TSTP Solution File: SET351+4 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET351+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_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 18:20:25 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   49 (   9 unt;   0 def)
%            Number of atoms       :  127 (   9 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  127 (  49   ~;  45   |;  19   &)
%                                         (   7 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   97 (  88   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f101,plain,
    $false,
    inference(resolution,[],[f100,f41]) ).

fof(f41,plain,
    ~ equal_set(sum(singleton(sK2)),sK2),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ~ equal_set(sum(singleton(sK2)),sK2),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f20,f31]) ).

fof(f31,plain,
    ( ? [X0] : ~ equal_set(sum(singleton(X0)),X0)
   => ~ equal_set(sum(singleton(sK2)),sK2) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ? [X0] : ~ equal_set(sum(singleton(X0)),X0),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X0] : equal_set(sum(singleton(X0)),X0),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X0] : equal_set(sum(singleton(X0)),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI39) ).

fof(f100,plain,
    ! [X0] : equal_set(sum(singleton(X0)),X0),
    inference(subsumption_resolution,[],[f96,f43]) ).

fof(f43,plain,
    ! [X1] : member(X1,singleton(X1)),
    inference(equality_resolution,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( member(X0,singleton(X1))
      | X0 != X1 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ member(X0,singleton(X1)) )
      & ( member(X0,singleton(X1))
        | X0 != X1 ) ),
    inference(rectify,[],[f23]) ).

fof(f23,plain,
    ! [X1,X0] :
      ( ( X0 = X1
        | ~ member(X1,singleton(X0)) )
      & ( member(X1,singleton(X0))
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X1,X0] :
      ( X0 = X1
    <=> member(X1,singleton(X0)) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X2] :
      ( member(X2,singleton(X0))
    <=> X0 = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).

fof(f96,plain,
    ! [X0] :
      ( equal_set(sum(singleton(X0)),X0)
      | ~ member(X0,singleton(X0)) ),
    inference(resolution,[],[f87,f73]) ).

fof(f73,plain,
    ! [X0] : subset(sum(singleton(X0)),X0),
    inference(duplicate_literal_removal,[],[f69]) ).

fof(f69,plain,
    ! [X0] :
      ( subset(sum(singleton(X0)),X0)
      | subset(sum(singleton(X0)),X0) ),
    inference(resolution,[],[f62,f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ~ member(sK1(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ( ~ member(sK1(X0,X1),X1)
        & member(sK1(X0,X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f19,f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK1(X0,X1),X1)
        & member(sK1(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) ) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) )
     => subset(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).

fof(f62,plain,
    ! [X3,X4] :
      ( member(sK1(sum(singleton(X3)),X4),X3)
      | subset(sum(singleton(X3)),X4) ),
    inference(resolution,[],[f60,f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( member(sK1(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f60,plain,
    ! [X2,X3] :
      ( ~ member(X3,sum(singleton(X2)))
      | member(X3,X2) ),
    inference(duplicate_literal_removal,[],[f58]) ).

fof(f58,plain,
    ! [X2,X3] :
      ( member(X3,X2)
      | ~ member(X3,sum(singleton(X2)))
      | ~ member(X3,sum(singleton(X2))) ),
    inference(superposition,[],[f37,f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( sK0(singleton(X1),X0) = X1
      | ~ member(X0,sum(singleton(X1))) ),
    inference(resolution,[],[f38,f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( member(sK0(X0,X1),X0)
      | ~ member(X1,sum(X0)) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ( ( member(sK0(X0,X1),X0)
          & member(X1,sK0(X0,X1)) )
        | ~ member(X1,sum(X0)) )
      & ( member(X1,sum(X0))
        | ! [X3] :
            ( ~ member(X3,X0)
            | ~ member(X1,X3) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f26,f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( member(X2,X0)
          & member(X1,X2) )
     => ( member(sK0(X0,X1),X0)
        & member(X1,sK0(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( ? [X2] :
            ( member(X2,X0)
            & member(X1,X2) )
        | ~ member(X1,sum(X0)) )
      & ( member(X1,sum(X0))
        | ! [X3] :
            ( ~ member(X3,X0)
            | ~ member(X1,X3) ) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X1,X0] :
      ( ( ? [X2] :
            ( member(X2,X1)
            & member(X0,X2) )
        | ~ member(X0,sum(X1)) )
      & ( member(X0,sum(X1))
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X0,X2) ) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X1,X0] :
      ( ? [X2] :
          ( member(X2,X1)
          & member(X0,X2) )
    <=> member(X0,sum(X1)) ),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X2,X0] :
      ( ? [X4] :
          ( member(X2,X4)
          & member(X4,X0) )
    <=> member(X2,sum(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).

