%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP685-11 : 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 : n024.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 01:19:42 EDT 2023

% Result   : Unsatisfiable 0.20s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP685-11 : 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
% 0.14/0.34  % Computer : n024.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Tue Aug 29 02:16:08 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.39  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.39  
% 0.20/0.39  % SZS status Unsatisfiable
% 0.20/0.39  
% 0.20/0.39  % SZS output start Proof
% 0.20/0.39  Axiom 1 (f01): ld(X, mult(X, X)) = X.
% 0.20/0.39  Axiom 2 (f02): rd(mult(X, X), X) = X.
% 0.20/0.39  Axiom 3 (f03): mult(X, ld(X, Y)) = ld(X, mult(X, Y)).
% 0.20/0.39  Axiom 4 (f04): mult(rd(X, Y), Y) = rd(mult(X, Y), Y).
% 0.20/0.39  Axiom 5 (f07): ld(X, mult(X, ld(Y, Y))) = rd(mult(rd(X, X), Y), Y).
% 0.20/0.39  Axiom 6 (f06): rd(mult(mult(X, Y), rd(Z, W)), rd(Z, W)) = mult(X, rd(mult(Y, W), W)).
% 0.20/0.39  
% 0.20/0.39  Lemma 7: mult(ld(X, X), X) = X.
% 0.20/0.39  Proof:
% 0.20/0.39    mult(ld(X, X), X)
% 0.20/0.39  = { by axiom 1 (f01) R->L }
% 0.20/0.39    mult(ld(X, ld(X, mult(X, X))), X)
% 0.20/0.39  = { by axiom 3 (f03) R->L }
% 0.20/0.39    mult(ld(X, mult(X, ld(X, X))), X)
% 0.20/0.39  = { by axiom 5 (f07) }
% 0.20/0.39    mult(rd(mult(rd(X, X), X), X), X)
% 0.20/0.39  = { by axiom 4 (f04) }
% 0.20/0.39    mult(rd(rd(mult(X, X), X), X), X)
% 0.20/0.39  = { by axiom 2 (f02) }
% 0.20/0.39    mult(rd(X, X), X)
% 0.20/0.39  = { by axiom 4 (f04) }
% 0.20/0.39    rd(mult(X, X), X)
% 0.20/0.39  = { by axiom 2 (f02) }
% 0.20/0.39    X
% 0.20/0.39  
% 0.20/0.39  Goal 1 (goal): rd(mult(x6, rd(x7, x8)), rd(x7, x8)) = rd(mult(x6, x8), x8).
% 0.20/0.39  Proof:
% 0.20/0.39    rd(mult(x6, rd(x7, x8)), rd(x7, x8))
% 0.20/0.39  = { by lemma 7 R->L }
% 0.20/0.39    rd(mult(mult(ld(x6, x6), x6), rd(x7, x8)), rd(x7, x8))
% 0.20/0.39  = { by axiom 6 (f06) }
% 0.20/0.40    mult(ld(x6, x6), rd(mult(x6, x8), x8))
% 0.20/0.40  = { by axiom 6 (f06) R->L }
% 0.20/0.40    rd(mult(mult(ld(x6, x6), x6), rd(mult(x8, x8), x8)), rd(mult(x8, x8), x8))
% 0.20/0.40  = { by axiom 2 (f02) }
% 0.20/0.40    rd(mult(mult(ld(x6, x6), x6), x8), rd(mult(x8, x8), x8))
% 0.20/0.40  = { by axiom 2 (f02) }
% 0.20/0.40    rd(mult(mult(ld(x6, x6), x6), x8), x8)
% 0.20/0.40  = { by lemma 7 }
% 0.20/0.40    rd(mult(x6, x8), x8)
% 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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