TSTP Solution File: SET956+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET956+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : n001.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 18:26:11 EDT 2022

% Result   : Theorem 0.18s 0.53s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   45 (  12 unt;   0 def)
%            Number of atoms       :  135 (  19 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  141 (  51   ~;  37   |;  41   &)
%                                         (   2 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-3 aty)
%            Number of variables   :  134 ( 109   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f155,plain,
    $false,
    inference(subsumption_resolution,[],[f154,f44]) ).

fof(f44,plain,
    ~ subset(sK1,sK3),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ( subset(sK1,cartesian_product2(sK2,sK4))
    & ~ subset(sK1,sK3)
    & ! [X4,X5] :
        ( in(ordered_pair(X5,X4),sK3)
        | ~ in(ordered_pair(X5,X4),sK1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f26,f27]) ).

fof(f27,plain,
    ( ? [X0,X1,X2,X3] :
        ( subset(X0,cartesian_product2(X1,X3))
        & ~ subset(X0,X2)
        & ! [X4,X5] :
            ( in(ordered_pair(X5,X4),X2)
            | ~ in(ordered_pair(X5,X4),X0) ) )
   => ( subset(sK1,cartesian_product2(sK2,sK4))
      & ~ subset(sK1,sK3)
      & ! [X5,X4] :
          ( in(ordered_pair(X5,X4),sK3)
          | ~ in(ordered_pair(X5,X4),sK1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ? [X0,X1,X2,X3] :
      ( subset(X0,cartesian_product2(X1,X3))
      & ~ subset(X0,X2)
      & ! [X4,X5] :
          ( in(ordered_pair(X5,X4),X2)
          | ~ in(ordered_pair(X5,X4),X0) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ? [X2,X3,X1,X0] :
      ( subset(X2,cartesian_product2(X3,X0))
      & ~ subset(X2,X1)
      & ! [X4,X5] :
          ( in(ordered_pair(X5,X4),X1)
          | ~ in(ordered_pair(X5,X4),X2) ) ),
    inference(flattening,[],[f19]) ).

fof(f19,plain,
    ? [X0,X3,X1,X2] :
      ( ~ subset(X2,X1)
      & subset(X2,cartesian_product2(X3,X0))
      & ! [X4,X5] :
          ( in(ordered_pair(X5,X4),X1)
          | ~ in(ordered_pair(X5,X4),X2) ) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ~ ! [X0,X3,X1,X2] :
        ( ( subset(X2,cartesian_product2(X3,X0))
          & ! [X4,X5] :
              ( in(ordered_pair(X5,X4),X2)
             => in(ordered_pair(X5,X4),X1) ) )
       => subset(X2,X1) ),
    inference(rectify,[],[f11]) ).

fof(f11,negated_conjecture,
    ~ ! [X2,X3,X0,X1] :
        ( ( subset(X0,cartesian_product2(X1,X2))
          & ! [X5,X4] :
              ( in(ordered_pair(X4,X5),X0)
             => in(ordered_pair(X4,X5),X3) ) )
       => subset(X0,X3) ),
    inference(negated_conjecture,[],[f10]) ).

fof(f10,conjecture,
    ! [X2,X3,X0,X1] :
      ( ( subset(X0,cartesian_product2(X1,X2))
        & ! [X5,X4] :
            ( in(ordered_pair(X4,X5),X0)
           => in(ordered_pair(X4,X5),X3) ) )
     => subset(X0,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_zfmisc_1) ).

fof(f154,plain,
    subset(sK1,sK3),
    inference(resolution,[],[f147,f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( in(sK7(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ( ~ in(sK7(X0,X1),X1)
          & in(sK7(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f33,f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ in(X3,X1)
          & in(X3,X0) )
     => ( ~ in(sK7(X0,X1),X1)
        & in(sK7(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X3] :
            ( ~ in(X3,X1)
            & in(X3,X0) ) ) ),
    inference(rectify,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) )
    <=> subset(X0,X1) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f147,plain,
    ~ in(sK7(sK1,sK3),sK1),
    inference(subsumption_resolution,[],[f145,f44]) ).

