%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN010-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 10:19:01 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.44s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN010-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n015.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 10:54:30 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.44 Command-line arguments: --no-flatten-goal
% 0.12/0.44
% 0.12/0.44 % SZS status Unsatisfiable
% 0.12/0.44
% 0.12/0.45 % SZS output start Proof
% 0.12/0.45 Axiom 1 (zero_is_smallest): less_equal(zero, X) = true.
% 0.12/0.45 Axiom 2 (x_divide_x_is_zero): divide(X, X) = zero.
% 0.12/0.45 Axiom 3 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 0.12/0.45 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.12/0.45 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.12/0.45 Axiom 6 (quotient_smaller_than_numerator): less_equal(divide(X, Y), X) = true.
% 0.12/0.45 Axiom 7 (one_inversion_equals_three): divide(identity, divide(identity, divide(identity, X))) = divide(identity, X).
% 0.12/0.45 Axiom 8 (quotient_less_equal2): ifeq3(divide(X, Y), zero, less_equal(X, Y), true) = true.
% 0.12/0.45 Axiom 9 (less_equal_and_equal): ifeq2(less_equal(X, Y), true, ifeq2(less_equal(Y, X), true, Y, X), X) = X.
% 0.12/0.45 Axiom 10 (property_of_divide3): ifeq(less_equal(X, Y), true, less_equal(divide(X, Z), divide(Y, Z)), true) = true.
% 0.12/0.45 Axiom 11 (property_of_divide1): ifeq(less_equal(divide(X, Y), Z), true, less_equal(divide(X, Z), Y), true) = true.
% 0.12/0.45 Axiom 12 (quotient_property): less_equal(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y)) = true.
% 0.12/0.45
% 0.12/0.45 Goal 1 (prove_property_of_inversion): divide(identity, a) = divide(divide(identity, a), divide(identity, divide(identity, a))).
% 0.12/0.45 Proof:
% 0.12/0.45 divide(identity, a)
% 0.12/0.45 = { by axiom 7 (one_inversion_equals_three) R->L }
% 0.12/0.45 divide(identity, divide(identity, divide(identity, a)))
% 0.12/0.45 = { by axiom 9 (less_equal_and_equal) R->L }
% 0.12/0.46 ifeq2(less_equal(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.46 = { by axiom 9 (less_equal_and_equal) R->L }
% 0.12/0.46 ifeq2(less_equal(ifeq2(less_equal(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.46 = { by axiom 3 (ifeq_axiom) R->L }
% 0.12/0.46 ifeq2(less_equal(ifeq2(ifeq3(zero, zero, less_equal(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), true), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.46 = { by axiom 4 (ifeq_axiom) R->L }
% 0.12/0.46 ifeq2(less_equal(ifeq2(ifeq3(ifeq2(true, true, zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero))), zero, less_equal(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), true), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.46 = { by axiom 11 (property_of_divide1) R->L }
% 0.12/0.46 ifeq2(less_equal(ifeq2(ifeq3(ifeq2(ifeq(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(divide(identity, divide(identity, divide(identity, a))), zero)), true, less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), zero), true), true, zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero))), zero, less_equal(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), true), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.46 = { by axiom 3 (ifeq_axiom) R->L }
% 0.12/0.46 ifeq2(less_equal(ifeq2(ifeq3(ifeq2(ifeq(ifeq3(zero, zero, less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(divide(identity, divide(identity, divide(identity, a))), zero)), true), true, less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), zero), true), true, zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero))), zero, less_equal(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), true), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.46 = { by axiom 2 (x_divide_x_is_zero) R->L }
% 0.12/0.46 ifeq2(less_equal(ifeq2(ifeq3(ifeq2(ifeq(ifeq3(divide(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(divide(identity, divide(identity, divide(identity, a))), zero)), zero, less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(divide(identity, divide(identity, divide(identity, a))), zero)), true), true, less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), zero), true), true, zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero))), zero, less_equal(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), true), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.46 = { by axiom 8 (quotient_less_equal2) }
% 0.12/0.46 ifeq2(less_equal(ifeq2(ifeq3(ifeq2(ifeq(true, true, less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), zero), true), true, zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero))), zero, less_equal(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), true), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.46 = { by axiom 5 (ifeq_axiom) }
% 0.12/0.47 ifeq2(less_equal(ifeq2(ifeq3(ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), zero), true, zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero))), zero, less_equal(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), true), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.47 = { by axiom 4 (ifeq_axiom) R->L }
% 0.12/0.47 ifeq2(less_equal(ifeq2(ifeq3(ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), zero), true, ifeq2(true, true, zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero))), divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero))), zero, less_equal(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), true), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.47 = { by axiom 1 (zero_is_smallest) R->L }
% 0.12/0.47 ifeq2(less_equal(ifeq2(ifeq3(ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), zero), true, ifeq2(less_equal(zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero))), true, zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero))), divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero))), zero, less_equal(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), true), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.47 = { by axiom 9 (less_equal_and_equal) }
% 0.12/0.47 ifeq2(less_equal(ifeq2(ifeq3(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), zero, less_equal(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), zero)), true), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.47 = { by axiom 8 (quotient_less_equal2) }
% 0.12/0.47 ifeq2(less_equal(ifeq2(true, true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.47 = { by axiom 4 (ifeq_axiom) }
% 0.12/0.47 ifeq2(less_equal(ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.47 = { by axiom 6 (quotient_smaller_than_numerator) }
% 0.12/0.47 ifeq2(less_equal(ifeq2(true, true, divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(identity, divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.47 = { by axiom 4 (ifeq_axiom) }
% 0.12/0.47 ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.47 = { by axiom 2 (x_divide_x_is_zero) R->L }
% 0.12/0.47 ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, a)), divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.47 = { by axiom 12 (quotient_property) }
% 0.12/0.47 ifeq2(true, true, ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.47 = { by axiom 4 (ifeq_axiom) }
% 0.12/0.47 ifeq2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.47 = { by axiom 5 (ifeq_axiom) R->L }
% 0.12/0.47 ifeq2(ifeq(true, true, less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.47 = { by axiom 6 (quotient_smaller_than_numerator) R->L }
% 0.12/0.47 ifeq2(ifeq(less_equal(divide(identity, divide(identity, divide(identity, a))), identity), true, less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), true), true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.47 = { by axiom 10 (property_of_divide3) }
% 0.12/0.47 ifeq2(true, true, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a))))
% 0.12/0.47 = { by axiom 4 (ifeq_axiom) }
% 0.12/0.47 divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))
% 0.12/0.47 = { by axiom 7 (one_inversion_equals_three) }
% 0.12/0.47 divide(divide(identity, a), divide(identity, divide(identity, a)))
% 0.12/0.47 % SZS output end Proof
% 0.12/0.47
% 0.12/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
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