TSTP Solution File: SEU165+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU165+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : 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 : Wed Aug 31 18:32:16 EDT 2022

% Result   : Theorem 0.20s 0.52s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   47 (  12 unt;   0 def)
%            Number of atoms       :  133 (   6 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  145 (  59   ~;  55   |;  24   &)
%                                         (   5 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :  104 (  84   !;  20   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f96,plain,
    $false,
    inference(subsumption_resolution,[],[f95,f60]) ).

fof(f60,plain,
    in(sK2,sK3),
    inference(subsumption_resolution,[],[f59,f52]) ).

fof(f52,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),cartesian_product2(X2,X0))
      | in(X3,X0) ),
    inference(backward_demodulation,[],[f47,f36]) ).

fof(f36,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f47,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X0)
      | ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X0)) ),
    inference(definition_unfolding,[],[f38,f34]) ).

fof(f34,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(rectify,[],[f16]) ).

fof(f16,plain,
    ! [X1,X0] : ordered_pair(X1,X0) = unordered_pair(unordered_pair(X1,X0),singleton(X1)),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).

fof(f38,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X0)
      | ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X0)) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X1,X3),cartesian_product2(X2,X0))
        | ~ in(X1,X2)
        | ~ in(X3,X0) )
      & ( ( in(X1,X2)
          & in(X3,X0) )
        | ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X0)) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X0,X3,X1,X2] :
      ( ( in(ordered_pair(X3,X2),cartesian_product2(X1,X0))
        | ~ in(X3,X1)
        | ~ in(X2,X0) )
      & ( ( in(X3,X1)
          & in(X2,X0) )
        | ~ in(ordered_pair(X3,X2),cartesian_product2(X1,X0)) ) ),
    inference(flattening,[],[f24]) ).

fof(f24,plain,
    ! [X0,X3,X1,X2] :
      ( ( in(ordered_pair(X3,X2),cartesian_product2(X1,X0))
        | ~ in(X3,X1)
        | ~ in(X2,X0) )
      & ( ( in(X3,X1)
          & in(X2,X0) )
        | ~ in(ordered_pair(X3,X2),cartesian_product2(X1,X0)) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X3,X1,X2] :
      ( in(ordered_pair(X3,X2),cartesian_product2(X1,X0))
    <=> ( in(X3,X1)
        & in(X2,X0) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X3,X2,X1,X0] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
    <=> ( in(X0,X2)
        & in(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).

fof(f59,plain,
    ( in(unordered_pair(singleton(sK4),unordered_pair(sK4,sK2)),cartesian_product2(sK5,sK3))
    | in(sK2,sK3) ),
    inference(forward_demodulation,[],[f51,f36]) ).

fof(f51,plain,
    ( in(unordered_pair(unordered_pair(sK4,sK2),singleton(sK4)),cartesian_product2(sK5,sK3))
    | in(sK2,sK3) ),
    inference(definition_unfolding,[],[f42,f34]) ).

fof(f42,plain,
    ( in(sK2,sK3)
    | in(ordered_pair(sK4,sK2),cartesian_product2(sK5,sK3)) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ( ( ~ in(sK4,sK5)
      | ~ in(sK2,sK3)
      | ~ in(ordered_pair(sK4,sK2),cartesian_product2(sK5,sK3)) )
    & ( ( in(sK4,sK5)
        & in(sK2,sK3) )
      | in(ordered_pair(sK4,sK2),cartesian_product2(sK5,sK3)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f30,f31]) ).

fof(f31,plain,
    ( ? [X0,X1,X2,X3] :
        ( ( ~ in(X2,X3)
          | ~ in(X0,X1)
          | ~ in(ordered_pair(X2,X0),cartesian_product2(X3,X1)) )
        & ( ( in(X2,X3)
            & in(X0,X1) )
          | in(ordered_pair(X2,X0),cartesian_product2(X3,X1)) ) )
   => ( ( ~ in(sK4,sK5)
        | ~ in(sK2,sK3)
        | ~ in(ordered_pair(sK4,sK2),cartesian_product2(sK5,sK3)) )
      & ( ( in(sK4,sK5)
          & in(sK2,sK3) )
        | in(ordered_pair(sK4,sK2),cartesian_product2(sK5,sK3)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ? [X0,X1,X2,X3] :
      ( ( ~ in(X2,X3)
        | ~ in(X0,X1)
        | ~ in(ordered_pair(X2,X0),cartesian_product2(X3,X1)) )
      & ( ( in(X2,X3)
          & in(X0,X1) )
        | in(ordered_pair(X2,X0),cartesian_product2(X3,X1)) ) ),
    inference(rectify,[],[f29]) ).

