TSTP Solution File: SET642+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET642+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 : n029.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 18:21:43 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   25 (   8 unt;   0 def)
%            Number of atoms       :  118 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  134 (  41   ~;  27   |;  43   &)
%                                         (   0 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   62 (  38   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f67,plain,
    $false,
    inference(subsumption_resolution,[],[f66,f63]) ).

fof(f63,plain,
    ~ subset(sK2,cross_product(sK3,sK4)),
    inference(unit_resulting_resolution,[],[f55,f55,f55,f58,f54]) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X0,cross_product(X1,X2))
      | ~ ilf_type(X2,set_type)
      | ilf_type(X0,relation_type(X1,X2))
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ! [X2] :
              ( ilf_type(X0,relation_type(X1,X2))
              | ~ ilf_type(X2,set_type)
              | ~ subset(X0,cross_product(X1,X2)) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(flattening,[],[f28]) ).

fof(f28,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ilf_type(X0,relation_type(X1,X2))
              | ~ subset(X0,cross_product(X1,X2))
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ( subset(X0,cross_product(X1,X2))
               => ilf_type(X0,relation_type(X1,X2)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).

fof(f58,plain,
    ~ ilf_type(sK2,relation_type(sK3,sK4)),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ( ilf_type(sK2,set_type)
    & subset(sK2,sK5)
    & ilf_type(sK5,relation_type(sK3,sK4))
    & ~ ilf_type(sK2,relation_type(sK3,sK4))
    & ilf_type(sK4,set_type)
    & ilf_type(sK3,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f32,f44,f43,f42,f41]) ).

fof(f41,plain,
    ( ? [X0] :
        ( ilf_type(X0,set_type)
        & ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( subset(X0,X3)
                    & ilf_type(X3,relation_type(X1,X2))
                    & ~ ilf_type(X0,relation_type(X1,X2)) )
                & ilf_type(X2,set_type) )
            & ilf_type(X1,set_type) ) )
   => ( ilf_type(sK2,set_type)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( subset(sK2,X3)
                  & ilf_type(X3,relation_type(X1,X2))
                  & ~ ilf_type(sK2,relation_type(X1,X2)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( subset(sK2,X3)
                & ilf_type(X3,relation_type(X1,X2))
                & ~ ilf_type(sK2,relation_type(X1,X2)) )
            & ilf_type(X2,set_type) )
        & ilf_type(X1,set_type) )
   => ( ? [X2] :
          ( ? [X3] :
              ( subset(sK2,X3)
              & ilf_type(X3,relation_type(sK3,X2))
              & ~ ilf_type(sK2,relation_type(sK3,X2)) )
          & ilf_type(X2,set_type) )
      & ilf_type(sK3,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( subset(sK2,X3)
            & ilf_type(X3,relation_type(sK3,X2))
            & ~ ilf_type(sK2,relation_type(sK3,X2)) )
        & ilf_type(X2,set_type) )
   => ( ? [X3] :
          ( subset(sK2,X3)
          & ilf_type(X3,relation_type(sK3,sK4))
          & ~ ilf_type(sK2,relation_type(sK3,sK4)) )
      & ilf_type(sK4,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ( ? [X3] :
        ( subset(sK2,X3)
        & ilf_type(X3,relation_type(sK3,sK4))
        & ~ ilf_type(sK2,relation_type(sK3,sK4)) )
   => ( subset(sK2,sK5)
      & ilf_type(sK5,relation_type(sK3,sK4))
      & ~ ilf_type(sK2,relation_type(sK3,sK4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ? [X0] :
      ( ilf_type(X0,set_type)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( subset(X0,X3)
                  & ilf_type(X3,relation_type(X1,X2))
                  & ~ ilf_type(X0,relation_type(X1,X2)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) ) ),
    inference(flattening,[],[f31]) ).

fof(f31,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ ilf_type(X0,relation_type(X1,X2))
                  & subset(X0,X3)
                  & ilf_type(X3,relation_type(X1,X2)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ! [X2] :
                ( ilf_type(X2,set_type)
               => ! [X3] :
                    ( ilf_type(X3,relation_type(X1,X2))
                   => ( subset(X0,X3)
                     => ilf_type(X0,relation_type(X1,X2)) ) ) ) ) ),
    inference(negated_conjecture,[],[f20]) ).

