TSTP Solution File: SWC098+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SWC098+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n021.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 : Tue May 21 04:36:13 EDT 2024
% Result : Theorem 0.49s 0.72s
% Output : Refutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 99 ( 3 unt; 1 typ; 0 def)
% Number of atoms : 1105 ( 175 equ)
% Maximal formula atoms : 48 ( 11 avg)
% Number of connectives : 815 ( 297 ~; 295 |; 189 &)
% ( 10 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 489 ( 489 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 24 ( 22 usr; 16 prp; 0-3 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 125 ( 72 !; 52 ?; 29 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_20,type,
sQ17_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f447,plain,
$false,
inference(avatar_sat_refutation,[],[f319,f324,f329,f334,f339,f340,f341,f342,f343,f406,f423,f428,f446]) ).
tff(f446,plain,
( ~ spl18_3
| ~ spl18_4
| ~ spl18_5
| spl18_13 ),
inference(avatar_contradiction_clause,[],[f445]) ).
tff(f445,plain,
( $false
| ~ spl18_3
| ~ spl18_4
| ~ spl18_5
| spl18_13 ),
inference(subsumption_resolution,[],[f444,f333]) ).
tff(f333,plain,
( ssItem(sK4)
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f331]) ).
tff(f331,plain,
( spl18_5
<=> ssItem(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_5])]) ).
tff(f444,plain,
( ~ ssItem(sK4)
| ~ spl18_3
| ~ spl18_4
| spl18_13 ),
inference(subsumption_resolution,[],[f443,f323]) ).
tff(f323,plain,
( memberP(sK3,sK4)
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f321]) ).
tff(f321,plain,
( spl18_3
<=> memberP(sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_3])]) ).
tff(f443,plain,
( ~ memberP(sK3,sK4)
| ~ ssItem(sK4)
| ~ spl18_4
| spl18_13 ),
inference(subsumption_resolution,[],[f442,f328]) ).
tff(f328,plain,
( sQ17_eqProxy($i,sK2,cons(sK4,nil))
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f326]) ).
tff(f326,plain,
( spl18_4
<=> sQ17_eqProxy($i,sK2,cons(sK4,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_4])]) ).
tff(f442,plain,
( ~ sQ17_eqProxy($i,sK2,cons(sK4,nil))
| ~ memberP(sK3,sK4)
| ~ ssItem(sK4)
| spl18_13 ),
inference(resolution,[],[f401,f376]) ).
tff(f376,plain,
! [X0: $i] :
( leq(X0,sK5(X0))
| ~ sQ17_eqProxy($i,sK2,cons(X0,nil))
| ~ memberP(sK3,X0)
| ~ ssItem(X0) ),
inference(resolution,[],[f308,f276]) ).
tff(f276,plain,
! [X6: $i] :
( ~ sQ17_eqProxy($i,cons(X6,nil),sK2)
| leq(X6,sK5(X6))
| ~ memberP(sK3,X6)
| ~ ssItem(X6) ),
inference(equality_proxy_replacement,[],[f252,f265]) ).
tff(f265,plain,
! [X0: $tType,X2: X0,X1: X0] :
( sQ17_eqProxy(X0,X1,X2)
<=> ( X1 = X2 ) ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ17_eqProxy])]) ).
tff(f252,plain,
! [X6: $i] :
( ~ memberP(sK3,X6)
| leq(X6,sK5(X6))
| ( cons(X6,nil) != sK2 )
| ~ ssItem(X6) ),
inference(definition_unfolding,[],[f182,f178,f179]) ).
tff(f179,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f143]) ).
