TSTP Solution File: KLE007+4 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : KLE007+4 : TPTP v8.1.0. Released v4.0.0.
% 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 : n027.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 17:28:43 EDT 2022

% Result   : Theorem 0.19s 0.57s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   63 (  32 unt;   0 def)
%            Number of atoms       :  140 (  58 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  125 (  48   ~;  34   |;  30   &)
%                                         (   6 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;  10 con; 0-2 aty)
%            Number of variables   :   57 (  49   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f174,plain,
    $false,
    inference(subsumption_resolution,[],[f173,f84]) ).

fof(f84,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] : addition(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).

fof(f173,plain,
    one != addition(one,one),
    inference(resolution,[],[f170,f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( leq(X1,X0)
      | addition(X1,X0) != X0 ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( leq(X1,X0)
      | addition(X1,X0) != X0 ),
    inference(rectify,[],[f41]) ).

fof(f41,plain,
    ! [X1,X0] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X1,X0] :
      ( addition(X0,X1) = X1
     => leq(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f12]) ).

fof(f12,axiom,
    ! [X1,X0] :
      ( leq(X0,X1)
    <=> addition(X0,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).

fof(f170,plain,
    ~ leq(one,one),
    inference(duplicate_literal_removal,[],[f169]) ).

fof(f169,plain,
    ( ~ leq(one,one)
    | ~ leq(one,one) ),
    inference(forward_demodulation,[],[f168,f165]) ).

fof(f165,plain,
    one = sF8,
    inference(backward_demodulation,[],[f137,f161]) ).

fof(f161,plain,
    one = addition(sK1,sF6),
    inference(superposition,[],[f122,f76]) ).

fof(f76,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] : addition(X0,X1) = addition(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).

fof(f122,plain,
    one = addition(sF6,sK1),
    inference(resolution,[],[f69,f99]) ).

fof(f99,plain,
    complement(sK1,sF6),
    inference(subsumption_resolution,[],[f97,f65]) ).

fof(f65,plain,
    test(sK1),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ( test(sK1)
    & test(sK0)
    & ( ~ leq(addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1))),one)
      | ~ leq(one,addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1)))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f45,f46]) ).

fof(f46,plain,
    ( ? [X0,X1] :
        ( test(X1)
        & test(X0)
        & ( ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
          | ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) ) )
   => ( test(sK1)
      & test(sK0)
      & ( ~ leq(addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1))),one)
        | ~ leq(one,addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1)))) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f45,plain,
    ? [X0,X1] :
      ( test(X1)
      & test(X0)
      & ( ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
        | ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) ) ),
    inference(rectify,[],[f35]) ).

fof(f35,plain,
    ? [X1,X0] :
      ( test(X0)
      & test(X1)
      & ( ~ leq(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X1,c(X1)),c(X0))),one)
        | ~ leq(one,addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X1,c(X1)),c(X0)))) ) ),
    inference(flattening,[],[f34]) ).

fof(f34,plain,
    ? [X1,X0] :
      ( ( ~ leq(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X1,c(X1)),c(X0))),one)
        | ~ leq(one,addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X1,c(X1)),c(X0)))) )
      & test(X1)
      & test(X0) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,plain,
    ~ ! [X1,X0] :
        ( ( test(X1)
          & test(X0) )
       => ( leq(one,addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X1,c(X1)),c(X0))))
          & leq(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X1,c(X1)),c(X0))),one) ) ),
    inference(rectify,[],[f20]) ).

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

fof(f19,conjecture,
    ! [X4,X3] :
      ( ( test(X3)
        & test(X4) )
     => ( leq(addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4))),one)
        & leq(one,addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f97,plain,
    ( ~ test(sK1)
    | complement(sK1,sF6) ),
    inference(superposition,[],[f86,f90]) ).

fof(f90,plain,
    sF6 = c(sK1),
    introduced(function_definition,[]) ).

fof(f86,plain,
    ! [X0] :
      ( complement(X0,c(X0))
      | ~ test(X0) ),
    inference(equality_resolution,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( complement(X0,X1)
      | c(X0) != X1
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ( ( complement(X0,X1)
          | c(X0) != X1 )
        & ( c(X0) = X1
          | ~ complement(X0,X1) ) )
      | ~ test(X0) ),
    inference(rectify,[],[f57]) ).

