%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN007-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 10:18:58 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.48s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN007-3 : 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 : n007.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 10:48:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.48 Command-line arguments: --flatten --complete-subsets
% 0.16/0.48
% 0.16/0.48 % SZS status Unsatisfiable
% 0.16/0.48
% 0.16/0.51 % SZS output start Proof
% 0.16/0.51 Axiom 1 (zero_is_smallest): less_equal(zero, X) = true.
% 0.16/0.51 Axiom 2 (a_LE_b): less_equal(a, b) = true.
% 0.16/0.51 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.16/0.51 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.16/0.51 Axiom 5 (quotient_smaller_than_numerator): less_equal(divide(X, Y), X) = true.
% 0.16/0.51 Axiom 6 (quotient_less_equal2): ifeq2(divide(X, Y), zero, less_equal(X, Y), true) = true.
% 0.16/0.51 Axiom 7 (quotient_less_equal1): ifeq(less_equal(X, Y), true, divide(X, Y), zero) = zero.
% 0.16/0.51 Axiom 8 (less_equal_and_equal): ifeq(less_equal(X, Y), true, ifeq(less_equal(Y, X), true, Y, X), X) = X.
% 0.16/0.51 Axiom 9 (quotient_property): less_equal(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y)) = true.
% 0.16/0.51
% 0.16/0.51 Lemma 10: ifeq(less_equal(X, Y), less_equal(a, b), divide(X, Y), zero) = zero.
% 0.16/0.51 Proof:
% 0.16/0.51 ifeq(less_equal(X, Y), less_equal(a, b), divide(X, Y), zero)
% 0.16/0.51 = { by axiom 2 (a_LE_b) }
% 0.16/0.51 ifeq(less_equal(X, Y), true, divide(X, Y), zero)
% 0.16/0.51 = { by axiom 7 (quotient_less_equal1) }
% 0.16/0.51 zero
% 0.16/0.51
% 0.16/0.51 Lemma 11: divide(zero, X) = zero.
% 0.16/0.51 Proof:
% 0.16/0.51 divide(zero, X)
% 0.16/0.51 = { by axiom 4 (ifeq_axiom) R->L }
% 0.16/0.51 ifeq(less_equal(a, b), less_equal(a, b), divide(zero, X), zero)
% 0.16/0.51 = { by axiom 2 (a_LE_b) }
% 0.16/0.51 ifeq(true, less_equal(a, b), divide(zero, X), zero)
% 0.16/0.51 = { by axiom 1 (zero_is_smallest) R->L }
% 0.16/0.51 ifeq(less_equal(zero, X), less_equal(a, b), divide(zero, X), zero)
% 0.16/0.51 = { by lemma 10 }
% 0.16/0.51 zero
% 0.16/0.51
% 0.16/0.51 Lemma 12: less_equal(divide(X, Y), X) = less_equal(a, b).
% 0.16/0.52 Proof:
% 0.16/0.52 less_equal(divide(X, Y), X)
% 0.16/0.52 = { by axiom 5 (quotient_smaller_than_numerator) }
% 0.16/0.52 true
% 0.16/0.52 = { by axiom 2 (a_LE_b) R->L }
% 0.16/0.52 less_equal(a, b)
% 0.16/0.52
% 0.16/0.52 Lemma 13: ifeq2(divide(X, Y), zero, less_equal(X, Y), less_equal(a, b)) = less_equal(a, b).
% 0.16/0.52 Proof:
% 0.16/0.52 ifeq2(divide(X, Y), zero, less_equal(X, Y), less_equal(a, b))
% 0.16/0.52 = { by axiom 2 (a_LE_b) }
% 0.16/0.52 ifeq2(divide(X, Y), zero, less_equal(X, Y), true)
% 0.16/0.52 = { by axiom 6 (quotient_less_equal2) }
% 0.16/0.52 true
% 0.16/0.52 = { by axiom 2 (a_LE_b) R->L }
% 0.16/0.52 less_equal(a, b)
% 0.16/0.52
% 0.16/0.52 Lemma 14: less_equal(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y)) = less_equal(a, b).
% 0.16/0.52 Proof:
% 0.16/0.52 less_equal(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y))
% 0.16/0.52 = { by axiom 9 (quotient_property) }
% 0.16/0.52 true
% 0.16/0.52 = { by axiom 2 (a_LE_b) R->L }
% 0.16/0.52 less_equal(a, b)
% 0.16/0.52
% 0.16/0.52 Lemma 15: ifeq(less_equal(X, Y), less_equal(a, b), ifeq(less_equal(Y, X), less_equal(a, b), Y, X), X) = X.
