TSTP Solution File: NUN067+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : NUN067+1 : TPTP v8.1.0. Released v7.3.0.
% 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 : n010.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 18:07:40 EDT 2022

% Result   : Theorem 0.18s 0.51s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   39 (  10 unt;   0 def)
%            Number of atoms       :  105 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  123 (  57   ~;  35   |;  28   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   70 (  60   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f104,plain,
    $false,
    inference(resolution,[],[f102,f51]) ).

fof(f51,plain,
    ! [X0] : id(X0,X0),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0] : id(X0,X0),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X13] : id(X13,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).

fof(f102,plain,
    ! [X4] : ~ id(X4,sK1),
    inference(resolution,[],[f99,f94]) ).

fof(f94,plain,
    ! [X0] : r2(X0,sK1),
    inference(resolution,[],[f93,f83]) ).

fof(f83,plain,
    ! [X2] :
      ( ~ r1(sK0(X2))
      | r2(X2,sK1) ),
    inference(resolution,[],[f47,f76]) ).

fof(f76,plain,
    ! [X2] :
      ( id(sK1,X2)
      | ~ r1(X2) ),
    inference(resolution,[],[f52,f56]) ).

fof(f56,plain,
    ! [X1] :
      ( id(X1,sK1)
      | ~ r1(X1) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X1] :
      ( ( id(X1,sK1)
        & r1(X1) )
      | ( ~ r1(X1)
        & ~ id(X1,sK1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f1,f36]) ).

fof(f36,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( id(X1,X0)
          & r1(X1) )
        | ( ~ r1(X1)
          & ~ id(X1,X0) ) )
   => ! [X1] :
        ( ( id(X1,sK1)
          & r1(X1) )
        | ( ~ r1(X1)
          & ~ id(X1,sK1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f1,axiom,
    ? [X0] :
    ! [X1] :
      ( ( id(X1,X0)
        & r1(X1) )
      | ( ~ r1(X1)
        & ~ id(X1,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ~ id(X0,X1)
      | id(X1,X0) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ~ id(X0,X1)
      | id(X1,X0) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X14,X15] :
      ( ~ id(X14,X15)
      | id(X15,X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).

fof(f47,plain,
    ! [X2,X0] :
      ( ~ id(X2,sK0(X0))
      | r2(X0,X2) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X2] :
      ( ( id(X2,sK0(X0))
        & r2(X0,X2) )
      | ( ~ r2(X0,X2)
        & ~ id(X2,sK0(X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f28,f34]) ).

fof(f34,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
          ( ( id(X2,X1)
            & r2(X0,X2) )
          | ( ~ r2(X0,X2)
            & ~ id(X2,X1) ) )
     => ! [X2] :
          ( ( id(X2,sK0(X0))
            & r2(X0,X2) )
          | ( ~ r2(X0,X2)
            & ~ id(X2,sK0(X0)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( ( id(X2,X1)
        & r2(X0,X2) )
      | ( ~ r2(X0,X2)
        & ~ id(X2,X1) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X2] :
    ? [X3] :
    ! [X4] :
      ( ( id(X4,X3)
        & r2(X2,X4) )
      | ( ~ id(X4,X3)
        & ~ r2(X2,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

fof(f93,plain,
    ! [X5] : r1(X5),
    inference(subsumption_resolution,[],[f90,f67]) ).

fof(f67,plain,
    ! [X0] : r1(sK5(X0)),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0] :
      ( r1(sK5(X0))
      & id(X0,sK5(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f31,f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ? [X1] :
          ( r1(X1)
          & id(X0,X1) )
     => ( r1(sK5(X0))
        & id(X0,sK5(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0] :
    ? [X1] :
      ( r1(X1)
      & id(X0,X1) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ~ ? [X0] :
      ! [X1] :
        ( ~ id(X0,X1)
        | ~ r1(X1) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ? [X62] :
      ! [X45] :
        ( ~ id(X62,X45)
        | ~ r1(X45) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ? [X62] :
    ! [X45] :
      ( ~ id(X62,X45)
      | ~ r1(X45) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonzerosexistid) ).

fof(f90,plain,
    ! [X5] :
      ( r1(X5)
      | ~ r1(sK5(X5)) ),
    inference(resolution,[],[f58,f74]) ).

fof(f74,plain,
    ! [X0] : id(sK5(X0),X0),
    inference(resolution,[],[f52,f66]) ).

fof(f66,plain,
    ! [X0] : id(X0,sK5(X0)),
    inference(cnf_transformation,[],[f43]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ~ id(X1,X0)
      | r1(X0)
      | ~ r1(X1) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ( r1(X1)
        & r1(X0) )
      | ( ~ r1(X0)
        & ~ r1(X1) )
      | ~ id(X1,X0) ),
    inference(rectify,[],[f27]) ).

fof(f27,plain,
    ! [X1,X0] :
      ( ( r1(X0)
        & r1(X1) )
      | ( ~ r1(X1)
        & ~ r1(X0) )
      | ~ id(X0,X1) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X19,X20] :
      ( ~ id(X19,X20)
      | ( r1(X19)
        & r1(X20) )
      | ( ~ r1(X20)
        & ~ r1(X19) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).

fof(f99,plain,
    ! [X2,X0,X1] :
      ( ~ r2(X0,X1)
      | ~ id(X2,X1) ),
    inference(subsumption_resolution,[],[f57,f93]) ).

fof(f57,plain,
    ! [X2,X0,X1] :
      ( ~ id(X2,X1)
      | ~ r2(X0,X1)
      | ~ r1(X2) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ~ r2(X0,X1)
      | ! [X2] :
          ( ~ r1(X2)
          | ~ id(X2,X1) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ! [X64,X65] :
      ( ! [X66] :
          ( ~ id(X66,X65)
          | ~ r1(X66) )
      | ~ r2(X64,X65) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7a) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : NUN067+1 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.11/0.33  % Computer : n010.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Tue Aug 30 09:37:29 EDT 2022
% 0.11/0.33  % CPUTime    : 
% 0.18/0.49  % (7411)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)
% 0.18/0.49  % (7403)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.50  % (7403)Instruction limit reached!
% 0.18/0.50  % (7403)------------------------------
% 0.18/0.50  % (7403)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50  % (7403)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50  % (7403)Termination reason: Unknown
% 0.18/0.50  % (7403)Termination phase: Saturation
% 0.18/0.50  
% 0.18/0.50  % (7403)Memory used [KB]: 6012
% 0.18/0.50  % (7403)Time elapsed: 0.005 s
% 0.18/0.50  % (7403)Instructions burned: 3 (million)
% 0.18/0.50  % (7403)------------------------------
% 0.18/0.50  % (7403)------------------------------
% 0.18/0.50  % (7395)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)
% 0.18/0.50  % (7395)First to succeed.
% 0.18/0.51  % (7395)Refutation found. Thanks to Tanya!
% 0.18/0.51  % SZS status Theorem for theBenchmark
% 0.18/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.51  % (7395)------------------------------
% 0.18/0.51  % (7395)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51  % (7395)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51  % (7395)Termination reason: Refutation
% 0.18/0.51  
% 0.18/0.51  % (7395)Memory used [KB]: 6012
% 0.18/0.51  % (7395)Time elapsed: 0.073 s
% 0.18/0.51  % (7395)Instructions burned: 3 (million)
% 0.18/0.51  % (7395)------------------------------
% 0.18/0.51  % (7395)------------------------------
% 0.18/0.51  % (7388)Success in time 0.166 s
%------------------------------------------------------------------------------