%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN009-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 10:19:00 AM UTC 2026
% Result : Unsatisfiable 0.80s 0.58s
% Output : Proof 1.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.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 10:50:59 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.80/0.58 Command-line arguments: --no-flatten-goal
% 0.80/0.58
% 0.80/0.58 % SZS status Unsatisfiable
% 0.80/0.58
% 0.80/0.66 % SZS output start Proof
% 0.80/0.66 Axiom 1 (identity_is_largest): less_equal(X, identity) = true.
% 0.80/0.66 Axiom 2 (zero_is_smallest): less_equal(zero, X) = true.
% 0.80/0.66 Axiom 3 (x_divide_x_is_zero): divide(X, X) = zero.
% 0.80/0.66 Axiom 4 (id_divide_c_is_d): divide(identity, c) = d.
% 0.80/0.66 Axiom 5 (id_divide_a_is_b): divide(identity, a) = b.
% 0.80/0.66 Axiom 6 (id_divide_b_is_c): divide(identity, b) = c.
% 0.80/0.66 Axiom 7 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 0.80/0.66 Axiom 8 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.80/0.66 Axiom 9 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.80/0.66 Axiom 10 (quotient_smaller_than_numerator): less_equal(divide(X, Y), X) = true.
% 0.80/0.66 Axiom 11 (quotient_less_equal2): ifeq3(divide(X, Y), zero, less_equal(X, Y), true) = true.
% 0.80/0.66 Axiom 12 (quotient_less_equal1): ifeq2(less_equal(X, Y), true, divide(X, Y), zero) = zero.
% 0.80/0.66 Axiom 13 (property_of_divide3): ifeq(less_equal(X, Y), true, less_equal(divide(X, Z), divide(Y, Z)), true) = true.
% 0.80/0.66 Axiom 14 (property_of_divide1): ifeq(less_equal(divide(X, Y), Z), true, less_equal(divide(X, Z), Y), true) = true.
% 0.80/0.66 Axiom 15 (less_equal_and_equal): ifeq2(less_equal(X, Y), true, ifeq2(less_equal(Y, X), true, Y, X), X) = X.
% 0.80/0.66
% 0.80/0.66 Lemma 16: b = d.
% 0.80/0.66 Proof:
% 0.80/0.66 b
% 0.80/0.66 = { by axiom 15 (less_equal_and_equal) R->L }
% 0.80/0.66 ifeq2(less_equal(b, d), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.66 = { by axiom 5 (id_divide_a_is_b) R->L }
% 0.80/0.66 ifeq2(less_equal(divide(identity, a), d), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.66 = { by axiom 8 (ifeq_axiom) R->L }
% 0.80/0.66 ifeq2(ifeq(true, true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.66 = { by axiom 14 (property_of_divide1) R->L }
% 0.80/0.66 ifeq2(ifeq(ifeq(less_equal(divide(divide(identity, d), a), zero), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.66 = { by axiom 12 (quotient_less_equal1) R->L }
% 0.80/0.66 ifeq2(ifeq(ifeq(less_equal(divide(divide(identity, d), a), ifeq2(less_equal(c, a), true, divide(c, a), zero)), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.66 = { by axiom 6 (id_divide_b_is_c) R->L }
% 0.80/0.67 ifeq2(ifeq(ifeq(less_equal(divide(divide(identity, d), a), ifeq2(less_equal(divide(identity, b), a), true, divide(c, a), zero)), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.67 = { by axiom 8 (ifeq_axiom) R->L }
% 0.80/0.67 ifeq2(ifeq(ifeq(less_equal(divide(divide(identity, d), a), ifeq2(ifeq(true, true, less_equal(divide(identity, b), a), true), true, divide(c, a), zero)), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.67 = { by axiom 13 (property_of_divide3) R->L }
