TSTP Solution File: GEO084+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : GEO084+1 : TPTP v8.1.0. Released v2.4.0.
% 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 : n004.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 16:11:46 EDT 2022

% Result   : Theorem 0.20s 0.55s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   38 (   9 unt;   0 def)
%            Number of atoms       :  168 (  11 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  194 (  64   ~;  62   |;  53   &)
%                                         (   7 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   94 (  75   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f253,plain,
    $false,
    inference(subsumption_resolution,[],[f252,f159]) ).

fof(f159,plain,
    ~ incident_c(sK6(sum(sK3,sK5),sK4),sK4),
    inference(resolution,[],[f117,f110]) ).

fof(f110,plain,
    ~ part_of(sum(sK3,sK5),sK4),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ( part_of(sK5,sK4)
    & meet(sK2,sK3,sK5)
    & part_of(sK3,sK4)
    & ~ part_of(sum(sK3,sK5),sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f39,f66]) ).

fof(f66,plain,
    ( ? [X0,X1,X2,X3] :
        ( part_of(X3,X2)
        & meet(X0,X1,X3)
        & part_of(X1,X2)
        & ~ part_of(sum(X1,X3),X2) )
   => ( part_of(sK5,sK4)
      & meet(sK2,sK3,sK5)
      & part_of(sK3,sK4)
      & ~ part_of(sum(sK3,sK5),sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f39,plain,
    ? [X0,X1,X2,X3] :
      ( part_of(X3,X2)
      & meet(X0,X1,X3)
      & part_of(X1,X2)
      & ~ part_of(sum(X1,X3),X2) ),
    inference(flattening,[],[f38]) ).

fof(f38,plain,
    ? [X1,X2,X3,X0] :
      ( ~ part_of(sum(X1,X3),X2)
      & part_of(X3,X2)
      & meet(X0,X1,X3)
      & part_of(X1,X2) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,plain,
    ~ ! [X1,X2,X3,X0] :
        ( ( part_of(X3,X2)
          & meet(X0,X1,X3)
          & part_of(X1,X2) )
       => part_of(sum(X1,X3),X2) ),
    inference(rectify,[],[f18]) ).

fof(f18,negated_conjecture,
    ~ ! [X2,X1,X5,X3] :
        ( ( meet(X2,X1,X3)
          & part_of(X3,X5)
          & part_of(X1,X5) )
       => part_of(sum(X1,X3),X5) ),
    inference(negated_conjecture,[],[f17]) ).

fof(f17,conjecture,
    ! [X2,X1,X5,X3] :
      ( ( meet(X2,X1,X3)
        & part_of(X3,X5)
        & part_of(X1,X5) )
     => part_of(sum(X1,X3),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_6_2) ).

fof(f117,plain,
    ! [X0,X1] :
      ( part_of(X0,X1)
      | ~ incident_c(sK6(X0,X1),X1) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ incident_c(X2,X0)
            | incident_c(X2,X1) )
        | ~ part_of(X0,X1) )
      & ( part_of(X0,X1)
        | ( incident_c(sK6(X0,X1),X0)
          & ~ incident_c(sK6(X0,X1),X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f72,f73]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( incident_c(X3,X0)
          & ~ incident_c(X3,X1) )
     => ( incident_c(sK6(X0,X1),X0)
        & ~ incident_c(sK6(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ incident_c(X2,X0)
            | incident_c(X2,X1) )
        | ~ part_of(X0,X1) )
      & ( part_of(X0,X1)
        | ? [X3] :
            ( incident_c(X3,X0)
            & ~ incident_c(X3,X1) ) ) ),
    inference(rectify,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ incident_c(X2,X0)
            | incident_c(X2,X1) )
        | ~ part_of(X0,X1) )
      & ( part_of(X0,X1)
        | ? [X2] :
            ( incident_c(X2,X0)
            & ~ incident_c(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ incident_c(X2,X0)
          | incident_c(X2,X1) )
    <=> part_of(X0,X1) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( part_of(X0,X1)
    <=> ! [X2] :
          ( incident_c(X2,X0)
         => incident_c(X2,X1) ) ),
    inference(rectify,[],[f1]) ).