tff(f143,plain,
( ( ( ( nil = sK2 )
& ( nil = sK3 ) )
| ( ! [X5] :
( ~ leq(sK4,X5)
| ~ memberP(sK3,X5)
| ( sK4 = X5 )
| ~ ssItem(X5) )
& memberP(sK3,sK4)
& ( sK2 = cons(sK4,nil) )
& ssItem(sK4) ) )
& ( ( nil != sK0 )
| ( nil != sK1 ) )
& ! [X6] :
( ~ memberP(sK1,X6)
| ( ( sK5(X6) != X6 )
& leq(X6,sK5(X6))
& memberP(sK1,sK5(X6))
& ssItem(sK5(X6)) )
| ( cons(X6,nil) != sK0 )
| ~ ssItem(X6) )
& ( sK0 = sK2 )
& ( sK1 = sK3 )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f100,f142,f141,f140,f139,f138,f137]) ).
tff(f137,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ( nil = X2 )
& ( nil = X3 ) )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| ( X4 = X5 )
| ~ ssItem(X5) )
& memberP(X3,X4)
& ( cons(X4,nil) = X2 )
& ssItem(X4) ) )
& ( ( nil != X0 )
| ( nil != X1 ) )
& ! [X6] :
( ~ memberP(X1,X6)
| ? [X7] :
( ( X6 != X7 )
& leq(X6,X7)
& memberP(X1,X7)
& ssItem(X7) )
| ( cons(X6,nil) != X0 )
| ~ ssItem(X6) )
& ( X0 = X2 )
& ( X1 = X3 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ( nil = X2 )
& ( nil = X3 ) )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| ( X4 = X5 )
| ~ ssItem(X5) )
& memberP(X3,X4)
& ( cons(X4,nil) = X2 )
& ssItem(X4) ) )
& ( ( nil != sK0 )
| ( nil != X1 ) )
& ! [X6] :
( ~ memberP(X1,X6)
| ? [X7] :
( ( X6 != X7 )
& leq(X6,X7)
& memberP(X1,X7)
& ssItem(X7) )
| ( cons(X6,nil) != sK0 )
| ~ ssItem(X6) )
& ( sK0 = X2 )
& ( X1 = X3 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f138,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ( nil = X2 )
& ( nil = X3 ) )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| ( X4 = X5 )
| ~ ssItem(X5) )
& memberP(X3,X4)
& ( cons(X4,nil) = X2 )
& ssItem(X4) ) )
& ( ( nil != sK0 )
| ( nil != X1 ) )
& ! [X6] :
( ~ memberP(X1,X6)
| ? [X7] :
( ( X6 != X7 )
& leq(X6,X7)
& memberP(X1,X7)
& ssItem(X7) )
| ( cons(X6,nil) != sK0 )
| ~ ssItem(X6) )
& ( sK0 = X2 )
& ( X1 = X3 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( ( nil = X2 )
& ( nil = X3 ) )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| ( X4 = X5 )
| ~ ssItem(X5) )
& memberP(X3,X4)
& ( cons(X4,nil) = X2 )
& ssItem(X4) ) )
& ( ( nil != sK0 )
| ( nil != sK1 ) )
& ! [X6] :
( ~ memberP(sK1,X6)
| ? [X7] :
( ( X6 != X7 )
& leq(X6,X7)
& memberP(sK1,X7)
& ssItem(X7) )
| ( cons(X6,nil) != sK0 )
| ~ ssItem(X6) )
& ( sK0 = X2 )
& ( sK1 = X3 )
& ssList(X3) )
& ssList(X2) )
& ssList(sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f139,plain,
( ? [X2] :
( ? [X3] :
( ( ( ( nil = X2 )
& ( nil = X3 ) )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| ( X4 = X5 )
| ~ ssItem(X5) )
& memberP(X3,X4)
& ( cons(X4,nil) = X2 )
& ssItem(X4) ) )
& ( ( nil != sK0 )
| ( nil != sK1 ) )
& ! [X6] :
( ~ memberP(sK1,X6)
| ? [X7] :
( ( X6 != X7 )
& leq(X6,X7)
& memberP(sK1,X7)
& ssItem(X7) )
| ( cons(X6,nil) != sK0 )
| ~ ssItem(X6) )
& ( sK0 = X2 )
& ( sK1 = X3 )
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ( nil = sK2 )
& ( nil = X3 ) )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| ( X4 = X5 )
| ~ ssItem(X5) )
& memberP(X3,X4)
& ( cons(X4,nil) = sK2 )
& ssItem(X4) ) )
& ( ( nil != sK0 )
| ( nil != sK1 ) )
& ! [X6] :
( ~ memberP(sK1,X6)
| ? [X7] :
( ( X6 != X7 )
& leq(X6,X7)
& memberP(sK1,X7)
& ssItem(X7) )
| ( cons(X6,nil) != sK0 )
| ~ ssItem(X6) )
& ( sK0 = sK2 )
& ( sK1 = X3 )
& ssList(X3) )
& ssList(sK2) ) ),
introduced(choice_axiom,[]) ).
