%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP702+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 10:11:47 AM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP702+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 : n016.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 10:41:46 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.44 Command-line arguments: --no-flatten-goal
% 0.13/0.44
% 0.13/0.44 % SZS status Theorem
% 0.13/0.44
% 0.13/0.45 % SZS output start Proof
% 0.13/0.45 Axiom 1 (f05): mult(X, unit) = X.
% 0.13/0.45 Axiom 2 (f06): mult(unit, X) = X.
% 0.13/0.45 Axiom 3 (f02): ld(X, mult(X, Y)) = Y.
% 0.13/0.45 Axiom 4 (f11): op_d = ld(X, mult(op_c, X)).
% 0.13/0.45 Axiom 5 (f01): mult(X, ld(X, Y)) = Y.
% 0.13/0.45 Axiom 6 (f03): mult(rd(X, Y), Y) = X.
% 0.13/0.45 Axiom 7 (f09): mult(X, mult(Y, op_c)) = mult(mult(X, Y), op_c).
% 0.13/0.45 Axiom 8 (f08): mult(op_c, mult(X, Y)) = mult(mult(op_c, X), Y).
% 0.13/0.45 Axiom 9 (f13): op_f = mult(X, mult(Y, ld(mult(X, Y), op_c))).
% 0.13/0.45 Axiom 10 (f12): op_e = mult(mult(rd(op_c, mult(X, Y)), Y), X).
% 0.13/0.45
% 0.13/0.45 Lemma 11: op_c = op_d.
% 0.13/0.45 Proof:
% 0.13/0.45 op_c
% 0.13/0.45 = { by axiom 3 (f02) R->L }
% 0.13/0.45 ld(op_c, mult(op_c, op_c))
% 0.13/0.45 = { by axiom 4 (f11) R->L }
% 0.13/0.45 op_d
% 0.13/0.45
% 0.13/0.45 Lemma 12: op_d = op_f.
% 0.13/0.45 Proof:
% 0.13/0.45 op_d
% 0.13/0.45 = { by lemma 11 R->L }
% 0.13/0.45 op_c
% 0.13/0.45 = { by axiom 5 (f01) R->L }
% 0.13/0.45 mult(X, ld(X, op_c))
% 0.13/0.45 = { by axiom 2 (f06) R->L }
% 0.13/0.45 mult(X, mult(unit, ld(X, op_c)))
% 0.13/0.45 = { by axiom 1 (f05) R->L }
% 0.13/0.45 mult(X, mult(unit, ld(mult(X, unit), op_c)))
% 0.13/0.45 = { by axiom 9 (f13) R->L }
% 0.13/0.45 op_f
% 0.13/0.45
% 0.13/0.45 Lemma 13: op_f = op_e.
% 0.13/0.45 Proof:
% 0.13/0.45 op_f
% 0.13/0.45 = { by axiom 6 (f03) R->L }
% 0.13/0.45 mult(rd(op_f, X), X)
% 0.13/0.46 = { by axiom 2 (f06) R->L }
% 0.13/0.46 mult(rd(op_f, mult(unit, X)), X)
% 0.13/0.46 = { by lemma 12 R->L }
% 0.13/0.46 mult(rd(op_d, mult(unit, X)), X)
% 0.13/0.46 = { by lemma 11 R->L }
% 0.13/0.46 mult(rd(op_c, mult(unit, X)), X)
% 0.13/0.46 = { by axiom 1 (f05) R->L }
% 0.13/0.46 mult(mult(rd(op_c, mult(unit, X)), X), unit)
% 0.13/0.46 = { by axiom 10 (f12) R->L }
% 0.13/0.46 op_e
% 0.13/0.46
% 0.13/0.46 Lemma 14: mult(op_e, X) = mult(X, op_e).
% 0.13/0.46 Proof:
% 0.13/0.46 mult(op_e, X)
% 0.13/0.46 = { by lemma 13 R->L }
% 0.13/0.46 mult(op_f, X)
% 0.13/0.46 = { by lemma 12 R->L }
% 0.13/0.46 mult(op_d, X)
% 0.13/0.46 = { by lemma 11 R->L }
% 0.13/0.46 mult(op_c, X)
% 0.13/0.46 = { by axiom 5 (f01) R->L }
% 0.13/0.46 mult(X, ld(X, mult(op_c, X)))
% 0.13/0.46 = { by axiom 4 (f11) R->L }
% 0.13/0.46 mult(X, op_d)
% 0.13/0.46 = { by lemma 12 }
% 0.13/0.46 mult(X, op_f)
% 0.13/0.46 = { by lemma 13 }
% 0.13/0.46 mult(X, op_e)
% 0.13/0.46
% 0.13/0.46 Lemma 15: mult(op_e, mult(X, Y)) = mult(X, mult(Y, op_e)).
