TSTP Solution File: SET013-1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET013-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 : n023.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 18:23:04 EDT 2022

% Result   : Unsatisfiable 0.20s 0.54s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   39 (   9 unt;   0 def)
%            Number of atoms       :   75 (   2 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   62 (  26   ~;  34   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   31 (  31   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f241,plain,
    $false,
    inference(avatar_sat_refutation,[],[f181,f215,f240]) ).

fof(f240,plain,
    ~ spl2_9,
    inference(avatar_contradiction_clause,[],[f239]) ).

fof(f239,plain,
    ( $false
    | ~ spl2_9 ),
    inference(subsumption_resolution,[],[f236,f25]) ).

fof(f25,plain,
    ~ equal_sets(sF0,sF1),
    inference(definition_folding,[],[f22,f24,f23]) ).

fof(f23,plain,
    intersection(as,bs) = sF0,
    introduced(function_definition,[]) ).

fof(f24,plain,
    intersection(bs,as) = sF1,
    introduced(function_definition,[]) ).

fof(f22,axiom,
    ~ equal_sets(intersection(as,bs),intersection(bs,as)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).

fof(f236,plain,
    ( equal_sets(sF0,sF1)
    | ~ spl2_9 ),
    inference(resolution,[],[f176,f17]) ).

fof(f17,axiom,
    ! [X4,X5] :
      ( ~ equal_sets(X4,X5)
      | equal_sets(X5,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_for_set_equal) ).

fof(f176,plain,
    ( equal_sets(sF1,sF0)
    | ~ spl2_9 ),
    inference(avatar_component_clause,[],[f174]) ).

fof(f174,plain,
    ( spl2_9
  <=> equal_sets(sF1,sF0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).

fof(f215,plain,
    spl2_10,
    inference(avatar_split_clause,[],[f212,f178]) ).

fof(f178,plain,
    ( spl2_10
  <=> subset(sF0,sF1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).

fof(f212,plain,
    subset(sF0,sF1),
    inference(duplicate_literal_removal,[],[f207]) ).

fof(f207,plain,
    ( subset(sF0,sF1)
    | subset(sF0,sF1) ),
    inference(resolution,[],[f206,f4]) ).

fof(f4,axiom,
    ! [X2,X3] :
      ( ~ member(member_of_1_not_of_2(X2,X3),X3)
      | subset(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom2) ).

fof(f206,plain,
    ! [X1] :
      ( member(member_of_1_not_of_2(sF0,X1),sF1)
      | subset(sF0,X1) ),
    inference(subsumption_resolution,[],[f203,f41]) ).

fof(f41,plain,
    ! [X0] :
      ( member(member_of_1_not_of_2(sF0,X0),as)
      | subset(sF0,X0) ),
    inference(resolution,[],[f39,f3]) ).

fof(f3,axiom,
    ! [X2,X3] :
      ( member(member_of_1_not_of_2(X2,X3),X2)
      | subset(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom1) ).

fof(f39,plain,
    ! [X0] :
      ( ~ member(X0,sF0)
      | member(X0,as) ),
    inference(superposition,[],[f11,f23]) ).

fof(f11,axiom,
    ! [X0,X4,X5] :
      ( ~ member(X0,intersection(X4,X5))
      | member(X0,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).

fof(f203,plain,
    ! [X1] :
      ( ~ member(member_of_1_not_of_2(sF0,X1),as)
      | subset(sF0,X1)
      | member(member_of_1_not_of_2(sF0,X1),sF1) ),
    inference(resolution,[],[f150,f46]) ).

fof(f46,plain,
    ! [X0] :
      ( member(member_of_1_not_of_2(sF0,X0),bs)
      | subset(sF0,X0) ),
    inference(resolution,[],[f44,f3]) ).

fof(f44,plain,
    ! [X0] :
      ( ~ member(X0,sF0)
      | member(X0,bs) ),
    inference(superposition,[],[f12,f23]) ).

fof(f12,axiom,
    ! [X0,X4,X5] :
      ( ~ member(X0,intersection(X4,X5))
      | member(X0,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set2) ).

fof(f150,plain,
    ! [X1] :
      ( ~ member(X1,bs)
      | ~ member(X1,as)
      | member(X1,sF1) ),
    inference(superposition,[],[f10,f24]) ).

fof(f10,axiom,
    ! [X0,X4,X5] :
      ( member(X0,intersection(X4,X5))
      | ~ member(X0,X5)
      | ~ member(X0,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_both_is_member_of_intersection) ).

fof(f181,plain,
    ( spl2_9
    | ~ spl2_10 ),
    inference(avatar_split_clause,[],[f171,f178,f174]) ).

