%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP680-1 : 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 : n029.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 01:19:40 EDT 2023

% Result   : Unsatisfiable 0.21s 0.41s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP680-1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13  % 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 : n029.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 01:31:11 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.41  Command-line arguments: --no-flatten-goal
% 0.21/0.41  
% 0.21/0.41  % SZS status Unsatisfiable
% 0.21/0.41  
% 0.21/0.41  % SZS output start Proof
% 0.21/0.41  Axiom 1 (c05): mult(X, unit) = X.
% 0.21/0.41  Axiom 2 (c09): mult(op_c, X) = mult(X, op_c).
% 0.21/0.41  Axiom 3 (c01): mult(X, ld(X, Y)) = Y.
% 0.21/0.41  Axiom 4 (c08): mult(i(X), mult(X, Y)) = Y.
% 0.21/0.41  Axiom 5 (c07): mult(X, mult(Y, mult(X, Z))) = mult(mult(X, mult(Y, X)), Z).
% 0.21/0.41  
% 0.21/0.41  Lemma 6: mult(i(X), Y) = ld(X, Y).
% 0.21/0.41  Proof:
% 0.21/0.41    mult(i(X), Y)
% 0.21/0.41  = { by axiom 3 (c01) R->L }
% 0.21/0.41    mult(i(X), mult(X, ld(X, Y)))
% 0.21/0.41  = { by axiom 4 (c08) }
% 0.21/0.41    ld(X, Y)
% 0.21/0.41  
% 0.21/0.41  Goal 1 (goals): mult(i(op_c), a) = mult(a, i(op_c)).
% 0.21/0.41  Proof:
% 0.21/0.41    mult(i(op_c), a)
% 0.21/0.41  = { by lemma 6 }
% 0.21/0.41    ld(op_c, a)
% 0.21/0.41  = { by axiom 1 (c05) R->L }
% 0.21/0.41    ld(op_c, mult(a, unit))
% 0.21/0.41  = { by lemma 6 R->L }
% 0.21/0.42    mult(i(op_c), mult(a, unit))
% 0.21/0.42  = { by axiom 4 (c08) R->L }
% 0.21/0.42    mult(i(op_c), mult(a, mult(i(op_c), mult(op_c, unit))))
% 0.21/0.42  = { by axiom 1 (c05) }
% 0.21/0.42    mult(i(op_c), mult(a, mult(i(op_c), op_c)))
% 0.21/0.42  = { by axiom 5 (c07) }
% 0.21/0.42    mult(mult(i(op_c), mult(a, i(op_c))), op_c)
% 0.21/0.42  = { by axiom 2 (c09) R->L }
% 0.21/0.42    mult(op_c, mult(i(op_c), mult(a, i(op_c))))
% 0.21/0.42  = { by lemma 6 }
% 0.21/0.42    mult(op_c, ld(op_c, mult(a, i(op_c))))
% 0.21/0.42  = { by axiom 3 (c01) }
% 0.21/0.42    mult(a, i(op_c))
% 0.21/0.42  % SZS output end Proof
% 0.21/0.42  
% 0.21/0.42  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------