TSTP Solution File: SET002+4 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET002+4 : 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_uns --cores 0 -t %d %s

% Computer : n014.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 18:18:16 EDT 2022

% Result   : Theorem 1.33s 0.54s
% Output   : Refutation 1.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   37 (   9 unt;   0 def)
%            Number of atoms       :   94 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   88 (  31   ~;  32   |;  13   &)
%                                         (   5 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   76 (  71   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f126,plain,
    $false,
    inference(resolution,[],[f122,f36]) ).

fof(f36,plain,
    ~ equal_set(union(sK1,sK1),sK1),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ~ equal_set(union(sK1,sK1),sK1),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f20,f28]) ).

fof(f28,plain,
    ( ? [X0] : ~ equal_set(union(X0,X0),X0)
   => ~ equal_set(union(sK1,sK1),sK1) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ? [X0] : ~ equal_set(union(X0,X0),X0),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X0] : equal_set(union(X0,X0),X0),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X0] : equal_set(union(X0,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI14) ).

fof(f122,plain,
    ! [X0] : equal_set(union(X0,X0),X0),
    inference(resolution,[],[f119,f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ~ subset(union(X0,X1),X1)
      | equal_set(union(X0,X1),X1) ),
    inference(resolution,[],[f49,f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | equal_set(X0,X1)
      | ~ subset(X1,X0) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
     => equal_set(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
    <=> equal_set(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).

fof(f49,plain,
    ! [X0,X1] : subset(X0,union(X1,X0)),
    inference(duplicate_literal_removal,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( subset(X0,union(X1,X0))
      | subset(X0,union(X1,X0)) ),
    inference(resolution,[],[f39,f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( member(sK0(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) )
      | subset(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f22,f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
      | subset(X0,X1) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X1,X0] :
      ( ? [X2] :
          ( ~ member(X2,X0)
          & member(X2,X1) )
      | subset(X1,X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) )
     => subset(X1,X0) ),
    inference(unused_predicate_definition_removal,[],[f15]) ).

fof(f15,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) ) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).

fof(f39,plain,
    ! [X2,X0,X1] :
      ( ~ member(sK0(X0,union(X1,X2)),X2)
      | subset(X0,union(X1,X2)) ),
    inference(resolution,[],[f33,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ member(sK0(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f33,plain,
    ! [X2,X0,X1] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,X1)
        | member(X0,X2)
        | ~ member(X0,union(X1,X2)) )
      & ( member(X0,union(X1,X2))
        | ( ~ member(X0,X1)
          & ~ member(X0,X2) ) ) ),
    inference(rectify,[],[f26]) ).

fof(f26,plain,
    ! [X0,X2,X1] :
      ( ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X2,X1)) )
      & ( member(X0,union(X2,X1))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) ) ),
    inference(flattening,[],[f25]) ).

fof(f25,plain,
    ! [X0,X2,X1] :
      ( ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X2,X1)) )
      & ( member(X0,union(X2,X1))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X2,X1] :
      ( ( member(X0,X2)
        | member(X0,X1) )
    <=> member(X0,union(X2,X1)) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X2,X1,X0] :
      ( ( member(X2,X0)
        | member(X2,X1) )
    <=> member(X2,union(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).

fof(f119,plain,
    ! [X0] : subset(union(X0,X0),X0),
    inference(duplicate_literal_removal,[],[f107]) ).

fof(f107,plain,
    ! [X0] :
      ( subset(union(X0,X0),X0)
      | subset(union(X0,X0),X0) ),
    inference(resolution,[],[f92,f32]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( member(sK0(union(X0,X0),X1),X0)
      | subset(union(X0,X0),X1) ),
    inference(factoring,[],[f43]) ).

