TSTP Solution File: GRP183-2 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : GRP183-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n007.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 : Thu Aug 31 01:22:32 EDT 2023

% Result   : Unsatisfiable 2.50s 0.82s
% Output   : Refutation 2.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   85 (  85 unt;   0 def)
%            Number of atoms       :   85 (  84 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   92 (;  92   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f23683,plain,
    $false,
    inference(subsumption_resolution,[],[f23682,f24]) ).

fof(f24,plain,
    identity != sF3,
    inference(definition_folding,[],[f19,f23,f22,f21,f20]) ).

fof(f20,plain,
    least_upper_bound(a,identity) = sF0,
    introduced(function_definition,[]) ).

fof(f21,plain,
    greatest_lower_bound(a,identity) = sF1,
    introduced(function_definition,[]) ).

fof(f22,plain,
    inverse(sF1) = sF2,
    introduced(function_definition,[]) ).

fof(f23,plain,
    greatest_lower_bound(sF0,sF2) = sF3,
    introduced(function_definition,[]) ).

fof(f19,axiom,
    identity != greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
    file('/export/starexec/sandbox2/tmp/tmp.IpKlGD2JvG/Vampire---4.8_32354',prove_p20) ).

fof(f23682,plain,
    identity = sF3,
    inference(forward_demodulation,[],[f23658,f14334]) ).

fof(f14334,plain,
    identity = greatest_lower_bound(sF3,multiply(sF2,a)),
    inference(forward_demodulation,[],[f14319,f84]) ).

fof(f84,plain,
    identity = greatest_lower_bound(sF0,identity),
    inference(forward_demodulation,[],[f74,f4]) ).

fof(f4,axiom,
    ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
    file('/export/starexec/sandbox2/tmp/tmp.IpKlGD2JvG/Vampire---4.8_32354',symmetry_of_glb) ).

fof(f74,plain,
    identity = greatest_lower_bound(identity,sF0),
    inference(superposition,[],[f44,f20]) ).

fof(f44,plain,
    ! [X2,X1] : greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
    inference(superposition,[],[f11,f5]) ).

fof(f5,axiom,
    ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
    file('/export/starexec/sandbox2/tmp/tmp.IpKlGD2JvG/Vampire---4.8_32354',symmetry_of_lub) ).

fof(f11,axiom,
    ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
    file('/export/starexec/sandbox2/tmp/tmp.IpKlGD2JvG/Vampire---4.8_32354',glb_absorbtion) ).

fof(f14319,plain,
    greatest_lower_bound(sF0,identity) = greatest_lower_bound(sF3,multiply(sF2,a)),
    inference(superposition,[],[f799,f14287]) ).

fof(f14287,plain,
    identity = greatest_lower_bound(sF2,multiply(sF2,a)),
    inference(forward_demodulation,[],[f14286,f4]) ).

fof(f14286,plain,
    identity = greatest_lower_bound(multiply(sF2,a),sF2),
    inference(forward_demodulation,[],[f14272,f1]) ).

fof(f1,axiom,
    ! [X0] : multiply(identity,X0) = X0,
    file('/export/starexec/sandbox2/tmp/tmp.IpKlGD2JvG/Vampire---4.8_32354',left_identity) ).

fof(f14272,plain,
    identity = multiply(identity,greatest_lower_bound(multiply(sF2,a),sF2)),
    inference(superposition,[],[f10373,f11016]) ).

fof(f11016,plain,
    identity = inverse(greatest_lower_bound(sF2,multiply(sF2,a))),
    inference(forward_demodulation,[],[f11015,f3046]) ).

fof(f3046,plain,
    ! [X11,X12] : greatest_lower_bound(X11,multiply(X11,X12)) = multiply(X11,greatest_lower_bound(X12,identity)),
    inference(forward_demodulation,[],[f3007,f4]) ).

fof(f3007,plain,
    ! [X11,X12] : multiply(X11,greatest_lower_bound(X12,identity)) = greatest_lower_bound(multiply(X11,X12),X11),
    inference(superposition,[],[f13,f145]) ).

fof(f145,plain,
    ! [X6] : multiply(X6,identity) = X6,
    inference(forward_demodulation,[],[f138,f17]) ).

fof(f17,axiom,
    ! [X0] : inverse(inverse(X0)) = X0,
    file('/export/starexec/sandbox2/tmp/tmp.IpKlGD2JvG/Vampire---4.8_32354',p20_2) ).

fof(f138,plain,
    ! [X6] : multiply(X6,identity) = inverse(inverse(X6)),
    inference(superposition,[],[f17,f127]) ).

