%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP703+1 : 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 10:11:48 AM UTC 2026
% Result : Theorem 0.07s 0.38s
% Output : Proof 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP703+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.32 % CPULimit : 300
% 0.04/0.32 % WCLimit : 300
% 0.04/0.32 % DateTime : Sun Sep 27 10:36:19 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.38 Command-line arguments: --no-flatten-goal
% 0.07/0.38
% 0.07/0.38 % SZS status Theorem
% 0.07/0.38
% 0.07/0.38 % SZS output start Proof
% 0.07/0.38 Axiom 1 (f05): mult(X, unit) = X.
% 0.07/0.38 Axiom 2 (f06): mult(unit, X) = X.
% 0.07/0.38 Axiom 3 (f02): ld(X, mult(X, Y)) = Y.
% 0.07/0.38 Axiom 4 (f11): op_d = ld(X, mult(op_c, X)).
% 0.07/0.38 Axiom 5 (f01): mult(X, ld(X, Y)) = Y.
% 0.07/0.38 Axiom 6 (f03): mult(rd(X, Y), Y) = X.
% 0.07/0.38 Axiom 7 (f09): mult(X, mult(Y, op_c)) = mult(mult(X, Y), op_c).
% 0.07/0.38 Axiom 8 (f08): mult(op_c, mult(X, Y)) = mult(mult(op_c, X), Y).
% 0.07/0.38 Axiom 9 (f12): op_e = mult(mult(rd(op_c, mult(X, Y)), Y), X).
% 0.07/0.38
% 0.07/0.38 Lemma 10: op_c = op_d.
% 0.07/0.38 Proof:
% 0.07/0.38 op_c
% 0.07/0.38 = { by axiom 3 (f02) R->L }
% 0.07/0.38 ld(op_c, mult(op_c, op_c))
% 0.07/0.38 = { by axiom 4 (f11) R->L }
% 0.07/0.38 op_d
% 0.07/0.38
% 0.07/0.38 Lemma 11: op_e = op_d.
% 0.07/0.38 Proof:
% 0.07/0.38 op_e
% 0.07/0.38 = { by axiom 9 (f12) }
% 0.07/0.38 mult(mult(rd(op_c, mult(unit, X)), X), unit)
% 0.07/0.38 = { by axiom 1 (f05) }
% 0.07/0.38 mult(rd(op_c, mult(unit, X)), X)
% 0.07/0.38 = { by lemma 10 }
% 0.07/0.38 mult(rd(op_d, mult(unit, X)), X)
% 0.07/0.38 = { by axiom 2 (f06) }
% 0.07/0.38 mult(rd(op_d, X), X)
% 0.07/0.38 = { by axiom 6 (f03) }
% 0.07/0.38 op_d
% 0.07/0.38
% 0.07/0.38 Lemma 12: mult(op_d, X) = mult(X, op_d).
% 0.07/0.38 Proof:
% 0.07/0.38 mult(op_d, X)
% 0.07/0.38 = { by lemma 10 R->L }
% 0.07/0.38 mult(op_c, X)
% 0.07/0.38 = { by axiom 5 (f01) R->L }
% 0.07/0.38 mult(X, ld(X, mult(op_c, X)))
% 0.07/0.38 = { by axiom 4 (f11) R->L }
% 0.07/0.38 mult(X, op_d)
% 0.07/0.38
% 0.07/0.38 Lemma 13: mult(op_d, mult(X, Y)) = mult(X, mult(Y, op_d)).
% 0.07/0.38 Proof:
% 0.07/0.38 mult(op_d, mult(X, Y))
% 0.07/0.38 = { by lemma 12 }
% 0.07/0.38 mult(mult(X, Y), op_d)
% 0.07/0.38 = { by lemma 10 R->L }
% 0.07/0.38 mult(mult(X, Y), op_c)
% 0.07/0.38 = { by axiom 7 (f09) R->L }
% 0.07/0.38 mult(X, mult(Y, op_c))
% 0.07/0.38 = { by lemma 10 }
% 0.07/0.38 mult(X, mult(Y, op_d))
% 0.07/0.38
% 0.07/0.38 Lemma 14: mult(op_d, mult(X, Y)) = mult(X, mult(op_d, Y)).
% 0.07/0.38 Proof:
% 0.07/0.38 mult(op_d, mult(X, Y))
% 0.07/0.38 = { by lemma 13 }
% 0.07/0.38 mult(X, mult(Y, op_d))
% 0.07/0.38 = { by lemma 12 R->L }
% 0.07/0.38 mult(X, mult(op_d, Y))
% 0.07/0.38
% 0.07/0.38 Lemma 15: mult(mult(op_d, X), Y) = mult(X, mult(Y, op_d)).