tff(f140,plain,
( ? [X3] :
( ( ( ( nil = sK2 )
& ( nil = X3 ) )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| ( X4 = X5 )
| ~ ssItem(X5) )
& memberP(X3,X4)
& ( cons(X4,nil) = sK2 )
& ssItem(X4) ) )
& ( ( nil != sK0 )
| ( nil != sK1 ) )
& ! [X6] :
( ~ memberP(sK1,X6)
| ? [X7] :
( ( X6 != X7 )
& leq(X6,X7)
& memberP(sK1,X7)
& ssItem(X7) )
| ( cons(X6,nil) != sK0 )
| ~ ssItem(X6) )
& ( sK0 = sK2 )
& ( sK1 = X3 )
& ssList(X3) )
=> ( ( ( ( nil = sK2 )
& ( nil = sK3 ) )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(sK3,X5)
| ( X4 = X5 )
| ~ ssItem(X5) )
& memberP(sK3,X4)
& ( cons(X4,nil) = sK2 )
& ssItem(X4) ) )
& ( ( nil != sK0 )
| ( nil != sK1 ) )
& ! [X6] :
( ~ memberP(sK1,X6)
| ? [X7] :
( ( X6 != X7 )
& leq(X6,X7)
& memberP(sK1,X7)
& ssItem(X7) )
| ( cons(X6,nil) != sK0 )
| ~ ssItem(X6) )
& ( sK0 = sK2 )
& ( sK1 = sK3 )
& ssList(sK3) ) ),
introduced(choice_axiom,[]) ).
tff(f141,plain,
( ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(sK3,X5)
| ( X4 = X5 )
| ~ ssItem(X5) )
& memberP(sK3,X4)
& ( cons(X4,nil) = sK2 )
& ssItem(X4) )
=> ( ! [X5] :
( ~ leq(sK4,X5)
| ~ memberP(sK3,X5)
| ( sK4 = X5 )
| ~ ssItem(X5) )
& memberP(sK3,sK4)
& ( sK2 = cons(sK4,nil) )
& ssItem(sK4) ) ),
introduced(choice_axiom,[]) ).
tff(f142,plain,
! [X6] :
( ? [X7] :
( ( X6 != X7 )
& leq(X6,X7)
& memberP(sK1,X7)
& ssItem(X7) )
=> ( ( sK5(X6) != X6 )
& leq(X6,sK5(X6))
& memberP(sK1,sK5(X6))
& ssItem(sK5(X6)) ) ),
introduced(choice_axiom,[]) ).
