------------------------------
% 0.20/0.50 % (29170)------------------------------
% 0.20/0.51 % (29177)lrs+1_1:1_aac=none:add=large:anc=all_dependent:cond=fast:ep=RST:fsr=off:lma=on:nm=2:sos=on:sp=reverse_arity:stl=30:uhcvi=on:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.51 % (29177)Refutation not found, incomplete strategy% (29177)------------------------------
% 0.20/0.51 % (29177)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (29177)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (29177)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.51
% 0.20/0.51 % (29177)Memory used [KB]: 5756
% 0.20/0.51 % (29177)Time elapsed: 0.003 s
% 0.20/0.51 % (29177)Instructions burned: 1 (million)
% 0.20/0.51 % (29177)------------------------------
% 0.20/0.51 % (29177)------------------------------
% 0.20/0.51 % (29169)Refutation not found, incomplete strategy% (29169)------------------------------
% 0.20/0.51 % (29169)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (29169)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (29169)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.51
% 0.20/0.51 % (29169)Memory used [KB]: 5756
% 0.20/0.51 % (29169)Time elapsed: 0.003 s
% 0.20/0.51 % (29169)Instructions burned: 1 (million)
% 0.20/0.51 % (29169)------------------------------
% 0.20/0.51 % (29169)------------------------------
% 0.20/0.51 % (29162)dis+21_1:1_av=off:fd=off:lcm=predicate:sos=on:spb=goal:urr=ec_only:i=42:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/42Mi)
% 0.20/0.51 % (29162)Refutation not found, incomplete strategy% (29162)------------------------------
% 0.20/0.51 % (29162)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (29162)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (29162)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.51
% 0.20/0.51 % (29162)Memory used [KB]: 1279
% 0.20/0.51 % (29162)Time elapsed: 0.001 s
% 0.20/0.51 % (29162)------------------------------
% 0.20/0.51 % (29162)------------------------------
% 0.20/0.51 % (29181)lrs+10_1:7_av=off:awrs=converge:awrsf=40:br=off:bsd=on:cond=on:drc=off:nwc=3.0:plsq=on:plsqc=1:s2a=on:s2agt=16:to=lpo:urr=on:i=6:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.51 % (29185)First to succeed.
% 0.20/0.51 % (29181)Instruction limit reached!
% 0.20/0.51 % (29181)------------------------------
% 0.20/0.51 % (29181)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (29181)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (29181)Termination reason: Unknown
% 0.20/0.51 % (29181)Termination phase: Saturation
% 0.20/0.51
% 0.20/0.51 % (29181)Memory used [KB]: 1407
% 0.20/0.51 % (29181)Time elapsed: 0.004 s
% 0.20/0.51 % (29181)Instructions burned: 6 (million)
% 0.20/0.51 % (29181)------------------------------
% 0.20/0.51 % (29181)------------------------------
% 0.20/0.52 % (29185)Refutation found. Thanks to Tanya!
% 0.20/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52 % (29185)------------------------------
% 0.20/0.52 % (29185)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (29185)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (29185)Termination reason: Refutation
% 0.20/0.52
% 0.20/0.52 % (29185)Memory used [KB]: 6012
% 0.20/0.52 % (29185)Time elapsed: 0.114 s
% 0.20/0.52 % (29185)Instructions burned: 8 (million)
% 0.20/0.52 % (29185)------------------------------
% 0.20/0.52 % (29185)------------------------------
% 0.20/0.52 % (29160)Success in time 0.166 s
%------------------------------------------------------------------------------