%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP466-1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n025.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 01:18:33 EDT 2023

% Result   : Unsatisfiable 0.20s 0.37s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP466-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue Aug 29 01:56:09 EDT 2023
% 0.20/0.34  % CPUTime  : 
% 0.20/0.37  Command-line arguments: --no-flatten-goal
% 0.20/0.37  
% 0.20/0.37  % SZS status Unsatisfiable
% 0.20/0.37  
% 0.20/0.38  % SZS output start Proof
% 0.20/0.38  Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.20/0.38  Axiom 2 (single_axiom): divide(divide(X, X), divide(Y, divide(divide(Z, divide(W, Y)), inverse(W)))) = Z.
% 0.20/0.38  
% 0.20/0.38  Lemma 3: divide(divide(X, X), divide(Y, multiply(divide(Z, divide(W, Y)), W))) = Z.
% 0.20/0.38  Proof:
% 0.20/0.38    divide(divide(X, X), divide(Y, multiply(divide(Z, divide(W, Y)), W)))
% 0.20/0.38  = { by axiom 1 (multiply) }
% 0.20/0.38    divide(divide(X, X), divide(Y, divide(divide(Z, divide(W, Y)), inverse(W))))
% 0.20/0.38  = { by axiom 2 (single_axiom) }
% 0.20/0.38    Z
% 0.20/0.38  
% 0.20/0.38  Lemma 4: multiply(inverse(X), X) = divide(Y, Y).
% 0.20/0.38  Proof:
% 0.20/0.38    multiply(inverse(X), X)
% 0.20/0.38  = { by axiom 1 (multiply) }
% 0.20/0.38    divide(inverse(X), inverse(X))
% 0.20/0.38  = { by lemma 3 R->L }
% 0.20/0.38    divide(divide(Z, Z), divide(multiply(divide(W, divide(V, U)), V), multiply(divide(divide(inverse(X), inverse(X)), divide(U, multiply(divide(W, divide(V, U)), V))), U)))
% 0.20/0.38  = { by lemma 3 }
% 0.20/0.38    divide(divide(Z, Z), divide(multiply(divide(W, divide(V, U)), V), multiply(W, U)))
% 0.20/0.38  = { by lemma 3 R->L }
% 0.20/0.38    divide(divide(Z, Z), divide(multiply(divide(W, divide(V, U)), V), multiply(divide(divide(Y, Y), divide(U, multiply(divide(W, divide(V, U)), V))), U)))
% 0.20/0.38  = { by lemma 3 }
% 0.20/0.38    divide(Y, Y)
% 0.20/0.38  
% 0.20/0.38  Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.20/0.38  Proof:
% 0.20/0.38    multiply(inverse(a1), a1)
% 0.20/0.38  = { by lemma 4 }
% 0.20/0.38    divide(X, X)
% 0.20/0.38  = { by lemma 4 R->L }
% 0.20/0.38    multiply(inverse(b1), b1)
% 0.20/0.38  % SZS output end Proof
% 0.20/0.38  
% 0.20/0.38  RESULT: Unsatisfiable (the axioms are contradictory).
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