TSTP Solution File: ALG002-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ALG002-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n003.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 : Sun May  5 04:14:37 EDT 2024

% Result   : Unsatisfiable 0.11s 0.28s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   36 (  11 unt;   0 def)
%            Number of atoms       :   73 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   70 (  33   ~;  37   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-1 aty)
%            Number of variables   :   37 (  37   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f407,plain,
    $false,
    inference(subsumption_resolution,[],[f396,f14]) ).

fof(f14,axiom,
    ~ greater_than_0(multiplicative_inverse(a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_inverse_greater_than_0) ).

fof(f396,plain,
    greater_than_0(multiplicative_inverse(a)),
    inference(resolution,[],[f394,f13]) ).

fof(f13,axiom,
    greater_than_0(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_greater_than_0) ).

fof(f394,plain,
    ! [X0] :
      ( ~ greater_than_0(X0)
      | greater_than_0(multiplicative_inverse(X0)) ),
    inference(subsumption_resolution,[],[f383,f335]) ).

fof(f335,plain,
    ! [X0] :
      ( ~ greater_than_0(additive_inverse(multiplicative_inverse(X0)))
      | ~ greater_than_0(X0) ),
    inference(subsumption_resolution,[],[f334,f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( ~ product(X0,X0,additive_identity)
      | ~ greater_than_0(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greater_than_0_square) ).

fof(f334,plain,
    ! [X0] :
      ( product(X0,X0,additive_identity)
      | ~ greater_than_0(additive_inverse(multiplicative_inverse(X0)))
      | ~ greater_than_0(X0) ),
    inference(subsumption_resolution,[],[f329,f91]) ).

fof(f91,plain,
    ~ greater_than_0(additive_inverse(multiplicative_identity)),
    inference(resolution,[],[f87,f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ~ greater_than_0(additive_inverse(X0))
      | ~ greater_than_0(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_greater_than_0) ).

fof(f87,plain,
    greater_than_0(additive_inverse(additive_inverse(multiplicative_identity))),
    inference(resolution,[],[f84,f71]) ).

fof(f71,plain,
    greater_than_0(multiplicative_identity),
    inference(resolution,[],[f70,f13]) ).

fof(f70,plain,
    ! [X0] :
      ( ~ greater_than_0(X0)
      | greater_than_0(multiplicative_identity) ),
    inference(resolution,[],[f69,f18]) ).

fof(f18,plain,
    ( greater_than_0(additive_inverse(multiplicative_identity))
    | greater_than_0(multiplicative_identity) ),
    inference(resolution,[],[f10,f2]) ).

fof(f2,axiom,
    ~ product(multiplicative_identity,multiplicative_identity,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_abelian) ).

fof(f10,axiom,
    ! [X0] :
      ( product(X0,X0,additive_identity)
      | greater_than_0(additive_inverse(X0))
      | greater_than_0(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_and_inverse) ).

fof(f69,plain,
    ! [X0] :
      ( ~ greater_than_0(additive_inverse(multiplicative_identity))
      | ~ greater_than_0(X0) ),
    inference(subsumption_resolution,[],[f63,f7]) ).

fof(f63,plain,
    ! [X0] :
      ( ~ greater_than_0(additive_inverse(multiplicative_identity))
      | greater_than_0(additive_inverse(X0))
      | ~ greater_than_0(X0) ),
    inference(resolution,[],[f12,f41]) ).

fof(f41,plain,
    ! [X0] : product(X0,additive_inverse(multiplicative_identity),additive_inverse(X0)),
    inference(resolution,[],[f5,f1]) ).

fof(f1,axiom,
    ! [X0] : product(X0,multiplicative_identity,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).

fof(f5,axiom,
    ! [X2,X0,X1] :
      ( ~ product(X0,X1,X2)
      | product(X0,additive_inverse(X1),additive_inverse(X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_inverse) ).

fof(f12,axiom,
    ! [X2,X0,X1] :
      ( ~ product(X1,X2,X0)
      | ~ greater_than_0(X2)
      | greater_than_0(X0)
      | ~ greater_than_0(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_and_greater_than_0) ).

fof(f84,plain,
    ! [X0] :
      ( ~ greater_than_0(X0)
      | greater_than_0(additive_inverse(additive_inverse(X0))) ),
    inference(subsumption_resolution,[],[f80,f71]) ).

fof(f80,plain,
    ! [X0] :
      ( ~ greater_than_0(multiplicative_identity)
      | greater_than_0(additive_inverse(additive_inverse(X0)))
      | ~ greater_than_0(X0) ),
    inference(resolution,[],[f53,f12]) ).

fof(f53,plain,
    ! [X0] : product(X0,multiplicative_identity,additive_inverse(additive_inverse(X0))),
    inference(resolution,[],[f41,f4]) ).

