TSTP Solution File: HEN010-5 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : HEN010-5 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:57:02 EDT 2023
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : HEN010-5 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 14:05:11 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.45 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.45
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 Take the following subset of the input axioms:
% 0.20/0.48 fof(divide_and_equal, axiom, ![X, Y]: (divide(X, Y)!=zero | (divide(Y, X)!=zero | X=Y))).
% 0.20/0.48 fof(identity_is_largest, axiom, ![X2]: divide(X2, identity)=zero).
% 0.20/0.48 fof(property_of_divide1, axiom, ![Z, X2, Y2]: (divide(divide(X2, Y2), Z)!=zero | divide(divide(X2, Z), Y2)=zero)).
% 0.20/0.48 fof(property_of_divide3, axiom, ![X2, Y2, Z2]: (divide(X2, Y2)!=zero | divide(divide(X2, Z2), divide(Y2, Z2))=zero)).
% 0.20/0.48 fof(prove_this, negated_conjecture, divide(identity, a)!=divide(divide(identity, a), divide(identity, divide(identity, a)))).
% 0.20/0.48 fof(quotient_property, axiom, ![X2, Y2, Z2]: divide(divide(divide(X2, Z2), divide(Y2, Z2)), divide(divide(X2, Y2), Z2))=zero).
% 0.20/0.48 fof(quotient_smaller_than_numerator, axiom, ![X2, Y2]: divide(divide(X2, Y2), X2)=zero).
% 0.20/0.48 fof(transitivity_of_divide_to_zero, axiom, ![X2, Y2, Z2]: (divide(X2, Y2)!=zero | (divide(Y2, Z2)!=zero | divide(X2, Z2)=zero))).
% 0.20/0.48 fof(zero_is_smallest, axiom, ![X2]: divide(zero, X2)=zero).
% 0.20/0.48
% 0.20/0.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.48 fresh(y, y, x1...xn) = u
% 0.20/0.48 C => fresh(s, t, x1...xn) = v
% 0.20/0.48 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.48 variables of u and v.
% 0.20/0.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.48 input problem has no model of domain size 1).
% 0.20/0.48
% 0.20/0.48 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.48
% 0.20/0.48 Axiom 1 (identity_is_largest): divide(X, identity) = zero.
% 0.20/0.48 Axiom 2 (zero_is_smallest): divide(zero, X) = zero.
% 0.20/0.48 Axiom 3 (quotient_smaller_than_numerator): divide(divide(X, Y), X) = zero.
% 0.20/0.48 Axiom 4 (divide_and_equal): fresh(X, X, Y, Z) = Z.
% 0.20/0.48 Axiom 5 (transitivity_of_divide_to_zero): fresh3(X, X, Y, Z) = zero.
% 0.20/0.48 Axiom 6 (divide_and_equal): fresh2(X, X, Y, Z) = Y.
% 0.20/0.48 Axiom 7 (property_of_divide3): fresh6(X, X, Y, Z, W) = zero.
% 0.20/0.48 Axiom 8 (property_of_divide1): fresh5(X, X, Y, Z, W) = zero.
% 0.20/0.48 Axiom 9 (transitivity_of_divide_to_zero): fresh4(X, X, Y, Z, W) = divide(Y, W).
% 0.20/0.48 Axiom 10 (divide_and_equal): fresh2(divide(X, Y), zero, Y, X) = fresh(divide(Y, X), zero, Y, X).
% 0.20/0.48 Axiom 11 (property_of_divide3): fresh6(divide(X, Y), zero, X, Y, Z) = divide(divide(X, Z), divide(Y, Z)).
% 0.20/0.48 Axiom 12 (transitivity_of_divide_to_zero): fresh4(divide(X, Y), zero, Z, X, Y) = fresh3(divide(Z, X), zero, Z, Y).
% 0.20/0.48 Axiom 13 (property_of_divide1): fresh5(divide(divide(X, Y), Z), zero, X, Y, Z) = divide(divide(X, Z), Y).