fof(f127,plain,
    ! [X0] : inverse(X0) = inverse(multiply(X0,identity)),
    inference(forward_demodulation,[],[f115,f1]) ).

fof(f115,plain,
    ! [X0] : inverse(multiply(X0,identity)) = multiply(identity,inverse(X0)),
    inference(superposition,[],[f18,f16]) ).

fof(f16,axiom,
    identity = inverse(identity),
    file('/export/starexec/sandbox2/tmp/tmp.IpKlGD2JvG/Vampire---4.8_32354',p20_1) ).

fof(f18,axiom,
    ! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
    file('/export/starexec/sandbox2/tmp/tmp.IpKlGD2JvG/Vampire---4.8_32354',p20_3) ).

fof(f13,axiom,
    ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
    file('/export/starexec/sandbox2/tmp/tmp.IpKlGD2JvG/Vampire---4.8_32354',monotony_glb1) ).

fof(f11015,plain,
    identity = inverse(multiply(sF2,greatest_lower_bound(a,identity))),
    inference(forward_demodulation,[],[f11014,f10579]) ).

fof(f10579,plain,
    ! [X40,X41,X42] : inverse(multiply(X40,greatest_lower_bound(X41,X42))) = inverse(multiply(X40,greatest_lower_bound(X42,X41))),
    inference(forward_demodulation,[],[f10540,f13]) ).

fof(f10540,plain,
    ! [X40,X41,X42] : inverse(greatest_lower_bound(multiply(X40,X42),multiply(X40,X41))) = inverse(multiply(X40,greatest_lower_bound(X41,X42))),
    inference(superposition,[],[f10466,f13]) ).

fof(f10466,plain,
    ! [X65,X64] : inverse(greatest_lower_bound(X64,X65)) = inverse(greatest_lower_bound(X65,X64)),
    inference(forward_demodulation,[],[f10409,f518]) ).

fof(f518,plain,
    ! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),X0),
    inference(superposition,[],[f120,f466]) ).

fof(f466,plain,
    ! [X2,X3] : multiply(inverse(X2),multiply(X2,X3)) = X3,
    inference(forward_demodulation,[],[f448,f1]) ).

fof(f448,plain,
    ! [X2,X3] : multiply(inverse(X2),multiply(X2,X3)) = multiply(identity,X3),
    inference(superposition,[],[f3,f2]) ).

fof(f2,axiom,
    ! [X0] : identity = multiply(inverse(X0),X0),
    file('/export/starexec/sandbox2/tmp/tmp.IpKlGD2JvG/Vampire---4.8_32354',left_inverse) ).

fof(f3,axiom,
    ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
    file('/export/starexec/sandbox2/tmp/tmp.IpKlGD2JvG/Vampire---4.8_32354',associativity) ).

fof(f120,plain,
    ! [X2,X1] : inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
    inference(superposition,[],[f18,f17]) ).

fof(f10409,plain,
    ! [X65,X63,X64] : inverse(greatest_lower_bound(X64,X65)) = multiply(inverse(multiply(X63,greatest_lower_bound(X65,X64))),X63),
    inference(superposition,[],[f518,f3052]) ).

fof(f3052,plain,
    ! [X6,X7,X5] : multiply(X5,greatest_lower_bound(X6,X7)) = multiply(X5,greatest_lower_bound(X7,X6)),
    inference(forward_demodulation,[],[f3022,f13]) ).

fof(f3022,plain,
    ! [X6,X7,X5] : greatest_lower_bound(multiply(X5,X7),multiply(X5,X6)) = multiply(X5,greatest_lower_bound(X6,X7)),
    inference(superposition,[],[f13,f4]) ).

fof(f11014,plain,
    identity = inverse(multiply(sF2,greatest_lower_bound(identity,a))),
    inference(forward_demodulation,[],[f10718,f122]) ).

fof(f122,plain,
    ! [X4] : inverse(multiply(sF2,X4)) = multiply(inverse(X4),sF1),
    inference(superposition,[],[f18,f26]) ).

fof(f26,plain,
    sF1 = inverse(sF2),
    inference(superposition,[],[f17,f22]) ).

fof(f10718,plain,
    identity = multiply(inverse(greatest_lower_bound(identity,a)),sF1),
    inference(superposition,[],[f10373,f21]) ).

fof(f10373,plain,
    ! [X8,X9] : identity = multiply(inverse(greatest_lower_bound(X8,X9)),greatest_lower_bound(X9,X8)),
    inference(superposition,[],[f3052,f2]) ).

fof(f799,plain,
    ! [X27] : greatest_lower_bound(sF0,greatest_lower_bound(sF2,X27)) = greatest_lower_bound(sF3,X27),
    inference(superposition,[],[f6,f23]) ).

