TSTP Solution File: SEU147+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU147+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : n026.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 18:32:08 EDT 2022

% Result   : Theorem 0.21s 0.53s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   47 (  12 unt;   0 def)
%            Number of atoms       :  167 (  59 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  191 (  71   ~;  79   |;  26   &)
%                                         (   8 <=>;   6  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   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;   1 con; 0-2 aty)
%            Number of variables   :   88 (  79   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f110,plain,
    $false,
    inference(subsumption_resolution,[],[f109,f59]) ).

fof(f59,plain,
    ! [X2] : in(X2,singleton(X2)),
    inference(equality_resolution,[],[f58]) ).

fof(f58,plain,
    ! [X2,X0] :
      ( in(X2,X0)
      | singleton(X2) != X0 ),
    inference(equality_resolution,[],[f52]) ).

fof(f52,plain,
    ! [X2,X0,X1] :
      ( in(X2,X0)
      | X1 != X2
      | singleton(X1) != X0 ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( X1 = X2
              | ~ in(X2,X0) )
            & ( in(X2,X0)
              | X1 != X2 ) )
        | singleton(X1) != X0 )
      & ( singleton(X1) = X0
        | ( ( ~ in(sK4(X0,X1),X0)
            | sK4(X0,X1) != X1 )
          & ( in(sK4(X0,X1),X0)
            | sK4(X0,X1) = X1 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f35,f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ( ~ in(X3,X0)
            | X1 != X3 )
          & ( in(X3,X0)
            | X1 = X3 ) )
     => ( ( ~ in(sK4(X0,X1),X0)
          | sK4(X0,X1) != X1 )
        & ( in(sK4(X0,X1),X0)
          | sK4(X0,X1) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( X1 = X2
              | ~ in(X2,X0) )
            & ( in(X2,X0)
              | X1 != X2 ) )
        | singleton(X1) != X0 )
      & ( singleton(X1) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | X1 != X3 )
            & ( in(X3,X0)
              | X1 = X3 ) ) ) ),
    inference(rectify,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( X1 = X2
              | ~ in(X2,X0) )
            & ( in(X2,X0)
              | X1 != X2 ) )
        | singleton(X1) != X0 )
      & ( singleton(X1) = X0
        | ? [X2] :
            ( ( ~ in(X2,X0)
              | X1 != X2 )
            & ( in(X2,X0)
              | X1 = X2 ) ) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( X1 = X2
        <=> in(X2,X0) )
    <=> singleton(X1) = X0 ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 )
    <=> singleton(X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(f109,plain,
    ~ in(empty_set,singleton(empty_set)),
    inference(subsumption_resolution,[],[f108,f62]) ).

fof(f62,plain,
    ! [X0] : in(X0,powerset(X0)),
    inference(resolution,[],[f55,f45]) ).

fof(f45,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f55,plain,
    ! [X3,X0] :
      ( ~ subset(X3,X0)
      | in(X3,powerset(X0)) ),
    inference(equality_resolution,[],[f47]) ).

fof(f47,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ subset(X3,X0)
      | powerset(X0) != X1 ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ( ( ~ subset(sK3(X0,X1),X0)
            | ~ in(sK3(X0,X1),X1) )
          & ( subset(sK3(X0,X1),X0)
            | in(sK3(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f31,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ subset(X2,X0)
            | ~ in(X2,X1) )
          & ( subset(X2,X0)
            | in(X2,X1) ) )
     => ( ( ~ subset(sK3(X0,X1),X0)
          | ~ in(sK3(X0,X1),X1) )
        & ( subset(sK3(X0,X1),X0)
          | in(sK3(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f30,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ? [X2] :
            ( ( ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( subset(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ~ subset(X2,X0) )
            & ( subset(X2,X0)
              | ~ in(X2,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( powerset(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> subset(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).

fof(f108,plain,
    ( ~ in(empty_set,powerset(empty_set))
    | ~ in(empty_set,singleton(empty_set)) ),
    inference(subsumption_resolution,[],[f105,f38]) ).

fof(f38,plain,
    powerset(empty_set) != singleton(empty_set),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    powerset(empty_set) != singleton(empty_set),
    inference(flattening,[],[f12]) ).

fof(f12,negated_conjecture,
    powerset(empty_set) != singleton(empty_set),
    inference(negated_conjecture,[],[f11]) ).

fof(f11,conjecture,
    powerset(empty_set) = singleton(empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).

fof(f105,plain,
    ( powerset(empty_set) = singleton(empty_set)
    | ~ in(empty_set,powerset(empty_set))
    | ~ in(empty_set,singleton(empty_set)) ),
    inference(superposition,[],[f42,f88]) ).

fof(f88,plain,
    empty_set = sK1(singleton(empty_set),powerset(empty_set)),
    inference(subsumption_resolution,[],[f86,f57]) ).

fof(f57,plain,
    ! [X2,X1] :
      ( ~ in(X2,singleton(X1))
      | X1 = X2 ),
    inference(equality_resolution,[],[f53]) ).

fof(f53,plain,
    ! [X2,X0,X1] :
      ( X1 = X2
      | ~ in(X2,X0)
      | singleton(X1) != X0 ),
    inference(cnf_transformation,[],[f37]) ).

fof(f86,plain,
    ( empty_set = sK1(singleton(empty_set),powerset(empty_set))
    | in(sK1(singleton(empty_set),powerset(empty_set)),singleton(empty_set)) ),
    inference(resolution,[],[f64,f70]) ).

