TSTP Solution File: GRP767-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP767-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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 20:21:34 EDT 2024

% Result   : Unsatisfiable 13.65s 2.11s
% Output   : CNFRefutation 14.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   83 (  83 unt;   0 def)
%            Number of atoms       :   83 (  82 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   3 con; 0-3 aty)
%            Number of variables   :  124 ( 124   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A] : product(A,one) = A,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [A,B] : product(A,difference(A,B)) = B,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A,B] : difference(A,product(A,B)) = B,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [A,B] : quotient(product(A,B),B) = A,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [A,B] : product(quotient(A,B),B) = A,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A,B,C] : difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [A] : i(A) = difference(A,one),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [A] : j(A) = quotient(one,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [A] : product(i(A),A) = product(A,j(A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [A] : eta(A) = product(i(A),A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [A,B] : product(i(i(A)),B) = product(eta(A),product(A,B)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [A,B] : product(A,product(eta(A),B)) = product(j(j(A)),B),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [A,B,C] : product(eta(A),product(B,C)) = product(product(eta(A),B),C),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [A,B,C] : l(A,B,C) = difference(product(A,B),product(A,product(B,C))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f21,negated_conjecture,
    product(j(j(x0)),j(product(x1,x0))) != j(x1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f22,plain,
    ! [X0] : product(X0,one) = X0,
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f24,plain,
    ! [X0,X1] : product(X0,difference(X0,X1)) = X1,
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f25,plain,
    ! [X0,X1] : difference(X0,product(X0,X1)) = X1,
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f26,plain,
    ! [X0,X1] : quotient(product(X0,X1),X1) = X0,
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f27,plain,
    ! [X0,X1] : product(quotient(X0,X1),X1) = X0,
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f28,plain,
    ! [X0,X1,X2] : difference(X0,product(product(X0,X1),X2)) = quotient(product(X1,product(X2,X0)),X0),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f30,plain,
    ! [X0] : i(X0) = difference(X0,one),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f31,plain,
    ! [X0] : j(X0) = quotient(one,X0),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f32,plain,
    ! [X0] : product(i(X0),X0) = product(X0,j(X0)),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f33,plain,
    ! [X0] : eta(X0) = product(i(X0),X0),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f34,plain,
    ! [X0,X1] : product(i(i(X0)),X1) = product(eta(X0),product(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f35,plain,
    ! [X0,X1] : product(X0,product(eta(X0),X1)) = product(j(j(X0)),X1),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f37,plain,
    ! [X0,X1,X2] : product(eta(X0),product(X1,X2)) = product(product(eta(X0),X1),X2),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f38,plain,
    ! [X0,X1,X2] : l(X0,X1,X2) = difference(product(X0,X1),product(X0,product(X1,X2))),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f42,plain,
    product(j(j(x0)),j(product(x1,x0))) != j(x1),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f44,plain,
    ! [X0] : eta(X0) = product(X0,j(X0)),
    inference(forward_demodulation,[status(thm)],[f32,f33]) ).

fof(f54,plain,
    ! [X0] : product(X0,eta(X0)) = product(j(j(X0)),one),
    inference(paramodulation,[status(thm)],[f22,f35]) ).

fof(f55,plain,
    ! [X0] : product(X0,eta(X0)) = j(j(X0)),
    inference(forward_demodulation,[status(thm)],[f22,f54]) ).

fof(f78,plain,
    ! [X0] : product(j(X0),X0) = one,
    inference(paramodulation,[status(thm)],[f31,f27]) ).

fof(f151,plain,
    ! [X0] : product(X0,i(X0)) = one,
    inference(paramodulation,[status(thm)],[f30,f24]) ).

fof(f188,plain,
    ! [X0] : quotient(one,i(X0)) = X0,
    inference(paramodulation,[status(thm)],[f151,f26]) ).

fof(f189,plain,
    ! [X0] : j(i(X0)) = X0,
    inference(forward_demodulation,[status(thm)],[f31,f188]) ).

fof(f190,plain,
    ! [X0,X1] : quotient(X0,difference(X1,X0)) = X1,
    inference(paramodulation,[status(thm)],[f24,f26]) ).

fof(f191,plain,
    ! [X0] : quotient(j(j(X0)),eta(X0)) = X0,
    inference(paramodulation,[status(thm)],[f55,f26]) ).