fof(f29,plain,
    ? [X3,X0,X1,X2] :
      ( ( ~ in(X1,X2)
        | ~ in(X3,X0)
        | ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X0)) )
      & ( ( in(X1,X2)
          & in(X3,X0) )
        | in(ordered_pair(X1,X3),cartesian_product2(X2,X0)) ) ),
    inference(flattening,[],[f28]) ).

fof(f28,plain,
    ? [X3,X0,X1,X2] :
      ( ( ~ in(X1,X2)
        | ~ in(X3,X0)
        | ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X0)) )
      & ( ( in(X1,X2)
          & in(X3,X0) )
        | in(ordered_pair(X1,X3),cartesian_product2(X2,X0)) ) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f17,plain,
    ? [X3,X0,X1,X2] :
      ( in(ordered_pair(X1,X3),cartesian_product2(X2,X0))
    <~> ( in(X1,X2)
        & in(X3,X0) ) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ! [X3,X0,X1,X2] :
        ( ( in(X1,X2)
          & in(X3,X0) )
      <=> in(ordered_pair(X1,X3),cartesian_product2(X2,X0)) ),
    inference(rectify,[],[f12]) ).

fof(f12,negated_conjecture,
    ~ ! [X3,X0,X2,X1] :
        ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      <=> ( in(X1,X3)
          & in(X0,X2) ) ),
    inference(negated_conjecture,[],[f11]) ).

fof(f11,conjecture,
    ! [X3,X0,X2,X1] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
    <=> ( in(X1,X3)
        & in(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).

fof(f95,plain,
    ~ in(sK2,sK3),
    inference(subsumption_resolution,[],[f87,f62]) ).

fof(f62,plain,
    in(sK4,sK5),
    inference(subsumption_resolution,[],[f61,f54]) ).

fof(f54,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),cartesian_product2(X2,X0))
      | in(X1,X2) ),
    inference(forward_demodulation,[],[f46,f36]) ).

fof(f46,plain,
    ! [X2,X3,X0,X1] :
      ( in(X1,X2)
      | ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X0)) ),
    inference(definition_unfolding,[],[f39,f34]) ).

fof(f39,plain,
    ! [X2,X3,X0,X1] :
      ( in(X1,X2)
      | ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X0)) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f61,plain,
    ( in(sK4,sK5)
    | in(unordered_pair(singleton(sK4),unordered_pair(sK4,sK2)),cartesian_product2(sK5,sK3)) ),
    inference(forward_demodulation,[],[f50,f36]) ).

fof(f50,plain,
    ( in(sK4,sK5)
    | in(unordered_pair(unordered_pair(sK4,sK2),singleton(sK4)),cartesian_product2(sK5,sK3)) ),
    inference(definition_unfolding,[],[f43,f34]) ).

fof(f43,plain,
    ( in(sK4,sK5)
    | in(ordered_pair(sK4,sK2),cartesian_product2(sK5,sK3)) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f87,plain,
    ( ~ in(sK4,sK5)
    | ~ in(sK2,sK3) ),
    inference(resolution,[],[f77,f58]) ).

fof(f58,plain,
    ~ in(unordered_pair(singleton(sK4),unordered_pair(sK2,sK4)),cartesian_product2(sK5,sK3)),
    inference(forward_demodulation,[],[f57,f36]) ).

fof(f57,plain,
    ~ in(unordered_pair(singleton(sK4),unordered_pair(sK4,sK2)),cartesian_product2(sK5,sK3)),
    inference(subsumption_resolution,[],[f56,f54]) ).

