TSTP Solution File: SWC002+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SWC002+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 : n005.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 18:38:09 EDT 2022
% Result : Theorem 0.21s 0.54s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 99 ( 5 unt; 0 def)
% Number of atoms : 551 ( 59 equ)
% Maximal formula atoms : 27 ( 5 avg)
% Number of connectives : 837 ( 385 ~; 371 |; 52 &)
% ( 13 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 13 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 117 ( 93 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f967,plain,
$false,
inference(avatar_sat_refutation,[],[f569,f578,f583,f588,f605,f606,f607,f608,f615,f617,f619,f945,f966]) ).
fof(f966,plain,
( ~ spl56_2
| ~ spl56_5
| ~ spl56_6
| ~ spl56_7
| ~ spl56_8
| ~ spl56_11
| ~ spl56_36 ),
inference(avatar_contradiction_clause,[],[f965]) ).
fof(f965,plain,
( $false
| ~ spl56_2
| ~ spl56_5
| ~ spl56_6
| ~ spl56_7
| ~ spl56_8
| ~ spl56_11
| ~ spl56_36 ),
inference(subsumption_resolution,[],[f960,f835]) ).
fof(f835,plain,
( ~ sQ55_eqProxy(sK54(sK51),sK51)
| ~ spl56_2
| ~ spl56_5
| ~ spl56_6
| ~ spl56_7
| ~ spl56_8
| ~ spl56_11 ),
inference(subsumption_resolution,[],[f834,f592]) ).
fof(f592,plain,
( sQ55_eqProxy(app(sK52,sK53),sK49)
| ~ spl56_7 ),
inference(avatar_component_clause,[],[f590]) ).
fof(f590,plain,
( spl56_7
<=> sQ55_eqProxy(app(sK52,sK53),sK49) ),
introduced(avatar_definition,[new_symbols(naming,[spl56_7])]) ).
fof(f834,plain,
( ~ sQ55_eqProxy(app(sK52,sK53),sK49)
| ~ sQ55_eqProxy(sK54(sK51),sK51)
| ~ spl56_2
| ~ spl56_5
| ~ spl56_6
| ~ spl56_8
| ~ spl56_11 ),
inference(subsumption_resolution,[],[f833,f613]) ).
fof(f613,plain,
( ssList(sK52)
| ~ spl56_11 ),
inference(avatar_component_clause,[],[f611]) ).
fof(f611,plain,
( spl56_11
<=> ssList(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl56_11])]) ).
fof(f833,plain,
( ~ ssList(sK52)
| ~ sQ55_eqProxy(sK54(sK51),sK51)
| ~ sQ55_eqProxy(app(sK52,sK53),sK49)
| ~ spl56_2
| ~ spl56_5
| ~ spl56_6
| ~ spl56_8 ),
inference(subsumption_resolution,[],[f832,f582]) ).
fof(f582,plain,
( ssItem(sK51)
| ~ spl56_5 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f580,plain,
( spl56_5
<=> ssItem(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl56_5])]) ).
fof(f832,plain,
( ~ ssItem(sK51)
| ~ ssList(sK52)
| ~ sQ55_eqProxy(sK54(sK51),sK51)
| ~ sQ55_eqProxy(app(sK52,sK53),sK49)
| ~ spl56_2
| ~ spl56_6
| ~ spl56_8 ),
inference(subsumption_resolution,[],[f819,f568]) ).
fof(f568,plain,
( ssList(sK53)
| ~ spl56_2 ),
inference(avatar_component_clause,[],[f566]) ).
fof(f566,plain,
( spl56_2
<=> ssList(sK53) ),
introduced(avatar_definition,[new_symbols(naming,[spl56_2])]) ).
fof(f819,plain,
( ~ ssList(sK53)
| ~ sQ55_eqProxy(app(sK52,sK53),sK49)
| ~ ssList(sK52)
| ~ ssItem(sK51)
| ~ sQ55_eqProxy(sK54(sK51),sK51)
| ~ spl56_6
| ~ spl56_8 ),
inference(resolution,[],[f793,f596]) ).
