%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP704-11 : TPTP v8.1.2. Released v8.1.0.
% 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 : n011.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 01:19:48 EDT 2023

% Result   : Unsatisfiable 0.19s 0.39s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP704-11 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34  % Computer : n011.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue Aug 29 00:55:26 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.39  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.39  
% 0.19/0.39  % SZS status Unsatisfiable
% 0.19/0.39  
% 0.19/0.39  % SZS output start Proof
% 0.19/0.39  Axiom 1 (f05): mult(X, unit) = X.
% 0.19/0.39  Axiom 2 (f06): mult(unit, X) = X.
% 0.19/0.39  Axiom 3 (f01): mult(X, ld(X, Y)) = Y.
% 0.19/0.39  Axiom 4 (f09): mult(X, mult(Y, op_c)) = mult(mult(X, Y), op_c).
% 0.19/0.39  Axiom 5 (f02): ld(X, mult(X, Y)) = Y.
% 0.19/0.39  Axiom 6 (f11): op_d = ld(X, mult(op_c, X)).
% 0.19/0.39  Axiom 7 (f13): op_f = mult(X, mult(Y, ld(mult(X, Y), op_c))).
% 0.19/0.39  
% 0.19/0.40  Lemma 8: mult(op_c, X) = mult(X, op_c).
% 0.19/0.40  Proof:
% 0.19/0.40    mult(op_c, X)
% 0.19/0.40  = { by axiom 3 (f01) R->L }
% 0.19/0.40    mult(X, ld(X, mult(op_c, X)))
% 0.19/0.40  = { by axiom 6 (f11) R->L }
% 0.19/0.40    mult(X, op_d)
% 0.19/0.40  = { by axiom 6 (f11) }
% 0.19/0.40    mult(X, ld(op_c, mult(op_c, op_c)))
% 0.19/0.40  = { by axiom 5 (f02) }
% 0.19/0.40    mult(X, op_c)
% 0.19/0.40  
% 0.19/0.40  Lemma 9: mult(op_c, X) = mult(X, op_f).
% 0.19/0.40  Proof:
% 0.19/0.40    mult(op_c, X)
% 0.19/0.40  = { by lemma 8 }
% 0.19/0.40    mult(X, op_c)
% 0.19/0.40  = { by axiom 3 (f01) R->L }
% 0.19/0.40    mult(X, mult(Y, ld(Y, op_c)))
% 0.19/0.40  = { by axiom 2 (f06) R->L }
% 0.19/0.40    mult(X, mult(Y, mult(unit, ld(Y, op_c))))
% 0.19/0.40  = { by axiom 1 (f05) R->L }
% 0.19/0.40    mult(X, mult(Y, mult(unit, ld(mult(Y, unit), op_c))))
% 0.19/0.40  = { by axiom 7 (f13) R->L }
% 0.19/0.40    mult(X, op_f)
% 0.19/0.40  
% 0.19/0.40  Goal 1 (goal): mult(x4, mult(x5, op_f)) = mult(mult(x4, x5), op_f).
% 0.19/0.40  Proof:
% 0.19/0.40    mult(x4, mult(x5, op_f))
% 0.19/0.40  = { by lemma 9 R->L }
% 0.19/0.40    mult(x4, mult(op_c, x5))
% 0.19/0.40  = { by lemma 8 }
% 0.19/0.40    mult(x4, mult(x5, op_c))
% 0.19/0.40  = { by axiom 4 (f09) }
% 0.19/0.40    mult(mult(x4, x5), op_c)
% 0.19/0.40  = { by lemma 8 R->L }
% 0.19/0.40    mult(op_c, mult(x4, x5))
% 0.19/0.40  = { by lemma 9 }
% 0.19/0.40    mult(mult(x4, x5), op_f)
% 0.19/0.40  % SZS output end Proof
% 0.19/0.40  
% 0.19/0.40  RESULT: Unsatisfiable (the axioms are contradictory).
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