%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN012-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 10:19:02 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.35s
% Output : Proof 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : HEN012-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 27 10:51:05 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 Command-line arguments: --no-flatten-goal
% 0.07/0.35
% 0.07/0.35 % SZS status Unsatisfiable
% 0.07/0.35
% 0.07/0.36 % SZS output start Proof
% 0.07/0.36 Axiom 1 (zero_is_smallest): less_equal(zero, X) = true.
% 0.07/0.36 Axiom 2 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.07/0.36 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.07/0.36 Axiom 4 (quotient_smaller_than_numerator): less_equal(divide(X, Y), X) = true.
% 0.07/0.36 Axiom 5 (quotient_less_equal2): ifeq2(divide(X, Y), zero, less_equal(X, Y), true) = true.
% 0.07/0.36 Axiom 6 (quotient_less_equal1): ifeq(less_equal(X, Y), true, divide(X, Y), zero) = zero.
% 0.07/0.36 Axiom 7 (less_equal_and_equal): ifeq(less_equal(X, Y), true, ifeq(less_equal(Y, X), true, Y, X), X) = X.
% 0.07/0.36 Axiom 8 (quotient_property): less_equal(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y)) = true.
% 0.07/0.36
% 0.07/0.36 Goal 1 (prove_a_LE_a): less_equal(a, a) = true.
% 0.07/0.36 Proof:
% 0.07/0.36 less_equal(a, a)
% 0.07/0.36 = { by axiom 2 (ifeq_axiom) R->L }
% 0.07/0.36 ifeq2(zero, zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 3 (ifeq_axiom) R->L }
% 0.07/0.36 ifeq2(ifeq(true, true, zero, divide(a, a)), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 1 (zero_is_smallest) R->L }
% 0.07/0.36 ifeq2(ifeq(less_equal(zero, divide(a, a)), true, zero, divide(a, a)), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 3 (ifeq_axiom) R->L }
% 0.07/0.36 ifeq2(ifeq(true, true, ifeq(less_equal(zero, divide(a, a)), true, zero, divide(a, a)), divide(a, a)), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 5 (quotient_less_equal2) R->L }
% 0.07/0.36 ifeq2(ifeq(ifeq2(divide(divide(a, a), zero), zero, less_equal(divide(a, a), zero), true), true, ifeq(less_equal(zero, divide(a, a)), true, zero, divide(a, a)), divide(a, a)), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 6 (quotient_less_equal1) R->L }
% 0.07/0.36 ifeq2(ifeq(ifeq2(divide(divide(a, a), ifeq(less_equal(zero, a), true, divide(zero, a), zero)), zero, less_equal(divide(a, a), zero), true), true, ifeq(less_equal(zero, divide(a, a)), true, zero, divide(a, a)), divide(a, a)), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 1 (zero_is_smallest) }
% 0.07/0.36 ifeq2(ifeq(ifeq2(divide(divide(a, a), ifeq(true, true, divide(zero, a), zero)), zero, less_equal(divide(a, a), zero), true), true, ifeq(less_equal(zero, divide(a, a)), true, zero, divide(a, a)), divide(a, a)), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 3 (ifeq_axiom) }
% 0.07/0.36 ifeq2(ifeq(ifeq2(divide(divide(a, a), divide(zero, a)), zero, less_equal(divide(a, a), zero), true), true, ifeq(less_equal(zero, divide(a, a)), true, zero, divide(a, a)), divide(a, a)), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 7 (less_equal_and_equal) R->L }
% 0.07/0.36 ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(a, a), divide(zero, a)), zero), true, ifeq(less_equal(zero, divide(divide(a, a), divide(zero, a))), true, zero, divide(divide(a, a), divide(zero, a))), divide(divide(a, a), divide(zero, a))), zero, less_equal(divide(a, a), zero), true), true, ifeq(less_equal(zero, divide(a, a)), true, zero, divide(a, a)), divide(a, a)), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 6 (quotient_less_equal1) R->L }
% 0.07/0.36 ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(a, a), divide(zero, a)), ifeq(less_equal(divide(a, zero), a), true, divide(divide(a, zero), a), zero)), true, ifeq(less_equal(zero, divide(divide(a, a), divide(zero, a))), true, zero, divide(divide(a, a), divide(zero, a))), divide(divide(a, a), divide(zero, a))), zero, less_equal(divide(a, a), zero), true), true, ifeq(less_equal(zero, divide(a, a)), true, zero, divide(a, a)), divide(a, a)), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 4 (quotient_smaller_than_numerator) }
% 0.07/0.36 ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(a, a), divide(zero, a)), ifeq(true, true, divide(divide(a, zero), a), zero)), true, ifeq(less_equal(zero, divide(divide(a, a), divide(zero, a))), true, zero, divide(divide(a, a), divide(zero, a))), divide(divide(a, a), divide(zero, a))), zero, less_equal(divide(a, a), zero), true), true, ifeq(less_equal(zero, divide(a, a)), true, zero, divide(a, a)), divide(a, a)), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 3 (ifeq_axiom) }
% 0.07/0.36 ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(a, a), divide(zero, a)), divide(divide(a, zero), a)), true, ifeq(less_equal(zero, divide(divide(a, a), divide(zero, a))), true, zero, divide(divide(a, a), divide(zero, a))), divide(divide(a, a), divide(zero, a))), zero, less_equal(divide(a, a), zero), true), true, ifeq(less_equal(zero, divide(a, a)), true, zero, divide(a, a)), divide(a, a)), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 8 (quotient_property) }
% 0.07/0.36 ifeq2(ifeq(ifeq2(ifeq(true, true, ifeq(less_equal(zero, divide(divide(a, a), divide(zero, a))), true, zero, divide(divide(a, a), divide(zero, a))), divide(divide(a, a), divide(zero, a))), zero, less_equal(divide(a, a), zero), true), true, ifeq(less_equal(zero, divide(a, a)), true, zero, divide(a, a)), divide(a, a)), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 3 (ifeq_axiom) }
% 0.07/0.36 ifeq2(ifeq(ifeq2(ifeq(less_equal(zero, divide(divide(a, a), divide(zero, a))), true, zero, divide(divide(a, a), divide(zero, a))), zero, less_equal(divide(a, a), zero), true), true, ifeq(less_equal(zero, divide(a, a)), true, zero, divide(a, a)), divide(a, a)), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 1 (zero_is_smallest) }
% 0.07/0.36 ifeq2(ifeq(ifeq2(ifeq(true, true, zero, divide(divide(a, a), divide(zero, a))), zero, less_equal(divide(a, a), zero), true), true, ifeq(less_equal(zero, divide(a, a)), true, zero, divide(a, a)), divide(a, a)), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 3 (ifeq_axiom) }
% 0.07/0.36 ifeq2(ifeq(ifeq2(zero, zero, less_equal(divide(a, a), zero), true), true, ifeq(less_equal(zero, divide(a, a)), true, zero, divide(a, a)), divide(a, a)), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 2 (ifeq_axiom) }
% 0.07/0.36 ifeq2(ifeq(less_equal(divide(a, a), zero), true, ifeq(less_equal(zero, divide(a, a)), true, zero, divide(a, a)), divide(a, a)), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 7 (less_equal_and_equal) }
% 0.07/0.36 ifeq2(divide(a, a), zero, less_equal(a, a), true)
% 0.07/0.36 = { by axiom 5 (quotient_less_equal2) }
% 0.07/0.36 true
% 0.07/0.36 % SZS output end Proof
% 0.07/0.36
% 0.07/0.36 RESULT: Unsatisfiable (the axioms are contradictory).
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