fof(f596,plain,
( ! [X6,X4,X5] :
( ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
| ~ sQ55_eqProxy(app(X5,X6),sK49)
| ~ ssList(X5)
| ~ sQ55_eqProxy(sK54(X4),X4)
| ~ ssItem(X4)
| ~ ssList(X6) )
| ~ spl56_8 ),
inference(avatar_component_clause,[],[f595]) ).
fof(f595,plain,
( spl56_8
<=> ! [X6,X4,X5] :
( ~ sQ55_eqProxy(app(X5,X6),sK49)
| ~ sQ55_eqProxy(sK54(X4),X4)
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
| ~ ssList(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl56_8])]) ).
fof(f793,plain,
( sQ55_eqProxy(app(app(sK52,cons(sK51,nil)),sK53),sK48)
| ~ spl56_6 ),
inference(resolution,[],[f560,f587]) ).
fof(f587,plain,
( sQ55_eqProxy(sK48,app(app(sK52,cons(sK51,nil)),sK53))
| ~ spl56_6 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f585,plain,
( spl56_6
<=> sQ55_eqProxy(sK48,app(app(sK52,cons(sK51,nil)),sK53)) ),
introduced(avatar_definition,[new_symbols(naming,[spl56_6])]) ).
fof(f560,plain,
! [X0,X1] :
( ~ sQ55_eqProxy(X0,X1)
| sQ55_eqProxy(X1,X0) ),
inference(equality_proxy_axiom,[],[f458]) ).
fof(f458,plain,
! [X0,X1] :
( sQ55_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ55_eqProxy])]) ).
fof(f960,plain,
( sQ55_eqProxy(sK54(sK51),sK51)
| ~ spl56_36 ),
inference(resolution,[],[f914,f560]) ).
fof(f914,plain,
( sQ55_eqProxy(sK51,sK54(sK51))
| ~ spl56_36 ),
inference(avatar_component_clause,[],[f912]) ).
fof(f912,plain,
( spl56_36
<=> sQ55_eqProxy(sK51,sK54(sK51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl56_36])]) ).
fof(f945,plain,
( spl56_36
| ~ spl56_2
| ~ spl56_3
| ~ spl56_4
| ~ spl56_5
| ~ spl56_6
| ~ spl56_7
| ~ spl56_9
| ~ spl56_10
| ~ spl56_11 ),
inference(avatar_split_clause,[],[f900,f611,f603,f599,f590,f585,f580,f575,f571,f566,f912]) ).
fof(f571,plain,
( spl56_3
<=> ! [X11] :
( ~ geq(X11,sK51)
| ~ ssItem(X11)
| sQ55_eqProxy(sK51,X11)
| ~ memberP(sK48,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl56_3])]) ).
fof(f575,plain,
( spl56_4
<=> ! [X6,X4,X5] :
( ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
| ssItem(sK54(X4))
| ~ ssItem(X4)
| ~ ssList(X6)
| ~ sQ55_eqProxy(app(X5,X6),sK49)
| ~ ssList(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl56_4])]) ).
fof(f599,plain,
( spl56_9
<=> ! [X6,X4,X5] :
( geq(sK54(X4),X4)
| ~ ssItem(X4)
| ~ sQ55_eqProxy(app(X5,X6),sK49)
| ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
| ~ ssList(X5)
| ~ ssList(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl56_9])]) ).
fof(f603,plain,
( spl56_10
<=> ! [X6,X4,X5] :
( memberP(sK48,sK54(X4))
| ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
| ~ ssItem(X4)
| ~ ssList(X6)
| ~ ssList(X5)
| ~ sQ55_eqProxy(app(X5,X6),sK49) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl56_10])]) ).
fof(f900,plain,
( sQ55_eqProxy(sK51,sK54(sK51))
| ~ spl56_2
| ~ spl56_3
| ~ spl56_4
| ~ spl56_5
| ~ spl56_6
| ~ spl56_7
| ~ spl56_9
| ~ spl56_10
| ~ spl56_11 ),
inference(subsumption_resolution,[],[f899,f827]) ).
fof(f827,plain,
( memberP(sK48,sK54(sK51))
| ~ spl56_2
| ~ spl56_5
| ~ spl56_6
| ~ spl56_7
| ~ spl56_10
| ~ spl56_11 ),
inference(subsumption_resolution,[],[f826,f568]) ).