fof(f4,axiom,
    ! [X2,X0,X1] :
      ( ~ product(additive_inverse(X0),additive_inverse(X1),X2)
      | product(X0,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_of_inverses2) ).

fof(f329,plain,
    ! [X0] :
      ( product(X0,X0,additive_identity)
      | ~ greater_than_0(additive_inverse(multiplicative_inverse(X0)))
      | greater_than_0(additive_inverse(multiplicative_identity))
      | ~ greater_than_0(X0) ),
    inference(resolution,[],[f47,f12]) ).

fof(f47,plain,
    ! [X0] :
      ( product(X0,additive_inverse(multiplicative_inverse(X0)),additive_inverse(multiplicative_identity))
      | product(X0,X0,additive_identity) ),
    inference(resolution,[],[f5,f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( product(X0,multiplicative_inverse(X0),multiplicative_identity)
      | product(X0,X0,additive_identity) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_and_identity) ).

fof(f383,plain,
    ! [X0] :
      ( greater_than_0(additive_inverse(multiplicative_inverse(X0)))
      | greater_than_0(multiplicative_inverse(X0))
      | ~ greater_than_0(X0) ),
    inference(resolution,[],[f189,f8]) ).

fof(f189,plain,
    ! [X0] :
      ( product(X0,X0,additive_identity)
      | greater_than_0(additive_inverse(multiplicative_inverse(X0)))
      | greater_than_0(multiplicative_inverse(X0)) ),
    inference(resolution,[],[f118,f10]) ).

fof(f118,plain,
    ! [X0] :
      ( ~ product(multiplicative_inverse(X0),multiplicative_inverse(X0),additive_identity)
      | product(X0,X0,additive_identity) ),
    inference(subsumption_resolution,[],[f112,f2]) ).

fof(f112,plain,
    ! [X0] :
      ( ~ product(multiplicative_inverse(X0),multiplicative_inverse(X0),additive_identity)
      | product(multiplicative_identity,multiplicative_identity,additive_identity)
      | product(X0,X0,additive_identity) ),
    inference(resolution,[],[f11,f17]) ).

fof(f17,plain,
    ! [X0] :
      ( product(multiplicative_inverse(X0),X0,multiplicative_identity)
      | product(X0,X0,additive_identity) ),
    inference(resolution,[],[f6,f9]) ).

fof(f9,axiom,
    ! [X2,X0,X1] :
      ( ~ product(X0,X1,X2)
      | product(X1,X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_product) ).

fof(f11,axiom,
    ! [X2,X0,X1] :
      ( ~ product(X1,X2,X0)
      | ~ product(X1,X1,additive_identity)
      | product(X0,X0,additive_identity) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',square_to_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07  % Problem    : ALG002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.02/0.08  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.26  % Computer : n003.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit   : 300
% 0.07/0.26  % WCLimit    : 300
% 0.07/0.26  % DateTime   : Fri May  3 19:57:37 EDT 2024
% 0.11/0.26  % CPUTime    : 
% 0.11/0.27  % (9640)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.28  % (9642)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.28  % (9645)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.11/0.28  % (9644)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.11/0.28  % (9647)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.28  % (9646)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.11/0.28  % (9643)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.11/0.28  % (9641)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.28  TRYING [1]
% 0.11/0.28  TRYING [1]
% 0.11/0.28  TRYING [1]
% 0.11/0.28  TRYING [1]
% 0.11/0.28  TRYING [2]
% 0.11/0.28  TRYING [2]
% 0.11/0.28  TRYING [2]
% 0.11/0.28  TRYING [2]
% 0.11/0.28  TRYING [3]
% 0.11/0.28  TRYING [3]
% 0.11/0.28  TRYING [3]
% 0.11/0.28  TRYING [3]
% 0.11/0.28  TRYING [4]
% 0.11/0.28  TRYING [4]
% 0.11/0.28  TRYING [4]
% 0.11/0.28  TRYING [4]
% 0.11/0.28  % (9645)First to succeed.
% 0.11/0.28  % (9645)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9640"
% 0.11/0.28  % (9645)Refutation found. Thanks to Tanya!
% 0.11/0.28  % SZS status Unsatisfiable for theBenchmark
% 0.11/0.28  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.28  % (9645)------------------------------
% 0.11/0.28  % (9645)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.28  % (9645)Termination reason: Refutation
% 0.11/0.28  
% 0.11/0.28  % (9645)Memory used [KB]: 784
% 0.11/0.28  % (9645)Time elapsed: 0.006 s
% 0.11/0.28  % (9645)Instructions burned: 15 (million)
% 0.11/0.28  % (9640)Success in time 0.008 s
%------------------------------------------------------------------------------