tff(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ( nil = X2 )
& ( nil = X3 ) )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| ( X4 = X5 )
| ~ ssItem(X5) )
& memberP(X3,X4)
& ( cons(X4,nil) = X2 )
& ssItem(X4) ) )
& ( ( nil != X0 )
| ( nil != X1 ) )
& ! [X6] :
( ~ memberP(X1,X6)
| ? [X7] :
( ( X6 != X7 )
& leq(X6,X7)
& memberP(X1,X7)
& ssItem(X7) )
| ( cons(X6,nil) != X0 )
| ~ ssItem(X6) )
& ( X0 = X2 )
& ( X1 = X3 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
tff(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ( nil = X2 )
& ( nil = X3 ) )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| ( X4 = X5 )
| ~ ssItem(X5) )
& memberP(X3,X4)
& ( cons(X4,nil) = X2 )
& ssItem(X4) ) )
& ( ( nil != X0 )
| ( nil != X1 ) )
& ! [X6] :
( ~ memberP(X1,X6)
| ? [X7] :
( ( X6 != X7 )
& leq(X6,X7)
& memberP(X1,X7)
& ssItem(X7) )
| ( cons(X6,nil) != X0 )
| ~ ssItem(X6) )
& ( X0 = X2 )
& ( X1 = X3 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
tff(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ( nil != X2 )
| ( nil != X3 ) )
& ! [X4] :
( ssItem(X4)
=> ( ? [X5] :
( leq(X4,X5)
& memberP(X3,X5)
& ( X4 != X5 )
& ssItem(X5) )
| ~ memberP(X3,X4)
| ( cons(X4,nil) != X2 ) ) ) )
| ( ( nil = X0 )
& ( nil = X1 ) )
| ? [X6] :
( memberP(X1,X6)
& ! [X7] :
( ssItem(X7)
=> ( ( X6 = X7 )
| ~ leq(X6,X7)
| ~ memberP(X1,X7) ) )
& ( cons(X6,nil) = X0 )
& ssItem(X6) )
| ( X0 != X2 )
| ( X1 != X3 ) ) ) ) ) ),
inference(rectify,[],[f97]) ).
tff(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ( nil != X2 )
| ( nil != X3 ) )
& ! [X6] :
( ssItem(X6)
=> ( ? [X7] :
( leq(X6,X7)
& memberP(X3,X7)
& ( X6 != X7 )
& ssItem(X7) )
| ~ memberP(X3,X6)
| ( cons(X6,nil) != X2 ) ) ) )
| ( ( nil = X0 )
& ( nil = X1 ) )
| ? [X4] :
( memberP(X1,X4)
& ! [X5] :
( ssItem(X5)
=> ( ( X4 = X5 )
| ~ leq(X4,X5)
| ~ memberP(X1,X5) ) )
& ( cons(X4,nil) = X0 )
& ssItem(X4) )
| ( X0 != X2 )
| ( X1 != X3 ) ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
tff(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ( nil != X2 )
| ( nil != X3 ) )
& ! [X6] :
( ssItem(X6)
=> ( ? [X7] :
( leq(X6,X7)
& memberP(X3,X7)
& ( X6 != X7 )
& ssItem(X7) )
| ~ memberP(X3,X6)
| ( cons(X6,nil) != X2 ) ) ) )
| ( ( nil = X0 )
& ( nil = X1 ) )
| ? [X4] :
( memberP(X1,X4)
& ! [X5] :
( ssItem(X5)
=> ( ( X4 = X5 )
| ~ leq(X4,X5)
| ~ memberP(X1,X5) ) )
& ( cons(X4,nil) = X0 )
& ssItem(X4) )
| ( X0 != X2 )
| ( X1 != X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f178,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f143]) ).
tff(f182,plain,
! [X6: $i] :
( ~ memberP(sK1,X6)
| leq(X6,sK5(X6))
| ( cons(X6,nil) != sK0 )
| ~ ssItem(X6) ),
inference(cnf_transformation,[],[f143]) ).
tff(f308,plain,
! [X0: $tType,X2: X0,X1: X0] :
( sQ17_eqProxy(X0,X2,X1)
| ~ sQ17_eqProxy(X0,X1,X2) ),
inference(equality_proxy_axiom,[],[f265]) ).
tff(f401,plain,
( ~ leq(sK4,sK5(sK4))
| spl18_13 ),
inference(avatar_component_clause,[],[f399]) ).
