TSTP Solution File: SET162+3 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET162+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_sat --cores 0 -t %d %s

% Computer : n004.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 18:24:00 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   44 (  13 unt;   0 def)
%            Number of atoms       :  123 (  19 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  128 (  49   ~;  46   |;  22   &)
%                                         (   7 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   71 (  66   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f169,plain,
    $false,
    inference(subsumption_resolution,[],[f168,f82]) ).

fof(f82,plain,
    ~ subset(sF3,sK0),
    inference(subsumption_resolution,[],[f81,f56]) ).

fof(f56,plain,
    sK0 != sF3,
    inference(definition_folding,[],[f35,f55]) ).

fof(f55,plain,
    union(sK0,empty_set) = sF3,
    introduced(function_definition,[]) ).

fof(f35,plain,
    union(sK0,empty_set) != sK0,
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    union(sK0,empty_set) != sK0,
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f18]) ).

fof(f18,plain,
    ( ? [X0] : union(X0,empty_set) != X0
   => union(sK0,empty_set) != sK0 ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ? [X0] : union(X0,empty_set) != X0,
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0] : union(X0,empty_set) = X0,
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0] : union(X0,empty_set) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_empty_set) ).

fof(f81,plain,
    ( sK0 = sF3
    | ~ subset(sF3,sK0) ),
    inference(resolution,[],[f80,f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f29]) ).

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

fof(f28,plain,
    ! [X1,X0] :
      ( ( ( subset(X0,X1)
          & subset(X1,X0) )
        | X0 != X1 )
      & ( X0 = X1
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) ) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ! [X1,X0] :
      ( ( ( subset(X0,X1)
          & subset(X1,X0) )
        | X0 != X1 )
      & ( X0 = X1
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X1,X0] :
      ( ( subset(X0,X1)
        & subset(X1,X0) )
    <=> X0 = X1 ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] :
      ( ( subset(X0,X1)
        & subset(X1,X0) )
    <=> X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).

fof(f80,plain,
    subset(sK0,sF3),
    inference(duplicate_literal_removal,[],[f79]) ).

fof(f79,plain,
    ( subset(sK0,sF3)
    | subset(sK0,sF3) ),
    inference(resolution,[],[f70,f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ~ member(sK2(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK2(X0,X1),X1)
          & member(sK2(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f31,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK2(X0,X1),X1)
        & member(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f30]) ).

fof(f30,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        | ? [X2] :
            ( ~ member(X2,X0)
            & member(X2,X1) ) )
      & ( ! [X2] :
            ( member(X2,X0)
            | ~ member(X2,X1) )
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( member(X2,X0)
          | ~ member(X2,X1) ) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) )
    <=> subset(X1,X0) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).

fof(f70,plain,
    ! [X1] :
      ( member(sK2(sK0,X1),sF3)
      | subset(sK0,X1) ),
    inference(resolution,[],[f49,f61]) ).

fof(f61,plain,
    ! [X0] :
      ( ~ member(X0,sK0)
      | member(X0,sF3) ),
    inference(superposition,[],[f43,f55]) ).

fof(f43,plain,
    ! [X2,X0,X1] :
      ( member(X1,union(X2,X0))
      | ~ member(X1,X2) ),
    inference(cnf_transformation,[],[f26]) ).

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

fof(f25,plain,
    ! [X0,X2,X1] :
      ( ( member(X2,union(X1,X0))
        | ( ~ member(X2,X0)
          & ~ member(X2,X1) ) )
      & ( member(X2,X0)
        | member(X2,X1)
        | ~ member(X2,union(X1,X0)) ) ),
    inference(flattening,[],[f24]) ).

fof(f24,plain,
    ! [X0,X2,X1] :
      ( ( member(X2,union(X1,X0))
        | ( ~ member(X2,X0)
          & ~ member(X2,X1) ) )
      & ( member(X2,X0)
        | member(X2,X1)
        | ~ member(X2,union(X1,X0)) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0,X2,X1] :
      ( member(X2,union(X1,X0))
    <=> ( member(X2,X0)
        | member(X2,X1) ) ),
    inference(rectify,[],[f1]) ).

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

fof(f49,plain,
    ! [X0,X1] :
      ( member(sK2(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f168,plain,
    subset(sF3,sK0),
    inference(duplicate_literal_removal,[],[f166]) ).

fof(f166,plain,
    ( subset(sF3,sK0)
    | subset(sF3,sK0) ),
    inference(resolution,[],[f102,f50]) ).

fof(f102,plain,
    ! [X1] :
      ( member(sK2(sF3,X1),sK0)
      | subset(sF3,X1) ),
    inference(resolution,[],[f93,f49]) ).

fof(f93,plain,
    ! [X0] :
      ( ~ member(X0,sF3)
      | member(X0,sK0) ),
    inference(subsumption_resolution,[],[f89,f36]) ).

fof(f36,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] : ~ member(X0,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).

fof(f89,plain,
    ! [X0] :
      ( member(X0,empty_set)
      | ~ member(X0,sF3)
      | member(X0,sK0) ),
    inference(superposition,[],[f42,f55]) ).

fof(f42,plain,
    ! [X2,X0,X1] :
      ( ~ member(X1,union(X2,X0))
      | member(X1,X2)
      | member(X1,X0) ),
    inference(cnf_transformation,[],[f26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET162+3 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35  % Computer : n004.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 13:20:49 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.47  % (4280)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)
% 0.20/0.47  TRYING [1]
% 0.20/0.47  TRYING [2]
% 0.20/0.47  TRYING [3]
% 0.20/0.47  TRYING [4]
% 0.20/0.48  % (4296)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.49  % (4294)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)
% 0.20/0.49  TRYING [5]
% 0.20/0.49  % (4288)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.49  % (4288)Instruction limit reached!
% 0.20/0.49  % (4288)------------------------------
% 0.20/0.49  % (4288)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (4288)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (4288)Termination reason: Unknown
% 0.20/0.49  % (4288)Termination phase: Clausification
% 0.20/0.49  
% 0.20/0.49  % (4288)Memory used [KB]: 895
% 0.20/0.49  % (4288)Time elapsed: 0.002 s
% 0.20/0.49  % (4288)Instructions burned: 2 (million)
% 0.20/0.49  % (4288)------------------------------
% 0.20/0.49  % (4288)------------------------------
% 0.20/0.50  % (4286)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)
% 0.20/0.50  % (4282)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)
% 0.20/0.50  TRYING [6]
% 0.20/0.50  % (4307)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.51  % (4304)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)
% 0.20/0.51  % (4303)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)
% 0.20/0.51  % (4283)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)
% 0.20/0.51  % (4307)First to succeed.
% 0.20/0.51  % (4284)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51  % (4307)Refutation found. Thanks to Tanya!
% 0.20/0.51  % SZS status Theorem for theBenchmark
% 0.20/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51  % (4307)------------------------------
% 0.20/0.51  % (4307)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (4307)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (4307)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (4307)Memory used [KB]: 5500
% 0.20/0.51  % (4307)Time elapsed: 0.121 s
% 0.20/0.51  % (4307)Instructions burned: 4 (million)
% 0.20/0.51  % (4307)------------------------------
% 0.20/0.51  % (4307)------------------------------
% 0.20/0.51  % (4277)Success in time 0.159 s
%------------------------------------------------------------------------------