TSTP Solution File: LCL531+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : LCL531+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : n024.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 17:48:38 EDT 2022

% Result   : Theorem 0.20s 0.52s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   56 (  22 unt;   0 def)
%            Number of atoms       :  107 (   5 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   88 (  37   ~;  29   |;   3   &)
%                                         (   7 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    9 (   7 usr;   7 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   62 (  60   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f316,plain,
    $false,
    inference(resolution,[],[f305,f272]) ).

fof(f272,plain,
    ~ is_a_theorem(implies(sK0,and(sK0,sK0))),
    inference(resolution,[],[f271,f243]) ).

fof(f243,plain,
    ! [X0] :
      ( is_a_theorem(necessarily(X0))
      | ~ is_a_theorem(X0) ),
    inference(subsumption_resolution,[],[f215,f232]) ).

fof(f232,plain,
    necessitation,
    inference(cnf_transformation,[],[f78]) ).

fof(f78,axiom,
    necessitation,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_necessitation) ).

fof(f215,plain,
    ! [X0] :
      ( is_a_theorem(necessarily(X0))
      | ~ necessitation
      | ~ is_a_theorem(X0) ),
    inference(cnf_transformation,[],[f167]) ).

fof(f167,plain,
    ( ~ necessitation
    | ! [X0] :
        ( ~ is_a_theorem(X0)
        | is_a_theorem(necessarily(X0)) ) ),
    inference(ennf_transformation,[],[f128]) ).

fof(f128,plain,
    ( necessitation
   => ! [X0] :
        ( is_a_theorem(X0)
       => is_a_theorem(necessarily(X0)) ) ),
    inference(unused_predicate_definition_removal,[],[f50]) ).

fof(f50,axiom,
    ( necessitation
  <=> ! [X0] :
        ( is_a_theorem(X0)
       => is_a_theorem(necessarily(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation) ).

fof(f271,plain,
    ~ is_a_theorem(necessarily(implies(sK0,and(sK0,sK0)))),
    inference(backward_demodulation,[],[f245,f270]) ).

fof(f270,plain,
    ! [X0,X1] : strict_implies(X1,X0) = necessarily(implies(X1,X0)),
    inference(subsumption_resolution,[],[f226,f240]) ).

fof(f240,plain,
    op_strict_implies,
    inference(cnf_transformation,[],[f85]) ).

fof(f85,axiom,
    op_strict_implies,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).

fof(f226,plain,
    ! [X0,X1] :
      ( strict_implies(X1,X0) = necessarily(implies(X1,X0))
      | ~ op_strict_implies ),
    inference(cnf_transformation,[],[f183]) ).

fof(f183,plain,
    ( ! [X0,X1] : strict_implies(X1,X0) = necessarily(implies(X1,X0))
    | ~ op_strict_implies ),
    inference(rectify,[],[f150]) ).

fof(f150,plain,
    ( ! [X1,X0] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
    | ~ op_strict_implies ),
    inference(ennf_transformation,[],[f75]) ).

fof(f75,axiom,
    ( op_strict_implies
   => ! [X1,X0] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).

fof(f245,plain,
    ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))),
    inference(subsumption_resolution,[],[f194,f203]) ).

fof(f203,plain,
    ~ axiom_m4,
    inference(cnf_transformation,[],[f115]) ).

fof(f115,plain,
    ~ axiom_m4,
    inference(flattening,[],[f89]) ).

fof(f89,negated_conjecture,
    ~ axiom_m4,
    inference(negated_conjecture,[],[f88]) ).

fof(f88,conjecture,
    axiom_m4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m4) ).

fof(f194,plain,
    ( axiom_m4
    | ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f178,plain,
    ( axiom_m4
    | ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f152,f177]) ).

fof(f177,plain,
    ( ? [X0] : ~ is_a_theorem(strict_implies(X0,and(X0,X0)))
   => ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))) ),
    introduced(choice_axiom,[]) ).

fof(f152,plain,
    ( axiom_m4
    | ? [X0] : ~ is_a_theorem(strict_implies(X0,and(X0,X0))) ),
    inference(ennf_transformation,[],[f124]) ).

fof(f124,plain,
    ( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
   => axiom_m4 ),
    inference(unused_predicate_definition_removal,[],[f66]) ).

fof(f66,axiom,
    ( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
  <=> axiom_m4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m4) ).

fof(f305,plain,
    ! [X1] : is_a_theorem(implies(X1,and(X1,X1))),
    inference(resolution,[],[f277,f256]) ).

fof(f256,plain,
    ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
    inference(subsumption_resolution,[],[f192,f206]) ).

fof(f206,plain,
    and_3,
    inference(cnf_transformation,[],[f42]) ).

fof(f42,axiom,
    and_3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).

fof(f192,plain,
    ! [X0,X1] :
      ( ~ and_3
      | is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
    inference(cnf_transformation,[],[f176]) ).

fof(f176,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
    | ~ and_3 ),
    inference(rectify,[],[f155]) ).

fof(f155,plain,
    ( ! [X1,X0] : is_a_theorem(implies(X1,implies(X0,and(X1,X0))))
    | ~ and_3 ),
    inference(ennf_transformation,[],[f135]) ).

fof(f135,plain,
    ( and_3
   => ! [X1,X0] : is_a_theorem(implies(X1,implies(X0,and(X1,X0)))) ),
    inference(unused_predicate_definition_removal,[],[f121]) ).

