TSTP Solution File: SWC096+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC096+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 31 18:38:47 EDT 2022

% Result   : Theorem 0.20s 0.54s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   41 (  11 unt;   0 def)
%            Number of atoms       :  231 (  72 equ)
%            Maximal formula atoms :   18 (   5 avg)
%            Number of connectives :  269 (  79   ~;  68   |; 108   &)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-4 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :  127 (  87   !;  40   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f411,plain,
    $false,
    inference(resolution,[],[f390,f234]) ).

fof(f234,plain,
    sP0(sK8,sK7,sK8,sK7),
    inference(subsumption_resolution,[],[f184,f195]) ).

fof(f195,plain,
    neq(sK8,nil),
    inference(subsumption_resolution,[],[f183,f160]) ).

fof(f160,plain,
    ! [X2,X3,X0,X1] :
      ( neq(X0,nil)
      | ~ sP0(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f130,plain,
    ! [X0,X1,X2,X3] :
      ( ( neq(X0,nil)
        & ! [X4] :
            ( ! [X5] :
                ( app(X5,cons(X4,nil)) != X0
                | cons(X4,nil) != X1
                | ~ ssList(X5) )
            | ~ ssItem(X4) )
        & ssItem(sK3(X2,X3))
        & ssList(sK4(X2,X3))
        & app(sK4(X2,X3),cons(sK3(X2,X3),nil)) = X2
        & cons(sK3(X2,X3),nil) = X3 )
      | ~ sP0(X0,X1,X2,X3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f127,f129,f128]) ).

fof(f128,plain,
    ! [X2,X3] :
      ( ? [X6] :
          ( ssItem(X6)
          & ? [X7] :
              ( ssList(X7)
              & app(X7,cons(X6,nil)) = X2
              & cons(X6,nil) = X3 ) )
     => ( ssItem(sK3(X2,X3))
        & ? [X7] :
            ( ssList(X7)
            & app(X7,cons(sK3(X2,X3),nil)) = X2
            & cons(sK3(X2,X3),nil) = X3 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f129,plain,
    ! [X2,X3] :
      ( ? [X7] :
          ( ssList(X7)
          & app(X7,cons(sK3(X2,X3),nil)) = X2
          & cons(sK3(X2,X3),nil) = X3 )
     => ( ssList(sK4(X2,X3))
        & app(sK4(X2,X3),cons(sK3(X2,X3),nil)) = X2
        & cons(sK3(X2,X3),nil) = X3 ) ),
    introduced(choice_axiom,[]) ).

fof(f127,plain,
    ! [X0,X1,X2,X3] :
      ( ( neq(X0,nil)
        & ! [X4] :
            ( ! [X5] :
                ( app(X5,cons(X4,nil)) != X0
                | cons(X4,nil) != X1
                | ~ ssList(X5) )
            | ~ ssItem(X4) )
        & ? [X6] :
            ( ssItem(X6)
            & ? [X7] :
                ( ssList(X7)
                & app(X7,cons(X6,nil)) = X2
                & cons(X6,nil) = X3 ) ) )
      | ~ sP0(X0,X1,X2,X3) ),
    inference(rectify,[],[f126]) ).

fof(f126,plain,
    ! [X1,X0,X3,X2] :
      ( ( neq(X1,nil)
        & ! [X4] :
            ( ! [X5] :
                ( app(X5,cons(X4,nil)) != X1
                | cons(X4,nil) != X0
                | ~ ssList(X5) )
            | ~ ssItem(X4) )
        & ? [X6] :
            ( ssItem(X6)
            & ? [X7] :
                ( ssList(X7)
                & app(X7,cons(X6,nil)) = X3
                & cons(X6,nil) = X2 ) ) )
      | ~ sP0(X1,X0,X3,X2) ),
    inference(nnf_transformation,[],[f119]) ).

fof(f119,plain,
    ! [X1,X0,X3,X2] :
      ( ( neq(X1,nil)
        & ! [X4] :
            ( ! [X5] :
                ( app(X5,cons(X4,nil)) != X1
                | cons(X4,nil) != X0
                | ~ ssList(X5) )
            | ~ ssItem(X4) )
        & ? [X6] :
            ( ssItem(X6)
            & ? [X7] :
                ( ssList(X7)
                & app(X7,cons(X6,nil)) = X3
                & cons(X6,nil) = X2 ) ) )
      | ~ sP0(X1,X0,X3,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f183,plain,
    ( neq(sK8,nil)
    | sP0(sK8,sK7,sK8,sK7) ),
    inference(definition_unfolding,[],[f164,f165,f166,f165]) ).

fof(f166,plain,
    sK5 = sK7,
    inference(cnf_transformation,[],[f135]) ).

fof(f135,plain,
    ( ssList(sK5)
    & ssList(sK8)
    & sK5 = sK7
    & sK6 = sK8
    & ( sP0(sK6,sK5,sK8,sK7)
      | ( neq(sK6,nil)
        & ~ neq(sK8,nil) ) )
    & ssList(sK7)
    & ssList(sK6) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f120,f134,f133,f132,f131]) ).

