%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP036-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 10:09:07 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.44s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP036-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 09:18:59 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.44 Command-line arguments: --flatten --complete-subsets
% 0.13/0.44
% 0.13/0.44 % SZS status Unsatisfiable
% 0.13/0.44
% 0.13/0.45 % SZS output start Proof
% 0.13/0.45 Axiom 1 (another_identity_in_subgroup): subgroup_member(another_identity) = true.
% 0.13/0.45 Axiom 2 (left_identity): product(identity, X, X) = true.
% 0.13/0.45 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.13/0.45 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.13/0.45 Axiom 5 (right_inverse): product(X, inverse(X), identity) = true.
% 0.13/0.45 Axiom 6 (another_right_identity): ifeq(subgroup_member(X), true, product(X, another_identity, X), true) = true.
% 0.13/0.45 Axiom 7 (total_function2): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 0.13/0.45 Axiom 8 (closure_of_product_and_inverse): ifeq(subgroup_member(X), true, ifeq(subgroup_member(Y), true, ifeq(product(Y, inverse(X), Z), true, subgroup_member(Z), true), true), true) = true.
% 0.13/0.45
% 0.13/0.45 Goal 1 (prove_identity_equals_another_identity): identity = another_identity.
% 0.13/0.45 Proof:
% 0.13/0.45 identity
% 0.13/0.45 = { by axiom 3 (ifeq_axiom) R->L }
% 0.13/0.45 ifeq2(subgroup_member(another_identity), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 1 (another_identity_in_subgroup) }
% 0.13/0.45 ifeq2(true, subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 6 (another_right_identity) R->L }
% 0.13/0.45 ifeq2(ifeq(subgroup_member(identity), true, product(identity, another_identity, identity), true), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 1 (another_identity_in_subgroup) R->L }
% 0.13/0.45 ifeq2(ifeq(subgroup_member(identity), true, product(identity, another_identity, identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 1 (another_identity_in_subgroup) R->L }
% 0.13/0.45 ifeq2(ifeq(subgroup_member(identity), subgroup_member(another_identity), product(identity, another_identity, identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.13/0.45 ifeq2(ifeq(ifeq(subgroup_member(another_identity), subgroup_member(another_identity), subgroup_member(identity), subgroup_member(another_identity)), subgroup_member(another_identity), product(identity, another_identity, identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.13/0.45 ifeq2(ifeq(ifeq(subgroup_member(another_identity), subgroup_member(another_identity), ifeq(subgroup_member(another_identity), subgroup_member(another_identity), subgroup_member(identity), subgroup_member(another_identity)), subgroup_member(another_identity)), subgroup_member(another_identity), product(identity, another_identity, identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.13/0.45 ifeq2(ifeq(ifeq(subgroup_member(another_identity), subgroup_member(another_identity), ifeq(subgroup_member(another_identity), subgroup_member(another_identity), ifeq(subgroup_member(another_identity), subgroup_member(another_identity), subgroup_member(identity), subgroup_member(another_identity)), subgroup_member(another_identity)), subgroup_member(another_identity)), subgroup_member(another_identity), product(identity, another_identity, identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 1 (another_identity_in_subgroup) }
% 0.13/0.45 ifeq2(ifeq(ifeq(subgroup_member(another_identity), subgroup_member(another_identity), ifeq(subgroup_member(another_identity), subgroup_member(another_identity), ifeq(true, subgroup_member(another_identity), subgroup_member(identity), subgroup_member(another_identity)), subgroup_member(another_identity)), subgroup_member(another_identity)), subgroup_member(another_identity), product(identity, another_identity, identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 5 (right_inverse) R->L }
% 0.13/0.45 ifeq2(ifeq(ifeq(subgroup_member(another_identity), subgroup_member(another_identity), ifeq(subgroup_member(another_identity), subgroup_member(another_identity), ifeq(product(another_identity, inverse(another_identity), identity), subgroup_member(another_identity), subgroup_member(identity), subgroup_member(another_identity)), subgroup_member(another_identity)), subgroup_member(another_identity)), subgroup_member(another_identity), product(identity, another_identity, identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 1 (another_identity_in_subgroup) }