% 0.07/0.38 Proof:
% 0.07/0.38 mult(mult(op_d, X), Y)
% 0.07/0.38 = { by lemma 10 R->L }
% 0.07/0.38 mult(mult(op_c, X), Y)
% 0.07/0.38 = { by axiom 8 (f08) R->L }
% 0.07/0.38 mult(op_c, mult(X, Y))
% 0.07/0.38 = { by lemma 10 }
% 0.07/0.38 mult(op_d, mult(X, Y))
% 0.07/0.38 = { by lemma 13 }
% 0.07/0.38 mult(X, mult(Y, op_d))
% 0.07/0.38
% 0.07/0.38 Goal 1 (goals): tuple(mult(op_e, mult(x2_3, x3_3)), mult(x2_2, mult(x3_2, op_e)), mult(x2, mult(op_e, x3))) = tuple(mult(mult(op_e, x2_3), x3_3), mult(mult(x2_2, x3_2), op_e), mult(mult(x2, op_e), x3)).
% 0.07/0.38 Proof:
% 0.07/0.38 tuple(mult(op_e, mult(x2_3, x3_3)), mult(x2_2, mult(x3_2, op_e)), mult(x2, mult(op_e, x3)))
% 0.07/0.38 = { by lemma 11 }
% 0.07/0.38 tuple(mult(op_d, mult(x2_3, x3_3)), mult(x2_2, mult(x3_2, op_e)), mult(x2, mult(op_e, x3)))
% 0.07/0.38 = { by lemma 11 }
% 0.07/0.38 tuple(mult(op_d, mult(x2_3, x3_3)), mult(x2_2, mult(x3_2, op_d)), mult(x2, mult(op_e, x3)))
% 0.07/0.38 = { by lemma 11 }
% 0.07/0.38 tuple(mult(op_d, mult(x2_3, x3_3)), mult(x2_2, mult(x3_2, op_d)), mult(x2, mult(op_d, x3)))
% 0.07/0.38 = { by lemma 12 R->L }
% 0.07/0.38 tuple(mult(op_d, mult(x2_3, x3_3)), mult(x2_2, mult(op_d, x3_2)), mult(x2, mult(op_d, x3)))
% 0.07/0.38 = { by lemma 14 R->L }
% 0.07/0.38 tuple(mult(op_d, mult(x2_3, x3_3)), mult(op_d, mult(x2_2, x3_2)), mult(x2, mult(op_d, x3)))
% 0.07/0.38 = { by lemma 14 R->L }
% 0.07/0.38 tuple(mult(op_d, mult(x2_3, x3_3)), mult(op_d, mult(x2_2, x3_2)), mult(op_d, mult(x2, x3)))
% 0.07/0.38 = { by lemma 13 }
% 0.07/0.38 tuple(mult(op_d, mult(x2_3, x3_3)), mult(op_d, mult(x2_2, x3_2)), mult(x2, mult(x3, op_d)))
% 0.07/0.38 = { by lemma 15 R->L }
% 0.07/0.38 tuple(mult(op_d, mult(x2_3, x3_3)), mult(op_d, mult(x2_2, x3_2)), mult(mult(op_d, x2), x3))
% 0.07/0.38 = { by lemma 13 }
% 0.07/0.38 tuple(mult(x2_3, mult(x3_3, op_d)), mult(op_d, mult(x2_2, x3_2)), mult(mult(op_d, x2), x3))
% 0.07/0.38 = { by lemma 15 R->L }
% 0.07/0.38 tuple(mult(mult(op_d, x2_3), x3_3), mult(op_d, mult(x2_2, x3_2)), mult(mult(op_d, x2), x3))
% 0.07/0.38 = { by lemma 12 }
% 0.07/0.38 tuple(mult(mult(op_d, x2_3), x3_3), mult(op_d, mult(x2_2, x3_2)), mult(mult(x2, op_d), x3))
% 0.07/0.38 = { by lemma 12 }
% 0.07/0.38 tuple(mult(mult(op_d, x2_3), x3_3), mult(mult(x2_2, x3_2), op_d), mult(mult(x2, op_d), x3))
% 0.07/0.38 = { by lemma 11 R->L }
% 0.07/0.38 tuple(mult(mult(op_e, x2_3), x3_3), mult(mult(x2_2, x3_2), op_d), mult(mult(x2, op_d), x3))
% 0.07/0.38 = { by lemma 11 R->L }
% 0.07/0.38 tuple(mult(mult(op_e, x2_3), x3_3), mult(mult(x2_2, x3_2), op_e), mult(mult(x2, op_d), x3))
% 0.07/0.38 = { by lemma 11 R->L }
% 0.07/0.38 tuple(mult(mult(op_e, x2_3), x3_3), mult(mult(x2_2, x3_2), op_e), mult(mult(x2, op_e), x3))
% 0.07/0.38 % SZS output end Proof
% 0.07/0.38
% 0.07/0.38 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------