fof(f193,plain,
    ! [X0,X1] : quotient(product(j(j(X0)),X1),product(eta(X0),X1)) = X0,
    inference(paramodulation,[status(thm)],[f35,f26]) ).

fof(f219,plain,
    ! [X0] : difference(j(X0),one) = X0,
    inference(paramodulation,[status(thm)],[f78,f25]) ).

fof(f220,plain,
    ! [X0] : i(j(X0)) = X0,
    inference(forward_demodulation,[status(thm)],[f30,f219]) ).

fof(f248,plain,
    ! [X0] : eta(i(X0)) = product(i(X0),X0),
    inference(paramodulation,[status(thm)],[f189,f44]) ).

fof(f256,plain,
    ! [X0] : quotient(eta(X0),j(X0)) = X0,
    inference(paramodulation,[status(thm)],[f44,f26]) ).

fof(f318,plain,
    ! [X0,X1,X2] : product(difference(X0,product(product(X0,X1),X2)),X0) = product(X1,product(X2,X0)),
    inference(paramodulation,[status(thm)],[f28,f27]) ).

fof(f348,plain,
    ! [X0] : product(i(i(X0)),i(X0)) = product(eta(X0),one),
    inference(paramodulation,[status(thm)],[f151,f34]) ).

fof(f349,plain,
    ! [X0] : eta(i(i(X0))) = product(eta(X0),one),
    inference(forward_demodulation,[status(thm)],[f248,f348]) ).

fof(f350,plain,
    ! [X0] : eta(i(i(X0))) = eta(X0),
    inference(forward_demodulation,[status(thm)],[f22,f349]) ).

fof(f352,plain,
    ! [X0] : product(i(i(X0)),eta(X0)) = product(eta(X0),j(j(X0))),
    inference(paramodulation,[status(thm)],[f55,f34]) ).

fof(f418,plain,
    ! [X0] : quotient(j(X0),eta(i(X0))) = i(X0),
    inference(paramodulation,[status(thm)],[f189,f191]) ).

fof(f441,plain,
    ! [X0] : quotient(X0,eta(i(i(X0)))) = i(i(X0)),
    inference(paramodulation,[status(thm)],[f189,f418]) ).

fof(f442,plain,
    ! [X0] : quotient(X0,eta(X0)) = i(i(X0)),
    inference(forward_demodulation,[status(thm)],[f350,f441]) ).

fof(f471,plain,
    ! [X0] : product(i(i(X0)),eta(X0)) = X0,
    inference(paramodulation,[status(thm)],[f442,f27]) ).

fof(f472,plain,
    ! [X0] : product(eta(X0),j(j(X0))) = X0,
    inference(forward_demodulation,[status(thm)],[f352,f471]) ).

fof(f497,plain,
    ! [X0] : quotient(one,product(eta(X0),j(X0))) = X0,
    inference(paramodulation,[status(thm)],[f78,f193]) ).

fof(f498,plain,
    ! [X0] : j(product(eta(X0),j(X0))) = X0,
    inference(forward_demodulation,[status(thm)],[f31,f497]) ).

fof(f579,plain,
    ! [X0] : quotient(X0,j(j(X0))) = eta(X0),
    inference(paramodulation,[status(thm)],[f472,f26]) ).

fof(f619,plain,
    ! [X0] : quotient(product(eta(X0),j(X0)),j(X0)) = eta(product(eta(X0),j(X0))),
    inference(paramodulation,[status(thm)],[f498,f579]) ).

fof(f620,plain,
    ! [X0] : eta(X0) = eta(product(eta(X0),j(X0))),
    inference(forward_demodulation,[status(thm)],[f26,f619]) ).

fof(f629,plain,
    ! [X0] : quotient(eta(product(eta(X0),j(X0))),X0) = product(eta(X0),j(X0)),
    inference(paramodulation,[status(thm)],[f498,f256]) ).

fof(f630,plain,
    ! [X0] : quotient(eta(X0),X0) = product(eta(X0),j(X0)),
    inference(forward_demodulation,[status(thm)],[f620,f629]) ).

fof(f635,plain,
    ! [X0] : i(X0) = product(eta(X0),j(X0)),
    inference(paramodulation,[status(thm)],[f498,f220]) ).

fof(f636,plain,
    ! [X0] : i(X0) = quotient(eta(X0),X0),
    inference(forward_demodulation,[status(thm)],[f630,f635]) ).

fof(f708,plain,
    ! [X0] : product(i(X0),X0) = eta(X0),
    inference(paramodulation,[status(thm)],[f636,f27]) ).

