TSTP Solution File: KLE007+2 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : KLE007+2 : 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_uns --cores 0 -t %d %s

% Computer : n010.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 17:27:32 EDT 2022

% Result   : Theorem 1.87s 0.60s
% Output   : Refutation 1.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   66 (  26 unt;   0 def)
%            Number of atoms       :  147 (  49 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  129 (  48   ~;  39   |;  27   &)
%                                         (   8 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    7 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   69 (  63   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f231,plain,
    $false,
    inference(avatar_sat_refutation,[],[f84,f213,f227]) ).

fof(f227,plain,
    spl3_2,
    inference(avatar_contradiction_clause,[],[f226]) ).

fof(f226,plain,
    ( $false
    | spl3_2 ),
    inference(subsumption_resolution,[],[f225,f166]) ).

fof(f166,plain,
    ! [X0] : leq(X0,X0),
    inference(trivial_inequality_removal,[],[f153]) ).

fof(f153,plain,
    ! [X0] :
      ( X0 != X0
      | leq(X0,X0) ),
    inference(superposition,[],[f61,f66]) ).

fof(f66,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(f61,plain,
    ! [X0,X1] :
      ( addition(X0,X1) != X1
      | leq(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,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(f225,plain,
    ( ~ leq(one,one)
    | spl3_2 ),
    inference(forward_demodulation,[],[f224,f132]) ).

fof(f132,plain,
    one = addition(sK1,c(sK1)),
    inference(superposition,[],[f55,f127]) ).

fof(f127,plain,
    one = addition(c(sK1),sK1),
    inference(unit_resulting_resolution,[],[f87,f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | addition(X0,X1) = one ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ( ( zero = multiplication(X0,X1)
          & addition(X0,X1) = one
          & zero = multiplication(X1,X0) )
        | ~ complement(X1,X0) )
      & ( complement(X1,X0)
        | zero != multiplication(X0,X1)
        | addition(X0,X1) != one
        | zero != multiplication(X1,X0) ) ),
    inference(flattening,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ( ( zero = multiplication(X0,X1)
          & addition(X0,X1) = one
          & zero = multiplication(X1,X0) )
        | ~ complement(X1,X0) )
      & ( complement(X1,X0)
        | zero != multiplication(X0,X1)
        | addition(X0,X1) != one
        | zero != multiplication(X1,X0) ) ),
    inference(nnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( zero = multiplication(X0,X1)
        & addition(X0,X1) = one
        & zero = multiplication(X1,X0) )
    <=> complement(X1,X0) ),
    inference(rectify,[],[f14]) ).

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

fof(f87,plain,
    complement(sK1,c(sK1)),
    inference(unit_resulting_resolution,[],[f71,f73]) ).

fof(f73,plain,
    ! [X1] :
      ( complement(X1,c(X1))
      | ~ test(X1) ),
    inference(equality_resolution,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ~ test(X1)
      | complement(X1,X0)
      | c(X1) != X0 ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ test(X1)
      | ( ( complement(X1,X0)
          | c(X1) != X0 )
        & ( c(X1) = X0
          | ~ complement(X1,X0) ) ) ),
    inference(nnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ test(X1)
      | ( complement(X1,X0)
      <=> c(X1) = X0 ) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( test(X1)
     => ( complement(X1,X0)
      <=> c(X1) = X0 ) ),
    inference(rectify,[],[f15]) ).

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

fof(f71,plain,
    test(sK1),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ( test(sK2)
    & test(sK1)
    & ( ~ leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
      | ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2)))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f31,f47]) ).

fof(f47,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(sK2)
      & test(sK1)
      & ( ~ leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
        | ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2)))) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,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(flattening,[],[f30]) ).

fof(f30,plain,
    ? [X1,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(X1)
      & test(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ~ ! [X1,X0] :
        ( ( test(X1)
          & test(X0) )
       => ( leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
          & leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,negated_conjecture,
    ~ ! [X3,X4] :
        ( ( test(X3)
          & test(X4) )
       => ( leq(one,addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4))))
          & leq(addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4))),one) ) ),
    inference(negated_conjecture,[],[f17]) ).

fof(f17,conjecture,
    ! [X3,X4] :
      ( ( test(X3)
        & test(X4) )
     => ( leq(one,addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4))))
        & leq(addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4))),one) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(f55,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(rectify,[],[f24]) ).

fof(f24,plain,
    ! [X1,X0] : addition(X0,X1) = addition(X1,X0),
    inference(rectify,[],[f1]) ).

