TSTP Solution File: KRS131+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KRS131+1 : TPTP v8.2.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n020.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 : Mon May 20 23:22:04 EDT 2024

% Result   : Theorem 0.16s 0.39s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   69 (   9 unt;   0 def)
%            Number of atoms       :  237 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  278 ( 110   ~; 106   |;  38   &)
%                                         (  10 <=>;  10  =>;   0  <=;   4 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   11 (  10 usr;   2 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-1 aty)
%            Number of variables   :   85 (  58   !;  27   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f75,plain,
    $false,
    inference(subsumption_resolution,[],[f74,f71]) ).

fof(f71,plain,
    cnotA(sK2),
    inference(subsumption_resolution,[],[f69,f60]) ).

fof(f60,plain,
    ~ sP0,
    inference(subsumption_resolution,[],[f59,f58]) ).

fof(f58,plain,
    ( ~ sP0
    | xsd_string(sK1) ),
    inference(subsumption_resolution,[],[f37,f46]) ).

fof(f46,plain,
    ! [X0] :
      ( xsd_integer(X0)
      | xsd_string(X0) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0] :
      ( ( xsd_string(X0)
        | xsd_integer(X0) )
      & ( ~ xsd_integer(X0)
        | ~ xsd_string(X0) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( xsd_string(X0)
    <=> ~ xsd_integer(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

fof(f37,plain,
    ( ~ xsd_integer(sK1)
    | xsd_string(sK1)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ( ( ( xsd_integer(sK1)
        | ~ xsd_string(sK1) )
      & ( ~ xsd_integer(sK1)
        | xsd_string(sK1) ) )
    | ~ sP0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f18,f19]) ).

fof(f19,plain,
    ( ? [X0] :
        ( ( xsd_integer(X0)
          | ~ xsd_string(X0) )
        & ( ~ xsd_integer(X0)
          | xsd_string(X0) ) )
   => ( ( xsd_integer(sK1)
        | ~ xsd_string(sK1) )
      & ( ~ xsd_integer(sK1)
        | xsd_string(sK1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ( ? [X0] :
        ( ( xsd_integer(X0)
          | ~ xsd_string(X0) )
        & ( ~ xsd_integer(X0)
          | xsd_string(X0) ) )
    | ~ sP0 ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ( ? [X1] :
        ( ( xsd_integer(X1)
          | ~ xsd_string(X1) )
        & ( ~ xsd_integer(X1)
          | xsd_string(X1) ) )
    | ~ sP0 ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ( ? [X1] :
        ( xsd_string(X1)
      <~> ~ xsd_integer(X1) )
    | ~ sP0 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f59,plain,
    ( ~ xsd_string(sK1)
    | ~ sP0 ),
    inference(subsumption_resolution,[],[f38,f45]) ).

fof(f45,plain,
    ! [X0] :
      ( ~ xsd_integer(X0)
      | ~ xsd_string(X0) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f38,plain,
    ( xsd_integer(sK1)
    | ~ xsd_string(sK1)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f20]) ).

fof(f69,plain,
    ( cnotA(sK2)
    | sP0 ),
    inference(resolution,[],[f68,f55]) ).

fof(f55,plain,
    ( ~ cA(sK2)
    | cnotA(sK2)
    | sP0 ),
    inference(subsumption_resolution,[],[f54,f41]) ).

fof(f41,plain,
    ! [X0] : cowlThing(X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( ~ cowlNothing(X0)
      & cowlThing(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).

fof(f54,plain,
    ( ~ cA(sK2)
    | cnotA(sK2)
    | sP0
    | ~ cowlThing(sK3) ),
    inference(subsumption_resolution,[],[f39,f42]) ).

fof(f42,plain,
    ! [X0] : ~ cowlNothing(X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f39,plain,
    ( ~ cA(sK2)
    | cnotA(sK2)
    | sP0
    | cowlNothing(sK3)
    | ~ cowlThing(sK3) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ( ( ( cA(sK2)
        | ~ cnotA(sK2) )
      & ( ~ cA(sK2)
        | cnotA(sK2) ) )
    | sP0
    | cowlNothing(sK3)
    | ~ cowlThing(sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f22,f24,f23]) ).

fof(f23,plain,
    ( ? [X0] :
        ( ( cA(X0)
          | ~ cnotA(X0) )
        & ( ~ cA(X0)
          | cnotA(X0) ) )
   => ( ( cA(sK2)
        | ~ cnotA(sK2) )
      & ( ~ cA(sK2)
        | cnotA(sK2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ( ? [X1] :
        ( cowlNothing(X1)
        | ~ cowlThing(X1) )
   => ( cowlNothing(sK3)
      | ~ cowlThing(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ( ? [X0] :
        ( ( cA(X0)
          | ~ cnotA(X0) )
        & ( ~ cA(X0)
          | cnotA(X0) ) )
    | sP0
    | ? [X1] :
        ( cowlNothing(X1)
        | ~ cowlThing(X1) ) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ( ? [X0] :
        ( ( cA(X0)
          | ~ cnotA(X0) )
        & ( ~ cA(X0)
          | cnotA(X0) ) )
    | sP0
    | ? [X2] :
        ( cowlNothing(X2)
        | ~ cowlThing(X2) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ( ? [X0] :
        ( cnotA(X0)
      <~> ~ cA(X0) )
    | sP0
    | ? [X2] :
        ( cowlNothing(X2)
        | ~ cowlThing(X2) ) ),
    inference(definition_folding,[],[f11,f15]) ).