% 0.16/0.52 Proof:
% 0.16/0.52 ifeq(less_equal(X, Y), less_equal(a, b), ifeq(less_equal(Y, X), less_equal(a, b), Y, X), X)
% 0.16/0.52 = { by axiom 2 (a_LE_b) }
% 0.16/0.52 ifeq(less_equal(X, Y), true, ifeq(less_equal(Y, X), less_equal(a, b), Y, X), X)
% 0.16/0.52 = { by axiom 2 (a_LE_b) }
% 0.16/0.52 ifeq(less_equal(X, Y), true, ifeq(less_equal(Y, X), true, Y, X), X)
% 0.16/0.52 = { by axiom 8 (less_equal_and_equal) }
% 0.16/0.52 X
% 0.16/0.52
% 0.16/0.52 Goal 1 (prove_c_divide_b_LE_c_divide_a): less_equal(divide(c, b), divide(c, a)) = true.
% 0.16/0.52 Proof:
% 0.16/0.52 less_equal(divide(c, b), divide(c, a))
% 0.16/0.52 = { by lemma 15 R->L }
% 0.16/0.52 less_equal(ifeq(less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.52 = { by axiom 3 (ifeq_axiom) R->L }
% 0.16/0.52 less_equal(ifeq(ifeq2(zero, zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.52 = { by axiom 4 (ifeq_axiom) R->L }
% 0.16/0.52 less_equal(ifeq(ifeq2(ifeq(less_equal(a, b), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.52 = { by axiom 2 (a_LE_b) }
% 0.16/0.52 less_equal(ifeq(ifeq2(ifeq(true, less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.52 = { by axiom 1 (zero_is_smallest) R->L }
% 0.16/0.52 less_equal(ifeq(ifeq2(ifeq(less_equal(zero, divide(divide(c, b), divide(divide(c, a), b))), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.52 = { by axiom 4 (ifeq_axiom) R->L }
% 0.16/0.52 less_equal(ifeq(ifeq2(ifeq(less_equal(a, b), less_equal(a, b), ifeq(less_equal(zero, divide(divide(c, b), divide(divide(c, a), b))), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.52 = { by lemma 13 R->L }
% 0.16/0.52 less_equal(ifeq(ifeq2(ifeq(ifeq2(divide(divide(divide(c, b), divide(divide(c, a), b)), zero), zero, less_equal(divide(divide(c, b), divide(divide(c, a), b)), zero), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(c, b), divide(divide(c, a), b))), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.53 = { by lemma 15 R->L }
% 0.16/0.53 less_equal(ifeq(ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(divide(c, b), divide(divide(c, a), b)), zero), zero), less_equal(a, b), ifeq(less_equal(zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), less_equal(a, b), zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), zero, less_equal(divide(divide(c, b), divide(divide(c, a), b)), zero), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(c, b), divide(divide(c, a), b))), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.53 = { by lemma 11 R->L }
% 0.16/0.53 less_equal(ifeq(ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(divide(c, b), divide(divide(c, a), b)), divide(zero, divide(divide(c, a), b))), zero), less_equal(a, b), ifeq(less_equal(zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), less_equal(a, b), zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), zero, less_equal(divide(divide(c, b), divide(divide(c, a), b)), zero), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(c, b), divide(divide(c, a), b))), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.53 = { by lemma 10 R->L }
% 0.16/0.53 less_equal(ifeq(ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(divide(c, b), divide(divide(c, a), b)), divide(zero, divide(divide(c, a), b))), ifeq(less_equal(divide(divide(c, b), zero), divide(divide(c, a), b)), less_equal(a, b), divide(divide(divide(c, b), zero), divide(divide(c, a), b)), zero)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), less_equal(a, b), zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), zero, less_equal(divide(divide(c, b), divide(divide(c, a), b)), zero), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(c, b), divide(divide(c, a), b))), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.53 = { by lemma 10 R->L }
% 0.16/0.53 less_equal(ifeq(ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(divide(c, b), divide(divide(c, a), b)), divide(zero, divide(divide(c, a), b))), ifeq(less_equal(divide(divide(c, b), ifeq(less_equal(a, b), less_equal(a, b), divide(a, b), zero)), divide(divide(c, a), b)), less_equal(a, b), divide(divide(divide(c, b), zero), divide(divide(c, a), b)), zero)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), less_equal(a, b), zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), zero, less_equal(divide(divide(c, b), divide(divide(c, a), b)), zero), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(c, b), divide(divide(c, a), b))), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.53 = { by axiom 4 (ifeq_axiom) }
