TSTP Solution File: SWC224+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SWC224+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 : n028.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 18:39:43 EDT 2022
% Result : Theorem 0.21s 0.53s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 19
% Syntax : Number of formulae : 83 ( 7 unt; 0 def)
% Number of atoms : 672 ( 193 equ)
% Maximal formula atoms : 52 ( 8 avg)
% Number of connectives : 920 ( 331 ~; 317 |; 235 &)
% ( 4 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 234 ( 154 !; 80 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f449,plain,
$false,
inference(avatar_sat_refutation,[],[f257,f258,f408,f414,f448]) ).
fof(f448,plain,
( spl16_2
| ~ spl16_4
| ~ spl16_5
| ~ spl16_6 ),
inference(avatar_contradiction_clause,[],[f447]) ).
fof(f447,plain,
( $false
| spl16_2
| ~ spl16_4
| ~ spl16_5
| ~ spl16_6 ),
inference(subsumption_resolution,[],[f446,f403]) ).
fof(f403,plain,
( ssItem(sK14(sK3(sK10),nil,sK2(sK10)))
| ~ spl16_5 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f401,plain,
( spl16_5
<=> ssItem(sK14(sK3(sK10),nil,sK2(sK10))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_5])]) ).
fof(f446,plain,
( ~ ssItem(sK14(sK3(sK10),nil,sK2(sK10)))
| spl16_2
| ~ spl16_4
| ~ spl16_6 ),
inference(resolution,[],[f445,f197]) ).
fof(f197,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,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(f445,plain,
( memberP(nil,sK14(sK3(sK10),nil,sK2(sK10)))
| spl16_2
| ~ spl16_4
| ~ spl16_6 ),
inference(subsumption_resolution,[],[f444,f246]) ).
fof(f246,plain,
( nil != sK10
| spl16_2 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f244,plain,
( spl16_2
<=> nil = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_2])]) ).
fof(f444,plain,
( memberP(nil,sK14(sK3(sK10),nil,sK2(sK10)))
| nil = sK10
| ~ spl16_4
| ~ spl16_6 ),
inference(subsumption_resolution,[],[f443,f203]) ).
fof(f203,plain,
ssList(sK10),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
( ssList(sK11)
& ssList(sK12)
& ( nil = sK13
| nil != sK12 )
& ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( app(app(X5,cons(X4,nil)),X6) != sK10
| ~ ssList(X6)
| ( memberP(X5,sK14(X4,X5,X6))
& ssItem(sK14(X4,X5,X6))
& memberP(X6,sK14(X4,X5,X6))
& ~ leq(sK14(X4,X5,X6),X4)
& leq(X4,sK14(X4,X5,X6)) ) ) )
| ~ ssItem(X4) )
& sK11 = sK13
& sK12 = sK10
& ssList(sK15)
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != sK12 )
| app(cons(X9,nil),X10) != sK15 ) )
& equalelemsP(sK12)
& app(sK12,sK15) = sK13
& nil != sK10
& ssList(sK13)
& ssList(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14,sK15])],[f153,f159,f158,f157,f156,f155,f154]) ).
