%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP660+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 10:11:37 AM UTC 2026
% Result : Theorem 0.06s 0.42s
% Output : Proof 0.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP660+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 27 10:32:50 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.42 Command-line arguments: --no-flatten-goal
% 0.06/0.42
% 0.06/0.42 % SZS status Theorem
% 0.06/0.42
% 0.06/0.44 % SZS output start Proof
% 0.06/0.44 Axiom 1 (f04): rd(mult(X, Y), Y) = X.
% 0.06/0.44 Axiom 2 (f02): ld(X, mult(X, Y)) = Y.
% 0.06/0.44 Axiom 3 (f01): mult(X, ld(X, Y)) = Y.
% 0.06/0.44 Axiom 4 (f03): mult(rd(X, Y), Y) = X.
% 0.06/0.44 Axiom 5 (f05): mult(mult(mult(X, Y), Z), X) = mult(X, mult(Y, mult(Z, X))).
% 0.06/0.44
% 0.06/0.44 Lemma 6: ld(rd(X, Y), X) = Y.
% 0.06/0.44 Proof:
% 0.06/0.44 ld(rd(X, Y), X)
% 0.06/0.44 = { by axiom 4 (f03) R->L }
% 0.06/0.44 ld(rd(X, Y), mult(rd(X, Y), Y))
% 0.06/0.44 = { by axiom 2 (f02) }
% 0.06/0.44 Y
% 0.06/0.44
% 0.06/0.44 Lemma 7: rd(mult(X, mult(Y, mult(Z, X))), X) = mult(mult(X, Y), Z).
% 0.06/0.44 Proof:
% 0.06/0.44 rd(mult(X, mult(Y, mult(Z, X))), X)
% 0.06/0.44 = { by axiom 5 (f05) R->L }
% 0.06/0.44 rd(mult(mult(mult(X, Y), Z), X), X)
% 0.06/0.44 = { by axiom 1 (f04) }
% 0.06/0.44 mult(mult(X, Y), Z)
% 0.06/0.44
% 0.06/0.44 Lemma 8: mult(mult(X, rd(Y, mult(Z, X))), Z) = rd(mult(X, Y), X).
% 0.06/0.44 Proof:
% 0.06/0.44 mult(mult(X, rd(Y, mult(Z, X))), Z)
% 0.06/0.44 = { by lemma 7 R->L }
% 0.06/0.44 rd(mult(X, mult(rd(Y, mult(Z, X)), mult(Z, X))), X)
% 0.06/0.44 = { by axiom 4 (f03) }
% 0.06/0.44 rd(mult(X, Y), X)
% 0.06/0.44
% 0.06/0.44 Lemma 9: mult(X, rd(Y, mult(Z, X))) = rd(rd(mult(X, Y), X), Z).
% 0.06/0.44 Proof:
% 0.06/0.44 mult(X, rd(Y, mult(Z, X)))
% 0.06/0.44 = { by axiom 1 (f04) R->L }
% 0.06/0.44 rd(mult(mult(X, rd(Y, mult(Z, X))), Z), Z)
% 0.06/0.44 = { by lemma 8 }
% 0.06/0.44 rd(rd(mult(X, Y), X), Z)
% 0.06/0.44
% 0.06/0.44 Lemma 10: mult(X, rd(X, Y)) = rd(X, rd(Y, X)).
% 0.06/0.44 Proof:
% 0.06/0.44 mult(X, rd(X, Y))
% 0.06/0.44 = { by axiom 4 (f03) R->L }
% 0.06/0.44 mult(X, rd(X, mult(rd(Y, X), X)))
% 0.06/0.44 = { by lemma 9 }
% 0.06/0.44 rd(rd(mult(X, X), X), rd(Y, X))
% 0.06/0.44 = { by axiom 1 (f04) }
% 0.06/0.44 rd(X, rd(Y, X))
% 0.06/0.44
% 0.06/0.44 Lemma 11: mult(mult(X, Y), rd(Z, X)) = rd(mult(X, mult(Y, Z)), X).