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/tmp/tmp.IpKlGD2JvG/Vampire---4.8_32354',associativity_of_glb) ).

fof(f23658,plain,
    sF3 = greatest_lower_bound(sF3,multiply(sF2,a)),
    inference(superposition,[],[f1703,f19313]) ).

fof(f19313,plain,
    multiply(sF2,a) = least_upper_bound(sF0,multiply(sF2,a)),
    inference(forward_demodulation,[],[f19290,f12494]) ).

fof(f12494,plain,
    ! [X11] : multiply(sF2,X11) = least_upper_bound(X11,multiply(sF2,X11)),
    inference(forward_demodulation,[],[f12493,f1]) ).

fof(f12493,plain,
    ! [X11] : least_upper_bound(X11,multiply(sF2,X11)) = multiply(identity,multiply(sF2,X11)),
    inference(forward_demodulation,[],[f12492,f61]) ).

fof(f61,plain,
    identity = least_upper_bound(sF1,identity),
    inference(forward_demodulation,[],[f56,f5]) ).

fof(f56,plain,
    identity = least_upper_bound(identity,sF1),
    inference(superposition,[],[f39,f21]) ).

fof(f39,plain,
    ! [X2,X1] : least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
    inference(superposition,[],[f10,f4]) ).

fof(f10,axiom,
    ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
    file('/export/starexec/sandbox2/tmp/tmp.IpKlGD2JvG/Vampire---4.8_32354',lub_absorbtion) ).

fof(f12492,plain,
    ! [X11] : least_upper_bound(X11,multiply(sF2,X11)) = multiply(least_upper_bound(sF1,identity),multiply(sF2,X11)),
    inference(forward_demodulation,[],[f12491,f4533]) ).

fof(f4533,plain,
    ! [X8,X9,X7] : multiply(least_upper_bound(X7,X9),X8) = multiply(least_upper_bound(X9,X7),X8),
    inference(forward_demodulation,[],[f4503,f14]) ).

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/tmp/tmp.IpKlGD2JvG/Vampire---4.8_32354',monotony_lub2) ).

fof(f4503,plain,
    ! [X8,X9,X7] : least_upper_bound(multiply(X9,X8),multiply(X7,X8)) = multiply(least_upper_bound(X7,X9),X8),
    inference(superposition,[],[f14,f5]) ).

fof(f12491,plain,
    ! [X11] : multiply(least_upper_bound(identity,sF1),multiply(sF2,X11)) = least_upper_bound(X11,multiply(sF2,X11)),
    inference(forward_demodulation,[],[f12395,f5]) ).

fof(f12395,plain,
    ! [X11] : multiply(least_upper_bound(identity,sF1),multiply(sF2,X11)) = least_upper_bound(multiply(sF2,X11),X11),
    inference(superposition,[],[f4465,f474]) ).

fof(f474,plain,
    ! [X24] : multiply(sF1,multiply(sF2,X24)) = X24,
    inference(forward_demodulation,[],[f459,f1]) ).

fof(f459,plain,
    ! [X24] : multiply(sF1,multiply(sF2,X24)) = multiply(identity,X24),
    inference(superposition,[],[f3,f31]) ).

fof(f31,plain,
    identity = multiply(sF1,sF2),
    inference(superposition,[],[f2,f26]) ).

fof(f4465,plain,
    ! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)),
    inference(superposition,[],[f14,f1]) ).

fof(f19290,plain,
    least_upper_bound(a,multiply(sF2,a)) = least_upper_bound(sF0,multiply(sF2,a)),
    inference(superposition,[],[f984,f11733]) ).

fof(f11733,plain,
    multiply(sF2,a) = least_upper_bound(identity,multiply(sF2,a)),
    inference(forward_demodulation,[],[f11719,f5]) ).

fof(f11719,plain,
    multiply(sF2,a) = least_upper_bound(multiply(sF2,a),identity),
    inference(superposition,[],[f39,f10859]) ).

fof(f10859,plain,
    identity = greatest_lower_bound(identity,multiply(sF2,a)),
    inference(forward_demodulation,[],[f10858,f22]) ).

fof(f10858,plain,
    identity = greatest_lower_bound(identity,multiply(inverse(sF1),a)),
    inference(forward_demodulation,[],[f10643,f2986]) ).

