TSTP Solution File: NLP143+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NLP143+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 : n002.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 10:07:38 EDT 2023
% Result : Theorem 0.18s 0.54s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NLP143+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.13 % 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 : n002.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 11:22:46 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.54 Command-line arguments: --ground-connectedness --complete-subsets
% 0.18/0.54
% 0.18/0.54 % SZS status Theorem
% 0.18/0.54
% 0.18/0.55 % SZS output start Proof
% 0.18/0.55 Take the following subset of the input axioms:
% 0.18/0.55 fof(ax1, axiom, ![U, V]: (furniture(U, V) => instrumentality(U, V))).
% 0.18/0.55 fof(ax16, axiom, ![V2, U2]: (object(U2, V2) => unisex(U2, V2))).
% 0.18/0.55 fof(ax2, axiom, ![V2, U2]: (seat(U2, V2) => furniture(U2, V2))).
% 0.18/0.55 fof(ax20, axiom, ![V2, U2]: (artifact(U2, V2) => object(U2, V2))).
% 0.18/0.56 fof(ax21, axiom, ![V2, U2]: (instrumentality(U2, V2) => artifact(U2, V2))).
% 0.18/0.56 fof(ax3, axiom, ![V2, U2]: (frontseat(U2, V2) => seat(U2, V2))).
% 0.18/0.56 fof(ax37, axiom, ![V2, U2]: (man(U2, V2) => male(U2, V2))).
% 0.18/0.56 fof(ax49, axiom, ![V2, U2]: (fellow(U2, V2) => man(U2, V2))).
% 0.18/0.56 fof(ax50, axiom, ![V2, U2]: (animate(U2, V2) => ~nonliving(U2, V2))).
% 0.18/0.56 fof(ax51, axiom, ![V2, U2]: (existent(U2, V2) => ~nonexistent(U2, V2))).
% 0.18/0.56 fof(ax52, axiom, ![V2, U2]: (nonhuman(U2, V2) => ~human(U2, V2))).
% 0.18/0.56 fof(ax53, axiom, ![V2, U2]: (nonliving(U2, V2) => ~living(U2, V2))).
% 0.18/0.56 fof(ax54, axiom, ![V2, U2]: (singleton(U2, V2) => ~multiple(U2, V2))).
% 0.18/0.56 fof(ax55, axiom, ![V2, U2]: (specific(U2, V2) => ~general(U2, V2))).
% 0.18/0.56 fof(ax56, axiom, ![V2, U2]: (unisex(U2, V2) => ~male(U2, V2))).
% 0.18/0.56 fof(ax57, axiom, ![V2, U2]: (young(U2, V2) => ~old(U2, V2))).
% 0.18/0.56 fof(ax59, axiom, ![W, X, V2, U2]: (be(U2, V2, W, X) => W=X)).
% 0.18/0.56 fof(ax60, axiom, ![V2, U2]: (two(U2, V2) <=> ?[W2]: (member(U2, W2, V2) & ?[X5]: (member(U2, X5, V2) & (X5!=W2 & ![Y]: (member(U2, Y, V2) => (Y=X5 | Y=W2))))))).
% 0.18/0.56 fof(ax61, axiom, ![U2]: ~?[V2]: member(U2, V2, V2)).
% 0.18/0.56 fof(co1, conjecture, ~?[U2]: (actual_world(U2) & ?[Z, V2, W2, X5, Y2]: (of(U2, V2, W2) & (city(U2, W2) & (hollywood_placename(U2, V2) & (placename(U2, V2) & (chevy(U2, W2) & (white(U2, W2) & (dirty(U2, W2) & (old(U2, W2) & (street(U2, X5) & (lonely(U2, X5) & (event(U2, Y2) & (agent(U2, Y2, W2) & (present(U2, Y2) & (barrel(U2, Y2) & (down(U2, Y2, X5) & (in(U2, Y2, W2) & (![X1]: (member(U2, X1, Z) => ?[X2, X3]: (frontseat(U2, X3) & (state(U2, X2) & (be(U2, X2, X1, X3) & in(U2, X3, X3))))) & (two(U2, Z) & (group(U2, Z) & ![X4]: (member(U2, X4, Z) => (fellow(U2, X4) & young(U2, X4)))))))))))))))))))))))).
% 0.18/0.56
% 0.18/0.56 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.56 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.56 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.56 fresh(y, y, x1...xn) = u
% 0.18/0.56 C => fresh(s, t, x1...xn) = v
% 0.18/0.56 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.56 variables of u and v.
% 0.18/0.56 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.56 input problem has no model of domain size 1).
