TSTP Solution File: SWC240+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SWC240+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 : n013.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 18:39:49 EDT 2022
% Result : Theorem 0.17s 0.53s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 22
% Syntax : Number of formulae : 111 ( 11 unt; 0 def)
% Number of atoms : 640 ( 134 equ)
% Maximal formula atoms : 40 ( 5 avg)
% Number of connectives : 849 ( 320 ~; 307 |; 184 &)
% ( 8 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 213 ( 143 !; 70 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f438,plain,
$false,
inference(avatar_sat_refutation,[],[f248,f328,f332,f359,f406,f410,f437]) ).
fof(f437,plain,
( ~ spl12_2
| ~ spl12_3
| ~ spl12_5
| ~ spl12_7
| ~ spl12_8 ),
inference(avatar_contradiction_clause,[],[f436]) ).
fof(f436,plain,
( $false
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5
| ~ spl12_7
| ~ spl12_8 ),
inference(subsumption_resolution,[],[f435,f401]) ).
fof(f401,plain,
( ssItem(sK11(sK10,nil,sK0(sK8)))
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f399,plain,
( spl12_7
<=> ssItem(sK11(sK10,nil,sK0(sK8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_7])]) ).
fof(f435,plain,
( ~ ssItem(sK11(sK10,nil,sK0(sK8)))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5
| ~ spl12_8 ),
inference(resolution,[],[f432,f184]) ).
fof(f184,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f432,plain,
( memberP(nil,sK11(sK10,nil,sK0(sK8)))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5
| ~ spl12_8 ),
inference(subsumption_resolution,[],[f431,f349]) ).
fof(f349,plain,
( ssList(sK0(sK8))
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f348,plain,
( spl12_5
<=> ssList(sK0(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_5])]) ).
fof(f431,plain,
( memberP(nil,sK11(sK10,nil,sK0(sK8)))
| ~ ssList(sK0(sK8))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_8 ),
inference(subsumption_resolution,[],[f430,f218]) ).
fof(f218,plain,
ssItem(sK10),
inference(cnf_transformation,[],[f163]) ).
fof(f163,plain,
( ssList(sK7)
& ssList(sK8)
& ssList(sK9)
& ! [X5] :
( ~ memberP(sK8,X5)
| sK10 = X5
| ~ ssItem(X5) )
& ssItem(sK10)
& nil != sK6
& sK7 = sK9
& sK6 = sK8
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| ( ssItem(sK11(X6,X7,X8))
& ~ leq(X6,sK11(X6,X7,X8))
& lt(X6,sK11(X6,X7,X8))
& memberP(X7,sK11(X6,X7,X8))
& memberP(X8,sK11(X6,X7,X8)) )
| sK6 != app(app(X7,cons(X6,nil)),X8) ) ) )
& ssList(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11])],[f156,f162,f161,f160,f159,f158,f157]) ).
fof(f157,plain,
( ? [X0] :
( ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ! [X5] :
( ~ memberP(X2,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& nil != X0
& X1 = X3
& X0 = X2
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| ? [X9] :
( ssItem(X9)
& ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X7,X9)
& memberP(X8,X9) )
| app(app(X7,cons(X6,nil)),X8) != X0 ) ) ) ) ) )
& ssList(X0) )
=> ( ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ! [X5] :
( ~ memberP(X2,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& nil != sK6
& X1 = X3
& sK6 = X2
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| ? [X9] :
( ssItem(X9)
& ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X7,X9)
& memberP(X8,X9) )
| sK6 != app(app(X7,cons(X6,nil)),X8) ) ) ) ) ) )
& ssList(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f158,plain,
( ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ! [X5] :
( ~ memberP(X2,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& nil != sK6
& X1 = X3
& sK6 = X2
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| ? [X9] :
( ssItem(X9)
& ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X7,X9)
& memberP(X8,X9) )
| sK6 != app(app(X7,cons(X6,nil)),X8) ) ) ) ) ) )
=> ( ssList(sK7)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ! [X5] :
( ~ memberP(X2,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& nil != sK6
& sK7 = X3
& sK6 = X2
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| ? [X9] :
( ssItem(X9)
& ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X7,X9)
& memberP(X8,X9) )
| sK6 != app(app(X7,cons(X6,nil)),X8) ) ) ) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f159,plain,
( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ! [X5] :
( ~ memberP(X2,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& nil != sK6
& sK7 = X3
& sK6 = X2
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| ? [X9] :
( ssItem(X9)
& ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X7,X9)
& memberP(X8,X9) )
| sK6 != app(app(X7,cons(X6,nil)),X8) ) ) ) ) )
=> ( ssList(sK8)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ! [X5] :
( ~ memberP(sK8,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& nil != sK6
& sK7 = X3
& sK6 = sK8
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| ? [X9] :
( ssItem(X9)
& ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X7,X9)
& memberP(X8,X9) )
| sK6 != app(app(X7,cons(X6,nil)),X8) ) ) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
( ? [X3] :
( ssList(X3)
& ? [X4] :
( ! [X5] :
( ~ memberP(sK8,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& nil != sK6
& sK7 = X3
& sK6 = sK8
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| ? [X9] :
( ssItem(X9)
& ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X7,X9)
& memberP(X8,X9) )
| sK6 != app(app(X7,cons(X6,nil)),X8) ) ) ) )
=> ( ssList(sK9)
& ? [X4] :
( ! [X5] :
( ~ memberP(sK8,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& nil != sK6
& sK7 = sK9
& sK6 = sK8
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| ? [X9] :
( ssItem(X9)
& ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X7,X9)
& memberP(X8,X9) )
| sK6 != app(app(X7,cons(X6,nil)),X8) ) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f161,plain,
( ? [X4] :
( ! [X5] :
( ~ memberP(sK8,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
=> ( ! [X5] :
( ~ memberP(sK8,X5)
| sK10 = X5
| ~ ssItem(X5) )
& ssItem(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f162,plain,
! [X6,X7,X8] :
( ? [X9] :
( ssItem(X9)
& ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X7,X9)
& memberP(X8,X9) )
=> ( ssItem(sK11(X6,X7,X8))
& ~ leq(X6,sK11(X6,X7,X8))
& lt(X6,sK11(X6,X7,X8))
& memberP(X7,sK11(X6,X7,X8))
& memberP(X8,sK11(X6,X7,X8)) ) ),
introduced(choice_axiom,[]) ).
fof(f156,plain,
? [X0] :
( ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ! [X5] :
( ~ memberP(X2,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& nil != X0
& X1 = X3
& X0 = X2
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| ? [X9] :
( ssItem(X9)
& ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X7,X9)
& memberP(X8,X9) )
| app(app(X7,cons(X6,nil)),X8) != X0 ) ) ) ) ) )
& ssList(X0) ),
inference(rectify,[],[f126]) ).
fof(f126,plain,
? [X0] :
( ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X8] :
( ! [X9] :
( ~ memberP(X2,X9)
| X8 = X9
| ~ ssItem(X9) )
& ssItem(X8) )
& nil != X0
& X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ? [X7] :
( ssItem(X7)
& ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X5,X7)
& memberP(X6,X7) )
| app(app(X5,cons(X4,nil)),X6) != X0 ) ) ) ) ) )
& ssList(X0) ),
inference(flattening,[],[f125]) ).
fof(f125,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ? [X7] :
( memberP(X6,X7)
& lt(X4,X7)
& ~ leq(X4,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) ) )
| ~ ssItem(X4) )
& X1 = X3
& ? [X8] :
( ! [X9] :
( ~ memberP(X2,X9)
| X8 = X9
| ~ ssItem(X9) )
& ssItem(X8) )
& X0 = X2
& nil != X0
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X4] :
( ? [X5] :
( ssList(X5)
& ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X6,X7)
| ~ lt(X4,X7)
| leq(X4,X7)
| ~ memberP(X5,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) ) )
& ssItem(X4) )
| X1 != X3
| ! [X8] :
( ssItem(X8)
=> ? [X9] :
( X8 != X9
& ssItem(X9)
& memberP(X2,X9) ) )
| X0 != X2
| nil = X0 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X4] :
( ? [X5] :
( ssList(X5)
& ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X6,X7)
| ~ lt(X4,X7)
| leq(X4,X7)
| ~ memberP(X5,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) ) )
& ssItem(X4) )
| X1 != X3
| ! [X8] :
( ssItem(X8)
=> ? [X9] :
( X8 != X9
& ssItem(X9)
& memberP(X2,X9) ) )
| X0 != X2
| nil = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f430,plain,
( memberP(nil,sK11(sK10,nil,sK0(sK8)))
| ~ ssItem(sK10)
| ~ ssList(sK0(sK8))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_8 ),
inference(subsumption_resolution,[],[f429,f404]) ).