tff(f399,plain,
( spl18_13
<=> leq(sK4,sK5(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_13])]) ).
tff(f428,plain,
( ~ spl18_3
| ~ spl18_4
| ~ spl18_5
| spl18_14 ),
inference(avatar_contradiction_clause,[],[f427]) ).
tff(f427,plain,
( $false
| ~ spl18_3
| ~ spl18_4
| ~ spl18_5
| spl18_14 ),
inference(subsumption_resolution,[],[f426,f333]) ).
tff(f426,plain,
( ~ ssItem(sK4)
| ~ spl18_3
| ~ spl18_4
| spl18_14 ),
inference(subsumption_resolution,[],[f425,f323]) ).
tff(f425,plain,
( ~ memberP(sK3,sK4)
| ~ ssItem(sK4)
| ~ spl18_4
| spl18_14 ),
inference(subsumption_resolution,[],[f424,f328]) ).
tff(f424,plain,
( ~ sQ17_eqProxy($i,sK2,cons(sK4,nil))
| ~ memberP(sK3,sK4)
| ~ ssItem(sK4)
| spl18_14 ),
inference(resolution,[],[f405,f377]) ).
tff(f377,plain,
! [X0: $i] :
( ssItem(sK5(X0))
| ~ sQ17_eqProxy($i,sK2,cons(X0,nil))
| ~ memberP(sK3,X0)
| ~ ssItem(X0) ),
inference(resolution,[],[f308,f278]) ).
tff(f278,plain,
! [X6: $i] :
( ~ sQ17_eqProxy($i,cons(X6,nil),sK2)
| ssItem(sK5(X6))
| ~ memberP(sK3,X6)
| ~ ssItem(X6) ),
inference(equality_proxy_replacement,[],[f254,f265]) ).
tff(f254,plain,
! [X6: $i] :
( ~ memberP(sK3,X6)
| ssItem(sK5(X6))
| ( cons(X6,nil) != sK2 )
| ~ ssItem(X6) ),
inference(definition_unfolding,[],[f180,f178,f179]) ).
tff(f180,plain,
! [X6: $i] :
( ~ memberP(sK1,X6)
| ssItem(sK5(X6))
| ( cons(X6,nil) != sK0 )
| ~ ssItem(X6) ),
inference(cnf_transformation,[],[f143]) ).
tff(f405,plain,
( ~ ssItem(sK5(sK4))
| spl18_14 ),
inference(avatar_component_clause,[],[f403]) ).
tff(f403,plain,
( spl18_14
<=> ssItem(sK5(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_14])]) ).
tff(f423,plain,
( ~ spl18_3
| ~ spl18_4
| ~ spl18_5
| spl18_12 ),
inference(avatar_contradiction_clause,[],[f422]) ).
tff(f422,plain,
( $false
| ~ spl18_3
| ~ spl18_4
| ~ spl18_5
| spl18_12 ),
inference(subsumption_resolution,[],[f421,f333]) ).
tff(f421,plain,
( ~ ssItem(sK4)
| ~ spl18_3
| ~ spl18_4
| spl18_12 ),
inference(subsumption_resolution,[],[f420,f323]) ).
tff(f420,plain,
( ~ memberP(sK3,sK4)
| ~ ssItem(sK4)
| ~ spl18_4
| spl18_12 ),
inference(subsumption_resolution,[],[f419,f328]) ).
tff(f419,plain,
( ~ sQ17_eqProxy($i,sK2,cons(sK4,nil))
| ~ memberP(sK3,sK4)
| ~ ssItem(sK4)
| spl18_12 ),
inference(resolution,[],[f397,f375]) ).
tff(f375,plain,
! [X0: $i] :
( memberP(sK3,sK5(X0))
| ~ sQ17_eqProxy($i,sK2,cons(X0,nil))
| ~ memberP(sK3,X0)
| ~ ssItem(X0) ),
inference(resolution,[],[f308,f277]) ).