fof(f2986,plain,
    ! [X2,X3] : multiply(inverse(X2),greatest_lower_bound(X2,X3)) = greatest_lower_bound(identity,multiply(inverse(X2),X3)),
    inference(superposition,[],[f13,f2]) ).

fof(f10643,plain,
    identity = multiply(inverse(sF1),greatest_lower_bound(sF1,a)),
    inference(superposition,[],[f10373,f85]) ).

fof(f85,plain,
    sF1 = greatest_lower_bound(a,sF1),
    inference(forward_demodulation,[],[f75,f4]) ).

fof(f75,plain,
    sF1 = greatest_lower_bound(sF1,a),
    inference(superposition,[],[f44,f41]) ).

fof(f41,plain,
    a = least_upper_bound(a,sF1),
    inference(superposition,[],[f10,f21]) ).

fof(f984,plain,
    ! [X24] : least_upper_bound(a,least_upper_bound(identity,X24)) = least_upper_bound(sF0,X24),
    inference(superposition,[],[f7,f20]) ).

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/tmp/tmp.IpKlGD2JvG/Vampire---4.8_32354',associativity_of_lub) ).

fof(f1703,plain,
    ! [X0] : sF3 = greatest_lower_bound(sF3,least_upper_bound(sF0,X0)),
    inference(superposition,[],[f1601,f5]) ).

fof(f1601,plain,
    ! [X63] : sF3 = greatest_lower_bound(sF3,least_upper_bound(X63,sF0)),
    inference(superposition,[],[f1005,f42]) ).

fof(f42,plain,
    sF0 = least_upper_bound(sF0,sF3),
    inference(superposition,[],[f10,f23]) ).

fof(f1005,plain,
    ! [X11,X12,X13] : greatest_lower_bound(X13,least_upper_bound(X11,least_upper_bound(X12,X13))) = X13,
    inference(superposition,[],[f44,f7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem    : GRP183-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.13/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35  % Computer : n007.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon Aug 28 20:45:13 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a CNF_UNS_RFO_PEQ_UEQ problem
% 0.15/0.36  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.IpKlGD2JvG/Vampire---4.8_32354
% 0.15/0.36  % (32463)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.42  % (32468)ott+10_4_av=off:drc=off:fde=none:nwc=1.2:sims=off:to=lpo:tgt=ground_606 on Vampire---4 for (606ds/0Mi)
% 0.15/0.42  % (32464)lrs+10_6_av=off:drc=off:fde=unused:nwc=2.5:sims=off:sp=reverse_frequency:stl=188_1200 on Vampire---4 for (1200ds/0Mi)
% 0.15/0.42  % (32467)ott+10_32_av=off:drc=off:fde=none:nwc=5.0:sp=reverse_weighted_frequency:tgt=full_1200 on Vampire---4 for (1200ds/0Mi)
% 0.15/0.42  % (32465)ott+10_14_av=off:bd=preordered:drc=off:sp=weighted_frequency_1200 on Vampire---4 for (1200ds/0Mi)
% 0.21/0.43  % (32469)dis+10_7_av=off:drc=off:nwc=1.5:sims=off:sp=scramble:tgt=ground_485 on Vampire---4 for (485ds/0Mi)
% 0.21/0.45  % (32470)lrs+10_50_av=off:bd=off:drc=off:sp=reverse_arity:tgt=ground:stl=62_361 on Vampire---4 for (361ds/0Mi)
% 0.21/0.48  % (32466)ott+10_11_av=off:bd=off:drc=off:fde=none:nwc=1.2:to=lpo:tgt=ground_1200 on Vampire---4 for (1200ds/0Mi)
% 2.50/0.82  % (32467)First to succeed.
% 2.50/0.82  % (32467)Refutation found. Thanks to Tanya!
% 2.50/0.82  % SZS status Unsatisfiable for Vampire---4
% 2.50/0.82  % SZS output start Proof for Vampire---4
% See solution above
% 2.50/0.82  % (32467)------------------------------
% 2.50/0.82  % (32467)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 2.50/0.82  % (32467)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 2.50/0.82  % (32467)Termination reason: Refutation
% 2.50/0.82  
% 2.50/0.82  % (32467)Memory used [KB]: 14583
% 2.50/0.82  % (32467)Time elapsed: 0.400 s
% 2.50/0.82  % (32467)------------------------------
% 2.50/0.82  % (32467)------------------------------
% 2.50/0.82  % (32463)Success in time 0.458 s
% 2.50/0.82  % Vampire---4.8 exiting
%------------------------------------------------------------------------------