fof(f131,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ssList(X3)
                    & X0 = X2
                    & X1 = X3
                    & ( sP0(X1,X0,X3,X2)
                      | ( neq(X1,nil)
                        & ~ neq(X3,nil) ) ) )
                & ssList(X2) )
            & ssList(X1) ) )
   => ( ssList(sK5)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ssList(X3)
                  & sK5 = X2
                  & X1 = X3
                  & ( sP0(X1,sK5,X3,X2)
                    | ( neq(X1,nil)
                      & ~ neq(X3,nil) ) ) )
              & ssList(X2) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f132,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ssList(X3)
                & sK5 = X2
                & X1 = X3
                & ( sP0(X1,sK5,X3,X2)
                  | ( neq(X1,nil)
                    & ~ neq(X3,nil) ) ) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ssList(X3)
              & sK5 = X2
              & sK6 = X3
              & ( sP0(sK6,sK5,X3,X2)
                | ( neq(sK6,nil)
                  & ~ neq(X3,nil) ) ) )
          & ssList(X2) )
      & ssList(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f133,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ssList(X3)
            & sK5 = X2
            & sK6 = X3
            & ( sP0(sK6,sK5,X3,X2)
              | ( neq(sK6,nil)
                & ~ neq(X3,nil) ) ) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ssList(X3)
          & sK5 = sK7
          & sK6 = X3
          & ( sP0(sK6,sK5,X3,sK7)
            | ( neq(sK6,nil)
              & ~ neq(X3,nil) ) ) )
      & ssList(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f134,plain,
    ( ? [X3] :
        ( ssList(X3)
        & sK5 = sK7
        & sK6 = X3
        & ( sP0(sK6,sK5,X3,sK7)
          | ( neq(sK6,nil)
            & ~ neq(X3,nil) ) ) )
   => ( ssList(sK8)
      & sK5 = sK7
      & sK6 = sK8
      & ( sP0(sK6,sK5,sK8,sK7)
        | ( neq(sK6,nil)
          & ~ neq(sK8,nil) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f120,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ssList(X3)
                  & X0 = X2
                  & X1 = X3
                  & ( sP0(X1,X0,X3,X2)
                    | ( neq(X1,nil)
                      & ~ neq(X3,nil) ) ) )
              & ssList(X2) )
          & ssList(X1) ) ),
    inference(definition_folding,[],[f114,f119]) ).

fof(f114,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ssList(X3)
                  & X0 = X2
                  & X1 = X3
                  & ( ( neq(X1,nil)
                      & ! [X4] :
                          ( ! [X5] :
                              ( app(X5,cons(X4,nil)) != X1
                              | cons(X4,nil) != X0
                              | ~ ssList(X5) )
                          | ~ ssItem(X4) )
                      & ? [X6] :
                          ( ssItem(X6)
                          & ? [X7] :
                              ( ssList(X7)
                              & app(X7,cons(X6,nil)) = X3
                              & cons(X6,nil) = X2 ) ) )
                    | ( neq(X1,nil)
                      & ~ neq(X3,nil) ) ) )
              & ssList(X2) )
          & ssList(X1) ) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ( ( neq(X3,nil)
                        | ~ neq(X1,nil) )
                      & ( ~ neq(X1,nil)
                        | ? [X4] :
                            ( ? [X5] :
                                ( app(X5,cons(X4,nil)) = X1
                                & cons(X4,nil) = X0
                                & ssList(X5) )
                            & ssItem(X4) )
                        | ! [X6] :
                            ( ssItem(X6)
                           => ! [X7] :
                                ( cons(X6,nil) != X2
                                | app(X7,cons(X6,nil)) != X3
                                | ~ ssList(X7) ) ) ) )
                    | X0 != X2
                    | ~ ssList(X3)
                    | X1 != X3 ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ( ( neq(X3,nil)
                      | ~ neq(X1,nil) )
                    & ( ~ neq(X1,nil)
                      | ? [X4] :
                          ( ? [X5] :
                              ( app(X5,cons(X4,nil)) = X1
                              & cons(X4,nil) = X0
                              & ssList(X5) )
                          & ssItem(X4) )
                      | ! [X6] :
                          ( ssItem(X6)
                         => ! [X7] :
                              ( cons(X6,nil) != X2
                              | app(X7,cons(X6,nil)) != X3
                              | ~ ssList(X7) ) ) ) )
                  | X0 != X2
                  | ~ ssList(X3)
                  | X1 != X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f165,plain,
    sK6 = sK8,
    inference(cnf_transformation,[],[f135]) ).

fof(f164,plain,
    ( sP0(sK6,sK5,sK8,sK7)
    | neq(sK6,nil) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f184,plain,
    ( ~ neq(sK8,nil)
    | sP0(sK8,sK7,sK8,sK7) ),
    inference(definition_unfolding,[],[f163,f165,f166]) ).