fof(f404,plain,
( ssList(cons(sK10,nil))
| ~ spl12_8 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f403,plain,
( spl12_8
<=> ssList(cons(sK10,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_8])]) ).
fof(f429,plain,
( ~ ssList(cons(sK10,nil))
| ~ ssItem(sK10)
| memberP(nil,sK11(sK10,nil,sK0(sK8)))
| ~ ssList(sK0(sK8))
| ~ spl12_2
| ~ spl12_3 ),
inference(trivial_inequality_removal,[],[f428]) ).
fof(f428,plain,
( memberP(nil,sK11(sK10,nil,sK0(sK8)))
| ~ ssItem(sK10)
| sK8 != sK8
| ~ ssList(cons(sK10,nil))
| ~ ssList(sK0(sK8))
| ~ spl12_2
| ~ spl12_3 ),
inference(superposition,[],[f384,f338]) ).
fof(f338,plain,
( cons(sK10,sK0(sK8)) = sK8
| ~ spl12_3 ),
inference(subsumption_resolution,[],[f337,f221]) ).
fof(f221,plain,
ssList(sK8),
inference(cnf_transformation,[],[f163]) ).
fof(f337,plain,
( ~ ssList(sK8)
| cons(sK10,sK0(sK8)) = sK8
| ~ spl12_3 ),
inference(subsumption_resolution,[],[f335,f224]) ).
fof(f224,plain,
nil != sK8,
inference(definition_unfolding,[],[f217,f215]) ).
fof(f215,plain,
sK6 = sK8,
inference(cnf_transformation,[],[f163]) ).
fof(f217,plain,
nil != sK6,
inference(cnf_transformation,[],[f163]) ).
fof(f335,plain,
( nil = sK8
| ~ ssList(sK8)
| cons(sK10,sK0(sK8)) = sK8
| ~ spl12_3 ),
inference(superposition,[],[f183,f323]) ).
fof(f323,plain,
( sK10 = sK1(sK8)
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f321,plain,
( spl12_3
<=> sK10 = sK1(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).
fof(f183,plain,
! [X0] :
( cons(sK1(X0),sK0(X0)) = X0
| ~ ssList(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ( cons(sK1(X0),sK0(X0)) = X0
& ssItem(sK1(X0))
& ssList(sK0(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f108,f144,f143]) ).
fof(f143,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK0(X0)) = X0
& ssItem(X2) )
& ssList(sK0(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f144,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK0(X0)) = X0
& ssItem(X2) )
=> ( cons(sK1(X0),sK0(X0)) = X0
& ssItem(sK1(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f108,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) ) ),
inference(flattening,[],[f107]) ).
fof(f107,plain,
! [X0] :
( nil = X0
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( nil = X0
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
fof(f384,plain,
( ! [X0,X1] :
( cons(X0,X1) != sK8
| ~ ssList(X1)
| memberP(nil,sK11(X0,nil,X1))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl12_2 ),
inference(duplicate_literal_removal,[],[f360]) ).
fof(f360,plain,
( ! [X0,X1] :
( ~ ssItem(X0)
| memberP(nil,sK11(X0,nil,X1))
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| cons(X0,X1) != sK8
| ~ ssList(X1) )
| ~ spl12_2 ),
inference(superposition,[],[f257,f174]) ).
fof(f174,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssList(X0)
| ~ ssItem(X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),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(f257,plain,
( ! [X2,X3] :
( app(cons(X2,nil),X3) != sK8
| ~ ssList(X3)
| ~ ssItem(X2)
| memberP(nil,sK11(X2,nil,X3))
| ~ ssList(cons(X2,nil)) )
| ~ spl12_2 ),
inference(subsumption_resolution,[],[f250,f245]) ).
fof(f245,plain,
( ssList(nil)
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f244,plain,
( spl12_2
<=> ssList(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).
