TSTP Solution File: HEN007-6 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : HEN007-6 : 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 01:56:58 EDT 2023
% Result : Unsatisfiable 0.19s 0.76s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN007-6 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 13:30:48 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.76 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.19/0.76
% 0.19/0.76 % SZS status Unsatisfiable
% 0.19/0.76
% 0.19/0.76 % SZS output start Proof
% 0.19/0.76 Take the following subset of the input axioms:
% 0.19/0.77 fof(closure, axiom, ![X, Y]: quotient(X, Y, divide(X, Y))).
% 0.19/0.77 fof(divisor_existence, axiom, ![Z, X2, Y2]: (~quotient(X2, Y2, Z) | less_equal(Z, X2))).
% 0.19/0.77 fof(prove_zQyLEzQx, negated_conjecture, ~less_equal(zQy, zQx)).
% 0.19/0.77 fof(quotient_less_equal, axiom, ![X2, Y2]: (~less_equal(X2, Y2) | quotient(X2, Y2, zero))).
% 0.19/0.77 fof(quotient_property, axiom, ![V1, V2, V3, V4, V5, X2, Y2, Z2]: (~quotient(X2, Y2, V1) | (~quotient(Y2, Z2, V2) | (~quotient(X2, Z2, V3) | (~quotient(V3, V2, V4) | (~quotient(V1, Z2, V5) | less_equal(V4, V5))))))).
% 0.19/0.77 fof(transitivity_of_less_equal, axiom, ![X2, Y2, Z2]: (~less_equal(X2, Y2) | (~less_equal(Y2, Z2) | less_equal(X2, Z2)))).
% 0.19/0.77 fof(well_defined, axiom, ![W, X2, Y2, Z2]: (~quotient(X2, Y2, Z2) | (~quotient(X2, Y2, W) | Z2=W))).
% 0.19/0.77 fof(xLEy, hypothesis, less_equal(x, y)).
% 0.19/0.77 fof(x_divde_zero_is_x, axiom, ![X2]: quotient(X2, zero, X2)).
% 0.19/0.77 fof(zQx, hypothesis, quotient(z, x, zQx)).
% 0.19/0.77 fof(zQy, hypothesis, quotient(z, y, zQy)).
% 0.19/0.77
% 0.19/0.77 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.77 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.77 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.77 fresh(y, y, x1...xn) = u
% 0.19/0.77 C => fresh(s, t, x1...xn) = v
% 0.19/0.77 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.77 variables of u and v.
% 0.19/0.77 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.77 input problem has no model of domain size 1).
% 0.19/0.77
% 0.19/0.77 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.77
% 0.19/0.77 Axiom 1 (xLEy): less_equal(x, y) = true.
% 0.19/0.77 Axiom 2 (x_divde_zero_is_x): quotient(X, zero, X) = true.
% 0.19/0.77 Axiom 3 (zQx): quotient(z, x, zQx) = true.
% 0.19/0.77 Axiom 4 (zQy): quotient(z, y, zQy) = true.
% 0.19/0.77 Axiom 5 (well_defined): fresh(X, X, Y, Z) = Z.
% 0.19/0.77 Axiom 6 (quotient_property): fresh14(X, X, Y, Z) = true.
% 0.19/0.77 Axiom 7 (divisor_existence): fresh8(X, X, Y, Z) = true.
% 0.19/0.77 Axiom 8 (quotient_less_equal): fresh7(X, X, Y, Z) = true.
% 0.19/0.77 Axiom 9 (transitivity_of_less_equal): fresh5(X, X, Y, Z) = true.
% 0.19/0.77 Axiom 10 (closure): quotient(X, Y, divide(X, Y)) = true.
% 0.19/0.77 Axiom 11 (transitivity_of_less_equal): fresh6(X, X, Y, Z, W) = less_equal(Y, W).
% 0.19/0.77 Axiom 12 (quotient_less_equal): fresh7(less_equal(X, Y), true, X, Y) = quotient(X, Y, zero).
% 0.19/0.77 Axiom 13 (well_defined): fresh2(X, X, Y, Z, W, V) = W.
% 0.19/0.77 Axiom 14 (quotient_property): fresh12(X, X, Y, Z, W, V, U) = less_equal(V, U).
% 0.19/0.77 Axiom 15 (divisor_existence): fresh8(quotient(X, Y, Z), true, X, Z) = less_equal(Z, X).
% 0.19/0.77 Axiom 16 (transitivity_of_less_equal): fresh6(less_equal(X, Y), true, Z, X, Y) = fresh5(less_equal(Z, X), true, Z, Y).
% 0.19/0.77 Axiom 17 (quotient_property): fresh13(X, X, Y, Z, W, V, U, T, S) = fresh14(quotient(Y, Z, W), true, T, S).
% 0.19/0.77 Axiom 18 (well_defined): fresh2(quotient(X, Y, Z), true, X, Y, W, Z) = fresh(quotient(X, Y, W), true, W, Z).
% 0.19/0.77 Axiom 19 (quotient_property): fresh11(X, X, Y, Z, W, V, U, T, S, X2) = fresh12(quotient(Y, V, T), true, Y, Z, W, S, X2).
