TSTP Solution File: SET578+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET578+3 : 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_uns --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 18:21:29 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   55 (  10 unt;   0 def)
%            Number of atoms       :  187 (  24 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  212 (  80   ~;  73   |;  44   &)
%                                         (   9 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  109 (  91   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f608,plain,
    $false,
    inference(subsumption_resolution,[],[f602,f356]) ).

fof(f356,plain,
    ~ subset(sK1,sF5),
    inference(subsumption_resolution,[],[f355,f56]) ).

fof(f56,plain,
    sF5 != sK1,
    inference(definition_folding,[],[f43,f55]) ).

fof(f55,plain,
    sF5 = intersection(sK3,sK2),
    introduced(function_definition,[]) ).

fof(f43,plain,
    sK1 != intersection(sK3,sK2),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ( sK1 != intersection(sK3,sK2)
    & ! [X3] :
        ( ( ( member(X3,sK3)
            & member(X3,sK2) )
          | ~ member(X3,sK1) )
        & ( member(X3,sK1)
          | ~ member(X3,sK3)
          | ~ member(X3,sK2) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f22,f23]) ).

fof(f23,plain,
    ( ? [X0,X1,X2] :
        ( intersection(X2,X1) != X0
        & ! [X3] :
            ( ( ( member(X3,X2)
                & member(X3,X1) )
              | ~ member(X3,X0) )
            & ( member(X3,X0)
              | ~ member(X3,X2)
              | ~ member(X3,X1) ) ) )
   => ( sK1 != intersection(sK3,sK2)
      & ! [X3] :
          ( ( ( member(X3,sK3)
              & member(X3,sK2) )
            | ~ member(X3,sK1) )
          & ( member(X3,sK1)
            | ~ member(X3,sK3)
            | ~ member(X3,sK2) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ? [X0,X1,X2] :
      ( intersection(X2,X1) != X0
      & ! [X3] :
          ( ( ( member(X3,X2)
              & member(X3,X1) )
            | ~ member(X3,X0) )
          & ( member(X3,X0)
            | ~ member(X3,X2)
            | ~ member(X3,X1) ) ) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ? [X1,X2,X0] :
      ( intersection(X0,X2) != X1
      & ! [X3] :
          ( ( ( member(X3,X0)
              & member(X3,X2) )
            | ~ member(X3,X1) )
          & ( member(X3,X1)
            | ~ member(X3,X0)
            | ~ member(X3,X2) ) ) ),
    inference(flattening,[],[f20]) ).

fof(f20,plain,
    ? [X1,X2,X0] :
      ( intersection(X0,X2) != X1
      & ! [X3] :
          ( ( ( member(X3,X0)
              & member(X3,X2) )
            | ~ member(X3,X1) )
          & ( member(X3,X1)
            | ~ member(X3,X0)
            | ~ member(X3,X2) ) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ? [X1,X2,X0] :
      ( intersection(X0,X2) != X1
      & ! [X3] :
          ( ( member(X3,X0)
            & member(X3,X2) )
        <=> member(X3,X1) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,plain,
    ~ ! [X1,X2,X0] :
        ( ! [X3] :
            ( ( member(X3,X0)
              & member(X3,X2) )
          <=> member(X3,X1) )
       => intersection(X0,X2) = X1 ),
    inference(rectify,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X1,X0,X2] :
        ( ! [X3] :
            ( member(X3,X0)
          <=> ( member(X3,X2)
              & member(X3,X1) ) )
       => intersection(X1,X2) = X0 ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X1,X0,X2] :
      ( ! [X3] :
          ( member(X3,X0)
        <=> ( member(X3,X2)
            & member(X3,X1) ) )
     => intersection(X1,X2) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th19) ).

fof(f355,plain,
    ( sF5 = sK1
    | ~ subset(sK1,sF5) ),
    inference(resolution,[],[f351,f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | X0 = X1
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( ( subset(X0,X1)
        & subset(X1,X0) )
    <=> X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).

fof(f351,plain,
    subset(sF5,sK1),
    inference(subsumption_resolution,[],[f345,f147]) ).

fof(f147,plain,
    ! [X6] :
      ( member(sK4(X6,sF5),sK2)
      | subset(sF5,X6) ),
    inference(superposition,[],[f69,f57]) ).

fof(f57,plain,
    sF5 = intersection(sK2,sK3),
    inference(backward_demodulation,[],[f55,f32]) ).

fof(f32,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).

fof(f69,plain,
    ! [X2,X3,X1] :
      ( member(sK4(X3,intersection(X1,X2)),X1)
      | subset(intersection(X1,X2),X3) ),
    inference(resolution,[],[f49,f45]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,intersection(X1,X0))
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,intersection(X1,X0))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X1,X0)) ) ),
    inference(rectify,[],[f26]) ).

fof(f26,plain,
    ! [X1,X0,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X0)
        | ~ member(X2,X1) )
      & ( ( member(X2,X0)
          & member(X2,X1) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(flattening,[],[f25]) ).

fof(f25,plain,
    ! [X1,X0,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X0)
        | ~ member(X2,X1) )
      & ( ( member(X2,X0)
          & member(X2,X1) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0,X2] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X0)
        & member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).

fof(f49,plain,
    ! [X0,X1] :
      ( member(sK4(X0,X1),X1)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ( member(sK4(X0,X1),X1)
          & ~ member(sK4(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f29,f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X1)
          & ~ member(X3,X0) )
     => ( member(sK4(X0,X1),X1)
        & ~ member(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X3] :
            ( member(X3,X1)
            & ~ member(X3,X0) ) ) ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X2] :
            ( member(X2,X0)
            & ~ member(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ member(X2,X0)
          | member(X2,X1) )
    <=> subset(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).

