TSTP Solution File: SWC210+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWC210+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_sat --cores 0 -t %d %s

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 31 18:42:25 EDT 2022

% Result   : Theorem 1.37s 0.54s
% Output   : Refutation 1.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   43 (  16 unt;   3 typ;   0 def)
%            Number of atoms       :  190 (  37 equ)
%            Maximal formula atoms :   22 (   4 avg)
%            Number of connectives :  211 (  61   ~;  44   |;  90   &)
%                                         (   2 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    4 (   0 usr;   3 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   42 (  18   !;  24   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_27,type,
    sQ58_eqProxy: ( $int * $int ) > $o ).

tff(pred_def_28,type,
    sQ59_eqProxy: ( $rat * $rat ) > $o ).

tff(pred_def_29,type,
    sQ60_eqProxy: ( $real * $real ) > $o ).

fof(f1199,plain,
    $false,
    inference(subsumption_resolution,[],[f1180,f733]) ).

fof(f733,plain,
    ~ singletonP(nil),
    inference(literal_reordering,[],[f405]) ).

fof(f405,plain,
    ~ singletonP(nil),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,axiom,
    ~ singletonP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).

fof(f1180,plain,
    singletonP(nil),
    inference(backward_demodulation,[],[f978,f1176]) ).

fof(f1176,plain,
    nil = sK53,
    inference(subsumption_resolution,[],[f1175,f783]) ).

fof(f783,plain,
    ssList(nil),
    inference(literal_reordering,[],[f413]) ).

fof(f413,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

fof(f1175,plain,
    ( nil = sK53
    | ~ ssList(nil) ),
    inference(subsumption_resolution,[],[f1170,f714]) ).

fof(f714,plain,
    ssList(sK53),
    inference(literal_reordering,[],[f547]) ).

fof(f547,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f347]) ).

fof(f347,plain,
    ( ssList(sK55)
    & sK55 = sK53
    & sK56 = sK54
    & ssList(sK56)
    & ( ( ~ neq(sK53,nil)
        & singletonP(sK55)
        & neq(sK54,nil) )
      | ( ~ neq(sK56,nil)
        & neq(sK54,nil) ) )
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56])],[f198,f346,f345,f344,f343]) ).

fof(f343,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( X0 = X2
                    & X1 = X3
                    & ssList(X3)
                    & ( ( ~ neq(X0,nil)
                        & singletonP(X2)
                        & neq(X1,nil) )
                      | ( ~ neq(X3,nil)
                        & neq(X1,nil) ) ) ) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( sK53 = X2
                  & X1 = X3
                  & ssList(X3)
                  & ( ( ~ neq(sK53,nil)
                      & singletonP(X2)
                      & neq(X1,nil) )
                    | ( ~ neq(X3,nil)
                      & neq(X1,nil) ) ) ) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( sK53 = X2
                & X1 = X3
                & ssList(X3)
                & ( ( ~ neq(sK53,nil)
                    & singletonP(X2)
                    & neq(X1,nil) )
                  | ( ~ neq(X3,nil)
                    & neq(X1,nil) ) ) ) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( sK53 = X2
              & sK54 = X3
              & ssList(X3)
              & ( ( ~ neq(sK53,nil)
                  & singletonP(X2)
                  & neq(sK54,nil) )
                | ( ~ neq(X3,nil)
                  & neq(sK54,nil) ) ) ) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( sK53 = X2
            & sK54 = X3
            & ssList(X3)
            & ( ( ~ neq(sK53,nil)
                & singletonP(X2)
                & neq(sK54,nil) )
              | ( ~ neq(X3,nil)
                & neq(sK54,nil) ) ) ) )
   => ( ssList(sK55)
      & ? [X3] :
          ( sK55 = sK53
          & sK54 = X3
          & ssList(X3)
          & ( ( ~ neq(sK53,nil)
              & singletonP(sK55)
              & neq(sK54,nil) )
            | ( ~ neq(X3,nil)
              & neq(sK54,nil) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X3] :
        ( sK55 = sK53
        & sK54 = X3
        & ssList(X3)
        & ( ( ~ neq(sK53,nil)
            & singletonP(sK55)
            & neq(sK54,nil) )
          | ( ~ neq(X3,nil)
            & neq(sK54,nil) ) ) )
   => ( sK55 = sK53
      & sK56 = sK54
      & ssList(sK56)
      & ( ( ~ neq(sK53,nil)
          & singletonP(sK55)
          & neq(sK54,nil) )
        | ( ~ neq(sK56,nil)
          & neq(sK54,nil) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f198,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X0 = X2
                  & X1 = X3
                  & ssList(X3)
                  & ( ( ~ neq(X0,nil)
                      & singletonP(X2)
                      & neq(X1,nil) )
                    | ( ~ neq(X3,nil)
                      & neq(X1,nil) ) ) ) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f197]) ).

