%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP682+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 10:11:42 AM UTC 2026
% Result : Theorem 2.20s 0.71s
% Output : Proof 2.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP682+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:31:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.20/0.71 Command-line arguments: --no-flatten-goal
% 2.20/0.71
% 2.20/0.71 % SZS status Theorem
% 2.20/0.71
% 2.20/0.72 % SZS output start Proof
% 2.20/0.72 Axiom 1 (f02): rd(mult(X, X), X) = X.
% 2.20/0.72 Axiom 2 (f01): ld(X, mult(X, X)) = X.
% 2.20/0.72 Axiom 3 (f03): mult(X, ld(X, Y)) = ld(X, mult(X, Y)).
% 2.20/0.72 Axiom 4 (f04): mult(rd(X, Y), Y) = rd(mult(X, Y), Y).
% 2.20/0.72 Axiom 5 (f07): ld(X, mult(X, ld(Y, Y))) = rd(mult(rd(X, X), Y), Y).
% 2.20/0.72 Axiom 6 (f06): rd(mult(mult(X, Y), rd(Z, W)), rd(Z, W)) = mult(X, rd(mult(Y, W), W)).
% 2.20/0.72 Axiom 7 (f05): ld(ld(X, Y), mult(ld(X, Y), mult(Z, W))) = mult(ld(X, mult(X, Z)), W).
% 2.20/0.72
% 2.20/0.72 Lemma 8: ld(X, X) = rd(X, X).
% 2.20/0.73 Proof:
% 2.20/0.73 ld(X, X)
% 2.20/0.73 = { by axiom 2 (f01) R->L }
% 2.20/0.73 ld(X, ld(X, mult(X, X)))
% 2.20/0.73 = { by axiom 3 (f03) R->L }
% 2.20/0.73 ld(X, mult(X, ld(X, X)))
% 2.20/0.73 = { by axiom 5 (f07) }
% 2.20/0.73 rd(mult(rd(X, X), X), X)
% 2.20/0.73 = { by axiom 4 (f04) }
% 2.20/0.73 rd(rd(mult(X, X), X), X)
% 2.20/0.73 = { by axiom 1 (f02) }
% 2.20/0.73 rd(X, X)
% 2.20/0.73
% 2.20/0.73 Lemma 9: mult(X, rd(X, X)) = X.
% 2.20/0.73 Proof:
% 2.20/0.73 mult(X, rd(X, X))
% 2.20/0.73 = { by lemma 8 R->L }
% 2.20/0.73 mult(X, ld(X, X))
% 2.20/0.73 = { by axiom 3 (f03) }
% 2.20/0.73 ld(X, mult(X, X))
% 2.20/0.73 = { by axiom 2 (f01) }
% 2.20/0.73 X
% 2.20/0.73
% 2.20/0.73 Lemma 10: mult(ld(X, mult(X, Y)), Z) = ld(X, mult(X, mult(Y, Z))).
% 2.20/0.73 Proof:
% 2.20/0.73 mult(ld(X, mult(X, Y)), Z)
% 2.20/0.73 = { by axiom 7 (f05) R->L }
% 2.20/0.73 ld(ld(X, mult(X, X)), mult(ld(X, mult(X, X)), mult(Y, Z)))
% 2.20/0.73 = { by axiom 2 (f01) }
% 2.20/0.73 ld(X, mult(ld(X, mult(X, X)), mult(Y, Z)))
% 2.20/0.73 = { by axiom 2 (f01) }
% 2.20/0.73 ld(X, mult(X, mult(Y, Z)))
% 2.20/0.73
% 2.20/0.73 Lemma 11: ld(X, mult(X, mult(X, Y))) = mult(X, Y).
% 2.20/0.73 Proof:
% 2.20/0.73 ld(X, mult(X, mult(X, Y)))
% 2.20/0.73 = { by lemma 10 R->L }
% 2.20/0.73 mult(ld(X, mult(X, X)), Y)
% 2.20/0.73 = { by axiom 2 (f01) }
% 2.20/0.73 mult(X, Y)
% 2.20/0.73
% 2.20/0.73 Lemma 12: mult(X, rd(mult(Y, Z), Z)) = rd(mult(mult(X, Y), Z), Z).
% 2.20/0.73 Proof:
% 2.20/0.73 mult(X, rd(mult(Y, Z), Z))
% 2.20/0.73 = { by axiom 6 (f06) R->L }
% 2.20/0.73 rd(mult(mult(X, Y), rd(mult(Z, Z), Z)), rd(mult(Z, Z), Z))
% 2.20/0.73 = { by axiom 1 (f02) }
% 2.20/0.73 rd(mult(mult(X, Y), Z), rd(mult(Z, Z), Z))
% 2.20/0.73 = { by axiom 1 (f02) }
% 2.20/0.73 rd(mult(mult(X, Y), Z), Z)
% 2.20/0.73
% 2.20/0.73 Lemma 13: mult(X, rd(Y, Y)) = rd(mult(X, Y), Y).
