%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 10:18:59 AM UTC 2026
% Result : Unsatisfiable 3.16s 0.84s
% Output : Proof 3.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 27 10:50:21 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.16/0.84 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.16/0.84
% 3.16/0.84 % SZS status Unsatisfiable
% 3.16/0.84
% 3.16/0.85 % SZS output start Proof
% 3.16/0.85 Axiom 1 (zero_is_smallest): less_equal(zero, X) = true.
% 3.16/0.85 Axiom 2 (aLEb): less_equal(a, b) = true.
% 3.16/0.85 Axiom 3 (aQc): quotient(a, c, aQc) = true.
% 3.16/0.85 Axiom 4 (bQc): quotient(b, c, bQc) = true.
% 3.16/0.85 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 3.16/0.85 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 3.16/0.85 Axiom 7 (closure): quotient(X, Y, divide(X, Y)) = true.
% 3.16/0.85 Axiom 8 (quotient_less_equal): ifeq(less_equal(X, Y), true, quotient(X, Y, zero), true) = true.
% 3.16/0.85 Axiom 9 (less_equal_quotient): ifeq(quotient(X, Y, zero), true, less_equal(X, Y), true) = true.
% 3.16/0.86 Axiom 10 (less_equal_and_equal): ifeq2(less_equal(X, Y), true, ifeq2(less_equal(Y, X), true, Y, X), X) = X.
% 3.16/0.86 Axiom 11 (quotient_property): ifeq(quotient(X, Y, Z), true, ifeq(quotient(W, V, U), true, ifeq(quotient(T, V, Y), true, ifeq(quotient(S, V, X), true, ifeq(quotient(S, T, W), true, less_equal(Z, U), true), true), true), true), true) = true.
% 3.16/0.86
% 3.16/0.86 Goal 1 (prove_aQcLEbQc): less_equal(aQc, bQc) = true.
% 3.16/0.86 Proof:
% 3.16/0.86 less_equal(aQc, bQc)
% 3.16/0.86 = { by axiom 5 (ifeq_axiom) R->L }
% 3.16/0.86 ifeq(true, true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 7 (closure) R->L }
% 3.16/0.86 ifeq(quotient(aQc, bQc, divide(aQc, bQc)), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 10 (less_equal_and_equal) R->L }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(less_equal(divide(aQc, bQc), zero), true, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc)), divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 5 (ifeq_axiom) R->L }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(ifeq(true, true, less_equal(divide(aQc, bQc), zero), true), true, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc)), divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 7 (closure) R->L }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(ifeq(quotient(aQc, bQc, divide(aQc, bQc)), true, less_equal(divide(aQc, bQc), zero), true), true, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc)), divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 5 (ifeq_axiom) R->L }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(ifeq(quotient(aQc, bQc, divide(aQc, bQc)), true, ifeq(true, true, less_equal(divide(aQc, bQc), zero), true), true), true, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc)), divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 4 (bQc) R->L }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(ifeq(quotient(aQc, bQc, divide(aQc, bQc)), true, ifeq(quotient(b, c, bQc), true, less_equal(divide(aQc, bQc), zero), true), true), true, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc)), divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 5 (ifeq_axiom) R->L }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(ifeq(quotient(aQc, bQc, divide(aQc, bQc)), true, ifeq(quotient(b, c, bQc), true, ifeq(true, true, less_equal(divide(aQc, bQc), zero), true), true), true), true, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc)), divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 3 (aQc) R->L }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(ifeq(quotient(aQc, bQc, divide(aQc, bQc)), true, ifeq(quotient(b, c, bQc), true, ifeq(quotient(a, c, aQc), true, less_equal(divide(aQc, bQc), zero), true), true), true), true, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc)), divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 5 (ifeq_axiom) R->L }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(ifeq(quotient(aQc, bQc, divide(aQc, bQc)), true, ifeq(quotient(b, c, bQc), true, ifeq(quotient(a, c, aQc), true, ifeq(true, true, less_equal(divide(aQc, bQc), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc)), divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 8 (quotient_less_equal) R->L }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(ifeq(quotient(aQc, bQc, divide(aQc, bQc)), true, ifeq(quotient(b, c, bQc), true, ifeq(quotient(a, c, aQc), true, ifeq(ifeq(less_equal(a, b), true, quotient(a, b, zero), true), true, less_equal(divide(aQc, bQc), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc)), divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 2 (aLEb) }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(ifeq(quotient(aQc, bQc, divide(aQc, bQc)), true, ifeq(quotient(b, c, bQc), true, ifeq(quotient(a, c, aQc), true, ifeq(ifeq(true, true, quotient(a, b, zero), true), true, less_equal(divide(aQc, bQc), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc)), divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 5 (ifeq_axiom) }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(ifeq(quotient(aQc, bQc, divide(aQc, bQc)), true, ifeq(quotient(b, c, bQc), true, ifeq(quotient(a, c, aQc), true, ifeq(quotient(a, b, zero), true, less_equal(divide(aQc, bQc), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc)), divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 5 (ifeq_axiom) R->L }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(ifeq(quotient(aQc, bQc, divide(aQc, bQc)), true, ifeq(true, true, ifeq(quotient(b, c, bQc), true, ifeq(quotient(a, c, aQc), true, ifeq(quotient(a, b, zero), true, less_equal(divide(aQc, bQc), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc)), divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 8 (quotient_less_equal) R->L }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(ifeq(quotient(aQc, bQc, divide(aQc, bQc)), true, ifeq(ifeq(less_equal(zero, c), true, quotient(zero, c, zero), true), true, ifeq(quotient(b, c, bQc), true, ifeq(quotient(a, c, aQc), true, ifeq(quotient(a, b, zero), true, less_equal(divide(aQc, bQc), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc)), divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 1 (zero_is_smallest) }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(ifeq(quotient(aQc, bQc, divide(aQc, bQc)), true, ifeq(ifeq(true, true, quotient(zero, c, zero), true), true, ifeq(quotient(b, c, bQc), true, ifeq(quotient(a, c, aQc), true, ifeq(quotient(a, b, zero), true, less_equal(divide(aQc, bQc), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc)), divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 5 (ifeq_axiom) }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(ifeq(quotient(aQc, bQc, divide(aQc, bQc)), true, ifeq(quotient(zero, c, zero), true, ifeq(quotient(b, c, bQc), true, ifeq(quotient(a, c, aQc), true, ifeq(quotient(a, b, zero), true, less_equal(divide(aQc, bQc), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc)), divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 11 (quotient_property) }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(true, true, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc)), divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 6 (ifeq_axiom) }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(less_equal(zero, divide(aQc, bQc)), true, zero, divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 1 (zero_is_smallest) }
% 3.16/0.86 ifeq(quotient(aQc, bQc, ifeq2(true, true, zero, divide(aQc, bQc))), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 6 (ifeq_axiom) }
% 3.16/0.86 ifeq(quotient(aQc, bQc, zero), true, less_equal(aQc, bQc), true)
% 3.16/0.86 = { by axiom 9 (less_equal_quotient) }
% 3.16/0.86 true
% 3.16/0.86 % SZS output end Proof
% 3.16/0.86
% 3.16/0.86 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------