TSTP Solution File: SET679+3 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET679+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n013.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 18:25:19 EDT 2022

% Result   : Theorem 1.26s 0.53s
% Output   : Refutation 1.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   43 (  14 unt;   0 def)
%            Number of atoms       :  125 (  10 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  144 (  62   ~;  43   |;  22   &)
%                                         (   6 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   50 (  44   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f211,plain,
    $false,
    inference(subsumption_resolution,[],[f210,f153]) ).

fof(f153,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(resolution,[],[f115,f99]) ).

fof(f99,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).

fof(f115,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ~ member(X0,empty_set) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0] :
      ( ~ member(X0,empty_set)
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ~ member(X0,empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

fof(f210,plain,
    member(ordered_pair(sK0(sK8),sK0(sK8)),empty_set),
    inference(forward_demodulation,[],[f207,f158]) ).

fof(f158,plain,
    empty_set = identity_relation_of(sK8),
    inference(backward_demodulation,[],[f140,f156]) ).

fof(f156,plain,
    empty_set = sF10,
    inference(resolution,[],[f149,f141]) ).

fof(f141,plain,
    ~ not_equal(sF10,empty_set),
    inference(definition_folding,[],[f129,f140]) ).

fof(f129,plain,
    ~ not_equal(identity_relation_of(sK8),empty_set),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ( ilf_type(sK8,set_type)
    & ~ empty(sK8)
    & ~ not_equal(identity_relation_of(sK8),empty_set) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f48,f83]) ).

fof(f83,plain,
    ( ? [X0] :
        ( ilf_type(X0,set_type)
        & ~ empty(X0)
        & ~ not_equal(identity_relation_of(X0),empty_set) )
   => ( ilf_type(sK8,set_type)
      & ~ empty(sK8)
      & ~ not_equal(identity_relation_of(sK8),empty_set) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ? [X0] :
      ( ilf_type(X0,set_type)
      & ~ empty(X0)
      & ~ not_equal(identity_relation_of(X0),empty_set) ),
    inference(flattening,[],[f47]) ).

fof(f47,plain,
    ? [X0] :
      ( ~ not_equal(identity_relation_of(X0),empty_set)
      & ~ empty(X0)
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,negated_conjecture,
    ~ ! [X0] :
        ( ( ~ empty(X0)
          & ilf_type(X0,set_type) )
       => not_equal(identity_relation_of(X0),empty_set) ),
    inference(negated_conjecture,[],[f24]) ).

fof(f24,conjecture,
    ! [X0] :
      ( ( ~ empty(X0)
        & ilf_type(X0,set_type) )
     => not_equal(identity_relation_of(X0),empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_46) ).

fof(f149,plain,
    ! [X0,X1] :
      ( not_equal(X0,X1)
      | X0 = X1 ),
    inference(subsumption_resolution,[],[f148,f99]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( X0 = X1
      | not_equal(X0,X1)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f117,f99]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type)
      | not_equal(X0,X1) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ( ( not_equal(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ not_equal(X0,X1) ) ) ) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ( not_equal(X0,X1)
          <=> X0 != X1 ) ) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( not_equal(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).

fof(f140,plain,
    sF10 = identity_relation_of(sK8),
    introduced(function_definition,[]) ).

fof(f207,plain,
    member(ordered_pair(sK0(sK8),sK0(sK8)),identity_relation_of(sK8)),
    inference(resolution,[],[f200,f164]) ).

fof(f164,plain,
    member(sK0(sK8),sK8),
    inference(subsumption_resolution,[],[f162,f130]) ).

fof(f130,plain,
    ~ empty(sK8),
    inference(cnf_transformation,[],[f84]) ).

fof(f162,plain,
    ( empty(sK8)
    | member(sK0(sK8),sK8) ),
    inference(resolution,[],[f96,f131]) ).

fof(f131,plain,
    ilf_type(sK8,set_type),
    inference(cnf_transformation,[],[f84]) ).

fof(f96,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | member(sK0(X0),X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ( ( ! [X1] :
              ( ~ member(X1,X0)
              | ~ ilf_type(X1,set_type) )
          | ~ empty(X0) )
        & ( empty(X0)
          | ( member(sK0(X0),X0)
            & ilf_type(sK0(X0),set_type) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f57,f58]) ).

fof(f58,plain,
    ! [X0] :
      ( ? [X2] :
          ( member(X2,X0)
          & ilf_type(X2,set_type) )
     => ( member(sK0(X0),X0)
        & ilf_type(sK0(X0),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f57,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ( ( ! [X1] :
              ( ~ member(X1,X0)
              | ~ ilf_type(X1,set_type) )
          | ~ empty(X0) )
        & ( empty(X0)
          | ? [X2] :
              ( member(X2,X0)
              & ilf_type(X2,set_type) ) ) ) ),
    inference(rectify,[],[f56]) ).