% 0.06/0.44 Proof:
% 0.06/0.44 mult(mult(X, Y), rd(Z, X))
% 0.06/0.44 = { by lemma 7 R->L }
% 0.06/0.44 rd(mult(X, mult(Y, mult(rd(Z, X), X))), X)
% 0.06/0.44 = { by axiom 4 (f03) }
% 0.06/0.44 rd(mult(X, mult(Y, Z)), X)
% 0.06/0.44
% 0.06/0.44 Lemma 12: rd(X, rd(X, X)) = X.
% 0.06/0.44 Proof:
% 0.06/0.44 rd(X, rd(X, X))
% 0.06/0.44 = { by lemma 6 R->L }
% 0.06/0.44 ld(rd(rd(X, X), rd(X, rd(X, X))), rd(X, X))
% 0.06/0.44 = { by lemma 10 R->L }
% 0.06/0.44 ld(mult(rd(X, X), rd(rd(X, X), X)), rd(X, X))
% 0.06/0.44 = { by axiom 3 (f01) R->L }
% 0.06/0.44 ld(mult(mult(X, ld(X, rd(X, X))), rd(rd(X, X), X)), rd(X, X))
% 0.06/0.44 = { by lemma 11 }
% 0.06/0.44 ld(rd(mult(X, mult(ld(X, rd(X, X)), rd(X, X))), X), rd(X, X))
% 0.06/0.44 = { by axiom 2 (f02) R->L }
% 0.06/0.44 ld(rd(ld(rd(X, X), mult(rd(X, X), mult(X, mult(ld(X, rd(X, X)), rd(X, X))))), X), rd(X, X))
% 0.06/0.44 = { by axiom 5 (f05) R->L }
% 0.06/0.44 ld(rd(ld(rd(X, X), mult(mult(mult(rd(X, X), X), ld(X, rd(X, X))), rd(X, X))), X), rd(X, X))
% 0.06/0.44 = { by axiom 4 (f03) }
% 0.06/0.44 ld(rd(ld(rd(X, X), mult(mult(X, ld(X, rd(X, X))), rd(X, X))), X), rd(X, X))
% 0.06/0.44 = { by axiom 3 (f01) }
% 0.06/0.44 ld(rd(ld(rd(X, X), mult(rd(X, X), rd(X, X))), X), rd(X, X))
% 0.06/0.44 = { by axiom 2 (f02) }
% 0.06/0.44 ld(rd(rd(X, X), X), rd(X, X))
% 0.06/0.44 = { by lemma 6 }
% 0.06/0.44 X
% 0.06/0.44
% 0.06/0.44 Lemma 13: ld(X, X) = rd(X, X).
% 0.06/0.44 Proof:
% 0.06/0.44 ld(X, X)
% 0.06/0.44 = { by lemma 12 R->L }
% 0.06/0.44 ld(rd(X, rd(X, X)), X)
% 0.06/0.44 = { by lemma 6 }
% 0.06/0.44 rd(X, X)
% 0.06/0.44
% 0.06/0.44 Lemma 14: ld(X, rd(rd(mult(X, Y), X), Z)) = rd(Y, mult(Z, X)).
% 0.06/0.44 Proof:
% 0.06/0.44 ld(X, rd(rd(mult(X, Y), X), Z))
% 0.06/0.44 = { by lemma 9 R->L }
% 0.06/0.44 ld(X, mult(X, rd(Y, mult(Z, X))))
% 0.06/0.44 = { by axiom 2 (f02) }
% 0.06/0.44 rd(Y, mult(Z, X))
% 0.06/0.44
% 0.06/0.44 Lemma 15: ld(rd(X, X), rd(X, Y)) = rd(X, mult(Y, rd(X, X))).
