%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP540-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : n001.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 01:18:50 EDT 2023

% Result   : Unsatisfiable 0.21s 0.38s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GRP540-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35  % Computer : n001.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Tue Aug 29 02:54:21 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.38  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.38  
% 0.21/0.38  % SZS status Unsatisfiable
% 0.21/0.38  
% 0.21/0.39  % SZS output start Proof
% 0.21/0.39  Axiom 1 (identity): identity = divide(X, X).
% 0.21/0.39  Axiom 2 (inverse): inverse(X) = divide(divide(Y, Y), X).
% 0.21/0.39  Axiom 3 (multiply): multiply(X, Y) = divide(X, divide(divide(Z, Z), Y)).
% 0.21/0.39  Axiom 4 (single_axiom): divide(divide(X, Y), divide(divide(X, Z), Y)) = Z.
% 0.21/0.39  
% 0.21/0.39  Lemma 5: divide(identity, X) = inverse(X).
% 0.21/0.39  Proof:
% 0.21/0.39    divide(identity, X)
% 0.21/0.39  = { by axiom 1 (identity) }
% 0.21/0.39    divide(divide(Y, Y), X)
% 0.21/0.39  = { by axiom 2 (inverse) R->L }
% 0.21/0.39    inverse(X)
% 0.21/0.39  
% 0.21/0.39  Lemma 6: divide(X, inverse(Y)) = multiply(X, Y).
% 0.21/0.39  Proof:
% 0.21/0.39    divide(X, inverse(Y))
% 0.21/0.39  = { by lemma 5 R->L }
% 0.21/0.39    divide(X, divide(identity, Y))
% 0.21/0.39  = { by axiom 1 (identity) }
% 0.21/0.39    divide(X, divide(divide(Z, Z), Y))
% 0.21/0.39  = { by axiom 3 (multiply) R->L }
% 0.21/0.39    multiply(X, Y)
% 0.21/0.39  
% 0.21/0.39  Lemma 7: multiply(divide(X, Y), Y) = X.
% 0.21/0.39  Proof:
% 0.21/0.39    multiply(divide(X, Y), Y)
% 0.21/0.39  = { by lemma 6 R->L }
% 0.21/0.39    divide(divide(X, Y), inverse(Y))
% 0.21/0.39  = { by lemma 5 R->L }
% 0.21/0.39    divide(divide(X, Y), divide(identity, Y))
% 0.21/0.39  = { by axiom 1 (identity) }
% 0.21/0.39    divide(divide(X, Y), divide(divide(X, X), Y))
% 0.21/0.39  = { by axiom 4 (single_axiom) }
% 0.21/0.39    X
% 0.21/0.39  
% 0.21/0.39  Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.21/0.39  Proof:
% 0.21/0.39    multiply(a, b)
% 0.21/0.39  = { by axiom 4 (single_axiom) R->L }
% 0.21/0.39    multiply(divide(divide(b, inverse(a)), divide(divide(b, a), inverse(a))), b)
% 0.21/0.39  = { by lemma 6 }
% 0.21/0.39    multiply(divide(multiply(b, a), divide(divide(b, a), inverse(a))), b)
% 0.21/0.39  = { by lemma 6 }
% 0.21/0.39    multiply(divide(multiply(b, a), multiply(divide(b, a), a)), b)
% 0.21/0.39  = { by lemma 7 }
% 0.21/0.39    multiply(divide(multiply(b, a), b), b)
% 0.21/0.39  = { by lemma 7 }
% 0.21/0.39    multiply(b, a)
% 0.21/0.39  % SZS output end Proof
% 0.21/0.39  
% 0.21/0.39  RESULT: Unsatisfiable (the axioms are contradictory).
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