%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 10:08:53 AM UTC 2026
% Result : Theorem 52.64s 7.11s
% Output : Proof 52.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 09:13:44 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 52.64/7.11 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
% 52.64/7.11
% 52.64/7.11 % SZS status Theorem
% 52.64/7.11
% 52.64/7.13 % SZS output start Proof
% 52.64/7.13 Axiom 1 (prove_distribution_1): product(X, e, X) = true.
% 52.64/7.13 Axiom 2 (prove_distribution_2): product(X, inverse(X), e) = true.
% 52.64/7.13 Axiom 3 (prove_distribution_5): product(e, X, X) = true.
% 52.64/7.13 Axiom 4 (prove_distribution_6): product(v, u, x) = true.
% 52.64/7.13 Axiom 5 (prove_distribution_3): product(inverse(X), X, e) = true.
% 52.64/7.13 Axiom 6 (prove_distribution_4): product(inverse(u), inverse(v), w) = true.
% 52.64/7.13 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 52.64/7.13 Axiom 8 (prove_distribution_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.
% 52.64/7.13 Axiom 9 (prove_distribution_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.
% 52.64/7.13
% 52.64/7.13 Goal 1 (prove_distribution_9): product(inverse(w), inverse(x), e) = true.
% 52.64/7.13 Proof:
% 52.64/7.13 product(inverse(w), inverse(x), e)
% 52.64/7.13 = { by axiom 7 (ifeq_axiom) R->L }
% 52.64/7.13 ifeq(true, true, product(inverse(w), inverse(x), e), true)
% 52.64/7.13 = { by axiom 8 (prove_distribution_7) R->L }
% 52.64/7.13 ifeq(ifeq(product(v, u, inverse(w)), true, ifeq(product(v, u, x), true, ifeq(product(e, v, v), true, product(e, x, inverse(w)), true), true), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.13 = { by axiom 3 (prove_distribution_5) }
% 52.64/7.13 ifeq(ifeq(product(v, u, inverse(w)), true, ifeq(product(v, u, x), true, ifeq(true, true, product(e, x, inverse(w)), true), true), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.13 = { by axiom 7 (ifeq_axiom) }
% 52.64/7.13 ifeq(ifeq(product(v, u, inverse(w)), true, ifeq(product(v, u, x), true, product(e, x, inverse(w)), true), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.13 = { by axiom 4 (prove_distribution_6) }
% 52.64/7.13 ifeq(ifeq(product(v, u, inverse(w)), true, ifeq(true, true, product(e, x, inverse(w)), true), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.13 = { by axiom 7 (ifeq_axiom) }
% 52.64/7.13 ifeq(ifeq(product(v, u, inverse(w)), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.13 = { by axiom 7 (ifeq_axiom) R->L }
% 52.64/7.13 ifeq(ifeq(ifeq(true, true, product(v, u, inverse(w)), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.13 = { by axiom 8 (prove_distribution_7) R->L }
% 52.64/7.13 ifeq(ifeq(ifeq(ifeq(product(e, v, v), true, ifeq(product(w, v, inverse(u)), true, ifeq(product(inverse(w), w, e), true, product(inverse(w), inverse(u), v), true), true), true), true, product(v, u, inverse(w)), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.13 = { by axiom 3 (prove_distribution_5) }
% 52.64/7.13 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(w, v, inverse(u)), true, ifeq(product(inverse(w), w, e), true, product(inverse(w), inverse(u), v), true), true), true), true, product(v, u, inverse(w)), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.13 = { by axiom 7 (ifeq_axiom) }
% 52.64/7.13 ifeq(ifeq(ifeq(ifeq(product(w, v, inverse(u)), true, ifeq(product(inverse(w), w, e), true, product(inverse(w), inverse(u), v), true), true), true, product(v, u, inverse(w)), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.13 = { by axiom 5 (prove_distribution_3) }
% 52.64/7.13 ifeq(ifeq(ifeq(ifeq(product(w, v, inverse(u)), true, ifeq(true, true, product(inverse(w), inverse(u), v), true), true), true, product(v, u, inverse(w)), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.13 = { by axiom 7 (ifeq_axiom) }
% 52.64/7.13 ifeq(ifeq(ifeq(ifeq(product(w, v, inverse(u)), true, product(inverse(w), inverse(u), v), true), true, product(v, u, inverse(w)), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.13 = { by axiom 7 (ifeq_axiom) R->L }
% 52.64/7.13 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, product(w, v, inverse(u)), true), true, product(inverse(w), inverse(u), v), true), true, product(v, u, inverse(w)), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.13 = { by axiom 6 (prove_distribution_4) R->L }