% 0.13/0.45 ifeq2(ifeq(ifeq(subgroup_member(another_identity), true, ifeq(subgroup_member(another_identity), subgroup_member(another_identity), ifeq(product(another_identity, inverse(another_identity), identity), subgroup_member(another_identity), subgroup_member(identity), subgroup_member(another_identity)), subgroup_member(another_identity)), subgroup_member(another_identity)), subgroup_member(another_identity), product(identity, another_identity, identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 1 (another_identity_in_subgroup) }
% 0.13/0.45 ifeq2(ifeq(ifeq(subgroup_member(another_identity), true, ifeq(subgroup_member(another_identity), true, ifeq(product(another_identity, inverse(another_identity), identity), subgroup_member(another_identity), subgroup_member(identity), subgroup_member(another_identity)), subgroup_member(another_identity)), subgroup_member(another_identity)), subgroup_member(another_identity), product(identity, another_identity, identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 1 (another_identity_in_subgroup) }
% 0.13/0.45 ifeq2(ifeq(ifeq(subgroup_member(another_identity), true, ifeq(subgroup_member(another_identity), true, ifeq(product(another_identity, inverse(another_identity), identity), true, subgroup_member(identity), subgroup_member(another_identity)), subgroup_member(another_identity)), subgroup_member(another_identity)), subgroup_member(another_identity), product(identity, another_identity, identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 1 (another_identity_in_subgroup) }
% 0.13/0.45 ifeq2(ifeq(ifeq(subgroup_member(another_identity), true, ifeq(subgroup_member(another_identity), true, ifeq(product(another_identity, inverse(another_identity), identity), true, subgroup_member(identity), true), subgroup_member(another_identity)), subgroup_member(another_identity)), subgroup_member(another_identity), product(identity, another_identity, identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 1 (another_identity_in_subgroup) }
% 0.13/0.45 ifeq2(ifeq(ifeq(subgroup_member(another_identity), true, ifeq(subgroup_member(another_identity), true, ifeq(product(another_identity, inverse(another_identity), identity), true, subgroup_member(identity), true), true), subgroup_member(another_identity)), subgroup_member(another_identity), product(identity, another_identity, identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 1 (another_identity_in_subgroup) }
% 0.13/0.45 ifeq2(ifeq(ifeq(subgroup_member(another_identity), true, ifeq(subgroup_member(another_identity), true, ifeq(product(another_identity, inverse(another_identity), identity), true, subgroup_member(identity), true), true), true), subgroup_member(another_identity), product(identity, another_identity, identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 8 (closure_of_product_and_inverse) }
% 0.13/0.45 ifeq2(ifeq(true, subgroup_member(another_identity), product(identity, another_identity, identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 1 (another_identity_in_subgroup) R->L }
% 0.13/0.45 ifeq2(ifeq(subgroup_member(another_identity), subgroup_member(another_identity), product(identity, another_identity, identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 4 (ifeq_axiom) }
% 0.13/0.45 ifeq2(product(identity, another_identity, identity), subgroup_member(another_identity), identity, another_identity)
% 0.13/0.45 = { by axiom 3 (ifeq_axiom) R->L }
% 0.13/0.45 ifeq2(subgroup_member(another_identity), subgroup_member(another_identity), ifeq2(product(identity, another_identity, identity), subgroup_member(another_identity), identity, another_identity), another_identity)
% 0.13/0.45 = { by axiom 1 (another_identity_in_subgroup) }
% 0.13/0.45 ifeq2(true, subgroup_member(another_identity), ifeq2(product(identity, another_identity, identity), subgroup_member(another_identity), identity, another_identity), another_identity)
% 0.13/0.45 = { by axiom 2 (left_identity) R->L }
% 0.13/0.45 ifeq2(product(identity, another_identity, another_identity), subgroup_member(another_identity), ifeq2(product(identity, another_identity, identity), subgroup_member(another_identity), identity, another_identity), another_identity)
% 0.13/0.45 = { by axiom 1 (another_identity_in_subgroup) }
% 0.13/0.45 ifeq2(product(identity, another_identity, another_identity), true, ifeq2(product(identity, another_identity, identity), subgroup_member(another_identity), identity, another_identity), another_identity)
% 0.13/0.45 = { by axiom 1 (another_identity_in_subgroup) }
% 0.13/0.45 ifeq2(product(identity, another_identity, another_identity), true, ifeq2(product(identity, another_identity, identity), true, identity, another_identity), another_identity)
% 0.13/0.45 = { by axiom 7 (total_function2) }
% 0.13/0.45 another_identity
% 0.13/0.45 % SZS output end Proof
% 0.13/0.45
% 0.13/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
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