tff(f277,plain,
! [X6: $i] :
( ~ sQ17_eqProxy($i,cons(X6,nil),sK2)
| memberP(sK3,sK5(X6))
| ~ memberP(sK3,X6)
| ~ ssItem(X6) ),
inference(equality_proxy_replacement,[],[f253,f265]) ).
tff(f253,plain,
! [X6: $i] :
( ~ memberP(sK3,X6)
| memberP(sK3,sK5(X6))
| ( cons(X6,nil) != sK2 )
| ~ ssItem(X6) ),
inference(definition_unfolding,[],[f181,f178,f178,f179]) ).
tff(f181,plain,
! [X6: $i] :
( ~ memberP(sK1,X6)
| memberP(sK1,sK5(X6))
| ( cons(X6,nil) != sK0 )
| ~ ssItem(X6) ),
inference(cnf_transformation,[],[f143]) ).
tff(f397,plain,
( ~ memberP(sK3,sK5(sK4))
| spl18_12 ),
inference(avatar_component_clause,[],[f395]) ).
tff(f395,plain,
( spl18_12
<=> memberP(sK3,sK5(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_12])]) ).
tff(f406,plain,
( ~ spl18_12
| ~ spl18_13
| ~ spl18_14
| ~ spl18_1
| ~ spl18_3
| ~ spl18_4
| ~ spl18_5 ),
inference(avatar_split_clause,[],[f392,f331,f326,f321,f313,f403,f399,f395]) ).
tff(f313,plain,
( spl18_1
<=> ! [X5] :
( ~ leq(sK4,X5)
| ~ ssItem(X5)
| sQ17_eqProxy($i,sK4,X5)
| ~ memberP(sK3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).
tff(f392,plain,
( ~ ssItem(sK5(sK4))
| ~ leq(sK4,sK5(sK4))
| ~ memberP(sK3,sK5(sK4))
| ~ spl18_1
| ~ spl18_3
| ~ spl18_4
| ~ spl18_5 ),
inference(resolution,[],[f387,f314]) ).
tff(f314,plain,
( ! [X5: $i] :
( sQ17_eqProxy($i,sK4,X5)
| ~ ssItem(X5)
| ~ leq(sK4,X5)
| ~ memberP(sK3,X5) )
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f313]) ).
tff(f387,plain,
( ~ sQ17_eqProxy($i,sK4,sK5(sK4))
| ~ spl18_3
| ~ spl18_4
| ~ spl18_5 ),
inference(subsumption_resolution,[],[f386,f333]) ).
tff(f386,plain,
( ~ sQ17_eqProxy($i,sK4,sK5(sK4))
| ~ ssItem(sK4)
| ~ spl18_3
| ~ spl18_4 ),
inference(subsumption_resolution,[],[f384,f323]) ).
tff(f384,plain,
( ~ sQ17_eqProxy($i,sK4,sK5(sK4))
| ~ memberP(sK3,sK4)
| ~ ssItem(sK4)
| ~ spl18_4 ),
inference(resolution,[],[f380,f328]) ).
tff(f380,plain,
! [X0: $i] :
( ~ sQ17_eqProxy($i,sK2,cons(X0,nil))
| ~ sQ17_eqProxy($i,X0,sK5(X0))
| ~ memberP(sK3,X0)
| ~ ssItem(X0) ),
inference(forward_literal_rewriting,[],[f374,f308]) ).
tff(f374,plain,
! [X0: $i] :
( ~ sQ17_eqProxy($i,sK2,cons(X0,nil))
| ~ sQ17_eqProxy($i,sK5(X0),X0)
| ~ memberP(sK3,X0)
| ~ ssItem(X0) ),
inference(resolution,[],[f308,f275]) ).