% 0.13/0.46 Proof:
% 0.13/0.46 mult(op_e, mult(X, Y))
% 0.13/0.46 = { by lemma 14 }
% 0.13/0.46 mult(mult(X, Y), op_e)
% 0.13/0.46 = { by lemma 13 R->L }
% 0.13/0.46 mult(mult(X, Y), op_f)
% 0.13/0.46 = { by lemma 12 R->L }
% 0.13/0.46 mult(mult(X, Y), op_d)
% 0.13/0.46 = { by lemma 11 R->L }
% 0.13/0.46 mult(mult(X, Y), op_c)
% 0.13/0.46 = { by axiom 7 (f09) R->L }
% 0.13/0.46 mult(X, mult(Y, op_c))
% 0.13/0.46 = { by lemma 11 }
% 0.13/0.46 mult(X, mult(Y, op_d))
% 0.13/0.46 = { by lemma 12 }
% 0.13/0.46 mult(X, mult(Y, op_f))
% 0.13/0.46 = { by lemma 13 }
% 0.13/0.46 mult(X, mult(Y, op_e))
% 0.13/0.46
% 0.13/0.46 Lemma 16: mult(op_e, mult(X, Y)) = mult(X, mult(op_e, Y)).
% 0.13/0.46 Proof:
% 0.13/0.46 mult(op_e, mult(X, Y))
% 0.13/0.46 = { by lemma 15 }
% 0.13/0.46 mult(X, mult(Y, op_e))
% 0.13/0.46 = { by lemma 14 R->L }
% 0.13/0.46 mult(X, mult(op_e, Y))
% 0.13/0.46
% 0.13/0.46 Lemma 17: mult(mult(op_e, X), Y) = mult(X, mult(Y, op_e)).
% 0.13/0.46 Proof:
% 0.13/0.46 mult(mult(op_e, X), Y)
% 0.13/0.46 = { by lemma 13 R->L }
% 0.13/0.46 mult(mult(op_f, X), Y)
% 0.13/0.46 = { by lemma 12 R->L }
% 0.13/0.46 mult(mult(op_d, X), Y)
% 0.13/0.46 = { by lemma 11 R->L }
% 0.13/0.46 mult(mult(op_c, X), Y)
% 0.13/0.46 = { by axiom 8 (f08) R->L }
% 0.13/0.46 mult(op_c, mult(X, Y))
% 0.13/0.46 = { by lemma 11 }
% 0.13/0.46 mult(op_d, mult(X, Y))
% 0.13/0.46 = { by lemma 12 }
% 0.13/0.46 mult(op_f, mult(X, Y))
% 0.13/0.46 = { by lemma 13 }
% 0.13/0.46 mult(op_e, mult(X, Y))
% 0.13/0.46 = { by lemma 15 }
% 0.13/0.46 mult(X, mult(Y, op_e))
% 0.13/0.46
% 0.13/0.46 Goal 1 (goals): tuple(mult(op_d, mult(x0_3, x1_3)), mult(x0_2, mult(x1_2, op_d)), mult(x0, mult(op_d, x1))) = tuple(mult(mult(op_d, x0_3), x1_3), mult(mult(x0_2, x1_2), op_d), mult(mult(x0, op_d), x1)).