fof(f826,plain,
( ~ ssList(sK53)
| memberP(sK48,sK54(sK51))
| ~ spl56_5
| ~ spl56_6
| ~ spl56_7
| ~ spl56_10
| ~ spl56_11 ),
inference(subsumption_resolution,[],[f825,f592]) ).
fof(f825,plain,
( memberP(sK48,sK54(sK51))
| ~ sQ55_eqProxy(app(sK52,sK53),sK49)
| ~ ssList(sK53)
| ~ spl56_5
| ~ spl56_6
| ~ spl56_10
| ~ spl56_11 ),
inference(subsumption_resolution,[],[f824,f613]) ).
fof(f824,plain,
( ~ ssList(sK52)
| ~ ssList(sK53)
| ~ sQ55_eqProxy(app(sK52,sK53),sK49)
| memberP(sK48,sK54(sK51))
| ~ spl56_5
| ~ spl56_6
| ~ spl56_10 ),
inference(subsumption_resolution,[],[f817,f582]) ).
fof(f817,plain,
( ~ ssItem(sK51)
| ~ ssList(sK52)
| ~ ssList(sK53)
| ~ sQ55_eqProxy(app(sK52,sK53),sK49)
| memberP(sK48,sK54(sK51))
| ~ spl56_6
| ~ spl56_10 ),
inference(resolution,[],[f793,f604]) ).
fof(f604,plain,
( ! [X6,X4,X5] :
( ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
| memberP(sK48,sK54(X4))
| ~ ssItem(X4)
| ~ ssList(X6)
| ~ sQ55_eqProxy(app(X5,X6),sK49)
| ~ ssList(X5) )
| ~ spl56_10 ),
inference(avatar_component_clause,[],[f603]) ).
fof(f899,plain,
( sQ55_eqProxy(sK51,sK54(sK51))
| ~ memberP(sK48,sK54(sK51))
| ~ spl56_2
| ~ spl56_3
| ~ spl56_4
| ~ spl56_5
| ~ spl56_6
| ~ spl56_7
| ~ spl56_9
| ~ spl56_11 ),
inference(subsumption_resolution,[],[f895,f831]) ).
fof(f831,plain,
( ssItem(sK54(sK51))
| ~ spl56_2
| ~ spl56_4
| ~ spl56_5
| ~ spl56_6
| ~ spl56_7
| ~ spl56_11 ),
inference(subsumption_resolution,[],[f830,f613]) ).
fof(f830,plain,
( ~ ssList(sK52)
| ssItem(sK54(sK51))
| ~ spl56_2
| ~ spl56_4
| ~ spl56_5
| ~ spl56_6
| ~ spl56_7 ),
inference(subsumption_resolution,[],[f829,f592]) ).
fof(f829,plain,
( ~ sQ55_eqProxy(app(sK52,sK53),sK49)
| ssItem(sK54(sK51))
| ~ ssList(sK52)
| ~ spl56_2
| ~ spl56_4
| ~ spl56_5
| ~ spl56_6 ),
inference(subsumption_resolution,[],[f828,f568]) ).
fof(f828,plain,
( ~ ssList(sK53)
| ~ sQ55_eqProxy(app(sK52,sK53),sK49)
| ~ ssList(sK52)
| ssItem(sK54(sK51))
| ~ spl56_4
| ~ spl56_5
| ~ spl56_6 ),
inference(subsumption_resolution,[],[f820,f582]) ).
fof(f820,plain,
( ~ ssItem(sK51)
| ~ sQ55_eqProxy(app(sK52,sK53),sK49)
| ~ ssList(sK53)
| ssItem(sK54(sK51))
| ~ ssList(sK52)
| ~ spl56_4
| ~ spl56_6 ),
inference(resolution,[],[f793,f576]) ).
fof(f576,plain,
( ! [X6,X4,X5] :
( ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
| ~ ssList(X5)
| ssItem(sK54(X4))
| ~ ssList(X6)
| ~ ssItem(X4)
| ~ sQ55_eqProxy(app(X5,X6),sK49) )
| ~ spl56_4 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f895,plain,
( sQ55_eqProxy(sK51,sK54(sK51))
| ~ ssItem(sK54(sK51))
| ~ memberP(sK48,sK54(sK51))
| ~ spl56_2
| ~ spl56_3
| ~ spl56_5
| ~ spl56_6
| ~ spl56_7
| ~ spl56_9
| ~ spl56_11 ),
inference(resolution,[],[f845,f572]) ).