fof(f154,plain,
( ? [X0] :
( ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( nil = X3
| nil != X2 )
& ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6)
| ? [X7] :
( memberP(X5,X7)
& ssItem(X7)
& memberP(X6,X7)
& ~ leq(X7,X4)
& leq(X4,X7) ) ) )
| ~ ssItem(X4) )
& X1 = X3
& X0 = X2
& ? [X8] :
( ssList(X8)
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != X2 )
| app(cons(X9,nil),X10) != X8 ) )
& equalelemsP(X2)
& app(X2,X8) = X3 )
& nil != X0
& ssList(X3) ) ) )
& ssList(X0) )
=> ( ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( nil = X3
| nil != X2 )
& ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( app(app(X5,cons(X4,nil)),X6) != sK10
| ~ ssList(X6)
| ? [X7] :
( memberP(X5,X7)
& ssItem(X7)
& memberP(X6,X7)
& ~ leq(X7,X4)
& leq(X4,X7) ) ) )
| ~ ssItem(X4) )
& X1 = X3
& sK10 = X2
& ? [X8] :
( ssList(X8)
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != X2 )
| app(cons(X9,nil),X10) != X8 ) )
& equalelemsP(X2)
& app(X2,X8) = X3 )
& nil != sK10
& ssList(X3) ) ) )
& ssList(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f155,plain,
( ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( nil = X3
| nil != X2 )
& ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( app(app(X5,cons(X4,nil)),X6) != sK10
| ~ ssList(X6)
| ? [X7] :
( memberP(X5,X7)
& ssItem(X7)
& memberP(X6,X7)
& ~ leq(X7,X4)
& leq(X4,X7) ) ) )
| ~ ssItem(X4) )
& X1 = X3
& sK10 = X2
& ? [X8] :
( ssList(X8)
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != X2 )
| app(cons(X9,nil),X10) != X8 ) )
& equalelemsP(X2)
& app(X2,X8) = X3 )
& nil != sK10
& ssList(X3) ) ) )
=> ( ssList(sK11)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( nil = X3
| nil != X2 )
& ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( app(app(X5,cons(X4,nil)),X6) != sK10
| ~ ssList(X6)
| ? [X7] :
( memberP(X5,X7)
& ssItem(X7)
& memberP(X6,X7)
& ~ leq(X7,X4)
& leq(X4,X7) ) ) )
| ~ ssItem(X4) )
& sK11 = X3
& sK10 = X2
& ? [X8] :
( ssList(X8)
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != X2 )
| app(cons(X9,nil),X10) != X8 ) )
& equalelemsP(X2)
& app(X2,X8) = X3 )
& nil != sK10
& ssList(X3) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f156,plain,
( ? [X2] :
( ssList(X2)
& ? [X3] :
( ( nil = X3
| nil != X2 )
& ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( app(app(X5,cons(X4,nil)),X6) != sK10
| ~ ssList(X6)
| ? [X7] :
( memberP(X5,X7)
& ssItem(X7)
& memberP(X6,X7)
& ~ leq(X7,X4)
& leq(X4,X7) ) ) )
| ~ ssItem(X4) )
& sK11 = X3
& sK10 = X2
& ? [X8] :
( ssList(X8)
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != X2 )
| app(cons(X9,nil),X10) != X8 ) )
& equalelemsP(X2)
& app(X2,X8) = X3 )
& nil != sK10
& ssList(X3) ) )
=> ( ssList(sK12)
& ? [X3] :
( ( nil = X3
| nil != sK12 )
& ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( app(app(X5,cons(X4,nil)),X6) != sK10
| ~ ssList(X6)
| ? [X7] :
( memberP(X5,X7)
& ssItem(X7)
& memberP(X6,X7)
& ~ leq(X7,X4)
& leq(X4,X7) ) ) )
| ~ ssItem(X4) )
& sK11 = X3
& sK12 = sK10
& ? [X8] :
( ssList(X8)
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != sK12 )
| app(cons(X9,nil),X10) != X8 ) )
& equalelemsP(sK12)
& app(sK12,X8) = X3 )
& nil != sK10
& ssList(X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f157,plain,
( ? [X3] :
( ( nil = X3
| nil != sK12 )
& ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( app(app(X5,cons(X4,nil)),X6) != sK10
| ~ ssList(X6)
| ? [X7] :
( memberP(X5,X7)
& ssItem(X7)
& memberP(X6,X7)
& ~ leq(X7,X4)
& leq(X4,X7) ) ) )
| ~ ssItem(X4) )
& sK11 = X3
& sK12 = sK10
& ? [X8] :
( ssList(X8)
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != sK12 )
| app(cons(X9,nil),X10) != X8 ) )
& equalelemsP(sK12)
& app(sK12,X8) = X3 )
& nil != sK10
& ssList(X3) )
=> ( ( nil = sK13
| nil != sK12 )
& ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( app(app(X5,cons(X4,nil)),X6) != sK10
| ~ ssList(X6)
| ? [X7] :
( memberP(X5,X7)
& ssItem(X7)
& memberP(X6,X7)
& ~ leq(X7,X4)
& leq(X4,X7) ) ) )
| ~ ssItem(X4) )
& sK11 = sK13
& sK12 = sK10
& ? [X8] :
( ssList(X8)
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != sK12 )
| app(cons(X9,nil),X10) != X8 ) )
& equalelemsP(sK12)
& sK13 = app(sK12,X8) )
& nil != sK10
& ssList(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f158,plain,
! [X4,X5,X6] :
( ? [X7] :
( memberP(X5,X7)
& ssItem(X7)
& memberP(X6,X7)
& ~ leq(X7,X4)
& leq(X4,X7) )
=> ( memberP(X5,sK14(X4,X5,X6))
& ssItem(sK14(X4,X5,X6))
& memberP(X6,sK14(X4,X5,X6))
& ~ leq(sK14(X4,X5,X6),X4)
& leq(X4,sK14(X4,X5,X6)) ) ),
introduced(choice_axiom,[]) ).