% 0.19/0.77 Axiom 20 (quotient_property): fresh10(X, X, Y, Z, W, V, U, T, S, X2) = fresh13(quotient(Z, V, U), true, Y, Z, W, V, T, S, X2).
% 0.19/0.77 Axiom 21 (quotient_property): fresh10(quotient(X, Y, Z), true, W, V, U, T, Y, X, Z, S) = fresh11(quotient(U, T, S), true, W, V, U, T, Y, X, Z, S).
% 0.19/0.77
% 0.19/0.77 Goal 1 (prove_zQyLEzQx): less_equal(zQy, zQx) = true.
% 0.19/0.77 Proof:
% 0.19/0.77 less_equal(zQy, zQx)
% 0.19/0.77 = { by axiom 11 (transitivity_of_less_equal) R->L }
% 0.19/0.77 fresh6(true, true, zQy, divide(zQx, y), zQx)
% 0.19/0.77 = { by axiom 7 (divisor_existence) R->L }
% 0.19/0.77 fresh6(fresh8(true, true, zQx, divide(zQx, y)), true, zQy, divide(zQx, y), zQx)
% 0.19/0.77 = { by axiom 10 (closure) R->L }
% 0.19/0.77 fresh6(fresh8(quotient(zQx, y, divide(zQx, y)), true, zQx, divide(zQx, y)), true, zQy, divide(zQx, y), zQx)
% 0.19/0.77 = { by axiom 15 (divisor_existence) }
% 0.19/0.77 fresh6(less_equal(divide(zQx, y), zQx), true, zQy, divide(zQx, y), zQx)
% 0.19/0.77 = { by axiom 16 (transitivity_of_less_equal) }
% 0.19/0.77 fresh5(less_equal(zQy, divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 5 (well_defined) R->L }
% 0.19/0.77 fresh5(less_equal(fresh(true, true, divide(z, y), zQy), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 10 (closure) R->L }
% 0.19/0.77 fresh5(less_equal(fresh(quotient(z, y, divide(z, y)), true, divide(z, y), zQy), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 18 (well_defined) R->L }
% 0.19/0.77 fresh5(less_equal(fresh2(quotient(z, y, zQy), true, z, y, divide(z, y), zQy), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 4 (zQy) }
% 0.19/0.77 fresh5(less_equal(fresh2(true, true, z, y, divide(z, y), zQy), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 13 (well_defined) }
% 0.19/0.77 fresh5(less_equal(divide(z, y), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 14 (quotient_property) R->L }
% 0.19/0.77 fresh5(fresh12(true, true, z, x, zQx, divide(z, y), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 10 (closure) R->L }
% 0.19/0.77 fresh5(fresh12(quotient(z, y, divide(z, y)), true, z, x, zQx, divide(z, y), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 19 (quotient_property) R->L }
% 0.19/0.77 fresh5(fresh11(true, true, z, x, zQx, y, zero, divide(z, y), divide(z, y), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 10 (closure) R->L }
% 0.19/0.77 fresh5(fresh11(quotient(zQx, y, divide(zQx, y)), true, z, x, zQx, y, zero, divide(z, y), divide(z, y), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 21 (quotient_property) R->L }
% 0.19/0.77 fresh5(fresh10(quotient(divide(z, y), zero, divide(z, y)), true, z, x, zQx, y, zero, divide(z, y), divide(z, y), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 2 (x_divde_zero_is_x) }
% 0.19/0.77 fresh5(fresh10(true, true, z, x, zQx, y, zero, divide(z, y), divide(z, y), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 20 (quotient_property) }
% 0.19/0.77 fresh5(fresh13(quotient(x, y, zero), true, z, x, zQx, y, divide(z, y), divide(z, y), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 12 (quotient_less_equal) R->L }
% 0.19/0.77 fresh5(fresh13(fresh7(less_equal(x, y), true, x, y), true, z, x, zQx, y, divide(z, y), divide(z, y), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 1 (xLEy) }
% 0.19/0.77 fresh5(fresh13(fresh7(true, true, x, y), true, z, x, zQx, y, divide(z, y), divide(z, y), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 8 (quotient_less_equal) }
% 0.19/0.77 fresh5(fresh13(true, true, z, x, zQx, y, divide(z, y), divide(z, y), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 17 (quotient_property) }
% 0.19/0.77 fresh5(fresh14(quotient(z, x, zQx), true, divide(z, y), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 3 (zQx) }
% 0.19/0.77 fresh5(fresh14(true, true, divide(z, y), divide(zQx, y)), true, zQy, zQx)
% 0.19/0.77 = { by axiom 6 (quotient_property) }
% 0.19/0.77 fresh5(true, true, zQy, zQx)
% 0.19/0.77 = { by axiom 9 (transitivity_of_less_equal) }
% 0.19/0.77 true
% 0.19/0.77 % SZS output end Proof
% 0.19/0.77
% 0.19/0.77 RESULT: Unsatisfiable (the axioms are contradictory).
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