fof(f121,plain,
    ( ! [X1,X0] : is_a_theorem(implies(X1,implies(X0,and(X1,X0))))
  <=> and_3 ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ( ! [X1,X0] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
  <=> and_3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3) ).

fof(f277,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(implies(X0,implies(X0,X1)))
      | is_a_theorem(implies(X0,X1)) ),
    inference(resolution,[],[f276,f258]) ).

fof(f258,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(implies(X1,X0))
      | is_a_theorem(X0)
      | ~ is_a_theorem(X1) ),
    inference(subsumption_resolution,[],[f216,f229]) ).

fof(f229,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f35]) ).

fof(f35,axiom,
    modus_ponens,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).

fof(f216,plain,
    ! [X0,X1] :
      ( ~ modus_ponens
      | is_a_theorem(X0)
      | ~ is_a_theorem(implies(X1,X0))
      | ~ is_a_theorem(X1) ),
    inference(cnf_transformation,[],[f174]) ).

fof(f174,plain,
    ( ~ modus_ponens
    | ! [X0,X1] :
        ( ~ is_a_theorem(implies(X1,X0))
        | is_a_theorem(X0)
        | ~ is_a_theorem(X1) ) ),
    inference(flattening,[],[f173]) ).

fof(f173,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X0)
        | ~ is_a_theorem(X1)
        | ~ is_a_theorem(implies(X1,X0)) )
    | ~ modus_ponens ),
    inference(ennf_transformation,[],[f143]) ).

fof(f143,plain,
    ( modus_ponens
   => ! [X0,X1] :
        ( ( is_a_theorem(X1)
          & is_a_theorem(implies(X1,X0)) )
       => is_a_theorem(X0) ) ),
    inference(unused_predicate_definition_removal,[],[f98]) ).

fof(f98,plain,
    ( ! [X0,X1] :
        ( ( is_a_theorem(X1)
          & is_a_theorem(implies(X1,X0)) )
       => is_a_theorem(X0) )
  <=> modus_ponens ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ( modus_ponens
  <=> ! [X1,X0] :
        ( ( is_a_theorem(X0)
          & is_a_theorem(implies(X0,X1)) )
       => is_a_theorem(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).

fof(f276,plain,
    ! [X0,X1] : is_a_theorem(implies(implies(X1,implies(X1,X0)),implies(X1,X0))),
    inference(subsumption_resolution,[],[f201,f188]) ).

fof(f188,plain,
    implies_2,
    inference(cnf_transformation,[],[f38]) ).

fof(f38,axiom,
    implies_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).

fof(f201,plain,
    ! [X0,X1] :
      ( ~ implies_2
      | is_a_theorem(implies(implies(X1,implies(X1,X0)),implies(X1,X0))) ),
    inference(cnf_transformation,[],[f179]) ).

fof(f179,plain,
    ( ! [X0,X1] : is_a_theorem(implies(implies(X1,implies(X1,X0)),implies(X1,X0)))
    | ~ implies_2 ),
    inference(rectify,[],[f160]) ).

fof(f160,plain,
    ( ! [X1,X0] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
    | ~ implies_2 ),
    inference(ennf_transformation,[],[f139]) ).

fof(f139,plain,
    ( implies_2
   => ! [X1,X0] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
    inference(unused_predicate_definition_removal,[],[f5]) ).

fof(f5,axiom,
    ( ! [X1,X0] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
  <=> implies_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : LCL531+1 : TPTP v8.1.0. Released v3.3.0.
% 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
% 0.13/0.35  % Computer : n024.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 02:09:19 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  % (5150)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)
% 0.20/0.50  % (5159)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)
% 0.20/0.50  % (5161)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  % (5146)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.51  % (5153)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)
% 0.20/0.51  % (5146)Instruction limit reached!
% 0.20/0.51  % (5146)------------------------------
% 0.20/0.51  % (5146)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (5145)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)
% 0.20/0.51  % (5149)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  % (5165)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)
% 0.20/0.51  % (5146)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (5146)Termination reason: Unknown
% 0.20/0.51  % (5146)Termination phase: Saturation
% 0.20/0.51  
% 0.20/0.51  % (5146)Memory used [KB]: 5756
% 0.20/0.51  % (5146)Time elapsed: 0.105 s
% 0.20/0.51  % (5146)Instructions burned: 8 (million)
% 0.20/0.51  % (5146)------------------------------
% 0.20/0.51  % (5146)------------------------------
% 0.20/0.51  % (5148)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  % (5161)First to succeed.
% 0.20/0.52  % (5139)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  TRYING [1]
% 0.20/0.52  TRYING [1]
% 0.20/0.52  % (5161)Refutation found. Thanks to Tanya!
% 0.20/0.52  % SZS status Theorem for theBenchmark
% 0.20/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52  % (5161)------------------------------
% 0.20/0.52  % (5161)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (5161)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (5161)Termination reason: Refutation
% 0.20/0.52  
% 0.20/0.52  % (5161)Memory used [KB]: 1151
% 0.20/0.52  % (5161)Time elapsed: 0.065 s
% 0.20/0.52  % (5161)Instructions burned: 6 (million)
% 0.20/0.52  % (5161)------------------------------
% 0.20/0.52  % (5161)------------------------------
% 0.20/0.52  % (5138)Success in time 0.163 s
%------------------------------------------------------------------------------