fof(f57,plain,
    ! [X1,X0] :
      ( ( ( complement(X1,X0)
          | c(X1) != X0 )
        & ( c(X1) = X0
          | ~ complement(X1,X0) ) )
      | ~ test(X1) ),
    inference(nnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X1,X0] :
      ( ( complement(X1,X0)
      <=> c(X1) = X0 )
      | ~ test(X1) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X1,X0] :
      ( test(X1)
     => ( complement(X1,X0)
      <=> c(X1) = X0 ) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X4,X3] :
      ( test(X3)
     => ( complement(X3,X4)
      <=> c(X3) = X4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ~ complement(X0,X1)
      | addition(X1,X0) = one ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ( ( addition(X1,X0) = one
          & zero = multiplication(X0,X1)
          & zero = multiplication(X1,X0) )
        | ~ complement(X0,X1) )
      & ( complement(X0,X1)
        | addition(X1,X0) != one
        | zero != multiplication(X0,X1)
        | zero != multiplication(X1,X0) ) ),
    inference(flattening,[],[f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ( ( addition(X1,X0) = one
          & zero = multiplication(X0,X1)
          & zero = multiplication(X1,X0) )
        | ~ complement(X0,X1) )
      & ( complement(X0,X1)
        | addition(X1,X0) != one
        | zero != multiplication(X0,X1)
        | zero != multiplication(X1,X0) ) ),
    inference(nnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( addition(X1,X0) = one
        & zero = multiplication(X0,X1)
        & zero = multiplication(X1,X0) )
    <=> complement(X0,X1) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X4,X3] :
      ( ( zero = multiplication(X4,X3)
        & one = addition(X3,X4)
        & zero = multiplication(X3,X4) )
    <=> complement(X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).

fof(f137,plain,
    sF8 = addition(sK1,sF6),
    inference(backward_demodulation,[],[f135,f136]) ).

fof(f136,plain,
    sK1 = sF5,
    inference(forward_demodulation,[],[f132,f75]) ).

fof(f75,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] : multiplication(one,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).

fof(f132,plain,
    multiplication(one,sK1) = sF5,
    inference(backward_demodulation,[],[f89,f131]) ).

fof(f131,plain,
    one = sF4,
    inference(backward_demodulation,[],[f88,f128]) ).

fof(f128,plain,
    one = addition(sK0,sF3),
    inference(superposition,[],[f121,f76]) ).

fof(f121,plain,
    one = addition(sF3,sK0),
    inference(resolution,[],[f69,f98]) ).

fof(f98,plain,
    complement(sK0,sF3),
    inference(subsumption_resolution,[],[f96,f64]) ).

fof(f64,plain,
    test(sK0),
    inference(cnf_transformation,[],[f47]) ).

fof(f96,plain,
    ( complement(sK0,sF3)
    | ~ test(sK0) ),
    inference(superposition,[],[f86,f87]) ).

fof(f87,plain,
    c(sK0) = sF3,
    introduced(function_definition,[]) ).

fof(f88,plain,
    addition(sK0,sF3) = sF4,
    introduced(function_definition,[]) ).

fof(f89,plain,
    sF5 = multiplication(sF4,sK1),
    introduced(function_definition,[]) ).

fof(f135,plain,
    addition(sF5,sF6) = sF8,
    inference(backward_demodulation,[],[f92,f134]) ).

fof(f134,plain,
    sF7 = sF6,
    inference(forward_demodulation,[],[f133,f75]) ).

fof(f133,plain,
    sF7 = multiplication(one,sF6),
    inference(backward_demodulation,[],[f91,f131]) ).

fof(f91,plain,
    sF7 = multiplication(sF4,sF6),
    introduced(function_definition,[]) ).

fof(f92,plain,
    sF8 = addition(sF5,sF7),
    introduced(function_definition,[]) ).

fof(f168,plain,
    ( ~ leq(sF8,one)
    | ~ leq(one,one) ),
    inference(backward_demodulation,[],[f93,f165]) ).

fof(f93,plain,
    ( ~ leq(sF8,one)
    | ~ leq(one,sF8) ),
    inference(definition_folding,[],[f63,f92,f91,f90,f88,f87,f89,f88,f87,f92,f91,f90,f88,f87,f89,f88,f87]) ).

fof(f63,plain,
    ( ~ leq(addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1))),one)
    | ~ leq(one,addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1)))) ),
    inference(cnf_transformation,[],[f47]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : KLE007+4 : TPTP v8.1.0. Released v4.0.0.
% 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 : n027.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   : Tue Aug 30 00:36:30 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.54  % (3540)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.55  % (3548)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)
% 0.19/0.55  % (3555)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)
% 0.19/0.55  % (3539)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)
% 0.19/0.55  % (3548)First to succeed.
% 0.19/0.56  % (3547)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)
% 0.19/0.56  TRYING [1]
% 0.19/0.56  % (3540)Instruction limit reached!
% 0.19/0.56  % (3540)------------------------------
% 0.19/0.56  % (3540)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.56  TRYING [2]
% 0.19/0.56  TRYING [3]
% 0.19/0.56  % (3556)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)
% 0.19/0.57  % (3548)Refutation found. Thanks to Tanya!
% 0.19/0.57  % SZS status Theorem for theBenchmark
% 0.19/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.57  % (3548)------------------------------
% 0.19/0.57  % (3548)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.57  % (3548)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.57  % (3548)Termination reason: Refutation
% 0.19/0.57  
% 0.19/0.57  % (3548)Memory used [KB]: 1023
% 0.19/0.57  % (3548)Time elapsed: 0.131 s
% 0.19/0.57  % (3548)Instructions burned: 7 (million)
% 0.19/0.57  % (3548)------------------------------
% 0.19/0.57  % (3548)------------------------------
% 0.19/0.57  % (3532)Success in time 0.219 s
%------------------------------------------------------------------------------