TSTP Solution File: SWC310+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SWC310+1 : TPTP v8.1.0. Released v2.4.0.
% 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 : n017.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 18:40:20 EDT 2022
% Result : Theorem 0.21s 0.53s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 31
% Syntax : Number of formulae : 139 ( 7 unt; 0 def)
% Number of atoms : 766 ( 272 equ)
% Maximal formula atoms : 54 ( 5 avg)
% Number of connectives : 1033 ( 406 ~; 411 |; 168 &)
% ( 16 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 15 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 178 ( 122 !; 56 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f603,plain,
$false,
inference(avatar_sat_refutation,[],[f246,f251,f256,f261,f291,f301,f306,f307,f308,f320,f323,f327,f336,f340,f569,f572]) ).
fof(f572,plain,
( ~ spl12_4
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5 ),
inference(avatar_split_clause,[],[f571,f258,f248,f243,f253]) ).
fof(f253,plain,
( spl12_4
<=> nil = sK7 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_4])]) ).
fof(f243,plain,
( spl12_2
<=> ssItem(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).
fof(f248,plain,
( spl12_3
<=> app(cons(sK8,nil),sK9) = sK7 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).
fof(f258,plain,
( spl12_5
<=> ssList(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_5])]) ).
fof(f571,plain,
( nil != sK7
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5 ),
inference(subsumption_resolution,[],[f570,f260]) ).
fof(f260,plain,
( ssList(sK9)
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f570,plain,
( ~ ssList(sK9)
| nil != sK7
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5 ),
inference(subsumption_resolution,[],[f437,f245]) ).
fof(f245,plain,
( ssItem(sK8)
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f437,plain,
( ~ ssItem(sK8)
| ~ ssList(sK9)
| nil != sK7
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5 ),
inference(superposition,[],[f159,f431]) ).
fof(f431,plain,
( cons(sK8,sK9) = sK7
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5 ),
inference(subsumption_resolution,[],[f430,f260]) ).
fof(f430,plain,
( cons(sK8,sK9) = sK7
| ~ ssList(sK9)
| ~ spl12_2
| ~ spl12_3 ),
inference(subsumption_resolution,[],[f422,f245]) ).
fof(f422,plain,
( ~ ssItem(sK8)
| cons(sK8,sK9) = sK7
| ~ ssList(sK9)
| ~ spl12_3 ),
inference(superposition,[],[f209,f250]) ).
fof(f250,plain,
( app(cons(sK8,nil),sK9) = sK7
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f209,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssList(X0)
| ~ ssItem(X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).
fof(f159,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f569,plain,
( ~ spl12_2
| ~ spl12_3
| ~ spl12_5
| spl12_10
| ~ spl12_15 ),
inference(avatar_contradiction_clause,[],[f568]) ).
fof(f568,plain,
( $false
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5
| spl12_10
| ~ spl12_15 ),
inference(subsumption_resolution,[],[f567,f305]) ).
fof(f305,plain,
( app(sK9,cons(sK8,nil)) = sK4
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f303,plain,
( spl12_15
<=> app(sK9,cons(sK8,nil)) = sK4 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_15])]) ).
fof(f567,plain,
( app(sK9,cons(sK8,nil)) != sK4
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5
| spl12_10 ),
inference(forward_demodulation,[],[f445,f444]) ).
fof(f444,plain,
( sK8 = hd(sK7)
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5 ),
inference(subsumption_resolution,[],[f443,f260]) ).
fof(f443,plain,
( sK8 = hd(sK7)
| ~ ssList(sK9)
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5 ),
inference(subsumption_resolution,[],[f434,f245]) ).
fof(f434,plain,
( ~ ssItem(sK8)
| ~ ssList(sK9)
| sK8 = hd(sK7)
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5 ),
inference(superposition,[],[f207,f431]) ).
fof(f207,plain,
! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssList(X0)
| ~ ssItem(X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
fof(f445,plain,
( sK4 != app(sK9,cons(hd(sK7),nil))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5
| spl12_10 ),
inference(backward_demodulation,[],[f281,f440]) ).
fof(f440,plain,
( tl(sK7) = sK9
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5 ),
inference(subsumption_resolution,[],[f439,f260]) ).
fof(f439,plain,
( ~ ssList(sK9)
| tl(sK7) = sK9
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5 ),
inference(subsumption_resolution,[],[f435,f245]) ).