fof(f20,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ! [X3] :
                  ( ilf_type(X3,relation_type(X1,X2))
                 => ( subset(X0,X3)
                   => ilf_type(X0,relation_type(X1,X2)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_4) ).

fof(f55,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).

fof(f66,plain,
    subset(sK2,cross_product(sK3,sK4)),
    inference(unit_resulting_resolution,[],[f55,f60,f55,f55,f59,f50]) ).

fof(f50,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ilf_type(X3,relation_type(X1,X2))
      | ~ ilf_type(X2,set_type)
      | ~ subset(X0,X3)
      | ~ ilf_type(X1,set_type)
      | subset(X0,cross_product(X1,X2))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ! [X2] :
              ( ! [X3] :
                  ( subset(X0,cross_product(X1,X2))
                  | ~ subset(X0,X3)
                  | ~ ilf_type(X3,relation_type(X1,X2)) )
              | ~ ilf_type(X2,set_type) ) ) ),
    inference(flattening,[],[f23]) ).

fof(f23,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( subset(X0,cross_product(X1,X2))
                  | ~ subset(X0,X3)
                  | ~ ilf_type(X3,relation_type(X1,X2)) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ! [X3] :
                  ( ilf_type(X3,relation_type(X1,X2))
                 => ( subset(X0,X3)
                   => subset(X0,cross_product(X1,X2)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

fof(f59,plain,
    ilf_type(sK5,relation_type(sK3,sK4)),
    inference(cnf_transformation,[],[f45]) ).

fof(f60,plain,
    subset(sK2,sK5),
    inference(cnf_transformation,[],[f45]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET642+3 : 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 : n029.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
% 0.20/0.34  % DateTime   : Tue Aug 30 14:19:27 EDT 2022
% 0.20/0.34  % CPUTime    : 
% 0.20/0.49  % (32210)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)
% 0.20/0.49  % (32210)Instruction limit reached!
% 0.20/0.49  % (32210)------------------------------
% 0.20/0.49  % (32210)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (32210)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (32210)Termination reason: Unknown
% 0.20/0.49  % (32210)Termination phase: Saturation
% 0.20/0.49  
% 0.20/0.49  % (32210)Memory used [KB]: 6012
% 0.20/0.49  % (32210)Time elapsed: 0.004 s
% 0.20/0.49  % (32210)Instructions burned: 3 (million)
% 0.20/0.49  % (32210)------------------------------
% 0.20/0.49  % (32210)------------------------------
% 0.20/0.49  % (32198)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)
% 0.20/0.49  % (32197)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)
% 0.20/0.49  % (32197)Refutation not found, incomplete strategy% (32197)------------------------------
% 0.20/0.49  % (32197)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (32197)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (32197)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.49  
% 0.20/0.49  % (32197)Memory used [KB]: 6012
% 0.20/0.49  % (32197)Time elapsed: 0.091 s
% 0.20/0.49  % (32197)Instructions burned: 2 (million)
% 0.20/0.49  % (32197)------------------------------
% 0.20/0.49  % (32197)------------------------------
% 0.20/0.50  % (32202)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)
% 0.20/0.50  % (32207)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.50  % (32206)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)
% 0.20/0.50  % (32206)Refutation not found, incomplete strategy% (32206)------------------------------
% 0.20/0.50  % (32206)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (32206)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (32206)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.50  
% 0.20/0.50  % (32206)Memory used [KB]: 6012
% 0.20/0.50  % (32206)Time elapsed: 0.097 s
% 0.20/0.50  % (32206)Instructions burned: 2 (million)
% 0.20/0.50  % (32206)------------------------------
% 0.20/0.50  % (32206)------------------------------
% 0.20/0.50  % (32198)First to succeed.
% 0.20/0.50  % (32224)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.20/0.51  % (32198)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  % (32198)------------------------------
% 0.20/0.51  % (32198)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (32198)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (32198)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (32198)Memory used [KB]: 6012
% 0.20/0.51  % (32198)Time elapsed: 0.091 s
% 0.20/0.51  % (32198)Instructions burned: 1 (million)
% 0.20/0.51  % (32198)------------------------------
% 0.20/0.51  % (32198)------------------------------
% 0.20/0.51  % (32190)Success in time 0.152 s
%------------------------------------------------------------------------------