%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP709-1 : TPTP v8.1.2. Released v4.0.0.
% 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 01:19:50 EDT 2023

% Result   : Unsatisfiable 0.12s 0.37s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : GRP709-1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.32  % Computer : n016.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Tue Aug 29 00:01:15 EDT 2023
% 0.12/0.32  % CPUTime  : 
% 0.12/0.37  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.12/0.37  
% 0.12/0.37  % SZS status Unsatisfiable
% 0.12/0.37  
% 0.12/0.38  % SZS output start Proof
% 0.12/0.38  Axiom 1 (c06): mult(unit, X) = X.
% 0.12/0.38  Axiom 2 (c08): mult(op_c, X) = mult(X, op_c).
% 0.12/0.38  Axiom 3 (c09): mult(X, mult(Y, op_c)) = mult(mult(X, Y), op_c).
% 0.12/0.38  Axiom 4 (c07): mult(X, mult(Y, mult(X, Z))) = mult(mult(X, mult(Y, X)), Z).
% 0.12/0.38  
% 0.12/0.38  Lemma 5: mult(op_c, mult(X, Y)) = mult(X, mult(Y, op_c)).
% 0.12/0.38  Proof:
% 0.12/0.38    mult(op_c, mult(X, Y))
% 0.12/0.38  = { by axiom 2 (c08) }
% 0.12/0.38    mult(mult(X, Y), op_c)
% 0.12/0.38  = { by axiom 3 (c09) R->L }
% 0.12/0.38    mult(X, mult(Y, op_c))
% 0.12/0.38  
% 0.12/0.38  Lemma 6: mult(mult(X, X), Y) = mult(X, mult(X, Y)).
% 0.12/0.38  Proof:
% 0.12/0.38    mult(mult(X, X), Y)
% 0.12/0.38  = { by axiom 1 (c06) R->L }
% 0.12/0.38    mult(mult(X, mult(unit, X)), Y)
% 0.12/0.38  = { by axiom 4 (c07) R->L }
% 0.12/0.38    mult(X, mult(unit, mult(X, Y)))
% 0.12/0.38  = { by axiom 1 (c06) }
% 0.12/0.38    mult(X, mult(X, Y))
% 0.12/0.38  
% 0.12/0.38  Goal 1 (goals): mult(mult(op_c, op_c), mult(a, b)) = mult(mult(mult(op_c, op_c), a), b).
% 0.12/0.38  Proof:
% 0.12/0.38    mult(mult(op_c, op_c), mult(a, b))
% 0.12/0.38  = { by lemma 6 }
% 0.12/0.38    mult(op_c, mult(op_c, mult(a, b)))
% 0.12/0.38  = { by lemma 5 }
% 0.12/0.38    mult(op_c, mult(a, mult(b, op_c)))
% 0.12/0.38  = { by lemma 5 }
% 0.12/0.38    mult(a, mult(mult(b, op_c), op_c))
% 0.12/0.38  = { by axiom 2 (c08) R->L }
% 0.12/0.38    mult(a, mult(op_c, mult(b, op_c)))
% 0.12/0.38  = { by axiom 2 (c08) R->L }
% 0.12/0.38    mult(a, mult(op_c, mult(op_c, b)))
% 0.12/0.38  = { by axiom 2 (c08) }
% 0.12/0.38    mult(a, mult(mult(op_c, b), op_c))
% 0.12/0.38  = { by lemma 5 R->L }
% 0.12/0.38    mult(op_c, mult(a, mult(op_c, b)))
% 0.12/0.38  = { by axiom 4 (c07) }
% 0.12/0.38    mult(mult(op_c, mult(a, op_c)), b)
% 0.12/0.38  = { by axiom 2 (c08) R->L }
% 0.12/0.38    mult(mult(op_c, mult(op_c, a)), b)
% 0.12/0.38  = { by lemma 6 R->L }
% 0.12/0.38    mult(mult(mult(op_c, op_c), a), b)
% 0.12/0.38  % SZS output end Proof
% 0.12/0.38  
% 0.12/0.38  RESULT: Unsatisfiable (the axioms are contradictory).
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