%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP715+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 10:11:50 AM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP715+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.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 10:39:23 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.46 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.10/0.46
% 0.10/0.46 % SZS status Theorem
% 0.10/0.46
% 0.10/0.46 % SZS output start Proof
% 0.10/0.46 Axiom 1 (f08): mult(X, unit) = X.
% 0.10/0.46 Axiom 2 (f10): mult(op_a, op_b) = unit.
% 0.10/0.46 Axiom 3 (f11): mult(op_b, op_a) = unit.
% 0.10/0.46 Axiom 4 (f09): mult(unit, X) = X.
% 0.10/0.46 Axiom 5 (f07): mult(X, mult(Y, Y)) = mult(mult(X, Y), Y).
% 0.10/0.46 Axiom 6 (f06): mult(mult(mult(X, Y), Z), Y) = mult(X, mult(mult(Y, Z), Y)).
% 0.10/0.46
% 0.10/0.46 Lemma 7: mult(op_a, mult(op_b, op_b)) = op_b.
% 0.10/0.46 Proof:
% 0.10/0.46 mult(op_a, mult(op_b, op_b))
% 0.10/0.46 = { by axiom 5 (f07) }
% 0.10/0.46 mult(mult(op_a, op_b), op_b)
% 0.10/0.46 = { by axiom 2 (f10) }
% 0.10/0.46 mult(unit, op_b)
% 0.10/0.46 = { by axiom 4 (f09) }
% 0.10/0.46 op_b
% 0.10/0.46
% 0.10/0.46 Lemma 8: mult(op_b, mult(op_a, op_a)) = op_a.
% 0.10/0.46 Proof:
% 0.10/0.46 mult(op_b, mult(op_a, op_a))
% 0.10/0.46 = { by axiom 5 (f07) }
% 0.10/0.46 mult(mult(op_b, op_a), op_a)
% 0.10/0.46 = { by axiom 3 (f11) }
% 0.10/0.46 mult(unit, op_a)
% 0.10/0.46 = { by axiom 4 (f09) }
% 0.10/0.46 op_a
% 0.10/0.46
% 0.10/0.46 Lemma 9: mult(mult(mult(mult(X, op_a), op_b), op_b), op_a) = X.
% 0.10/0.46 Proof:
% 0.10/0.46 mult(mult(mult(mult(X, op_a), op_b), op_b), op_a)
% 0.10/0.46 = { by axiom 5 (f07) R->L }
% 0.10/0.46 mult(mult(mult(X, op_a), mult(op_b, op_b)), op_a)
% 0.10/0.46 = { by axiom 6 (f06) }
% 0.10/0.46 mult(X, mult(mult(op_a, mult(op_b, op_b)), op_a))
% 0.10/0.46 = { by lemma 7 }
% 0.10/0.46 mult(X, mult(op_b, op_a))
% 0.10/0.46 = { by axiom 3 (f11) }
% 0.10/0.46 mult(X, unit)
% 0.10/0.46 = { by axiom 1 (f08) }
% 0.10/0.46 X
% 0.10/0.46
% 0.10/0.46 Lemma 10: mult(mult(mult(mult(X, op_b), op_a), op_a), op_b) = X.
% 0.10/0.46 Proof:
% 0.10/0.46 mult(mult(mult(mult(X, op_b), op_a), op_a), op_b)
% 0.10/0.46 = { by axiom 5 (f07) R->L }
% 0.10/0.46 mult(mult(mult(X, op_b), mult(op_a, op_a)), op_b)
% 0.10/0.46 = { by axiom 6 (f06) }
% 0.10/0.46 mult(X, mult(mult(op_b, mult(op_a, op_a)), op_b))
% 0.10/0.46 = { by lemma 8 }
% 0.10/0.46 mult(X, mult(op_a, op_b))
% 0.10/0.46 = { by axiom 2 (f10) }
% 0.10/0.46 mult(X, unit)
% 0.10/0.46 = { by axiom 1 (f08) }
% 0.10/0.46 X
% 0.10/0.46
% 0.10/0.46 Goal 1 (goals): tuple(mult(mult(x0_2, op_a), op_b), mult(mult(x0, op_b), op_a)) = tuple(x0_2, x0).