fof(f250,plain,
! [X2,X3] :
( app(cons(X2,nil),X3) != sK8
| ~ ssList(nil)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssList(cons(X2,nil))
| memberP(nil,sK11(X2,nil,X3)) ),
inference(superposition,[],[f228,f179]) ).
fof(f179,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f228,plain,
! [X8,X6,X7] :
( app(app(X7,cons(X6,nil)),X8) != sK8
| ~ ssList(X7)
| memberP(X7,sK11(X6,X7,X8))
| ~ ssItem(X6)
| ~ ssList(X8) ),
inference(definition_unfolding,[],[f211,f215]) ).
fof(f211,plain,
! [X8,X6,X7] :
( ~ ssItem(X6)
| ~ ssList(X7)
| ~ ssList(X8)
| memberP(X7,sK11(X6,X7,X8))
| sK6 != app(app(X7,cons(X6,nil)),X8) ),
inference(cnf_transformation,[],[f163]) ).
fof(f410,plain,
( ~ spl12_2
| spl12_8 ),
inference(avatar_contradiction_clause,[],[f409]) ).
fof(f409,plain,
( $false
| ~ spl12_2
| spl12_8 ),
inference(subsumption_resolution,[],[f408,f245]) ).
fof(f408,plain,
( ~ ssList(nil)
| spl12_8 ),
inference(subsumption_resolution,[],[f407,f218]) ).
fof(f407,plain,
( ~ ssItem(sK10)
| ~ ssList(nil)
| spl12_8 ),
inference(resolution,[],[f405,f188]) ).
fof(f188,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) )
| ~ ssList(X0) ),
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(f405,plain,
( ~ ssList(cons(sK10,nil))
| spl12_8 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f406,plain,
( spl12_7
| ~ spl12_8
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5 ),
inference(avatar_split_clause,[],[f397,f348,f321,f244,f403,f399]) ).
fof(f397,plain,
( ~ ssList(cons(sK10,nil))
| ssItem(sK11(sK10,nil,sK0(sK8)))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5 ),
inference(subsumption_resolution,[],[f396,f349]) ).
fof(f396,plain,
( ~ ssList(cons(sK10,nil))
| ~ ssList(sK0(sK8))
| ssItem(sK11(sK10,nil,sK0(sK8)))
| ~ spl12_2
| ~ spl12_3 ),
inference(subsumption_resolution,[],[f393,f218]) ).
fof(f393,plain,
( ~ ssItem(sK10)
| ~ ssList(sK0(sK8))
| ~ ssList(cons(sK10,nil))
| ssItem(sK11(sK10,nil,sK0(sK8)))
| ~ spl12_2
| ~ spl12_3 ),
inference(trivial_inequality_removal,[],[f392]) ).
fof(f392,plain,
( ~ ssItem(sK10)
| ~ ssList(sK0(sK8))
| sK8 != sK8
| ssItem(sK11(sK10,nil,sK0(sK8)))
| ~ ssList(cons(sK10,nil))
| ~ spl12_2
| ~ spl12_3 ),
inference(superposition,[],[f379,f338]) ).
fof(f379,plain,
( ! [X8,X9] :
( sK8 != cons(X8,X9)
| ssItem(sK11(X8,nil,X9))
| ~ ssList(X9)
| ~ ssList(cons(X8,nil))
| ~ ssItem(X8) )
| ~ spl12_2 ),
inference(duplicate_literal_removal,[],[f364]) ).
fof(f364,plain,
( ! [X8,X9] :
( ~ ssList(X9)
| sK8 != cons(X8,X9)
| ~ ssList(X9)
| ~ ssList(cons(X8,nil))
| ~ ssItem(X8)
| ~ ssItem(X8)
| ssItem(sK11(X8,nil,X9)) )
| ~ spl12_2 ),
inference(superposition,[],[f258,f174]) ).
fof(f258,plain,
( ! [X8,X9] :
( app(cons(X8,nil),X9) != sK8
| ~ ssItem(X8)
| ~ ssList(cons(X8,nil))
| ~ ssList(X9)
| ssItem(sK11(X8,nil,X9)) )
| ~ spl12_2 ),
inference(subsumption_resolution,[],[f253,f245]) ).