fof(f56,plain,
    ( ~ in(unordered_pair(singleton(sK4),unordered_pair(sK4,sK2)),cartesian_product2(sK5,sK3))
    | ~ in(sK4,sK5) ),
    inference(subsumption_resolution,[],[f55,f52]) ).

fof(f55,plain,
    ( ~ in(sK4,sK5)
    | ~ in(sK2,sK3)
    | ~ in(unordered_pair(singleton(sK4),unordered_pair(sK4,sK2)),cartesian_product2(sK5,sK3)) ),
    inference(forward_demodulation,[],[f49,f36]) ).

fof(f49,plain,
    ( ~ in(sK2,sK3)
    | ~ in(sK4,sK5)
    | ~ in(unordered_pair(unordered_pair(sK4,sK2),singleton(sK4)),cartesian_product2(sK5,sK3)) ),
    inference(definition_unfolding,[],[f44,f34]) ).

fof(f44,plain,
    ( ~ in(sK4,sK5)
    | ~ in(sK2,sK3)
    | ~ in(ordered_pair(sK4,sK2),cartesian_product2(sK5,sK3)) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f77,plain,
    ! [X2,X3,X0,X1] :
      ( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
      | ~ in(X0,X2)
      | ~ in(X1,X3) ),
    inference(superposition,[],[f63,f36]) ).

fof(f63,plain,
    ! [X2,X3,X0,X1] :
      ( in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),cartesian_product2(X2,X0))
      | ~ in(X3,X0)
      | ~ in(X1,X2) ),
    inference(forward_demodulation,[],[f45,f36]) ).

fof(f45,plain,
    ! [X2,X3,X0,X1] :
      ( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X0))
      | ~ in(X1,X2)
      | ~ in(X3,X0) ),
    inference(definition_unfolding,[],[f40,f34]) ).

fof(f40,plain,
    ! [X2,X3,X0,X1] :
      ( in(ordered_pair(X1,X3),cartesian_product2(X2,X0))
      | ~ in(X1,X2)
      | ~ in(X3,X0) ),
    inference(cnf_transformation,[],[f26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU165+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : n020.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   : Tue Aug 30 14:46:45 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.49  % (5249)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)
% 0.20/0.50  % (5243)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)
% 0.20/0.50  TRYING [1]
% 0.20/0.50  TRYING [2]
% 0.20/0.50  TRYING [3]
% 0.20/0.51  % (5254)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.51  % (5265)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)
% 0.20/0.51  % (5251)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.51  TRYING [1]
% 0.20/0.51  TRYING [2]
% 0.20/0.51  % (5251)Instruction limit reached!
% 0.20/0.51  % (5251)------------------------------
% 0.20/0.51  % (5251)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (5251)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (5251)Termination reason: Unknown
% 0.20/0.51  % (5251)Termination phase: Saturation
% 0.20/0.51  
% 0.20/0.51  % (5251)Memory used [KB]: 5373
% 0.20/0.51  % (5251)Time elapsed: 0.107 s
% 0.20/0.51  % (5251)Instructions burned: 2 (million)
% 0.20/0.51  % (5251)------------------------------
% 0.20/0.51  % (5251)------------------------------
% 0.20/0.51  % (5248)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)
% 0.20/0.51  TRYING [3]
% 0.20/0.51  % (5258)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)
% 0.20/0.51  % (5266)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)
% 0.20/0.51  % (5264)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.52  % (5264)First to succeed.
% 0.20/0.52  % (5257)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)
% 0.20/0.52  % (5264)Refutation found. Thanks to Tanya!
% 0.20/0.52  % SZS status Theorem for theBenchmark
% 0.20/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52  % (5264)------------------------------
% 0.20/0.52  % (5264)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (5264)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (5264)Termination reason: Refutation
% 0.20/0.52  
% 0.20/0.52  % (5264)Memory used [KB]: 5500
% 0.20/0.52  % (5264)Time elapsed: 0.112 s
% 0.20/0.52  % (5264)Instructions burned: 4 (million)
% 0.20/0.52  % (5264)------------------------------
% 0.20/0.52  % (5264)------------------------------
% 0.20/0.52  % (5242)Success in time 0.167 s
%------------------------------------------------------------------------------