TSTP Solution File: KLE022+4 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KLE022+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n006.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 13:11:42 EDT 2024

% Result   : Theorem 0.21s 0.38s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   44 (  13 unt;   0 def)
%            Number of atoms       :  107 (  41 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  109 (  46   ~;  32   |;  18   &)
%                                         (   6 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   57 (  53   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f128,plain,
    $false,
    inference(resolution,[],[f127,f98]) ).

fof(f98,plain,
    ! [X0] : leq(X0,X0),
    inference(trivial_inequality_removal,[],[f93]) ).

fof(f93,plain,
    ! [X0] :
      ( X0 != X0
      | leq(X0,X0) ),
    inference(superposition,[],[f67,f54]) ).

fof(f54,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] : addition(X0,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).

fof(f67,plain,
    ! [X0,X1] :
      ( addition(X0,X1) != X1
      | leq(X0,X1) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( addition(X0,X1) = X1
     => leq(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( leq(X0,X1)
    <=> addition(X0,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).

fof(f127,plain,
    ~ leq(sK0,sK0),
    inference(duplicate_literal_removal,[],[f126]) ).

fof(f126,plain,
    ( ~ leq(sK0,sK0)
    | ~ leq(sK0,sK0) ),
    inference(forward_demodulation,[],[f125,f52]) ).

fof(f52,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : multiplication(X0,one) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).

fof(f125,plain,
    ( ~ leq(multiplication(sK0,one),sK0)
    | ~ leq(sK0,sK0) ),
    inference(forward_demodulation,[],[f124,f120]) ).

fof(f120,plain,
    one = addition(sK1,c(sK1)),
    inference(resolution,[],[f91,f47]) ).

fof(f47,plain,
    test(sK1),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ( ( ~ leq(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),sK0)
      | ~ leq(sK0,addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1)))) )
    & test(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f30,f38]) ).

fof(f38,plain,
    ( ? [X0,X1] :
        ( ( ~ leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0)
          | ~ leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))) )
        & test(X1) )
   => ( ( ~ leq(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),sK0)
        | ~ leq(sK0,addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1)))) )
      & test(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ? [X0,X1] :
      ( ( ~ leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0)
        | ~ leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))) )
      & test(X1) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ~ ! [X0,X1] :
        ( test(X1)
       => ( leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0)
          & leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ! [X3,X4] :
        ( test(X4)
       => ( leq(addition(multiplication(X3,X4),multiplication(X3,c(X4))),X3)
          & leq(X3,addition(multiplication(X3,X4),multiplication(X3,c(X4)))) ) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ! [X3,X4] :
      ( test(X4)
     => ( leq(addition(multiplication(X3,X4),multiplication(X3,c(X4))),X3)
        & leq(X3,addition(multiplication(X3,X4),multiplication(X3,c(X4)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(f91,plain,
    ! [X0] :
      ( ~ test(X0)
      | one = addition(X0,c(X0)) ),
    inference(forward_demodulation,[],[f90,f58]) ).

fof(f58,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).

fof(f90,plain,
    ! [X0] :
      ( one = addition(c(X0),X0)
      | ~ test(X0) ),
    inference(resolution,[],[f65,f72]) ).

fof(f72,plain,
    ! [X0] :
      ( complement(X0,c(X0))
      | ~ test(X0) ),
    inference(equality_resolution,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( complement(X0,X1)
      | c(X0) != X1
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ( ( c(X0) = X1
          | ~ complement(X0,X1) )
        & ( complement(X0,X1)
          | c(X0) != X1 ) )
      | ~ test(X0) ),
    inference(nnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ( c(X0) = X1
      <=> complement(X0,X1) )
      | ~ test(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( test(X0)
     => ( c(X0) = X1
      <=> complement(X0,X1) ) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X3,X4] :
      ( test(X3)
     => ( c(X3) = X4
      <=> complement(X3,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | addition(X0,X1) = one ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ( complement(X1,X0)
        | addition(X0,X1) != one
        | zero != multiplication(X1,X0)
        | zero != multiplication(X0,X1) )
      & ( ( addition(X0,X1) = one
          & zero = multiplication(X1,X0)
          & zero = multiplication(X0,X1) )
        | ~ complement(X1,X0) ) ),
    inference(flattening,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ( complement(X1,X0)
        | addition(X0,X1) != one
        | zero != multiplication(X1,X0)
        | zero != multiplication(X0,X1) )
      & ( ( addition(X0,X1) = one
          & zero = multiplication(X1,X0)
          & zero = multiplication(X0,X1) )
        | ~ complement(X1,X0) ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( complement(X1,X0)
    <=> ( addition(X0,X1) = one
        & zero = multiplication(X1,X0)
        & zero = multiplication(X0,X1) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X3,X4] :
      ( complement(X4,X3)
    <=> ( one = addition(X3,X4)
        & zero = multiplication(X4,X3)
        & zero = multiplication(X3,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).

fof(f124,plain,
    ( ~ leq(sK0,sK0)
    | ~ leq(multiplication(sK0,addition(sK1,c(sK1))),sK0) ),
    inference(forward_demodulation,[],[f123,f52]) ).

fof(f123,plain,
    ( ~ leq(sK0,multiplication(sK0,one))
    | ~ leq(multiplication(sK0,addition(sK1,c(sK1))),sK0) ),
    inference(backward_demodulation,[],[f74,f120]) ).

fof(f74,plain,
    ( ~ leq(multiplication(sK0,addition(sK1,c(sK1))),sK0)
    | ~ leq(sK0,multiplication(sK0,addition(sK1,c(sK1)))) ),
    inference(forward_demodulation,[],[f73,f70]) ).

fof(f70,plain,
    ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    inference(cnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).

fof(f73,plain,
    ( ~ leq(sK0,multiplication(sK0,addition(sK1,c(sK1))))
    | ~ leq(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),sK0) ),
    inference(backward_demodulation,[],[f48,f70]) ).

fof(f48,plain,
    ( ~ leq(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),sK0)
    | ~ leq(sK0,addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1)))) ),
    inference(cnf_transformation,[],[f39]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : KLE022+4 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n006.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Apr 30 04:58:20 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  % (16882)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.36  % (16886)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37  TRYING [1]
% 0.15/0.37  TRYING [2]
% 0.15/0.37  TRYING [3]
% 0.15/0.37  % (16885)WARNING: value z3 for option sas not known
% 0.15/0.37  % (16883)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37  % (16884)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37  % (16885)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)
% 0.15/0.37  % (16887)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)
% 0.15/0.37  % (16888)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)
% 0.15/0.37  % (16889)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)
% 0.15/0.37  TRYING [4]
% 0.15/0.38  % (16888)First to succeed.
% 0.21/0.38  % (16888)Refutation found. Thanks to Tanya!
% 0.21/0.38  % SZS status Theorem for theBenchmark
% 0.21/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38  % (16888)------------------------------
% 0.21/0.38  % (16888)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.38  % (16888)Termination reason: Refutation
% 0.21/0.38  
% 0.21/0.38  % (16888)Memory used [KB]: 896
% 0.21/0.38  % (16888)Time elapsed: 0.007 s
% 0.21/0.38  % (16888)Instructions burned: 8 (million)
% 0.21/0.38  % (16888)------------------------------
% 0.21/0.38  % (16888)------------------------------
% 0.21/0.38  % (16882)Success in time 0.024 s
%------------------------------------------------------------------------------