TSTP Solution File: SET843-1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET843-1 : 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 : 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 18:25:51 EDT 2022

% Result   : Unsatisfiable 1.32s 0.62s
% Output   : Refutation 1.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   38 (   6 unt;   0 def)
%            Number of atoms       :   85 (  15 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   90 (  43   ~;  45   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    7 (   5 usr;   3 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   29 (  29   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1511,plain,
    $false,
    inference(avatar_sat_refutation,[],[f1376,f1378,f1481,f1510]) ).

fof(f1510,plain,
    ( ~ spl0_1
    | spl0_2 ),
    inference(avatar_contradiction_clause,[],[f1509]) ).

fof(f1509,plain,
    ( $false
    | ~ spl0_1
    | spl0_2 ),
    inference(subsumption_resolution,[],[f1508,f1492]) ).

fof(f1492,plain,
    ( ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | spl0_2 ),
    inference(subsumption_resolution,[],[f1488,f1374]) ).

fof(f1374,plain,
    ( v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
    | spl0_2 ),
    inference(avatar_component_clause,[],[f1373]) ).

fof(f1373,plain,
    ( spl0_2
  <=> v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f1488,plain,
    ( ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
    inference(resolution,[],[f1379,f309]) ).

fof(f309,axiom,
    ! [X2,X15,X13] :
      ( ~ c_lessequals(X15,X13,tc_set(X2))
      | ~ c_lessequals(X13,X15,tc_set(X2))
      | X13 = X15 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).

fof(f1379,plain,
    c_lessequals(v_m,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
    inference(resolution,[],[f1360,f1365]) ).

fof(f1365,axiom,
    c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

fof(f1360,axiom,
    ! [X2,X15,X13] :
      ( ~ c_in(X15,X13,tc_set(X2))
      | c_lessequals(X15,c_Union(X13,X2),tc_set(X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__upper_0) ).

fof(f1508,plain,
    ( c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | ~ spl0_1 ),
    inference(subsumption_resolution,[],[f1505,f447]) ).

fof(f447,axiom,
    ! [X51] : class_Orderings_Oorder(tc_set(X51)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).

fof(f1505,plain,
    ( ~ class_Orderings_Oorder(tc_set(tc_set(tc_set(t_a))))
    | c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | ~ spl0_1 ),
    inference(resolution,[],[f1497,f266]) ).

fof(f266,axiom,
    ! [X2,X0] :
      ( c_lessequals(X0,X0,X2)
      | ~ class_Orderings_Oorder(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).

fof(f1497,plain,
    ( ! [X1] :
        ( ~ c_lessequals(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a))))
        | c_lessequals(c_Union(X1,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) )
    | ~ spl0_1 ),
    inference(resolution,[],[f1487,f1363]) ).

fof(f1363,axiom,
    ! [X2,X40,X54] :
      ( c_in(c_Union(X54,tc_set(X2)),c_Zorn_OTFin(X40,X2),tc_set(tc_set(X2)))
      | ~ c_lessequals(X54,c_Zorn_OTFin(X40,X2),tc_set(tc_set(tc_set(X2)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).

fof(f1487,plain,
    ( ! [X0] :
        ( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
        | c_lessequals(X0,v_m,tc_set(tc_set(t_a))) )
    | ~ spl0_1 ),
    inference(subsumption_resolution,[],[f1486,f1365]) ).

fof(f1486,plain,
    ( ! [X0] :
        ( c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
        | ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
        | ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )
    | ~ spl0_1 ),
    inference(trivial_inequality_removal,[],[f1483]) ).

fof(f1483,plain,
    ( ! [X0] :
        ( v_m != v_m
        | ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
        | ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
        | c_lessequals(X0,v_m,tc_set(tc_set(t_a))) )
    | ~ spl0_1 ),
    inference(superposition,[],[f1364,f1371]) ).

fof(f1371,plain,
    ( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f1369]) ).

fof(f1369,plain,
    ( spl0_1
  <=> v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f1364,axiom,
    ! [X40,X2,X18,X12] :
      ( c_Zorn_Osucc(X40,X12,X2) != X12
      | ~ c_in(X12,c_Zorn_OTFin(X40,X2),tc_set(tc_set(X2)))
      | ~ c_in(X18,c_Zorn_OTFin(X40,X2),tc_set(tc_set(X2)))
      | c_lessequals(X18,X12,tc_set(tc_set(X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Oeq__succ__upper_0) ).

fof(f1481,plain,
    ( spl0_1
    | ~ spl0_2 ),
    inference(avatar_contradiction_clause,[],[f1480]) ).

fof(f1480,plain,
    ( $false
    | spl0_1
    | ~ spl0_2 ),
    inference(subsumption_resolution,[],[f1479,f1361]) ).

fof(f1361,axiom,
    ! [X40,X2,X0] : c_lessequals(X0,c_Zorn_Osucc(X40,X0,X2),tc_set(tc_set(X2))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).

fof(f1479,plain,
    ( ~ c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
    | spl0_1
    | ~ spl0_2 ),
    inference(subsumption_resolution,[],[f1472,f1370]) ).

fof(f1370,plain,
    ( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
    | spl0_1 ),
    inference(avatar_component_clause,[],[f1369]) ).

