TSTP Solution File: GEO083+1 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : GEO083+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n024.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 Jun 24 06:25:07 EDT 2024

% Result   : Theorem 0.17s 0.41s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   48 (   8 unt;   1 typ;   0 def)
%            Number of atoms       :  354 (  13 equ)
%            Maximal formula atoms :   14 (   7 avg)
%            Number of connectives :  219 (  77   ~;  74   |;  53   &)
%                                         (   8 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  165 ( 165 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   7 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :  114 (  94   !;  19   ?;  39   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_8,type,
    sQ10_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f686,plain,
    $false,
    inference(avatar_sat_refutation,[],[f235,f255,f685]) ).

tff(f685,plain,
    ~ spl11_12,
    inference(avatar_contradiction_clause,[],[f684]) ).

tff(f684,plain,
    ( $false
    | ~ spl11_12 ),
    inference(subsumption_resolution,[],[f681,f234]) ).

tff(f234,plain,
    ( incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),sK1)
    | ~ spl11_12 ),
    inference(avatar_component_clause,[],[f232]) ).

tff(f232,plain,
    ( spl11_12
  <=> incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_12])]) ).

tff(f681,plain,
    ~ incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),sK1),
    inference(resolution,[],[f249,f64]) ).

tff(f64,plain,
    part_of(sK1,sK2),
    inference(cnf_transformation,[],[f41]) ).

tff(f41,plain,
    ( ~ part_of(sum(sK0,sK1),sum(sK0,sK2))
    & meet(sK3,sK0,sK2)
    & meet(sK3,sK0,sK1)
    & part_of(sK1,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f31,f40]) ).

tff(f40,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ part_of(sum(X0,X1),sum(X0,X2))
        & meet(X3,X0,X2)
        & meet(X3,X0,X1)
        & part_of(X1,X2) )
   => ( ~ part_of(sum(sK0,sK1),sum(sK0,sK2))
      & meet(sK3,sK0,sK2)
      & meet(sK3,sK0,sK1)
      & part_of(sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

tff(f31,plain,
    ? [X0,X1,X2,X3] :
      ( ~ part_of(sum(X0,X1),sum(X0,X2))
      & meet(X3,X0,X2)
      & meet(X3,X0,X1)
      & part_of(X1,X2) ),
    inference(flattening,[],[f30]) ).

tff(f30,plain,
    ? [X0,X1,X2,X3] :
      ( ~ part_of(sum(X0,X1),sum(X0,X2))
      & meet(X3,X0,X2)
      & meet(X3,X0,X1)
      & part_of(X1,X2) ),
    inference(ennf_transformation,[],[f19]) ).

tff(f19,plain,
    ~ ! [X0,X1,X2,X3] :
        ( ( meet(X3,X0,X2)
          & meet(X3,X0,X1)
          & part_of(X1,X2) )
       => part_of(sum(X0,X1),sum(X0,X2)) ),
    inference(rectify,[],[f18]) ).

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

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

tff(f249,plain,
    ! [X0: $i] :
      ( ~ part_of(X0,sK2)
      | ~ incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),X0) ),
    inference(resolution,[],[f190,f76]) ).

tff(f76,plain,
    ! [X3: $i,X0: $i,X1: $i] :
      ( incident_c(X3,X0)
      | ~ incident_c(X3,X1)
      | ~ part_of(X1,X0) ),
    inference(cnf_transformation,[],[f53]) ).

tff(f53,plain,
    ! [X0,X1] :
      ( ( part_of(X1,X0)
        | ( ~ incident_c(sK6(X0,X1),X0)
          & incident_c(sK6(X0,X1),X1) ) )
      & ( ! [X3] :
            ( incident_c(X3,X0)
            | ~ incident_c(X3,X1) )
        | ~ part_of(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f51,f52]) ).