fof(f1141,plain,
    ! [X0,X1,X2] : difference(product(eta(X0),X1),product(eta(X0),product(X1,X2))) = X2,
    inference(paramodulation,[status(thm)],[f37,f25]) ).

fof(f1142,plain,
    ! [X0,X1,X2] : l(eta(X0),X1,X2) = X2,
    inference(forward_demodulation,[status(thm)],[f38,f1141]) ).

fof(f1237,plain,
    ! [X0,X1] : l(X0,j(X1),X1) = difference(product(X0,j(X1)),product(X0,one)),
    inference(paramodulation,[status(thm)],[f78,f38]) ).

fof(f1238,plain,
    ! [X0,X1] : l(X0,j(X1),X1) = difference(product(X0,j(X1)),X0),
    inference(forward_demodulation,[status(thm)],[f22,f1237]) ).

fof(f4428,plain,
    ! [X0,X1] : product(difference(X0,one),X0) = product(X1,product(i(product(X0,X1)),X0)),
    inference(paramodulation,[status(thm)],[f151,f318]) ).

fof(f4429,plain,
    ! [X0,X1] : product(i(X0),X0) = product(X1,product(i(product(X0,X1)),X0)),
    inference(forward_demodulation,[status(thm)],[f30,f4428]) ).

fof(f4430,plain,
    ! [X0,X1] : eta(X0) = product(X1,product(i(product(X0,X1)),X0)),
    inference(forward_demodulation,[status(thm)],[f708,f4429]) ).

fof(f9847,plain,
    ! [X0,X1] : X0 = difference(product(eta(X1),j(X0)),eta(X1)),
    inference(paramodulation,[status(thm)],[f1142,f1238]) ).

fof(f10050,plain,
    ! [X0,X1] : quotient(eta(X0),X1) = product(eta(X0),j(X1)),
    inference(paramodulation,[status(thm)],[f9847,f190]) ).

fof(f11868,plain,
    ! [X0,X1] : eta(X0) = product(difference(X0,X1),product(i(X1),X0)),
    inference(paramodulation,[status(thm)],[f24,f4430]) ).

fof(f12771,plain,
    ! [X0,X1] : product(X0,quotient(eta(X0),X1)) = product(j(j(X0)),j(X1)),
    inference(paramodulation,[status(thm)],[f10050,f35]) ).

fof(f13660,plain,
    ! [X0,X1] : eta(X0) = product(difference(X0,j(X1)),product(X1,X0)),
    inference(paramodulation,[status(thm)],[f220,f11868]) ).

fof(f18800,plain,
    ! [X0,X1] : eta(X0) = product(difference(X0,j(quotient(X1,X0))),X1),
    inference(paramodulation,[status(thm)],[f27,f13660]) ).

fof(f23826,plain,
    ! [X0,X1] : quotient(eta(X0),X1) = difference(X0,j(quotient(X1,X0))),
    inference(paramodulation,[status(thm)],[f18800,f26]) ).

fof(f24516,plain,
    ! [X0,X1] : product(X0,quotient(eta(X0),X1)) = j(quotient(X1,X0)),
    inference(paramodulation,[status(thm)],[f23826,f24]) ).

fof(f24530,plain,
    ! [X0,X1] : j(quotient(X0,X1)) = product(j(j(X1)),j(X0)),
    inference(backward_demodulation,[status(thm)],[f24516,f12771]) ).

fof(f24562,plain,
    j(quotient(product(x1,x0),x0)) != j(x1),
    inference(backward_demodulation,[status(thm)],[f24530,f42]) ).

fof(f24563,plain,
    j(x1) != j(x1),
    inference(forward_demodulation,[status(thm)],[f26,f24562]) ).

fof(f24564,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f24563]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12  % Problem  : GRP767-1 : TPTP v8.1.2. Released v4.1.0.
% 0.02/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33  % Computer : n005.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Tue Apr 30 00:21:56 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.11/0.34  % Drodi V3.6.0
% 13.65/2.11  % Refutation found
% 13.65/2.11  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 13.65/2.11  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.03/2.21  % Elapsed time: 1.857994 seconds
% 14.03/2.21  % CPU time: 14.370200 seconds
% 14.03/2.21  % Total memory used: 277.475 MB
% 14.03/2.21  % Net memory used: 269.957 MB
%------------------------------------------------------------------------------