% 0.80/0.67 ifeq2(ifeq(ifeq(less_equal(divide(divide(identity, d), a), ifeq2(ifeq(ifeq(less_equal(identity, identity), true, less_equal(divide(identity, a), divide(identity, a)), true), true, less_equal(divide(identity, b), a), true), true, divide(c, a), zero)), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.67 = { by axiom 5 (id_divide_a_is_b) }
% 0.80/0.67 ifeq2(ifeq(ifeq(less_equal(divide(divide(identity, d), a), ifeq2(ifeq(ifeq(less_equal(identity, identity), true, less_equal(divide(identity, a), b), true), true, less_equal(divide(identity, b), a), true), true, divide(c, a), zero)), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.67 = { by axiom 1 (identity_is_largest) }
% 0.80/0.67 ifeq2(ifeq(ifeq(less_equal(divide(divide(identity, d), a), ifeq2(ifeq(ifeq(true, true, less_equal(divide(identity, a), b), true), true, less_equal(divide(identity, b), a), true), true, divide(c, a), zero)), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.67 = { by axiom 8 (ifeq_axiom) }
% 0.80/0.67 ifeq2(ifeq(ifeq(less_equal(divide(divide(identity, d), a), ifeq2(ifeq(less_equal(divide(identity, a), b), true, less_equal(divide(identity, b), a), true), true, divide(c, a), zero)), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.67 = { by axiom 14 (property_of_divide1) }
% 0.80/0.67 ifeq2(ifeq(ifeq(less_equal(divide(divide(identity, d), a), ifeq2(true, true, divide(c, a), zero)), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.67 = { by axiom 9 (ifeq_axiom) }
% 0.80/0.67 ifeq2(ifeq(ifeq(less_equal(divide(divide(identity, d), a), divide(c, a)), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.67 = { by axiom 8 (ifeq_axiom) R->L }
% 0.80/0.67 ifeq2(ifeq(ifeq(ifeq(true, true, less_equal(divide(divide(identity, d), a), divide(c, a)), true), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.67 = { by axiom 14 (property_of_divide1) R->L }
% 0.80/0.67 ifeq2(ifeq(ifeq(ifeq(ifeq(less_equal(divide(identity, c), d), true, less_equal(divide(identity, d), c), true), true, less_equal(divide(divide(identity, d), a), divide(c, a)), true), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.67 = { by axiom 8 (ifeq_axiom) R->L }
% 0.80/0.67 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, less_equal(divide(identity, c), d), true), true, less_equal(divide(identity, d), c), true), true, less_equal(divide(divide(identity, d), a), divide(c, a)), true), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.67 = { by axiom 1 (identity_is_largest) R->L }
% 0.80/0.67 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(less_equal(identity, identity), true, less_equal(divide(identity, c), d), true), true, less_equal(divide(identity, d), c), true), true, less_equal(divide(divide(identity, d), a), divide(c, a)), true), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.67 = { by axiom 4 (id_divide_c_is_d) R->L }
% 0.80/0.67 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(less_equal(identity, identity), true, less_equal(divide(identity, c), divide(identity, c)), true), true, less_equal(divide(identity, d), c), true), true, less_equal(divide(divide(identity, d), a), divide(c, a)), true), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.67 = { by axiom 13 (property_of_divide3) }
% 0.80/0.67 ifeq2(ifeq(ifeq(ifeq(ifeq(true, true, less_equal(divide(identity, d), c), true), true, less_equal(divide(divide(identity, d), a), divide(c, a)), true), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.67 = { by axiom 8 (ifeq_axiom) }