fof(f159,plain,
( ? [X8] :
( ssList(X8)
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != sK12 )
| app(cons(X9,nil),X10) != X8 ) )
& equalelemsP(sK12)
& sK13 = app(sK12,X8) )
=> ( ssList(sK15)
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != sK12 )
| app(cons(X9,nil),X10) != sK15 ) )
& equalelemsP(sK12)
& app(sK12,sK15) = sK13 ) ),
introduced(choice_axiom,[]) ).
fof(f153,plain,
? [X0] :
( ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( nil = X3
| nil != X2 )
& ! [X4] :
( ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6)
| ? [X7] :
( memberP(X5,X7)
& ssItem(X7)
& memberP(X6,X7)
& ~ leq(X7,X4)
& leq(X4,X7) ) ) )
| ~ ssItem(X4) )
& X1 = X3
& X0 = X2
& ? [X8] :
( ssList(X8)
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != X2 )
| app(cons(X9,nil),X10) != X8 ) )
& equalelemsP(X2)
& app(X2,X8) = X3 )
& nil != X0
& ssList(X3) ) ) )
& ssList(X0) ),
inference(rectify,[],[f124]) ).
fof(f124,plain,
? [X0] :
( ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( nil = X3
| nil != X2 )
& ! [X8] :
( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( app(app(X9,cons(X8,nil)),X10) != X0
| ~ ssList(X10)
| ? [X11] :
( memberP(X9,X11)
& ssItem(X11)
& memberP(X10,X11)
& ~ leq(X11,X8)
& leq(X8,X11) ) ) )
| ~ ssItem(X8) )
& X1 = X3
& X0 = X2
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != X2 )
| app(cons(X5,nil),X6) != X4 ) )
& equalelemsP(X2)
& app(X2,X4) = X3 )
& nil != X0
& ssList(X3) ) ) )
& ssList(X0) ),
inference(flattening,[],[f123]) ).
fof(f123,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& nil != X0
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ? [X11] :
( memberP(X10,X11)
& leq(X8,X11)
& ~ leq(X11,X8)
& memberP(X9,X11)
& ssItem(X11) )
| app(app(X9,cons(X8,nil)),X10) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& ? [X4] :
( app(X2,X4) = X3
& equalelemsP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != X2 )
| app(cons(X5,nil),X6) != X4 ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& X0 = X2
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| nil = X0
| ? [X8] :
( ? [X9] :
( ? [X10] :
( ! [X11] :
( ssItem(X11)
=> ( ~ memberP(X10,X11)
| ~ leq(X8,X11)
| leq(X11,X8)
| ~ memberP(X9,X11) ) )
& app(app(X9,cons(X8,nil)),X10) = X0
& ssList(X10) )
& ssList(X9) )
& ssItem(X8) )
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ equalelemsP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4 ) ) ) )
| ( nil = X2
& nil != X3 )
| X0 != X2 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X0 != X2
| ( nil = X2
& nil != X3 )
| X1 != X3
| ! [X8] :
( ssList(X8)
=> ( app(X2,X8) != X3
| ~ equalelemsP(X2)
| ? [X9] :
( ? [X10] :
( ? [X11] :
( ssList(X11)
& app(X11,cons(X9,nil)) = X2 )
& ssList(X10)
& app(cons(X9,nil),X10) = X8 )
& ssItem(X9) ) ) )
| nil = X0
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X5,X7)
| ~ leq(X4,X7)
| leq(X7,X4)
| ~ memberP(X6,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) ) ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X0 != X2
| ( nil = X2
& nil != X3 )
| X1 != X3
| ! [X8] :
( ssList(X8)
=> ( app(X2,X8) != X3
| ~ equalelemsP(X2)
| ? [X9] :
( ? [X10] :
( ? [X11] :
( ssList(X11)
& app(X11,cons(X9,nil)) = X2 )
& ssList(X10)
& app(cons(X9,nil),X10) = X8 )
& ssItem(X9) ) ) )
| nil = X0
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X5,X7)
| ~ leq(X4,X7)
| leq(X7,X4)
| ~ memberP(X6,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f443,plain,
( ~ ssList(sK10)
| nil = sK10
| memberP(nil,sK14(sK3(sK10),nil,sK2(sK10)))
| ~ spl16_4
| ~ spl16_6 ),
inference(subsumption_resolution,[],[f442,f406]) ).