tff(f275,plain,
! [X6: $i] :
( ~ sQ17_eqProxy($i,cons(X6,nil),sK2)
| ~ sQ17_eqProxy($i,sK5(X6),X6)
| ~ memberP(sK3,X6)
| ~ ssItem(X6) ),
inference(equality_proxy_replacement,[],[f251,f265]) ).
tff(f251,plain,
! [X6: $i] :
( ~ memberP(sK3,X6)
| ( sK5(X6) != X6 )
| ( cons(X6,nil) != sK2 )
| ~ ssItem(X6) ),
inference(definition_unfolding,[],[f183,f178,f179]) ).
tff(f183,plain,
! [X6: $i] :
( ~ memberP(sK1,X6)
| ( sK5(X6) != X6 )
| ( cons(X6,nil) != sK0 )
| ~ ssItem(X6) ),
inference(cnf_transformation,[],[f143]) ).
tff(f343,plain,
( ~ spl18_6
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f274,f316,f336]) ).
tff(f336,plain,
( spl18_6
<=> sQ17_eqProxy($i,nil,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_6])]) ).
tff(f316,plain,
( spl18_2
<=> sQ17_eqProxy($i,nil,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).
tff(f274,plain,
( ~ sQ17_eqProxy($i,nil,sK2)
| ~ sQ17_eqProxy($i,nil,sK3) ),
inference(equality_proxy_replacement,[],[f250,f265]) ).
tff(f250,plain,
( ( nil != sK2 )
| ( nil != sK3 ) ),
inference(definition_unfolding,[],[f184,f179,f178]) ).
tff(f184,plain,
( ( nil != sK0 )
| ( nil != sK1 ) ),
inference(cnf_transformation,[],[f143]) ).
tff(f342,plain,
( spl18_5
| spl18_6 ),
inference(avatar_split_clause,[],[f273,f336,f331]) ).
tff(f273,plain,
( sQ17_eqProxy($i,nil,sK3)
| ssItem(sK4) ),
inference(equality_proxy_replacement,[],[f185,f265]) ).
tff(f185,plain,
( ( nil = sK3 )
| ssItem(sK4) ),
inference(cnf_transformation,[],[f143]) ).
tff(f341,plain,
( spl18_4
| spl18_6 ),
inference(avatar_split_clause,[],[f272,f336,f326]) ).
tff(f272,plain,
( sQ17_eqProxy($i,nil,sK3)
| sQ17_eqProxy($i,sK2,cons(sK4,nil)) ),
inference(equality_proxy_replacement,[],[f186,f265]) ).
tff(f186,plain,
( ( nil = sK3 )
| ( sK2 = cons(sK4,nil) ) ),
inference(cnf_transformation,[],[f143]) ).
tff(f340,plain,
( spl18_3
| spl18_6 ),
inference(avatar_split_clause,[],[f271,f336,f321]) ).
tff(f271,plain,
( sQ17_eqProxy($i,nil,sK3)
| memberP(sK3,sK4) ),
inference(equality_proxy_replacement,[],[f187,f265]) ).
tff(f187,plain,
( ( nil = sK3 )
| memberP(sK3,sK4) ),
inference(cnf_transformation,[],[f143]) ).
tff(f339,plain,
( spl18_1
| spl18_6 ),
inference(avatar_split_clause,[],[f270,f336,f313]) ).
tff(f270,plain,
! [X5: $i] :
( sQ17_eqProxy($i,nil,sK3)
| ~ leq(sK4,X5)
| ~ memberP(sK3,X5)
| sQ17_eqProxy($i,sK4,X5)
| ~ ssItem(X5) ),
inference(equality_proxy_replacement,[],[f188,f265]) ).
tff(f188,plain,
! [X5: $i] :
( ( nil = sK3 )
| ~ leq(sK4,X5)
| ~ memberP(sK3,X5)
| ( sK4 = X5 )
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f143]) ).
tff(f334,plain,
( spl18_5
| spl18_2 ),
inference(avatar_split_clause,[],[f269,f316,f331]) ).
