TSTP Solution File: SEU056+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU056+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n002.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 : Sun May  5 09:26:54 EDT 2024

% Result   : Theorem 0.21s 0.40s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   39 (  13 unt;   0 def)
%            Number of atoms       :   99 (  23 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   92 (  32   ~;  24   |;  26   &)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   58 (  49   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f709,plain,
    $false,
    inference(resolution,[],[f706,f162]) ).

fof(f162,plain,
    ~ disjoint(relation_image(sK2,sK1),relation_image(sK2,sK0)),
    inference(resolution,[],[f122,f97]) ).

fof(f97,plain,
    ~ disjoint(relation_image(sK2,sK0),relation_image(sK2,sK1)),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ( ~ disjoint(relation_image(sK2,sK0),relation_image(sK2,sK1))
    & one_to_one(sK2)
    & disjoint(sK0,sK1)
    & function(sK2)
    & relation(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f45,f68]) ).

fof(f68,plain,
    ( ? [X0,X1,X2] :
        ( ~ disjoint(relation_image(X2,X0),relation_image(X2,X1))
        & one_to_one(X2)
        & disjoint(X0,X1)
        & function(X2)
        & relation(X2) )
   => ( ~ disjoint(relation_image(sK2,sK0),relation_image(sK2,sK1))
      & one_to_one(sK2)
      & disjoint(sK0,sK1)
      & function(sK2)
      & relation(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f45,plain,
    ? [X0,X1,X2] :
      ( ~ disjoint(relation_image(X2,X0),relation_image(X2,X1))
      & one_to_one(X2)
      & disjoint(X0,X1)
      & function(X2)
      & relation(X2) ),
    inference(flattening,[],[f44]) ).

fof(f44,plain,
    ? [X0,X1,X2] :
      ( ~ disjoint(relation_image(X2,X0),relation_image(X2,X1))
      & one_to_one(X2)
      & disjoint(X0,X1)
      & function(X2)
      & relation(X2) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( function(X2)
          & relation(X2) )
       => ( ( one_to_one(X2)
            & disjoint(X0,X1) )
         => disjoint(relation_image(X2,X0),relation_image(X2,X1)) ) ),
    inference(negated_conjecture,[],[f27]) ).

fof(f27,conjecture,
    ! [X0,X1,X2] :
      ( ( function(X2)
        & relation(X2) )
     => ( ( one_to_one(X2)
          & disjoint(X0,X1) )
       => disjoint(relation_image(X2,X0),relation_image(X2,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_funct_1) ).

fof(f122,plain,
    ! [X0,X1] :
      ( disjoint(X1,X0)
      | ~ disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( disjoint(X1,X0)
      | ~ disjoint(X0,X1) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0,X1] :
      ( disjoint(X0,X1)
     => disjoint(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).

fof(f706,plain,
    disjoint(relation_image(sK2,sK1),relation_image(sK2,sK0)),
    inference(trivial_inequality_removal,[],[f705]) ).

fof(f705,plain,
    ( empty_set != empty_set
    | disjoint(relation_image(sK2,sK1),relation_image(sK2,sK0)) ),
    inference(forward_demodulation,[],[f695,f166]) ).

fof(f166,plain,
    empty_set = relation_image(sK2,empty_set),
    inference(resolution,[],[f110,f93]) ).

fof(f93,plain,
    relation(sK2),
    inference(cnf_transformation,[],[f69]) ).

fof(f110,plain,
    ! [X0] :
      ( ~ relation(X0)
      | empty_set = relation_image(X0,empty_set) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0] :
      ( empty_set = relation_image(X0,empty_set)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,axiom,
    ! [X0] :
      ( relation(X0)
     => empty_set = relation_image(X0,empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_relat_1) ).

fof(f695,plain,
    ( empty_set != relation_image(sK2,empty_set)
    | disjoint(relation_image(sK2,sK1),relation_image(sK2,sK0)) ),
    inference(superposition,[],[f609,f196]) ).

fof(f196,plain,
    empty_set = set_intersection2(sK0,sK1),
    inference(resolution,[],[f125,f95]) ).