% 0.06/0.44 Proof:
% 0.06/0.44 ld(rd(X, X), rd(X, Y))
% 0.06/0.44 = { by lemma 12 R->L }
% 0.06/0.44 ld(rd(X, X), rd(rd(X, rd(X, X)), Y))
% 0.06/0.44 = { by axiom 3 (f01) R->L }
% 0.06/0.44 ld(rd(X, X), rd(rd(mult(rd(X, X), ld(rd(X, X), X)), rd(X, X)), Y))
% 0.06/0.44 = { by lemma 14 }
% 0.06/0.44 rd(ld(rd(X, X), X), mult(Y, rd(X, X)))
% 0.06/0.44 = { by lemma 6 }
% 0.06/0.44 rd(X, mult(Y, rd(X, X)))
% 0.06/0.44
% 0.06/0.44 Lemma 16: mult(X, mult(ld(X, Y), mult(Z, X))) = mult(mult(Y, Z), X).
% 0.06/0.44 Proof:
% 0.06/0.44 mult(X, mult(ld(X, Y), mult(Z, X)))
% 0.06/0.44 = { by axiom 5 (f05) R->L }
% 0.06/0.44 mult(mult(mult(X, ld(X, Y)), Z), X)
% 0.06/0.44 = { by axiom 3 (f01) }
% 0.06/0.45 mult(mult(Y, Z), X)
% 0.06/0.45
% 0.06/0.45 Lemma 17: mult(rd(X, X), Y) = rd(Y, rd(X, X)).
% 0.06/0.45 Proof:
% 0.06/0.45 mult(rd(X, X), Y)
% 0.06/0.45 = { by axiom 3 (f01) R->L }
% 0.06/0.45 mult(rd(X, X), mult(rd(X, X), ld(rd(X, X), Y)))
% 0.06/0.45 = { by axiom 1 (f04) R->L }
% 0.06/0.45 mult(rd(X, X), mult(rd(X, rd(mult(X, X), X)), ld(rd(X, X), Y)))
% 0.06/0.45 = { by axiom 4 (f03) R->L }
% 0.06/0.45 mult(rd(X, X), mult(rd(X, rd(mult(X, mult(rd(X, X), X)), X)), ld(rd(X, X), Y)))
% 0.06/0.45 = { by lemma 11 R->L }
% 0.06/0.45 mult(rd(X, X), mult(rd(X, mult(mult(X, rd(X, X)), rd(X, X))), ld(rd(X, X), Y)))
% 0.06/0.45 = { by lemma 15 R->L }
% 0.06/0.45 mult(rd(X, X), mult(ld(rd(X, X), rd(X, mult(X, rd(X, X)))), ld(rd(X, X), Y)))
% 0.06/0.45 = { by lemma 15 R->L }
% 0.06/0.45 mult(rd(X, X), mult(ld(rd(X, X), ld(rd(X, X), rd(X, X))), ld(rd(X, X), Y)))
% 0.06/0.45 = { by axiom 4 (f03) R->L }
% 0.06/0.45 mult(rd(X, X), mult(ld(rd(X, X), ld(rd(X, X), rd(X, X))), mult(rd(ld(rd(X, X), Y), rd(X, X)), rd(X, X))))
% 0.06/0.45 = { by lemma 16 }
% 0.06/0.45 mult(mult(ld(rd(X, X), rd(X, X)), rd(ld(rd(X, X), Y), rd(X, X))), rd(X, X))
% 0.06/0.45 = { by axiom 3 (f01) R->L }
% 0.06/0.45 mult(mult(ld(rd(X, X), rd(X, X)), rd(ld(rd(X, X), Y), mult(rd(X, X), ld(rd(X, X), rd(X, X))))), rd(X, X))
% 0.06/0.45 = { by lemma 8 }
% 0.06/0.45 rd(mult(ld(rd(X, X), rd(X, X)), ld(rd(X, X), Y)), ld(rd(X, X), rd(X, X)))
% 0.06/0.45 = { by lemma 15 }
% 0.06/0.45 rd(mult(rd(X, mult(X, rd(X, X))), ld(rd(X, X), Y)), ld(rd(X, X), rd(X, X)))
% 0.06/0.45 = { by lemma 15 }
% 0.06/0.45 rd(mult(rd(X, mult(X, rd(X, X))), ld(rd(X, X), Y)), rd(X, mult(X, rd(X, X))))
% 0.06/0.45 = { by lemma 10 }
% 0.06/0.45 rd(mult(rd(X, rd(X, rd(X, X))), ld(rd(X, X), Y)), rd(X, mult(X, rd(X, X))))
% 0.06/0.45 = { by lemma 10 }
% 0.06/0.45 rd(mult(rd(X, rd(X, rd(X, X))), ld(rd(X, X), Y)), rd(X, rd(X, rd(X, X))))
% 0.06/0.45 = { by lemma 12 }
% 0.06/0.45 rd(mult(rd(X, X), ld(rd(X, X), Y)), rd(X, rd(X, rd(X, X))))
% 0.06/0.45 = { by lemma 12 }
% 0.06/0.45 rd(mult(rd(X, X), ld(rd(X, X), Y)), rd(X, X))
% 0.06/0.45 = { by axiom 3 (f01) }
% 0.06/0.45 rd(Y, rd(X, X))
% 0.06/0.45
% 0.06/0.45 Lemma 18: mult(X, rd(Y, Y)) = ld(rd(Y, Y), X).
