%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN009-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 0.13s 0.48s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN009-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 10:53:23 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.48 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.13/0.48
% 0.13/0.48 % SZS status Unsatisfiable
% 0.13/0.48
% 0.13/0.48 % SZS output start Proof
% 0.13/0.48 Axiom 1 (identity_is_largest): less_equal(X, identity) = true.
% 0.13/0.48 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.13/0.48 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.13/0.48 Axiom 4 (property_of_divide3): ifeq(less_equal(X, Y), true, less_equal(divide(X, Z), divide(Y, Z)), true) = true.
% 0.13/0.48 Axiom 5 (property_of_divide2): ifeq(less_equal(X, Y), true, less_equal(divide(Z, Y), divide(Z, X)), true) = true.
% 0.13/0.48 Axiom 6 (property_of_divide1): ifeq(less_equal(divide(X, Y), Z), true, less_equal(divide(X, Z), Y), true) = true.
% 0.13/0.48 Axiom 7 (less_equal_and_equal): ifeq2(less_equal(X, Y), true, ifeq2(less_equal(Y, X), true, Y, X), X) = X.
% 0.13/0.48
% 0.13/0.48 Goal 1 (prove_this): divide(identity, a) = divide(identity, divide(identity, divide(identity, a))).
% 0.13/0.48 Proof:
% 0.13/0.48 divide(identity, a)
% 0.13/0.48 = { by axiom 7 (less_equal_and_equal) R->L }
% 0.13/0.48 ifeq2(less_equal(divide(identity, a), divide(identity, divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), true, divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), divide(identity, a))
% 0.13/0.48 = { by axiom 2 (ifeq_axiom) R->L }
% 0.13/0.48 ifeq2(ifeq(true, true, less_equal(divide(identity, a), divide(identity, divide(identity, divide(identity, a)))), true), true, ifeq2(less_equal(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), true, divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), divide(identity, a))
% 0.13/0.48 = { by axiom 6 (property_of_divide1) R->L }
% 0.13/0.48 ifeq2(ifeq(ifeq(less_equal(divide(identity, a), divide(identity, a)), true, less_equal(divide(identity, divide(identity, a)), a), true), true, less_equal(divide(identity, a), divide(identity, divide(identity, divide(identity, a)))), true), true, ifeq2(less_equal(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), true, divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), divide(identity, a))
% 0.13/0.48 = { by axiom 2 (ifeq_axiom) R->L }
% 0.13/0.48 ifeq2(ifeq(ifeq(ifeq(true, true, less_equal(divide(identity, a), divide(identity, a)), true), true, less_equal(divide(identity, divide(identity, a)), a), true), true, less_equal(divide(identity, a), divide(identity, divide(identity, divide(identity, a)))), true), true, ifeq2(less_equal(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), true, divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), divide(identity, a))
% 0.13/0.48 = { by axiom 1 (identity_is_largest) R->L }
% 0.13/0.48 ifeq2(ifeq(ifeq(ifeq(less_equal(identity, identity), true, less_equal(divide(identity, a), divide(identity, a)), true), true, less_equal(divide(identity, divide(identity, a)), a), true), true, less_equal(divide(identity, a), divide(identity, divide(identity, divide(identity, a)))), true), true, ifeq2(less_equal(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), true, divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), divide(identity, a))
% 0.13/0.48 = { by axiom 4 (property_of_divide3) }
% 0.13/0.48 ifeq2(ifeq(ifeq(true, true, less_equal(divide(identity, divide(identity, a)), a), true), true, less_equal(divide(identity, a), divide(identity, divide(identity, divide(identity, a)))), true), true, ifeq2(less_equal(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), true, divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), divide(identity, a))
% 0.13/0.48 = { by axiom 2 (ifeq_axiom) }
% 0.13/0.48 ifeq2(ifeq(less_equal(divide(identity, divide(identity, a)), a), true, less_equal(divide(identity, a), divide(identity, divide(identity, divide(identity, a)))), true), true, ifeq2(less_equal(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), true, divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), divide(identity, a))
% 0.13/0.48 = { by axiom 5 (property_of_divide2) }
% 0.13/0.48 ifeq2(true, true, ifeq2(less_equal(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), true, divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), divide(identity, a))
% 0.13/0.48 = { by axiom 3 (ifeq_axiom) }
% 0.13/0.48 ifeq2(less_equal(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), true, divide(identity, divide(identity, divide(identity, a))), divide(identity, a))
% 0.13/0.48 = { by axiom 2 (ifeq_axiom) R->L }
% 0.13/0.48 ifeq2(ifeq(true, true, less_equal(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), true), true, divide(identity, divide(identity, divide(identity, a))), divide(identity, a))
% 0.13/0.48 = { by axiom 4 (property_of_divide3) R->L }
% 0.13/0.48 ifeq2(ifeq(ifeq(less_equal(identity, identity), true, less_equal(divide(identity, divide(identity, a)), divide(identity, divide(identity, a))), true), true, less_equal(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), true), true, divide(identity, divide(identity, divide(identity, a))), divide(identity, a))
% 0.13/0.48 = { by axiom 1 (identity_is_largest) }
% 0.13/0.48 ifeq2(ifeq(ifeq(true, true, less_equal(divide(identity, divide(identity, a)), divide(identity, divide(identity, a))), true), true, less_equal(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), true), true, divide(identity, divide(identity, divide(identity, a))), divide(identity, a))
% 0.13/0.48 = { by axiom 2 (ifeq_axiom) }
% 0.13/0.48 ifeq2(ifeq(less_equal(divide(identity, divide(identity, a)), divide(identity, divide(identity, a))), true, less_equal(divide(identity, divide(identity, divide(identity, a))), divide(identity, a)), true), true, divide(identity, divide(identity, divide(identity, a))), divide(identity, a))
% 0.13/0.48 = { by axiom 6 (property_of_divide1) }
% 0.13/0.48 ifeq2(true, true, divide(identity, divide(identity, divide(identity, a))), divide(identity, a))
% 0.13/0.48 = { by axiom 3 (ifeq_axiom) }
% 0.13/0.48 divide(identity, divide(identity, divide(identity, a)))
% 0.13/0.48 % SZS output end Proof
% 0.13/0.48
% 0.13/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
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