fof(f95,plain,
    disjoint(sK0,sK1),
    inference(cnf_transformation,[],[f69]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X1)
      | set_intersection2(X0,X1) = empty_set ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ( disjoint(X0,X1)
        | set_intersection2(X0,X1) != empty_set )
      & ( set_intersection2(X0,X1) = empty_set
        | ~ disjoint(X0,X1) ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( disjoint(X0,X1)
    <=> set_intersection2(X0,X1) = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).

fof(f609,plain,
    ! [X0,X1] :
      ( empty_set != relation_image(sK2,set_intersection2(X0,X1))
      | disjoint(relation_image(sK2,X1),relation_image(sK2,X0)) ),
    inference(superposition,[],[f201,f601]) ).

fof(f601,plain,
    ! [X0,X1] : relation_image(sK2,set_intersection2(X0,X1)) = set_intersection2(relation_image(sK2,X0),relation_image(sK2,X1)),
    inference(resolution,[],[f349,f93]) ).

fof(f349,plain,
    ! [X0,X1] :
      ( ~ relation(sK2)
      | relation_image(sK2,set_intersection2(X0,X1)) = set_intersection2(relation_image(sK2,X0),relation_image(sK2,X1)) ),
    inference(resolution,[],[f287,f94]) ).

fof(f94,plain,
    function(sK2),
    inference(cnf_transformation,[],[f69]) ).

fof(f287,plain,
    ! [X0,X1] :
      ( ~ function(sK2)
      | relation_image(sK2,set_intersection2(X0,X1)) = set_intersection2(relation_image(sK2,X0),relation_image(sK2,X1))
      | ~ relation(sK2) ),
    inference(resolution,[],[f130,f96]) ).

fof(f96,plain,
    one_to_one(sK2),
    inference(cnf_transformation,[],[f69]) ).

fof(f130,plain,
    ! [X2,X0,X1] :
      ( ~ one_to_one(X2)
      | relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1))
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1))
      | ~ one_to_one(X2)
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(flattening,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1))
      | ~ one_to_one(X2)
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0,X1,X2] :
      ( ( function(X2)
        & relation(X2) )
     => ( one_to_one(X2)
       => relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_funct_1) ).

fof(f201,plain,
    ! [X0,X1] :
      ( set_intersection2(X1,X0) != empty_set
      | disjoint(X0,X1) ),
    inference(superposition,[],[f126,f119]) ).

fof(f119,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f126,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,X1) != empty_set
      | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f76]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU056+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n002.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri May  3 11:44:57 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  % (23198)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (23204)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37  TRYING [1]
% 0.15/0.37  TRYING [2]
% 0.15/0.37  % (23203)WARNING: value z3 for option sas not known
% 0.15/0.37  TRYING [3]
% 0.15/0.37  % (23201)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37  % (23202)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37  % (23203)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.37  % (23205)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.37  % (23206)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.37  % (23207)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38  TRYING [4]
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.39  TRYING [1]
% 0.15/0.39  TRYING [2]
% 0.15/0.39  TRYING [3]
% 0.15/0.39  TRYING [3]
% 0.21/0.39  TRYING [5]
% 0.21/0.39  TRYING [4]
% 0.21/0.39  % (23206)First to succeed.
% 0.21/0.39  % (23206)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-23198"
% 0.21/0.40  % (23205)Also succeeded, but the first one will report.
% 0.21/0.40  % (23206)Refutation found. Thanks to Tanya!
% 0.21/0.40  % SZS status Theorem for theBenchmark
% 0.21/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.40  % (23206)------------------------------
% 0.21/0.40  % (23206)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.40  % (23206)Termination reason: Refutation
% 0.21/0.40  
% 0.21/0.40  % (23206)Memory used [KB]: 1120
% 0.21/0.40  % (23206)Time elapsed: 0.024 s
% 0.21/0.40  % (23206)Instructions burned: 35 (million)
% 0.21/0.40  % (23198)Success in time 0.039 s
%------------------------------------------------------------------------------