%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP034-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 0.14s 0.46s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP034-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 09:20:31 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.46 Command-line arguments: --no-flatten-goal
% 0.14/0.46
% 0.14/0.46 % SZS status Unsatisfiable
% 0.14/0.46
% 0.14/0.46 % SZS output start Proof
% 0.14/0.46 Axiom 1 (a_is_in_subgroup): subgroup_member(a) = true.
% 0.14/0.46 Axiom 2 (left_identity): product(identity, X, X) = true.
% 0.14/0.46 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.14/0.46 Axiom 4 (right_inverse): product(X, inverse(X), identity) = true.
% 0.14/0.46 Axiom 5 (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.
% 0.14/0.46
% 0.14/0.46 Goal 1 (prove_a_inverse_is_in_subgroup): subgroup_member(inverse(a)) = true.
% 0.14/0.46 Proof:
% 0.14/0.46 subgroup_member(inverse(a))
% 0.14/0.46 = { by axiom 3 (ifeq_axiom) R->L }
% 0.14/0.46 ifeq(true, true, subgroup_member(inverse(a)), true)
% 0.14/0.46 = { by axiom 1 (a_is_in_subgroup) R->L }
% 0.14/0.46 ifeq(subgroup_member(a), true, subgroup_member(inverse(a)), true)
% 0.14/0.46 = { by axiom 3 (ifeq_axiom) R->L }
% 0.14/0.46 ifeq(subgroup_member(a), true, ifeq(true, true, subgroup_member(inverse(a)), true), true)
% 0.14/0.46 = { by axiom 3 (ifeq_axiom) R->L }
% 0.14/0.46 ifeq(subgroup_member(a), true, ifeq(true, true, ifeq(true, true, subgroup_member(inverse(a)), true), true), true)
% 0.14/0.46 = { by axiom 5 (closure_of_product_and_inverse) R->L }
% 0.14/0.46 ifeq(subgroup_member(a), true, ifeq(ifeq(subgroup_member(a), true, ifeq(subgroup_member(a), true, ifeq(product(a, inverse(a), identity), true, subgroup_member(identity), true), true), true), true, ifeq(true, true, subgroup_member(inverse(a)), true), true), true)
% 0.14/0.46 = { by axiom 4 (right_inverse) }
% 0.14/0.46 ifeq(subgroup_member(a), true, ifeq(ifeq(subgroup_member(a), true, ifeq(subgroup_member(a), true, ifeq(true, true, subgroup_member(identity), true), true), true), true, ifeq(true, true, subgroup_member(inverse(a)), true), true), true)
% 0.14/0.46 = { by axiom 3 (ifeq_axiom) }
% 0.14/0.46 ifeq(subgroup_member(a), true, ifeq(ifeq(subgroup_member(a), true, ifeq(subgroup_member(a), true, subgroup_member(identity), true), true), true, ifeq(true, true, subgroup_member(inverse(a)), true), true), true)
% 0.14/0.46 = { by axiom 1 (a_is_in_subgroup) }
% 0.14/0.46 ifeq(subgroup_member(a), true, ifeq(ifeq(true, true, ifeq(subgroup_member(a), true, subgroup_member(identity), true), true), true, ifeq(true, true, subgroup_member(inverse(a)), true), true), true)
% 0.14/0.46 = { by axiom 3 (ifeq_axiom) }
% 0.14/0.46 ifeq(subgroup_member(a), true, ifeq(ifeq(subgroup_member(a), true, subgroup_member(identity), true), true, ifeq(true, true, subgroup_member(inverse(a)), true), true), true)
% 0.14/0.46 = { by axiom 1 (a_is_in_subgroup) }
% 0.14/0.46 ifeq(subgroup_member(a), true, ifeq(ifeq(true, true, subgroup_member(identity), true), true, ifeq(true, true, subgroup_member(inverse(a)), true), true), true)
% 0.14/0.46 = { by axiom 3 (ifeq_axiom) }
% 0.14/0.46 ifeq(subgroup_member(a), true, ifeq(subgroup_member(identity), true, ifeq(true, true, subgroup_member(inverse(a)), true), true), true)
% 0.14/0.46 = { by axiom 2 (left_identity) R->L }
% 0.14/0.46 ifeq(subgroup_member(a), true, ifeq(subgroup_member(identity), true, ifeq(product(identity, inverse(a), inverse(a)), true, subgroup_member(inverse(a)), true), true), true)
% 0.14/0.46 = { by axiom 5 (closure_of_product_and_inverse) }
% 0.14/0.46 true
% 0.14/0.46 % SZS output end Proof
% 0.14/0.46
% 0.14/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------