tff(f52,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ incident_c(X2,X0)
          & incident_c(X2,X1) )
     => ( ~ incident_c(sK6(X0,X1),X0)
        & incident_c(sK6(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

tff(f51,plain,
    ! [X0,X1] :
      ( ( part_of(X1,X0)
        | ? [X2] :
            ( ~ incident_c(X2,X0)
            & incident_c(X2,X1) ) )
      & ( ! [X3] :
            ( incident_c(X3,X0)
            | ~ incident_c(X3,X1) )
        | ~ part_of(X1,X0) ) ),
    inference(rectify,[],[f50]) ).

tff(f50,plain,
    ! [X0,X1] :
      ( ( part_of(X1,X0)
        | ? [X2] :
            ( ~ incident_c(X2,X0)
            & incident_c(X2,X1) ) )
      & ( ! [X2] :
            ( incident_c(X2,X0)
            | ~ incident_c(X2,X1) )
        | ~ part_of(X1,X0) ) ),
    inference(nnf_transformation,[],[f35]) ).

tff(f35,plain,
    ! [X0,X1] :
      ( part_of(X1,X0)
    <=> ! [X2] :
          ( incident_c(X2,X0)
          | ~ incident_c(X2,X1) ) ),
    inference(ennf_transformation,[],[f1]) ).

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

tff(f190,plain,
    ~ incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),sK2),
    inference(resolution,[],[f111,f67]) ).

tff(f67,plain,
    ~ part_of(sum(sK0,sK1),sum(sK0,sK2)),
    inference(cnf_transformation,[],[f41]) ).

tff(f111,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( part_of(X2,sum(X0,X1))
      | ~ incident_c(sK6(sum(X0,X1),X2),X1) ),
    inference(resolution,[],[f94,f78]) ).

tff(f78,plain,
    ! [X0: $i,X1: $i] :
      ( ~ incident_c(sK6(X0,X1),X0)
      | part_of(X1,X0) ),
    inference(cnf_transformation,[],[f53]) ).

tff(f94,plain,
    ! [X2: $i,X1: $i,X4: $i] :
      ( incident_c(X4,sum(X1,X2))
      | ~ incident_c(X4,X2) ),
    inference(equality_resolution,[],[f70]) ).

tff(f70,plain,
    ! [X2: $i,X0: $i,X1: $i,X4: $i] :
      ( incident_c(X4,X0)
      | ~ incident_c(X4,X2)
      | ( sum(X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f46]) ).

tff(f46,plain,
    ! [X0,X1,X2] :
      ( ( ( sum(X1,X2) = X0 )
        | ( ( ( ~ incident_c(sK4(X0,X1,X2),X2)
              & ~ incident_c(sK4(X0,X1,X2),X1) )
            | ~ incident_c(sK4(X0,X1,X2),X0) )
          & ( incident_c(sK4(X0,X1,X2),X2)
            | incident_c(sK4(X0,X1,X2),X1)
            | incident_c(sK4(X0,X1,X2),X0) ) ) )
      & ( ! [X4] :
            ( ( incident_c(X4,X0)
              | ( ~ incident_c(X4,X2)
                & ~ incident_c(X4,X1) ) )
            & ( incident_c(X4,X2)
              | incident_c(X4,X1)
              | ~ incident_c(X4,X0) ) )
        | ( sum(X1,X2) != X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f44,f45]) ).