fof(f572,plain,
( ! [X11] :
( ~ geq(X11,sK51)
| ~ memberP(sK48,X11)
| ~ ssItem(X11)
| sQ55_eqProxy(sK51,X11) )
| ~ spl56_3 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f845,plain,
( geq(sK54(sK51),sK51)
| ~ spl56_2
| ~ spl56_5
| ~ spl56_6
| ~ spl56_7
| ~ spl56_9
| ~ spl56_11 ),
inference(subsumption_resolution,[],[f844,f613]) ).
fof(f844,plain,
( ~ ssList(sK52)
| geq(sK54(sK51),sK51)
| ~ spl56_2
| ~ spl56_5
| ~ spl56_6
| ~ spl56_7
| ~ spl56_9 ),
inference(subsumption_resolution,[],[f843,f592]) ).
fof(f843,plain,
( geq(sK54(sK51),sK51)
| ~ sQ55_eqProxy(app(sK52,sK53),sK49)
| ~ ssList(sK52)
| ~ spl56_2
| ~ spl56_5
| ~ spl56_6
| ~ spl56_9 ),
inference(subsumption_resolution,[],[f842,f582]) ).
fof(f842,plain,
( ~ ssItem(sK51)
| geq(sK54(sK51),sK51)
| ~ ssList(sK52)
| ~ sQ55_eqProxy(app(sK52,sK53),sK49)
| ~ spl56_2
| ~ spl56_6
| ~ spl56_9 ),
inference(subsumption_resolution,[],[f818,f568]) ).
fof(f818,plain,
( ~ ssList(sK53)
| ~ ssList(sK52)
| ~ ssItem(sK51)
| ~ sQ55_eqProxy(app(sK52,sK53),sK49)
| geq(sK54(sK51),sK51)
| ~ spl56_6
| ~ spl56_9 ),
inference(resolution,[],[f793,f600]) ).
fof(f600,plain,
( ! [X6,X4,X5] :
( ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
| geq(sK54(X4),X4)
| ~ sQ55_eqProxy(app(X5,X6),sK49)
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ ssList(X6) )
| ~ spl56_9 ),
inference(avatar_component_clause,[],[f599]) ).
fof(f619,plain,
( ~ spl56_1
| spl56_9 ),
inference(avatar_split_clause,[],[f552,f599,f562]) ).
fof(f562,plain,
( spl56_1
<=> neq(sK48,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl56_1])]) ).
fof(f552,plain,
! [X6,X4,X5] :
( ~ ssList(X5)
| ~ sQ55_eqProxy(app(X5,X6),sK49)
| ~ ssList(X6)
| ~ ssItem(X4)
| ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
| ~ neq(sK48,nil)
| geq(sK54(X4),X4) ),
inference(equality_proxy_replacement,[],[f454,f458,f458]) ).
fof(f454,plain,
! [X6,X4,X5] :
( ~ ssList(X6)
| app(X5,X6) != sK49
| geq(sK54(X4),X4)
| app(app(X5,cons(X4,nil)),X6) != sK48
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ neq(sK48,nil) ),
inference(definition_unfolding,[],[f407,f427,f426]) ).
