TSTP Solution File: KLE026+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KLE026+1 : 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 : n019.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 0.47s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   54 (  29 unt;   0 def)
%            Number of atoms       :  119 (  55 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   93 (  28   ~;  20   |;  31   &)
%                                         (   5 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   94 (  80   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4438,plain,
    $false,
    inference(subsumption_resolution,[],[f4426,f43]) ).

fof(f43,plain,
    ~ leq(multiplication(sK1,sK0),multiplication(sK0,sK2)),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ( ~ leq(multiplication(sK1,sK0),multiplication(sK0,sK2))
    & multiplication(sK1,sK0) = multiplication(multiplication(sK1,sK0),sK2)
    & test(sK2)
    & test(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f27,f31]) ).

fof(f31,plain,
    ( ? [X0,X1,X2] :
        ( ~ leq(multiplication(X1,X0),multiplication(X0,X2))
        & multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
        & test(X2)
        & test(X1) )
   => ( ~ leq(multiplication(sK1,sK0),multiplication(sK0,sK2))
      & multiplication(sK1,sK0) = multiplication(multiplication(sK1,sK0),sK2)
      & test(sK2)
      & test(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ? [X0,X1,X2] :
      ( ~ leq(multiplication(X1,X0),multiplication(X0,X2))
      & multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
      & test(X2)
      & test(X1) ),
    inference(flattening,[],[f26]) ).

fof(f26,plain,
    ? [X0,X1,X2] :
      ( ~ leq(multiplication(X1,X0),multiplication(X0,X2))
      & multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
      & test(X2)
      & test(X1) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ~ ! [X0,X1,X2] :
        ( ( test(X2)
          & test(X1) )
       => ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
         => leq(multiplication(X1,X0),multiplication(X0,X2)) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,negated_conjecture,
    ~ ! [X3,X4,X5] :
        ( ( test(X5)
          & test(X4) )
       => ( multiplication(X4,X3) = multiplication(multiplication(X4,X3),X5)
         => leq(multiplication(X4,X3),multiplication(X3,X5)) ) ),
    inference(negated_conjecture,[],[f17]) ).

fof(f17,conjecture,
    ! [X3,X4,X5] :
      ( ( test(X5)
        & test(X4) )
     => ( multiplication(X4,X3) = multiplication(multiplication(X4,X3),X5)
       => leq(multiplication(X4,X3),multiplication(X3,X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(f4426,plain,
    leq(multiplication(sK1,sK0),multiplication(sK0,sK2)),
    inference(superposition,[],[f4332,f168]) ).

fof(f168,plain,
    multiplication(sK1,sK0) = multiplication(sK1,multiplication(sK0,sK2)),
    inference(superposition,[],[f62,f42]) ).

fof(f42,plain,
    multiplication(sK1,sK0) = multiplication(multiplication(sK1,sK0),sK2),
    inference(cnf_transformation,[],[f32]) ).

fof(f62,plain,
    ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).

fof(f4332,plain,
    ! [X0] : leq(multiplication(sK1,X0),X0),
    inference(superposition,[],[f1377,f4160]) ).

fof(f4160,plain,
    ! [X0] : addition(X0,multiplication(sK1,X0)) = X0,
    inference(forward_demodulation,[],[f4044,f48]) ).

fof(f48,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(f4044,plain,
    ! [X0] : multiplication(one,X0) = addition(X0,multiplication(sK1,X0)),
    inference(superposition,[],[f492,f1279]) ).

fof(f1279,plain,
    one = addition(one,sK1),
    inference(superposition,[],[f1259,f53]) ).

fof(f53,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(f1259,plain,
    one = addition(sK1,one),
    inference(superposition,[],[f106,f128]) ).

fof(f128,plain,
    one = addition(sK1,sK3(sK1)),
    inference(resolution,[],[f80,f40]) ).

fof(f40,plain,
    test(sK1),
    inference(cnf_transformation,[],[f32]) ).

fof(f80,plain,
    ! [X0] :
      ( ~ test(X0)
      | one = addition(X0,sK3(X0)) ),
    inference(resolution,[],[f58,f51]) ).

fof(f51,plain,
    ! [X0] :
      ( complement(sK3(X0),X0)
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( complement(sK3(X0),X0)
        | ~ test(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f34,f35]) ).

fof(f35,plain,
    ! [X0] :
      ( ? [X2] : complement(X2,X0)
     => complement(sK3(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( ? [X2] : complement(X2,X0)
        | ~ test(X0) ) ),
    inference(rectify,[],[f33]) ).

fof(f33,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( ? [X1] : complement(X1,X0)
        | ~ test(X0) ) ),
    inference(nnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0] :
      ( test(X0)
    <=> ? [X1] : complement(X1,X0) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X3] :
      ( test(X3)
    <=> ? [X4] : complement(X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_1) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | addition(X0,X1) = one ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,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,[],[f38]) ).

fof(f38,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,[],[f23]) ).

fof(f23,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(f106,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
    inference(superposition,[],[f61,f49]) ).

fof(f49,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,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).

fof(f492,plain,
    ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
    inference(superposition,[],[f64,f48]) ).

fof(f64,plain,
    ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).

fof(f1377,plain,
    ! [X0,X1] : leq(X0,addition(X1,X0)),
    inference(superposition,[],[f1272,f53]) ).

fof(f1272,plain,
    ! [X0,X1] : leq(X0,addition(X0,X1)),
    inference(trivial_inequality_removal,[],[f1268]) ).

fof(f1268,plain,
    ! [X0,X1] :
      ( addition(X0,X1) != addition(X0,X1)
      | leq(X0,addition(X0,X1)) ),
    inference(superposition,[],[f60,f106]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( addition(X0,X1) != X1
      | leq(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,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) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : KLE026+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n019.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Apr 30 05:04:14 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (26369)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (26372)WARNING: value z3 for option sas not known
% 0.14/0.37  % (26372)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)
% 0.14/0.37  % (26373)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  % (26371)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37  % (26375)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)
% 0.14/0.37  % (26376)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)
% 0.14/0.37  % (26374)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)
% 0.14/0.37  % (26370)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [3]
% 0.14/0.39  TRYING [4]
% 0.14/0.40  TRYING [3]
% 0.14/0.41  TRYING [5]
% 0.21/0.44  TRYING [4]
% 0.21/0.47  % (26372)First to succeed.
% 0.21/0.47  % (26372)Refutation found. Thanks to Tanya!
% 0.21/0.47  % SZS status Theorem for theBenchmark
% 0.21/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.47  % (26372)------------------------------
% 0.21/0.47  % (26372)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.47  % (26372)Termination reason: Refutation
% 0.21/0.47  
% 0.21/0.47  % (26372)Memory used [KB]: 2389
% 0.21/0.47  % (26372)Time elapsed: 0.101 s
% 0.21/0.47  % (26372)Instructions burned: 212 (million)
% 0.21/0.47  % (26372)------------------------------
% 0.21/0.47  % (26372)------------------------------
% 0.21/0.47  % (26369)Success in time 0.117 s
%------------------------------------------------------------------------------