fof(f435,plain,
( tl(sK7) = sK9
| ~ ssItem(sK8)
| ~ ssList(sK9)
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5 ),
inference(superposition,[],[f185,f431]) ).
fof(f185,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssList(X0)
| ~ ssItem(X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
fof(f281,plain,
( sK4 != app(tl(sK7),cons(hd(sK7),nil))
| spl12_10 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f279,plain,
( spl12_10
<=> sK4 = app(tl(sK7),cons(hd(sK7),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_10])]) ).
fof(f340,plain,
( ~ spl12_6
| ~ spl12_7
| spl12_12 ),
inference(avatar_contradiction_clause,[],[f339]) ).
fof(f339,plain,
( $false
| ~ spl12_6
| ~ spl12_7
| spl12_12 ),
inference(subsumption_resolution,[],[f338,f268]) ).
fof(f268,plain,
( ssList(cons(hd(sK7),nil))
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f267,plain,
( spl12_7
<=> ssList(cons(hd(sK7),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_7])]) ).
fof(f338,plain,
( ~ ssList(cons(hd(sK7),nil))
| ~ spl12_6
| spl12_12 ),
inference(subsumption_resolution,[],[f337,f264]) ).
fof(f264,plain,
( ssList(tl(sK7))
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f263,plain,
( spl12_6
<=> ssList(tl(sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_6])]) ).
fof(f337,plain,
( ~ ssList(tl(sK7))
| ~ ssList(cons(hd(sK7),nil))
| spl12_12 ),
inference(resolution,[],[f289,f172]) ).
fof(f172,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f289,plain,
( ~ ssList(app(tl(sK7),cons(hd(sK7),nil)))
| spl12_12 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f287,plain,
( spl12_12
<=> ssList(app(tl(sK7),cons(hd(sK7),nil))) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_12])]) ).
fof(f336,plain,
( spl12_4
| spl12_8
| ~ spl12_14 ),
inference(avatar_contradiction_clause,[],[f335]) ).
fof(f335,plain,
( $false
| spl12_4
| spl12_8
| ~ spl12_14 ),
inference(subsumption_resolution,[],[f334,f254]) ).
fof(f254,plain,
( nil != sK7
| spl12_4 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f334,plain,
( nil = sK7
| spl12_8
| ~ spl12_14 ),
inference(subsumption_resolution,[],[f333,f298]) ).
fof(f298,plain,
( ssList(nil)
| ~ spl12_14 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f297,plain,
( spl12_14
<=> ssList(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_14])]) ).
fof(f333,plain,
( ~ ssList(nil)
| nil = sK7
| spl12_8 ),
inference(subsumption_resolution,[],[f330,f199]) ).
fof(f199,plain,
ssList(sK7),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
( ssList(sK4)
& ssList(sK7)
& sK5 = sK7
& ( ( nil != sK4
& nil = sK5 )
| ( ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ neq(nil,sK5)
| ~ ssList(X6)
| ! [X7] :
( cons(X7,nil) != X6
| ~ neq(nil,sK5)
| hd(sK5) != X7
| ~ ssItem(X7) )
| tl(sK5) != X5
| app(X5,X6) != X4 ) )
| ~ ssList(X4)
| sK4 != X4 )
& neq(sK5,nil) ) )
& sK6 = sK4
& ( nil != sK7
| nil = sK6 )
& ( ( ssItem(sK8)
& ssList(sK9)
& app(cons(sK8,nil),sK9) = sK7
& sK6 = app(sK9,cons(sK8,nil)) )
| ~ neq(sK7,nil) )
& ssList(sK6)
& ssList(sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9])],[f147,f153,f152,f151,f150,f149,f148]) ).