fof(f56,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ( ( ! [X1] :
              ( ~ member(X1,X0)
              | ~ ilf_type(X1,set_type) )
          | ~ empty(X0) )
        & ( empty(X0)
          | ? [X1] :
              ( member(X1,X0)
              & ilf_type(X1,set_type) ) ) ) ),
    inference(nnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ( ! [X1] :
            ( ~ member(X1,X0)
            | ~ ilf_type(X1,set_type) )
      <=> empty(X0) ) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( empty(X0)
      <=> ! [X1] :
            ( ilf_type(X1,set_type)
           => ~ member(X1,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).

fof(f200,plain,
    ! [X2,X1] :
      ( ~ member(X1,X2)
      | member(ordered_pair(X1,X1),identity_relation_of(X2)) ),
    inference(subsumption_resolution,[],[f199,f99]) ).

fof(f199,plain,
    ! [X2,X1] :
      ( member(ordered_pair(X1,X1),identity_relation_of(X2))
      | ~ member(X1,X2)
      | ~ ilf_type(X2,set_type) ),
    inference(resolution,[],[f89,f99]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | member(ordered_pair(X1,X1),identity_relation_of(X0))
      | ~ member(X1,X0)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ( ( member(X1,X0)
              | ~ member(ordered_pair(X1,X1),identity_relation_of(X0)) )
            & ( member(ordered_pair(X1,X1),identity_relation_of(X0))
              | ~ member(X1,X0) ) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(nnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ( member(X1,X0)
          <=> member(ordered_pair(X1,X1),identity_relation_of(X0)) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( member(X1,X0)
          <=> member(ordered_pair(X1,X1),identity_relation_of(X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET679+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % 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 : n013.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 14:10:02 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.51  % (31496)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)
% 1.26/0.52  % (31501)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.26/0.52  % (31520)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)
% 1.26/0.52  % (31497)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.26/0.52  % (31505)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.26/0.52  % (31494)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)
% 1.26/0.52  % (31493)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)
% 1.26/0.52  % (31521)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.26/0.52  % (31494)Refutation not found, incomplete strategy% (31494)------------------------------
% 1.26/0.52  % (31494)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.26/0.52  % (31494)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.26/0.52  % (31494)Termination reason: Refutation not found, incomplete strategy
% 1.26/0.52  
% 1.26/0.52  % (31494)Memory used [KB]: 5500
% 1.26/0.52  % (31494)Time elapsed: 0.124 s
% 1.26/0.52  % (31494)Instructions burned: 5 (million)
% 1.26/0.52  % (31494)------------------------------
% 1.26/0.52  % (31494)------------------------------
% 1.26/0.52  % (31504)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)
% 1.26/0.53  % (31509)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.26/0.53  % (31511)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.26/0.53  % (31513)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)
% 1.26/0.53  % (31522)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)
% 1.26/0.53  % (31501)Instruction limit reached!
% 1.26/0.53  % (31501)------------------------------
% 1.26/0.53  % (31501)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.26/0.53  % (31501)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.26/0.53  % (31501)Termination reason: Unknown
% 1.26/0.53  % (31501)Termination phase: Preprocessing 2
% 1.26/0.53  
% 1.26/0.53  % (31501)Memory used [KB]: 895
% 1.26/0.53  % (31501)Time elapsed: 0.003 s
% 1.26/0.53  % (31501)Instructions burned: 2 (million)
% 1.26/0.53  % (31501)------------------------------
% 1.26/0.53  % (31501)------------------------------
% 1.26/0.53  % (31515)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)
% 1.26/0.53  % (31497)First to succeed.
% 1.26/0.53  % (31496)Also succeeded, but the first one will report.
% 1.26/0.53  % (31497)Refutation found. Thanks to Tanya!
% 1.26/0.53  % SZS status Theorem for theBenchmark
% 1.26/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 1.26/0.53  % (31497)------------------------------
% 1.26/0.53  % (31497)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.26/0.53  % (31497)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.26/0.53  % (31497)Termination reason: Refutation
% 1.26/0.53  
% 1.26/0.53  % (31497)Memory used [KB]: 5500
% 1.26/0.53  % (31497)Time elapsed: 0.127 s
% 1.26/0.53  % (31497)Instructions burned: 5 (million)
% 1.26/0.53  % (31497)------------------------------
% 1.26/0.53  % (31497)------------------------------
% 1.26/0.53  % (31492)Success in time 0.176 s
%------------------------------------------------------------------------------