fof(f37,plain,
    ! [X0,X1] :
      ( member(X1,sK0(X0,X1))
      | ~ member(X1,sum(X0)) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f87,plain,
    ! [X2,X1] :
      ( ~ subset(sum(X2),X1)
      | ~ member(X1,X2)
      | equal_set(sum(X2),X1) ),
    inference(resolution,[],[f83,f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | equal_set(X0,X1) ),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ! [X1,X0] :
      ( ~ subset(X0,X1)
      | ~ subset(X1,X0)
      | equal_set(X1,X0) ),
    inference(flattening,[],[f21]) ).

fof(f21,plain,
    ! [X1,X0] :
      ( equal_set(X1,X0)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
     => equal_set(X1,X0) ),
    inference(unused_predicate_definition_removal,[],[f14]) ).

fof(f14,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
    <=> equal_set(X1,X0) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( ( subset(X0,X1)
        & subset(X1,X0) )
    <=> equal_set(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).

fof(f83,plain,
    ! [X0,X1] :
      ( subset(X0,sum(X1))
      | ~ member(X0,X1) ),
    inference(duplicate_literal_removal,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | subset(X0,sum(X1))
      | subset(X0,sum(X1)) ),
    inference(resolution,[],[f51,f39]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( ~ member(sK1(X2,sum(X1)),X0)
      | subset(X2,sum(X1))
      | ~ member(X0,X1) ),
    inference(resolution,[],[f36,f40]) ).

fof(f36,plain,
    ! [X3,X0,X1] :
      ( member(X1,sum(X0))
      | ~ member(X3,X0)
      | ~ member(X1,X3) ),
    inference(cnf_transformation,[],[f28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SET351+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13  % 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 13:37:32 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.47  % (22014)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.20/0.48  % (22014)Refutation not found, incomplete strategy% (22014)------------------------------
% 0.20/0.48  % (22014)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.48  % (22014)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.48  % (22014)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.48  
% 0.20/0.48  % (22014)Memory used [KB]: 5884
% 0.20/0.48  % (22014)Time elapsed: 0.064 s
% 0.20/0.48  % (22014)Instructions burned: 2 (million)
% 0.20/0.48  % (22014)------------------------------
% 0.20/0.48  % (22014)------------------------------
% 0.20/0.48  % (22003)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)
% 0.20/0.48  % (22003)Refutation not found, incomplete strategy% (22003)------------------------------
% 0.20/0.48  % (22003)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.48  % (22003)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.48  % (22003)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.48  
% 0.20/0.48  % (22003)Memory used [KB]: 5884
% 0.20/0.48  % (22003)Time elapsed: 0.073 s
% 0.20/0.48  % (22003)Instructions burned: 2 (million)
% 0.20/0.48  % (22003)------------------------------
% 0.20/0.48  % (22003)------------------------------
% 0.20/0.51  % (22009)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)
% 0.20/0.51  % (22009)First to succeed.
% 0.20/0.51  % (22009)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  % (22009)------------------------------
% 0.20/0.51  % (22009)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (22009)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (22009)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (22009)Memory used [KB]: 5884
% 0.20/0.51  % (22009)Time elapsed: 0.095 s
% 0.20/0.51  % (22009)Instructions burned: 3 (million)
% 0.20/0.51  % (22009)------------------------------
% 0.20/0.51  % (22009)------------------------------
% 0.20/0.51  % (21996)Success in time 0.158 s
%------------------------------------------------------------------------------