fof(f163,plain,
    ( sP0(sK6,sK5,sK8,sK7)
    | ~ neq(sK8,nil) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f390,plain,
    ! [X2,X3] : ~ sP0(sK8,sK7,X2,X3),
    inference(subsumption_resolution,[],[f388,f236]) ).

fof(f236,plain,
    ssList(sK4(sK8,sK7)),
    inference(resolution,[],[f234,f157]) ).

fof(f157,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP0(X0,X1,X2,X3)
      | ssList(sK4(X2,X3)) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f388,plain,
    ! [X2,X3] :
      ( ~ sP0(sK8,sK7,X2,X3)
      | ~ ssList(sK4(sK8,sK7)) ),
    inference(superposition,[],[f291,f343]) ).

fof(f343,plain,
    app(sK4(sK8,sK7),sK7) = sK8,
    inference(forward_demodulation,[],[f237,f235]) ).

fof(f235,plain,
    cons(sK3(sK8,sK7),nil) = sK7,
    inference(resolution,[],[f234,f155]) ).

fof(f155,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP0(X0,X1,X2,X3)
      | cons(sK3(X2,X3),nil) = X3 ),
    inference(cnf_transformation,[],[f130]) ).

fof(f237,plain,
    sK8 = app(sK4(sK8,sK7),cons(sK3(sK8,sK7),nil)),
    inference(resolution,[],[f234,f156]) ).

fof(f156,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP0(X0,X1,X2,X3)
      | app(sK4(X2,X3),cons(sK3(X2,X3),nil)) = X2 ),
    inference(cnf_transformation,[],[f130]) ).

fof(f291,plain,
    ! [X2,X0,X1] :
      ( ~ sP0(app(X0,sK7),sK7,X1,X2)
      | ~ ssList(X0) ),
    inference(subsumption_resolution,[],[f278,f238]) ).

fof(f238,plain,
    ssItem(sK3(sK8,sK7)),
    inference(resolution,[],[f234,f158]) ).

fof(f158,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP0(X0,X1,X2,X3)
      | ssItem(sK3(X2,X3)) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f278,plain,
    ! [X2,X0,X1] :
      ( ~ sP0(app(X0,sK7),sK7,X1,X2)
      | ~ ssItem(sK3(sK8,sK7))
      | ~ ssList(X0) ),
    inference(superposition,[],[f189,f235]) ).

fof(f189,plain,
    ! [X2,X3,X4,X5] :
      ( ~ sP0(app(X5,cons(X4,nil)),cons(X4,nil),X2,X3)
      | ~ ssList(X5)
      | ~ ssItem(X4) ),
    inference(equality_resolution,[],[f188]) ).

fof(f188,plain,
    ! [X2,X3,X1,X4,X5] :
      ( cons(X4,nil) != X1
      | ~ ssList(X5)
      | ~ ssItem(X4)
      | ~ sP0(app(X5,cons(X4,nil)),X1,X2,X3) ),
    inference(equality_resolution,[],[f159]) ).

fof(f159,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( app(X5,cons(X4,nil)) != X0
      | cons(X4,nil) != X1
      | ~ ssList(X5)
      | ~ ssItem(X4)
      | ~ sP0(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f130]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SWC096+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13  % 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 : n017.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 17:38:35 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  % (30118)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)
% 0.20/0.52  % (30120)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)
% 0.20/0.52  % (30122)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.20/0.52  % (30118)First to succeed.
% 0.20/0.52  % (30144)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)
% 0.20/0.52  % (30127)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)
% 0.20/0.52  % (30113)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.53  % (30137)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)
% 0.20/0.53  % (30117)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)
% 0.20/0.53  % (30126)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)
% 0.20/0.53  % (30114)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)
% 0.20/0.54  % (30115)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)
% 0.20/0.54  % (30133)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)
% 0.20/0.54  % (30138)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)
% 0.20/0.54  % (30123)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.20/0.54  % (30116)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54  % (30124)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)
% 0.20/0.54  % (30133)Refutation not found, incomplete strategy% (30133)------------------------------
% 0.20/0.54  % (30133)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (30133)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (30133)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.54  
% 0.20/0.54  % (30133)Memory used [KB]: 6012
% 0.20/0.54  % (30133)Time elapsed: 0.136 s
% 0.20/0.54  % (30133)Instructions burned: 4 (million)
% 0.20/0.54  % (30133)------------------------------
% 0.20/0.54  % (30133)------------------------------
% 0.20/0.54  % (30118)Refutation found. Thanks to Tanya!
% 0.20/0.54  % SZS status Theorem for theBenchmark
% 0.20/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.54  % (30118)------------------------------
% 0.20/0.54  % (30118)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (30118)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (30118)Termination reason: Refutation
% 0.20/0.54  
% 0.20/0.54  % (30118)Memory used [KB]: 1663
% 0.20/0.54  % (30118)Time elapsed: 0.105 s
% 0.20/0.54  % (30118)Instructions burned: 12 (million)
% 0.20/0.54  % (30118)------------------------------
% 0.20/0.54  % (30118)------------------------------
% 0.20/0.54  % (30110)Success in time 0.185 s
%------------------------------------------------------------------------------