% 0.18/0.56
% 0.18/0.56 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.56
% 0.18/0.56 Axiom 1 (co1_7): two(u, z) = true2.
% 0.18/0.56 Axiom 2 (co1_19): fresh7(X, X, Y) = true2.
% 0.18/0.56 Axiom 3 (co1_21): fresh5(X, X, Y) = true2.
% 0.18/0.56 Axiom 4 (co1_23): fresh3(X, X, Y) = true2.
% 0.18/0.56 Axiom 5 (ax59): fresh(X, X, Y, Z) = Z.
% 0.18/0.56 Axiom 6 (ax1): fresh57(X, X, Y, Z) = true2.
% 0.18/0.56 Axiom 7 (ax16): fresh51(X, X, Y, Z) = true2.
% 0.18/0.56 Axiom 8 (ax2): fresh47(X, X, Y, Z) = true2.
% 0.18/0.56 Axiom 9 (ax20): fresh46(X, X, Y, Z) = true2.
% 0.18/0.56 Axiom 10 (ax21): fresh45(X, X, Y, Z) = true2.
% 0.18/0.56 Axiom 11 (ax3): fresh36(X, X, Y, Z) = true2.
% 0.18/0.56 Axiom 12 (ax37): fresh28(X, X, Y, Z) = true2.
% 0.18/0.56 Axiom 13 (ax49): fresh15(X, X, Y, Z) = true2.
% 0.18/0.56 Axiom 14 (ax60_3): fresh12(X, X, Y, Z) = true2.
% 0.18/0.56 Axiom 15 (ax1): fresh57(furniture(X, Y), true2, X, Y) = instrumentality(X, Y).
% 0.18/0.56 Axiom 16 (ax16): fresh51(object(X, Y), true2, X, Y) = unisex(X, Y).
% 0.18/0.56 Axiom 17 (ax2): fresh47(seat(X, Y), true2, X, Y) = furniture(X, Y).
% 0.18/0.56 Axiom 18 (ax20): fresh46(artifact(X, Y), true2, X, Y) = object(X, Y).
% 0.18/0.56 Axiom 19 (ax21): fresh45(instrumentality(X, Y), true2, X, Y) = artifact(X, Y).
% 0.18/0.56 Axiom 20 (ax3): fresh36(frontseat(X, Y), true2, X, Y) = seat(X, Y).
% 0.18/0.56 Axiom 21 (ax37): fresh28(man(X, Y), true2, X, Y) = male(X, Y).
% 0.18/0.56 Axiom 22 (ax49): fresh15(fellow(X, Y), true2, X, Y) = man(X, Y).
% 0.18/0.56 Axiom 23 (ax60_3): fresh12(two(X, Y), true2, X, Y) = member(X, w2(X, Y), Y).
% 0.18/0.56 Axiom 24 (co1_19): fresh7(member(u, X, z), true2, X) = frontseat(u, x3(X)).
% 0.18/0.56 Axiom 25 (co1_21): fresh5(member(u, X, z), true2, X) = be(u, x2(X), X, x3(X)).
% 0.18/0.56 Axiom 26 (co1_23): fresh3(member(u, X, z), true2, X) = fellow(u, X).
% 0.18/0.56 Axiom 27 (ax59): fresh(be(X, Y, Z, W), true2, Z, W) = Z.
% 0.18/0.56
% 0.18/0.56 Lemma 28: member(u, w2(u, z), z) = true2.
% 0.18/0.56 Proof:
% 0.18/0.56 member(u, w2(u, z), z)
% 0.18/0.56 = { by axiom 23 (ax60_3) R->L }
% 0.18/0.56 fresh12(two(u, z), true2, u, z)
% 0.18/0.56 = { by axiom 1 (co1_7) }
% 0.18/0.56 fresh12(true2, true2, u, z)
% 0.18/0.56 = { by axiom 14 (ax60_3) }
% 0.18/0.56 true2
% 0.18/0.56
% 0.18/0.56 Goal 1 (ax56): tuple(unisex(X, Y), male(X, Y)) = tuple(true2, true2).