fof(f253,plain,
! [X8,X9] :
( ~ ssItem(X8)
| ~ ssList(nil)
| ~ ssList(X9)
| ssItem(sK11(X8,nil,X9))
| ~ ssList(cons(X8,nil))
| app(cons(X8,nil),X9) != sK8 ),
inference(superposition,[],[f225,f179]) ).
fof(f225,plain,
! [X8,X6,X7] :
( app(app(X7,cons(X6,nil)),X8) != sK8
| ~ ssList(X8)
| ssItem(sK11(X6,X7,X8))
| ~ ssItem(X6)
| ~ ssList(X7) ),
inference(definition_unfolding,[],[f214,f215]) ).
fof(f214,plain,
! [X8,X6,X7] :
( ~ ssItem(X6)
| ~ ssList(X7)
| ~ ssList(X8)
| ssItem(sK11(X6,X7,X8))
| sK6 != app(app(X7,cons(X6,nil)),X8) ),
inference(cnf_transformation,[],[f163]) ).
fof(f359,plain,
spl12_5,
inference(avatar_contradiction_clause,[],[f358]) ).
fof(f358,plain,
( $false
| spl12_5 ),
inference(subsumption_resolution,[],[f357,f221]) ).
fof(f357,plain,
( ~ ssList(sK8)
| spl12_5 ),
inference(subsumption_resolution,[],[f356,f224]) ).
fof(f356,plain,
( nil = sK8
| ~ ssList(sK8)
| spl12_5 ),
inference(resolution,[],[f350,f181]) ).
fof(f181,plain,
! [X0] :
( ssList(sK0(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f350,plain,
( ~ ssList(sK0(sK8))
| spl12_5 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f332,plain,
spl12_4,
inference(avatar_contradiction_clause,[],[f331]) ).
fof(f331,plain,
( $false
| spl12_4 ),
inference(subsumption_resolution,[],[f330,f221]) ).
fof(f330,plain,
( ~ ssList(sK8)
| spl12_4 ),
inference(subsumption_resolution,[],[f329,f224]) ).
fof(f329,plain,
( nil = sK8
| ~ ssList(sK8)
| spl12_4 ),
inference(resolution,[],[f327,f182]) ).
fof(f182,plain,
! [X0] :
( ssItem(sK1(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f327,plain,
( ~ ssItem(sK1(sK8))
| spl12_4 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f325,plain,
( spl12_4
<=> ssItem(sK1(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_4])]) ).
fof(f328,plain,
( spl12_3
| ~ spl12_4 ),
inference(avatar_split_clause,[],[f319,f325,f321]) ).
fof(f319,plain,
( ~ ssItem(sK1(sK8))
| sK10 = sK1(sK8) ),
inference(subsumption_resolution,[],[f318,f221]) ).
fof(f318,plain,
( ~ ssItem(sK1(sK8))
| sK10 = sK1(sK8)
| ~ ssList(sK8) ),
inference(subsumption_resolution,[],[f316,f224]) ).
fof(f316,plain,
( sK10 = sK1(sK8)
| nil = sK8
| ~ ssList(sK8)
| ~ ssItem(sK1(sK8)) ),
inference(resolution,[],[f315,f219]) ).
fof(f219,plain,
! [X5] :
( ~ memberP(sK8,X5)
| sK10 = X5
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f163]) ).
fof(f315,plain,
! [X0] :
( memberP(X0,sK1(X0))
| ~ ssList(X0)
| nil = X0 ),
inference(subsumption_resolution,[],[f314,f182]) ).
fof(f314,plain,
! [X0] :
( memberP(X0,sK1(X0))
| ~ ssList(X0)
| ~ ssItem(sK1(X0))
| nil = X0 ),
inference(subsumption_resolution,[],[f308,f181]) ).
fof(f308,plain,
! [X0] :
( memberP(X0,sK1(X0))
| nil = X0
| ~ ssList(sK0(X0))
| ~ ssList(X0)
| ~ ssItem(sK1(X0)) ),
inference(superposition,[],[f237,f183]) ).
fof(f237,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f233]) ).
fof(f233,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f172]) ).
fof(f172,plain,
! [X2,X0,X1] :
( ~ ssItem(X1)
| memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0] :
( ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) ) )
| ~ ssItem(X0) ),
inference(flattening,[],[f141]) ).
fof(f141,plain,
! [X0] :
( ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) ) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) )
| ~ ssList(X2) ) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
fof(f248,plain,
spl12_2,
inference(avatar_split_clause,[],[f170,f244]) ).
fof(f170,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC240+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Aug 30 18:34:01 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.17/0.48 % (13385)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)
% 0.17/0.49 % (13385)Instruction limit reached!
