TSTP Solution File: GRP172-2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRP172-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -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 : Mon May 20 21:15:34 EDT 2024

% Result   : Unsatisfiable 0.21s 0.55s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   33 (  33 unt;   0 def)
%            Number of atoms       :   33 (  32 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    1 (   1   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   43 (  43   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7154,plain,
    $false,
    inference(subsumption_resolution,[],[f7148,f18]) ).

fof(f18,axiom,
    multiply(a,b) != least_upper_bound(identity,multiply(a,b)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p04d) ).

fof(f7148,plain,
    multiply(a,b) = least_upper_bound(identity,multiply(a,b)),
    inference(superposition,[],[f1252,f6518]) ).

fof(f6518,plain,
    identity = greatest_lower_bound(identity,multiply(a,b)),
    inference(forward_demodulation,[],[f6517,f17]) ).

fof(f17,axiom,
    identity = greatest_lower_bound(identity,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p04d_2) ).

fof(f6517,plain,
    greatest_lower_bound(identity,b) = greatest_lower_bound(identity,multiply(a,b)),
    inference(forward_demodulation,[],[f6505,f4]) ).

fof(f4,axiom,
    ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).

fof(f6505,plain,
    greatest_lower_bound(b,identity) = greatest_lower_bound(identity,multiply(a,b)),
    inference(superposition,[],[f2505,f6373]) ).

fof(f6373,plain,
    ! [X0] : greatest_lower_bound(X0,multiply(a,X0)) = X0,
    inference(superposition,[],[f6307,f36]) ).

fof(f36,plain,
    a = least_upper_bound(identity,a),
    inference(superposition,[],[f29,f5]) ).

fof(f5,axiom,
    ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).

fof(f29,plain,
    a = least_upper_bound(a,identity),
    inference(superposition,[],[f22,f16]) ).

fof(f16,axiom,
    identity = greatest_lower_bound(identity,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p04d_1) ).

fof(f22,plain,
    ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
    inference(superposition,[],[f10,f4]) ).

fof(f10,axiom,
    ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).

fof(f6307,plain,
    ! [X0,X1] : greatest_lower_bound(X0,multiply(least_upper_bound(identity,X1),X0)) = X0,
    inference(superposition,[],[f11,f645]) ).

fof(f645,plain,
    ! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)),
    inference(superposition,[],[f14,f1]) ).

fof(f1,axiom,
    ! [X0] : multiply(identity,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).

fof(f14,axiom,
    ! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).

fof(f11,axiom,
    ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).

fof(f2505,plain,
    ! [X0] : greatest_lower_bound(identity,X0) = greatest_lower_bound(greatest_lower_bound(b,X0),identity),
    inference(forward_demodulation,[],[f2423,f67]) ).

fof(f67,plain,
    ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1)),
    inference(superposition,[],[f6,f9]) ).

fof(f9,axiom,
    ! [X0] : greatest_lower_bound(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_gld) ).

fof(f6,axiom,
    ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).

fof(f2423,plain,
    ! [X0] : greatest_lower_bound(greatest_lower_bound(b,X0),identity) = greatest_lower_bound(identity,greatest_lower_bound(identity,X0)),
    inference(superposition,[],[f2047,f66]) ).

fof(f66,plain,
    ! [X0] : greatest_lower_bound(identity,X0) = greatest_lower_bound(identity,greatest_lower_bound(b,X0)),
    inference(superposition,[],[f6,f17]) ).

fof(f2047,plain,
    ! [X0,X1] : greatest_lower_bound(X1,X0) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1)),
    inference(superposition,[],[f74,f9]) ).

fof(f74,plain,
    ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X0,X1)),
    inference(superposition,[],[f6,f4]) ).

fof(f1252,plain,
    ! [X0,X1] : least_upper_bound(greatest_lower_bound(X1,X0),X0) = X0,
    inference(superposition,[],[f223,f22]) ).

fof(f223,plain,
    ! [X0,X1] : least_upper_bound(X1,X0) = least_upper_bound(X0,least_upper_bound(X1,X0)),
    inference(superposition,[],[f139,f5]) ).

fof(f139,plain,
    ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X0,X1)),
    inference(superposition,[],[f7,f8]) ).

fof(f8,axiom,
    ! [X0] : least_upper_bound(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_lub) ).

fof(f7,axiom,
    ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GRP172-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n010.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sun May 19 05:02:23 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (16927)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (16934)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)
% 0.14/0.38  % (16929)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (16933)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)
% 0.14/0.38  % (16931)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (16932)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)
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.39  % (16930)WARNING: value z3 for option sas not known
% 0.14/0.39  TRYING [3]
% 0.14/0.39  % (16930)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)
% 0.14/0.39  % (16928)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.40  TRYING [4]
% 0.21/0.41  TRYING [1]
% 0.21/0.41  TRYING [2]
% 0.21/0.42  TRYING [3]
% 0.21/0.45  TRYING [5]
% 0.21/0.46  TRYING [4]
% 0.21/0.55  % (16930)First to succeed.
% 0.21/0.55  % (16930)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16927"
% 0.21/0.55  % (16930)Refutation found. Thanks to Tanya!
% 0.21/0.55  % SZS status Unsatisfiable for theBenchmark
% 0.21/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.56  % (16930)------------------------------
% 0.21/0.56  % (16930)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.56  % (16930)Termination reason: Refutation
% 0.21/0.56  
% 0.21/0.56  % (16930)Memory used [KB]: 2948
% 0.21/0.56  % (16930)Time elapsed: 0.168 s
% 0.21/0.56  % (16930)Instructions burned: 370 (million)
% 0.21/0.56  % (16927)Success in time 0.19 s
%------------------------------------------------------------------------------