tff(f269,plain,
( sQ17_eqProxy($i,nil,sK2)
| ssItem(sK4) ),
inference(equality_proxy_replacement,[],[f189,f265]) ).
tff(f189,plain,
( ( nil = sK2 )
| ssItem(sK4) ),
inference(cnf_transformation,[],[f143]) ).
tff(f329,plain,
( spl18_4
| spl18_2 ),
inference(avatar_split_clause,[],[f268,f316,f326]) ).
tff(f268,plain,
( sQ17_eqProxy($i,nil,sK2)
| sQ17_eqProxy($i,sK2,cons(sK4,nil)) ),
inference(equality_proxy_replacement,[],[f190,f265]) ).
tff(f190,plain,
( ( nil = sK2 )
| ( sK2 = cons(sK4,nil) ) ),
inference(cnf_transformation,[],[f143]) ).
tff(f324,plain,
( spl18_3
| spl18_2 ),
inference(avatar_split_clause,[],[f267,f316,f321]) ).
tff(f267,plain,
( sQ17_eqProxy($i,nil,sK2)
| memberP(sK3,sK4) ),
inference(equality_proxy_replacement,[],[f191,f265]) ).
tff(f191,plain,
( ( nil = sK2 )
| memberP(sK3,sK4) ),
inference(cnf_transformation,[],[f143]) ).
tff(f319,plain,
( spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f266,f316,f313]) ).
tff(f266,plain,
! [X5: $i] :
( sQ17_eqProxy($i,nil,sK2)
| ~ leq(sK4,X5)
| ~ memberP(sK3,X5)
| sQ17_eqProxy($i,sK4,X5)
| ~ ssItem(X5) ),
inference(equality_proxy_replacement,[],[f192,f265]) ).
tff(f192,plain,
! [X5: $i] :
( ( nil = sK2 )
| ~ leq(sK4,X5)
| ~ memberP(sK3,X5)
| ( sK4 = X5 )
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SWC098+1 : TPTP v8.2.0. Released v2.4.0.
% 0.05/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.34 % Computer : n021.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8042.1875MB
% 0.10/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Sun May 19 03:20:38 EDT 2024
% 0.10/0.34 % CPUTime :
% 0.10/0.34 This is a FOF_THM_RFO_SEQ problem
% 0.10/0.34 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.49/0.71 % (18804)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2996ds/34Mi)
% 0.49/0.71 % (18806)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2996ds/78Mi)
% 0.49/0.71 % (18807)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2996ds/33Mi)
% 0.49/0.71 % (18809)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2996ds/45Mi)
% 0.49/0.71 % (18808)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on theBenchmark for (2996ds/34Mi)
% 0.49/0.71 % (18810)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on theBenchmark for (2996ds/83Mi)
% 0.49/0.71 % (18811)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2996ds/56Mi)
% 0.49/0.71 % (18804)First to succeed.
% 0.49/0.71 % (18806)Also succeeded, but the first one will report.
% 0.49/0.71 % (18805)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on theBenchmark for (2996ds/51Mi)
% 0.49/0.72 % (18804)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-18803"
% 0.49/0.72 % (18804)Refutation found. Thanks to Tanya!
% 0.49/0.72 % SZS status Theorem for theBenchmark
% 0.49/0.72 % SZS output start Proof for theBenchmark
% See solution above
% 0.49/0.72 % (18804)------------------------------
% 0.49/0.72 % (18804)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.49/0.72 % (18804)Termination reason: Refutation
% 0.49/0.72
% 0.49/0.72 % (18804)Memory used [KB]: 1228
% 0.49/0.72 % (18804)Time elapsed: 0.005 s
% 0.49/0.72 % (18804)Instructions burned: 14 (million)
% 0.49/0.72 % (18803)Success in time 0.376 s
% 0.49/0.72 % Vampire---4.8 exiting
%------------------------------------------------------------------------------