% 0.20/0.48 Axiom 14 (quotient_property): divide(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y)) = zero.
% 0.20/0.48
% 0.20/0.48 Lemma 15: fresh(divide(X, zero), zero, X, zero) = X.
% 0.20/0.48 Proof:
% 0.20/0.48 fresh(divide(X, zero), zero, X, zero)
% 0.20/0.48 = { by axiom 10 (divide_and_equal) R->L }
% 0.20/0.48 fresh2(divide(zero, X), zero, X, zero)
% 0.20/0.48 = { by axiom 2 (zero_is_smallest) }
% 0.20/0.48 fresh2(zero, zero, X, zero)
% 0.20/0.48 = { by axiom 6 (divide_and_equal) }
% 0.20/0.48 X
% 0.20/0.48
% 0.20/0.48 Lemma 16: divide(divide(X, Y), divide(identity, Y)) = zero.
% 0.20/0.48 Proof:
% 0.20/0.48 divide(divide(X, Y), divide(identity, Y))
% 0.20/0.48 = { by axiom 11 (property_of_divide3) R->L }
% 0.20/0.48 fresh6(divide(X, identity), zero, X, identity, Y)
% 0.20/0.48 = { by axiom 1 (identity_is_largest) }
% 0.20/0.48 fresh6(zero, zero, X, identity, Y)
% 0.20/0.48 = { by axiom 7 (property_of_divide3) }
% 0.20/0.48 zero
% 0.20/0.48
% 0.20/0.48 Goal 1 (prove_this): divide(identity, a) = divide(divide(identity, a), divide(identity, divide(identity, a))).
% 0.20/0.48 Proof:
% 0.20/0.48 divide(identity, a)
% 0.20/0.48 = { by axiom 4 (divide_and_equal) R->L }
% 0.20/0.48 fresh(zero, zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.48 = { by axiom 3 (quotient_smaller_than_numerator) R->L }
% 0.20/0.48 fresh(divide(divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a)), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.48 = { by axiom 10 (divide_and_equal) R->L }
% 0.20/0.48 fresh2(divide(divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.48 = { by axiom 13 (property_of_divide1) R->L }
% 0.20/0.48 fresh2(fresh5(divide(divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.48 = { by axiom 9 (transitivity_of_divide_to_zero) R->L }
% 0.20/0.48 fresh2(fresh5(fresh4(zero, zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(identity, divide(identity, a)), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.48 = { by axiom 8 (property_of_divide1) R->L }
% 0.20/0.48 fresh2(fresh5(fresh4(fresh5(zero, zero, identity, a, divide(identity, a)), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(identity, divide(identity, a)), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.48 = { by lemma 16 R->L }
% 0.20/0.48 fresh2(fresh5(fresh4(fresh5(divide(divide(identity, a), divide(identity, a)), zero, identity, a, divide(identity, a)), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(identity, divide(identity, a)), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.48 = { by axiom 13 (property_of_divide1) }
% 0.20/0.48 fresh2(fresh5(fresh4(divide(divide(identity, divide(identity, a)), a), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(identity, divide(identity, a)), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.48 = { by axiom 12 (transitivity_of_divide_to_zero) }
% 0.20/0.48 fresh2(fresh5(fresh3(divide(divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(identity, divide(identity, a))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.48 = { by axiom 13 (property_of_divide1) R->L }
% 0.20/0.48 fresh2(fresh5(fresh3(fresh5(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, identity, divide(identity, divide(identity, a)), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.48 = { by axiom 4 (divide_and_equal) R->L }
% 0.20/0.48 fresh2(fresh5(fresh3(fresh5(fresh(zero, zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, identity, divide(identity, divide(identity, a)), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.48 = { by axiom 3 (quotient_smaller_than_numerator) R->L }
% 0.20/0.48 fresh2(fresh5(fresh3(fresh5(fresh(divide(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, identity, divide(identity, divide(identity, a)), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.48 = { by axiom 10 (divide_and_equal) R->L }
% 0.20/0.48 fresh2(fresh5(fresh3(fresh5(fresh2(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, identity, divide(identity, divide(identity, a)), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.48 = { by lemma 15 R->L }
% 0.20/0.48 fresh2(fresh5(fresh3(fresh5(fresh2(fresh(divide(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, identity, divide(identity, divide(identity, a)), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.48 = { by axiom 13 (property_of_divide1) R->L }