fof(f426,plain,
sK50 = sK48,
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( neq(X1,nil)
& ~ neq(X3,nil) )
| ( neq(X1,nil)
& ? [X8] :
( ? [X9] :
( ? [X10] :
( app(app(X9,cons(X8,nil)),X10) = X3
& app(X9,X10) = X2
& ! [X11] :
( ~ geq(X11,X8)
| ~ memberP(X3,X11)
| ~ ssItem(X11)
| X8 = X11 )
& ssList(X10) )
& ssList(X9) )
& ssItem(X8) )
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( app(app(X5,cons(X4,nil)),X6) != X1
| ? [X7] :
( X4 != X7
& ssItem(X7)
& geq(X7,X4)
& memberP(X1,X7) )
| app(X5,X6) != X0
| ~ ssList(X6) ) ) ) ) )
& X0 = X2
& X1 = X3 ) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ~ neq(X3,nil) )
| ( neq(X1,nil)
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X1
| app(X5,X6) != X0
| ? [X7] :
( geq(X7,X4)
& X4 != X7
& memberP(X1,X7)
& ssItem(X7) ) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ? [X8] :
( ? [X9] :
( ? [X10] :
( app(app(X9,cons(X8,nil)),X10) = X3
& ! [X11] :
( ~ geq(X11,X8)
| ~ memberP(X3,X11)
| ~ ssItem(X11)
| X8 = X11 )
& app(X9,X10) = X2
& ssList(X10) )
& ssList(X9) )
& ssItem(X8) ) ) )
& 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)
=> ( X1 != X3
| X0 != X2
| ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ~ neq(X1,nil)
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X1
& app(X5,X6) = X0
& ! [X7] :
( ssItem(X7)
=> ( ~ geq(X7,X4)
| X4 = X7
| ~ memberP(X1,X7) ) ) )
& ssList(X5) )
& ssItem(X4) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(X9,cons(X8,nil)),X10) != X3
| ? [X11] :
( memberP(X3,X11)
& X8 != X11
& ssItem(X11)
& geq(X11,X8) )
| app(X9,X10) != X2 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ~ neq(X1,nil)
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X1
& app(X5,X6) = X0
& ! [X7] :
( ssItem(X7)
=> ( ~ geq(X7,X4)
| X4 = X7
| ~ memberP(X1,X7) ) ) )
& ssList(X5) )
& ssItem(X4) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(X9,cons(X8,nil)),X10) != X3
| ? [X11] :
( memberP(X3,X11)
& X8 != X11
& ssItem(X11)
& geq(X11,X8) )
| app(X9,X10) != X2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f427,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f99]) ).
fof(f407,plain,
! [X6,X4,X5] :
( ~ ssList(X6)
| app(X5,X6) != sK47
| geq(sK54(X4),X4)
| app(app(X5,cons(X4,nil)),X6) != sK48
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ neq(sK50,nil) ),
inference(cnf_transformation,[],[f99]) ).
fof(f617,plain,
spl56_1,
inference(avatar_split_clause,[],[f425,f562]) ).
fof(f425,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f99]) ).
fof(f615,plain,
( spl56_11
| ~ spl56_1 ),
inference(avatar_split_clause,[],[f443,f562,f611]) ).
fof(f443,plain,
( ~ neq(sK48,nil)
| ssList(sK52) ),
inference(definition_unfolding,[],[f420,f426]) ).
fof(f420,plain,
( ssList(sK52)
| ~ neq(sK50,nil) ),
inference(cnf_transformation,[],[f99]) ).
fof(f608,plain,
( ~ spl56_1
| spl56_8 ),
inference(avatar_split_clause,[],[f550,f595,f562]) ).
fof(f550,plain,
! [X6,X4,X5] :
( ~ ssList(X5)
| ~ ssList(X6)
| ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
| ~ neq(sK48,nil)
| ~ ssItem(X4)
| ~ sQ55_eqProxy(app(X5,X6),sK49)
| ~ sQ55_eqProxy(sK54(X4),X4) ),
inference(equality_proxy_replacement,[],[f452,f458,f458,f458]) ).
fof(f452,plain,
! [X6,X4,X5] :
( ~ ssList(X6)
| app(X5,X6) != sK49
| sK54(X4) != X4
| app(app(X5,cons(X4,nil)),X6) != sK48
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ neq(sK48,nil) ),
inference(definition_unfolding,[],[f409,f427,f426]) ).
fof(f409,plain,
! [X6,X4,X5] :
( ~ ssList(X6)
| app(X5,X6) != sK47
| sK54(X4) != X4
| app(app(X5,cons(X4,nil)),X6) != sK48
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ neq(sK50,nil) ),
inference(cnf_transformation,[],[f99]) ).
fof(f607,plain,
( ~ spl56_1
| spl56_4 ),
inference(avatar_split_clause,[],[f551,f575,f562]) ).
fof(f551,plain,
! [X6,X4,X5] :
( ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48)
| ~ ssItem(X4)
| ssItem(sK54(X4))
| ~ ssList(X6)
| ~ neq(sK48,nil)
| ~ ssList(X5)
| ~ sQ55_eqProxy(app(X5,X6),sK49) ),
inference(equality_proxy_replacement,[],[f453,f458,f458]) ).
