%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP001-4 : TPTP v8.1.2. Released v1.0.0.
% 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 01:16:28 EDT 2023

% Result   : Unsatisfiable 0.14s 0.39s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP001-4 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14  % 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 : n016.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 01:31:30 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.38  Command-line arguments: --no-flatten-goal
% 0.14/0.38  
% 0.14/0.39  % SZS status Unsatisfiable
% 0.14/0.39  
% 0.14/0.39  % SZS output start Proof
% 0.14/0.39  Axiom 1 (squareness): multiply(X, X) = identity.
% 0.14/0.39  Axiom 2 (left_identity): multiply(identity, X) = X.
% 0.14/0.39  Axiom 3 (a_times_b_is_c): multiply(a, b) = c.
% 0.14/0.39  Axiom 4 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.14/0.39  
% 0.14/0.39  Lemma 5: multiply(X, multiply(X, Y)) = Y.
% 0.14/0.39  Proof:
% 0.14/0.39    multiply(X, multiply(X, Y))
% 0.14/0.39  = { by axiom 4 (associativity) R->L }
% 0.14/0.39    multiply(multiply(X, X), Y)
% 0.14/0.39  = { by axiom 1 (squareness) }
% 0.14/0.39    multiply(identity, Y)
% 0.14/0.39  = { by axiom 2 (left_identity) }
% 0.14/0.39    Y
% 0.14/0.39  
% 0.14/0.39  Lemma 6: multiply(a, multiply(b, X)) = multiply(c, X).
% 0.14/0.39  Proof:
% 0.14/0.39    multiply(a, multiply(b, X))
% 0.14/0.39  = { by axiom 4 (associativity) R->L }
% 0.14/0.39    multiply(multiply(a, b), X)
% 0.14/0.39  = { by axiom 3 (a_times_b_is_c) }
% 0.14/0.39    multiply(c, X)
% 0.14/0.39  
% 0.14/0.39  Goal 1 (prove_b_times_a_is_c): multiply(b, a) = c.
% 0.14/0.39  Proof:
% 0.14/0.39    multiply(b, a)
% 0.14/0.39  = { by lemma 5 R->L }
% 0.14/0.39    multiply(a, multiply(a, multiply(b, a)))
% 0.14/0.39  = { by lemma 6 }
% 0.14/0.39    multiply(a, multiply(c, a))
% 0.14/0.39  = { by lemma 5 R->L }
% 0.14/0.39    multiply(a, multiply(c, multiply(a, multiply(a, a))))
% 0.14/0.39  = { by axiom 1 (squareness) }
% 0.14/0.39    multiply(a, multiply(c, multiply(a, identity)))
% 0.14/0.39  = { by axiom 1 (squareness) R->L }
% 0.14/0.39    multiply(a, multiply(c, multiply(a, multiply(b, b))))
% 0.14/0.39  = { by lemma 6 }
% 0.14/0.39    multiply(a, multiply(c, multiply(c, b)))
% 0.14/0.39  = { by lemma 5 }
% 0.14/0.39    multiply(a, b)
% 0.14/0.39  = { by axiom 3 (a_times_b_is_c) }
% 0.14/0.39    c
% 0.14/0.39  % SZS output end Proof
% 0.14/0.39  
% 0.14/0.39  RESULT: Unsatisfiable (the axioms are contradictory).
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