fof(f148,plain,
( ? [X0] :
( ssList(X0)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& ( ( nil != X0
& nil = X1 )
| ( ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ neq(nil,X1)
| ~ ssList(X6)
| ! [X7] :
( cons(X7,nil) != X6
| ~ neq(nil,X1)
| hd(X1) != X7
| ~ ssItem(X7) )
| tl(X1) != X5
| app(X5,X6) != X4 ) )
| ~ ssList(X4)
| X0 != X4 )
& neq(X1,nil) ) )
& X0 = X2
& ( nil != X3
| nil = X2 )
& ( ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X3
& app(X9,cons(X8,nil)) = X2 ) )
| ~ neq(X3,nil) ) )
& ssList(X2) )
& ssList(X1) ) )
=> ( ssList(sK4)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& ( ( nil != sK4
& nil = X1 )
| ( ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ neq(nil,X1)
| ~ ssList(X6)
| ! [X7] :
( cons(X7,nil) != X6
| ~ neq(nil,X1)
| hd(X1) != X7
| ~ ssItem(X7) )
| tl(X1) != X5
| app(X5,X6) != X4 ) )
| ~ ssList(X4)
| sK4 != X4 )
& neq(X1,nil) ) )
& sK4 = X2
& ( nil != X3
| nil = X2 )
& ( ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X3
& app(X9,cons(X8,nil)) = X2 ) )
| ~ neq(X3,nil) ) )
& ssList(X2) )
& ssList(X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f149,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& ( ( nil != sK4
& nil = X1 )
| ( ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ neq(nil,X1)
| ~ ssList(X6)
| ! [X7] :
( cons(X7,nil) != X6
| ~ neq(nil,X1)
| hd(X1) != X7
| ~ ssItem(X7) )
| tl(X1) != X5
| app(X5,X6) != X4 ) )
| ~ ssList(X4)
| sK4 != X4 )
& neq(X1,nil) ) )
& sK4 = X2
& ( nil != X3
| nil = X2 )
& ( ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X3
& app(X9,cons(X8,nil)) = X2 ) )
| ~ neq(X3,nil) ) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ssList(X3)
& sK5 = X3
& ( ( nil != sK4
& nil = sK5 )
| ( ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ neq(nil,sK5)
| ~ ssList(X6)
| ! [X7] :
( cons(X7,nil) != X6
| ~ neq(nil,sK5)
| hd(sK5) != X7
| ~ ssItem(X7) )
| tl(sK5) != X5
| app(X5,X6) != X4 ) )
| ~ ssList(X4)
| sK4 != X4 )
& neq(sK5,nil) ) )
& sK4 = X2
& ( nil != X3
| nil = X2 )
& ( ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X3
& app(X9,cons(X8,nil)) = X2 ) )
| ~ neq(X3,nil) ) )
& ssList(X2) )
& ssList(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f150,plain,
( ? [X2] :
( ? [X3] :
( ssList(X3)
& sK5 = X3
& ( ( nil != sK4
& nil = sK5 )
| ( ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ neq(nil,sK5)
| ~ ssList(X6)
| ! [X7] :
( cons(X7,nil) != X6
| ~ neq(nil,sK5)
| hd(sK5) != X7
| ~ ssItem(X7) )
| tl(sK5) != X5
| app(X5,X6) != X4 ) )
| ~ ssList(X4)
| sK4 != X4 )
& neq(sK5,nil) ) )
& sK4 = X2
& ( nil != X3
| nil = X2 )
& ( ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X3
& app(X9,cons(X8,nil)) = X2 ) )
| ~ neq(X3,nil) ) )
& ssList(X2) )
=> ( ? [X3] :
( ssList(X3)
& sK5 = X3
& ( ( nil != sK4
& nil = sK5 )
| ( ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ neq(nil,sK5)
| ~ ssList(X6)
| ! [X7] :
( cons(X7,nil) != X6
| ~ neq(nil,sK5)
| hd(sK5) != X7
| ~ ssItem(X7) )
| tl(sK5) != X5
| app(X5,X6) != X4 ) )
| ~ ssList(X4)
| sK4 != X4 )
& neq(sK5,nil) ) )
& sK6 = sK4
& ( nil != X3
| nil = sK6 )
& ( ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X3
& app(X9,cons(X8,nil)) = sK6 ) )
| ~ neq(X3,nil) ) )
& ssList(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f151,plain,
( ? [X3] :
( ssList(X3)
& sK5 = X3
& ( ( nil != sK4
& nil = sK5 )
| ( ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ neq(nil,sK5)
| ~ ssList(X6)
| ! [X7] :
( cons(X7,nil) != X6
| ~ neq(nil,sK5)
| hd(sK5) != X7
| ~ ssItem(X7) )
| tl(sK5) != X5
| app(X5,X6) != X4 ) )
| ~ ssList(X4)
| sK4 != X4 )
& neq(sK5,nil) ) )
& sK6 = sK4
& ( nil != X3
| nil = sK6 )
& ( ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X3
& app(X9,cons(X8,nil)) = sK6 ) )
| ~ neq(X3,nil) ) )
=> ( ssList(sK7)
& sK5 = sK7
& ( ( nil != sK4
& nil = sK5 )
| ( ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ neq(nil,sK5)
| ~ ssList(X6)
| ! [X7] :
( cons(X7,nil) != X6
| ~ neq(nil,sK5)
| hd(sK5) != X7
| ~ ssItem(X7) )
| tl(sK5) != X5
| app(X5,X6) != X4 ) )
| ~ ssList(X4)
| sK4 != X4 )
& neq(sK5,nil) ) )
& sK6 = sK4
& ( nil != sK7
| nil = sK6 )
& ( ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = sK7
& app(X9,cons(X8,nil)) = sK6 ) )
| ~ neq(sK7,nil) ) ) ),
introduced(choice_axiom,[]) ).
