%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP037-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 0.10s 0.45s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:16:01 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.45 Command-line arguments: --flatten --complete-subsets
% 0.10/0.45
% 0.10/0.45 % SZS status Unsatisfiable
% 0.10/0.45
% 0.10/0.46 % SZS output start Proof
% 0.10/0.46 Axiom 1 (another_identity_in_subgroup): subgroup_member(another_identity) = true.
% 0.10/0.46 Axiom 2 (a_is_in_subgroup): subgroup_member(a) = true.
% 0.10/0.46 Axiom 3 (right_identity): product(X, identity, X) = true.
% 0.10/0.46 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.10/0.46 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.10/0.46 Axiom 6 (right_inverse): product(X, inverse(X), identity) = true.
% 0.10/0.46 Axiom 7 (another_right_identity): ifeq(subgroup_member(X), true, product(X, another_identity, X), true) = true.
% 0.10/0.46 Axiom 8 (another_right_inverse): ifeq(subgroup_member(X), true, product(X, another_inverse(X), another_identity), true) = true.
% 0.10/0.46 Axiom 9 (product_right_cancellation): ifeq2(product(X, Y, Z), true, ifeq2(product(X, W, Z), true, Y, W), W) = W.
% 0.10/0.46
% 0.10/0.46 Lemma 10: ifeq2(product(X, Y, Z), subgroup_member(another_identity), ifeq2(product(X, W, Z), subgroup_member(another_identity), Y, W), W) = W.
% 0.10/0.46 Proof:
% 0.10/0.46 ifeq2(product(X, Y, Z), subgroup_member(another_identity), ifeq2(product(X, W, Z), subgroup_member(another_identity), Y, W), W)
% 0.10/0.46 = { by axiom 1 (another_identity_in_subgroup) }
% 0.10/0.46 ifeq2(product(X, Y, Z), true, ifeq2(product(X, W, Z), subgroup_member(another_identity), Y, W), W)
% 0.10/0.46 = { by axiom 1 (another_identity_in_subgroup) }
% 0.10/0.46 ifeq2(product(X, Y, Z), true, ifeq2(product(X, W, Z), true, Y, W), W)
% 0.10/0.46 = { by axiom 9 (product_right_cancellation) }
% 0.10/0.46 W
% 0.10/0.46
% 0.10/0.46 Goal 1 (prove_two_inverses_are_equal): inverse(a) = another_inverse(a).
% 0.10/0.46 Proof:
% 0.10/0.46 inverse(a)
% 0.10/0.46 = { by axiom 4 (ifeq_axiom) R->L }
% 0.10/0.46 ifeq2(subgroup_member(another_identity), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 1 (another_identity_in_subgroup) }
% 0.10/0.46 ifeq2(true, subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 8 (another_right_inverse) R->L }
% 0.10/0.46 ifeq2(ifeq(subgroup_member(a), true, product(a, another_inverse(a), another_identity), true), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 1 (another_identity_in_subgroup) R->L }
% 0.10/0.46 ifeq2(ifeq(subgroup_member(a), true, product(a, another_inverse(a), another_identity), subgroup_member(another_identity)), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 1 (another_identity_in_subgroup) R->L }
% 0.10/0.46 ifeq2(ifeq(subgroup_member(a), subgroup_member(another_identity), product(a, another_inverse(a), another_identity), subgroup_member(another_identity)), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 2 (a_is_in_subgroup) }
% 0.10/0.46 ifeq2(ifeq(true, subgroup_member(another_identity), product(a, another_inverse(a), another_identity), subgroup_member(another_identity)), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 1 (another_identity_in_subgroup) R->L }
% 0.10/0.46 ifeq2(ifeq(subgroup_member(another_identity), subgroup_member(another_identity), product(a, another_inverse(a), another_identity), subgroup_member(another_identity)), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 5 (ifeq_axiom) }
% 0.10/0.46 ifeq2(product(a, another_inverse(a), another_identity), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by lemma 10 R->L }
% 0.10/0.46 ifeq2(product(a, another_inverse(a), ifeq2(product(another_identity, identity, another_identity), subgroup_member(another_identity), ifeq2(product(another_identity, another_identity, another_identity), subgroup_member(another_identity), identity, another_identity), another_identity)), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 3 (right_identity) }
% 0.10/0.46 ifeq2(product(a, another_inverse(a), ifeq2(true, subgroup_member(another_identity), ifeq2(product(another_identity, another_identity, another_identity), subgroup_member(another_identity), identity, another_identity), another_identity)), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 1 (another_identity_in_subgroup) R->L }
% 0.10/0.46 ifeq2(product(a, another_inverse(a), ifeq2(subgroup_member(another_identity), subgroup_member(another_identity), ifeq2(product(another_identity, another_identity, another_identity), subgroup_member(another_identity), identity, another_identity), another_identity)), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 4 (ifeq_axiom) }
% 0.10/0.46 ifeq2(product(a, another_inverse(a), ifeq2(product(another_identity, another_identity, another_identity), subgroup_member(another_identity), identity, another_identity)), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 5 (ifeq_axiom) R->L }
% 0.10/0.46 ifeq2(product(a, another_inverse(a), ifeq2(ifeq(subgroup_member(another_identity), subgroup_member(another_identity), product(another_identity, another_identity, another_identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 1 (another_identity_in_subgroup) }
% 0.10/0.46 ifeq2(product(a, another_inverse(a), ifeq2(ifeq(subgroup_member(another_identity), true, product(another_identity, another_identity, another_identity), subgroup_member(another_identity)), subgroup_member(another_identity), identity, another_identity)), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 1 (another_identity_in_subgroup) }
% 0.10/0.46 ifeq2(product(a, another_inverse(a), ifeq2(ifeq(subgroup_member(another_identity), true, product(another_identity, another_identity, another_identity), true), subgroup_member(another_identity), identity, another_identity)), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 7 (another_right_identity) }
% 0.10/0.46 ifeq2(product(a, another_inverse(a), ifeq2(true, subgroup_member(another_identity), identity, another_identity)), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 1 (another_identity_in_subgroup) R->L }
% 0.10/0.46 ifeq2(product(a, another_inverse(a), ifeq2(subgroup_member(another_identity), subgroup_member(another_identity), identity, another_identity)), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 4 (ifeq_axiom) }
% 0.10/0.46 ifeq2(product(a, another_inverse(a), identity), subgroup_member(another_identity), inverse(a), another_inverse(a))
% 0.10/0.46 = { by axiom 4 (ifeq_axiom) R->L }
% 0.10/0.46 ifeq2(subgroup_member(another_identity), subgroup_member(another_identity), ifeq2(product(a, another_inverse(a), identity), subgroup_member(another_identity), inverse(a), another_inverse(a)), another_inverse(a))
% 0.10/0.46 = { by axiom 1 (another_identity_in_subgroup) }
% 0.10/0.46 ifeq2(true, subgroup_member(another_identity), ifeq2(product(a, another_inverse(a), identity), subgroup_member(another_identity), inverse(a), another_inverse(a)), another_inverse(a))
% 0.10/0.46 = { by axiom 6 (right_inverse) R->L }
% 0.10/0.46 ifeq2(product(a, inverse(a), identity), subgroup_member(another_identity), ifeq2(product(a, another_inverse(a), identity), subgroup_member(another_identity), inverse(a), another_inverse(a)), another_inverse(a))
% 0.10/0.46 = { by lemma 10 }
% 0.10/0.46 another_inverse(a)
% 0.10/0.46 % SZS output end Proof
% 0.10/0.46
% 0.10/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------