%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP001+6 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 10:08:50 AM UTC 2026
% Result : Theorem 2.20s 0.78s
% Output : Proof 2.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP001+6 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:13:01 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.20/0.78 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
% 2.20/0.78
% 2.20/0.78 % SZS status Theorem
% 2.20/0.78
% 2.20/0.78 % SZS output start Proof
% 2.20/0.78 Axiom 1 (commutativity_3): product(X, X, e) = true.
% 2.20/0.78 Axiom 2 (commutativity_1): product(X, e, X) = true.
% 2.20/0.78 Axiom 3 (commutativity_5): product(e, X, X) = true.
% 2.20/0.78 Axiom 4 (commutativity_6): product(u, v, w) = true.
% 2.20/0.79 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.20/0.79 Axiom 6 (commutativity_7): ifeq(product(X, Y, Z), true, ifeq(product(W, Y, V), true, ifeq(product(U, W, X), true, product(U, V, Z), true), true), true) = true.
% 2.20/0.79 Axiom 7 (commutativity_8): ifeq(product(X, Y, Z), true, ifeq(product(W, Z, V), true, ifeq(product(W, X, U), true, product(U, Y, V), true), true), true) = true.
% 2.20/0.79
% 2.20/0.79 Goal 1 (commutativity_9): product(v, u, w) = true.
% 2.20/0.79 Proof:
% 2.20/0.79 product(v, u, w)
% 2.20/0.79 = { by axiom 5 (ifeq_axiom) R->L }
% 2.20/0.79 ifeq(true, true, product(v, u, w), true)
% 2.20/0.79 = { by axiom 7 (commutativity_8) R->L }
% 2.20/0.79 ifeq(ifeq(product(w, w, e), true, ifeq(product(u, e, u), true, ifeq(product(u, w, v), true, product(v, w, u), true), true), true), true, product(v, u, w), true)
% 2.20/0.79 = { by axiom 1 (commutativity_3) }
% 2.20/0.79 ifeq(ifeq(true, true, ifeq(product(u, e, u), true, ifeq(product(u, w, v), true, product(v, w, u), true), true), true), true, product(v, u, w), true)
% 2.20/0.79 = { by axiom 5 (ifeq_axiom) }
% 2.20/0.79 ifeq(ifeq(product(u, e, u), true, ifeq(product(u, w, v), true, product(v, w, u), true), true), true, product(v, u, w), true)
% 2.20/0.79 = { by axiom 2 (commutativity_1) }
% 2.20/0.79 ifeq(ifeq(true, true, ifeq(product(u, w, v), true, product(v, w, u), true), true), true, product(v, u, w), true)
% 2.20/0.79 = { by axiom 5 (ifeq_axiom) }
% 2.20/0.79 ifeq(ifeq(product(u, w, v), true, product(v, w, u), true), true, product(v, u, w), true)
% 2.20/0.79 = { by axiom 5 (ifeq_axiom) R->L }
% 2.20/0.79 ifeq(ifeq(ifeq(true, true, product(u, w, v), true), true, product(v, w, u), true), true, product(v, u, w), true)
% 2.20/0.79 = { by axiom 4 (commutativity_6) R->L }
% 2.20/0.79 ifeq(ifeq(ifeq(product(u, v, w), true, product(u, w, v), true), true, product(v, w, u), true), true, product(v, u, w), true)
% 2.20/0.79 = { by axiom 5 (ifeq_axiom) R->L }
% 2.20/0.79 ifeq(ifeq(ifeq(true, true, ifeq(product(u, v, w), true, product(u, w, v), true), true), true, product(v, w, u), true), true, product(v, u, w), true)
% 2.20/0.79 = { by axiom 3 (commutativity_5) R->L }
% 2.20/0.79 ifeq(ifeq(ifeq(product(e, v, v), true, ifeq(product(u, v, w), true, product(u, w, v), true), true), true, product(v, w, u), true), true, product(v, u, w), true)
% 2.20/0.79 = { by axiom 5 (ifeq_axiom) R->L }
% 2.20/0.79 ifeq(ifeq(ifeq(product(e, v, v), true, ifeq(product(u, v, w), true, ifeq(true, true, product(u, w, v), true), true), true), true, product(v, w, u), true), true, product(v, u, w), true)
% 2.20/0.79 = { by axiom 1 (commutativity_3) R->L }
% 2.20/0.79 ifeq(ifeq(ifeq(product(e, v, v), true, ifeq(product(u, v, w), true, ifeq(product(u, u, e), true, product(u, w, v), true), true), true), true, product(v, w, u), true), true, product(v, u, w), true)
% 2.20/0.79 = { by axiom 6 (commutativity_7) }
% 2.20/0.79 ifeq(ifeq(true, true, product(v, w, u), true), true, product(v, u, w), true)
% 2.20/0.79 = { by axiom 5 (ifeq_axiom) }
% 2.20/0.79 ifeq(product(v, w, u), true, product(v, u, w), true)
% 2.20/0.79 = { by axiom 5 (ifeq_axiom) R->L }
% 2.20/0.79 ifeq(true, true, ifeq(product(v, w, u), true, product(v, u, w), true), true)
% 2.20/0.79 = { by axiom 3 (commutativity_5) R->L }
% 2.20/0.79 ifeq(product(e, w, w), true, ifeq(product(v, w, u), true, product(v, u, w), true), true)
% 2.20/0.79 = { by axiom 5 (ifeq_axiom) R->L }
% 2.20/0.79 ifeq(product(e, w, w), true, ifeq(product(v, w, u), true, ifeq(true, true, product(v, u, w), true), true), true)
% 2.20/0.79 = { by axiom 1 (commutativity_3) R->L }
% 2.20/0.79 ifeq(product(e, w, w), true, ifeq(product(v, w, u), true, ifeq(product(v, v, e), true, product(v, u, w), true), true), true)
% 2.20/0.79 = { by axiom 6 (commutativity_7) }
% 2.20/0.79 true
% 2.20/0.79 % SZS output end Proof
% 2.20/0.79
% 2.20/0.79 RESULT: Theorem (the conjecture is true).
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