fof(f70,plain,
    ( in(sK1(singleton(empty_set),powerset(empty_set)),powerset(empty_set))
    | in(sK1(singleton(empty_set),powerset(empty_set)),singleton(empty_set)) ),
    inference(extensionality_resolution,[],[f41,f38]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( in(sK1(X0,X1),X1)
      | in(sK1(X0,X1),X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( ( ~ in(sK1(X0,X1),X0)
          | ~ in(sK1(X0,X1),X1) )
        & ( in(sK1(X0,X1),X0)
          | in(sK1(X0,X1),X1) ) )
      | X0 = X1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f24,f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X0)
            | ~ in(X2,X1) )
          & ( in(X2,X0)
            | in(X2,X1) ) )
     => ( ( ~ in(sK1(X0,X1),X0)
          | ~ in(sK1(X0,X1),X1) )
        & ( in(sK1(X0,X1),X0)
          | in(sK1(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X0)
            | ~ in(X2,X1) )
          & ( in(X2,X0)
            | in(X2,X1) ) )
      | X0 = X1 ),
    inference(nnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( in(X2,X1)
        <~> in(X2,X0) )
      | X0 = X1 ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> in(X2,X1) )
     => X0 = X1 ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> in(X2,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).

fof(f64,plain,
    ! [X0] :
      ( ~ in(X0,powerset(empty_set))
      | empty_set = X0 ),
    inference(resolution,[],[f56,f39]) ).

fof(f39,plain,
    ! [X0] :
      ( ~ subset(X0,empty_set)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0] :
      ( ~ subset(X0,empty_set)
      | empty_set = X0 ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0] :
      ( subset(X0,empty_set)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).

fof(f56,plain,
    ! [X3,X0] :
      ( subset(X3,X0)
      | ~ in(X3,powerset(X0)) ),
    inference(equality_resolution,[],[f46]) ).

fof(f46,plain,
    ! [X3,X0,X1] :
      ( subset(X3,X0)
      | ~ in(X3,X1)
      | powerset(X0) != X1 ),
    inference(cnf_transformation,[],[f33]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ~ in(sK1(X0,X1),X1)
      | ~ in(sK1(X0,X1),X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU147+1 : TPTP v8.1.0. Released v3.3.0.
% 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
% 0.14/0.34  % Computer : n026.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 15:00:06 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.21/0.52  % (7955)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 (3000ds/498Mi)
% 0.21/0.52  % (7947)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 (3000ds/68Mi)
% 0.21/0.52  % (7935)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 (3000ds/37Mi)
% 0.21/0.52  % (7954)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/138Mi)
% 0.21/0.53  % (7939)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.21/0.53  % (7955)First to succeed.
% 0.21/0.53  % (7933)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 (3000ds/191324Mi)
% 0.21/0.53  % (7934)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.21/0.53  % (7943)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.21/0.53  % (7940)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/7Mi)
% 0.21/0.53  % (7944)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/100Mi)
% 0.21/0.53  % (7941)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.21/0.53  % (7953)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 (3000ds/176Mi)
% 0.21/0.53  % (7941)Instruction limit reached!
% 0.21/0.53  % (7941)------------------------------
% 0.21/0.53  % (7941)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53  % (7941)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53  % (7941)Termination reason: Unknown
% 0.21/0.53  % (7941)Termination phase: Saturation
% 0.21/0.53  
% 0.21/0.53  % (7941)Memory used [KB]: 5373
% 0.21/0.53  % (7941)Time elapsed: 0.125 s
% 0.21/0.53  % (7941)Instructions burned: 2 (million)
% 0.21/0.53  % (7941)------------------------------
% 0.21/0.53  % (7941)------------------------------
% 0.21/0.53  TRYING [1]
% 0.21/0.53  % (7942)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.21/0.53  TRYING [2]
% 0.21/0.53  TRYING [3]
% 0.21/0.53  % (7944)Also succeeded, but the first one will report.
% 0.21/0.53  % (7946)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/99Mi)
% 0.21/0.53  % (7940)Instruction limit reached!
% 0.21/0.53  % (7940)------------------------------
% 0.21/0.53  % (7940)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53  % (7940)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53  % (7940)Termination reason: Unknown
% 0.21/0.53  % (7940)Termination phase: Saturation
% 0.21/0.53  
% 0.21/0.53  % (7940)Memory used [KB]: 5500
% 0.21/0.53  % (7940)Time elapsed: 0.130 s
% 0.21/0.53  % (7940)Instructions burned: 7 (million)
% 0.21/0.53  % (7940)------------------------------
% 0.21/0.53  % (7940)------------------------------
% 0.21/0.53  % (7955)Refutation found. Thanks to Tanya!
% 0.21/0.53  % SZS status Theorem for theBenchmark
% 0.21/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53  % (7955)------------------------------
% 0.21/0.53  % (7955)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53  % (7955)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53  % (7955)Termination reason: Refutation
% 0.21/0.53  
% 0.21/0.53  % (7955)Memory used [KB]: 1023
% 0.21/0.53  % (7955)Time elapsed: 0.076 s
% 0.21/0.53  % (7955)Instructions burned: 4 (million)
% 0.21/0.53  % (7955)------------------------------
% 0.21/0.53  % (7955)------------------------------
% 0.21/0.53  % (7932)Success in time 0.181 s
%------------------------------------------------------------------------------