% 2.20/0.73 Proof:
% 2.20/0.73 mult(X, rd(Y, Y))
% 2.20/0.73 = { by lemma 11 R->L }
% 2.20/0.73 ld(X, mult(X, mult(X, rd(Y, Y))))
% 2.20/0.73 = { by axiom 3 (f03) R->L }
% 2.20/0.73 mult(X, ld(X, mult(X, rd(Y, Y))))
% 2.20/0.73 = { by lemma 8 R->L }
% 2.20/0.73 mult(X, ld(X, mult(X, ld(Y, Y))))
% 2.20/0.73 = { by axiom 5 (f07) }
% 2.20/0.73 mult(X, rd(mult(rd(X, X), Y), Y))
% 2.20/0.73 = { by lemma 12 }
% 2.20/0.73 rd(mult(mult(X, rd(X, X)), Y), Y)
% 2.20/0.73 = { by lemma 9 }
% 2.20/0.73 rd(mult(X, Y), Y)
% 2.20/0.73
% 2.20/0.73 Lemma 14: rd(mult(X, rd(Y, Z)), rd(Y, Z)) = rd(mult(X, Z), Z).
% 2.20/0.73 Proof:
% 2.20/0.73 rd(mult(X, rd(Y, Z)), rd(Y, Z))
% 2.20/0.73 = { by lemma 9 R->L }
% 2.20/0.73 rd(mult(mult(X, rd(X, X)), rd(Y, Z)), rd(Y, Z))
% 2.20/0.73 = { by axiom 6 (f06) }
% 2.20/0.73 mult(X, rd(mult(rd(X, X), Z), Z))
% 2.20/0.73 = { by lemma 12 }
% 2.20/0.73 rd(mult(mult(X, rd(X, X)), Z), Z)
% 2.20/0.73 = { by lemma 9 }
% 2.20/0.73 rd(mult(X, Z), Z)
% 2.20/0.73
% 2.20/0.73 Lemma 15: rd(mult(X, Y), Y) = rd(X, rd(Y, Y)).
% 2.20/0.73 Proof:
% 2.20/0.73 rd(mult(X, Y), Y)
% 2.20/0.73 = { by lemma 14 R->L }
% 2.20/0.73 rd(mult(X, rd(Y, Y)), rd(Y, Y))
% 2.20/0.73 = { by lemma 14 R->L }
% 2.20/0.73 rd(mult(X, rd(rd(Y, Y), rd(Y, Y))), rd(rd(Y, Y), rd(Y, Y)))
% 2.20/0.73 = { by lemma 13 }
% 2.20/0.73 rd(rd(mult(X, rd(Y, Y)), rd(Y, Y)), rd(rd(Y, Y), rd(Y, Y)))
% 2.20/0.73 = { by axiom 1 (f02) R->L }
% 2.20/0.73 rd(rd(mult(X, rd(Y, Y)), rd(Y, Y)), rd(rd(rd(mult(Y, Y), Y), Y), rd(Y, Y)))
% 2.20/0.73 = { by axiom 4 (f04) R->L }
% 2.20/0.73 rd(rd(mult(X, rd(Y, Y)), rd(Y, Y)), rd(rd(mult(rd(Y, Y), Y), Y), rd(Y, Y)))
% 2.20/0.73 = { by lemma 13 R->L }
% 2.20/0.73 rd(rd(mult(X, rd(Y, Y)), rd(Y, Y)), rd(mult(rd(Y, Y), rd(Y, Y)), rd(Y, Y)))
% 2.20/0.74 = { by axiom 1 (f02) }
% 2.20/0.74 rd(rd(mult(X, rd(Y, Y)), rd(Y, Y)), rd(Y, Y))
% 2.20/0.74 = { by axiom 4 (f04) R->L }
% 2.20/0.74 rd(mult(rd(X, rd(Y, Y)), rd(Y, Y)), rd(Y, Y))
% 2.20/0.74 = { by lemma 14 R->L }
% 2.20/0.74 rd(mult(rd(X, rd(Y, Y)), rd(X, rd(Y, Y))), rd(X, rd(Y, Y)))
% 2.20/0.74 = { by axiom 1 (f02) }
% 2.20/0.74 rd(X, rd(Y, Y))
% 2.20/0.74
% 2.20/0.74 Lemma 16: ld(ld(X, Y), mult(ld(X, Y), Z)) = ld(X, mult(X, Z)).