% 0.16/0.53 less_equal(ifeq(ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(divide(c, b), divide(divide(c, a), b)), divide(zero, divide(divide(c, a), b))), ifeq(less_equal(divide(divide(c, b), divide(a, b)), divide(divide(c, a), b)), less_equal(a, b), divide(divide(divide(c, b), zero), divide(divide(c, a), b)), zero)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), less_equal(a, b), zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), zero, less_equal(divide(divide(c, b), divide(divide(c, a), b)), zero), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(c, b), divide(divide(c, a), b))), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.53 = { by lemma 14 }
% 0.16/0.53 less_equal(ifeq(ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(divide(c, b), divide(divide(c, a), b)), divide(zero, divide(divide(c, a), b))), ifeq(less_equal(a, b), less_equal(a, b), divide(divide(divide(c, b), zero), divide(divide(c, a), b)), zero)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), less_equal(a, b), zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), zero, less_equal(divide(divide(c, b), divide(divide(c, a), b)), zero), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(c, b), divide(divide(c, a), b))), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.53 = { by axiom 4 (ifeq_axiom) }
% 0.16/0.53 less_equal(ifeq(ifeq2(ifeq(ifeq2(ifeq(less_equal(divide(divide(divide(c, b), divide(divide(c, a), b)), divide(zero, divide(divide(c, a), b))), divide(divide(divide(c, b), zero), divide(divide(c, a), b))), less_equal(a, b), ifeq(less_equal(zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), less_equal(a, b), zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), zero, less_equal(divide(divide(c, b), divide(divide(c, a), b)), zero), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(c, b), divide(divide(c, a), b))), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by lemma 14 }
% 0.16/0.54 less_equal(ifeq(ifeq2(ifeq(ifeq2(ifeq(less_equal(a, b), less_equal(a, b), ifeq(less_equal(zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), less_equal(a, b), zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), zero, less_equal(divide(divide(c, b), divide(divide(c, a), b)), zero), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(c, b), divide(divide(c, a), b))), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by axiom 4 (ifeq_axiom) }
% 0.16/0.54 less_equal(ifeq(ifeq2(ifeq(ifeq2(ifeq(less_equal(zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), less_equal(a, b), zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), zero, less_equal(divide(divide(c, b), divide(divide(c, a), b)), zero), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(c, b), divide(divide(c, a), b))), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by axiom 1 (zero_is_smallest) }
% 0.16/0.54 less_equal(ifeq(ifeq2(ifeq(ifeq2(ifeq(true, less_equal(a, b), zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), zero, less_equal(divide(divide(c, b), divide(divide(c, a), b)), zero), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(c, b), divide(divide(c, a), b))), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by axiom 2 (a_LE_b) R->L }
% 0.16/0.54 less_equal(ifeq(ifeq2(ifeq(ifeq2(ifeq(less_equal(a, b), less_equal(a, b), zero, divide(divide(divide(c, b), divide(divide(c, a), b)), zero)), zero, less_equal(divide(divide(c, b), divide(divide(c, a), b)), zero), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(c, b), divide(divide(c, a), b))), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by axiom 4 (ifeq_axiom) }
% 0.16/0.54 less_equal(ifeq(ifeq2(ifeq(ifeq2(zero, zero, less_equal(divide(divide(c, b), divide(divide(c, a), b)), zero), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(c, b), divide(divide(c, a), b))), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by axiom 3 (ifeq_axiom) }
% 0.16/0.54 less_equal(ifeq(ifeq2(ifeq(less_equal(divide(divide(c, b), divide(divide(c, a), b)), zero), less_equal(a, b), ifeq(less_equal(zero, divide(divide(c, b), divide(divide(c, a), b))), less_equal(a, b), zero, divide(divide(c, b), divide(divide(c, a), b))), divide(divide(c, b), divide(divide(c, a), b))), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by lemma 15 }
% 0.16/0.54 less_equal(ifeq(ifeq2(divide(divide(c, b), divide(divide(c, a), b)), zero, less_equal(divide(c, b), divide(divide(c, a), b)), less_equal(a, b)), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by lemma 13 }
