TSTP Solution File: NLP204+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NLP204+1 : TPTP v8.1.2. Released v2.4.0.
% 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 : 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 10:08:00 EDT 2023
% Result : Theorem 0.21s 0.60s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NLP204+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n001.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 24 13:16:41 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.60 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.60
% 0.21/0.60 % SZS status Theorem
% 0.21/0.60
% 0.21/0.60 % SZS output start Proof
% 0.21/0.60 Take the following subset of the input axioms:
% 0.21/0.61 fof(ax24, axiom, ![U, V]: (man(U, V) => male(U, V))).
% 0.21/0.61 fof(ax38, axiom, ![V2, U2]: (object(U2, V2) => unisex(U2, V2))).
% 0.21/0.61 fof(ax45, axiom, ![V2, U2]: (artifact(U2, V2) => object(U2, V2))).
% 0.21/0.61 fof(ax46, axiom, ![V2, U2]: (instrumentality(U2, V2) => artifact(U2, V2))).
% 0.21/0.61 fof(ax47, axiom, ![V2, U2]: (device(U2, V2) => instrumentality(U2, V2))).
% 0.21/0.61 fof(ax48, axiom, ![V2, U2]: (wheel(U2, V2) => device(U2, V2))).
% 0.21/0.61 fof(ax57, axiom, ![V2, U2]: (animate(U2, V2) => ~nonliving(U2, V2))).
% 0.21/0.61 fof(ax58, axiom, ![V2, U2]: (existent(U2, V2) => ~nonexistent(U2, V2))).
% 0.21/0.61 fof(ax59, axiom, ![V2, U2]: (nonhuman(U2, V2) => ~human(U2, V2))).
% 0.21/0.61 fof(ax60, axiom, ![V2, U2]: (nonliving(U2, V2) => ~living(U2, V2))).
% 0.21/0.61 fof(ax61, axiom, ![V2, U2]: (singleton(U2, V2) => ~multiple(U2, V2))).
% 0.21/0.61 fof(ax62, axiom, ![V2, U2]: (specific(U2, V2) => ~general(U2, V2))).
% 0.21/0.61 fof(ax63, axiom, ![V2, U2]: (unisex(U2, V2) => ~male(U2, V2))).
% 0.21/0.61 fof(ax64, axiom, ![V2, U2]: (white(U2, V2) => ~black(U2, V2))).
% 0.21/0.61 fof(ax65, axiom, ![V2, U2]: (young(U2, V2) => ~old(U2, V2))).
% 0.21/0.61 fof(ax68, axiom, ![V2, U2]: (two(U2, V2) <=> ?[W]: (member(U2, W, V2) & ?[X]: (member(U2, X, V2) & (X!=W & ![Y]: (member(U2, Y, V2) => (Y=X | Y=W))))))).
% 0.21/0.61 fof(ax69, axiom, ![V2, W2, X15, U2]: ((nonreflexive(U2, V2) & (agent(U2, V2, W2) & patient(U2, V2, X15))) => W2!=X15)).
% 0.21/0.61 fof(ax70, axiom, ![U2]: ~?[V2]: member(U2, V2, V2)).
% 0.21/0.61 fof(ax71, axiom, ![V2, W2, X15, U2]: (be(U2, V2, W2, X15) => W2=X15)).