fof(f11,plain,
    ( ? [X0] :
        ( cnotA(X0)
      <~> ~ cA(X0) )
    | ? [X1] :
        ( xsd_string(X1)
      <~> ~ xsd_integer(X1) )
    | ? [X2] :
        ( cowlNothing(X2)
        | ~ cowlThing(X2) ) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,plain,
    ~ ( ! [X0] :
          ( cnotA(X0)
        <=> ~ cA(X0) )
      & ! [X1] :
          ( xsd_string(X1)
        <=> ~ xsd_integer(X1) )
      & ! [X2] :
          ( ~ cowlNothing(X2)
          & cowlThing(X2) ) ),
    inference(rectify,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ( ! [X0] :
          ( cnotA(X0)
        <=> ~ cA(X0) )
      & ! [X0] :
          ( xsd_string(X0)
        <=> ~ xsd_integer(X0) )
      & ! [X0] :
          ( ~ cowlNothing(X0)
          & cowlThing(X0) ) ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ( ! [X0] :
        ( cnotA(X0)
      <=> ~ cA(X0) )
    & ! [X0] :
        ( xsd_string(X0)
      <=> ~ xsd_integer(X0) )
    & ! [X0] :
        ( ~ cowlNothing(X0)
        & cowlThing(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).

fof(f68,plain,
    cA(sK2),
    inference(subsumption_resolution,[],[f67,f60]) ).

fof(f67,plain,
    ( cA(sK2)
    | sP0 ),
    inference(duplicate_literal_removal,[],[f66]) ).

fof(f66,plain,
    ( cA(sK2)
    | cA(sK2)
    | sP0 ),
    inference(resolution,[],[f65,f57]) ).

fof(f57,plain,
    ( ~ cnotA(sK2)
    | cA(sK2)
    | sP0 ),
    inference(subsumption_resolution,[],[f56,f41]) ).

fof(f56,plain,
    ( cA(sK2)
    | ~ cnotA(sK2)
    | sP0
    | ~ cowlThing(sK3) ),
    inference(subsumption_resolution,[],[f40,f42]) ).

fof(f40,plain,
    ( cA(sK2)
    | ~ cnotA(sK2)
    | sP0
    | cowlNothing(sK3)
    | ~ cowlThing(sK3) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f65,plain,
    ! [X0] :
      ( cnotA(X0)
      | cA(X0) ),
    inference(resolution,[],[f64,f48]) ).

fof(f48,plain,
    ! [X0] :
      ( rq(X0,sK5(X0))
      | cnotA(X0) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0] :
      ( ( cnotA(X0)
        | ( ~ cNothing(sK5(X0))
          & rq(X0,sK5(X0)) ) )
      & ( ! [X2] :
            ( cNothing(X2)
            | ~ rq(X0,X2) )
        | ~ cnotA(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f30,f31]) ).

fof(f31,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ cNothing(X1)
          & rq(X0,X1) )
     => ( ~ cNothing(sK5(X0))
        & rq(X0,sK5(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ! [X0] :
      ( ( cnotA(X0)
        | ? [X1] :
            ( ~ cNothing(X1)
            & rq(X0,X1) ) )
      & ( ! [X2] :
            ( cNothing(X2)
            | ~ rq(X0,X2) )
        | ~ cnotA(X0) ) ),
    inference(rectify,[],[f29]) ).

fof(f29,plain,
    ! [X0] :
      ( ( cnotA(X0)
        | ? [X1] :
            ( ~ cNothing(X1)
            & rq(X0,X1) ) )
      & ( ! [X1] :
            ( cNothing(X1)
            | ~ rq(X0,X1) )
        | ~ cnotA(X0) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0] :
      ( cnotA(X0)
    <=> ! [X1] :
          ( cNothing(X1)
          | ~ rq(X0,X1) ) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( cnotA(X0)
    <=> ! [X1] :
          ( rq(X0,X1)
         => cNothing(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ~ rq(X0,X1)
      | cA(X0) ),
    inference(subsumption_resolution,[],[f52,f41]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( cA(X0)
      | ~ cowlThing(X1)
      | ~ rq(X0,X1) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0] :
      ( ( cA(X0)
        | ! [X1] :
            ( ~ cowlThing(X1)
            | ~ rq(X0,X1) ) )
      & ( ( cowlThing(sK6(X0))
          & rq(X0,sK6(X0)) )
        | ~ cA(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f34,f35]) ).

fof(f35,plain,
    ! [X0] :
      ( ? [X2] :
          ( cowlThing(X2)
          & rq(X0,X2) )
     => ( cowlThing(sK6(X0))
        & rq(X0,sK6(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ! [X0] :
      ( ( cA(X0)
        | ! [X1] :
            ( ~ cowlThing(X1)
            | ~ rq(X0,X1) ) )
      & ( ? [X2] :
            ( cowlThing(X2)
            & rq(X0,X2) )
        | ~ cA(X0) ) ),
    inference(rectify,[],[f33]) ).

