%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP045-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 10:09:09 AM UTC 2026
% Result : Unsatisfiable 3.58s 0.90s
% Output : Proof 3.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP045-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.39 % Computer : n001.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Sun Sep 27 09:22:00 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.58/0.90 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
% 3.58/0.90
% 3.58/0.90 % SZS status Unsatisfiable
% 3.58/0.90
% 3.58/0.92 % SZS output start Proof
% 3.58/0.92 Axiom 1 (a_equals_b): equalish(a, b) = true.
% 3.58/0.92 Axiom 2 (product_with_a): product(c, a, result) = true.
% 3.58/0.92 Axiom 3 (left_identity): product(identity, X, X) = true.
% 3.58/0.92 Axiom 4 (left_inverse): product(inverse(X), X, identity) = true.
% 3.58/0.92 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 3.58/0.92 Axiom 6 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 3.58/0.92 Axiom 7 (product_substitution3): ifeq(equalish(X, Y), true, ifeq(product(Z, W, X), true, product(Z, W, Y), true), true) = true.
% 3.58/0.92 Axiom 8 (total_function2): ifeq(product(X, Y, Z), true, ifeq(product(X, Y, W), true, equalish(W, Z), true), true) = true.
% 3.58/0.92 Axiom 9 (associativity1): 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.
% 3.58/0.92
% 3.58/0.92 Goal 1 (prove_product_with_b): product(c, b, result) = true.
% 3.58/0.92 Proof:
% 3.58/0.92 product(c, b, result)
% 3.58/0.92 = { by axiom 5 (ifeq_axiom) R->L }
% 3.58/0.92 ifeq(true, true, product(c, b, result), true)
% 3.58/0.92 = { by axiom 7 (product_substitution3) R->L }
% 3.58/0.92 ifeq(ifeq(equalish(multiply(c, inverse(c)), identity), true, ifeq(product(c, inverse(c), multiply(c, inverse(c))), true, product(c, inverse(c), identity), true), true), true, product(c, b, result), true)
% 3.58/0.92 = { by axiom 6 (total_function1) }
% 3.58/0.92 ifeq(ifeq(equalish(multiply(c, inverse(c)), identity), true, ifeq(true, true, product(c, inverse(c), identity), true), true), true, product(c, b, result), true)
% 3.58/0.92 = { by axiom 5 (ifeq_axiom) }
% 3.58/0.92 ifeq(ifeq(equalish(multiply(c, inverse(c)), identity), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.92 = { by axiom 5 (ifeq_axiom) R->L }
% 3.58/0.92 ifeq(ifeq(ifeq(true, true, equalish(multiply(c, inverse(c)), identity), true), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.92 = { by axiom 9 (associativity1) R->L }
% 3.58/0.92 ifeq(ifeq(ifeq(ifeq(product(identity, multiply(c, inverse(c)), multiply(c, inverse(c))), true, ifeq(product(inverse(c), multiply(c, inverse(c)), inverse(c)), true, ifeq(product(inverse(inverse(c)), inverse(c), identity), true, product(inverse(inverse(c)), inverse(c), multiply(c, inverse(c))), true), true), true), true, equalish(multiply(c, inverse(c)), identity), true), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.92 = { by axiom 3 (left_identity) }
% 3.58/0.93 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(c), multiply(c, inverse(c)), inverse(c)), true, ifeq(product(inverse(inverse(c)), inverse(c), identity), true, product(inverse(inverse(c)), inverse(c), multiply(c, inverse(c))), true), true), true), true, equalish(multiply(c, inverse(c)), identity), true), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.93 = { by axiom 5 (ifeq_axiom) }
% 3.58/0.93 ifeq(ifeq(ifeq(ifeq(product(inverse(c), multiply(c, inverse(c)), inverse(c)), true, ifeq(product(inverse(inverse(c)), inverse(c), identity), true, product(inverse(inverse(c)), inverse(c), multiply(c, inverse(c))), true), true), true, equalish(multiply(c, inverse(c)), identity), true), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.93 = { by axiom 4 (left_inverse) }
% 3.58/0.93 ifeq(ifeq(ifeq(ifeq(product(inverse(c), multiply(c, inverse(c)), inverse(c)), true, ifeq(true, true, product(inverse(inverse(c)), inverse(c), multiply(c, inverse(c))), true), true), true, equalish(multiply(c, inverse(c)), identity), true), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.93 = { by axiom 5 (ifeq_axiom) }
