%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP035-3 : 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 10:09:07 AM UTC 2026
% Result : Unsatisfiable 2.96s 0.80s
% Output : Proof 2.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP035-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n026.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 27 09:18:41 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.96/0.80 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
% 2.96/0.80
% 2.96/0.80 % SZS status Unsatisfiable
% 2.96/0.80
% 2.96/0.82 % SZS output start Proof
% 2.96/0.82 Axiom 1 (a_is_in_subgroup): subgroup_member(a) = true.
% 2.96/0.82 Axiom 2 (b_is_in_subgroup): subgroup_member(b) = true.
% 2.96/0.82 Axiom 3 (right_identity): product(X, identity, X) = true.
% 2.96/0.82 Axiom 4 (left_identity): product(identity, X, X) = true.
% 2.96/0.82 Axiom 5 (a_times_b_is_c): product(a, b, c) = true.
% 2.96/0.82 Axiom 6 (right_inverse): product(X, inverse(X), identity) = true.
% 2.96/0.82 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.96/0.82 Axiom 8 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 2.96/0.82 Axiom 9 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 2.96/0.82 Axiom 10 (total_function2): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 2.96/0.82 Axiom 11 (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.
% 2.96/0.82 Axiom 12 (associativity2): ifeq(product(X, Y, Z), true, ifeq(product(W, Z, V), true, ifeq(product(W, X, U), true, product(U, Y, V), true), true), true) = true.
% 2.96/0.82
% 2.96/0.82 Goal 1 (prove_c_is_in_subgroup): subgroup_member(c) = true.
% 2.96/0.82 Proof:
% 2.96/0.82 subgroup_member(c)
% 2.96/0.82 = { by axiom 8 (ifeq_axiom) R->L }
% 2.96/0.82 subgroup_member(ifeq2(true, true, c, multiply(a, b)))
% 2.96/0.82 = { by axiom 9 (total_function1) R->L }
% 2.96/0.82 subgroup_member(ifeq2(product(a, b, multiply(a, b)), true, c, multiply(a, b)))
% 2.96/0.82 = { by axiom 8 (ifeq_axiom) R->L }
% 2.96/0.82 subgroup_member(ifeq2(product(a, b, multiply(a, b)), true, ifeq2(true, true, c, multiply(a, b)), multiply(a, b)))
% 2.96/0.82 = { by axiom 5 (a_times_b_is_c) R->L }
% 2.96/0.82 subgroup_member(ifeq2(product(a, b, multiply(a, b)), true, ifeq2(product(a, b, c), true, c, multiply(a, b)), multiply(a, b)))
% 2.96/0.82 = { by axiom 10 (total_function2) }
% 2.96/0.82 subgroup_member(multiply(a, b))
% 2.96/0.82 = { by axiom 8 (ifeq_axiom) R->L }
% 2.96/0.82 subgroup_member(multiply(a, ifeq2(true, true, b, inverse(inverse(b)))))
% 2.96/0.82 = { by axiom 12 (associativity2) R->L }
% 2.96/0.82 subgroup_member(multiply(a, ifeq2(ifeq(product(inverse(b), inverse(inverse(b)), identity), true, ifeq(product(b, identity, b), true, ifeq(product(b, inverse(b), identity), true, product(identity, inverse(inverse(b)), b), true), true), true), true, b, inverse(inverse(b)))))
% 2.96/0.82 = { by axiom 3 (right_identity) }
% 2.96/0.82 subgroup_member(multiply(a, ifeq2(ifeq(product(inverse(b), inverse(inverse(b)), identity), true, ifeq(true, true, ifeq(product(b, inverse(b), identity), true, product(identity, inverse(inverse(b)), b), true), true), true), true, b, inverse(inverse(b)))))