% 0.80/0.67 ifeq2(ifeq(ifeq(ifeq(less_equal(divide(identity, d), c), true, less_equal(divide(divide(identity, d), a), divide(c, a)), true), true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.68 = { by axiom 13 (property_of_divide3) }
% 0.80/0.68 ifeq2(ifeq(ifeq(true, true, less_equal(divide(divide(identity, d), zero), a), true), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.68 = { by axiom 8 (ifeq_axiom) }
% 0.80/0.68 ifeq2(ifeq(less_equal(divide(divide(identity, d), zero), a), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.68 = { by axiom 9 (ifeq_axiom) R->L }
% 0.80/0.68 ifeq2(ifeq(less_equal(ifeq2(true, true, divide(divide(identity, d), zero), divide(identity, d)), a), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.68 = { by axiom 10 (quotient_smaller_than_numerator) R->L }
% 0.80/0.68 ifeq2(ifeq(less_equal(ifeq2(less_equal(divide(divide(identity, d), zero), divide(identity, d)), true, divide(divide(identity, d), zero), divide(identity, d)), a), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.68 = { by axiom 9 (ifeq_axiom) R->L }
% 0.80/0.68 ifeq2(ifeq(less_equal(ifeq2(true, true, ifeq2(less_equal(divide(divide(identity, d), zero), divide(identity, d)), true, divide(divide(identity, d), zero), divide(identity, d)), divide(identity, d)), a), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.68 = { by axiom 11 (quotient_less_equal2) R->L }
% 0.80/0.68 ifeq2(ifeq(less_equal(ifeq2(ifeq3(divide(divide(identity, d), divide(divide(identity, d), zero)), zero, less_equal(divide(identity, d), divide(divide(identity, d), zero)), true), true, ifeq2(less_equal(divide(divide(identity, d), zero), divide(identity, d)), true, divide(divide(identity, d), zero), divide(identity, d)), divide(identity, d)), a), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.68 = { by axiom 15 (less_equal_and_equal) R->L }
% 0.80/0.68 ifeq2(ifeq(less_equal(ifeq2(ifeq3(ifeq2(less_equal(divide(divide(identity, d), divide(divide(identity, d), zero)), zero), true, ifeq2(less_equal(zero, divide(divide(identity, d), divide(divide(identity, d), zero))), true, zero, divide(divide(identity, d), divide(divide(identity, d), zero))), divide(divide(identity, d), divide(divide(identity, d), zero))), zero, less_equal(divide(identity, d), divide(divide(identity, d), zero)), true), true, ifeq2(less_equal(divide(divide(identity, d), zero), divide(identity, d)), true, divide(divide(identity, d), zero), divide(identity, d)), divide(identity, d)), a), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.68 = { by axiom 2 (zero_is_smallest) }
% 0.80/0.68 ifeq2(ifeq(less_equal(ifeq2(ifeq3(ifeq2(less_equal(divide(divide(identity, d), divide(divide(identity, d), zero)), zero), true, ifeq2(true, true, zero, divide(divide(identity, d), divide(divide(identity, d), zero))), divide(divide(identity, d), divide(divide(identity, d), zero))), zero, less_equal(divide(identity, d), divide(divide(identity, d), zero)), true), true, ifeq2(less_equal(divide(divide(identity, d), zero), divide(identity, d)), true, divide(divide(identity, d), zero), divide(identity, d)), divide(identity, d)), a), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 0.80/0.68 = { by axiom 9 (ifeq_axiom) }