fof(f152,plain,
( ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = sK7
& app(X9,cons(X8,nil)) = sK6 ) )
=> ( ssItem(sK8)
& ? [X9] :
( ssList(X9)
& app(cons(sK8,nil),X9) = sK7
& sK6 = app(X9,cons(sK8,nil)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f153,plain,
( ? [X9] :
( ssList(X9)
& app(cons(sK8,nil),X9) = sK7
& sK6 = app(X9,cons(sK8,nil)) )
=> ( ssList(sK9)
& app(cons(sK8,nil),sK9) = sK7
& sK6 = app(sK9,cons(sK8,nil)) ) ),
introduced(choice_axiom,[]) ).
fof(f147,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& ( ( nil != X0
& nil = X1 )
| ( ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ neq(nil,X1)
| ~ ssList(X6)
| ! [X7] :
( cons(X7,nil) != X6
| ~ neq(nil,X1)
| hd(X1) != X7
| ~ ssItem(X7) )
| tl(X1) != X5
| app(X5,X6) != X4 ) )
| ~ ssList(X4)
| X0 != X4 )
& neq(X1,nil) ) )
& X0 = X2
& ( nil != X3
| nil = X2 )
& ( ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X3
& app(X9,cons(X8,nil)) = X2 ) )
| ~ neq(X3,nil) ) )
& ssList(X2) )
& ssList(X1) ) ),
inference(rectify,[],[f123]) ).
fof(f123,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& ( ( nil != X0
& nil = X1 )
| ( ! [X6] :
( ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ neq(nil,X1)
| ~ ssList(X8)
| ! [X9] :
( cons(X9,nil) != X8
| ~ neq(nil,X1)
| hd(X1) != X9
| ~ ssItem(X9) )
| tl(X1) != X7
| app(X7,X8) != X6 ) )
| ~ ssList(X6)
| X0 != X6 )
& neq(X1,nil) ) )
& X0 = X2
& ( nil != X3
| nil = X2 )
& ( ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(cons(X4,nil),X5) = X3
& app(X5,cons(X4,nil)) = X2 ) )
| ~ neq(X3,nil) ) )
& ssList(X2) )
& ssList(X1) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( X1 != X3
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X2
| app(cons(X4,nil),X5) != X3
| ~ ssList(X5) ) ) )
| ~ ssList(X3)
| ( ( ~ neq(X1,nil)
| ? [X6] :
( ssList(X6)
& ? [X7] :
( ? [X8] :
( ? [X9] :
( hd(X1) = X9
& cons(X9,nil) = X8
& ssItem(X9)
& neq(nil,X1) )
& tl(X1) = X7
& neq(nil,X1)
& app(X7,X8) = X6
& ssList(X8) )
& ssList(X7) )
& X0 = X6 ) )
& ( nil != X1
| nil = X0 ) )
| X0 != X2
| ( nil != X2
& nil = X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( X1 != X3
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X2
| app(cons(X4,nil),X5) != X3
| ~ ssList(X5) ) ) )
| ~ ssList(X3)
| ( ( ~ neq(X1,nil)
| ? [X6] :
( ssList(X6)
& ? [X7] :
( ? [X8] :
( ? [X9] :
( hd(X1) = X9
& cons(X9,nil) = X8
& ssItem(X9)
& neq(nil,X1) )
& tl(X1) = X7
& neq(nil,X1)
& app(X7,X8) = X6
& ssList(X8) )
& ssList(X7) )
& X0 = X6 ) )
& ( nil != X1
| nil = X0 ) )
| X0 != X2
| ( nil != X2
& nil = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f330,plain,
( ~ ssList(sK7)
| ~ ssList(nil)
| nil = sK7
| spl12_8 ),
inference(resolution,[],[f168,f273]) ).