% 0.06/0.45 Proof:
% 0.06/0.45 mult(X, rd(Y, Y))
% 0.06/0.45 = { by axiom 1 (f04) R->L }
% 0.06/0.45 rd(mult(mult(X, rd(Y, Y)), rd(Y, Y)), rd(Y, Y))
% 0.06/0.45 = { by lemma 12 R->L }
% 0.06/0.45 rd(mult(mult(X, rd(Y, Y)), rd(Y, rd(Y, rd(Y, Y)))), rd(Y, Y))
% 0.06/0.45 = { by lemma 10 R->L }
% 0.06/0.45 rd(mult(mult(X, rd(Y, Y)), rd(Y, mult(Y, rd(Y, Y)))), rd(Y, Y))
% 0.06/0.45 = { by lemma 15 R->L }
% 0.06/0.45 rd(mult(mult(X, rd(Y, Y)), ld(rd(Y, Y), rd(Y, Y))), rd(Y, Y))
% 0.06/0.45 = { by lemma 17 R->L }
% 0.06/0.45 mult(rd(Y, Y), mult(mult(X, rd(Y, Y)), ld(rd(Y, Y), rd(Y, Y))))
% 0.06/0.45 = { by lemma 16 R->L }
% 0.06/0.45 mult(rd(Y, Y), mult(ld(rd(Y, Y), rd(Y, Y)), mult(ld(ld(rd(Y, Y), rd(Y, Y)), X), mult(rd(Y, Y), ld(rd(Y, Y), rd(Y, Y))))))
% 0.06/0.45 = { by axiom 3 (f01) }
% 0.06/0.45 mult(rd(Y, Y), mult(ld(rd(Y, Y), rd(Y, Y)), mult(ld(ld(rd(Y, Y), rd(Y, Y)), X), rd(Y, Y))))
% 0.06/0.45 = { by lemma 16 }
% 0.06/0.45 mult(mult(rd(Y, Y), ld(ld(rd(Y, Y), rd(Y, Y)), X)), rd(Y, Y))
% 0.06/0.45 = { by lemma 17 }
% 0.06/0.45 mult(rd(ld(ld(rd(Y, Y), rd(Y, Y)), X), rd(Y, Y)), rd(Y, Y))
% 0.06/0.45 = { by axiom 4 (f03) }
% 0.06/0.45 ld(ld(rd(Y, Y), rd(Y, Y)), X)
% 0.06/0.45 = { by lemma 15 }
% 0.06/0.45 ld(rd(Y, mult(Y, rd(Y, Y))), X)
% 0.06/0.45 = { by lemma 10 }
% 0.06/0.45 ld(rd(Y, rd(Y, rd(Y, Y))), X)
% 0.06/0.45 = { by lemma 12 }
% 0.06/0.45 ld(rd(Y, Y), X)
% 0.06/0.45
% 0.06/0.45 Lemma 19: rd(rd(X, rd(Y, Y)), X) = rd(Y, Y).