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

fof(f252,plain,
    incident_c(sK6(sum(sK3,sK5),sK4),sK4),
    inference(resolution,[],[f251,f167]) ).

fof(f167,plain,
    ! [X1] :
      ( ~ incident_c(X1,sK5)
      | incident_c(X1,sK4) ),
    inference(resolution,[],[f119,f113]) ).

fof(f113,plain,
    part_of(sK5,sK4),
    inference(cnf_transformation,[],[f67]) ).

fof(f119,plain,
    ! [X2,X0,X1] :
      ( ~ part_of(X0,X1)
      | incident_c(X2,X1)
      | ~ incident_c(X2,X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f251,plain,
    incident_c(sK6(sum(sK3,sK5),sK4),sK5),
    inference(subsumption_resolution,[],[f250,f170]) ).

fof(f170,plain,
    ~ incident_c(sK6(sum(sK3,sK5),sK4),sK3),
    inference(resolution,[],[f166,f159]) ).

fof(f166,plain,
    ! [X0] :
      ( incident_c(X0,sK4)
      | ~ incident_c(X0,sK3) ),
    inference(resolution,[],[f119,f111]) ).

fof(f111,plain,
    part_of(sK3,sK4),
    inference(cnf_transformation,[],[f67]) ).

fof(f250,plain,
    ( incident_c(sK6(sum(sK3,sK5),sK4),sK5)
    | incident_c(sK6(sum(sK3,sK5),sK4),sK3) ),
    inference(resolution,[],[f154,f160]) ).

fof(f160,plain,
    incident_c(sK6(sum(sK3,sK5),sK4),sum(sK3,sK5)),
    inference(resolution,[],[f118,f110]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( part_of(X0,X1)
      | incident_c(sK6(X0,X1),X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f154,plain,
    ! [X2,X3,X1] :
      ( ~ incident_c(X3,sum(X1,X2))
      | incident_c(X3,X2)
      | incident_c(X3,X1) ),
    inference(equality_resolution,[],[f144]) ).

fof(f144,plain,
    ! [X2,X3,X0,X1] :
      ( incident_c(X3,X1)
      | incident_c(X3,X2)
      | ~ incident_c(X3,X0)
      | sum(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( incident_c(X3,X0)
              | ( ~ incident_c(X3,X1)
                & ~ incident_c(X3,X2) ) )
            & ( incident_c(X3,X1)
              | incident_c(X3,X2)
              | ~ incident_c(X3,X0) ) )
        | sum(X1,X2) != X0 )
      & ( sum(X1,X2) = X0
        | ( ( ( ~ incident_c(sK15(X0,X1,X2),X1)
              & ~ incident_c(sK15(X0,X1,X2),X2) )
            | ~ incident_c(sK15(X0,X1,X2),X0) )
          & ( incident_c(sK15(X0,X1,X2),X1)
            | incident_c(sK15(X0,X1,X2),X2)
            | incident_c(sK15(X0,X1,X2),X0) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f98,f99]) ).

fof(f99,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ( ~ incident_c(X4,X1)
              & ~ incident_c(X4,X2) )
            | ~ incident_c(X4,X0) )
          & ( incident_c(X4,X1)
            | incident_c(X4,X2)
            | incident_c(X4,X0) ) )
     => ( ( ( ~ incident_c(sK15(X0,X1,X2),X1)
            & ~ incident_c(sK15(X0,X1,X2),X2) )
          | ~ incident_c(sK15(X0,X1,X2),X0) )
        & ( incident_c(sK15(X0,X1,X2),X1)
          | incident_c(sK15(X0,X1,X2),X2)
          | incident_c(sK15(X0,X1,X2),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( incident_c(X3,X0)
              | ( ~ incident_c(X3,X1)
                & ~ incident_c(X3,X2) ) )
            & ( incident_c(X3,X1)
              | incident_c(X3,X2)
              | ~ incident_c(X3,X0) ) )
        | sum(X1,X2) != X0 )
      & ( sum(X1,X2) = X0
        | ? [X4] :
            ( ( ( ~ incident_c(X4,X1)
                & ~ incident_c(X4,X2) )
              | ~ incident_c(X4,X0) )
            & ( incident_c(X4,X1)
              | incident_c(X4,X2)
              | incident_c(X4,X0) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( incident_c(X3,X0)
              | ( ~ incident_c(X3,X1)
                & ~ incident_c(X3,X2) ) )
            & ( incident_c(X3,X1)
              | incident_c(X3,X2)
              | ~ incident_c(X3,X0) ) )
        | sum(X1,X2) != X0 )
      & ( sum(X1,X2) = X0
        | ? [X3] :
            ( ( ( ~ incident_c(X3,X1)
                & ~ incident_c(X3,X2) )
              | ~ incident_c(X3,X0) )
            & ( incident_c(X3,X1)
              | incident_c(X3,X2)
              | incident_c(X3,X0) ) ) ) ),
    inference(flattening,[],[f96]) ).