% 2.96/0.82 = { by axiom 7 (ifeq_axiom) }
% 2.96/0.82 subgroup_member(multiply(a, ifeq2(ifeq(product(inverse(b), inverse(inverse(b)), identity), true, ifeq(product(b, inverse(b), identity), true, product(identity, inverse(inverse(b)), b), true), true), true, b, inverse(inverse(b)))))
% 2.96/0.82 = { by axiom 6 (right_inverse) }
% 2.96/0.82 subgroup_member(multiply(a, ifeq2(ifeq(true, true, ifeq(product(b, inverse(b), identity), true, product(identity, inverse(inverse(b)), b), true), true), true, b, inverse(inverse(b)))))
% 2.96/0.82 = { by axiom 7 (ifeq_axiom) }
% 2.96/0.82 subgroup_member(multiply(a, ifeq2(ifeq(product(b, inverse(b), identity), true, product(identity, inverse(inverse(b)), b), true), true, b, inverse(inverse(b)))))
% 2.96/0.82 = { by axiom 6 (right_inverse) }
% 2.96/0.82 subgroup_member(multiply(a, ifeq2(ifeq(true, true, product(identity, inverse(inverse(b)), b), true), true, b, inverse(inverse(b)))))
% 2.96/0.82 = { by axiom 7 (ifeq_axiom) }
% 2.96/0.82 subgroup_member(multiply(a, ifeq2(product(identity, inverse(inverse(b)), b), true, b, inverse(inverse(b)))))
% 2.96/0.82 = { by axiom 8 (ifeq_axiom) R->L }
% 2.96/0.82 subgroup_member(multiply(a, ifeq2(true, true, ifeq2(product(identity, inverse(inverse(b)), b), true, b, inverse(inverse(b))), inverse(inverse(b)))))
% 2.96/0.82 = { by axiom 4 (left_identity) R->L }
% 2.96/0.82 subgroup_member(multiply(a, ifeq2(product(identity, inverse(inverse(b)), inverse(inverse(b))), true, ifeq2(product(identity, inverse(inverse(b)), b), true, b, inverse(inverse(b))), inverse(inverse(b)))))
% 2.96/0.82 = { by axiom 10 (total_function2) }
% 2.96/0.82 subgroup_member(multiply(a, inverse(inverse(b))))
% 2.96/0.82 = { by axiom 7 (ifeq_axiom) R->L }
% 2.96/0.82 ifeq(true, true, subgroup_member(multiply(a, inverse(inverse(b)))), true)
% 2.96/0.82 = { by axiom 11 (closure_of_product_and_inverse) R->L }
% 2.96/0.82 ifeq(ifeq(subgroup_member(b), true, ifeq(subgroup_member(identity), true, ifeq(product(identity, inverse(b), inverse(b)), true, subgroup_member(inverse(b)), true), true), true), true, subgroup_member(multiply(a, inverse(inverse(b)))), true)
% 2.96/0.82 = { by axiom 4 (left_identity) }
% 2.96/0.82 ifeq(ifeq(subgroup_member(b), true, ifeq(subgroup_member(identity), true, ifeq(true, true, subgroup_member(inverse(b)), true), true), true), true, subgroup_member(multiply(a, inverse(inverse(b)))), true)
% 2.96/0.82 = { by axiom 7 (ifeq_axiom) R->L }
% 2.96/0.82 ifeq(ifeq(subgroup_member(b), true, ifeq(ifeq(true, true, subgroup_member(identity), true), true, ifeq(true, true, subgroup_member(inverse(b)), true), true), true), true, subgroup_member(multiply(a, inverse(inverse(b)))), true)
% 2.96/0.82 = { by axiom 1 (a_is_in_subgroup) R->L }
% 2.96/0.82 ifeq(ifeq(subgroup_member(b), true, ifeq(ifeq(subgroup_member(a), true, subgroup_member(identity), true), true, ifeq(true, true, subgroup_member(inverse(b)), true), true), true), true, subgroup_member(multiply(a, inverse(inverse(b)))), true)
% 2.96/0.82 = { by axiom 7 (ifeq_axiom) R->L }