% 0.17/0.49 % (13385)------------------------------
% 0.17/0.49 % (13385)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.49 % (13385)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.49 % (13385)Termination reason: Unknown
% 0.17/0.49 % (13385)Termination phase: Preprocessing 3
% 0.17/0.49
% 0.17/0.49 % (13385)Memory used [KB]: 1663
% 0.17/0.49 % (13385)Time elapsed: 0.004 s
% 0.17/0.49 % (13385)Instructions burned: 4 (million)
% 0.17/0.49 % (13385)------------------------------
% 0.17/0.49 % (13385)------------------------------
% 0.17/0.49 % (13377)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)
% 0.17/0.49 % (13386)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)
% 0.17/0.49 % (13394)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)
% 0.17/0.50 % (13381)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.17/0.51 % (13386)Instruction limit reached!
% 0.17/0.51 % (13386)------------------------------
% 0.17/0.51 % (13386)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.51 % (13393)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)
% 0.17/0.51 % (13384)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.17/0.52 % (13378)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)
% 0.17/0.52 % (13386)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.52 % (13386)Termination reason: Unknown
% 0.17/0.52 % (13386)Termination phase: Property scanning
% 0.17/0.52
% 0.17/0.52 % (13386)Memory used [KB]: 1791
% 0.17/0.52 % (13386)Time elapsed: 0.007 s
% 0.17/0.52 % (13386)Instructions burned: 7 (million)
% 0.17/0.52 % (13386)------------------------------
% 0.17/0.52 % (13386)------------------------------
% 0.17/0.52 % (13377)First to succeed.
% 0.17/0.52 % (13372)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.17/0.52 % (13383)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)
% 0.17/0.52 % (13373)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.17/0.52 % (13371)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.17/0.52 % (13373)Instruction limit reached!
% 0.17/0.52 % (13373)------------------------------
% 0.17/0.52 % (13373)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.52 % (13373)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.52 % (13373)Termination reason: Unknown
% 0.17/0.52 % (13373)Termination phase: Preprocessing 3
% 0.17/0.52
% 0.17/0.52 % (13373)Memory used [KB]: 1663
% 0.17/0.52 % (13373)Time elapsed: 0.004 s
% 0.17/0.52 % (13373)Instructions burned: 4 (million)
% 0.17/0.52 % (13373)------------------------------
% 0.17/0.52 % (13373)------------------------------
% 0.17/0.53 % (13381)Refutation not found, incomplete strategy% (13381)------------------------------
% 0.17/0.53 % (13381)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.53 % (13381)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.53 % (13381)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.53
% 0.17/0.53 % (13381)Memory used [KB]: 6268
% 0.17/0.53 % (13381)Time elapsed: 0.142 s
% 0.17/0.53 % (13381)Instructions burned: 8 (million)
% 0.17/0.53 % (13381)------------------------------
% 0.17/0.53 % (13381)------------------------------
% 0.17/0.53 % (13376)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)
% 0.17/0.53 % (13377)Refutation found. Thanks to Tanya!
% 0.17/0.53 % SZS status Theorem for theBenchmark
% 0.17/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.53 % (13377)------------------------------
% 0.17/0.53 % (13377)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.53 % (13377)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.53 % (13377)Termination reason: Refutation
% 0.17/0.53
% 0.17/0.53 % (13377)Memory used [KB]: 6268
% 0.17/0.53 % (13377)Time elapsed: 0.125 s
% 0.17/0.53 % (13377)Instructions burned: 13 (million)
% 0.17/0.53 % (13377)------------------------------
% 0.17/0.53 % (13377)------------------------------
% 0.17/0.53 % (13370)Success in time 0.195 s
%------------------------------------------------------------------------------