% 0.06/0.45 Proof:
% 0.06/0.45 rd(rd(X, rd(Y, Y)), X)
% 0.06/0.45 = { by lemma 17 R->L }
% 0.06/0.45 rd(mult(rd(Y, Y), X), X)
% 0.06/0.45 = { by axiom 1 (f04) }
% 0.06/0.45 rd(Y, Y)
% 0.06/0.45
% 0.06/0.45 Lemma 20: rd(Y, Y) = rd(X, X).
% 0.06/0.45 Proof:
% 0.06/0.45 rd(Y, Y)
% 0.06/0.45 = { by axiom 2 (f02) R->L }
% 0.06/0.45 rd(Y, ld(rd(Z, Z), mult(rd(Z, Z), Y)))
% 0.06/0.45 = { by lemma 18 R->L }
% 0.06/0.45 rd(Y, mult(mult(rd(Z, Z), Y), rd(Z, Z)))
% 0.84/0.45 = { by lemma 14 R->L }
% 0.84/0.45 ld(rd(Z, Z), rd(rd(mult(rd(Z, Z), Y), rd(Z, Z)), mult(rd(Z, Z), Y)))
% 0.84/0.45 = { by lemma 19 }
% 0.84/0.45 ld(rd(Z, Z), rd(Z, Z))
% 0.84/0.45 = { by lemma 19 R->L }
% 0.84/0.45 ld(rd(Z, Z), rd(rd(mult(rd(Z, Z), X), rd(Z, Z)), mult(rd(Z, Z), X)))
% 0.84/0.45 = { by lemma 14 }
% 0.84/0.45 rd(X, mult(mult(rd(Z, Z), X), rd(Z, Z)))
% 0.84/0.45 = { by lemma 18 }
% 0.84/0.45 rd(X, ld(rd(Z, Z), mult(rd(Z, Z), X)))
% 0.84/0.45 = { by axiom 2 (f02) }
% 0.84/0.45 rd(X, X)
% 0.84/0.45
% 0.84/0.45 Goal 1 (goals): tuple(mult(ld(x1, x1), x0), mult(x0_2, ld(x1_2, x1_2))) = tuple(x0, x0_2).
% 0.84/0.45 Proof:
% 0.84/0.45 tuple(mult(ld(x1, x1), x0), mult(x0_2, ld(x1_2, x1_2)))
% 0.84/0.45 = { by lemma 13 }
% 0.84/0.45 tuple(mult(rd(x1, x1), x0), mult(x0_2, ld(x1_2, x1_2)))
% 0.84/0.45 = { by lemma 13 }
% 0.84/0.45 tuple(mult(rd(x1, x1), x0), mult(x0_2, rd(x1_2, x1_2)))
% 0.84/0.45 = { by lemma 17 }
% 0.84/0.45 tuple(rd(x0, rd(x1, x1)), mult(x0_2, rd(x1_2, x1_2)))
% 0.84/0.45 = { by lemma 18 }
% 0.84/0.45 tuple(rd(x0, rd(x1, x1)), ld(rd(x1_2, x1_2), x0_2))
% 0.84/0.45 = { by lemma 20 }
% 0.84/0.45 tuple(rd(x0, rd(x1, x1)), ld(rd(x0_2, x0_2), x0_2))
% 0.84/0.45 = { by lemma 6 }
% 0.84/0.45 tuple(rd(x0, rd(x1, x1)), x0_2)
% 0.84/0.45 = { by lemma 12 R->L }
% 0.84/0.45 tuple(rd(rd(x0, rd(x0, x0)), rd(x1, x1)), x0_2)
% 0.84/0.45 = { by lemma 20 }
% 0.84/0.45 tuple(rd(rd(x0, rd(x0, x0)), rd(x0, x0)), x0_2)
% 0.84/0.45 = { by lemma 10 R->L }
% 0.84/0.45 tuple(rd(mult(x0, rd(x0, x0)), rd(x0, x0)), x0_2)
% 0.84/0.45 = { by axiom 1 (f04) }
% 0.84/0.45 tuple(x0, x0_2)
% 0.84/0.45 % SZS output end Proof
% 0.84/0.45
% 0.84/0.45 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------