% 1.68/0.68 ifeq2(ifeq(less_equal(ifeq2(ifeq3(ifeq2(less_equal(divide(divide(identity, d), divide(divide(identity, d), zero)), zero), true, zero, divide(divide(identity, d), divide(divide(identity, d), zero))), zero, less_equal(divide(identity, d), divide(divide(identity, d), zero)), true), true, ifeq2(less_equal(divide(divide(identity, d), zero), divide(identity, d)), true, divide(divide(identity, d), zero), divide(identity, d)), divide(identity, d)), a), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 1.68/0.68 = { by axiom 8 (ifeq_axiom) R->L }
% 1.68/0.68 ifeq2(ifeq(less_equal(ifeq2(ifeq3(ifeq2(ifeq(true, true, less_equal(divide(divide(identity, d), divide(divide(identity, d), zero)), zero), true), true, zero, divide(divide(identity, d), divide(divide(identity, d), zero))), zero, less_equal(divide(identity, d), divide(divide(identity, d), zero)), true), true, ifeq2(less_equal(divide(divide(identity, d), zero), divide(identity, d)), true, divide(divide(identity, d), zero), divide(identity, d)), divide(identity, d)), a), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 1.68/0.68 = { by axiom 11 (quotient_less_equal2) R->L }
% 1.68/0.69 ifeq2(ifeq(less_equal(ifeq2(ifeq3(ifeq2(ifeq(ifeq3(divide(divide(divide(identity, d), zero), divide(divide(identity, d), zero)), zero, less_equal(divide(divide(identity, d), zero), divide(divide(identity, d), zero)), true), true, less_equal(divide(divide(identity, d), divide(divide(identity, d), zero)), zero), true), true, zero, divide(divide(identity, d), divide(divide(identity, d), zero))), zero, less_equal(divide(identity, d), divide(divide(identity, d), zero)), true), true, ifeq2(less_equal(divide(divide(identity, d), zero), divide(identity, d)), true, divide(divide(identity, d), zero), divide(identity, d)), divide(identity, d)), a), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 1.68/0.69 = { by axiom 3 (x_divide_x_is_zero) }
% 1.68/0.69 ifeq2(ifeq(less_equal(ifeq2(ifeq3(ifeq2(ifeq(ifeq3(zero, zero, less_equal(divide(divide(identity, d), zero), divide(divide(identity, d), zero)), true), true, less_equal(divide(divide(identity, d), divide(divide(identity, d), zero)), zero), true), true, zero, divide(divide(identity, d), divide(divide(identity, d), zero))), zero, less_equal(divide(identity, d), divide(divide(identity, d), zero)), true), true, ifeq2(less_equal(divide(divide(identity, d), zero), divide(identity, d)), true, divide(divide(identity, d), zero), divide(identity, d)), divide(identity, d)), a), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 1.68/0.69 = { by axiom 7 (ifeq_axiom) }
% 1.68/0.69 ifeq2(ifeq(less_equal(ifeq2(ifeq3(ifeq2(ifeq(less_equal(divide(divide(identity, d), zero), divide(divide(identity, d), zero)), true, less_equal(divide(divide(identity, d), divide(divide(identity, d), zero)), zero), true), true, zero, divide(divide(identity, d), divide(divide(identity, d), zero))), zero, less_equal(divide(identity, d), divide(divide(identity, d), zero)), true), true, ifeq2(less_equal(divide(divide(identity, d), zero), divide(identity, d)), true, divide(divide(identity, d), zero), divide(identity, d)), divide(identity, d)), a), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 1.68/0.69 = { by axiom 14 (property_of_divide1) }
% 1.68/0.69 ifeq2(ifeq(less_equal(ifeq2(ifeq3(ifeq2(true, true, zero, divide(divide(identity, d), divide(divide(identity, d), zero))), zero, less_equal(divide(identity, d), divide(divide(identity, d), zero)), true), true, ifeq2(less_equal(divide(divide(identity, d), zero), divide(identity, d)), true, divide(divide(identity, d), zero), divide(identity, d)), divide(identity, d)), a), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 1.68/0.69 = { by axiom 9 (ifeq_axiom) }
