TSTP Solution File: LCL488+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL488+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n025.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 : Tue Apr 30 13:42:33 EDT 2024

% Result   : Theorem 0.21s 0.41s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   68 (  34 unt;   0 def)
%            Number of atoms       :  113 (  20 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   77 (  32   ~;  26   |;   2   &)
%                                         (   6 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   11 (   9 usr;   9 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   94 (  90   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1472,plain,
    $false,
    inference(resolution,[],[f1410,f116]) ).

fof(f116,plain,
    ~ is_a_theorem(implies(and(sK0,sK1),sK1)),
    inference(subsumption_resolution,[],[f102,f83]) ).

fof(f83,plain,
    ~ and_2,
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ~ and_2,
    inference(flattening,[],[f46]) ).

fof(f46,negated_conjecture,
    ~ and_2,
    inference(negated_conjecture,[],[f45]) ).

fof(f45,conjecture,
    and_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).

fof(f102,plain,
    ( and_2
    | ~ is_a_theorem(implies(and(sK0,sK1),sK1)) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f82,plain,
    ( and_2
    | ~ is_a_theorem(implies(and(sK0,sK1),sK1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f72,f81]) ).

fof(f81,plain,
    ( ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X1))
   => ~ is_a_theorem(implies(and(sK0,sK1),sK1)) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ( and_2
    | ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X1)) ),
    inference(ennf_transformation,[],[f64]) ).

fof(f64,plain,
    ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
   => and_2 ),
    inference(unused_predicate_definition_removal,[],[f8]) ).

fof(f8,axiom,
    ( and_2
  <=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_2) ).

fof(f1410,plain,
    ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
    inference(forward_demodulation,[],[f1393,f1226]) ).

fof(f1226,plain,
    ! [X2,X0,X1] : or(implies(X0,not(X1)),X2) = implies(and(X0,X1),X2),
    inference(forward_demodulation,[],[f1204,f111]) ).

fof(f111,plain,
    ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
    inference(subsumption_resolution,[],[f98,f91]) ).

fof(f91,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f43]) ).

fof(f43,axiom,
    op_implies_and,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).

fof(f98,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = not(and(X0,not(X1)))
      | ~ op_implies_and ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
    | ~ op_implies_and ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,axiom,
    ( op_implies_and
   => ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and) ).

fof(f1204,plain,
    ! [X2,X0,X1] : or(implies(X0,not(X1)),X2) = not(and(and(X0,X1),not(X2))),
    inference(superposition,[],[f114,f113]) ).

fof(f113,plain,
    ! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
    inference(forward_demodulation,[],[f112,f110]) ).

fof(f110,plain,
    ! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
    inference(subsumption_resolution,[],[f97,f92]) ).

fof(f92,plain,
    op_implies_or,
    inference(cnf_transformation,[],[f32]) ).

fof(f32,axiom,
    op_implies_or,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).

fof(f97,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = or(not(X0),X1)
      | ~ op_implies_or ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
    | ~ op_implies_or ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,axiom,
    ( op_implies_or
   => ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_or) ).

fof(f112,plain,
    ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
    inference(subsumption_resolution,[],[f99,f94]) ).

fof(f94,plain,
    op_and,
    inference(cnf_transformation,[],[f33]) ).

fof(f33,axiom,
    op_and,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).

fof(f99,plain,
    ! [X0,X1] :
      ( and(X0,X1) = not(or(not(X0),not(X1)))
      | ~ op_and ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
    | ~ op_and ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ( op_and
   => ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_and) ).

fof(f114,plain,
    ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
    inference(subsumption_resolution,[],[f100,f93]) ).

fof(f93,plain,
    op_or,
    inference(cnf_transformation,[],[f42]) ).

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

fof(f100,plain,
    ! [X0,X1] :
      ( or(X0,X1) = not(and(not(X0),not(X1)))
      | ~ op_or ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
    | ~ op_or ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,axiom,
    ( op_or
   => ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).

fof(f1393,plain,
    ! [X0,X1] : is_a_theorem(or(implies(X0,not(X1)),X1)),
    inference(unit_resulting_resolution,[],[f119,f1341,f121]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(implies(X0,X1))
      | is_a_theorem(X1)
      | ~ is_a_theorem(X0) ),
    inference(subsumption_resolution,[],[f107,f90]) ).

fof(f90,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f35]) ).

