%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP665+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:11:38 AM UTC 2026
% Result : Theorem 0.03s 0.45s
% Output : Proof 0.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP665+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 10:34:01 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.45 Command-line arguments: --no-flatten-goal
% 0.03/0.45
% 0.03/0.45 % SZS status Theorem
% 0.03/0.45
% 0.03/0.45 % SZS output start Proof
% 0.03/0.45 Axiom 1 (f09): mult(op_c, X) = mult(X, op_c).
% 0.03/0.45 Axiom 2 (f02): ld(X, mult(X, Y)) = Y.
% 0.03/0.45 Axiom 3 (f04): rd(mult(X, Y), Y) = X.
% 0.03/0.45 Axiom 4 (f08): mult(mult(X, Y), Z) = mult(mult(X, Z), ld(Z, mult(Y, Z))).
% 0.03/0.45 Axiom 5 (f07): mult(X, mult(Y, Z)) = mult(rd(mult(X, Y), X), mult(X, Z)).
% 0.03/0.45
% 0.03/0.45 Lemma 6: mult(op_c, mult(X, Y)) = mult(X, mult(Y, op_c)).
% 0.03/0.45 Proof:
% 0.03/0.45 mult(op_c, mult(X, Y))
% 0.03/0.45 = { by axiom 5 (f07) }
% 0.03/0.45 mult(rd(mult(op_c, X), op_c), mult(op_c, Y))
% 0.03/0.45 = { by axiom 1 (f09) }
% 0.03/0.45 mult(rd(mult(X, op_c), op_c), mult(op_c, Y))
% 0.03/0.45 = { by axiom 3 (f04) }
% 0.03/0.45 mult(X, mult(op_c, Y))
% 0.03/0.45 = { by axiom 1 (f09) }
% 0.03/0.45 mult(X, mult(Y, op_c))
% 0.03/0.45
% 0.03/0.45 Lemma 7: mult(mult(X, op_c), Y) = mult(op_c, mult(X, Y)).
% 0.03/0.45 Proof:
% 0.03/0.45 mult(mult(X, op_c), Y)
% 0.03/0.45 = { by axiom 4 (f08) }
% 0.03/0.45 mult(mult(X, Y), ld(Y, mult(op_c, Y)))
% 0.03/0.45 = { by axiom 1 (f09) }
% 0.03/0.45 mult(mult(X, Y), ld(Y, mult(Y, op_c)))
% 0.03/0.45 = { by axiom 2 (f02) }
% 0.03/0.45 mult(mult(X, Y), op_c)
% 0.03/0.45 = { by axiom 1 (f09) R->L }
% 0.03/0.45 mult(op_c, mult(X, Y))
% 0.03/0.45
% 0.03/0.45 Goal 1 (goals): tuple(mult(op_c, mult(x0_3, x1_3)), mult(mult(x0_2, op_c), x1_2), mult(mult(x0, x1), op_c)) = tuple(mult(mult(op_c, x0_3), x1_3), mult(x0_2, mult(op_c, x1_2)), mult(x0, mult(x1, op_c))).
% 0.03/0.45 Proof:
% 0.03/0.45 tuple(mult(op_c, mult(x0_3, x1_3)), mult(mult(x0_2, op_c), x1_2), mult(mult(x0, x1), op_c))
% 0.03/0.45 = { by axiom 1 (f09) R->L }
% 0.03/0.45 tuple(mult(op_c, mult(x0_3, x1_3)), mult(mult(x0_2, op_c), x1_2), mult(op_c, mult(x0, x1)))
% 0.03/0.45 = { by lemma 7 }
% 0.03/0.45 tuple(mult(op_c, mult(x0_3, x1_3)), mult(op_c, mult(x0_2, x1_2)), mult(op_c, mult(x0, x1)))
% 0.03/0.45 = { by lemma 6 }
% 0.03/0.45 tuple(mult(x0_3, mult(x1_3, op_c)), mult(op_c, mult(x0_2, x1_2)), mult(op_c, mult(x0, x1)))
% 0.03/0.45 = { by lemma 6 }
% 0.03/0.45 tuple(mult(x0_3, mult(x1_3, op_c)), mult(x0_2, mult(x1_2, op_c)), mult(op_c, mult(x0, x1)))
% 0.03/0.45 = { by lemma 6 }
% 0.03/0.45 tuple(mult(x0_3, mult(x1_3, op_c)), mult(x0_2, mult(x1_2, op_c)), mult(x0, mult(x1, op_c)))
% 0.03/0.45 = { by lemma 6 R->L }
% 0.03/0.45 tuple(mult(op_c, mult(x0_3, x1_3)), mult(x0_2, mult(x1_2, op_c)), mult(x0, mult(x1, op_c)))
% 0.03/0.45 = { by lemma 7 R->L }
% 0.03/0.45 tuple(mult(mult(x0_3, op_c), x1_3), mult(x0_2, mult(x1_2, op_c)), mult(x0, mult(x1, op_c)))
% 0.03/0.45 = { by axiom 1 (f09) R->L }
% 0.03/0.45 tuple(mult(mult(x0_3, op_c), x1_3), mult(x0_2, mult(op_c, x1_2)), mult(x0, mult(x1, op_c)))
% 0.03/0.45 = { by axiom 1 (f09) R->L }
% 0.03/0.45 tuple(mult(mult(op_c, x0_3), x1_3), mult(x0_2, mult(op_c, x1_2)), mult(x0, mult(x1, op_c)))
% 0.03/0.45 % SZS output end Proof
% 0.03/0.45
% 0.03/0.45 RESULT: Theorem (the conjecture is true).
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