% 0.16/0.54 less_equal(ifeq(less_equal(a, b), less_equal(a, b), ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by axiom 4 (ifeq_axiom) }
% 0.16/0.54 less_equal(ifeq(less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by axiom 3 (ifeq_axiom) R->L }
% 0.16/0.54 less_equal(ifeq(ifeq2(zero, zero, less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by axiom 4 (ifeq_axiom) R->L }
% 0.16/0.54 less_equal(ifeq(ifeq2(ifeq(less_equal(a, b), less_equal(a, b), zero, divide(divide(divide(c, a), b), divide(c, b))), zero, less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by axiom 2 (a_LE_b) }
% 0.16/0.54 less_equal(ifeq(ifeq2(ifeq(true, less_equal(a, b), zero, divide(divide(divide(c, a), b), divide(c, b))), zero, less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by axiom 1 (zero_is_smallest) R->L }
% 0.16/0.54 less_equal(ifeq(ifeq2(ifeq(less_equal(zero, divide(divide(divide(c, a), b), divide(c, b))), less_equal(a, b), zero, divide(divide(divide(c, a), b), divide(c, b))), zero, less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by axiom 4 (ifeq_axiom) R->L }
% 0.16/0.54 less_equal(ifeq(ifeq2(ifeq(less_equal(a, b), less_equal(a, b), ifeq(less_equal(zero, divide(divide(divide(c, a), b), divide(c, b))), less_equal(a, b), zero, divide(divide(divide(c, a), b), divide(c, b))), divide(divide(divide(c, a), b), divide(c, b))), zero, less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by lemma 14 R->L }
% 0.16/0.54 less_equal(ifeq(ifeq2(ifeq(less_equal(divide(divide(divide(c, a), b), divide(c, b)), divide(divide(divide(c, a), c), b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(divide(c, a), b), divide(c, b))), less_equal(a, b), zero, divide(divide(divide(c, a), b), divide(c, b))), divide(divide(divide(c, a), b), divide(c, b))), zero, less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by axiom 4 (ifeq_axiom) R->L }
% 0.16/0.54 less_equal(ifeq(ifeq2(ifeq(less_equal(divide(divide(divide(c, a), b), divide(c, b)), divide(ifeq(less_equal(a, b), less_equal(a, b), divide(divide(c, a), c), zero), b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(divide(c, a), b), divide(c, b))), less_equal(a, b), zero, divide(divide(divide(c, a), b), divide(c, b))), divide(divide(divide(c, a), b), divide(c, b))), zero, less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by lemma 12 R->L }
% 0.16/0.54 less_equal(ifeq(ifeq2(ifeq(less_equal(divide(divide(divide(c, a), b), divide(c, b)), divide(ifeq(less_equal(divide(c, a), c), less_equal(a, b), divide(divide(c, a), c), zero), b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(divide(c, a), b), divide(c, b))), less_equal(a, b), zero, divide(divide(divide(c, a), b), divide(c, b))), divide(divide(divide(c, a), b), divide(c, b))), zero, less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by lemma 10 }
% 0.16/0.54 less_equal(ifeq(ifeq2(ifeq(less_equal(divide(divide(divide(c, a), b), divide(c, b)), divide(zero, b)), less_equal(a, b), ifeq(less_equal(zero, divide(divide(divide(c, a), b), divide(c, b))), less_equal(a, b), zero, divide(divide(divide(c, a), b), divide(c, b))), divide(divide(divide(c, a), b), divide(c, b))), zero, less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, a))
% 0.16/0.54 = { by lemma 11 }
% 0.16/0.55 less_equal(ifeq(ifeq2(ifeq(less_equal(divide(divide(divide(c, a), b), divide(c, b)), zero), less_equal(a, b), ifeq(less_equal(zero, divide(divide(divide(c, a), b), divide(c, b))), less_equal(a, b), zero, divide(divide(divide(c, a), b), divide(c, b))), divide(divide(divide(c, a), b), divide(c, b))), zero, less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, a))
% 0.16/0.55 = { by lemma 15 }
% 0.16/0.55 less_equal(ifeq(ifeq2(divide(divide(divide(c, a), b), divide(c, b)), zero, less_equal(divide(divide(c, a), b), divide(c, b)), less_equal(a, b)), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, a))
% 0.16/0.55 = { by lemma 13 }
% 0.16/0.55 less_equal(ifeq(less_equal(a, b), less_equal(a, b), divide(divide(c, a), b), divide(c, b)), divide(c, a))
% 0.16/0.55 = { by axiom 4 (ifeq_axiom) }
% 0.16/0.55 less_equal(divide(divide(c, a), b), divide(c, a))
% 0.16/0.55 = { by lemma 12 }
% 0.16/0.55 less_equal(a, b)
% 0.16/0.55 = { by axiom 2 (a_LE_b) }
% 0.16/0.55 true
% 0.16/0.55 % SZS output end Proof
% 0.16/0.55
% 0.16/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------