% 0.21/0.61 fof(co1, conjecture, ~?[U2]: (actual_world(U2) & ?[Z, X1, X2, X3, X4, X5, X6, V2, W2, X15, Y2]: (of(U2, W2, V2) & (man(U2, V2) & (jules_forename(U2, W2) & (forename(U2, W2) & (frontseat(U2, X15) & (chevy(U2, Y2) & (white(U2, Y2) & (dirty(U2, Y2) & (old(U2, Y2) & (of(U2, Z, X1) & (city(U2, X1) & (hollywood_placename(U2, Z) & (placename(U2, Z) & (street(U2, X1) & (lonely(U2, X1) & (event(U2, X2) & (agent(U2, X2, Y2) & (present(U2, X2) & (barrel(U2, X2) & (down(U2, X2, X1) & (in(U2, X2, X1) & (![X7]: (member(U2, X7, X3) => ?[X8, X9]: (state(U2, X8) & (be(U2, X8, X7, X9) & in(U2, X9, X15)))) & (two(U2, X3) & (group(U2, X3) & (![X10]: (member(U2, X10, X3) => (fellow(U2, X10) & young(U2, X10))) & (![X11]: (member(U2, X11, X4) => ![X12]: (member(U2, X12, X3) => ?[X13]: (event(U2, X13) & (agent(U2, X13, X12) & (patient(U2, X13, X11) & (present(U2, X13) & (nonreflexive(U2, X13) & wear(U2, X13)))))))) & (group(U2, X4) & (![X14]: (member(U2, X14, X4) => (coat(U2, X14) & (black(U2, X14) & cheap(U2, X14)))) & (wheel(U2, X6) & (state(U2, X5) & (be(U2, X5, V2, X6) & behind(U2, X6, X6)))))))))))))))))))))))))))))))))).
% 0.21/0.61
% 0.21/0.61 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.61 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.61 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.61 fresh(y, y, x1...xn) = u
% 0.21/0.61 C => fresh(s, t, x1...xn) = v
% 0.21/0.61 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.61 variables of u and v.
% 0.21/0.61 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.61 input problem has no model of domain size 1).
% 0.21/0.61
% 0.21/0.61 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.61
% 0.21/0.61 Axiom 1 (co1_14): wheel(u, x6) = true2.
% 0.21/0.61 Axiom 2 (co1_13): man(u, v) = true2.
% 0.21/0.61 Axiom 3 (ax71): fresh(X, X, Y, Z) = Z.
% 0.21/0.61 Axiom 4 (ax24): fresh63(X, X, Y, Z) = true2.
% 0.21/0.61 Axiom 5 (ax38): fresh48(X, X, Y, Z) = true2.
% 0.21/0.61 Axiom 6 (ax45): fresh40(X, X, Y, Z) = true2.
% 0.21/0.61 Axiom 7 (ax46): fresh39(X, X, Y, Z) = true2.
% 0.21/0.61 Axiom 8 (ax47): fresh38(X, X, Y, Z) = true2.
% 0.21/0.61 Axiom 9 (ax48): fresh37(X, X, Y, Z) = true2.
% 0.21/0.61 Axiom 10 (co1_21): be(u, x5, v, x6) = true2.
% 0.21/0.61 Axiom 11 (ax24): fresh63(man(X, Y), true2, X, Y) = male(X, Y).
% 0.21/0.61 Axiom 12 (ax38): fresh48(object(X, Y), true2, X, Y) = unisex(X, Y).
% 0.21/0.61 Axiom 13 (ax45): fresh40(artifact(X, Y), true2, X, Y) = object(X, Y).
% 0.21/0.61 Axiom 14 (ax46): fresh39(instrumentality(X, Y), true2, X, Y) = artifact(X, Y).
% 0.21/0.61 Axiom 15 (ax47): fresh38(device(X, Y), true2, X, Y) = instrumentality(X, Y).
% 0.21/0.61 Axiom 16 (ax48): fresh37(wheel(X, Y), true2, X, Y) = device(X, Y).
% 0.21/0.62 Axiom 17 (ax71): fresh(be(X, Y, Z, W), true2, Z, W) = Z.
% 0.21/0.62
% 0.21/0.62 Goal 1 (ax63): tuple2(unisex(X, Y), male(X, Y)) = tuple2(true2, true2).
