TSTP Solution File: NLP204-1 by Twee---2.4.2
View Problem
- 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 : n028.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 : Unsatisfiable 0.20s 0.56s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NLP204-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.35 % Computer : n028.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 24 11:04:19 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.56 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.56
% 0.20/0.56 % SZS status Unsatisfiable
% 0.20/0.56
% 0.20/0.57 % SZS output start Proof
% 0.20/0.57 Take the following subset of the input axioms:
% 0.20/0.57 fof(clause1, axiom, ![U, V]: ~member(U, V, V)).
% 0.20/0.57 fof(clause10, axiom, ![U2, V2]: (~wheel(U2, V2) | device(U2, V2))).
% 0.20/0.57 fof(clause106, negated_conjecture, be(skc12, skc14, skc16, skc13)).
% 0.20/0.57 fof(clause11, axiom, ![U2, V2]: (~device(U2, V2) | instrumentality(U2, V2))).
% 0.20/0.57 fof(clause12, axiom, ![U2, V2]: (~instrumentality(U2, V2) | artifact(U2, V2))).
% 0.20/0.57 fof(clause13, axiom, ![U2, V2]: (~artifact(U2, V2) | object(U2, V2))).
% 0.20/0.57 fof(clause18, axiom, ![U2, V2]: (~object(U2, V2) | nonliving(U2, V2))).
% 0.20/0.57 fof(clause27, axiom, ![U2, V2]: (~man(U2, V2) | human_person(U2, V2))).
% 0.20/0.57 fof(clause28, axiom, ![U2, V2]: (~human_person(U2, V2) | organism(U2, V2))).
% 0.20/0.57 fof(clause31, axiom, ![U2, V2]: (~organism(U2, V2) | living(U2, V2))).
% 0.20/0.57 fof(clause58, axiom, ![U2, V2]: (~old(U2, V2) | ~young(U2, V2))).
% 0.20/0.57 fof(clause59, axiom, ![U2, V2]: (~black(U2, V2) | ~white(U2, V2))).
% 0.20/0.57 fof(clause60, axiom, ![U2, V2]: (~male(U2, V2) | ~unisex(U2, V2))).
% 0.20/0.57 fof(clause61, axiom, ![U2, V2]: (~general(U2, V2) | ~specific(U2, V2))).
% 0.20/0.57 fof(clause62, axiom, ![U2, V2]: (~multiple(U2, V2) | ~singleton(U2, V2))).
% 0.20/0.57 fof(clause63, axiom, ![U2, V2]: (~living(U2, V2) | ~nonliving(U2, V2))).
% 0.20/0.57 fof(clause64, axiom, ![U2, V2]: (~human(U2, V2) | ~nonhuman(U2, V2))).
% 0.20/0.57 fof(clause65, axiom, ![U2, V2]: (~nonexistent(U2, V2) | ~existent(U2, V2))).
% 0.20/0.57 fof(clause66, axiom, ![U2, V2]: (~nonliving(U2, V2) | ~animate(U2, V2))).
% 0.20/0.57 fof(clause67, axiom, ![W, X, U2, V2]: (~be(U2, V2, W, X) | W=X)).
% 0.20/0.57 fof(clause70, axiom, ![U2, V2]: (skf12(U2, V2)!=skf10(U2, V2) | ~two(V2, U2))).
% 0.20/0.57 fof(clause71, axiom, ![U2, V2, W2]: (~nonreflexive(U2, V2) | (~patient(U2, V2, W2) | ~agent(U2, V2, W2)))).
% 0.20/0.57 fof(clause87, negated_conjecture, man(skc12, skc16)).
% 0.20/0.57 fof(clause91, negated_conjecture, wheel(skc12, skc13)).
% 0.20/0.57
% 0.20/0.57 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.57 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.57 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.57 fresh(y, y, x1...xn) = u
% 0.20/0.57 C => fresh(s, t, x1...xn) = v
% 0.20/0.57 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.57 variables of u and v.
% 0.20/0.57 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.57 input problem has no model of domain size 1).
% 0.20/0.57
% 0.20/0.57 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.57
% 0.20/0.57 Axiom 1 (clause87): man(skc12, skc16) = true2.
% 0.20/0.57 Axiom 2 (clause91): wheel(skc12, skc13) = true2.
% 0.20/0.57 Axiom 3 (clause106): be(skc12, skc14, skc16, skc13) = true2.
% 0.20/0.57 Axiom 4 (clause67): fresh(X, X, Y, Z) = Z.