% 0.10/0.46 Proof:
% 0.10/0.46 tuple(mult(mult(x0_2, op_a), op_b), mult(mult(x0, op_b), op_a))
% 0.10/0.46 = { by lemma 10 R->L }
% 0.10/0.46 tuple(mult(mult(x0_2, op_a), op_b), mult(mult(mult(mult(mult(mult(x0, op_b), op_a), op_a), op_b), op_b), op_a))
% 0.10/0.46 = { by axiom 5 (f07) R->L }
% 0.10/0.46 tuple(mult(mult(x0_2, op_a), op_b), mult(mult(mult(mult(mult(x0, op_b), op_a), op_a), mult(op_b, op_b)), op_a))
% 0.10/0.46 = { by axiom 4 (f09) R->L }
% 0.10/0.46 tuple(mult(mult(x0_2, op_a), op_b), mult(mult(mult(mult(mult(x0, op_b), op_a), mult(unit, op_a)), mult(op_b, op_b)), op_a))
% 0.10/0.46 = { by axiom 2 (f10) R->L }
% 0.10/0.46 tuple(mult(mult(x0_2, op_a), op_b), mult(mult(mult(mult(mult(x0, op_b), op_a), mult(mult(op_a, op_b), op_a)), mult(op_b, op_b)), op_a))
% 0.10/0.46 = { by axiom 6 (f06) R->L }
% 0.10/0.46 tuple(mult(mult(x0_2, op_a), op_b), mult(mult(mult(mult(mult(mult(mult(x0, op_b), op_a), op_a), op_b), op_a), mult(op_b, op_b)), op_a))
% 0.10/0.46 = { by lemma 10 }
% 0.10/0.46 tuple(mult(mult(x0_2, op_a), op_b), mult(mult(mult(x0, op_a), mult(op_b, op_b)), op_a))
% 0.10/0.46 = { by axiom 6 (f06) }
% 0.10/0.46 tuple(mult(mult(x0_2, op_a), op_b), mult(x0, mult(mult(op_a, mult(op_b, op_b)), op_a)))
% 0.10/0.46 = { by lemma 7 }
% 0.10/0.46 tuple(mult(mult(x0_2, op_a), op_b), mult(x0, mult(op_b, op_a)))
% 0.10/0.46 = { by axiom 3 (f11) }
% 0.10/0.46 tuple(mult(mult(x0_2, op_a), op_b), mult(x0, unit))
% 0.10/0.46 = { by axiom 1 (f08) }
% 0.10/0.46 tuple(mult(mult(x0_2, op_a), op_b), x0)
% 0.10/0.46 = { by lemma 9 R->L }
% 0.10/0.46 tuple(mult(mult(mult(mult(mult(mult(x0_2, op_a), op_b), op_b), op_a), op_a), op_b), x0)
% 0.10/0.46 = { by axiom 5 (f07) R->L }
% 0.10/0.46 tuple(mult(mult(mult(mult(mult(x0_2, op_a), op_b), op_b), mult(op_a, op_a)), op_b), x0)
% 0.10/0.46 = { by axiom 4 (f09) R->L }
% 0.10/0.46 tuple(mult(mult(mult(mult(mult(x0_2, op_a), op_b), mult(unit, op_b)), mult(op_a, op_a)), op_b), x0)
% 0.10/0.46 = { by axiom 3 (f11) R->L }
% 0.10/0.46 tuple(mult(mult(mult(mult(mult(x0_2, op_a), op_b), mult(mult(op_b, op_a), op_b)), mult(op_a, op_a)), op_b), x0)
% 0.10/0.46 = { by axiom 6 (f06) R->L }
% 0.10/0.46 tuple(mult(mult(mult(mult(mult(mult(mult(x0_2, op_a), op_b), op_b), op_a), op_b), mult(op_a, op_a)), op_b), x0)
% 0.10/0.46 = { by lemma 9 }
% 0.10/0.46 tuple(mult(mult(mult(x0_2, op_b), mult(op_a, op_a)), op_b), x0)
% 0.10/0.46 = { by axiom 6 (f06) }
% 0.10/0.46 tuple(mult(x0_2, mult(mult(op_b, mult(op_a, op_a)), op_b)), x0)
% 0.10/0.46 = { by lemma 8 }
% 0.10/0.46 tuple(mult(x0_2, mult(op_a, op_b)), x0)
% 0.10/0.46 = { by axiom 2 (f10) }
% 0.10/0.46 tuple(mult(x0_2, unit), x0)
% 0.10/0.46 = { by axiom 1 (f08) }
% 0.10/0.46 tuple(x0_2, x0)
% 0.10/0.46 % SZS output end Proof
% 0.10/0.46
% 0.10/0.46 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------