% 52.64/7.13 ifeq(ifeq(ifeq(ifeq(ifeq(product(inverse(u), inverse(v), w), true, product(w, v, inverse(u)), true), true, product(inverse(w), inverse(u), v), true), true, product(v, u, inverse(w)), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.13 = { by axiom 7 (ifeq_axiom) R->L }
% 52.64/7.13 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(u), inverse(v), w), true, product(w, v, inverse(u)), true), true), true, product(inverse(w), inverse(u), v), true), true, product(v, u, inverse(w)), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.14 = { by axiom 5 (prove_distribution_3) R->L }
% 52.64/7.14 ifeq(ifeq(ifeq(ifeq(ifeq(product(inverse(v), v, e), true, ifeq(product(inverse(u), inverse(v), w), true, product(w, v, inverse(u)), true), true), true, product(inverse(w), inverse(u), v), true), true, product(v, u, inverse(w)), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.14 = { by axiom 7 (ifeq_axiom) R->L }
% 52.64/7.14 ifeq(ifeq(ifeq(ifeq(ifeq(product(inverse(v), v, e), true, ifeq(true, true, ifeq(product(inverse(u), inverse(v), w), true, product(w, v, inverse(u)), true), true), true), true, product(inverse(w), inverse(u), v), true), true, product(v, u, inverse(w)), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.14 = { by axiom 1 (prove_distribution_1) R->L }
% 52.64/7.14 ifeq(ifeq(ifeq(ifeq(ifeq(product(inverse(v), v, e), true, ifeq(product(inverse(u), e, inverse(u)), true, ifeq(product(inverse(u), inverse(v), w), true, product(w, v, inverse(u)), true), true), true), true, product(inverse(w), inverse(u), v), true), true, product(v, u, inverse(w)), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.14 = { by axiom 9 (prove_distribution_8) }
% 52.64/7.14 ifeq(ifeq(ifeq(ifeq(true, true, product(inverse(w), inverse(u), v), true), true, product(v, u, inverse(w)), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.14 = { by axiom 7 (ifeq_axiom) }
% 52.64/7.14 ifeq(ifeq(ifeq(product(inverse(w), inverse(u), v), true, product(v, u, inverse(w)), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.14 = { by axiom 7 (ifeq_axiom) R->L }
% 52.64/7.14 ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(w), inverse(u), v), true, product(v, u, inverse(w)), true), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.14 = { by axiom 5 (prove_distribution_3) R->L }
% 52.64/7.14 ifeq(ifeq(ifeq(product(inverse(u), u, e), true, ifeq(product(inverse(w), inverse(u), v), true, product(v, u, inverse(w)), true), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.14 = { by axiom 7 (ifeq_axiom) R->L }
% 52.64/7.14 ifeq(ifeq(ifeq(product(inverse(u), u, e), true, ifeq(true, true, ifeq(product(inverse(w), inverse(u), v), true, product(v, u, inverse(w)), true), true), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.14 = { by axiom 1 (prove_distribution_1) R->L }
% 52.64/7.14 ifeq(ifeq(ifeq(product(inverse(u), u, e), true, ifeq(product(inverse(w), e, inverse(w)), true, ifeq(product(inverse(w), inverse(u), v), true, product(v, u, inverse(w)), true), true), true), true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.14 = { by axiom 9 (prove_distribution_8) }
% 52.64/7.14 ifeq(ifeq(true, true, product(e, x, inverse(w)), true), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.14 = { by axiom 7 (ifeq_axiom) }
% 52.64/7.14 ifeq(product(e, x, inverse(w)), true, product(inverse(w), inverse(x), e), true)
% 52.64/7.14 = { by axiom 7 (ifeq_axiom) R->L }
% 52.64/7.14 ifeq(true, true, ifeq(product(e, x, inverse(w)), true, product(inverse(w), inverse(x), e), true), true)
% 52.64/7.14 = { by axiom 2 (prove_distribution_2) R->L }
% 52.64/7.14 ifeq(product(x, inverse(x), e), true, ifeq(product(e, x, inverse(w)), true, product(inverse(w), inverse(x), e), true), true)
% 52.64/7.14 = { by axiom 7 (ifeq_axiom) R->L }
% 52.64/7.14 ifeq(product(x, inverse(x), e), true, ifeq(true, true, ifeq(product(e, x, inverse(w)), true, product(inverse(w), inverse(x), e), true), true), true)
% 52.64/7.14 = { by axiom 1 (prove_distribution_1) R->L }
% 52.64/7.14 ifeq(product(x, inverse(x), e), true, ifeq(product(e, e, e), true, ifeq(product(e, x, inverse(w)), true, product(inverse(w), inverse(x), e), true), true), true)
% 52.64/7.14 = { by axiom 9 (prove_distribution_8) }
% 52.64/7.14 true
% 52.64/7.14 % SZS output end Proof
% 52.64/7.14
% 52.64/7.14 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------