% 0.18/0.56 The goal is true when:
% 0.18/0.56 X = u
% 0.18/0.56 Y = w2(u, z)
% 0.18/0.56
% 0.18/0.56 Proof:
% 0.18/0.56 tuple(unisex(u, w2(u, z)), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 27 (ax59) R->L }
% 0.18/0.56 tuple(unisex(u, fresh(be(u, x2(w2(u, z)), w2(u, z), x3(w2(u, z))), true2, w2(u, z), x3(w2(u, z)))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 25 (co1_21) R->L }
% 0.18/0.56 tuple(unisex(u, fresh(fresh5(member(u, w2(u, z), z), true2, w2(u, z)), true2, w2(u, z), x3(w2(u, z)))), male(u, w2(u, z)))
% 0.18/0.56 = { by lemma 28 }
% 0.18/0.56 tuple(unisex(u, fresh(fresh5(true2, true2, w2(u, z)), true2, w2(u, z), x3(w2(u, z)))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 3 (co1_21) }
% 0.18/0.56 tuple(unisex(u, fresh(true2, true2, w2(u, z), x3(w2(u, z)))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 5 (ax59) }
% 0.18/0.56 tuple(unisex(u, x3(w2(u, z))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 16 (ax16) R->L }
% 0.18/0.56 tuple(fresh51(object(u, x3(w2(u, z))), true2, u, x3(w2(u, z))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 18 (ax20) R->L }
% 0.18/0.56 tuple(fresh51(fresh46(artifact(u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 19 (ax21) R->L }
% 0.18/0.56 tuple(fresh51(fresh46(fresh45(instrumentality(u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 15 (ax1) R->L }
% 0.18/0.56 tuple(fresh51(fresh46(fresh45(fresh57(furniture(u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 17 (ax2) R->L }
% 0.18/0.56 tuple(fresh51(fresh46(fresh45(fresh57(fresh47(seat(u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 20 (ax3) R->L }
% 0.18/0.56 tuple(fresh51(fresh46(fresh45(fresh57(fresh47(fresh36(frontseat(u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 24 (co1_19) R->L }
% 0.18/0.56 tuple(fresh51(fresh46(fresh45(fresh57(fresh47(fresh36(fresh7(member(u, w2(u, z), z), true2, w2(u, z)), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), male(u, w2(u, z)))
% 0.18/0.56 = { by lemma 28 }
% 0.18/0.56 tuple(fresh51(fresh46(fresh45(fresh57(fresh47(fresh36(fresh7(true2, true2, w2(u, z)), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 2 (co1_19) }
% 0.18/0.56 tuple(fresh51(fresh46(fresh45(fresh57(fresh47(fresh36(true2, true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 11 (ax3) }
% 0.18/0.56 tuple(fresh51(fresh46(fresh45(fresh57(fresh47(true2, true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 8 (ax2) }
% 0.18/0.56 tuple(fresh51(fresh46(fresh45(fresh57(true2, true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 6 (ax1) }
% 0.18/0.56 tuple(fresh51(fresh46(fresh45(true2, true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 10 (ax21) }
% 0.18/0.56 tuple(fresh51(fresh46(true2, true2, u, x3(w2(u, z))), true2, u, x3(w2(u, z))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 9 (ax20) }
% 0.18/0.56 tuple(fresh51(true2, true2, u, x3(w2(u, z))), male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 7 (ax16) }
% 0.18/0.56 tuple(true2, male(u, w2(u, z)))
% 0.18/0.56 = { by axiom 21 (ax37) R->L }
% 0.18/0.56 tuple(true2, fresh28(man(u, w2(u, z)), true2, u, w2(u, z)))
% 0.18/0.56 = { by axiom 22 (ax49) R->L }
% 0.18/0.56 tuple(true2, fresh28(fresh15(fellow(u, w2(u, z)), true2, u, w2(u, z)), true2, u, w2(u, z)))
% 0.18/0.56 = { by axiom 26 (co1_23) R->L }
% 0.18/0.56 tuple(true2, fresh28(fresh15(fresh3(member(u, w2(u, z), z), true2, w2(u, z)), true2, u, w2(u, z)), true2, u, w2(u, z)))
% 0.18/0.56 = { by lemma 28 }
% 0.18/0.56 tuple(true2, fresh28(fresh15(fresh3(true2, true2, w2(u, z)), true2, u, w2(u, z)), true2, u, w2(u, z)))
% 0.18/0.56 = { by axiom 4 (co1_23) }
% 0.18/0.56 tuple(true2, fresh28(fresh15(true2, true2, u, w2(u, z)), true2, u, w2(u, z)))
% 0.18/0.56 = { by axiom 13 (ax49) }
% 0.18/0.56 tuple(true2, fresh28(true2, true2, u, w2(u, z)))
% 0.18/0.56 = { by axiom 12 (ax37) }
% 0.18/0.56 tuple(true2, true2)
% 0.18/0.56 % SZS output end Proof
% 0.18/0.56
% 0.18/0.56 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------