fof(f273,plain,
( ~ neq(nil,sK7)
| spl12_8 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f271,plain,
( spl12_8
<=> neq(nil,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_8])]) ).
fof(f168,plain,
! [X0,X1] :
( neq(X0,X1)
| ~ ssList(X1)
| X0 = X1
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0] :
( ! [X1] :
( ( ( X0 != X1
| ~ neq(X0,X1) )
& ( neq(X0,X1)
| X0 = X1 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ( X0 != X1
<=> neq(X0,X1) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( X0 != X1
<=> neq(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f327,plain,
( spl12_4
| spl12_11 ),
inference(avatar_contradiction_clause,[],[f326]) ).
fof(f326,plain,
( $false
| spl12_4
| spl12_11 ),
inference(subsumption_resolution,[],[f325,f199]) ).
fof(f325,plain,
( ~ ssList(sK7)
| spl12_4
| spl12_11 ),
inference(subsumption_resolution,[],[f324,f254]) ).
fof(f324,plain,
( nil = sK7
| ~ ssList(sK7)
| spl12_11 ),
inference(resolution,[],[f204,f285]) ).
fof(f285,plain,
( ~ ssItem(hd(sK7))
| spl12_11 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f283,plain,
( spl12_11
<=> ssItem(hd(sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_11])]) ).
fof(f204,plain,
! [X0] :
( ssItem(hd(X0))
| ~ ssList(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(flattening,[],[f118]) ).
fof(f118,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f323,plain,
( ~ spl12_11
| spl12_7
| ~ spl12_14 ),
inference(avatar_split_clause,[],[f322,f297,f267,f283]) ).
fof(f322,plain,
( ~ ssItem(hd(sK7))
| spl12_7
| ~ spl12_14 ),
inference(subsumption_resolution,[],[f321,f298]) ).
fof(f321,plain,
( ~ ssItem(hd(sK7))
| ~ ssList(nil)
| spl12_7 ),
inference(resolution,[],[f269,f167]) ).
fof(f167,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssList(X0)
| ~ ssItem(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f269,plain,
( ~ ssList(cons(hd(sK7),nil))
| spl12_7 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f320,plain,
( spl12_4
| spl12_6 ),
inference(avatar_contradiction_clause,[],[f319]) ).
fof(f319,plain,
( $false
| spl12_4
| spl12_6 ),
inference(subsumption_resolution,[],[f318,f254]) ).
fof(f318,plain,
( nil = sK7
| spl12_6 ),
inference(subsumption_resolution,[],[f317,f199]) ).
fof(f317,plain,
( ~ ssList(sK7)
| nil = sK7
| spl12_6 ),
inference(resolution,[],[f183,f265]) ).
fof(f265,plain,
( ~ ssList(tl(sK7))
| spl12_6 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f183,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ssList(tl(X0)) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
fof(f308,plain,
spl12_14,
inference(avatar_split_clause,[],[f163,f297]) ).
fof(f163,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f307,plain,
( spl12_9
| ~ spl12_4 ),
inference(avatar_split_clause,[],[f217,f253,f275]) ).
fof(f275,plain,
( spl12_9
<=> nil = sK4 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_9])]) ).
fof(f217,plain,
( nil != sK7
| nil = sK4 ),
inference(definition_unfolding,[],[f192,f193]) ).
fof(f193,plain,
sK6 = sK4,
inference(cnf_transformation,[],[f154]) ).
fof(f192,plain,
( nil != sK7
| nil = sK6 ),
inference(cnf_transformation,[],[f154]) ).
fof(f306,plain,
( spl12_15
| ~ spl12_1 ),
inference(avatar_split_clause,[],[f218,f239,f303]) ).
fof(f239,plain,
( spl12_1
<=> neq(sK7,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).
fof(f218,plain,
( ~ neq(sK7,nil)
| app(sK9,cons(sK8,nil)) = sK4 ),
inference(definition_unfolding,[],[f188,f193]) ).