fof(f197,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X1 = X3
                  & ( ( ~ neq(X0,nil)
                      & singletonP(X2)
                      & neq(X1,nil) )
                    | ( ~ neq(X3,nil)
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & 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
                      | ( ( neq(X3,nil)
                          | ~ neq(X1,nil) )
                        & ( ~ neq(X1,nil)
                          | neq(X0,nil)
                          | ~ singletonP(X2) ) )
                      | X0 != X2 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( X1 != X3
                    | ( ( neq(X3,nil)
                        | ~ neq(X1,nil) )
                      & ( ~ neq(X1,nil)
                        | neq(X0,nil)
                        | ~ singletonP(X2) ) )
                    | X0 != X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f1170,plain,
    ( ~ ssList(sK53)
    | nil = sK53
    | ~ ssList(nil) ),
    inference(resolution,[],[f686,f979]) ).

fof(f979,plain,
    ~ neq(sK53,nil),
    inference(subsumption_resolution,[],[f708,f971]) ).

fof(f971,plain,
    neq(sK54,nil),
    inference(duplicate_literal_removal,[],[f671]) ).

fof(f671,plain,
    ( neq(sK54,nil)
    | neq(sK54,nil) ),
    inference(literal_reordering,[],[f549]) ).

fof(f549,plain,
    ( neq(sK54,nil)
    | neq(sK54,nil) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f708,plain,
    ( ~ neq(sK54,nil)
    | ~ neq(sK53,nil) ),
    inference(literal_reordering,[],[f561]) ).

fof(f561,plain,
    ( ~ neq(sK53,nil)
    | ~ neq(sK54,nil) ),
    inference(definition_unfolding,[],[f554,f556]) ).

fof(f556,plain,
    sK56 = sK54,
    inference(cnf_transformation,[],[f347]) ).

fof(f554,plain,
    ( ~ neq(sK53,nil)
    | ~ neq(sK56,nil) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f686,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(literal_reordering,[],[f412]) ).

fof(f412,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | ~ ssList(X0)
      | X0 = X1
      | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f269]) ).

fof(f269,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f173]) ).

fof(f173,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).

fof(f978,plain,
    singletonP(sK53),
    inference(subsumption_resolution,[],[f778,f971]) ).

fof(f778,plain,
    ( singletonP(sK53)
    | ~ neq(sK54,nil) ),
    inference(literal_reordering,[],[f562]) ).

fof(f562,plain,
    ( ~ neq(sK54,nil)
    | singletonP(sK53) ),
    inference(definition_unfolding,[],[f552,f557,f556]) ).

fof(f557,plain,
    sK55 = sK53,
    inference(cnf_transformation,[],[f347]) ).

fof(f552,plain,
    ( singletonP(sK55)
    | ~ neq(sK56,nil) ),
    inference(cnf_transformation,[],[f347]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SWC210+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34  % Computer : n013.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 18:31:02 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.50  % (8385)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.50  % (8377)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.50  % (8369)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51  % (8365)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.51  % (8366)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51  % (8370)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.51  % (8378)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.52  % (8368)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.37/0.52  % (8370)Instruction limit reached!
% 1.37/0.52  % (8370)------------------------------
% 1.37/0.52  % (8370)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.37/0.53  % (8390)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 1.37/0.53  % (8391)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.37/0.53  % (8370)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.37/0.53  % (8370)Termination reason: Unknown
% 1.37/0.53  % (8388)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.37/0.53  % (8370)Termination phase: shuffling
% 1.37/0.53  
% 1.37/0.53  % (8370)Memory used [KB]: 1279
% 1.37/0.53  % (8370)Time elapsed: 0.007 s
% 1.37/0.53  % (8370)Instructions burned: 8 (million)
% 1.37/0.53  % (8389)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.37/0.53  % (8370)------------------------------
% 1.37/0.53  % (8370)------------------------------
% 1.37/0.53  % (8386)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.37/0.53  % (8364)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.37/0.53  % (8363)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 1.37/0.53  % (8367)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.37/0.53  % (8392)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.37/0.54  % (8377)First to succeed.
% 1.37/0.54  % (8384)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.37/0.54  % (8377)Refutation found. Thanks to Tanya!
% 1.37/0.54  % SZS status Theorem for theBenchmark
% 1.37/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 1.37/0.54  % (8377)------------------------------
% 1.37/0.54  % (8377)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.37/0.54  % (8377)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.37/0.54  % (8377)Termination reason: Refutation
% 1.37/0.54  
% 1.37/0.54  % (8377)Memory used [KB]: 6524
% 1.37/0.54  % (8377)Time elapsed: 0.028 s
% 1.37/0.54  % (8377)Instructions burned: 28 (million)
% 1.37/0.54  % (8377)------------------------------
% 1.37/0.54  % (8377)------------------------------
% 1.37/0.54  % (8362)Success in time 0.19 s
%------------------------------------------------------------------------------