TSTP Solution File: DAT062_1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : DAT062_1 : TPTP v8.1.0. Released v5.5.0.
% 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 : n026.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 16:04:47 EDT 2022

% Result   : Theorem 0.20s 0.57s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   41 (  14 unt;  10 typ;   0 def)
%            Number of atoms       :   78 (  12 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   81 (  34   ~;  23   |;  14   &)
%                                         (   2 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :   73 (  31 atm;  10 fun;   8 num;  24 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    7 (   5   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   56 (  48   !;   8   ?;  56   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    heap: $tType ).

tff(func_def_0,type,
    empty: heap ).

tff(func_def_1,type,
    get: heap > heap ).

tff(func_def_2,type,
    app: ( heap * $int ) > heap ).

tff(func_def_3,type,
    toop: heap > $int ).

tff(func_def_4,type,
    length: heap > $int ).

tff(func_def_9,type,
    sK0: heap ).

tff(func_def_10,type,
    sK1: $int ).

tff(func_def_11,type,
    sK2: heap ).

tff(pred_def_1,type,
    lsls: ( heap * heap ) > $o ).

tff(f644,plain,
    $false,
    inference(resolution,[],[f466,f98]) ).

tff(f98,plain,
    ! [X1: $int] : $less(X1,$sum(1,X1)),
    inference(superposition,[],[f91,f14]) ).

tff(f14,plain,
    ! [X0: $int,X1: $int] : ( $sum(X1,X0) = $sum(X0,X1) ),
    introduced(theory_axiom_140,[]) ).

tff(f91,plain,
    ! [X0: $int] : $less(X0,$sum(X0,1)),
    inference(resolution,[],[f23,f19]) ).

tff(f19,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_147,[]) ).

tff(f23,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,$sum(X0,1))
      | $less(X0,X1) ),
    introduced(theory_axiom_152,[]) ).

tff(f466,plain,
    ~ $less(length(sK0),$sum(1,length(sK0))),
    inference(backward_demodulation,[],[f70,f461]) ).

tff(f461,plain,
    sK2 = sK0,
    inference(resolution,[],[f457,f62]) ).

tff(f62,plain,
    lsls(sK2,app(sK0,sK1)),
    inference(cnf_transformation,[],[f47]) ).

tff(f47,plain,
    ( ! [X2: heap] :
        ( ~ lsls(X2,sK0)
        | $less(length(X2),length(sK0)) )
    & ~ $less(length(sK2),length(app(sK0,sK1)))
    & lsls(sK2,app(sK0,sK1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f37,f46,f45]) ).

tff(f45,plain,
    ( ? [X0: heap,X1: $int] :
        ( ! [X2: heap] :
            ( ~ lsls(X2,X0)
            | $less(length(X2),length(X0)) )
        & ? [X3: heap] :
            ( ~ $less(length(X3),length(app(X0,X1)))
            & lsls(X3,app(X0,X1)) ) )
   => ( ! [X2: heap] :
          ( ~ lsls(X2,sK0)
          | $less(length(X2),length(sK0)) )
      & ? [X3: heap] :
          ( ~ $less(length(X3),length(app(sK0,sK1)))
          & lsls(X3,app(sK0,sK1)) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f46,plain,
    ( ? [X3: heap] :
        ( ~ $less(length(X3),length(app(sK0,sK1)))
        & lsls(X3,app(sK0,sK1)) )
   => ( ~ $less(length(sK2),length(app(sK0,sK1)))
      & lsls(sK2,app(sK0,sK1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f37,plain,
    ? [X0: heap,X1: $int] :
      ( ! [X2: heap] :
          ( ~ lsls(X2,X0)
          | $less(length(X2),length(X0)) )
      & ? [X3: heap] :
          ( ~ $less(length(X3),length(app(X0,X1)))
          & lsls(X3,app(X0,X1)) ) ),
    inference(ennf_transformation,[],[f31]) ).

tff(f31,plain,
    ~ ! [X1: $int,X0: heap] :
        ( ! [X3: heap] :
            ( lsls(X3,app(X0,X1))
           => $less(length(X3),length(app(X0,X1))) )
        | ~ ! [X2: heap] :
              ( lsls(X2,X0)
             => $less(length(X2),length(X0)) ) ),
    inference(rectify,[],[f13]) ).

