%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN005-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 10:18:57 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.46s
% Output : Proof 0.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN005-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:49:50 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.46 Command-line arguments: --no-flatten-goal
% 0.15/0.46
% 0.15/0.46 % SZS status Unsatisfiable
% 0.15/0.46
% 0.31/0.46 % SZS output start Proof
% 0.31/0.46 Axiom 1 (a_LE_b): less_equal(a, b) = true.
% 0.31/0.46 Axiom 2 (b_LE_c): less_equal(b, c) = true.
% 0.31/0.46 Axiom 3 (zero_is_smallest): less_equal(zero, X) = true.
% 0.31/0.46 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.31/0.46 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.31/0.47 Axiom 6 (quotient_less_equal2): ifeq2(divide(X, Y), zero, less_equal(X, Y), true) = true.
% 0.31/0.47 Axiom 7 (quotient_less_equal1): ifeq(less_equal(X, Y), true, divide(X, Y), zero) = zero.
% 0.31/0.47 Axiom 8 (less_equal_and_equal): ifeq(less_equal(X, Y), true, ifeq(less_equal(Y, X), true, Y, X), X) = X.
% 0.31/0.47 Axiom 9 (quotient_property): less_equal(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y)) = true.
% 0.31/0.47
% 0.31/0.47 Goal 1 (prove_a_LE_c): less_equal(a, c) = true.
% 0.31/0.47 Proof:
% 0.31/0.47 less_equal(a, c)
% 0.31/0.47 = { by axiom 4 (ifeq_axiom) R->L }
% 0.31/0.47 ifeq2(zero, zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 5 (ifeq_axiom) R->L }
% 0.31/0.47 ifeq2(ifeq(true, true, zero, divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 3 (zero_is_smallest) R->L }
% 0.31/0.47 ifeq2(ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 5 (ifeq_axiom) R->L }
% 0.31/0.47 ifeq2(ifeq(true, true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 6 (quotient_less_equal2) R->L }
% 0.31/0.47 ifeq2(ifeq(ifeq2(divide(divide(a, c), zero), zero, less_equal(divide(a, c), zero), true), true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 7 (quotient_less_equal1) R->L }
% 0.31/0.47 ifeq2(ifeq(ifeq2(divide(divide(a, c), ifeq(less_equal(b, c), true, divide(b, c), zero)), zero, less_equal(divide(a, c), zero), true), true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 2 (b_LE_c) }
% 0.31/0.47 ifeq2(ifeq(ifeq2(divide(divide(a, c), ifeq(true, true, divide(b, c), zero)), zero, less_equal(divide(a, c), zero), true), true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 5 (ifeq_axiom) }
% 0.31/0.47 ifeq2(ifeq(ifeq2(divide(divide(a, c), divide(b, c)), zero, less_equal(divide(a, c), zero), true), true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 8 (less_equal_and_equal) R->L }
% 0.31/0.47 ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(a, c), divide(b, c)), zero), true, ifeq(less_equal(zero, divide(divide(a, c), divide(b, c))), true, zero, divide(divide(a, c), divide(b, c))), divide(divide(a, c), divide(b, c))), zero, less_equal(divide(a, c), zero), true), true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 7 (quotient_less_equal1) R->L }
% 0.31/0.47 ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(a, c), divide(b, c)), ifeq(less_equal(zero, c), true, divide(zero, c), zero)), true, ifeq(less_equal(zero, divide(divide(a, c), divide(b, c))), true, zero, divide(divide(a, c), divide(b, c))), divide(divide(a, c), divide(b, c))), zero, less_equal(divide(a, c), zero), true), true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 3 (zero_is_smallest) }
% 0.31/0.47 ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(a, c), divide(b, c)), ifeq(true, true, divide(zero, c), zero)), true, ifeq(less_equal(zero, divide(divide(a, c), divide(b, c))), true, zero, divide(divide(a, c), divide(b, c))), divide(divide(a, c), divide(b, c))), zero, less_equal(divide(a, c), zero), true), true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 5 (ifeq_axiom) }
% 0.31/0.47 ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(a, c), divide(b, c)), divide(zero, c)), true, ifeq(less_equal(zero, divide(divide(a, c), divide(b, c))), true, zero, divide(divide(a, c), divide(b, c))), divide(divide(a, c), divide(b, c))), zero, less_equal(divide(a, c), zero), true), true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 7 (quotient_less_equal1) R->L }
% 0.31/0.47 ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(a, c), divide(b, c)), divide(ifeq(less_equal(a, b), true, divide(a, b), zero), c)), true, ifeq(less_equal(zero, divide(divide(a, c), divide(b, c))), true, zero, divide(divide(a, c), divide(b, c))), divide(divide(a, c), divide(b, c))), zero, less_equal(divide(a, c), zero), true), true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 1 (a_LE_b) }
% 0.31/0.47 ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(a, c), divide(b, c)), divide(ifeq(true, true, divide(a, b), zero), c)), true, ifeq(less_equal(zero, divide(divide(a, c), divide(b, c))), true, zero, divide(divide(a, c), divide(b, c))), divide(divide(a, c), divide(b, c))), zero, less_equal(divide(a, c), zero), true), true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 5 (ifeq_axiom) }
% 0.31/0.47 ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(a, c), divide(b, c)), divide(divide(a, b), c)), true, ifeq(less_equal(zero, divide(divide(a, c), divide(b, c))), true, zero, divide(divide(a, c), divide(b, c))), divide(divide(a, c), divide(b, c))), zero, less_equal(divide(a, c), zero), true), true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 9 (quotient_property) }
% 0.31/0.47 ifeq2(ifeq(ifeq2(ifeq(true, true, ifeq(less_equal(zero, divide(divide(a, c), divide(b, c))), true, zero, divide(divide(a, c), divide(b, c))), divide(divide(a, c), divide(b, c))), zero, less_equal(divide(a, c), zero), true), true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 5 (ifeq_axiom) }
% 0.31/0.47 ifeq2(ifeq(ifeq2(ifeq(less_equal(zero, divide(divide(a, c), divide(b, c))), true, zero, divide(divide(a, c), divide(b, c))), zero, less_equal(divide(a, c), zero), true), true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 3 (zero_is_smallest) }
% 0.31/0.47 ifeq2(ifeq(ifeq2(ifeq(true, true, zero, divide(divide(a, c), divide(b, c))), zero, less_equal(divide(a, c), zero), true), true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.47 = { by axiom 5 (ifeq_axiom) }
% 0.31/0.48 ifeq2(ifeq(ifeq2(zero, zero, less_equal(divide(a, c), zero), true), true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.48 = { by axiom 4 (ifeq_axiom) }
% 0.31/0.48 ifeq2(ifeq(less_equal(divide(a, c), zero), true, ifeq(less_equal(zero, divide(a, c)), true, zero, divide(a, c)), divide(a, c)), zero, less_equal(a, c), true)
% 0.31/0.48 = { by axiom 8 (less_equal_and_equal) }
% 0.31/0.48 ifeq2(divide(a, c), zero, less_equal(a, c), true)
% 0.31/0.48 = { by axiom 6 (quotient_less_equal2) }
% 0.31/0.48 true
% 0.31/0.48 % SZS output end Proof
% 0.31/0.48
% 0.31/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------