fof(f96,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( incident_c(X3,X0)
              | ( ~ incident_c(X3,X1)
                & ~ incident_c(X3,X2) ) )
            & ( incident_c(X3,X1)
              | incident_c(X3,X2)
              | ~ incident_c(X3,X0) ) )
        | sum(X1,X2) != X0 )
      & ( sum(X1,X2) = X0
        | ? [X3] :
            ( ( ( ~ incident_c(X3,X1)
                & ~ incident_c(X3,X2) )
              | ~ incident_c(X3,X0) )
            & ( incident_c(X3,X1)
              | incident_c(X3,X2)
              | incident_c(X3,X0) ) ) ) ),
    inference(nnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( incident_c(X3,X0)
        <=> ( incident_c(X3,X1)
            | incident_c(X3,X2) ) )
    <=> sum(X1,X2) = X0 ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1,X3] :
      ( ! [X4] :
          ( ( incident_c(X4,X1)
            | incident_c(X4,X3) )
        <=> incident_c(X4,X0) )
    <=> sum(X1,X3) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_defn) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : GEO084+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n004.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   : Mon Aug 29 21:09:50 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.52  % (19330)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53  % (19329)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 (2999ds/51Mi)
% 0.20/0.53  % (19343)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 (2999ds/498Mi)
% 0.20/0.53  % (19324)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53  % (19326)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53  % (19325)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.53  % (19334)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 (2999ds/68Mi)
% 0.20/0.53  % (19320)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 (2999ds/191324Mi)
% 0.20/0.53  % (19321)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53  TRYING [1]
% 0.20/0.53  TRYING [2]
% 0.20/0.53  TRYING [1]
% 0.20/0.53  TRYING [2]
% 0.20/0.53  % (19321)Refutation not found, incomplete strategy% (19321)------------------------------
% 0.20/0.53  % (19321)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (19321)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (19321)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.53  
% 0.20/0.53  % (19321)Memory used [KB]: 5500
% 0.20/0.53  % (19321)Time elapsed: 0.124 s
% 0.20/0.53  % (19321)Instructions burned: 5 (million)
% 0.20/0.53  % (19321)------------------------------
% 0.20/0.53  % (19321)------------------------------
% 0.20/0.53  TRYING [3]
% 0.20/0.54  % (19348)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.20/0.54  % (19346)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.54  % (19323)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54  % (19350)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.20/0.54  % (19349)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.54  % (19344)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.54  % (19340)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.54  % (19341)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 (2999ds/176Mi)
% 0.20/0.55  % (19342)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.55  % (19343)First to succeed.
% 0.20/0.55  % (19335)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.55  % (19347)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 (2999ds/68Mi)
% 0.20/0.55  % (19332)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.55  % (19338)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.55  % (19343)Refutation found. Thanks to Tanya!
% 0.20/0.55  % SZS status Theorem for theBenchmark
% 0.20/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.55  % (19343)------------------------------
% 0.20/0.55  % (19343)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (19343)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (19343)Termination reason: Refutation
% 0.20/0.55  
% 0.20/0.55  % (19343)Memory used [KB]: 1151
% 0.20/0.55  % (19343)Time elapsed: 0.023 s
% 0.20/0.55  % (19343)Instructions burned: 11 (million)
% 0.20/0.55  % (19343)------------------------------
% 0.20/0.55  % (19343)------------------------------
% 0.20/0.55  % (19319)Success in time 0.195 s
%------------------------------------------------------------------------------