fof(f188,plain,
( sK6 = app(sK9,cons(sK8,nil))
| ~ neq(sK7,nil) ),
inference(cnf_transformation,[],[f154]) ).
fof(f301,plain,
( ~ spl12_8
| ~ spl12_11
| ~ spl12_10
| ~ spl12_6
| ~ spl12_12
| spl12_4
| ~ spl12_7 ),
inference(avatar_split_clause,[],[f233,f267,f253,f287,f263,f279,f283,f271]) ).
fof(f233,plain,
( ~ ssList(cons(hd(sK7),nil))
| nil = sK7
| ~ ssList(app(tl(sK7),cons(hd(sK7),nil)))
| ~ ssList(tl(sK7))
| sK4 != app(tl(sK7),cons(hd(sK7),nil))
| ~ ssItem(hd(sK7))
| ~ neq(nil,sK7) ),
inference(duplicate_literal_removal,[],[f232]) ).
fof(f232,plain,
( ~ neq(nil,sK7)
| ~ ssList(tl(sK7))
| nil = sK7
| ~ ssList(cons(hd(sK7),nil))
| sK4 != app(tl(sK7),cons(hd(sK7),nil))
| ~ ssList(app(tl(sK7),cons(hd(sK7),nil)))
| ~ ssItem(hd(sK7))
| ~ neq(nil,sK7) ),
inference(equality_resolution,[],[f231]) ).
fof(f231,plain,
! [X4] :
( nil = sK7
| ~ ssList(tl(sK7))
| ~ neq(nil,sK7)
| ~ ssList(cons(hd(sK7),nil))
| ~ neq(nil,sK7)
| ~ ssItem(hd(sK7))
| app(tl(sK7),cons(hd(sK7),nil)) != X4
| ~ ssList(X4)
| sK4 != X4 ),
inference(equality_resolution,[],[f230]) ).
fof(f230,plain,
! [X4,X5] :
( nil = sK7
| ~ ssList(X5)
| ~ neq(nil,sK7)
| ~ ssList(cons(hd(sK7),nil))
| ~ neq(nil,sK7)
| ~ ssItem(hd(sK7))
| tl(sK7) != X5
| app(X5,cons(hd(sK7),nil)) != X4
| ~ ssList(X4)
| sK4 != X4 ),
inference(equality_resolution,[],[f229]) ).
fof(f229,plain,
! [X7,X4,X5] :
( nil = sK7
| ~ ssList(X5)
| ~ neq(nil,sK7)
| ~ ssList(cons(X7,nil))
| ~ neq(nil,sK7)
| hd(sK7) != X7
| ~ ssItem(X7)
| tl(sK7) != X5
| app(X5,cons(X7,nil)) != X4
| ~ ssList(X4)
| sK4 != X4 ),
inference(equality_resolution,[],[f215]) ).
fof(f215,plain,
! [X6,X7,X4,X5] :
( nil = sK7
| ~ ssList(X5)
| ~ neq(nil,sK7)
| ~ ssList(X6)
| cons(X7,nil) != X6
| ~ neq(nil,sK7)
| hd(sK7) != X7
| ~ ssItem(X7)
| tl(sK7) != X5
| app(X5,X6) != X4
| ~ ssList(X4)
| sK4 != X4 ),
inference(definition_unfolding,[],[f195,f198,f198,f198,f198,f198]) ).
fof(f198,plain,
sK5 = sK7,
inference(cnf_transformation,[],[f154]) ).
fof(f195,plain,
! [X6,X7,X4,X5] :
( nil = sK5
| ~ ssList(X5)
| ~ neq(nil,sK5)
| ~ ssList(X6)
| cons(X7,nil) != X6
| ~ neq(nil,sK5)
| hd(sK5) != X7
| ~ ssItem(X7)
| tl(sK5) != X5
| app(X5,X6) != X4
| ~ ssList(X4)
| sK4 != X4 ),
inference(cnf_transformation,[],[f154]) ).
fof(f291,plain,
( spl12_1
| ~ spl12_9 ),
inference(avatar_split_clause,[],[f214,f275,f239]) ).
fof(f214,plain,
( nil != sK4
| neq(sK7,nil) ),
inference(definition_unfolding,[],[f196,f198]) ).
fof(f196,plain,
( nil != sK4
| neq(sK5,nil) ),
inference(cnf_transformation,[],[f154]) ).