tff(f45,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ incident_c(X3,X2)
              & ~ incident_c(X3,X1) )
            | ~ incident_c(X3,X0) )
          & ( incident_c(X3,X2)
            | incident_c(X3,X1)
            | incident_c(X3,X0) ) )
     => ( ( ( ~ incident_c(sK4(X0,X1,X2),X2)
            & ~ incident_c(sK4(X0,X1,X2),X1) )
          | ~ incident_c(sK4(X0,X1,X2),X0) )
        & ( incident_c(sK4(X0,X1,X2),X2)
          | incident_c(sK4(X0,X1,X2),X1)
          | incident_c(sK4(X0,X1,X2),X0) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f44,plain,
    ! [X0,X1,X2] :
      ( ( ( sum(X1,X2) = X0 )
        | ? [X3] :
            ( ( ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) )
              | ~ incident_c(X3,X0) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | incident_c(X3,X0) ) ) )
      & ( ! [X4] :
            ( ( incident_c(X4,X0)
              | ( ~ incident_c(X4,X2)
                & ~ incident_c(X4,X1) ) )
            & ( incident_c(X4,X2)
              | incident_c(X4,X1)
              | ~ incident_c(X4,X0) ) )
        | ( sum(X1,X2) != X0 ) ) ),
    inference(rectify,[],[f43]) ).

tff(f43,plain,
    ! [X0,X1,X2] :
      ( ( ( sum(X1,X2) = X0 )
        | ? [X3] :
            ( ( ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) )
              | ~ incident_c(X3,X0) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | incident_c(X3,X0) ) ) )
      & ( ! [X3] :
            ( ( incident_c(X3,X0)
              | ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) ) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | ~ incident_c(X3,X0) ) )
        | ( sum(X1,X2) != X0 ) ) ),
    inference(flattening,[],[f42]) ).

tff(f42,plain,
    ! [X0,X1,X2] :
      ( ( ( sum(X1,X2) = X0 )
        | ? [X3] :
            ( ( ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) )
              | ~ incident_c(X3,X0) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | incident_c(X3,X0) ) ) )
      & ( ! [X3] :
            ( ( incident_c(X3,X0)
              | ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) ) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | ~ incident_c(X3,X0) ) )
        | ( sum(X1,X2) != X0 ) ) ),
    inference(nnf_transformation,[],[f21]) ).

tff(f21,plain,
    ! [X0,X1,X2] :
      ( ( sum(X1,X2) = X0 )
    <=> ! [X3] :
          ( incident_c(X3,X0)
        <=> ( incident_c(X3,X2)
            | incident_c(X3,X1) ) ) ),
    inference(rectify,[],[f2]) ).

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

tff(f255,plain,
    ~ spl11_11,
    inference(avatar_split_clause,[],[f195,f228]) ).

tff(f228,plain,
    ( spl11_11
  <=> incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_11])]) ).

tff(f195,plain,
    ~ incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),sK0),
    inference(resolution,[],[f112,f67]) ).

tff(f112,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( part_of(X2,sum(X0,X1))
      | ~ incident_c(sK6(sum(X0,X1),X2),X0) ),
    inference(resolution,[],[f95,f78]) ).

tff(f95,plain,
    ! [X2: $i,X1: $i,X4: $i] :
      ( incident_c(X4,sum(X1,X2))
      | ~ incident_c(X4,X1) ),
    inference(equality_resolution,[],[f69]) ).

tff(f69,plain,
    ! [X2: $i,X0: $i,X1: $i,X4: $i] :
      ( incident_c(X4,X0)
      | ~ incident_c(X4,X1)
      | ( sum(X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f46]) ).

tff(f235,plain,
    ( spl11_11
    | spl11_12 ),
    inference(avatar_split_clause,[],[f225,f232,f228]) ).

tff(f225,plain,
    ( incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),sK1)
    | incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),sK0) ),
    inference(resolution,[],[f118,f67]) ).

tff(f118,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( part_of(sum(X1,X2),X0)
      | incident_c(sK6(X0,sum(X1,X2)),X2)
      | incident_c(sK6(X0,sum(X1,X2)),X1) ),
    inference(resolution,[],[f96,f77]) ).

tff(f77,plain,
    ! [X0: $i,X1: $i] :
      ( incident_c(sK6(X0,X1),X1)
      | part_of(X1,X0) ),
    inference(cnf_transformation,[],[f53]) ).

