%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP704+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 10:11:48 AM UTC 2026
% Result : Theorem 0.15s 0.47s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP704+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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 10:32:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.47 Command-line arguments: --no-flatten-goal
% 0.15/0.47
% 0.15/0.47 % SZS status Theorem
% 0.15/0.47
% 0.15/0.47 % SZS output start Proof
% 0.15/0.47 Axiom 1 (f05): mult(X, unit) = X.
% 0.15/0.47 Axiom 2 (f06): mult(unit, X) = X.
% 0.15/0.47 Axiom 3 (f02): ld(X, mult(X, Y)) = Y.
% 0.15/0.47 Axiom 4 (f11): op_d = ld(X, mult(op_c, X)).
% 0.15/0.47 Axiom 5 (f01): mult(X, ld(X, Y)) = Y.
% 0.15/0.47 Axiom 6 (f09): mult(X, mult(Y, op_c)) = mult(mult(X, Y), op_c).
% 0.15/0.47 Axiom 7 (f08): mult(op_c, mult(X, Y)) = mult(mult(op_c, X), Y).
% 0.15/0.47 Axiom 8 (f13): op_f = mult(X, mult(Y, ld(mult(X, Y), op_c))).
% 0.15/0.47
% 0.15/0.47 Lemma 9: op_c = op_d.
% 0.15/0.47 Proof:
% 0.15/0.47 op_c
% 0.15/0.47 = { by axiom 3 (f02) R->L }
% 0.15/0.47 ld(op_c, mult(op_c, op_c))
% 0.15/0.47 = { by axiom 4 (f11) R->L }
% 0.15/0.47 op_d
% 0.15/0.47
% 0.15/0.47 Lemma 10: op_f = op_d.
% 0.15/0.47 Proof:
% 0.15/0.47 op_f
% 0.15/0.47 = { by axiom 8 (f13) }
% 0.15/0.47 mult(X, mult(unit, ld(mult(X, unit), op_c)))
% 0.15/0.47 = { by axiom 1 (f05) }
% 0.15/0.47 mult(X, mult(unit, ld(X, op_c)))
% 0.15/0.47 = { by axiom 2 (f06) }
% 0.15/0.47 mult(X, ld(X, op_c))
% 0.15/0.47 = { by axiom 5 (f01) }
% 0.15/0.47 op_c
% 0.15/0.47 = { by lemma 9 }
% 0.15/0.47 op_d
% 0.15/0.47
% 0.15/0.47 Lemma 11: mult(op_d, X) = mult(X, op_d).
% 0.15/0.47 Proof:
% 0.15/0.47 mult(op_d, X)
% 0.15/0.47 = { by lemma 9 R->L }
% 0.15/0.47 mult(op_c, X)
% 0.15/0.47 = { by axiom 5 (f01) R->L }
% 0.15/0.47 mult(X, ld(X, mult(op_c, X)))
% 0.15/0.47 = { by axiom 4 (f11) R->L }
% 0.15/0.47 mult(X, op_d)
% 0.15/0.47
% 0.15/0.47 Lemma 12: mult(op_d, mult(X, Y)) = mult(X, mult(Y, op_d)).
% 0.15/0.47 Proof:
% 0.15/0.47 mult(op_d, mult(X, Y))
% 0.15/0.47 = { by lemma 11 }
% 0.15/0.47 mult(mult(X, Y), op_d)
% 0.15/0.47 = { by lemma 9 R->L }
% 0.15/0.47 mult(mult(X, Y), op_c)
% 0.15/0.47 = { by axiom 6 (f09) R->L }
% 0.15/0.47 mult(X, mult(Y, op_c))
% 0.15/0.47 = { by lemma 9 }
% 0.15/0.47 mult(X, mult(Y, op_d))
% 0.15/0.47
% 0.15/0.47 Lemma 13: mult(op_d, mult(X, Y)) = mult(X, mult(op_d, Y)).
% 0.15/0.47 Proof:
% 0.15/0.47 mult(op_d, mult(X, Y))
% 0.15/0.47 = { by lemma 12 }
% 0.15/0.47 mult(X, mult(Y, op_d))
% 0.15/0.47 = { by lemma 11 R->L }
% 0.15/0.47 mult(X, mult(op_d, Y))
% 0.15/0.47
% 0.15/0.47 Lemma 14: mult(mult(op_d, X), Y) = mult(X, mult(Y, op_d)).
