%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN009-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 10:19:00 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.49s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 10:51:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.49 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.09/0.49
% 0.09/0.49 % SZS status Unsatisfiable
% 0.09/0.49
% 0.09/0.49 % SZS output start Proof
% 0.09/0.49 Axiom 1 (identity_is_largest): divide(X, identity) = zero.
% 0.09/0.49 Axiom 2 (zero_is_smallest): divide(zero, X) = zero.
% 0.09/0.49 Axiom 3 (quotient_smaller_than_numerator): divide(divide(X, Y), X) = zero.
% 0.09/0.49 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.09/0.49 Axiom 5 (quotient_property): divide(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y)) = zero.
% 0.09/0.49 Axiom 6 (property_of_divide2): ifeq(divide(X, Y), zero, divide(divide(Z, Y), divide(Z, X)), zero) = zero.
% 0.09/0.49 Axiom 7 (divide_and_equal): ifeq(divide(X, Y), zero, ifeq(divide(Y, X), zero, Y, X), X) = X.
% 0.09/0.49 Axiom 8 (property_of_divide1): ifeq(divide(divide(X, Y), Z), zero, divide(divide(X, Z), Y), zero) = zero.
% 0.09/0.49
% 0.09/0.49 Lemma 9: divide(divide(X, divide(identity, Y)), Y) = zero.
% 0.09/0.49 Proof:
% 0.09/0.49 divide(divide(X, divide(identity, Y)), Y)
% 0.09/0.49 = { by axiom 4 (ifeq_axiom) R->L }
% 0.09/0.49 ifeq(zero, zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 5 (quotient_property) R->L }
% 0.09/0.50 ifeq(divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(X, identity), Y)), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 1 (identity_is_largest) }
% 0.09/0.50 ifeq(divide(divide(divide(X, Y), divide(identity, Y)), divide(zero, Y)), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 2 (zero_is_smallest) }
% 0.09/0.50 ifeq(divide(divide(divide(X, Y), divide(identity, Y)), zero), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 4 (ifeq_axiom) R->L }
% 0.09/0.50 ifeq(ifeq(zero, zero, divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 3 (quotient_smaller_than_numerator) R->L }
% 0.09/0.50 ifeq(ifeq(divide(divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 4 (ifeq_axiom) R->L }
% 0.09/0.50 ifeq(ifeq(zero, zero, ifeq(divide(divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 4 (ifeq_axiom) R->L }
% 0.09/0.50 ifeq(ifeq(ifeq(zero, zero, zero, divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero))), zero, ifeq(divide(divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 8 (property_of_divide1) R->L }
% 0.09/0.50 ifeq(ifeq(ifeq(ifeq(divide(divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(divide(X, Y), divide(identity, Y)), zero)), zero, divide(divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero)), zero), zero), zero, zero, divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero))), zero, ifeq(divide(divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 4 (ifeq_axiom) R->L }
% 0.09/0.50 ifeq(ifeq(ifeq(ifeq(ifeq(zero, zero, divide(divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(divide(X, Y), divide(identity, Y)), zero)), zero), zero, divide(divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero)), zero), zero), zero, zero, divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero))), zero, ifeq(divide(divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 2 (zero_is_smallest) R->L }
% 0.09/0.50 ifeq(ifeq(ifeq(ifeq(ifeq(divide(zero, zero), zero, divide(divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(divide(X, Y), divide(identity, Y)), zero)), zero), zero, divide(divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero)), zero), zero), zero, zero, divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero))), zero, ifeq(divide(divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 6 (property_of_divide2) }
% 0.09/0.50 ifeq(ifeq(ifeq(ifeq(zero, zero, divide(divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero)), zero), zero), zero, zero, divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero))), zero, ifeq(divide(divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 4 (ifeq_axiom) }
% 0.09/0.50 ifeq(ifeq(ifeq(divide(divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero)), zero), zero, zero, divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero))), zero, ifeq(divide(divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 4 (ifeq_axiom) R->L }
% 0.09/0.50 ifeq(ifeq(ifeq(divide(divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero)), zero), zero, ifeq(zero, zero, zero, divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero))), divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero))), zero, ifeq(divide(divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 2 (zero_is_smallest) R->L }
% 0.09/0.50 ifeq(ifeq(ifeq(divide(divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero)), zero), zero, ifeq(divide(zero, divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero))), zero, zero, divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero))), divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero))), zero, ifeq(divide(divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 7 (divide_and_equal) }
% 0.09/0.50 ifeq(ifeq(divide(divide(divide(X, Y), divide(identity, Y)), divide(divide(divide(X, Y), divide(identity, Y)), zero)), zero, ifeq(divide(divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(divide(X, Y), divide(identity, Y)), zero), divide(divide(X, Y), divide(identity, Y))), divide(divide(X, Y), divide(identity, Y))), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 7 (divide_and_equal) }
% 0.09/0.50 ifeq(divide(divide(X, Y), divide(identity, Y)), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.09/0.50 = { by axiom 8 (property_of_divide1) }
% 0.09/0.50 zero
% 0.09/0.50
% 0.09/0.50 Goal 1 (prove_this): divide(identity, a) = divide(identity, divide(identity, divide(identity, a))).
% 0.09/0.50 Proof:
% 0.09/0.50 divide(identity, a)
% 0.09/0.50 = { by axiom 7 (divide_and_equal) R->L }
% 0.09/0.50 ifeq(divide(divide(identity, a), divide(identity, divide(identity, divide(identity, a)))), zero, ifeq(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), zero, divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), divide(identity, a))
% 0.61/0.50 = { by axiom 4 (ifeq_axiom) R->L }
% 0.61/0.50 ifeq(ifeq(zero, zero, divide(divide(identity, a), divide(identity, divide(identity, divide(identity, a)))), zero), zero, ifeq(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), zero, divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), divide(identity, a))
% 0.61/0.50 = { by lemma 9 R->L }
% 0.61/0.50 ifeq(ifeq(divide(divide(identity, divide(identity, a)), a), zero, divide(divide(identity, a), divide(identity, divide(identity, divide(identity, a)))), zero), zero, ifeq(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), zero, divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), divide(identity, a))
% 0.61/0.50 = { by axiom 6 (property_of_divide2) }
% 0.61/0.50 ifeq(zero, zero, ifeq(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), zero, divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), divide(identity, a))
% 0.61/0.50 = { by axiom 4 (ifeq_axiom) }
% 0.61/0.50 ifeq(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), zero, divide(identity, divide(identity, divide(identity, a))), divide(identity, a))
% 0.61/0.50 = { by lemma 9 }
% 0.61/0.50 ifeq(zero, zero, divide(identity, divide(identity, divide(identity, a))), divide(identity, a))
% 0.61/0.50 = { by axiom 4 (ifeq_axiom) }
% 0.61/0.50 divide(identity, divide(identity, divide(identity, a)))
% 0.61/0.50 % SZS output end Proof
% 0.61/0.50
% 0.61/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
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