fof(f33,plain,
    ! [X0] :
      ( ( cA(X0)
        | ! [X1] :
            ( ~ cowlThing(X1)
            | ~ rq(X0,X1) ) )
      & ( ? [X1] :
            ( cowlThing(X1)
            & rq(X0,X1) )
        | ~ cA(X0) ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( cA(X0)
    <=> ? [X1] :
          ( cowlThing(X1)
          & rq(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(f74,plain,
    ~ cnotA(sK2),
    inference(resolution,[],[f70,f62]) ).

fof(f62,plain,
    ! [X2,X0] :
      ( ~ rq(X0,X2)
      | ~ cnotA(X0) ),
    inference(subsumption_resolution,[],[f47,f61]) ).

fof(f61,plain,
    ! [X0] : ~ cNothing(X0),
    inference(subsumption_resolution,[],[f44,f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ~ rp(X0,X1)
      | ~ cNothing(X0) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0] :
      ( ! [X1] : ~ rp(X0,X1)
      | ~ cNothing(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( cNothing(X0)
     => ~ ? [X1] : rp(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

fof(f44,plain,
    ! [X0] :
      ( rp(X0,sK4(X0))
      | ~ cNothing(X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0] :
      ( rp(X0,sK4(X0))
      | ~ cNothing(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f13,f26]) ).

fof(f26,plain,
    ! [X0] :
      ( ? [X1] : rp(X0,X1)
     => rp(X0,sK4(X0)) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ! [X0] :
      ( ? [X1] : rp(X0,X1)
      | ~ cNothing(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X0] :
      ( cNothing(X0)
     => ? [X1] : rp(X0,X1) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( cNothing(X0)
     => ? [X2] : rp(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

fof(f47,plain,
    ! [X2,X0] :
      ( cNothing(X2)
      | ~ rq(X0,X2)
      | ~ cnotA(X0) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f70,plain,
    rq(sK2,sK6(sK2)),
    inference(resolution,[],[f68,f50]) ).

fof(f50,plain,
    ! [X0] :
      ( ~ cA(X0)
      | rq(X0,sK6(X0)) ),
    inference(cnf_transformation,[],[f36]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13  % Problem    : KRS131+1 : TPTP v8.2.0. Released v3.1.0.
% 0.09/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36  % Computer : n020.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Sat May 18 22:17:23 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  % (23205)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.39  % (23209)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.16/0.39  % (23207)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.39  % (23206)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.16/0.39  % (23208)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.16/0.39  % (23210)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.16/0.39  % (23211)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.16/0.39  % (23212)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.16/0.39  TRYING [1]
% 0.16/0.39  TRYING [1]
% 0.16/0.39  % (23210)First to succeed.
% 0.16/0.39  TRYING [2]
% 0.16/0.39  Detected minimum model sizes of [1,1,1,1]
% 0.16/0.39  Detected minimum model sizes of [1,1,1,1]
% 0.16/0.39  Detected maximum model sizes of [max,1,max,max]
% 0.16/0.39  Detected maximum model sizes of [max,1,max,max]
% 0.16/0.39  TRYING [1,1,1,1]
% 0.16/0.39  TRYING [2]
% 0.16/0.39  TRYING [1,1,1,1]
% 0.16/0.39  % (23211)Also succeeded, but the first one will report.
% 0.16/0.39  TRYING [3]
% 0.16/0.39  % (23208)Also succeeded, but the first one will report.
% 0.16/0.39  TRYING [3]
% 0.16/0.39  TRYING [2,1,2,1]
% 0.16/0.39  TRYING [2,1,2,1]
% 0.16/0.39  TRYING [4]
% 0.16/0.39  TRYING [4]
% 0.16/0.39  TRYING [2,1,1,2]
% 0.16/0.39  TRYING [2,1,1,2]
% 0.16/0.39  % (23210)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23205"
% 0.16/0.39  % (23206)Also succeeded, but the first one will report.
% 0.16/0.39  TRYING [2,1,2,2]
% 0.16/0.39  TRYING [2,1,2,2]
% 0.16/0.39  % (23212)Also succeeded, but the first one will report.
% 0.16/0.39  TRYING [3,1,3,1]
% 0.16/0.39  TRYING [3,1,3,1]
% 0.16/0.39  % (23210)Refutation found. Thanks to Tanya!
% 0.16/0.39  % SZS status Theorem for theBenchmark
% 0.16/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.39  % (23210)------------------------------
% 0.16/0.39  % (23210)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.39  % (23210)Termination reason: Refutation
% 0.16/0.39  
% 0.16/0.39  % (23210)Memory used [KB]: 753
% 0.16/0.39  % (23210)Time elapsed: 0.004 s
% 0.16/0.39  % (23210)Instructions burned: 4 (million)
% 0.16/0.39  % (23205)Success in time 0.008 s
%------------------------------------------------------------------------------