TSTP Solution File: HEN010-6 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : HEN010-6 : TPTP v8.1.2. Released v1.0.0.
% 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 : n014.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 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : HEN010-6 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Aug 24 13:28:33 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.40 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.18/0.40
% 0.18/0.40 % SZS status Unsatisfiable
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% 0.18/0.41 % SZS output start Proof
% 0.18/0.41 Take the following subset of the input axioms:
% 0.18/0.41 fof(less_equal_and_equal, axiom, ![X, Y]: (~less_equal(X, Y) | (~less_equal(Y, X) | X=Y))).
% 0.18/0.41 fof(one_inversion_equals_three, axiom, ![X2]: divide(identity, divide(identity, divide(identity, X2)))=divide(identity, X2)).
% 0.18/0.41 fof(prove_property_of_inversion, negated_conjecture, divide(identity, a)!=divide(divide(identity, a), divide(identity, divide(identity, a)))).
% 0.18/0.41 fof(quotient_less_equal2, axiom, ![X2, Y2]: (divide(X2, Y2)!=zero | less_equal(X2, Y2))).
% 0.18/0.41 fof(quotient_property, axiom, ![Z, X2, Y2]: less_equal(divide(divide(X2, Z), divide(Y2, Z)), divide(divide(X2, Y2), Z))).
% 0.18/0.41 fof(quotient_smaller_than_numerator, axiom, ![X2, Y2]: less_equal(divide(X2, Y2), X2)).
% 0.18/0.41 fof(x_divide_x_is_zero, axiom, ![X2]: divide(X2, X2)=zero).
% 0.18/0.41 fof(zero_is_smallest, axiom, ![X2]: less_equal(zero, X2)).
% 0.18/0.41
% 0.18/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.41 fresh(y, y, x1...xn) = u
% 0.18/0.41 C => fresh(s, t, x1...xn) = v
% 0.18/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.41 variables of u and v.
% 0.18/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.41 input problem has no model of domain size 1).
% 0.18/0.41
% 0.18/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.41
% 0.18/0.41 Axiom 1 (x_divide_x_is_zero): divide(X, X) = zero.
% 0.18/0.41 Axiom 2 (zero_is_smallest): less_equal(zero, X) = true.
% 0.18/0.41 Axiom 3 (quotient_smaller_than_numerator): less_equal(divide(X, Y), X) = true.
% 0.18/0.41 Axiom 4 (less_equal_and_equal): fresh(X, X, Y, Z) = Z.
% 0.18/0.41 Axiom 5 (quotient_less_equal2): fresh3(X, X, Y, Z) = true.
% 0.18/0.41 Axiom 6 (less_equal_and_equal): fresh2(X, X, Y, Z) = Y.
% 0.18/0.41 Axiom 7 (one_inversion_equals_three): divide(identity, divide(identity, divide(identity, X))) = divide(identity, X).
% 0.18/0.41 Axiom 8 (quotient_less_equal2): fresh3(divide(X, Y), zero, X, Y) = less_equal(X, Y).
% 0.18/0.41 Axiom 9 (less_equal_and_equal): fresh2(less_equal(X, Y), true, Y, X) = fresh(less_equal(Y, X), true, Y, X).
% 0.18/0.41 Axiom 10 (quotient_property): less_equal(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y)) = true.
% 0.18/0.41
% 0.18/0.41 Goal 1 (prove_property_of_inversion): divide(identity, a) = divide(divide(identity, a), divide(identity, divide(identity, a))).
% 0.18/0.41 Proof:
% 0.18/0.41 divide(identity, a)
% 0.18/0.41 = { by axiom 4 (less_equal_and_equal) R->L }
% 0.18/0.41 fresh(true, true, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.18/0.41 = { by axiom 3 (quotient_smaller_than_numerator) R->L }
% 0.18/0.41 fresh(less_equal(divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a)), true, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.18/0.41 = { by axiom 9 (less_equal_and_equal) R->L }
% 0.18/0.41 fresh2(less_equal(divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a)))), true, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.18/0.41 = { by axiom 8 (quotient_less_equal2) R->L }
% 0.18/0.41 fresh2(fresh3(divide(divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero, divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a)))), true, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.18/0.41 = { by axiom 4 (less_equal_and_equal) R->L }
% 0.18/0.41 fresh2(fresh3(fresh(true, true, zero, divide(divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a)))), true, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.18/0.41 = { by axiom 2 (zero_is_smallest) R->L }
% 0.18/0.41 fresh2(fresh3(fresh(less_equal(zero, divide(divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a))))), true, zero, divide(divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a)))), true, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.18/0.41 = { by axiom 9 (less_equal_and_equal) R->L }
% 0.18/0.41 fresh2(fresh3(fresh2(less_equal(divide(divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), true, zero, divide(divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a)))), true, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.18/0.41 = { by axiom 7 (one_inversion_equals_three) R->L }
% 0.18/0.41 fresh2(fresh3(fresh2(less_equal(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, a)))), zero), true, zero, divide(divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a)))), true, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.18/0.41 = { by axiom 1 (x_divide_x_is_zero) R->L }
% 0.18/0.41 fresh2(fresh3(fresh2(less_equal(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)))), true, zero, divide(divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a)))), true, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.18/0.41 = { by axiom 10 (quotient_property) }
% 0.18/0.41 fresh2(fresh3(fresh2(true, true, zero, divide(divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a))))), zero, divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a)))), true, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.18/0.41 = { by axiom 6 (less_equal_and_equal) }
% 0.18/0.41 fresh2(fresh3(zero, zero, divide(identity, a), divide(divide(identity, a), divide(identity, divide(identity, a)))), true, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.18/0.41 = { by axiom 5 (quotient_less_equal2) }
% 0.18/0.41 fresh2(true, true, divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a))
% 0.18/0.41 = { by axiom 6 (less_equal_and_equal) }
% 0.18/0.41 divide(divide(identity, a), divide(identity, divide(identity, a)))
% 0.18/0.41 % SZS output end Proof
% 0.18/0.41
% 0.18/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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