% 2.96/0.82 ifeq(ifeq(subgroup_member(b), true, ifeq(ifeq(true, true, ifeq(subgroup_member(a), true, subgroup_member(identity), true), true), true, ifeq(true, true, subgroup_member(inverse(b)), true), true), true), true, subgroup_member(multiply(a, inverse(inverse(b)))), true)
% 2.96/0.82 = { by axiom 1 (a_is_in_subgroup) R->L }
% 2.96/0.82 ifeq(ifeq(subgroup_member(b), true, ifeq(ifeq(subgroup_member(a), true, ifeq(subgroup_member(a), true, subgroup_member(identity), true), true), true, ifeq(true, true, subgroup_member(inverse(b)), true), true), true), true, subgroup_member(multiply(a, inverse(inverse(b)))), true)
% 2.96/0.82 = { by axiom 7 (ifeq_axiom) R->L }
% 2.96/0.82 ifeq(ifeq(subgroup_member(b), 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(b)), true), true), true), true, subgroup_member(multiply(a, inverse(inverse(b)))), true)
% 2.96/0.82 = { by axiom 6 (right_inverse) R->L }
% 2.96/0.82 ifeq(ifeq(subgroup_member(b), 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(b)), true), true), true), true, subgroup_member(multiply(a, inverse(inverse(b)))), true)
% 2.96/0.82 = { by axiom 11 (closure_of_product_and_inverse) }
% 2.96/0.82 ifeq(ifeq(subgroup_member(b), true, ifeq(true, true, ifeq(true, true, subgroup_member(inverse(b)), true), true), true), true, subgroup_member(multiply(a, inverse(inverse(b)))), true)
% 2.96/0.82 = { by axiom 7 (ifeq_axiom) }
% 2.96/0.82 ifeq(ifeq(subgroup_member(b), true, ifeq(true, true, subgroup_member(inverse(b)), true), true), true, subgroup_member(multiply(a, inverse(inverse(b)))), true)
% 2.96/0.82 = { by axiom 7 (ifeq_axiom) }
% 2.96/0.82 ifeq(ifeq(subgroup_member(b), true, subgroup_member(inverse(b)), true), true, subgroup_member(multiply(a, inverse(inverse(b)))), true)
% 2.96/0.82 = { by axiom 2 (b_is_in_subgroup) }
% 2.96/0.82 ifeq(ifeq(true, true, subgroup_member(inverse(b)), true), true, subgroup_member(multiply(a, inverse(inverse(b)))), true)
% 2.96/0.82 = { by axiom 7 (ifeq_axiom) }
% 2.96/0.82 ifeq(subgroup_member(inverse(b)), true, subgroup_member(multiply(a, inverse(inverse(b)))), true)
% 2.96/0.82 = { by axiom 7 (ifeq_axiom) R->L }
% 2.96/0.82 ifeq(subgroup_member(inverse(b)), true, ifeq(true, true, subgroup_member(multiply(a, inverse(inverse(b)))), true), true)
% 2.96/0.82 = { by axiom 9 (total_function1) R->L }
% 2.96/0.82 ifeq(subgroup_member(inverse(b)), true, ifeq(product(a, inverse(inverse(b)), multiply(a, inverse(inverse(b)))), true, subgroup_member(multiply(a, inverse(inverse(b)))), true), true)
% 2.96/0.82 = { by axiom 7 (ifeq_axiom) R->L }
% 2.96/0.82 ifeq(subgroup_member(inverse(b)), true, ifeq(true, true, ifeq(product(a, inverse(inverse(b)), multiply(a, inverse(inverse(b)))), true, subgroup_member(multiply(a, inverse(inverse(b)))), true), true), true)
% 2.96/0.83 = { by axiom 1 (a_is_in_subgroup) R->L }
% 2.96/0.83 ifeq(subgroup_member(inverse(b)), true, ifeq(subgroup_member(a), true, ifeq(product(a, inverse(inverse(b)), multiply(a, inverse(inverse(b)))), true, subgroup_member(multiply(a, inverse(inverse(b)))), true), true), true)
% 2.96/0.83 = { by axiom 11 (closure_of_product_and_inverse) }
% 2.96/0.83 true
% 2.96/0.83 % SZS output end Proof
% 2.96/0.83
% 2.96/0.83 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------