%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP029-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 10:09:06 AM UTC 2026
% Result : Unsatisfiable 1.80s 0.70s
% Output : Proof 2.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP029-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n026.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 09:18:11 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.80/0.70 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 1.80/0.70
% 1.80/0.70 % SZS status Unsatisfiable
% 1.80/0.70
% 2.22/0.71 % SZS output start Proof
% 2.22/0.71 Axiom 1 (left_identity): product(identity, X, X) = true.
% 2.22/0.71 Axiom 2 (left_inverse): product(inverse(X), X, identity) = true.
% 2.22/0.71 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.22/0.71 Axiom 4 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 2.22/0.71 Axiom 5 (product_substitution3): ifeq(product(X, Y, Z), true, ifeq(equalish(Z, W), true, product(X, Y, W), true), true) = true.
% 2.22/0.71 Axiom 6 (total_function2): ifeq(product(X, Y, Z), true, ifeq(product(X, Y, W), true, equalish(W, Z), true), true) = true.
% 2.22/0.71 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.
% 2.22/0.71
% 2.22/0.71 Goal 1 (prove_there_is_a_right_identity): product(not_right_identity(X), X, not_right_identity(X)) = true.
% 2.22/0.71 The goal is true when:
% 2.22/0.71 X = identity
% 2.22/0.71
% 2.22/0.71 Proof:
% 2.22/0.71 product(not_right_identity(identity), identity, not_right_identity(identity))
% 2.22/0.71 = { by axiom 3 (ifeq_axiom) R->L }
% 2.22/0.71 ifeq(true, true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.71 = { by axiom 5 (product_substitution3) R->L }
% 2.22/0.71 ifeq(ifeq(product(not_right_identity(identity), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true, ifeq(equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.71 = { by axiom 4 (total_function1) }
% 2.22/0.71 ifeq(ifeq(true, true, ifeq(equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.71 = { by axiom 3 (ifeq_axiom) }
% 2.22/0.71 ifeq(ifeq(equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.71 = { by axiom 3 (ifeq_axiom) R->L }
% 2.22/0.71 ifeq(ifeq(ifeq(true, true, equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.71 = { by axiom 7 (associativity1) R->L }
% 2.22/0.71 ifeq(ifeq(ifeq(ifeq(product(identity, multiply(not_right_identity(identity), inverse(not_right_identity(identity))), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true, ifeq(product(inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity))), inverse(not_right_identity(identity))), true, ifeq(product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), identity), true, product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true), true), true), true, equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.71 = { by axiom 1 (left_identity) }
% 2.22/0.71 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity))), inverse(not_right_identity(identity))), true, ifeq(product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), identity), true, product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true), true), true), true, equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.71 = { by axiom 3 (ifeq_axiom) }
% 2.22/0.71 ifeq(ifeq(ifeq(ifeq(product(inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity))), inverse(not_right_identity(identity))), true, ifeq(product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), identity), true, product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true), true), true, equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.72 = { by axiom 2 (left_inverse) }
% 2.22/0.72 ifeq(ifeq(ifeq(ifeq(product(inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity))), inverse(not_right_identity(identity))), true, ifeq(true, true, product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true), true), true, equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.72 = { by axiom 3 (ifeq_axiom) }
% 2.22/0.72 ifeq(ifeq(ifeq(ifeq(product(inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity))), inverse(not_right_identity(identity))), true, product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true), true, equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.72 = { by axiom 3 (ifeq_axiom) R->L }
% 2.22/0.72 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, product(inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity))), inverse(not_right_identity(identity))), true), true, product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true), true, equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.72 = { by axiom 4 (total_function1) R->L }
% 2.22/0.72 ifeq(ifeq(ifeq(ifeq(ifeq(product(not_right_identity(identity), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true, product(inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity))), inverse(not_right_identity(identity))), true), true, product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true), true, equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.72 = { by axiom 3 (ifeq_axiom) R->L }
% 2.22/0.72 ifeq(ifeq(ifeq(ifeq(ifeq(product(not_right_identity(identity), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true, ifeq(true, true, product(inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity))), inverse(not_right_identity(identity))), true), true), true, product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true), true, equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.72 = { by axiom 2 (left_inverse) R->L }
% 2.22/0.72 ifeq(ifeq(ifeq(ifeq(ifeq(product(not_right_identity(identity), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true, ifeq(product(inverse(not_right_identity(identity)), not_right_identity(identity), identity), true, product(inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity))), inverse(not_right_identity(identity))), true), true), true, product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true), true, equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.72 = { by axiom 3 (ifeq_axiom) R->L }
% 2.22/0.72 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(not_right_identity(identity), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true, ifeq(product(inverse(not_right_identity(identity)), not_right_identity(identity), identity), true, product(inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity))), inverse(not_right_identity(identity))), true), true), true), true, product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true), true, equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.72 = { by axiom 1 (left_identity) R->L }
% 2.22/0.72 ifeq(ifeq(ifeq(ifeq(ifeq(product(identity, inverse(not_right_identity(identity)), inverse(not_right_identity(identity))), true, ifeq(product(not_right_identity(identity), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true, ifeq(product(inverse(not_right_identity(identity)), not_right_identity(identity), identity), true, product(inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity))), inverse(not_right_identity(identity))), true), true), true), true, product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true), true, equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.72 = { by axiom 7 (associativity1) }
% 2.22/0.72 ifeq(ifeq(ifeq(ifeq(true, true, product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true), true, equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.72 = { by axiom 3 (ifeq_axiom) }
% 2.22/0.72 ifeq(ifeq(ifeq(product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true, equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.72 = { by axiom 3 (ifeq_axiom) R->L }
% 2.22/0.72 ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true, equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true), true), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.72 = { by axiom 2 (left_inverse) R->L }
% 2.22/0.72 ifeq(ifeq(ifeq(product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), identity), true, ifeq(product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), multiply(not_right_identity(identity), inverse(not_right_identity(identity)))), true, equalish(multiply(not_right_identity(identity), inverse(not_right_identity(identity))), identity), true), true), true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.72 = { by axiom 6 (total_function2) }
% 2.22/0.72 ifeq(ifeq(true, true, product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.72 = { by axiom 3 (ifeq_axiom) }
% 2.22/0.72 ifeq(product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true)
% 2.22/0.72 = { by axiom 3 (ifeq_axiom) R->L }
% 2.22/0.72 ifeq(true, true, ifeq(product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true), true)
% 2.22/0.72 = { by axiom 2 (left_inverse) R->L }
% 2.22/0.72 ifeq(product(inverse(not_right_identity(identity)), not_right_identity(identity), identity), true, ifeq(product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true), true)
% 2.22/0.72 = { by axiom 3 (ifeq_axiom) R->L }
% 2.22/0.72 ifeq(true, true, ifeq(product(inverse(not_right_identity(identity)), not_right_identity(identity), identity), true, ifeq(product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true), true), true)
% 2.22/0.72 = { by axiom 1 (left_identity) R->L }
% 2.22/0.72 ifeq(product(identity, not_right_identity(identity), not_right_identity(identity)), true, ifeq(product(inverse(not_right_identity(identity)), not_right_identity(identity), identity), true, ifeq(product(not_right_identity(identity), inverse(not_right_identity(identity)), identity), true, product(not_right_identity(identity), identity, not_right_identity(identity)), true), true), true)
% 2.22/0.72 = { by axiom 7 (associativity1) }
% 2.22/0.72 true
% 2.22/0.72 % SZS output end Proof
% 2.22/0.72
% 2.22/0.72 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------