fof(f406,plain,
( ssList(cons(sK3(sK10),nil))
| ~ spl16_6 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f405,plain,
( spl16_6
<=> ssList(cons(sK3(sK10),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_6])]) ).
fof(f442,plain,
( ~ ssList(cons(sK3(sK10),nil))
| nil = sK10
| memberP(nil,sK14(sK3(sK10),nil,sK2(sK10)))
| ~ ssList(sK10)
| ~ spl16_4 ),
inference(equality_resolution,[],[f396]) ).
fof(f396,plain,
( ! [X0] :
( sK10 != X0
| ~ ssList(cons(sK3(X0),nil))
| nil = X0
| ~ ssList(X0)
| memberP(nil,sK14(sK3(X0),nil,sK2(X0))) )
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f395,f173]) ).
fof(f173,plain,
! [X0] :
( ssList(sK2(X0))
| ~ ssList(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] :
( nil = X0
| ( ssList(sK2(X0))
& cons(sK3(X0),sK2(X0)) = X0
& ssItem(sK3(X0)) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f127,f135,f134]) ).
fof(f134,plain,
! [X0] :
( ? [X1] :
( ssList(X1)
& ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) ) )
=> ( ssList(sK2(X0))
& ? [X2] :
( cons(X2,sK2(X0)) = X0
& ssItem(X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f135,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK2(X0)) = X0
& ssItem(X2) )
=> ( cons(sK3(X0),sK2(X0)) = X0
& ssItem(sK3(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f127,plain,
! [X0] :
( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f126]) ).
fof(f126,plain,
! [X0] :
( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
fof(f395,plain,
( ! [X0] :
( ~ ssList(cons(sK3(X0),nil))
| memberP(nil,sK14(sK3(X0),nil,sK2(X0)))
| ~ ssList(X0)
| sK10 != X0
| nil = X0
| ~ ssList(sK2(X0)) )
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f394,f171]) ).
fof(f171,plain,
! [X0] :
( ssItem(sK3(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f394,plain,
( ! [X0] :
( ~ ssList(cons(sK3(X0),nil))
| ~ ssItem(sK3(X0))
| nil = X0
| sK10 != X0
| memberP(nil,sK14(sK3(X0),nil,sK2(X0)))
| ~ ssList(sK2(X0))
| ~ ssList(X0) )
| ~ spl16_4 ),
inference(superposition,[],[f369,f172]) ).
fof(f172,plain,
! [X0] :
( cons(sK3(X0),sK2(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f369,plain,
( ! [X10,X9] :
( cons(X9,X10) != sK10
| ~ ssList(X10)
| memberP(nil,sK14(X9,nil,X10))
| ~ ssItem(X9)
| ~ ssList(cons(X9,nil)) )
| ~ spl16_4 ),
inference(duplicate_literal_removal,[],[f345]) ).
fof(f345,plain,
( ! [X10,X9] :
( ~ ssList(X10)
| memberP(nil,sK14(X9,nil,X10))
| ~ ssList(cons(X9,nil))
| ~ ssItem(X9)
| cons(X9,X10) != sK10
| ~ ssList(X10)
| ~ ssItem(X9) )
| ~ spl16_4 ),
inference(superposition,[],[f297,f202]) ).
fof(f202,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) ) ),
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(f297,plain,
( ! [X8,X9] :
( app(cons(X8,nil),X9) != sK10
| ~ ssItem(X8)
| ~ ssList(cons(X8,nil))
| memberP(nil,sK14(X8,nil,X9))
| ~ ssList(X9) )
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f275,f254]) ).