% 0.20/0.48 fresh2(fresh5(fresh3(fresh5(fresh2(fresh(fresh5(divide(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, identity, divide(identity, divide(identity, a)), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.48 = { by lemma 15 R->L }
% 0.20/0.49 fresh2(fresh5(fresh3(fresh5(fresh2(fresh(fresh5(fresh(divide(divide(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero), zero, divide(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero), zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, identity, divide(identity, divide(identity, a)), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.49 = { by axiom 13 (property_of_divide1) R->L }
% 0.20/0.49 fresh2(fresh5(fresh3(fresh5(fresh2(fresh(fresh5(fresh(fresh5(divide(divide(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), zero), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero, divide(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero), zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, identity, divide(identity, divide(identity, a)), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.49 = { by axiom 3 (quotient_smaller_than_numerator) }
% 0.20/0.49 fresh2(fresh5(fresh3(fresh5(fresh2(fresh(fresh5(fresh(fresh5(zero, zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero, divide(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero), zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, identity, divide(identity, divide(identity, a)), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.49 = { by axiom 8 (property_of_divide1) }
% 0.20/0.49 fresh2(fresh5(fresh3(fresh5(fresh2(fresh(fresh5(fresh(zero, zero, divide(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero), zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, identity, divide(identity, divide(identity, a)), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.49 = { by axiom 4 (divide_and_equal) }
% 0.20/0.49 fresh2(fresh5(fresh3(fresh5(fresh2(fresh(fresh5(zero, zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, identity, divide(identity, divide(identity, a)), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.49 = { by axiom 8 (property_of_divide1) }
% 0.20/0.49 fresh2(fresh5(fresh3(fresh5(fresh2(fresh(zero, zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero)), zero), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, identity, divide(identity, divide(identity, a)), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.49 = { by axiom 4 (divide_and_equal) }
% 0.20/0.49 fresh2(fresh5(fresh3(fresh5(fresh2(zero, zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, identity, divide(identity, divide(identity, a)), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.49 = { by axiom 6 (divide_and_equal) }
% 0.20/0.49 fresh2(fresh5(fresh3(fresh5(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), zero, identity, divide(identity, divide(identity, a)), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.49 = { by lemma 16 R->L }
% 0.20/0.49 fresh2(fresh5(fresh3(fresh5(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, a)), divide(identity, divide(identity, a)))), zero, identity, divide(identity, divide(identity, a)), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.49 = { by axiom 14 (quotient_property) }
% 0.20/0.49 fresh2(fresh5(fresh3(fresh5(zero, zero, identity, divide(identity, divide(identity, a)), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.49 = { by axiom 8 (property_of_divide1) }
% 0.20/0.49 fresh2(fresh5(fresh3(zero, zero, divide(identity, divide(divide(identity, a), divide(identity, divide(identity, a)))), a), zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.49 = { by axiom 5 (transitivity_of_divide_to_zero) }
% 0.20/0.49 fresh2(fresh5(zero, zero, identity, divide(divide(identity, a), divide(identity, divide(identity, a))), a), zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.49 = { by axiom 8 (property_of_divide1) }
% 0.20/0.49 fresh2(zero, zero, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.20/0.49 = { by axiom 6 (divide_and_equal) }
% 0.20/0.49 divide(divide(identity, a), divide(identity, divide(identity, a)))
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49
% 0.20/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
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