fof(f1472,plain,
    ( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
    | ~ c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
    | ~ spl0_2 ),
    inference(resolution,[],[f1465,f309]) ).

fof(f1465,plain,
    ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a)))
    | ~ spl0_2 ),
    inference(forward_demodulation,[],[f1462,f1375]) ).

fof(f1375,plain,
    ( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f1373]) ).

fof(f1462,plain,
    c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
    inference(resolution,[],[f1384,f1365]) ).

fof(f1384,plain,
    ! [X6,X4,X5] :
      ( ~ c_in(X4,c_Zorn_OTFin(X5,X6),tc_set(tc_set(X6)))
      | c_lessequals(c_Zorn_Osucc(X5,X4,X6),c_Union(c_Zorn_OTFin(X5,X6),tc_set(X6)),tc_set(tc_set(X6))) ),
    inference(resolution,[],[f1362,f1360]) ).

fof(f1362,axiom,
    ! [X40,X2,X0] :
      ( c_in(c_Zorn_Osucc(X40,X0,X2),c_Zorn_OTFin(X40,X2),tc_set(tc_set(X2)))
      | ~ c_in(X0,c_Zorn_OTFin(X40,X2),tc_set(tc_set(X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin_OsuccI_0) ).

fof(f1378,plain,
    ( ~ spl0_1
    | ~ spl0_2 ),
    inference(avatar_split_clause,[],[f1366,f1373,f1369]) ).

fof(f1366,axiom,
    ( v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
    | v_m != c_Zorn_Osucc(v_S,v_m,t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f1376,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f1367,f1373,f1369]) ).

fof(f1367,axiom,
    ( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
    | v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET843-1 : TPTP v8.1.0. Released v3.2.0.
% 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
% 0.12/0.34  % Computer : n023.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 14:45:05 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 1.11/0.54  % (22503)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)
% 1.11/0.54  % (22507)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.32/0.54  % (22515)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.32/0.54  % (22525)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)
% 1.32/0.54  % (22517)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)
% 1.32/0.55  % (22504)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)
% 1.32/0.55  % (22532)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)
% 1.32/0.55  % (22524)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.32/0.55  % (22505)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)
% 1.32/0.55  % (22506)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)
% 1.32/0.55  % (22509)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)
% 1.32/0.55  % (22523)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)
% 1.32/0.55  % (22510)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.32/0.56  % (22530)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)
% 1.32/0.56  % (22508)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)
% 1.32/0.56  % (22529)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)
% 1.32/0.56  % (22520)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.32/0.56  % (22518)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)
% 1.32/0.56  % (22510)Instruction limit reached!
% 1.32/0.56  % (22510)------------------------------
% 1.32/0.56  % (22510)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.32/0.56  % (22519)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)
% 1.32/0.56  % (22531)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.32/0.57  % (22513)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.32/0.57  % (22511)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.32/0.57  % (22510)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.32/0.57  % (22510)Termination reason: Unknown
% 1.32/0.57  % (22510)Termination phase: Saturation
% 1.32/0.57  
% 1.32/0.57  % (22510)Memory used [KB]: 6652
% 1.32/0.57  % (22510)Time elapsed: 0.008 s
% 1.32/0.57  % (22510)Instructions burned: 8 (million)
% 1.32/0.57  % (22510)------------------------------
% 1.32/0.57  % (22510)------------------------------
% 1.32/0.57  % (22511)Instruction limit reached!
% 1.32/0.57  % (22511)------------------------------
% 1.32/0.57  % (22511)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.32/0.57  % (22511)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.32/0.57  % (22511)Termination reason: Unknown
% 1.32/0.57  % (22511)Termination phase: shuffling
% 1.32/0.57  
% 1.32/0.57  % (22511)Memory used [KB]: 1791
% 1.32/0.57  % (22511)Time elapsed: 0.002 s
% 1.32/0.57  % (22511)Instructions burned: 2 (million)
% 1.32/0.57  % (22511)------------------------------
% 1.32/0.57  % (22511)------------------------------
% 1.32/0.57  % (22512)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)
% 1.32/0.57  % (22522)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)
% 1.32/0.57  % (22528)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.32/0.57  % (22514)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)
% 1.32/0.58  % (22516)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.32/0.58  % (22526)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)
% 1.32/0.58  % (22521)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.32/0.58  % (22527)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.32/0.61  % (22523)First to succeed.
% 1.32/0.62  % (22523)Refutation found. Thanks to Tanya!
% 1.32/0.62  % SZS status Unsatisfiable for theBenchmark
% 1.32/0.62  % SZS output start Proof for theBenchmark
% See solution above
% 1.32/0.62  % (22523)------------------------------
% 1.32/0.62  % (22523)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.32/0.62  % (22523)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.32/0.62  % (22523)Termination reason: Refutation
% 1.32/0.62  
% 1.32/0.62  % (22523)Memory used [KB]: 7291
% 1.32/0.62  % (22523)Time elapsed: 0.174 s
% 1.32/0.62  % (22523)Instructions burned: 42 (million)
% 1.32/0.62  % (22523)------------------------------
% 1.32/0.62  % (22523)------------------------------
% 1.32/0.62  % (22502)Success in time 0.269 s
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