% 1.68/0.69 ifeq2(ifeq(less_equal(ifeq2(ifeq3(zero, zero, less_equal(divide(identity, d), divide(divide(identity, d), zero)), true), true, ifeq2(less_equal(divide(divide(identity, d), zero), divide(identity, d)), true, divide(divide(identity, d), zero), divide(identity, d)), divide(identity, d)), a), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 1.68/0.69 = { by axiom 7 (ifeq_axiom) }
% 1.68/0.69 ifeq2(ifeq(less_equal(ifeq2(less_equal(divide(identity, d), divide(divide(identity, d), zero)), true, ifeq2(less_equal(divide(divide(identity, d), zero), divide(identity, d)), true, divide(divide(identity, d), zero), divide(identity, d)), divide(identity, d)), a), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 1.68/0.69 = { by axiom 15 (less_equal_and_equal) }
% 1.68/0.69 ifeq2(ifeq(less_equal(divide(identity, d), a), true, less_equal(divide(identity, a), d), true), true, ifeq2(less_equal(d, b), true, d, b), b)
% 1.68/0.69 = { by axiom 14 (property_of_divide1) }
% 1.68/0.69 ifeq2(true, true, ifeq2(less_equal(d, b), true, d, b), b)
% 1.68/0.69 = { by axiom 9 (ifeq_axiom) }
% 1.68/0.69 ifeq2(less_equal(d, b), true, d, b)
% 1.68/0.69 = { by axiom 4 (id_divide_c_is_d) R->L }
% 1.68/0.69 ifeq2(less_equal(divide(identity, c), b), true, d, b)
% 1.68/0.69 = { by axiom 8 (ifeq_axiom) R->L }
% 1.68/0.69 ifeq2(ifeq(true, true, less_equal(divide(identity, c), b), true), true, d, b)
% 1.68/0.69 = { by axiom 13 (property_of_divide3) R->L }
% 1.68/0.69 ifeq2(ifeq(ifeq(less_equal(identity, identity), true, less_equal(divide(identity, b), divide(identity, b)), true), true, less_equal(divide(identity, c), b), true), true, d, b)
% 1.68/0.69 = { by axiom 6 (id_divide_b_is_c) }
% 1.68/0.69 ifeq2(ifeq(ifeq(less_equal(identity, identity), true, less_equal(divide(identity, b), c), true), true, less_equal(divide(identity, c), b), true), true, d, b)
% 1.68/0.69 = { by axiom 1 (identity_is_largest) }
% 1.68/0.69 ifeq2(ifeq(ifeq(true, true, less_equal(divide(identity, b), c), true), true, less_equal(divide(identity, c), b), true), true, d, b)
% 1.68/0.69 = { by axiom 8 (ifeq_axiom) }
% 1.68/0.69 ifeq2(ifeq(less_equal(divide(identity, b), c), true, less_equal(divide(identity, c), b), true), true, d, b)
% 1.68/0.69 = { by axiom 14 (property_of_divide1) }
% 1.68/0.69 ifeq2(true, true, d, b)
% 1.68/0.69 = { by axiom 9 (ifeq_axiom) }
% 1.68/0.69 d
% 1.68/0.69
% 1.68/0.69 Goal 1 (prove_b_equals_d): b = d.
% 1.68/0.69 Proof:
% 1.68/0.69 b
% 1.68/0.69 = { by lemma 16 }
% 1.68/0.69 d
% 1.68/0.69
% 1.68/0.69 Goal 2 (part_of_theorem): divide(identity, a) = divide(identity, divide(identity, divide(identity, a))).
% 1.68/0.69 Proof:
% 1.68/0.69 divide(identity, a)
% 1.68/0.69 = { by axiom 5 (id_divide_a_is_b) }
% 1.68/0.69 b
% 1.68/0.69 = { by lemma 16 }
% 1.68/0.69 d
% 1.68/0.69 = { by axiom 4 (id_divide_c_is_d) R->L }
% 1.68/0.69 divide(identity, c)
% 1.68/0.69 = { by axiom 6 (id_divide_b_is_c) R->L }
% 1.68/0.69 divide(identity, divide(identity, b))
% 1.68/0.69 = { by axiom 5 (id_divide_a_is_b) R->L }
% 1.68/0.69 divide(identity, divide(identity, divide(identity, a)))
% 1.68/0.69 % SZS output end Proof
% 1.68/0.69
% 1.68/0.69 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------