fof(f43,plain,
    ! [X2,X0,X1] :
      ( member(sK0(union(X0,X1),X2),X1)
      | member(sK0(union(X0,X1),X2),X0)
      | subset(union(X0,X1),X2) ),
    inference(resolution,[],[f35,f31]) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,union(X1,X2))
      | member(X0,X2)
      | member(X0,X1) ),
    inference(cnf_transformation,[],[f27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SET002+4 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35  % Computer : n014.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 30 12:50:48 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.20/0.52  % (2357)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.20/0.52  % (2346)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.52  % (2351)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.52  % (2353)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.52  % (2350)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.52  % (2357)Refutation not found, incomplete strategy% (2357)------------------------------
% 0.20/0.52  % (2357)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (2357)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (2357)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.52  
% 0.20/0.52  % (2357)Memory used [KB]: 5884
% 0.20/0.52  % (2357)Time elapsed: 0.104 s
% 0.20/0.52  % (2357)Instructions burned: 1 (million)
% 0.20/0.52  % (2357)------------------------------
% 0.20/0.52  % (2357)------------------------------
% 0.20/0.53  % (2348)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.53  % (2348)Refutation not found, incomplete strategy% (2348)------------------------------
% 0.20/0.53  % (2348)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (2348)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (2348)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.53  
% 0.20/0.53  % (2348)Memory used [KB]: 5884
% 0.20/0.53  % (2348)Time elapsed: 0.114 s
% 0.20/0.53  % (2348)Instructions burned: 2 (million)
% 0.20/0.53  % (2348)------------------------------
% 0.20/0.53  % (2348)------------------------------
% 0.20/0.53  % (2362)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.53  % (2355)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.20/0.53  % (2370)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.20/0.53  % (2370)Refutation not found, incomplete strategy% (2370)------------------------------
% 0.20/0.53  % (2370)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (2370)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (2370)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.53  
% 0.20/0.53  % (2370)Memory used [KB]: 1407
% 0.20/0.53  % (2370)Time elapsed: 0.077 s
% 0.20/0.53  % (2370)------------------------------
% 0.20/0.53  % (2370)------------------------------
% 0.20/0.53  % (2349)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54  % (2349)Refutation not found, incomplete strategy% (2349)------------------------------
% 0.20/0.54  % (2349)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (2349)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (2349)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.54  
% 0.20/0.54  % (2349)Memory used [KB]: 5884
% 0.20/0.54  % (2349)Time elapsed: 0.002 s
% 0.20/0.54  % (2349)Instructions burned: 1 (million)
% 0.20/0.54  % (2349)------------------------------
% 0.20/0.54  % (2349)------------------------------
% 1.33/0.54  % (2358)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.33/0.54  % (2366)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 1.33/0.54  % (2363)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.33/0.54  % (2366)Refutation not found, incomplete strategy% (2366)------------------------------
% 1.33/0.54  % (2366)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.33/0.54  % (2366)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.33/0.54  % (2366)Termination reason: Refutation not found, incomplete strategy
% 1.33/0.54  
% 1.33/0.54  % (2366)Memory used [KB]: 5884
% 1.33/0.54  % (2366)Time elapsed: 0.128 s
% 1.33/0.54  % (2366)Instructions burned: 2 (million)
% 1.33/0.54  % (2366)------------------------------
% 1.33/0.54  % (2366)------------------------------
% 1.33/0.54  % (2358)Refutation not found, incomplete strategy% (2358)------------------------------
% 1.33/0.54  % (2358)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.33/0.54  % (2358)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.33/0.54  % (2358)Termination reason: Refutation not found, incomplete strategy
% 1.33/0.54  
% 1.33/0.54  % (2358)Memory used [KB]: 5884
% 1.33/0.54  % (2358)Time elapsed: 0.125 s
% 1.33/0.54  % (2358)Instructions burned: 2 (million)
% 1.33/0.54  % (2358)------------------------------
% 1.33/0.54  % (2358)------------------------------
% 1.33/0.54  % (2350)First to succeed.
% 1.33/0.54  % (2356)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 1.33/0.54  % (2377)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 1.33/0.54  % (2350)Refutation found. Thanks to Tanya!
% 1.33/0.54  % SZS status Theorem for theBenchmark
% 1.33/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 1.33/0.54  % (2350)------------------------------
% 1.33/0.54  % (2350)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.33/0.54  % (2350)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.33/0.54  % (2350)Termination reason: Refutation
% 1.33/0.54  
% 1.33/0.54  % (2350)Memory used [KB]: 6012
% 1.33/0.54  % (2350)Time elapsed: 0.126 s
% 1.33/0.54  % (2350)Instructions burned: 3 (million)
% 1.33/0.54  % (2350)------------------------------
% 1.33/0.54  % (2350)------------------------------
% 1.33/0.54  % (2342)Success in time 0.176 s
%------------------------------------------------------------------------------