%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP538-1 : 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 : n017.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 0.16s 1.25s
% Output   : Proof 0.16s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.74  % Problem  : GRP538-1 : TPTP v8.1.2. Released v2.6.0.
% 0.09/0.83  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/1.15  % Computer : n017.cluster.edu
% 0.10/1.15  % Model    : x86_64 x86_64
% 0.10/1.15  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/1.15  % Memory   : 8042.1875MB
% 0.10/1.15  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/1.15  % CPULimit : 300
% 0.10/1.15  % WCLimit  : 300
% 0.10/1.15  % DateTime : Mon Aug 28 21:15:13 EDT 2023
% 0.10/1.16  % CPUTime  : 
% 0.16/1.25  Command-line arguments: --ground-connectedness --complete-subsets
% 0.16/1.25  
% 0.16/1.25  % SZS status Unsatisfiable
% 0.16/1.26  
% 0.16/1.26  % SZS output start Proof
% 0.16/1.26  Axiom 1 (identity): identity = divide(X, X).
% 0.16/1.26  Axiom 2 (inverse): inverse(X) = divide(divide(Y, Y), X).
% 0.16/1.26  Axiom 3 (multiply): multiply(X, Y) = divide(X, divide(divide(Z, Z), Y)).
% 0.16/1.26  Axiom 4 (single_axiom): divide(divide(X, Y), divide(divide(X, Z), Y)) = Z.
% 0.16/1.26  
% 0.16/1.26  Lemma 5: divide(identity, X) = inverse(X).
% 0.16/1.26  Proof:
% 0.16/1.26    divide(identity, X)
% 0.16/1.26  = { by axiom 1 (identity) }
% 0.16/1.26    divide(divide(Y, Y), X)
% 0.16/1.26  = { by axiom 2 (inverse) R->L }
% 0.16/1.26    inverse(X)
% 0.16/1.26  
% 0.16/1.26  Lemma 6: divide(X, inverse(Y)) = multiply(X, Y).
% 0.16/1.26  Proof:
% 0.16/1.26    divide(X, inverse(Y))
% 0.16/1.26  = { by lemma 5 R->L }
% 0.16/1.26    divide(X, divide(identity, Y))
% 0.16/1.26  = { by axiom 1 (identity) }
% 0.16/1.26    divide(X, divide(divide(Z, Z), Y))
% 0.16/1.26  = { by axiom 3 (multiply) R->L }
% 0.16/1.26    multiply(X, Y)
% 0.16/1.26  
% 0.16/1.26  Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.16/1.26  Proof:
% 0.16/1.26    multiply(multiply(inverse(b2), b2), a2)
% 0.16/1.26  = { by lemma 6 R->L }
% 0.16/1.26    multiply(divide(inverse(b2), inverse(b2)), a2)
% 0.16/1.26  = { by axiom 1 (identity) R->L }
% 0.16/1.26    multiply(identity, a2)
% 0.16/1.26  = { by axiom 1 (identity) }
% 0.16/1.26    multiply(divide(a2, a2), a2)
% 0.16/1.26  = { by lemma 6 R->L }
% 0.16/1.26    divide(divide(a2, a2), inverse(a2))
% 0.16/1.26  = { by lemma 5 R->L }
% 0.16/1.26    divide(divide(a2, a2), divide(identity, a2))
% 0.16/1.26  = { by axiom 1 (identity) }
% 0.16/1.26    divide(divide(a2, a2), divide(divide(a2, a2), a2))
% 0.16/1.26  = { by axiom 4 (single_axiom) }
% 0.16/1.26    a2
% 0.16/1.26  % SZS output end Proof
% 0.16/1.26  
% 0.16/1.26  RESULT: Unsatisfiable (the axioms are contradictory).
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