fof(f453,plain,
! [X6,X4,X5] :
( ~ ssList(X6)
| app(X5,X6) != sK49
| ssItem(sK54(X4))
| app(app(X5,cons(X4,nil)),X6) != sK48
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ neq(sK48,nil) ),
inference(definition_unfolding,[],[f408,f427,f426]) ).
fof(f408,plain,
! [X6,X4,X5] :
( ~ ssList(X6)
| app(X5,X6) != sK47
| ssItem(sK54(X4))
| app(app(X5,cons(X4,nil)),X6) != sK48
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ neq(sK50,nil) ),
inference(cnf_transformation,[],[f99]) ).
fof(f606,plain,
( ~ spl56_1
| spl56_7 ),
inference(avatar_split_clause,[],[f543,f590,f562]) ).
fof(f543,plain,
( sQ55_eqProxy(app(sK52,sK53),sK49)
| ~ neq(sK48,nil) ),
inference(equality_proxy_replacement,[],[f445,f458]) ).
fof(f445,plain,
( app(sK52,sK53) = sK49
| ~ neq(sK48,nil) ),
inference(definition_unfolding,[],[f418,f426]) ).
fof(f418,plain,
( app(sK52,sK53) = sK49
| ~ neq(sK50,nil) ),
inference(cnf_transformation,[],[f99]) ).
fof(f605,plain,
( ~ spl56_1
| spl56_10 ),
inference(avatar_split_clause,[],[f553,f603,f562]) ).
fof(f553,plain,
! [X6,X4,X5] :
( memberP(sK48,sK54(X4))
| ~ ssList(X6)
| ~ ssItem(X4)
| ~ ssList(X5)
| ~ sQ55_eqProxy(app(X5,X6),sK49)
| ~ neq(sK48,nil)
| ~ sQ55_eqProxy(app(app(X5,cons(X4,nil)),X6),sK48) ),
inference(equality_proxy_replacement,[],[f455,f458,f458]) ).
fof(f455,plain,
! [X6,X4,X5] :
( ~ ssList(X6)
| app(X5,X6) != sK49
| memberP(sK48,sK54(X4))
| app(app(X5,cons(X4,nil)),X6) != sK48
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ neq(sK48,nil) ),
inference(definition_unfolding,[],[f406,f427,f426]) ).
fof(f406,plain,
! [X6,X4,X5] :
( ~ ssList(X6)
| app(X5,X6) != sK47
| memberP(sK48,sK54(X4))
| app(app(X5,cons(X4,nil)),X6) != sK48
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ neq(sK50,nil) ),
inference(cnf_transformation,[],[f99]) ).
fof(f588,plain,
( ~ spl56_1
| spl56_6 ),
inference(avatar_split_clause,[],[f542,f585,f562]) ).
fof(f542,plain,
( sQ55_eqProxy(sK48,app(app(sK52,cons(sK51,nil)),sK53))
| ~ neq(sK48,nil) ),
inference(equality_proxy_replacement,[],[f444,f458]) ).
fof(f444,plain,
( sK48 = app(app(sK52,cons(sK51,nil)),sK53)
| ~ neq(sK48,nil) ),
inference(definition_unfolding,[],[f419,f426,f426]) ).
fof(f419,plain,
( sK50 = app(app(sK52,cons(sK51,nil)),sK53)
| ~ neq(sK50,nil) ),
inference(cnf_transformation,[],[f99]) ).
fof(f583,plain,
( ~ spl56_1
| spl56_5 ),
inference(avatar_split_clause,[],[f442,f580,f562]) ).
fof(f442,plain,
( ssItem(sK51)
| ~ neq(sK48,nil) ),
inference(definition_unfolding,[],[f423,f426]) ).
fof(f423,plain,
( ssItem(sK51)
| ~ neq(sK50,nil) ),
inference(cnf_transformation,[],[f99]) ).
fof(f578,plain,
( ~ spl56_1
| spl56_3 ),
inference(avatar_split_clause,[],[f555,f571,f562]) ).