% 3.58/0.93 ifeq(ifeq(ifeq(ifeq(product(inverse(c), multiply(c, inverse(c)), inverse(c)), true, product(inverse(inverse(c)), inverse(c), multiply(c, inverse(c))), true), true, equalish(multiply(c, inverse(c)), identity), true), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.93 = { by axiom 5 (ifeq_axiom) R->L }
% 3.58/0.93 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, product(inverse(c), multiply(c, inverse(c)), inverse(c)), true), true, product(inverse(inverse(c)), inverse(c), multiply(c, inverse(c))), true), true, equalish(multiply(c, inverse(c)), identity), true), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.93 = { by axiom 6 (total_function1) R->L }
% 3.58/0.93 ifeq(ifeq(ifeq(ifeq(ifeq(product(c, inverse(c), multiply(c, inverse(c))), true, product(inverse(c), multiply(c, inverse(c)), inverse(c)), true), true, product(inverse(inverse(c)), inverse(c), multiply(c, inverse(c))), true), true, equalish(multiply(c, inverse(c)), identity), true), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.93 = { by axiom 5 (ifeq_axiom) R->L }
% 3.58/0.93 ifeq(ifeq(ifeq(ifeq(ifeq(product(c, inverse(c), multiply(c, inverse(c))), true, ifeq(true, true, product(inverse(c), multiply(c, inverse(c)), inverse(c)), true), true), true, product(inverse(inverse(c)), inverse(c), multiply(c, inverse(c))), true), true, equalish(multiply(c, inverse(c)), identity), true), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.93 = { by axiom 4 (left_inverse) R->L }
% 3.58/0.93 ifeq(ifeq(ifeq(ifeq(ifeq(product(c, inverse(c), multiply(c, inverse(c))), true, ifeq(product(inverse(c), c, identity), true, product(inverse(c), multiply(c, inverse(c)), inverse(c)), true), true), true, product(inverse(inverse(c)), inverse(c), multiply(c, inverse(c))), true), true, equalish(multiply(c, inverse(c)), identity), true), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.93 = { by axiom 5 (ifeq_axiom) R->L }
% 3.58/0.93 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(c, inverse(c), multiply(c, inverse(c))), true, ifeq(product(inverse(c), c, identity), true, product(inverse(c), multiply(c, inverse(c)), inverse(c)), true), true), true), true, product(inverse(inverse(c)), inverse(c), multiply(c, inverse(c))), true), true, equalish(multiply(c, inverse(c)), identity), true), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.93 = { by axiom 3 (left_identity) R->L }
% 3.58/0.93 ifeq(ifeq(ifeq(ifeq(ifeq(product(identity, inverse(c), inverse(c)), true, ifeq(product(c, inverse(c), multiply(c, inverse(c))), true, ifeq(product(inverse(c), c, identity), true, product(inverse(c), multiply(c, inverse(c)), inverse(c)), true), true), true), true, product(inverse(inverse(c)), inverse(c), multiply(c, inverse(c))), true), true, equalish(multiply(c, inverse(c)), identity), true), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.93 = { by axiom 9 (associativity1) }
% 3.58/0.93 ifeq(ifeq(ifeq(ifeq(true, true, product(inverse(inverse(c)), inverse(c), multiply(c, inverse(c))), true), true, equalish(multiply(c, inverse(c)), identity), true), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.93 = { by axiom 5 (ifeq_axiom) }
% 3.58/0.93 ifeq(ifeq(ifeq(product(inverse(inverse(c)), inverse(c), multiply(c, inverse(c))), true, equalish(multiply(c, inverse(c)), identity), true), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.93 = { by axiom 5 (ifeq_axiom) R->L }
% 3.58/0.93 ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(inverse(c)), inverse(c), multiply(c, inverse(c))), true, equalish(multiply(c, inverse(c)), identity), true), true), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.93 = { by axiom 4 (left_inverse) R->L }
% 3.58/0.93 ifeq(ifeq(ifeq(product(inverse(inverse(c)), inverse(c), identity), true, ifeq(product(inverse(inverse(c)), inverse(c), multiply(c, inverse(c))), true, equalish(multiply(c, inverse(c)), identity), true), true), true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.93 = { by axiom 8 (total_function2) }
