%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP195-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof

% Computer : n016.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 01:17:44 EDT 2023

% Result   : Unsatisfiable 0.20s 0.40s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : GRP195-1 : TPTP v8.1.2. Released v2.2.0.
% 0.04/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Aug 28 21:22:30 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.40  Command-line arguments: --no-flatten-goal
% 0.20/0.40  
% 0.20/0.40  % SZS status Unsatisfiable
% 0.20/0.40  
% 0.20/0.40  % SZS output start Proof
% 0.20/0.40  Axiom 1 (condition): multiply(X, multiply(Y, Y)) = multiply(Y, multiply(Y, X)).
% 0.20/0.40  Axiom 2 (associativity_of_multiply): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.20/0.40  
% 0.20/0.40  Lemma 3: multiply(X, multiply(X, multiply(Y, Z))) = multiply(Y, multiply(X, multiply(X, Z))).
% 0.20/0.40  Proof:
% 0.20/0.40    multiply(X, multiply(X, multiply(Y, Z)))
% 0.20/0.40  = { by axiom 1 (condition) R->L }
% 0.20/0.40    multiply(multiply(Y, Z), multiply(X, X))
% 0.20/0.40  = { by axiom 2 (associativity_of_multiply) }
% 0.20/0.40    multiply(Y, multiply(Z, multiply(X, X)))
% 0.20/0.40  = { by axiom 1 (condition) }
% 0.20/0.40    multiply(Y, multiply(X, multiply(X, Z)))
% 0.20/0.40  
% 0.20/0.40  Goal 1 (prove_this): multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, b))))))) = multiply(a, multiply(a, multiply(a, multiply(a, multiply(b, multiply(b, multiply(b, b))))))).
% 0.20/0.40  Proof:
% 0.20/0.40    multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, multiply(b, multiply(a, b)))))))
% 0.20/0.40  = { by axiom 2 (associativity_of_multiply) R->L }
% 0.20/0.40    multiply(a, multiply(b, multiply(a, multiply(b, multiply(multiply(a, b), multiply(a, b))))))
% 0.20/0.40  = { by axiom 1 (condition) }
% 0.20/0.40    multiply(a, multiply(b, multiply(a, multiply(multiply(a, b), multiply(multiply(a, b), b)))))
% 0.20/0.40  = { by axiom 2 (associativity_of_multiply) }
% 0.20/0.40    multiply(a, multiply(b, multiply(a, multiply(a, multiply(b, multiply(multiply(a, b), b))))))
% 0.20/0.40  = { by axiom 2 (associativity_of_multiply) }
% 0.20/0.40    multiply(a, multiply(b, multiply(a, multiply(a, multiply(b, multiply(a, multiply(b, b)))))))
% 0.20/0.40  = { by lemma 3 R->L }
% 0.20/0.40    multiply(a, multiply(a, multiply(a, multiply(b, multiply(b, multiply(a, multiply(b, b)))))))
% 0.20/0.40  = { by lemma 3 }
% 0.20/0.40    multiply(a, multiply(a, multiply(a, multiply(a, multiply(b, multiply(b, multiply(b, b)))))))
% 0.20/0.40  % SZS output end Proof
% 0.20/0.40  
% 0.20/0.40  RESULT: Unsatisfiable (the axioms are contradictory).
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