fof(f145,plain,
    ( subset(sK1,sK3)
    | ~ in(sK7(sK1,sK3),sK1) ),
    inference(resolution,[],[f111,f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ~ in(sK7(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f111,plain,
    ( in(sK7(sK1,sK3),sK3)
    | ~ in(sK7(sK1,sK3),sK1) ),
    inference(superposition,[],[f59,f103]) ).

fof(f103,plain,
    sK7(sK1,sK3) = unordered_pair(singleton(sK6(sK2,sK4,sK7(sK1,sK3))),unordered_pair(sK6(sK2,sK4,sK7(sK1,sK3)),sK5(sK2,sK4,sK7(sK1,sK3)))),
    inference(resolution,[],[f94,f44]) ).

fof(f94,plain,
    ! [X0] :
      ( subset(sK1,X0)
      | sK7(sK1,X0) = unordered_pair(singleton(sK6(sK2,sK4,sK7(sK1,X0))),unordered_pair(sK6(sK2,sK4,sK7(sK1,X0)),sK5(sK2,sK4,sK7(sK1,X0)))) ),
    inference(resolution,[],[f86,f50]) ).

fof(f86,plain,
    ! [X0] :
      ( ~ in(X0,sK1)
      | unordered_pair(singleton(sK6(sK2,sK4,X0)),unordered_pair(sK6(sK2,sK4,X0),sK5(sK2,sK4,X0))) = X0 ),
    inference(forward_demodulation,[],[f84,f54]) ).

fof(f54,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f84,plain,
    ! [X0] :
      ( unordered_pair(unordered_pair(sK6(sK2,sK4,X0),sK5(sK2,sK4,X0)),singleton(sK6(sK2,sK4,X0))) = X0
      | ~ in(X0,sK1) ),
    inference(resolution,[],[f57,f45]) ).

fof(f45,plain,
    subset(sK1,cartesian_product2(sK2,sK4)),
    inference(cnf_transformation,[],[f28]) ).

fof(f57,plain,
    ! [X2,X3,X0,X1] :
      ( ~ subset(X3,cartesian_product2(X0,X1))
      | ~ in(X2,X3)
      | unordered_pair(unordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)),singleton(sK6(X0,X1,X2))) = X2 ),
    inference(definition_unfolding,[],[f47,f42]) ).

fof(f42,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(f47,plain,
    ! [X2,X3,X0,X1] :
      ( ~ subset(X3,cartesian_product2(X0,X1))
      | ordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)) = X2
      | ~ in(X2,X3) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X2,X3] :
      ( ~ subset(X3,cartesian_product2(X0,X1))
      | ( in(sK6(X0,X1,X2),X0)
        & in(sK5(X0,X1,X2),X1)
        & ordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)) = X2 )
      | ~ in(X2,X3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f29,f30]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ? [X4,X5] :
          ( in(X5,X0)
          & in(X4,X1)
          & ordered_pair(X5,X4) = X2 )
     => ( in(sK6(X0,X1,X2),X0)
        & in(sK5(X0,X1,X2),X1)
        & ordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)) = X2 ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ! [X0,X1,X2,X3] :
      ( ~ subset(X3,cartesian_product2(X0,X1))
      | ? [X4,X5] :
          ( in(X5,X0)
          & in(X4,X1)
          & ordered_pair(X5,X4) = X2 )
      | ~ in(X2,X3) ),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ! [X0,X2,X3,X1] :
      ( ~ subset(X1,cartesian_product2(X0,X2))
      | ? [X5,X4] :
          ( in(X4,X0)
          & in(X5,X2)
          & ordered_pair(X4,X5) = X3 )
      | ~ in(X3,X1) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X1,X2,X0,X3] :
      ~ ( in(X3,X1)
        & subset(X1,cartesian_product2(X0,X2))
        & ! [X5,X4] :
            ~ ( in(X4,X0)
              & in(X5,X2)
              & ordered_pair(X4,X5) = X3 ) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X1,X0,X2,X3] :
      ~ ( in(X3,X0)
        & ! [X4,X5] :
            ~ ( in(X5,X2)
              & ordered_pair(X4,X5) = X3
              & in(X4,X1) )
        & subset(X0,cartesian_product2(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).