tff(f13,negated_conjecture,
    ~ ! [X1: heap,X0: $int] :
        ( ~ ! [X2: heap] :
              ( lsls(X2,X1)
             => $less(length(X2),length(X1)) )
        | ! [X2: heap] :
            ( lsls(X2,app(X1,X0))
           => $less(length(X2),length(app(X1,X0))) ) ),
    inference(negated_conjecture,[],[f12]) ).

tff(f12,conjecture,
    ! [X1: heap,X0: $int] :
      ( ~ ! [X2: heap] :
            ( lsls(X2,X1)
           => $less(length(X2),length(X1)) )
      | ! [X2: heap] :
          ( lsls(X2,app(X1,X0))
         => $less(length(X2),length(app(X1,X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',th_lem_1a) ).

tff(f457,plain,
    ! [X71: $int] :
      ( ~ lsls(sK2,app(sK0,X71))
      | ( sK2 = sK0 ) ),
    inference(resolution,[],[f50,f136]) ).

tff(f136,plain,
    ~ lsls(sK2,sK0),
    inference(resolution,[],[f128,f64]) ).

tff(f64,plain,
    ! [X2: heap] :
      ( $less(length(X2),length(sK0))
      | ~ lsls(X2,sK0) ),
    inference(cnf_transformation,[],[f47]) ).

tff(f128,plain,
    ~ $less(length(sK2),length(sK0)),
    inference(resolution,[],[f123,f98]) ).

tff(f123,plain,
    ! [X0: $int] :
      ( ~ $less(X0,$sum(1,length(sK0)))
      | ~ $less(length(sK2),X0) ),
    inference(resolution,[],[f20,f70]) ).

tff(f20,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X0,X2)
      | ~ $less(X0,X1)
      | ~ $less(X1,X2) ),
    introduced(theory_axiom_148,[]) ).

tff(f50,plain,
    ! [X2: $int,X0: heap,X1: heap] :
      ( lsls(X0,X1)
      | ( X0 = X1 )
      | ~ lsls(X0,app(X1,X2)) ),
    inference(cnf_transformation,[],[f39]) ).

tff(f39,plain,
    ! [X0: heap,X1: heap,X2: $int] :
      ( ( lsls(X0,app(X1,X2))
        | ( ~ lsls(X0,X1)
          & ( X0 != X1 ) ) )
      & ( lsls(X0,X1)
        | ( X0 = X1 )
        | ~ lsls(X0,app(X1,X2)) ) ),
    inference(flattening,[],[f38]) ).

tff(f38,plain,
    ! [X0: heap,X1: heap,X2: $int] :
      ( ( lsls(X0,app(X1,X2))
        | ( ~ lsls(X0,X1)
          & ( X0 != X1 ) ) )
      & ( lsls(X0,X1)
        | ( X0 = X1 )
        | ~ lsls(X0,app(X1,X2)) ) ),
    inference(nnf_transformation,[],[f28]) ).

tff(f28,plain,
    ! [X0: heap,X1: heap,X2: $int] :
      ( lsls(X0,app(X1,X2))
    <=> ( lsls(X0,X1)
        | ( X0 = X1 ) ) ),
    inference(rectify,[],[f11]) ).

tff(f11,axiom,
    ! [X2: heap,X1: heap,X0: $int] :
      ( ( ( X1 = X2 )
        | lsls(X2,X1) )
    <=> lsls(X2,app(X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_27) ).

tff(f70,plain,
    ~ $less(length(sK2),$sum(1,length(sK0))),
    inference(forward_demodulation,[],[f63,f65]) ).

tff(f65,plain,
    ! [X0: $int,X1: heap] : ( length(app(X1,X0)) = $sum(1,length(X1)) ),
    inference(cnf_transformation,[],[f7]) ).

tff(f7,axiom,
    ! [X0: $int,X1: heap] : ( length(app(X1,X0)) = $sum(1,length(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_23) ).