% 0.15/0.47 Proof:
% 0.15/0.47 mult(mult(op_d, X), Y)
% 0.15/0.47 = { by lemma 9 R->L }
% 0.15/0.47 mult(mult(op_c, X), Y)
% 0.15/0.47 = { by axiom 7 (f08) R->L }
% 0.15/0.47 mult(op_c, mult(X, Y))
% 0.15/0.47 = { by lemma 9 }
% 0.15/0.47 mult(op_d, mult(X, Y))
% 0.15/0.47 = { by lemma 12 }
% 0.15/0.47 mult(X, mult(Y, op_d))
% 0.15/0.47
% 0.15/0.47 Goal 1 (goals): tuple(mult(op_f, mult(x4_3, x5_3)), mult(x4_2, mult(x5_2, op_f)), mult(x4, mult(op_f, x5))) = tuple(mult(mult(op_f, x4_3), x5_3), mult(mult(x4_2, x5_2), op_f), mult(mult(x4, op_f), x5)).
% 0.15/0.47 Proof:
% 0.15/0.47 tuple(mult(op_f, mult(x4_3, x5_3)), mult(x4_2, mult(x5_2, op_f)), mult(x4, mult(op_f, x5)))
% 0.15/0.47 = { by lemma 10 }
% 0.15/0.47 tuple(mult(op_d, mult(x4_3, x5_3)), mult(x4_2, mult(x5_2, op_f)), mult(x4, mult(op_f, x5)))
% 0.15/0.47 = { by lemma 10 }
% 0.15/0.47 tuple(mult(op_d, mult(x4_3, x5_3)), mult(x4_2, mult(x5_2, op_d)), mult(x4, mult(op_f, x5)))
% 0.15/0.47 = { by lemma 10 }
% 0.15/0.47 tuple(mult(op_d, mult(x4_3, x5_3)), mult(x4_2, mult(x5_2, op_d)), mult(x4, mult(op_d, x5)))
% 0.15/0.47 = { by lemma 11 R->L }
% 0.15/0.47 tuple(mult(op_d, mult(x4_3, x5_3)), mult(x4_2, mult(op_d, x5_2)), mult(x4, mult(op_d, x5)))
% 0.15/0.47 = { by lemma 13 R->L }
% 0.15/0.47 tuple(mult(op_d, mult(x4_3, x5_3)), mult(op_d, mult(x4_2, x5_2)), mult(x4, mult(op_d, x5)))
% 0.15/0.47 = { by lemma 13 R->L }
% 0.15/0.47 tuple(mult(op_d, mult(x4_3, x5_3)), mult(op_d, mult(x4_2, x5_2)), mult(op_d, mult(x4, x5)))
% 0.15/0.47 = { by lemma 12 }
% 0.15/0.47 tuple(mult(op_d, mult(x4_3, x5_3)), mult(op_d, mult(x4_2, x5_2)), mult(x4, mult(x5, op_d)))
% 0.15/0.47 = { by lemma 14 R->L }
% 0.15/0.47 tuple(mult(op_d, mult(x4_3, x5_3)), mult(op_d, mult(x4_2, x5_2)), mult(mult(op_d, x4), x5))
% 0.15/0.47 = { by lemma 12 }
% 0.15/0.47 tuple(mult(x4_3, mult(x5_3, op_d)), mult(op_d, mult(x4_2, x5_2)), mult(mult(op_d, x4), x5))
% 0.15/0.47 = { by lemma 14 R->L }
% 0.15/0.47 tuple(mult(mult(op_d, x4_3), x5_3), mult(op_d, mult(x4_2, x5_2)), mult(mult(op_d, x4), x5))
% 0.15/0.47 = { by lemma 11 }
% 0.15/0.47 tuple(mult(mult(op_d, x4_3), x5_3), mult(op_d, mult(x4_2, x5_2)), mult(mult(x4, op_d), x5))
% 0.15/0.47 = { by lemma 11 }
% 0.15/0.47 tuple(mult(mult(op_d, x4_3), x5_3), mult(mult(x4_2, x5_2), op_d), mult(mult(x4, op_d), x5))
% 0.15/0.47 = { by lemma 10 R->L }
% 0.15/0.47 tuple(mult(mult(op_f, x4_3), x5_3), mult(mult(x4_2, x5_2), op_d), mult(mult(x4, op_d), x5))
% 0.15/0.47 = { by lemma 10 R->L }
% 0.15/0.47 tuple(mult(mult(op_f, x4_3), x5_3), mult(mult(x4_2, x5_2), op_f), mult(mult(x4, op_d), x5))
% 0.15/0.47 = { by lemma 10 R->L }
% 0.15/0.47 tuple(mult(mult(op_f, x4_3), x5_3), mult(mult(x4_2, x5_2), op_f), mult(mult(x4, op_f), x5))
% 0.15/0.47 % SZS output end Proof
% 0.15/0.47
% 0.15/0.47 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------