%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN011-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 10:19:01 AM UTC 2026
% Result : Unsatisfiable 0.80s 0.56s
% Output : Proof 0.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN011-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.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 10:57:31 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.80/0.56 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
% 0.80/0.56
% 0.80/0.56 % SZS status Unsatisfiable
% 0.80/0.56
% 0.80/0.57 % SZS output start Proof
% 0.80/0.57 Axiom 1 (quotient_smaller_than_numerator): less_equal(divide(X, Y), X) = true.
% 0.80/0.57 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.80/0.57 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.80/0.57 Axiom 4 (one_inversion_equals_three): divide(identity, divide(identity, divide(identity, X))) = divide(identity, X).
% 0.80/0.57 Axiom 5 (quotient_property): less_equal(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y)) = true.
% 0.80/0.57 Axiom 6 (property_of_divide1): ifeq(less_equal(divide(X, Y), Z), true, less_equal(divide(X, Z), Y), true) = true.
% 0.80/0.57 Axiom 7 (less_equal_and_equal): ifeq2(less_equal(X, Y), true, ifeq2(less_equal(Y, X), true, Y, X), X) = X.
% 0.80/0.57 Axiom 8 (transitivity_of_less_equal): ifeq(less_equal(X, Y), true, ifeq(less_equal(Z, X), true, less_equal(Z, Y), true), true) = true.
% 0.80/0.57
% 0.80/0.57 Goal 1 (prove_this): divide(divide(identity, a), divide(identity, divide(identity, b))) = divide(divide(identity, b), divide(identity, divide(identity, a))).
% 0.80/0.57 Proof:
% 0.80/0.57 divide(divide(identity, a), divide(identity, divide(identity, b)))
% 0.80/0.57 = { by axiom 7 (less_equal_and_equal) R->L }
% 0.80/0.57 ifeq2(less_equal(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.57 = { by axiom 2 (ifeq_axiom) R->L }
% 0.80/0.57 ifeq2(ifeq(true, true, less_equal(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true), true, ifeq2(less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.57 = { by axiom 8 (transitivity_of_less_equal) R->L }
% 0.80/0.57 ifeq2(ifeq(ifeq(less_equal(divide(divide(identity, divide(identity, b)), divide(identity, divide(identity, a))), divide(identity, divide(identity, b))), true, ifeq(less_equal(divide(divide(identity, a), divide(divide(identity, b), divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, b)), divide(identity, divide(identity, a)))), true, less_equal(divide(divide(identity, a), divide(divide(identity, b), divide(identity, divide(identity, a)))), divide(identity, divide(identity, b))), true), true), true, less_equal(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true), true, ifeq2(less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.57 = { by axiom 1 (quotient_smaller_than_numerator) }
% 0.80/0.57 ifeq2(ifeq(ifeq(true, true, ifeq(less_equal(divide(divide(identity, a), divide(divide(identity, b), divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, b)), divide(identity, divide(identity, a)))), true, less_equal(divide(divide(identity, a), divide(divide(identity, b), divide(identity, divide(identity, a)))), divide(identity, divide(identity, b))), true), true), true, less_equal(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true), true, ifeq2(less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.57 = { by axiom 2 (ifeq_axiom) }
% 0.80/0.57 ifeq2(ifeq(ifeq(less_equal(divide(divide(identity, a), divide(divide(identity, b), divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, b)), divide(identity, divide(identity, a)))), true, less_equal(divide(divide(identity, a), divide(divide(identity, b), divide(identity, divide(identity, a)))), divide(identity, divide(identity, b))), true), true, less_equal(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true), true, ifeq2(less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.57 = { by axiom 4 (one_inversion_equals_three) R->L }
% 0.80/0.57 ifeq2(ifeq(ifeq(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, b), divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, b)), divide(identity, divide(identity, a)))), true, less_equal(divide(divide(identity, a), divide(divide(identity, b), divide(identity, divide(identity, a)))), divide(identity, divide(identity, b))), true), true, less_equal(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true), true, ifeq2(less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.57 = { by axiom 5 (quotient_property) }
% 0.80/0.57 ifeq2(ifeq(ifeq(true, true, less_equal(divide(divide(identity, a), divide(divide(identity, b), divide(identity, divide(identity, a)))), divide(identity, divide(identity, b))), true), true, less_equal(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true), true, ifeq2(less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.57 = { by axiom 2 (ifeq_axiom) }
% 0.80/0.57 ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(divide(identity, b), divide(identity, divide(identity, a)))), divide(identity, divide(identity, b))), true, less_equal(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true), true, ifeq2(less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.57 = { by axiom 6 (property_of_divide1) }
% 0.80/0.57 ifeq2(true, true, ifeq2(less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.58 = { by axiom 3 (ifeq_axiom) }
% 0.80/0.58 ifeq2(less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.58 = { by axiom 2 (ifeq_axiom) R->L }
% 0.80/0.58 ifeq2(ifeq(true, true, less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.58 = { by axiom 8 (transitivity_of_less_equal) R->L }
% 0.80/0.58 ifeq2(ifeq(ifeq(less_equal(divide(divide(identity, divide(identity, a)), divide(identity, divide(identity, b))), divide(identity, divide(identity, a))), true, ifeq(less_equal(divide(divide(identity, b), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(divide(identity, divide(identity, a)), divide(identity, divide(identity, b)))), true, less_equal(divide(divide(identity, b), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(identity, divide(identity, a))), true), true), true, less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.58 = { by axiom 1 (quotient_smaller_than_numerator) }
% 0.80/0.58 ifeq2(ifeq(ifeq(true, true, ifeq(less_equal(divide(divide(identity, b), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(divide(identity, divide(identity, a)), divide(identity, divide(identity, b)))), true, less_equal(divide(divide(identity, b), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(identity, divide(identity, a))), true), true), true, less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.58 = { by axiom 2 (ifeq_axiom) }
% 0.80/0.58 ifeq2(ifeq(ifeq(less_equal(divide(divide(identity, b), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(divide(identity, divide(identity, a)), divide(identity, divide(identity, b)))), true, less_equal(divide(divide(identity, b), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(identity, divide(identity, a))), true), true, less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.58 = { by axiom 4 (one_inversion_equals_three) R->L }
% 0.80/0.58 ifeq2(ifeq(ifeq(less_equal(divide(divide(identity, divide(identity, divide(identity, b))), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(divide(identity, divide(identity, a)), divide(identity, divide(identity, b)))), true, less_equal(divide(divide(identity, b), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(identity, divide(identity, a))), true), true, less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.58 = { by axiom 5 (quotient_property) }
% 0.80/0.58 ifeq2(ifeq(ifeq(true, true, less_equal(divide(divide(identity, b), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(identity, divide(identity, a))), true), true, less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.58 = { by axiom 2 (ifeq_axiom) }
% 0.80/0.58 ifeq2(ifeq(less_equal(divide(divide(identity, b), divide(divide(identity, a), divide(identity, divide(identity, b)))), divide(identity, divide(identity, a))), true, less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.58 = { by axiom 6 (property_of_divide1) }
% 0.80/0.58 ifeq2(true, true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 0.80/0.58 = { by axiom 3 (ifeq_axiom) }
% 0.80/0.58 divide(divide(identity, b), divide(identity, divide(identity, a)))
% 0.80/0.58 % SZS output end Proof
% 0.80/0.58
% 0.80/0.58 RESULT: Unsatisfiable (the axioms are contradictory).
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