fof(f59,plain,
    ! [X4,X5] :
      ( in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),sK3)
      | ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),sK1) ),
    inference(forward_demodulation,[],[f58,f54]) ).

fof(f58,plain,
    ! [X4,X5] :
      ( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),sK1)
      | in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),sK3) ),
    inference(forward_demodulation,[],[f56,f54]) ).

fof(f56,plain,
    ! [X4,X5] :
      ( ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),sK1)
      | in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),sK3) ),
    inference(definition_unfolding,[],[f43,f42,f42]) ).

fof(f43,plain,
    ! [X4,X5] :
      ( in(ordered_pair(X5,X4),sK3)
      | ~ in(ordered_pair(X5,X4),sK1) ),
    inference(cnf_transformation,[],[f28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET956+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33  % Computer : n001.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 14:53:46 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.18/0.50  % (29832)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.50  % (29833)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)
% 0.18/0.50  % (29835)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.18/0.51  % (29823)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)
% 0.18/0.51  % (29831)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)
% 0.18/0.51  % (29823)Refutation not found, incomplete strategy% (29823)------------------------------
% 0.18/0.51  % (29823)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51  % (29823)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51  % (29823)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.51  
% 0.18/0.51  % (29823)Memory used [KB]: 5373
% 0.18/0.51  % (29823)Time elapsed: 0.115 s
% 0.18/0.51  % (29823)Instructions burned: 2 (million)
% 0.18/0.51  % (29823)------------------------------
% 0.18/0.51  % (29823)------------------------------
% 0.18/0.51  % (29851)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)
% 0.18/0.51  % (29830)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.51  % (29836)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)
% 0.18/0.52  % (29825)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)
% 0.18/0.52  % (29830)Instruction limit reached!
% 0.18/0.52  % (29830)------------------------------
% 0.18/0.52  % (29830)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52  % (29830)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.52  % (29830)Termination reason: Unknown
% 0.18/0.52  % (29830)Termination phase: Blocked clause elimination
% 0.18/0.52  
% 0.18/0.52  % (29830)Memory used [KB]: 895
% 0.18/0.52  % (29830)Time elapsed: 0.004 s
% 0.18/0.52  % (29830)Instructions burned: 2 (million)
% 0.18/0.52  % (29830)------------------------------
% 0.18/0.52  % (29830)------------------------------
% 0.18/0.52  % (29834)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.18/0.52  % (29822)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)
% 0.18/0.52  % (29824)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.18/0.52  % (29826)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.52  TRYING [1]
% 0.18/0.52  TRYING [2]
% 0.18/0.52  TRYING [3]
% 0.18/0.52  % (29824)First to succeed.
% 0.18/0.52  % (29843)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.18/0.52  % (29832)Also succeeded, but the first one will report.
% 0.18/0.52  % (29845)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)
% 0.18/0.53  % (29824)Refutation found. Thanks to Tanya!
% 0.18/0.53  % SZS status Theorem for theBenchmark
% 0.18/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.53  % (29824)------------------------------
% 0.18/0.53  % (29824)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.53  % (29824)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.53  % (29824)Termination reason: Refutation
% 0.18/0.53  
% 0.18/0.53  % (29824)Memory used [KB]: 1023
% 0.18/0.53  % (29824)Time elapsed: 0.126 s
% 0.18/0.53  % (29824)Instructions burned: 6 (million)
% 0.18/0.53  % (29824)------------------------------
% 0.18/0.53  % (29824)------------------------------
% 0.18/0.53  % (29821)Success in time 0.182 s
%------------------------------------------------------------------------------