fof(f261,plain,
( ~ spl12_1
| spl12_5 ),
inference(avatar_split_clause,[],[f190,f258,f239]) ).
fof(f190,plain,
( ssList(sK9)
| ~ neq(sK7,nil) ),
inference(cnf_transformation,[],[f154]) ).
fof(f256,plain,
( spl12_4
| spl12_1 ),
inference(avatar_split_clause,[],[f216,f239,f253]) ).
fof(f216,plain,
( neq(sK7,nil)
| nil = sK7 ),
inference(definition_unfolding,[],[f194,f198,f198]) ).
fof(f194,plain,
( nil = sK5
| neq(sK5,nil) ),
inference(cnf_transformation,[],[f154]) ).
fof(f251,plain,
( ~ spl12_1
| spl12_3 ),
inference(avatar_split_clause,[],[f189,f248,f239]) ).
fof(f189,plain,
( app(cons(sK8,nil),sK9) = sK7
| ~ neq(sK7,nil) ),
inference(cnf_transformation,[],[f154]) ).
fof(f246,plain,
( ~ spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f191,f243,f239]) ).
fof(f191,plain,
( ssItem(sK8)
| ~ neq(sK7,nil) ),
inference(cnf_transformation,[],[f154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC310+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 30 18:09:35 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.21/0.48 % (31090)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.21/0.48 % (31089)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.49 % (31096)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.50 % (31089)Instruction limit reached!
% 0.21/0.50 % (31089)------------------------------
% 0.21/0.50 % (31089)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.50 % (31096)Instruction limit reached!
% 0.21/0.50 % (31096)------------------------------
% 0.21/0.50 % (31096)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.50 % (31089)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.50 % (31089)Termination reason: Unknown
% 0.21/0.50 % (31089)Termination phase: Saturation
% 0.21/0.50
% 0.21/0.50 % (31089)Memory used [KB]: 1663
% 0.21/0.50 % (31089)Time elapsed: 0.077 s
% 0.21/0.50 % (31089)Instructions burned: 15 (million)
% 0.21/0.50 % (31089)------------------------------
% 0.21/0.50 % (31089)------------------------------
% 0.21/0.50 % (31096)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.50 % (31096)Termination reason: Unknown
% 0.21/0.50 % (31096)Termination phase: Saturation
% 0.21/0.50
% 0.21/0.50 % (31096)Memory used [KB]: 2046
% 0.21/0.50 % (31107)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.21/0.50 % (31096)Time elapsed: 0.084 s
% 0.21/0.50 % (31096)Instructions burned: 16 (million)
% 0.21/0.50 % (31096)------------------------------
% 0.21/0.50 % (31096)------------------------------
% 0.21/0.51 % (31099)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.52 % (31098)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.52 % (31099)Instruction limit reached!
% 0.21/0.52 % (31099)------------------------------
% 0.21/0.52 % (31099)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52 % (31099)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52 % (31099)Termination reason: Unknown
% 0.21/0.52 % (31099)Termination phase: Function definition elimination
% 0.21/0.52
% 0.21/0.52 % (31099)Memory used [KB]: 1791
% 0.21/0.52 % (31099)Time elapsed: 0.005 s
% 0.21/0.52 % (31099)Instructions burned: 8 (million)
% 0.21/0.52 % (31099)------------------------------
% 0.21/0.52 % (31099)------------------------------
% 0.21/0.52 % (31091)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.21/0.52 % (31106)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.21/0.52 % (31088)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.21/0.52 % (31111)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.21/0.53 % (31090)First to succeed.
% 0.21/0.53 % (31090)Refutation found. Thanks to Tanya!
% 0.21/0.53 % SZS status Theorem for theBenchmark
% 0.21/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53 % (31090)------------------------------
% 0.21/0.53 % (31090)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53 % (31090)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53 % (31090)Termination reason: Refutation
% 0.21/0.53
% 0.21/0.53 % (31090)Memory used [KB]: 6268
% 0.21/0.53 % (31090)Time elapsed: 0.140 s
% 0.21/0.53 % (31090)Instructions burned: 14 (million)
% 0.21/0.53 % (31090)------------------------------
% 0.21/0.53 % (31090)------------------------------
% 0.21/0.53 % (31083)Success in time 0.173 s
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