TSTP Solution File: SET766+4 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET766+4 : TPTP v8.1.0. Released v2.2.0.
% 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 : n020.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 18:25:35 EDT 2022

% Result   : Theorem 1.40s 0.53s
% Output   : Refutation 1.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   32 (   9 unt;   0 def)
%            Number of atoms       :  148 (   1 equ)
%            Maximal formula atoms :   13 (   4 avg)
%            Number of connectives :  171 (  55   ~;  45   |;  47   &)
%                                         (   4 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-3 aty)
%            Number of variables   :   98 (  86   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f188,plain,
    $false,
    inference(subsumption_resolution,[],[f187,f113]) ).

fof(f113,plain,
    ~ member(sK2,sF6),
    inference(definition_folding,[],[f84,f112]) ).

fof(f112,plain,
    equivalence_class(sK2,sK0,sK1) = sF6,
    introduced(function_definition,[]) ).

fof(f84,plain,
    ~ member(sK2,equivalence_class(sK2,sK0,sK1)),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ( equivalence(sK1,sK0)
    & ~ member(sK2,equivalence_class(sK2,sK0,sK1))
    & member(sK2,sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f50,f51]) ).

fof(f51,plain,
    ( ? [X0,X1,X2] :
        ( equivalence(X1,X0)
        & ~ member(X2,equivalence_class(X2,X0,X1))
        & member(X2,X0) )
   => ( equivalence(sK1,sK0)
      & ~ member(sK2,equivalence_class(sK2,sK0,sK1))
      & member(sK2,sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f50,plain,
    ? [X0,X1,X2] :
      ( equivalence(X1,X0)
      & ~ member(X2,equivalence_class(X2,X0,X1))
      & member(X2,X0) ),
    inference(rectify,[],[f40]) ).

fof(f40,plain,
    ? [X0,X2,X1] :
      ( equivalence(X2,X0)
      & ~ member(X1,equivalence_class(X1,X0,X2))
      & member(X1,X0) ),
    inference(flattening,[],[f39]) ).

fof(f39,plain,
    ? [X0,X2,X1] :
      ( ~ member(X1,equivalence_class(X1,X0,X2))
      & member(X1,X0)
      & equivalence(X2,X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,plain,
    ~ ! [X0,X2,X1] :
        ( ( member(X1,X0)
          & equivalence(X2,X0) )
       => member(X1,equivalence_class(X1,X0,X2)) ),
    inference(rectify,[],[f18]) ).

fof(f18,negated_conjecture,
    ~ ! [X3,X0,X6] :
        ( ( equivalence(X6,X3)
          & member(X0,X3) )
       => member(X0,equivalence_class(X0,X3,X6)) ),
    inference(negated_conjecture,[],[f17]) ).

fof(f17,conjecture,
    ! [X3,X0,X6] :
      ( ( equivalence(X6,X3)
        & member(X0,X3) )
     => member(X0,equivalence_class(X0,X3,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII02) ).

fof(f187,plain,
    member(sK2,sF6),
    inference(forward_demodulation,[],[f171,f112]) ).

fof(f171,plain,
    member(sK2,equivalence_class(sK2,sK0,sK1)),
    inference(resolution,[],[f154,f83]) ).

fof(f83,plain,
    member(sK2,sK0),
    inference(cnf_transformation,[],[f52]) ).

fof(f154,plain,
    ! [X0] :
      ( ~ member(sK2,X0)
      | member(sK2,equivalence_class(sK2,X0,sK1)) ),
    inference(resolution,[],[f107,f128]) ).

fof(f128,plain,
    apply(sK1,sK2,sK2),
    inference(resolution,[],[f120,f85]) ).

fof(f85,plain,
    equivalence(sK1,sK0),
    inference(cnf_transformation,[],[f52]) ).

fof(f120,plain,
    ! [X0] :
      ( ~ equivalence(X0,sK0)
      | apply(X0,sK2,sK2) ),
    inference(resolution,[],[f94,f83]) ).

