TSTP Solution File: HEN005-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : HEN005-1 : 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 01:56:54 EDT 2023
% Result : Unsatisfiable 0.20s 0.47s
% 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 : HEN005-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.14 % 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 13:57:11 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.47 Command-line arguments: --no-flatten-goal
% 0.20/0.47
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 Take the following subset of the input axioms:
% 0.20/0.49 fof(closure, axiom, ![X, Y]: quotient(X, Y, divide(X, Y))).
% 0.20/0.49 fof(less_equal_and_equal, axiom, ![X2, Y2]: (~less_equal(X2, Y2) | (~less_equal(Y2, X2) | X2=Y2))).
% 0.20/0.49 fof(less_equal_quotient, axiom, ![X2, Y2]: (~quotient(X2, Y2, zero) | less_equal(X2, Y2))).
% 0.20/0.49 fof(prove_transitivity_of_less_equal, negated_conjecture, ~less_equal(x, z)).
% 0.20/0.49 fof(quotient_less_equal, axiom, ![X2, Y2]: (~less_equal(X2, Y2) | quotient(X2, Y2, zero))).
% 0.20/0.49 fof(quotient_property, axiom, ![Z, V1, V2, V3, V4, V5, X2, Y2]: (~quotient(X2, Y2, V1) | (~quotient(Y2, Z, V2) | (~quotient(X2, Z, V3) | (~quotient(V3, V2, V4) | (~quotient(V1, Z, V5) | less_equal(V4, V5))))))).
% 0.20/0.49 fof(xLEy, hypothesis, less_equal(x, y)).
% 0.20/0.49 fof(yLEz, hypothesis, less_equal(y, z)).
% 0.20/0.49 fof(zero_is_smallest, axiom, ![X2]: less_equal(zero, X2)).
% 0.20/0.49
% 0.20/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.49 fresh(y, y, x1...xn) = u
% 0.20/0.49 C => fresh(s, t, x1...xn) = v
% 0.20/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.49 variables of u and v.
% 0.20/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.49 input problem has no model of domain size 1).
% 0.20/0.49
% 0.20/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.49
% 0.20/0.49 Axiom 1 (xLEy): less_equal(x, y) = true.
% 0.20/0.49 Axiom 2 (yLEz): less_equal(y, z) = true.
% 0.20/0.49 Axiom 3 (zero_is_smallest): less_equal(zero, X) = true.
% 0.20/0.49 Axiom 4 (quotient_property): fresh12(X, X, Y, Z) = true.
% 0.20/0.49 Axiom 5 (less_equal_quotient): fresh7(X, X, Y, Z) = true.
% 0.20/0.49 Axiom 6 (quotient_less_equal): fresh5(X, X, Y, Z) = true.
% 0.20/0.49 Axiom 7 (less_equal_and_equal): fresh4(X, X, Y, Z) = Y.
% 0.20/0.49 Axiom 8 (less_equal_and_equal): fresh3(X, X, Y, Z) = Z.
% 0.20/0.49 Axiom 9 (closure): quotient(X, Y, divide(X, Y)) = true.
% 0.20/0.49 Axiom 10 (quotient_less_equal): fresh5(less_equal(X, Y), true, X, Y) = quotient(X, Y, zero).
% 0.20/0.49 Axiom 11 (less_equal_and_equal): fresh4(less_equal(X, Y), true, Y, X) = fresh3(less_equal(Y, X), true, Y, X).
% 0.20/0.49 Axiom 12 (quotient_property): fresh10(X, X, Y, Z, W, V, U) = less_equal(V, U).
% 0.20/0.49 Axiom 13 (less_equal_quotient): fresh7(quotient(X, Y, zero), true, X, Y) = less_equal(X, Y).
% 0.20/0.49 Axiom 14 (quotient_property): fresh11(X, X, Y, Z, W, V, U, T, S) = fresh12(quotient(Y, Z, W), true, T, S).
% 0.20/0.49 Axiom 15 (quotient_property): fresh9(X, X, Y, Z, W, V, U, T, S, X2) = fresh10(quotient(Y, V, T), true, Y, Z, W, S, X2).
% 0.20/0.49 Axiom 16 (quotient_property): fresh8(X, X, Y, Z, W, V, U, T, S, X2) = fresh11(quotient(Z, V, U), true, Y, Z, W, V, T, S, X2).