fof(f254,plain,
( ssList(nil)
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f253,plain,
( spl16_4
<=> ssList(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).
fof(f275,plain,
! [X8,X9] :
( ~ ssList(nil)
| app(cons(X8,nil),X9) != sK10
| ~ ssList(cons(X8,nil))
| ~ ssList(X9)
| ~ ssItem(X8)
| memberP(nil,sK14(X8,nil,X9)) ),
inference(superposition,[],[f216,f180]) ).
fof(f180,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f216,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK10
| ~ ssList(X6)
| memberP(X5,sK14(X4,X5,X6))
| ~ ssItem(X4)
| ~ ssList(X5) ),
inference(cnf_transformation,[],[f160]) ).
fof(f414,plain,
( spl16_2
| ~ spl16_4
| spl16_6 ),
inference(avatar_contradiction_clause,[],[f413]) ).
fof(f413,plain,
( $false
| spl16_2
| ~ spl16_4
| spl16_6 ),
inference(subsumption_resolution,[],[f412,f203]) ).
fof(f412,plain,
( ~ ssList(sK10)
| spl16_2
| ~ spl16_4
| spl16_6 ),
inference(subsumption_resolution,[],[f411,f246]) ).
fof(f411,plain,
( nil = sK10
| ~ ssList(sK10)
| ~ spl16_4
| spl16_6 ),
inference(resolution,[],[f410,f171]) ).
fof(f410,plain,
( ~ ssItem(sK3(sK10))
| ~ spl16_4
| spl16_6 ),
inference(subsumption_resolution,[],[f409,f254]) ).
fof(f409,plain,
( ~ ssItem(sK3(sK10))
| ~ ssList(nil)
| spl16_6 ),
inference(resolution,[],[f407,f220]) ).
fof(f220,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,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(f407,plain,
( ~ ssList(cons(sK3(sK10),nil))
| spl16_6 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f408,plain,
( spl16_5
| ~ spl16_6
| spl16_2
| ~ spl16_4 ),
inference(avatar_split_clause,[],[f399,f253,f244,f405,f401]) ).
fof(f399,plain,
( ~ ssList(cons(sK3(sK10),nil))
| ssItem(sK14(sK3(sK10),nil,sK2(sK10)))
| spl16_2
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f398,f203]) ).
fof(f398,plain,
( ~ ssList(cons(sK3(sK10),nil))
| ~ ssList(sK10)
| ssItem(sK14(sK3(sK10),nil,sK2(sK10)))
| spl16_2
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f397,f246]) ).
fof(f397,plain,
( ssItem(sK14(sK3(sK10),nil,sK2(sK10)))
| ~ ssList(cons(sK3(sK10),nil))
| nil = sK10
| ~ ssList(sK10)
| ~ spl16_4 ),
inference(equality_resolution,[],[f381]) ).
fof(f381,plain,
( ! [X0] :
( sK10 != X0
| ~ ssList(cons(sK3(X0),nil))
| ~ ssList(X0)
| nil = X0
| ssItem(sK14(sK3(X0),nil,sK2(X0))) )
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f380,f173]) ).
fof(f380,plain,
( ! [X0] :
( ~ ssList(cons(sK3(X0),nil))
| ssItem(sK14(sK3(X0),nil,sK2(X0)))
| ~ ssList(sK2(X0))
| sK10 != X0
| nil = X0
| ~ ssList(X0) )
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f379,f171]) ).
fof(f379,plain,
( ! [X0] :
( ~ ssList(cons(sK3(X0),nil))
| ~ ssItem(sK3(X0))
| ssItem(sK14(sK3(X0),nil,sK2(X0)))
| ~ ssList(sK2(X0))
| ~ ssList(X0)
| nil = X0
| sK10 != X0 )
| ~ spl16_4 ),
inference(superposition,[],[f365,f172]) ).
fof(f365,plain,
( ! [X8,X7] :
( sK10 != cons(X7,X8)
| ssItem(sK14(X7,nil,X8))
| ~ ssItem(X7)
| ~ ssList(X8)
| ~ ssList(cons(X7,nil)) )
| ~ spl16_4 ),
inference(duplicate_literal_removal,[],[f344]) ).