fof(f94,plain,
    ! [X0,X1,X4] :
      ( ~ member(X4,X0)
      | ~ equivalence(X1,X0)
      | apply(X1,X4,X4) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ~ equivalence(X1,X0)
      | ( ! [X2,X3] :
            ( ~ member(X2,X0)
            | apply(X1,X3,X2)
            | ~ member(X3,X0)
            | ~ apply(X1,X2,X3) )
        & ! [X4] :
            ( apply(X1,X4,X4)
            | ~ member(X4,X0) )
        & ! [X5,X6,X7] :
            ( ~ apply(X1,X5,X7)
            | ~ apply(X1,X6,X5)
            | ~ member(X7,X0)
            | apply(X1,X6,X7)
            | ~ member(X5,X0)
            | ~ member(X6,X0) ) ) ),
    inference(rectify,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ equivalence(X1,X0)
      | ( ! [X7,X6] :
            ( ~ member(X7,X0)
            | apply(X1,X6,X7)
            | ~ member(X6,X0)
            | ~ apply(X1,X7,X6) )
        & ! [X5] :
            ( apply(X1,X5,X5)
            | ~ member(X5,X0) )
        & ! [X2,X3,X4] :
            ( ~ apply(X1,X2,X4)
            | ~ apply(X1,X3,X2)
            | ~ member(X4,X0)
            | apply(X1,X3,X4)
            | ~ member(X2,X0)
            | ~ member(X3,X0) ) ) ),
    inference(flattening,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ( ! [X4,X2,X3] :
            ( apply(X1,X3,X4)
            | ~ apply(X1,X2,X4)
            | ~ apply(X1,X3,X2)
            | ~ member(X3,X0)
            | ~ member(X2,X0)
            | ~ member(X4,X0) )
        & ! [X5] :
            ( apply(X1,X5,X5)
            | ~ member(X5,X0) )
        & ! [X7,X6] :
            ( apply(X1,X6,X7)
            | ~ apply(X1,X7,X6)
            | ~ member(X7,X0)
            | ~ member(X6,X0) ) )
      | ~ equivalence(X1,X0) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
     => ( ! [X4,X2,X3] :
            ( ( member(X3,X0)
              & member(X2,X0)
              & member(X4,X0) )
           => ( ( apply(X1,X2,X4)
                & apply(X1,X3,X2) )
             => apply(X1,X3,X4) ) )
        & ! [X5] :
            ( member(X5,X0)
           => apply(X1,X5,X5) )
        & ! [X7,X6] :
            ( ( member(X7,X0)
              & member(X6,X0) )
           => ( apply(X1,X7,X6)
             => apply(X1,X6,X7) ) ) ) ),
    inference(unused_predicate_definition_removal,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
    <=> ( ! [X4,X2,X3] :
            ( ( member(X3,X0)
              & member(X2,X0)
              & member(X4,X0) )
           => ( ( apply(X1,X2,X4)
                & apply(X1,X3,X2) )
             => apply(X1,X3,X4) ) )
        & ! [X5] :
            ( member(X5,X0)
           => apply(X1,X5,X5) )
        & ! [X7,X6] :
            ( ( member(X7,X0)
              & member(X6,X0) )
           => ( apply(X1,X7,X6)
             => apply(X1,X6,X7) ) ) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X0,X6] :
      ( ( ! [X4,X2,X5] :
            ( ( member(X5,X0)
              & member(X2,X0)
              & member(X4,X0) )
           => ( ( apply(X6,X2,X4)
                & apply(X6,X4,X5) )
             => apply(X6,X2,X5) ) )
        & ! [X2] :
            ( member(X2,X0)
           => apply(X6,X2,X2) )
        & ! [X4,X2] :
            ( ( member(X2,X0)
              & member(X4,X0) )
           => ( apply(X6,X2,X4)
             => apply(X6,X4,X2) ) ) )
    <=> equivalence(X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence) ).

fof(f107,plain,
    ! [X2,X3,X0,X1] :
      ( ~ apply(X0,X1,X3)
      | ~ member(X3,X2)
      | member(X3,equivalence_class(X1,X2,X0)) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1,X2,X3] :
      ( ( member(X3,equivalence_class(X1,X2,X0))
        | ~ apply(X0,X1,X3)
        | ~ member(X3,X2) )
      & ( ( apply(X0,X1,X3)
          & member(X3,X2) )
        | ~ member(X3,equivalence_class(X1,X2,X0)) ) ),
    inference(rectify,[],[f72]) ).