% 0.20/0.49 Axiom 17 (quotient_property): fresh8(quotient(X, Y, Z), true, W, V, U, T, Y, X, Z, S) = fresh9(quotient(U, T, S), true, W, V, U, T, Y, X, Z, S).
% 0.20/0.49
% 0.20/0.49 Goal 1 (prove_transitivity_of_less_equal): less_equal(x, z) = true.
% 0.20/0.49 Proof:
% 0.20/0.49 less_equal(x, z)
% 0.20/0.49 = { by axiom 13 (less_equal_quotient) R->L }
% 0.20/0.49 fresh7(quotient(x, z, zero), true, x, z)
% 0.20/0.49 = { by axiom 8 (less_equal_and_equal) R->L }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(true, true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 5 (less_equal_quotient) R->L }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(true, true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 9 (closure) R->L }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, divide(divide(x, z), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 7 (less_equal_and_equal) R->L }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh4(true, true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 3 (zero_is_smallest) R->L }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh4(less_equal(zero, divide(divide(x, z), zero)), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 11 (less_equal_and_equal) }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(less_equal(divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 12 (quotient_property) R->L }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(fresh10(true, true, x, y, zero, divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 9 (closure) R->L }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(fresh10(quotient(x, z, divide(x, z)), true, x, y, zero, divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 15 (quotient_property) R->L }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(fresh9(true, true, x, y, zero, z, zero, divide(x, z), divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 6 (quotient_less_equal) R->L }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(fresh9(fresh5(true, true, zero, z), true, x, y, zero, z, zero, divide(x, z), divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 3 (zero_is_smallest) R->L }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(fresh9(fresh5(less_equal(zero, z), true, zero, z), true, x, y, zero, z, zero, divide(x, z), divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 10 (quotient_less_equal) }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(fresh9(quotient(zero, z, zero), true, x, y, zero, z, zero, divide(x, z), divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 17 (quotient_property) R->L }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(fresh8(quotient(divide(x, z), zero, divide(divide(x, z), zero)), true, x, y, zero, z, zero, divide(x, z), divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 9 (closure) }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(fresh8(true, true, x, y, zero, z, zero, divide(x, z), divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 16 (quotient_property) }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(fresh11(quotient(y, z, zero), true, x, y, zero, z, divide(x, z), divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 10 (quotient_less_equal) R->L }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(fresh11(fresh5(less_equal(y, z), true, y, z), true, x, y, zero, z, divide(x, z), divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 2 (yLEz) }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(fresh11(fresh5(true, true, y, z), true, x, y, zero, z, divide(x, z), divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 6 (quotient_less_equal) }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(fresh11(true, true, x, y, zero, z, divide(x, z), divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 14 (quotient_property) }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(fresh12(quotient(x, y, zero), true, divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 10 (quotient_less_equal) R->L }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(fresh12(fresh5(less_equal(x, y), true, x, y), true, divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 1 (xLEy) }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(fresh12(fresh5(true, true, x, y), true, divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 6 (quotient_less_equal) }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(fresh12(true, true, divide(divide(x, z), zero), zero), true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 4 (quotient_property) }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, fresh3(true, true, divide(divide(x, z), zero), zero)), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 8 (less_equal_and_equal) }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(fresh7(quotient(divide(x, z), zero, zero), true, divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 13 (less_equal_quotient) }
% 0.20/0.49 fresh7(quotient(x, z, fresh3(less_equal(divide(x, z), zero), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 11 (less_equal_and_equal) R->L }
% 0.20/0.49 fresh7(quotient(x, z, fresh4(less_equal(zero, divide(x, z)), true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 3 (zero_is_smallest) }
% 0.20/0.49 fresh7(quotient(x, z, fresh4(true, true, divide(x, z), zero)), true, x, z)
% 0.20/0.49 = { by axiom 7 (less_equal_and_equal) }
% 0.20/0.49 fresh7(quotient(x, z, divide(x, z)), true, x, z)
% 0.20/0.49 = { by axiom 9 (closure) }
% 0.20/0.49 fresh7(true, true, x, z)
% 0.20/0.49 = { by axiom 5 (less_equal_quotient) }
% 0.20/0.49 true
% 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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