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

fof(f224,plain,
    ( ~ leq(one,addition(sK1,c(sK1)))
    | spl3_2 ),
    inference(forward_demodulation,[],[f223,f59]) ).

fof(f59,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(f223,plain,
    ( ~ leq(one,multiplication(addition(sK1,c(sK1)),one))
    | spl3_2 ),
    inference(forward_demodulation,[],[f83,f138]) ).

fof(f138,plain,
    one = addition(sK2,c(sK2)),
    inference(superposition,[],[f55,f128]) ).

fof(f128,plain,
    one = addition(c(sK2),sK2),
    inference(unit_resulting_resolution,[],[f88,f52]) ).

fof(f88,plain,
    complement(sK2,c(sK2)),
    inference(unit_resulting_resolution,[],[f72,f73]) ).

fof(f72,plain,
    test(sK2),
    inference(cnf_transformation,[],[f48]) ).

fof(f83,plain,
    ( ~ leq(one,multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))))
    | spl3_2 ),
    inference(avatar_component_clause,[],[f81]) ).

fof(f81,plain,
    ( spl3_2
  <=> leq(one,multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f213,plain,
    spl3_1,
    inference(avatar_contradiction_clause,[],[f212]) ).

fof(f212,plain,
    ( $false
    | spl3_1 ),
    inference(subsumption_resolution,[],[f148,f66]) ).

fof(f148,plain,
    ( one != addition(one,one)
    | spl3_1 ),
    inference(unit_resulting_resolution,[],[f139,f61]) ).

fof(f139,plain,
    ( ~ leq(one,one)
    | spl3_1 ),
    inference(backward_demodulation,[],[f134,f138]) ).

fof(f134,plain,
    ( ~ leq(addition(sK2,c(sK2)),one)
    | spl3_1 ),
    inference(forward_demodulation,[],[f133,f56]) ).

fof(f56,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

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

fof(f133,plain,
    ( ~ leq(multiplication(one,addition(sK2,c(sK2))),one)
    | spl3_1 ),
    inference(backward_demodulation,[],[f79,f132]) ).

fof(f79,plain,
    ( ~ leq(multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),one)
    | spl3_1 ),
    inference(avatar_component_clause,[],[f77]) ).

fof(f77,plain,
    ( spl3_1
  <=> leq(multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f84,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f75,f81,f77]) ).

fof(f75,plain,
    ( ~ leq(one,multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))))
    | ~ leq(multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),one) ),
    inference(forward_demodulation,[],[f74,f58]) ).

fof(f58,plain,
    ! [X2,X0,X1] : multiplication(X2,addition(X0,X1)) = addition(multiplication(X2,X0),multiplication(X2,X1)),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1,X2] : multiplication(X2,addition(X0,X1)) = addition(multiplication(X2,X0),multiplication(X2,X1)),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ! [X2,X1,X0] : multiplication(X0,addition(X2,X1)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
    inference(rectify,[],[f8]) ).

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

fof(f74,plain,
    ( ~ leq(multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),one)
    | ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2)))) ),
    inference(forward_demodulation,[],[f70,f58]) ).

fof(f70,plain,
    ( ~ leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
    | ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2)))) ),
    inference(cnf_transformation,[],[f48]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : KLE007+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n010.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 00:14:14 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.55  % (13441)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.55  % (13433)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.57  % (13428)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.57  % (13433)Instruction limit reached!
% 0.19/0.57  % (13433)------------------------------
% 0.19/0.57  % (13433)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.57  % (13433)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.57  % (13433)Termination reason: Unknown
% 0.19/0.57  % (13433)Termination phase: Saturation
% 0.19/0.57  
% 0.19/0.57  % (13433)Memory used [KB]: 6012
% 0.19/0.57  % (13433)Time elapsed: 0.083 s
% 0.19/0.57  % (13433)Instructions burned: 7 (million)
% 0.19/0.57  % (13433)------------------------------
% 0.19/0.57  % (13433)------------------------------
% 0.19/0.57  % (13428)Refutation not found, incomplete strategy% (13428)------------------------------
% 0.19/0.57  % (13428)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.57  % (13428)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.57  % (13428)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.57  
% 0.19/0.57  % (13428)Memory used [KB]: 5884
% 0.19/0.57  % (13428)Time elapsed: 0.086 s
% 0.19/0.57  % (13428)Instructions burned: 3 (million)
% 0.19/0.57  % (13428)------------------------------
% 0.19/0.57  % (13428)------------------------------
% 0.19/0.57  % (13447)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.19/0.58  % (13439)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.58  % (13418)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 1.63/0.59  % (13431)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.63/0.59  % (13422)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 1.63/0.59  % (13423)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 1.63/0.59  % (13431)First to succeed.
% 1.63/0.59  % (13421)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.63/0.60  % (13424)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 1.87/0.60  % (13431)Refutation found. Thanks to Tanya!
% 1.87/0.60  % SZS status Theorem for theBenchmark
% 1.87/0.60  % SZS output start Proof for theBenchmark
% See solution above
% 1.87/0.60  % (13431)------------------------------
% 1.87/0.60  % (13431)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.87/0.60  % (13431)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.87/0.60  % (13431)Termination reason: Refutation
% 1.87/0.60  
% 1.87/0.60  % (13431)Memory used [KB]: 6012
% 1.87/0.60  % (13431)Time elapsed: 0.169 s
% 1.87/0.60  % (13431)Instructions burned: 7 (million)
% 1.87/0.60  % (13431)------------------------------
% 1.87/0.60  % (13431)------------------------------
% 1.87/0.60  % (13417)Success in time 0.25 s
%------------------------------------------------------------------------------