fof(f345,plain,
    ( subset(sF5,sK1)
    | ~ member(sK4(sK1,sF5),sK2) ),
    inference(duplicate_literal_removal,[],[f332]) ).

fof(f332,plain,
    ( subset(sF5,sK1)
    | ~ member(sK4(sK1,sF5),sK2)
    | subset(sF5,sK1) ),
    inference(resolution,[],[f82,f267]) ).

fof(f267,plain,
    ! [X6] :
      ( member(sK4(X6,sF5),sK3)
      | subset(sF5,X6) ),
    inference(superposition,[],[f70,f57]) ).

fof(f70,plain,
    ! [X6,X4,X5] :
      ( member(sK4(X6,intersection(X4,X5)),X5)
      | subset(intersection(X4,X5),X6) ),
    inference(resolution,[],[f49,f44]) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,intersection(X1,X0))
      | member(X2,X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f82,plain,
    ! [X2] :
      ( ~ member(sK4(sK1,X2),sK3)
      | subset(X2,sK1)
      | ~ member(sK4(sK1,X2),sK2) ),
    inference(resolution,[],[f40,f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ~ member(sK4(X0,X1),X0)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f40,plain,
    ! [X3] :
      ( member(X3,sK1)
      | ~ member(X3,sK2)
      | ~ member(X3,sK3) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f602,plain,
    subset(sK1,sF5),
    inference(duplicate_literal_removal,[],[f596]) ).

fof(f596,plain,
    ( subset(sK1,sF5)
    | subset(sK1,sF5) ),
    inference(resolution,[],[f516,f49]) ).

fof(f516,plain,
    ! [X7] :
      ( ~ member(sK4(sF5,X7),sK1)
      | subset(X7,sF5) ),
    inference(subsumption_resolution,[],[f504,f41]) ).

fof(f41,plain,
    ! [X3] :
      ( member(X3,sK2)
      | ~ member(X3,sK1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f504,plain,
    ! [X7] :
      ( ~ member(sK4(sF5,X7),sK2)
      | subset(X7,sF5)
      | ~ member(sK4(sF5,X7),sK1) ),
    inference(resolution,[],[f137,f42]) ).

fof(f42,plain,
    ! [X3] :
      ( member(X3,sK3)
      | ~ member(X3,sK1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f137,plain,
    ! [X2] :
      ( ~ member(sK4(sF5,X2),sK3)
      | ~ member(sK4(sF5,X2),sK2)
      | subset(X2,sF5) ),
    inference(resolution,[],[f134,f48]) ).

fof(f134,plain,
    ! [X6] :
      ( member(X6,sF5)
      | ~ member(X6,sK3)
      | ~ member(X6,sK2) ),
    inference(superposition,[],[f46,f57]) ).

fof(f46,plain,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X1,X0))
      | ~ member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET578+3 : 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_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n013.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 13:58:47 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.45  % (23858)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)
% 0.19/0.48  % (23847)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.48  % (23858)Refutation not found, incomplete strategy% (23858)------------------------------
% 0.19/0.48  % (23858)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.48  % (23858)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.48  % (23858)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.48  
% 0.19/0.48  % (23858)Memory used [KB]: 5884
% 0.19/0.48  % (23858)Time elapsed: 0.089 s
% 0.19/0.48  % (23858)Instructions burned: 2 (million)
% 0.19/0.48  % (23858)------------------------------
% 0.19/0.48  % (23858)------------------------------
% 0.19/0.49  % (23866)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50  % (23850)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)
% 0.19/0.50  % (23866)Instruction limit reached!
% 0.19/0.50  % (23866)------------------------------
% 0.19/0.50  % (23866)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (23866)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (23866)Termination reason: Unknown
% 0.19/0.50  % (23866)Termination phase: Finite model building preprocessing
% 0.19/0.50  
% 0.19/0.50  % (23866)Memory used [KB]: 5884
% 0.19/0.50  % (23866)Time elapsed: 0.004 s
% 0.19/0.50  % (23866)Instructions burned: 3 (million)
% 0.19/0.50  % (23866)------------------------------
% 0.19/0.50  % (23866)------------------------------
% 0.19/0.50  % (23857)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)
% 0.19/0.51  % (23849)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)
% 0.19/0.51  % (23853)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)
% 0.19/0.51  % (23850)Refutation not found, incomplete strategy% (23850)------------------------------
% 0.19/0.51  % (23850)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (23850)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (23850)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.51  
% 0.19/0.51  % (23850)Memory used [KB]: 5884
% 0.19/0.51  % (23850)Time elapsed: 0.113 s
% 0.19/0.51  % (23850)Instructions burned: 1 (million)
% 0.19/0.51  % (23850)------------------------------
% 0.19/0.51  % (23850)------------------------------
% 0.19/0.51  % (23864)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.51  % (23847)First to succeed.
% 0.19/0.51  % (23871)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)
% 0.19/0.51  % (23847)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (23847)------------------------------
% 0.19/0.51  % (23847)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (23847)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (23847)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (23847)Memory used [KB]: 6140
% 0.19/0.51  % (23847)Time elapsed: 0.115 s
% 0.19/0.51  % (23847)Instructions burned: 18 (million)
% 0.19/0.51  % (23847)------------------------------
% 0.19/0.51  % (23847)------------------------------
% 0.19/0.51  % (23844)Success in time 0.162 s
%------------------------------------------------------------------------------