fof(f344,plain,
( ! [X8,X7] :
( sK10 != cons(X7,X8)
| ~ ssList(cons(X7,nil))
| ~ ssItem(X7)
| ~ ssList(X8)
| ssItem(sK14(X7,nil,X8))
| ~ ssList(X8)
| ~ ssItem(X7) )
| ~ spl16_4 ),
inference(superposition,[],[f295,f202]) ).
fof(f295,plain,
( ! [X6,X7] :
( app(cons(X6,nil),X7) != sK10
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssList(cons(X6,nil))
| ssItem(sK14(X6,nil,X7)) )
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f274,f254]) ).
fof(f274,plain,
! [X6,X7] :
( ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssList(cons(X6,nil))
| ~ ssList(nil)
| app(cons(X6,nil),X7) != sK10
| ssItem(sK14(X6,nil,X7)) ),
inference(superposition,[],[f215,f180]) ).
fof(f215,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK10
| ~ ssList(X6)
| ~ ssItem(X4)
| ssItem(sK14(X4,X5,X6))
| ~ ssList(X5) ),
inference(cnf_transformation,[],[f160]) ).
fof(f258,plain,
spl16_4,
inference(avatar_split_clause,[],[f182,f253]) ).
fof(f182,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f257,plain,
~ spl16_2,
inference(avatar_split_clause,[],[f205,f244]) ).
fof(f205,plain,
nil != sK10,
inference(cnf_transformation,[],[f160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWC224+1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.13 % 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 : n028.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 18:45:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.49 % (27724)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)
% 0.21/0.50 % (27742)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)
% 0.21/0.50 % (27739)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.21/0.50 % (27725)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)
% 0.21/0.51 % (27732)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)
% 0.21/0.51 % (27724)Instruction limit reached!
% 0.21/0.51 % (27724)------------------------------
% 0.21/0.51 % (27724)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51 % (27726)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)
% 0.21/0.51 % (27725)Instruction limit reached!
% 0.21/0.51 % (27725)------------------------------
% 0.21/0.51 % (27725)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52 % (27726)First to succeed.
% 0.21/0.52 % (27732)Instruction limit reached!
% 0.21/0.52 % (27732)------------------------------
% 0.21/0.52 % (27732)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52 % (27721)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)
% 0.21/0.52 % (27736)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.52 % (27739)Instruction limit reached!
% 0.21/0.52 % (27739)------------------------------
% 0.21/0.52 % (27739)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52 % (27724)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52 % (27724)Termination reason: Unknown
% 0.21/0.52 % (27724)Termination phase: Saturation
% 0.21/0.52
% 0.21/0.52 % (27724)Memory used [KB]: 6268
% 0.21/0.52 % (27724)Time elapsed: 0.102 s
% 0.21/0.52 % (27724)Instructions burned: 13 (million)
% 0.21/0.52 % (27724)------------------------------
% 0.21/0.52 % (27724)------------------------------
% 0.21/0.53 % (27739)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53 % (27739)Termination reason: Unknown
% 0.21/0.53 % (27739)Termination phase: Saturation
% 0.21/0.53
% 0.21/0.53 % (27739)Memory used [KB]: 6396
% 0.21/0.53 % (27739)Time elapsed: 0.112 s
% 0.21/0.53 % (27739)Instructions burned: 12 (million)
% 0.21/0.53 % (27739)------------------------------
% 0.21/0.53 % (27739)------------------------------
% 0.21/0.53 % (27745)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)
% 0.21/0.53 % (27752)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.21/0.53 % (27726)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 % (27726)------------------------------
% 0.21/0.53 % (27726)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53 % (27726)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53 % (27726)Termination reason: Refutation
% 0.21/0.53
% 0.21/0.53 % (27726)Memory used [KB]: 6268
% 0.21/0.53 % (27726)Time elapsed: 0.113 s
% 0.21/0.53 % (27726)Instructions burned: 14 (million)
% 0.21/0.53 % (27726)------------------------------
% 0.21/0.53 % (27726)------------------------------
% 0.21/0.53 % (27715)Success in time 0.178 s
%------------------------------------------------------------------------------