fof(f72,plain,
    ! [X3,X1,X0,X2] :
      ( ( member(X2,equivalence_class(X1,X0,X3))
        | ~ apply(X3,X1,X2)
        | ~ member(X2,X0) )
      & ( ( apply(X3,X1,X2)
          & member(X2,X0) )
        | ~ member(X2,equivalence_class(X1,X0,X3)) ) ),
    inference(flattening,[],[f71]) ).

fof(f71,plain,
    ! [X3,X1,X0,X2] :
      ( ( member(X2,equivalence_class(X1,X0,X3))
        | ~ apply(X3,X1,X2)
        | ~ member(X2,X0) )
      & ( ( apply(X3,X1,X2)
          & member(X2,X0) )
        | ~ member(X2,equivalence_class(X1,X0,X3)) ) ),
    inference(nnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X3,X1,X0,X2] :
      ( member(X2,equivalence_class(X1,X0,X3))
    <=> ( apply(X3,X1,X2)
        & member(X2,X0) ) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X3,X0,X2,X6] :
      ( member(X2,equivalence_class(X0,X3,X6))
    <=> ( member(X2,X3)
        & apply(X6,X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_class) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET766+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n020.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 14:21:30 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.21/0.51  % (16022)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.28/0.51  % (16019)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.28/0.51  % (16039)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.28/0.51  % (16012)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)
% 1.28/0.52  % (16033)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)
% 1.28/0.52  % (16025)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)
% 1.28/0.52  % (16015)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.28/0.52  % (16019)Instruction limit reached!
% 1.28/0.52  % (16019)------------------------------
% 1.28/0.52  % (16019)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.28/0.52  % (16019)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.28/0.52  % (16019)Termination reason: Unknown
% 1.28/0.52  % (16019)Termination phase: Property scanning
% 1.28/0.52  
% 1.28/0.52  % (16019)Memory used [KB]: 895
% 1.28/0.52  % (16019)Time elapsed: 0.003 s
% 1.28/0.52  % (16019)Instructions burned: 2 (million)
% 1.28/0.52  % (16019)------------------------------
% 1.28/0.52  % (16019)------------------------------
% 1.28/0.52  % (16013)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)
% 1.28/0.53  % (16012)Refutation not found, incomplete strategy% (16012)------------------------------
% 1.28/0.53  % (16012)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.28/0.53  % (16040)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)
% 1.28/0.53  % (16012)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.28/0.53  % (16012)Termination reason: Refutation not found, incomplete strategy
% 1.28/0.53  
% 1.28/0.53  % (16012)Memory used [KB]: 5500
% 1.28/0.53  % (16012)Time elapsed: 0.128 s
% 1.28/0.53  % (16012)Instructions burned: 3 (million)
% 1.28/0.53  % (16012)------------------------------
% 1.28/0.53  % (16012)------------------------------
% 1.28/0.53  % (16016)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)
% 1.28/0.53  % (16014)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)
% 1.40/0.53  % (16011)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)
% 1.40/0.53  % (16024)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.40/0.53  % (16021)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.40/0.53  % (16031)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.40/0.53  % (16015)First to succeed.
% 1.40/0.53  TRYING [1]
% 1.40/0.53  TRYING [2]
% 1.40/0.53  % (16026)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)
% 1.40/0.53  % (16015)Refutation found. Thanks to Tanya!
% 1.40/0.53  % SZS status Theorem for theBenchmark
% 1.40/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 1.40/0.53  % (16015)------------------------------
% 1.40/0.53  % (16015)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.40/0.53  % (16015)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.40/0.53  % (16015)Termination reason: Refutation
% 1.40/0.53  
% 1.40/0.53  % (16015)Memory used [KB]: 5628
% 1.40/0.53  % (16015)Time elapsed: 0.136 s
% 1.40/0.53  % (16015)Instructions burned: 5 (million)
% 1.40/0.53  % (16015)------------------------------
% 1.40/0.53  % (16015)------------------------------
% 1.40/0.53  % (16010)Success in time 0.183 s
%------------------------------------------------------------------------------