%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 10:08:51 AM UTC 2026
% Result : Unsatisfiable 0.60s 0.55s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n003.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sun Sep 27 09:14:55 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.55 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
% 0.60/0.55
% 0.60/0.55 % SZS status Unsatisfiable
% 0.60/0.55
% 0.60/0.57 % SZS output start Proof
% 0.60/0.57 Axiom 1 (left_identity): product(identity, X, X) = true.
% 0.60/0.57 Axiom 2 (left_inverse): product(inverse(X), X, identity) = true.
% 0.60/0.57 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.60/0.57 Axiom 4 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 0.60/0.57 Axiom 5 (product_substitution3): ifeq(equalish(X, Y), true, ifeq(product(Z, W, X), true, product(Z, W, Y), true), true) = true.
% 0.60/0.57 Axiom 6 (total_function2): ifeq(product(X, Y, Z), true, ifeq(product(X, Y, W), true, equalish(W, Z), true), true) = true.
% 0.60/0.57 Axiom 7 (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.
% 0.60/0.57
% 0.60/0.57 Goal 1 (prove_right_identity): product(a, identity, a) = true.
% 0.60/0.57 Proof:
% 0.60/0.57 product(a, identity, a)
% 0.60/0.57 = { by axiom 3 (ifeq_axiom) R->L }
% 0.60/0.57 ifeq(true, true, product(a, identity, a), true)
% 0.60/0.57 = { by axiom 5 (product_substitution3) R->L }
% 0.60/0.57 ifeq(ifeq(equalish(multiply(a, inverse(a)), identity), true, ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, product(a, inverse(a), identity), true), true), true, product(a, identity, a), true)
% 0.60/0.57 = { by axiom 4 (total_function1) }
% 0.60/0.57 ifeq(ifeq(equalish(multiply(a, inverse(a)), identity), true, ifeq(true, true, product(a, inverse(a), identity), true), true), true, product(a, identity, a), true)
% 0.60/0.57 = { by axiom 3 (ifeq_axiom) }
% 0.60/0.57 ifeq(ifeq(equalish(multiply(a, inverse(a)), identity), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.57 = { by axiom 3 (ifeq_axiom) R->L }
% 0.60/0.57 ifeq(ifeq(ifeq(true, true, equalish(multiply(a, inverse(a)), identity), true), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.57 = { by axiom 7 (associativity1) R->L }
% 0.60/0.57 ifeq(ifeq(ifeq(ifeq(product(identity, multiply(a, inverse(a)), multiply(a, inverse(a))), true, ifeq(product(inverse(a), multiply(a, inverse(a)), inverse(a)), true, ifeq(product(inverse(inverse(a)), inverse(a), identity), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true), true), true, equalish(multiply(a, inverse(a)), identity), true), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.57 = { by axiom 1 (left_identity) }
% 0.60/0.57 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(a), multiply(a, inverse(a)), inverse(a)), true, ifeq(product(inverse(inverse(a)), inverse(a), identity), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true), true), true, equalish(multiply(a, inverse(a)), identity), true), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.57 = { by axiom 3 (ifeq_axiom) }
% 0.60/0.57 ifeq(ifeq(ifeq(ifeq(product(inverse(a), multiply(a, inverse(a)), inverse(a)), true, ifeq(product(inverse(inverse(a)), inverse(a), identity), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true), true, equalish(multiply(a, inverse(a)), identity), true), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.57 = { by axiom 2 (left_inverse) }
% 0.60/0.57 ifeq(ifeq(ifeq(ifeq(product(inverse(a), multiply(a, inverse(a)), inverse(a)), true, ifeq(true, true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true), true, equalish(multiply(a, inverse(a)), identity), true), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.57 = { by axiom 3 (ifeq_axiom) }
% 0.60/0.57 ifeq(ifeq(ifeq(ifeq(product(inverse(a), multiply(a, inverse(a)), inverse(a)), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, equalish(multiply(a, inverse(a)), identity), true), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.58 = { by axiom 3 (ifeq_axiom) R->L }
% 0.60/0.58 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, equalish(multiply(a, inverse(a)), identity), true), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.58 = { by axiom 4 (total_function1) R->L }
% 0.60/0.58 ifeq(ifeq(ifeq(ifeq(ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, equalish(multiply(a, inverse(a)), identity), true), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.58 = { by axiom 3 (ifeq_axiom) R->L }
% 0.60/0.58 ifeq(ifeq(ifeq(ifeq(ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, ifeq(true, true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, equalish(multiply(a, inverse(a)), identity), true), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.58 = { by axiom 2 (left_inverse) R->L }
% 0.60/0.58 ifeq(ifeq(ifeq(ifeq(ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, ifeq(product(inverse(a), a, identity), true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, equalish(multiply(a, inverse(a)), identity), true), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.58 = { by axiom 3 (ifeq_axiom) R->L }
% 0.60/0.58 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, ifeq(product(inverse(a), a, identity), true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, equalish(multiply(a, inverse(a)), identity), true), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.58 = { by axiom 1 (left_identity) R->L }
% 0.60/0.58 ifeq(ifeq(ifeq(ifeq(ifeq(product(identity, inverse(a), inverse(a)), true, ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, ifeq(product(inverse(a), a, identity), true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, equalish(multiply(a, inverse(a)), identity), true), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.58 = { by axiom 7 (associativity1) }
% 0.60/0.58 ifeq(ifeq(ifeq(ifeq(true, true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, equalish(multiply(a, inverse(a)), identity), true), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.58 = { by axiom 3 (ifeq_axiom) }
% 0.60/0.58 ifeq(ifeq(ifeq(product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true, equalish(multiply(a, inverse(a)), identity), true), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.58 = { by axiom 3 (ifeq_axiom) R->L }
% 0.60/0.58 ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true, equalish(multiply(a, inverse(a)), identity), true), true), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.58 = { by axiom 2 (left_inverse) R->L }
% 0.60/0.58 ifeq(ifeq(ifeq(product(inverse(inverse(a)), inverse(a), identity), true, ifeq(product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true, equalish(multiply(a, inverse(a)), identity), true), true), true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.58 = { by axiom 6 (total_function2) }
% 0.60/0.58 ifeq(ifeq(true, true, product(a, inverse(a), identity), true), true, product(a, identity, a), true)
% 0.60/0.58 = { by axiom 3 (ifeq_axiom) }
% 0.60/0.58 ifeq(product(a, inverse(a), identity), true, product(a, identity, a), true)
% 0.60/0.58 = { by axiom 3 (ifeq_axiom) R->L }
% 0.60/0.58 ifeq(true, true, ifeq(product(a, inverse(a), identity), true, product(a, identity, a), true), true)
% 0.60/0.58 = { by axiom 2 (left_inverse) R->L }
% 0.60/0.58 ifeq(product(inverse(a), a, identity), true, ifeq(product(a, inverse(a), identity), true, product(a, identity, a), true), true)
% 0.60/0.58 = { by axiom 3 (ifeq_axiom) R->L }
% 0.60/0.58 ifeq(true, true, ifeq(product(inverse(a), a, identity), true, ifeq(product(a, inverse(a), identity), true, product(a, identity, a), true), true), true)
% 0.60/0.58 = { by axiom 1 (left_identity) R->L }
% 0.60/0.58 ifeq(product(identity, a, a), true, ifeq(product(inverse(a), a, identity), true, ifeq(product(a, inverse(a), identity), true, product(a, identity, a), true), true), true)
% 0.60/0.58 = { by axiom 7 (associativity1) }
% 0.60/0.58 true
% 0.60/0.58 % SZS output end Proof
% 0.60/0.58
% 0.60/0.58 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------