% 3.58/0.93 ifeq(ifeq(true, true, product(c, inverse(c), identity), true), true, product(c, b, result), true)
% 3.58/0.93 = { by axiom 5 (ifeq_axiom) }
% 3.58/0.93 ifeq(product(c, inverse(c), identity), true, product(c, b, result), true)
% 3.58/0.93 = { by axiom 5 (ifeq_axiom) R->L }
% 3.58/0.93 ifeq(true, true, ifeq(product(c, inverse(c), identity), true, product(c, b, result), true), true)
% 3.58/0.93 = { by axiom 7 (product_substitution3) R->L }
% 3.58/0.93 ifeq(ifeq(equalish(a, b), true, ifeq(product(inverse(c), result, a), true, product(inverse(c), result, b), true), true), true, ifeq(product(c, inverse(c), identity), true, product(c, b, result), true), true)
% 3.58/0.93 = { by axiom 1 (a_equals_b) }
% 3.58/0.93 ifeq(ifeq(true, true, ifeq(product(inverse(c), result, a), true, product(inverse(c), result, b), true), true), true, ifeq(product(c, inverse(c), identity), true, product(c, b, result), true), true)
% 3.58/0.93 = { by axiom 5 (ifeq_axiom) }
% 3.58/0.93 ifeq(ifeq(product(inverse(c), result, a), true, product(inverse(c), result, b), true), true, ifeq(product(c, inverse(c), identity), true, product(c, b, result), true), true)
% 3.58/0.93 = { by axiom 5 (ifeq_axiom) R->L }
% 3.58/0.93 ifeq(ifeq(ifeq(true, true, product(inverse(c), result, a), true), true, product(inverse(c), result, b), true), true, ifeq(product(c, inverse(c), identity), true, product(c, b, result), true), true)
% 3.58/0.93 = { by axiom 4 (left_inverse) R->L }
% 3.58/0.93 ifeq(ifeq(ifeq(product(inverse(c), c, identity), true, product(inverse(c), result, a), true), true, product(inverse(c), result, b), true), true, ifeq(product(c, inverse(c), identity), true, product(c, b, result), true), true)
% 3.58/0.93 = { by axiom 5 (ifeq_axiom) R->L }
% 3.58/0.93 ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(c), c, identity), true, product(inverse(c), result, a), true), true), true, product(inverse(c), result, b), true), true, ifeq(product(c, inverse(c), identity), true, product(c, b, result), true), true)
% 3.58/0.93 = { by axiom 2 (product_with_a) R->L }
% 3.58/0.93 ifeq(ifeq(ifeq(product(c, a, result), true, ifeq(product(inverse(c), c, identity), true, product(inverse(c), result, a), true), true), true, product(inverse(c), result, b), true), true, ifeq(product(c, inverse(c), identity), true, product(c, b, result), true), true)
% 3.58/0.93 = { by axiom 5 (ifeq_axiom) R->L }
% 3.58/0.93 ifeq(ifeq(ifeq(true, true, ifeq(product(c, a, result), true, ifeq(product(inverse(c), c, identity), true, product(inverse(c), result, a), true), true), true), true, product(inverse(c), result, b), true), true, ifeq(product(c, inverse(c), identity), true, product(c, b, result), true), true)
% 3.58/0.93 = { by axiom 3 (left_identity) R->L }
% 3.58/0.93 ifeq(ifeq(ifeq(product(identity, a, a), true, ifeq(product(c, a, result), true, ifeq(product(inverse(c), c, identity), true, product(inverse(c), result, a), true), true), true), true, product(inverse(c), result, b), true), true, ifeq(product(c, inverse(c), identity), true, product(c, b, result), true), true)
% 3.58/0.93 = { by axiom 9 (associativity1) }
% 3.58/0.93 ifeq(ifeq(true, true, product(inverse(c), result, b), true), true, ifeq(product(c, inverse(c), identity), true, product(c, b, result), true), true)
% 3.58/0.93 = { by axiom 5 (ifeq_axiom) }
% 3.58/0.93 ifeq(product(inverse(c), result, b), true, ifeq(product(c, inverse(c), identity), true, product(c, b, result), true), true)
% 3.58/0.93 = { by axiom 5 (ifeq_axiom) R->L }
% 3.58/0.93 ifeq(true, true, ifeq(product(inverse(c), result, b), true, ifeq(product(c, inverse(c), identity), true, product(c, b, result), true), true), true)
% 3.58/0.93 = { by axiom 3 (left_identity) R->L }
% 3.58/0.93 ifeq(product(identity, result, result), true, ifeq(product(inverse(c), result, b), true, ifeq(product(c, inverse(c), identity), true, product(c, b, result), true), true), true)
% 3.58/0.93 = { by axiom 9 (associativity1) }
% 3.58/0.93 true
% 3.58/0.93 % SZS output end Proof
% 3.58/0.93
% 3.58/0.93 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------