fof(f171,plain,
    ( ~ subset(sF0,sF1)
    | equal_sets(sF1,sF0) ),
    inference(resolution,[],[f170,f15]) ).

fof(f15,axiom,
    ! [X6,X7] :
      ( ~ subset(X7,X6)
      | ~ subset(X6,X7)
      | equal_sets(X7,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).

fof(f170,plain,
    subset(sF1,sF0),
    inference(duplicate_literal_removal,[],[f166]) ).

fof(f166,plain,
    ( subset(sF1,sF0)
    | subset(sF1,sF0) ),
    inference(resolution,[],[f159,f4]) ).

fof(f159,plain,
    ! [X0] :
      ( member(member_of_1_not_of_2(sF1,X0),sF0)
      | subset(sF1,X0) ),
    inference(subsumption_resolution,[],[f155,f47]) ).

fof(f47,plain,
    ! [X0] :
      ( member(member_of_1_not_of_2(sF1,X0),as)
      | subset(sF1,X0) ),
    inference(resolution,[],[f45,f3]) ).

fof(f45,plain,
    ! [X1] :
      ( ~ member(X1,sF1)
      | member(X1,as) ),
    inference(superposition,[],[f12,f24]) ).

fof(f155,plain,
    ! [X0] :
      ( ~ member(member_of_1_not_of_2(sF1,X0),as)
      | member(member_of_1_not_of_2(sF1,X0),sF0)
      | subset(sF1,X0) ),
    inference(resolution,[],[f149,f42]) ).

fof(f42,plain,
    ! [X0] :
      ( member(member_of_1_not_of_2(sF1,X0),bs)
      | subset(sF1,X0) ),
    inference(resolution,[],[f40,f3]) ).

fof(f40,plain,
    ! [X1] :
      ( ~ member(X1,sF1)
      | member(X1,bs) ),
    inference(superposition,[],[f11,f24]) ).

fof(f149,plain,
    ! [X0] :
      ( ~ member(X0,bs)
      | ~ member(X0,as)
      | member(X0,sF0) ),
    inference(superposition,[],[f10,f23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET013-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 : n023.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 13:12:50 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.47  % (2520)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.48  % (2536)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)
% 0.20/0.48  % (2520)Instruction limit reached!
% 0.20/0.48  % (2520)------------------------------
% 0.20/0.48  % (2520)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (2520)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (2520)Termination reason: Unknown
% 0.20/0.50  % (2520)Termination phase: Saturation
% 0.20/0.50  
% 0.20/0.50  % (2520)Memory used [KB]: 5500
% 0.20/0.50  % (2520)Time elapsed: 0.071 s
% 0.20/0.50  % (2520)Instructions burned: 7 (million)
% 0.20/0.50  % (2520)------------------------------
% 0.20/0.50  % (2520)------------------------------
% 0.20/0.50  % (2517)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51  % (2526)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.52  % (2535)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)
% 0.20/0.52  % (2528)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)
% 0.20/0.52  % (2513)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)
% 0.20/0.52  % (2540)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)
% 0.20/0.52  TRYING [1]
% 0.20/0.52  TRYING [2]
% 0.20/0.52  TRYING [3]
% 0.20/0.52  % (2527)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  % (2516)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)
% 0.20/0.52  TRYING [4]
% 0.20/0.52  % (2539)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)
% 0.20/0.53  % (2518)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)
% 0.20/0.53  % (2514)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)
% 0.20/0.53  % (2515)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)
% 0.20/0.53  % (2514)Refutation not found, incomplete strategy% (2514)------------------------------
% 0.20/0.53  % (2514)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (2514)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (2514)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.53  
% 0.20/0.53  % (2514)Memory used [KB]: 5373
% 0.20/0.53  % (2514)Time elapsed: 0.126 s
% 0.20/0.53  % (2514)------------------------------
% 0.20/0.53  % (2514)------------------------------
% 0.20/0.53  % (2529)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)
% 0.20/0.53  % (2532)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.53  % (2541)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.53  % (2526)First to succeed.
% 0.20/0.53  % (2530)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.54  % (2538)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.54  % (2526)Refutation found. Thanks to Tanya!
% 0.20/0.54  % SZS status Unsatisfiable for theBenchmark
% 0.20/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.54  % (2526)------------------------------
% 0.20/0.54  % (2526)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (2526)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (2526)Termination reason: Refutation
% 0.20/0.54  
% 0.20/0.54  % (2526)Memory used [KB]: 5500
% 0.20/0.54  % (2526)Time elapsed: 0.111 s
% 0.20/0.54  % (2526)Instructions burned: 7 (million)
% 0.20/0.54  % (2526)------------------------------
% 0.20/0.54  % (2526)------------------------------
% 0.20/0.54  % (2512)Success in time 0.184 s
%------------------------------------------------------------------------------