% 0.13/0.46 Proof:
% 0.13/0.46 tuple(mult(op_d, mult(x0_3, x1_3)), mult(x0_2, mult(x1_2, op_d)), mult(x0, mult(op_d, x1)))
% 0.13/0.46 = { by lemma 12 }
% 0.13/0.46 tuple(mult(op_f, mult(x0_3, x1_3)), mult(x0_2, mult(x1_2, op_d)), mult(x0, mult(op_d, x1)))
% 0.13/0.46 = { by lemma 12 }
% 0.13/0.46 tuple(mult(op_f, mult(x0_3, x1_3)), mult(x0_2, mult(x1_2, op_f)), mult(x0, mult(op_d, x1)))
% 0.13/0.46 = { by lemma 12 }
% 0.13/0.46 tuple(mult(op_f, mult(x0_3, x1_3)), mult(x0_2, mult(x1_2, op_f)), mult(x0, mult(op_f, x1)))
% 0.13/0.46 = { by lemma 13 }
% 0.13/0.46 tuple(mult(op_e, mult(x0_3, x1_3)), mult(x0_2, mult(x1_2, op_f)), mult(x0, mult(op_f, x1)))
% 0.13/0.46 = { by lemma 13 }
% 0.13/0.46 tuple(mult(op_e, mult(x0_3, x1_3)), mult(x0_2, mult(x1_2, op_e)), mult(x0, mult(op_f, x1)))
% 0.13/0.46 = { by lemma 13 }
% 0.13/0.46 tuple(mult(op_e, mult(x0_3, x1_3)), mult(x0_2, mult(x1_2, op_e)), mult(x0, mult(op_e, x1)))
% 0.13/0.46 = { by lemma 14 R->L }
% 0.13/0.46 tuple(mult(op_e, mult(x0_3, x1_3)), mult(x0_2, mult(op_e, x1_2)), mult(x0, mult(op_e, x1)))
% 0.13/0.46 = { by lemma 16 R->L }
% 0.13/0.46 tuple(mult(op_e, mult(x0_3, x1_3)), mult(op_e, mult(x0_2, x1_2)), mult(x0, mult(op_e, x1)))
% 0.13/0.46 = { by lemma 16 R->L }
% 0.13/0.46 tuple(mult(op_e, mult(x0_3, x1_3)), mult(op_e, mult(x0_2, x1_2)), mult(op_e, mult(x0, x1)))
% 0.13/0.46 = { by lemma 15 }
% 0.13/0.46 tuple(mult(op_e, mult(x0_3, x1_3)), mult(op_e, mult(x0_2, x1_2)), mult(x0, mult(x1, op_e)))
% 0.13/0.46 = { by lemma 17 R->L }
% 0.13/0.46 tuple(mult(op_e, mult(x0_3, x1_3)), mult(op_e, mult(x0_2, x1_2)), mult(mult(op_e, x0), x1))
% 0.13/0.46 = { by lemma 15 }
% 0.13/0.46 tuple(mult(x0_3, mult(x1_3, op_e)), mult(op_e, mult(x0_2, x1_2)), mult(mult(op_e, x0), x1))
% 0.13/0.46 = { by lemma 17 R->L }
% 0.13/0.46 tuple(mult(mult(op_e, x0_3), x1_3), mult(op_e, mult(x0_2, x1_2)), mult(mult(op_e, x0), x1))
% 0.13/0.46 = { by lemma 14 }
% 0.13/0.46 tuple(mult(mult(op_e, x0_3), x1_3), mult(op_e, mult(x0_2, x1_2)), mult(mult(x0, op_e), x1))
% 0.13/0.46 = { by lemma 14 }
% 0.13/0.46 tuple(mult(mult(op_e, x0_3), x1_3), mult(mult(x0_2, x1_2), op_e), mult(mult(x0, op_e), x1))
% 0.13/0.46 = { by lemma 13 R->L }
% 0.13/0.46 tuple(mult(mult(op_f, x0_3), x1_3), mult(mult(x0_2, x1_2), op_e), mult(mult(x0, op_e), x1))
% 0.13/0.46 = { by lemma 13 R->L }
% 0.13/0.46 tuple(mult(mult(op_f, x0_3), x1_3), mult(mult(x0_2, x1_2), op_f), mult(mult(x0, op_e), x1))
% 0.13/0.46 = { by lemma 13 R->L }
% 0.13/0.46 tuple(mult(mult(op_f, x0_3), x1_3), mult(mult(x0_2, x1_2), op_f), mult(mult(x0, op_f), x1))
% 0.13/0.46 = { by lemma 12 R->L }
% 0.13/0.46 tuple(mult(mult(op_d, x0_3), x1_3), mult(mult(x0_2, x1_2), op_f), mult(mult(x0, op_f), x1))
% 0.13/0.46 = { by lemma 12 R->L }
% 0.13/0.46 tuple(mult(mult(op_d, x0_3), x1_3), mult(mult(x0_2, x1_2), op_d), mult(mult(x0, op_f), x1))
% 0.13/0.46 = { by lemma 12 R->L }
% 0.13/0.46 tuple(mult(mult(op_d, x0_3), x1_3), mult(mult(x0_2, x1_2), op_d), mult(mult(x0, op_d), x1))
% 0.13/0.46 % SZS output end Proof
% 0.13/0.46
% 0.13/0.46 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------