% 0.21/0.62 The goal is true when:
% 0.21/0.62 X = u
% 0.21/0.62 Y = v
% 0.21/0.62
% 0.21/0.62 Proof:
% 0.21/0.62 tuple2(unisex(u, v), male(u, v))
% 0.21/0.62 = { by axiom 12 (ax38) R->L }
% 0.21/0.62 tuple2(fresh48(object(u, v), true2, u, v), male(u, v))
% 0.21/0.62 = { by axiom 13 (ax45) R->L }
% 0.21/0.62 tuple2(fresh48(fresh40(artifact(u, v), true2, u, v), true2, u, v), male(u, v))
% 0.21/0.62 = { by axiom 14 (ax46) R->L }
% 0.21/0.62 tuple2(fresh48(fresh40(fresh39(instrumentality(u, v), true2, u, v), true2, u, v), true2, u, v), male(u, v))
% 0.21/0.62 = { by axiom 15 (ax47) R->L }
% 0.21/0.62 tuple2(fresh48(fresh40(fresh39(fresh38(device(u, v), true2, u, v), true2, u, v), true2, u, v), true2, u, v), male(u, v))
% 0.21/0.62 = { by axiom 17 (ax71) R->L }
% 0.21/0.62 tuple2(fresh48(fresh40(fresh39(fresh38(device(u, fresh(be(u, x5, v, x6), true2, v, x6)), true2, u, v), true2, u, v), true2, u, v), true2, u, v), male(u, v))
% 0.21/0.62 = { by axiom 10 (co1_21) }
% 0.21/0.62 tuple2(fresh48(fresh40(fresh39(fresh38(device(u, fresh(true2, true2, v, x6)), true2, u, v), true2, u, v), true2, u, v), true2, u, v), male(u, v))
% 0.21/0.62 = { by axiom 3 (ax71) }
% 0.21/0.62 tuple2(fresh48(fresh40(fresh39(fresh38(device(u, x6), true2, u, v), true2, u, v), true2, u, v), true2, u, v), male(u, v))
% 0.21/0.62 = { by axiom 16 (ax48) R->L }
% 0.21/0.62 tuple2(fresh48(fresh40(fresh39(fresh38(fresh37(wheel(u, x6), true2, u, x6), true2, u, v), true2, u, v), true2, u, v), true2, u, v), male(u, v))
% 0.21/0.62 = { by axiom 1 (co1_14) }
% 0.21/0.62 tuple2(fresh48(fresh40(fresh39(fresh38(fresh37(true2, true2, u, x6), true2, u, v), true2, u, v), true2, u, v), true2, u, v), male(u, v))
% 0.21/0.62 = { by axiom 9 (ax48) }
% 0.21/0.62 tuple2(fresh48(fresh40(fresh39(fresh38(true2, true2, u, v), true2, u, v), true2, u, v), true2, u, v), male(u, v))
% 0.21/0.62 = { by axiom 8 (ax47) }
% 0.21/0.62 tuple2(fresh48(fresh40(fresh39(true2, true2, u, v), true2, u, v), true2, u, v), male(u, v))
% 0.21/0.62 = { by axiom 7 (ax46) }
% 0.21/0.62 tuple2(fresh48(fresh40(true2, true2, u, v), true2, u, v), male(u, v))
% 0.21/0.62 = { by axiom 6 (ax45) }
% 0.21/0.62 tuple2(fresh48(true2, true2, u, v), male(u, v))
% 0.21/0.62 = { by axiom 5 (ax38) }
% 0.21/0.62 tuple2(true2, male(u, v))
% 0.21/0.62 = { by axiom 11 (ax24) R->L }
% 0.21/0.62 tuple2(true2, fresh63(man(u, v), true2, u, v))
% 0.21/0.62 = { by axiom 2 (co1_13) }
% 0.21/0.62 tuple2(true2, fresh63(true2, true2, u, v))
% 0.21/0.62 = { by axiom 4 (ax24) }
% 0.21/0.62 tuple2(true2, true2)
% 0.21/0.62 % SZS output end Proof
% 0.21/0.62
% 0.21/0.62 RESULT: Theorem (the conjecture is true).
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