tff(f96,plain,
    ! [X2: $i,X1: $i,X4: $i] :
      ( ~ incident_c(X4,sum(X1,X2))
      | incident_c(X4,X1)
      | incident_c(X4,X2) ),
    inference(equality_resolution,[],[f68]) ).

tff(f68,plain,
    ! [X2: $i,X0: $i,X1: $i,X4: $i] :
      ( incident_c(X4,X2)
      | incident_c(X4,X1)
      | ~ incident_c(X4,X0)
      | ( sum(X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f46]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : GEO083+1 : TPTP v8.2.0. Released v2.4.0.
% 0.00/0.10  % Command    : run_vampire %s %d THM
% 0.10/0.30  % Computer : n024.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Fri Jun 21 10:45:09 EDT 2024
% 0.10/0.31  % CPUTime    : 
% 0.17/0.32  This is a FOF_THM_RFO_SEQ problem
% 0.17/0.32  Running first-order theorem proving
% 0.17/0.32  Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.37  % (20239)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.37  % (20241)lrs+1002_74:59_drc=off:tgt=full:sos=all:cond=fast:i=124987:kws=inv_frequency:afp=300:afq=2.0744697298148953:rawr=on:urr=full:sil=128000:si=on:rtra=on:random_seed=3250543_0 on theBenchmark for (2999ds/124987Mi)
% 0.17/0.37  % (20239)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.37  % (20242)lrs+11_1:16_to=lpo:drc=off:bsd=on:sp=frequency:i=172350:bs=on:av=off:fsd=on:sil=256000:fdi=50_0 on theBenchmark for (2999ds/172350Mi)
% 0.17/0.38  % (20239)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.38  % (20240)lrs+2_5:39_bsr=unit_only:to=lpo:drc=off:sil=128000:plsq=on:plsqr=2,19:sp=frequency:lcm=reverse:fd=preordered:s2a=on:i=38749:s2at=-1.0:fsr=off:uhcvi=on:rawr=on:aer=off:lwlo=on:add=off:bce=on:acc=model:afr=on_0 on theBenchmark for (2999ds/38749Mi)
% 0.17/0.38  % (20239)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.38  % (20244)lrs+1011_1:1_sil=32000:rnwc=on:nwc=10.0:lwlo=on:i=121:bd=off:av=off_0 on theBenchmark for (2999ds/121Mi)
% 0.17/0.38  % (20239)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.38  % (20245)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=113:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2999ds/113Mi)
% 0.17/0.38  % (20239)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.38  % (20243)lrs+1011_1:1_sil=2000:i=103:ep=RS:nm=32:ss=axioms:sos=on_0 on theBenchmark for (2999ds/103Mi)
% 0.17/0.38  % (20239)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.38  % (20246)lrs+1010_1:1_to=lpo:sil=2000:plsq=on:plsqr=32,1:sp=reverse_arity:sos=on:spb=goal_then_units:i=128:ss=axioms:sgt=50:bd=off:sd=3_0 on theBenchmark for (2999ds/128Mi)
% 0.17/0.40  % (20245)First to succeed.
% 0.17/0.40  % (20245)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-20239"
% 0.17/0.41  % (20239)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.41  % (20245)Refutation found. Thanks to Tanya!
% 0.17/0.41  % SZS status Theorem for theBenchmark
% 0.17/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.41  % (20245)------------------------------
% 0.17/0.41  % (20245)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.17/0.41  % (20245)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.17/0.41  % (20245)Termination reason: Refutation
% 0.17/0.41  
% 0.17/0.41  % (20245)Memory used [KB]: 1511
% 0.17/0.41  % (20245)Time elapsed: 0.025 s
% 0.17/0.41  % (20245)Instructions burned: 49 (million)
% 0.17/0.41  % (20245)------------------------------
% 0.17/0.41  % (20245)------------------------------
% 0.17/0.41  % (20239)Success in time 0.078 s
%------------------------------------------------------------------------------