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

fof(f107,plain,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0)
      | ~ modus_ponens ),
    inference(cnf_transformation,[],[f78]) ).

fof(f78,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(flattening,[],[f77]) ).

fof(f77,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(ennf_transformation,[],[f66]) ).

fof(f66,plain,
    ( modus_ponens
   => ! [X0,X1] :
        ( ( is_a_theorem(implies(X0,X1))
          & is_a_theorem(X0) )
       => is_a_theorem(X1) ) ),
    inference(unused_predicate_definition_removal,[],[f1]) ).

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

fof(f1341,plain,
    ! [X0,X1] : is_a_theorem(or(X0,implies(X1,not(X0)))),
    inference(superposition,[],[f125,f1208]) ).

fof(f1208,plain,
    ! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
    inference(superposition,[],[f114,f111]) ).

fof(f125,plain,
    ! [X0,X1] : is_a_theorem(implies(X1,implies(X0,X1))),
    inference(superposition,[],[f118,f110]) ).

fof(f118,plain,
    ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
    inference(subsumption_resolution,[],[f104,f88]) ).

fof(f88,plain,
    r2,
    inference(cnf_transformation,[],[f37]) ).

fof(f37,axiom,
    r2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r2) ).

fof(f104,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(X1,or(X0,X1)))
      | ~ r2 ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
    | ~ r2 ),
    inference(ennf_transformation,[],[f62]) ).

fof(f62,plain,
    ( r2
   => ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
    inference(unused_predicate_definition_removal,[],[f55]) ).

fof(f55,plain,
    ( r2
  <=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
    inference(rectify,[],[f23]) ).

fof(f23,axiom,
    ( r2
  <=> ! [X3,X4] : is_a_theorem(implies(X4,or(X3,X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2) ).

fof(f119,plain,
    ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
    inference(subsumption_resolution,[],[f105,f87]) ).

fof(f87,plain,
    r3,
    inference(cnf_transformation,[],[f38]) ).

fof(f38,axiom,
    r3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).

fof(f105,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
      | ~ r3 ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
    | ~ r3 ),
    inference(ennf_transformation,[],[f61]) ).

fof(f61,plain,
    ( r3
   => ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
    inference(unused_predicate_definition_removal,[],[f56]) ).

fof(f56,plain,
    ( r3
  <=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
    inference(rectify,[],[f24]) ).

fof(f24,axiom,
    ( r3
  <=> ! [X3,X4] : is_a_theorem(implies(or(X3,X4),or(X4,X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : LCL488+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n025.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Mon Apr 29 22:57:41 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (25861)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38  % (25864)WARNING: value z3 for option sas not known
% 0.21/0.38  % (25865)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38  % (25867)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.38  % (25866)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.38  % (25862)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38  % (25868)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.38  % (25863)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38  % (25864)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.38  TRYING [1]
% 0.21/0.38  TRYING [2]
% 0.21/0.39  TRYING [1]
% 0.21/0.39  TRYING [2]
% 0.21/0.39  TRYING [3]
% 0.21/0.39  TRYING [1]
% 0.21/0.39  TRYING [2]
% 0.21/0.39  TRYING [3]
% 0.21/0.40  TRYING [3]
% 0.21/0.40  TRYING [4]
% 0.21/0.41  % (25868)First to succeed.
% 0.21/0.41  % (25864)Also succeeded, but the first one will report.
% 0.21/0.41  TRYING [4]
% 0.21/0.41  % (25868)Refutation found. Thanks to Tanya!
% 0.21/0.41  % SZS status Theorem for theBenchmark
% 0.21/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.41  % (25868)------------------------------
% 0.21/0.41  % (25868)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.41  % (25868)Termination reason: Refutation
% 0.21/0.41  
% 0.21/0.41  % (25868)Memory used [KB]: 1303
% 0.21/0.41  % (25868)Time elapsed: 0.032 s
% 0.21/0.41  % (25868)Instructions burned: 54 (million)
% 0.21/0.41  % (25868)------------------------------
% 0.21/0.41  % (25868)------------------------------
% 0.21/0.41  % (25861)Success in time 0.04 s
%------------------------------------------------------------------------------