%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP710-11 : 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 : n018.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 0.21s 0.40s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : GRP710-11 : TPTP v8.1.2. Released v8.1.0.
% 0.08/0.13  % 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 : n018.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 : Mon Aug 28 21:04:32 EDT 2023
% 0.21/0.36  % CPUTime  : 
% 0.21/0.40  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.40  
% 0.21/0.40  % SZS status Unsatisfiable
% 0.21/0.40  
% 0.21/0.41  % SZS output start Proof
% 0.21/0.41  Axiom 1 (f01): mult(X, unit) = X.
% 0.21/0.41  Axiom 2 (f02): mult(unit, X) = X.
% 0.21/0.41  Axiom 3 (f04): mult(X, i(X)) = unit.
% 0.21/0.41  Axiom 4 (f05): mult(i(X), X) = unit.
% 0.21/0.41  Axiom 5 (f03): mult(X, mult(Y, mult(Y, Z))) = mult(mult(mult(X, Y), Y), Z).
% 0.21/0.41  
% 0.21/0.41  Lemma 6: mult(mult(X, Y), Y) = mult(X, mult(Y, Y)).
% 0.21/0.41  Proof:
% 0.21/0.41    mult(mult(X, Y), Y)
% 0.21/0.41  = { by axiom 1 (f01) R->L }
% 0.21/0.41    mult(mult(mult(X, Y), Y), unit)
% 0.21/0.41  = { by axiom 5 (f03) R->L }
% 0.21/0.41    mult(X, mult(Y, mult(Y, unit)))
% 0.21/0.41  = { by axiom 1 (f01) }
% 0.21/0.41    mult(X, mult(Y, Y))
% 0.21/0.41  
% 0.21/0.41  Goal 1 (goal): mult(X, x4) = x3.
% 0.21/0.41  The goal is true when:
% 0.21/0.41    X = mult(mult(mult(x3, x4), i(x4)), i(x4))
% 0.21/0.41  
% 0.21/0.41  Proof:
% 0.21/0.41    mult(mult(mult(mult(x3, x4), i(x4)), i(x4)), x4)
% 0.21/0.41  = { by axiom 5 (f03) R->L }
% 0.21/0.41    mult(mult(x3, x4), mult(i(x4), mult(i(x4), x4)))
% 0.21/0.41  = { by axiom 4 (f05) }
% 0.21/0.41    mult(mult(x3, x4), mult(i(x4), unit))
% 0.21/0.41  = { by axiom 1 (f01) }
% 0.21/0.41    mult(mult(x3, x4), i(x4))
% 0.21/0.41  = { by axiom 1 (f01) R->L }
% 0.21/0.41    mult(mult(x3, mult(x4, unit)), i(x4))
% 0.21/0.41  = { by axiom 3 (f04) R->L }
% 0.21/0.41    mult(mult(x3, mult(x4, mult(x4, i(x4)))), i(x4))
% 0.21/0.41  = { by axiom 5 (f03) }
% 0.21/0.41    mult(mult(mult(mult(x3, x4), x4), i(x4)), i(x4))
% 0.21/0.41  = { by lemma 6 }
% 0.21/0.41    mult(mult(mult(x3, x4), x4), mult(i(x4), i(x4)))
% 0.21/0.41  = { by axiom 5 (f03) R->L }
% 0.21/0.41    mult(x3, mult(x4, mult(x4, mult(i(x4), i(x4)))))
% 0.21/0.41  = { by lemma 6 R->L }
% 0.21/0.41    mult(x3, mult(x4, mult(mult(x4, i(x4)), i(x4))))
% 0.21/0.41  = { by axiom 3 (f04) }
% 0.21/0.41    mult(x3, mult(x4, mult(unit, i(x4))))
% 0.21/0.41  = { by axiom 2 (f02) }
% 0.21/0.41    mult(x3, mult(x4, i(x4)))
% 0.21/0.41  = { by axiom 3 (f04) }
% 0.21/0.41    mult(x3, unit)
% 0.21/0.41  = { by axiom 1 (f01) }
% 0.21/0.41    x3
% 0.21/0.41  % SZS output end Proof
% 0.21/0.41  
% 0.21/0.41  RESULT: Unsatisfiable (the axioms are contradictory).
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