%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP703-10 : 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 : n026.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 01:19:47 EDT 2023

% Result   : Unsatisfiable 0.20s 0.40s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP703-10 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35  % Computer : n026.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue Aug 29 02:20:20 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.40  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.40  
% 0.20/0.40  % SZS status Unsatisfiable
% 0.20/0.40  
% 0.20/0.40  % SZS output start Proof
% 0.20/0.40  Axiom 1 (f05): mult(X, unit) = X.
% 0.20/0.40  Axiom 2 (f06): mult(unit, X) = X.
% 0.20/0.40  Axiom 3 (f02): ld(X, mult(X, Y)) = Y.
% 0.20/0.40  Axiom 4 (f11): op_d = ld(X, mult(op_c, X)).
% 0.20/0.40  Axiom 5 (f03): mult(rd(X, Y), Y) = X.
% 0.20/0.40  Axiom 6 (f08): mult(op_c, mult(X, Y)) = mult(mult(op_c, X), Y).
% 0.20/0.40  Axiom 7 (f12): op_e = mult(mult(rd(op_c, mult(X, Y)), Y), X).
% 0.20/0.40  
% 0.20/0.40  Lemma 8: op_c = op_d.
% 0.20/0.40  Proof:
% 0.20/0.40    op_c
% 0.20/0.40  = { by axiom 3 (f02) R->L }
% 0.20/0.40    ld(op_c, mult(op_c, op_c))
% 0.20/0.40  = { by axiom 4 (f11) R->L }
% 0.20/0.40    op_d
% 0.20/0.40  
% 0.20/0.40  Lemma 9: op_e = op_d.
% 0.20/0.40  Proof:
% 0.20/0.40    op_e
% 0.20/0.40  = { by axiom 7 (f12) }
% 0.20/0.40    mult(mult(rd(op_c, mult(unit, X)), X), unit)
% 0.20/0.40  = { by axiom 1 (f05) }
% 0.20/0.40    mult(rd(op_c, mult(unit, X)), X)
% 0.20/0.40  = { by lemma 8 }
% 0.20/0.40    mult(rd(op_d, mult(unit, X)), X)
% 0.20/0.40  = { by axiom 2 (f06) }
% 0.20/0.40    mult(rd(op_d, X), X)
% 0.20/0.40  = { by axiom 5 (f03) }
% 0.20/0.40    op_d
% 0.20/0.40  
% 0.20/0.40  Goal 1 (goal): mult(op_e, mult(x2, x3)) = mult(mult(op_e, x2), x3).
% 0.20/0.40  Proof:
% 0.20/0.40    mult(op_e, mult(x2, x3))
% 0.20/0.40  = { by lemma 9 }
% 0.20/0.40    mult(op_d, mult(x2, x3))
% 0.20/0.40  = { by lemma 8 R->L }
% 0.20/0.40    mult(op_c, mult(x2, x3))
% 0.20/0.40  = { by axiom 6 (f08) }
% 0.20/0.40    mult(mult(op_c, x2), x3)
% 0.20/0.40  = { by lemma 8 }
% 0.20/0.40    mult(mult(op_d, x2), x3)
% 0.20/0.40  = { by lemma 9 R->L }
% 0.20/0.40    mult(mult(op_e, x2), x3)
% 0.20/0.40  % SZS output end Proof
% 0.20/0.40  
% 0.20/0.40  RESULT: Unsatisfiable (the axioms are contradictory).
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