fof(f555,plain,
! [X11] :
( sQ55_eqProxy(sK51,X11)
| ~ ssItem(X11)
| ~ memberP(sK48,X11)
| ~ neq(sK48,nil)
| ~ geq(X11,sK51) ),
inference(equality_proxy_replacement,[],[f457,f458]) ).
fof(f457,plain,
! [X11] :
( sK51 = X11
| ~ ssItem(X11)
| ~ memberP(sK48,X11)
| ~ geq(X11,sK51)
| ~ neq(sK48,nil) ),
inference(definition_unfolding,[],[f404,f426,f426]) ).
fof(f404,plain,
! [X11] :
( sK51 = X11
| ~ ssItem(X11)
| ~ memberP(sK50,X11)
| ~ geq(X11,sK51)
| ~ neq(sK50,nil) ),
inference(cnf_transformation,[],[f99]) ).
fof(f569,plain,
( ~ spl56_1
| spl56_2 ),
inference(avatar_split_clause,[],[f446,f566,f562]) ).
fof(f446,plain,
( ssList(sK53)
| ~ neq(sK48,nil) ),
inference(definition_unfolding,[],[f417,f426]) ).
fof(f417,plain,
( ssList(sK53)
| ~ neq(sK50,nil) ),
inference(cnf_transformation,[],[f99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC002+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
% 0.13/0.36 % Computer : n005.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Tue Aug 30 17:52:48 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.21/0.49 % (22357)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)
% 0.21/0.49 % (22372)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)
% 0.21/0.50 % (22365)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.21/0.51 % (22357)Instruction limit reached!
% 0.21/0.51 % (22357)------------------------------
% 0.21/0.51 % (22357)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52 % (22357)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52 % (22357)Termination reason: Unknown
% 0.21/0.52 % (22357)Termination phase: Saturation
% 0.21/0.52
% 0.21/0.52 % (22357)Memory used [KB]: 2046
% 0.21/0.52 % (22357)Time elapsed: 0.102 s
% 0.21/0.52 % (22357)Instructions burned: 16 (million)
% 0.21/0.52 % (22357)------------------------------
% 0.21/0.52 % (22357)------------------------------
% 0.21/0.52 % (22345)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.21/0.54 % (22372)Instruction limit reached!
% 0.21/0.54 % (22372)------------------------------
% 0.21/0.54 % (22372)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.54 % (22359)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)
% 0.21/0.54 % (22365)First to succeed.
% 0.21/0.54 % (22372)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.54 % (22372)Termination reason: Unknown
% 0.21/0.54 % (22372)Termination phase: Saturation
% 0.21/0.54
% 0.21/0.54 % (22372)Memory used [KB]: 6652
% 0.21/0.54 % (22372)Time elapsed: 0.117 s
% 0.21/0.54 % (22372)Instructions burned: 25 (million)
% 0.21/0.54 % (22372)------------------------------
% 0.21/0.54 % (22372)------------------------------
% 0.21/0.54 % (22359)Instruction limit reached!
% 0.21/0.54 % (22359)------------------------------
% 0.21/0.54 % (22359)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.54 % (22359)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.54 % (22359)Termination reason: Unknown
% 0.21/0.54 % (22359)Termination phase: Naming
% 0.21/0.54
% 0.21/0.54 % (22359)Memory used [KB]: 1535
% 0.21/0.54 % (22359)Time elapsed: 0.003 s
% 0.21/0.54 % (22359)Instructions burned: 3 (million)
% 0.21/0.54 % (22359)------------------------------
% 0.21/0.54 % (22359)------------------------------
% 0.21/0.54 % (22365)Refutation found. Thanks to Tanya!
% 0.21/0.54 % SZS status Theorem for theBenchmark
% 0.21/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.54 % (22365)------------------------------
% 0.21/0.54 % (22365)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.54 % (22365)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.54 % (22365)Termination reason: Refutation
% 0.21/0.54
% 0.21/0.54 % (22365)Memory used [KB]: 6524
% 0.21/0.54 % (22365)Time elapsed: 0.128 s
% 0.21/0.54 % (22365)Instructions burned: 25 (million)
% 0.21/0.54 % (22365)------------------------------
% 0.21/0.54 % (22365)------------------------------
% 0.21/0.54 % (22344)Success in time 0.172 s
%------------------------------------------------------------------------------