% 2.20/0.74 Proof:
% 2.20/0.74 ld(ld(X, Y), mult(ld(X, Y), Z))
% 2.20/0.74 = { by lemma 9 R->L }
% 2.20/0.74 ld(ld(X, Y), mult(ld(X, Y), mult(Z, rd(Z, Z))))
% 2.20/0.74 = { by axiom 7 (f05) }
% 2.20/0.74 mult(ld(X, mult(X, Z)), rd(Z, Z))
% 2.20/0.74 = { by lemma 10 }
% 2.20/0.74 ld(X, mult(X, mult(Z, rd(Z, Z))))
% 2.20/0.74 = { by lemma 9 }
% 2.20/0.74 ld(X, mult(X, Z))
% 2.20/0.74
% 2.20/0.74 Lemma 17: ld(mult(X, Y), mult(mult(X, Y), Z)) = ld(X, mult(X, Z)).
% 2.20/0.74 Proof:
% 2.20/0.74 ld(mult(X, Y), mult(mult(X, Y), Z))
% 2.20/0.74 = { by lemma 11 R->L }
% 2.20/0.74 ld(mult(X, Y), mult(ld(X, mult(X, mult(X, Y))), Z))
% 2.20/0.74 = { by lemma 11 R->L }
% 2.20/0.74 ld(ld(X, mult(X, mult(X, Y))), mult(ld(X, mult(X, mult(X, Y))), Z))
% 2.20/0.74 = { by lemma 16 }
% 2.20/0.74 ld(X, mult(X, Z))
% 2.20/0.74
% 2.20/0.74 Goal 1 (goals): tuple(ld(ld(x0_2, x1_2), mult(ld(x0_2, x1_2), x2_2)), ld(rd(x0, x1), mult(rd(x0, x1), x2))) = tuple(ld(x0_2, mult(x0_2, x2_2)), ld(x0, mult(x0, x2))).
% 2.20/0.74 Proof:
% 2.20/0.74 tuple(ld(ld(x0_2, x1_2), mult(ld(x0_2, x1_2), x2_2)), ld(rd(x0, x1), mult(rd(x0, x1), x2)))
% 2.20/0.74 = { by lemma 16 }
% 2.20/0.74 tuple(ld(x0_2, mult(x0_2, x2_2)), ld(rd(x0, x1), mult(rd(x0, x1), x2)))
% 2.20/0.74 = { by lemma 17 R->L }
% 2.20/0.74 tuple(ld(x0_2, mult(x0_2, x2_2)), ld(mult(rd(x0, x1), x1), mult(mult(rd(x0, x1), x1), x2)))
% 2.20/0.74 = { by axiom 4 (f04) }
% 2.20/0.74 tuple(ld(x0_2, mult(x0_2, x2_2)), ld(rd(mult(x0, x1), x1), mult(mult(rd(x0, x1), x1), x2)))
% 2.20/0.74 = { by lemma 15 }
% 2.20/0.74 tuple(ld(x0_2, mult(x0_2, x2_2)), ld(rd(x0, rd(x1, x1)), mult(mult(rd(x0, x1), x1), x2)))
% 2.20/0.74 = { by axiom 4 (f04) }
% 2.20/0.74 tuple(ld(x0_2, mult(x0_2, x2_2)), ld(rd(x0, rd(x1, x1)), mult(rd(mult(x0, x1), x1), x2)))
% 2.20/0.74 = { by lemma 13 R->L }
% 2.20/0.74 tuple(ld(x0_2, mult(x0_2, x2_2)), ld(rd(x0, rd(x1, x1)), mult(mult(x0, rd(x1, x1)), x2)))
% 2.20/0.74 = { by lemma 15 R->L }
% 2.20/0.74 tuple(ld(x0_2, mult(x0_2, x2_2)), ld(rd(mult(x0, x1), x1), mult(mult(x0, rd(x1, x1)), x2)))
% 2.20/0.74 = { by lemma 13 R->L }
% 2.20/0.74 tuple(ld(x0_2, mult(x0_2, x2_2)), ld(mult(x0, rd(x1, x1)), mult(mult(x0, rd(x1, x1)), x2)))
% 2.20/0.74 = { by lemma 17 }
% 2.20/0.74 tuple(ld(x0_2, mult(x0_2, x2_2)), ld(x0, mult(x0, x2)))
% 2.20/0.74 % SZS output end Proof
% 2.20/0.74
% 2.20/0.74 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------