%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : GRP206-1 : TPTP v8.1.2. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %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 01:14:26 EDT 2023

% Result   : Unsatisfiable 0.50s 0.75s
% Output   : CNFRefutation 0.50s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : GRP206-1 : TPTP v8.1.2. Released v2.3.0.
% 0.11/0.13  % Command    : toma --casc %s
% 0.12/0.33  % Computer : n007.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon Aug 28 21:37:58 EDT 2023
% 0.12/0.34  % CPUTime    : 
% 0.50/0.75  % SZS status Unsatisfiable
% 0.50/0.75  % SZS output start Proof
% 0.50/0.75  original problem:
% 0.50/0.75  axioms:
% 0.50/0.75  multiply(identity(), X) = X
% 0.50/0.75  multiply(X, identity()) = X
% 0.50/0.75  multiply(X, left_division(X, Y)) = Y
% 0.50/0.75  left_division(X, multiply(X, Y)) = Y
% 0.50/0.75  multiply(right_division(X, Y), Y) = X
% 0.50/0.75  right_division(multiply(X, Y), Y) = X
% 0.50/0.75  multiply(X, right_inverse(X)) = identity()
% 0.50/0.75  multiply(left_inverse(X), X) = identity()
% 0.50/0.75  multiply(X, multiply(multiply(Y, Z), X)) = multiply(multiply(X, Y), multiply(Z, X))
% 0.50/0.75  goal:
% 0.50/0.75  multiply(multiply(a(), multiply(b(), c())), a()) != multiply(multiply(a(), b()), multiply(c(), a()))
% 0.50/0.75  To show the unsatisfiability of the original goal,
% 0.50/0.75  it suffices to show that multiply(multiply(a(), multiply(b(), c())), a()) = multiply(multiply(a(), b()), multiply(c(), a())) (skolemized goal) is valid under the axioms.
% 0.50/0.75  Here is an equational proof:
% 0.50/0.75  0: multiply(identity(), X0) = X0.
% 0.50/0.75  Proof: Axiom.
% 0.50/0.75  
% 0.50/0.75  1: multiply(X0, identity()) = X0.
% 0.50/0.75  Proof: Axiom.
% 0.50/0.75  
% 0.50/0.75  8: multiply(X0, multiply(multiply(X1, X2), X0)) = multiply(multiply(X0, X1), multiply(X2, X0)).
% 0.50/0.75  Proof: Axiom.
% 0.50/0.75  
% 0.50/0.75  21: multiply(multiply(X0, X3), multiply(identity(), X0)) = multiply(X0, multiply(X3, X0)).
% 0.50/0.75  Proof: A critical pair between equations 8 and 1.
% 0.50/0.75  
% 0.50/0.75  33: multiply(multiply(X0, X3), X0) = multiply(X0, multiply(X3, X0)).
% 0.50/0.75  Proof: Rewrite equation 21,
% 0.50/0.75                 lhs with equations [0]
% 0.50/0.75                 rhs with equations [].
% 0.50/0.75  
% 0.50/0.75  34: multiply(multiply(a(), multiply(b(), c())), a()) = multiply(multiply(a(), b()), multiply(c(), a())).
% 0.50/0.75  Proof: Rewrite lhs with equations [33,8]
% 0.50/0.75                 rhs with equations [].
% 0.50/0.75  
% 0.50/0.75  % SZS output end Proof
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