TSTP Solution File: GRP542-1 by Moca---0.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Moca---0.1
% Problem  : GRP542-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : moca.sh %s

% Computer : n008.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  : 600s
% DateTime : Sat Jul 16 10:56:09 EDT 2022

% Result   : Unsatisfiable 0.86s 1.00s
% Output   : Proof 0.86s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP542-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12  % Command  : moca.sh %s
% 0.13/0.33  % Computer : n008.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Tue Jun 14 08:08:07 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.86/1.00  % SZS status Unsatisfiable
% 0.86/1.00  % SZS output start Proof
% 0.86/1.00  The input problem is unsatisfiable because
% 0.86/1.00  
% 0.86/1.00  [1] the following set of Horn clauses is unsatisfiable:
% 0.86/1.00  
% 0.86/1.00  	divide(divide(identity, divide(divide(divide(A, B), C), A)), C) = B
% 0.86/1.00  	multiply(A, B) = divide(A, divide(identity, B))
% 0.86/1.00  	inverse(A) = divide(identity, A)
% 0.86/1.00  	identity = divide(A, A)
% 0.86/1.00  	multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom
% 0.86/1.00  
% 0.86/1.00  This holds because
% 0.86/1.00  
% 0.86/1.00  [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.86/1.00  
% 0.86/1.00  E:
% 0.86/1.00  	divide(divide(identity, divide(divide(divide(A, B), C), A)), C) = B
% 0.86/1.00  	f1(a2) = false__
% 0.86/1.00  	f1(multiply(multiply(inverse(b2), b2), a2)) = true__
% 0.86/1.00  	identity = divide(A, A)
% 0.86/1.00  	inverse(A) = divide(identity, A)
% 0.86/1.00  	multiply(A, B) = divide(A, divide(identity, B))
% 0.86/1.00  G:
% 0.86/1.00  	true__ = false__
% 0.86/1.00  
% 0.86/1.00  This holds because
% 0.86/1.00  
% 0.86/1.00  [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.86/1.00  
% 0.86/1.00  	divide(X0, Y1) = divide(inverse(divide(Y1, identity)), inverse(X0))
% 0.86/1.00  	divide(X0, inverse(Y1)) = divide(Y1, inverse(X0))
% 0.86/1.00  	divide(inverse(X1), inverse(X0)) = divide(X0, X1)
% 0.86/1.00  	divide(inverse(Y2), Y1) = divide(inverse(divide(Y1, identity)), Y2)
% 0.86/1.00  	divide(A, A) -> identity
% 0.86/1.00  	divide(Y0, divide(Y0, Y1)) -> Y1
% 0.86/1.00  	divide(Y1, identity) -> Y1
% 0.86/1.00  	divide(divide(divide(X0, X1), Y2), X0) -> divide(inverse(divide(X1, identity)), Y2)
% 0.86/1.00  	divide(divide(identity, divide(divide(divide(A, B), C), A)), C) -> B
% 0.86/1.00  	divide(divide(inverse(Y1), Y2), identity) -> divide(inverse(divide(Y1, identity)), Y2)
% 0.86/1.00  	divide(identity, A) -> inverse(A)
% 0.86/1.00  	divide(inverse(X0), divide(inverse(X0), Y1)) -> Y1
% 0.86/1.00  	divide(inverse(Y0), identity) -> inverse(Y0)
% 0.86/1.00  	divide(inverse(divide(Y1, identity)), divide(Y0, Y1)) -> inverse(Y0)
% 0.86/1.00  	divide(inverse(divide(divide(divide(Y0, Y1), Y2), Y0)), Y2) -> Y1
% 0.86/1.00  	divide(inverse(divide(divide(inverse(Y1), Y2), identity)), Y2) -> Y1
% 0.86/1.00  	divide(inverse(divide(inverse(Y2), Y1)), Y2) -> Y1
% 0.86/1.00  	divide(inverse(inverse(Y0)), divide(Y0, Y1)) -> Y1
% 0.86/1.00  	divide(inverse(inverse(Y1)), identity) -> Y1
% 0.86/1.00  	divide(inverse(inverse(inverse(inverse(X0)))), X1) -> divide(X0, X1)
% 0.86/1.00  	f1(a2) -> false__
% 0.86/1.00  	f1(inverse(inverse(a2))) -> true__
% 0.86/1.00  	f1(multiply(multiply(inverse(b2), b2), a2)) -> true__
% 0.86/1.00  	inverse(identity) -> identity
% 0.86/1.00  	inverse(inverse(Y1)) -> Y1
% 0.86/1.00  	multiply(A, B) -> divide(A, divide(identity, B))
% 0.86/1.00  	true__ -> false__
% 0.86/1.00  with the LPO induced by
% 0.86/1.00  	b2 > a2 > f1 > multiply > divide > identity > inverse > true__ > false__
% 0.86/1.00  
% 0.86/1.00  % SZS output end Proof
% 0.86/1.00  
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