tff(f63,plain,
    ~ $less(length(sK2),length(app(sK0,sK1))),
    inference(cnf_transformation,[],[f47]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : DAT062=1 : TPTP v8.1.0. Released v5.5.0.
% 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
% 0.13/0.34  % Computer : n026.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   : Mon Aug 29 21:27:35 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.47  % (305)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)
% 0.20/0.48  % (305)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.48  % (305)Terminated due to inappropriate strategy.
% 0.20/0.48  % (305)------------------------------
% 0.20/0.48  % (305)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.48  % (305)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.48  % (305)Termination reason: Inappropriate
% 0.20/0.48  
% 0.20/0.48  % (305)Memory used [KB]: 895
% 0.20/0.48  % (305)Time elapsed: 0.004 s
% 0.20/0.48  % (305)Instructions burned: 1 (million)
% 0.20/0.48  % (305)------------------------------
% 0.20/0.48  % (305)------------------------------
% 0.20/0.49  % (327)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)
% 0.20/0.50  % (306)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)
% 0.20/0.50  % (321)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)
% 0.20/0.50  % (314)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)
% 0.20/0.51  % (330)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.51  % (313)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.51  % (315)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.51  % (313)Instruction limit reached!
% 0.20/0.51  % (313)------------------------------
% 0.20/0.51  % (313)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (313)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (313)Termination reason: Unknown
% 0.20/0.51  % (313)Termination phase: Saturation
% 0.20/0.51  
% 0.20/0.51  % (313)Memory used [KB]: 5373
% 0.20/0.51  % (313)Time elapsed: 0.004 s
% 0.20/0.51  % (313)Instructions burned: 3 (million)
% 0.20/0.51  % (313)------------------------------
% 0.20/0.51  % (313)------------------------------
% 0.20/0.51  % (307)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)
% 0.20/0.52  % (328)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)
% 0.20/0.52  % (322)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.52  % (322)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.52  % (322)Terminated due to inappropriate strategy.
% 0.20/0.52  % (322)------------------------------
% 0.20/0.52  % (322)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (322)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (322)Termination reason: Inappropriate
% 0.20/0.52  
% 0.20/0.52  % (322)Memory used [KB]: 895
% 0.20/0.52  % (322)Time elapsed: 0.002 s
% 0.20/0.52  % (322)Instructions burned: 2 (million)
% 0.20/0.52  % (322)------------------------------
% 0.20/0.52  % (322)------------------------------
% 0.20/0.52  % (311)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)
% 0.20/0.52  % (311)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.52  % (311)Terminated due to inappropriate strategy.
% 0.20/0.52  % (311)------------------------------
% 0.20/0.52  % (311)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (311)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (311)Termination reason: Inappropriate
% 0.20/0.52  
% 0.20/0.52  % (311)Memory used [KB]: 895
% 0.20/0.52  % (311)Time elapsed: 0.001 s
% 0.20/0.52  % (311)------------------------------
% 0.20/0.52  % (311)------------------------------
% 0.20/0.52  % (320)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  % (319)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  % (308)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)
% 0.20/0.53  % (318)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.53  % (316)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)
% 0.20/0.53  % (317)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.53  % (312)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.53  % (334)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)
% 0.20/0.54  % (329)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.54  % (326)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.54  % (333)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.54  % (331)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)
% 0.20/0.54  % (324)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)
% 0.20/0.54  % (309)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54  % (325)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)
% 0.20/0.54  % (310)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)
% 0.20/0.54  % (323)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.55  % (312)Instruction limit reached!
% 0.20/0.55  % (312)------------------------------
% 0.20/0.55  % (312)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (332)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)
% 0.20/0.55  % (314)First to succeed.
% 0.20/0.56  % (312)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56  % (312)Termination reason: Unknown
% 0.20/0.56  % (312)Termination phase: Saturation
% 0.20/0.56  
% 0.20/0.56  % (312)Memory used [KB]: 5500
% 0.20/0.56  % (312)Time elapsed: 0.120 s
% 0.20/0.56  % (312)Instructions burned: 7 (million)
% 0.20/0.56  % (312)------------------------------
% 0.20/0.56  % (312)------------------------------
% 0.20/0.56  % (306)Instruction limit reached!
% 0.20/0.56  % (306)------------------------------
% 0.20/0.56  % (306)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.57  % (314)Refutation found. Thanks to Tanya!
% 0.20/0.57  % SZS status Theorem for theBenchmark
% 0.20/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.57  % (314)------------------------------
% 0.20/0.57  % (314)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.57  % (314)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.57  % (314)Termination reason: Refutation
% 0.20/0.57  
% 0.20/0.57  % (314)Memory used [KB]: 1407
% 0.20/0.57  % (314)Time elapsed: 0.154 s
% 0.20/0.57  % (314)Instructions burned: 37 (million)
% 0.20/0.57  % (314)------------------------------
% 0.20/0.57  % (314)------------------------------
% 0.20/0.57  % (302)Success in time 0.223 s
%------------------------------------------------------------------------------