% 0.20/0.57 Axiom 5 (clause10): fresh78(X, X, Y, Z) = true2.
% 0.20/0.57 Axiom 6 (clause11): fresh75(X, X, Y, Z) = true2.
% 0.20/0.57 Axiom 7 (clause12): fresh59(X, X, Y, Z) = true2.
% 0.20/0.57 Axiom 8 (clause13): fresh56(X, X, Y, Z) = true2.
% 0.20/0.57 Axiom 9 (clause18): fresh51(X, X, Y, Z) = true2.
% 0.20/0.57 Axiom 10 (clause27): fresh41(X, X, Y, Z) = true2.
% 0.20/0.57 Axiom 11 (clause28): fresh40(X, X, Y, Z) = true2.
% 0.20/0.57 Axiom 12 (clause31): fresh36(X, X, Y, Z) = true2.
% 0.20/0.57 Axiom 13 (clause10): fresh78(wheel(X, Y), true2, X, Y) = device(X, Y).
% 0.20/0.57 Axiom 14 (clause11): fresh75(device(X, Y), true2, X, Y) = instrumentality(X, Y).
% 0.20/0.57 Axiom 15 (clause12): fresh59(instrumentality(X, Y), true2, X, Y) = artifact(X, Y).
% 0.20/0.57 Axiom 16 (clause13): fresh56(artifact(X, Y), true2, X, Y) = object(X, Y).
% 0.20/0.57 Axiom 17 (clause18): fresh51(object(X, Y), true2, X, Y) = nonliving(X, Y).
% 0.20/0.57 Axiom 18 (clause27): fresh41(man(X, Y), true2, X, Y) = human_person(X, Y).
% 0.20/0.57 Axiom 19 (clause28): fresh40(human_person(X, Y), true2, X, Y) = organism(X, Y).
% 0.20/0.57 Axiom 20 (clause31): fresh36(organism(X, Y), true2, X, Y) = living(X, Y).
% 0.20/0.57 Axiom 21 (clause67): fresh(be(X, Y, Z, W), true2, Z, W) = Z.
% 0.20/0.57
% 0.20/0.57 Goal 1 (clause63): tuple2(nonliving(X, Y), living(X, Y)) = tuple2(true2, true2).
% 0.20/0.57 The goal is true when:
% 0.20/0.57 X = skc12
% 0.20/0.57 Y = skc13
% 0.20/0.57
% 0.20/0.57 Proof:
% 0.20/0.57 tuple2(nonliving(skc12, skc13), living(skc12, skc13))
% 0.20/0.57 = { by axiom 17 (clause18) R->L }
% 0.20/0.57 tuple2(fresh51(object(skc12, skc13), true2, skc12, skc13), living(skc12, skc13))
% 0.20/0.57 = { by axiom 16 (clause13) R->L }
% 0.20/0.57 tuple2(fresh51(fresh56(artifact(skc12, skc13), true2, skc12, skc13), true2, skc12, skc13), living(skc12, skc13))
% 0.20/0.57 = { by axiom 15 (clause12) R->L }
% 0.20/0.57 tuple2(fresh51(fresh56(fresh59(instrumentality(skc12, skc13), true2, skc12, skc13), true2, skc12, skc13), true2, skc12, skc13), living(skc12, skc13))
% 0.20/0.57 = { by axiom 14 (clause11) R->L }
% 0.20/0.57 tuple2(fresh51(fresh56(fresh59(fresh75(device(skc12, skc13), true2, skc12, skc13), true2, skc12, skc13), true2, skc12, skc13), true2, skc12, skc13), living(skc12, skc13))
% 0.20/0.57 = { by axiom 13 (clause10) R->L }
% 0.20/0.57 tuple2(fresh51(fresh56(fresh59(fresh75(fresh78(wheel(skc12, skc13), true2, skc12, skc13), true2, skc12, skc13), true2, skc12, skc13), true2, skc12, skc13), true2, skc12, skc13), living(skc12, skc13))
% 0.20/0.57 = { by axiom 2 (clause91) }
% 0.20/0.57 tuple2(fresh51(fresh56(fresh59(fresh75(fresh78(true2, true2, skc12, skc13), true2, skc12, skc13), true2, skc12, skc13), true2, skc12, skc13), true2, skc12, skc13), living(skc12, skc13))
% 0.20/0.57 = { by axiom 5 (clause10) }
% 0.20/0.57 tuple2(fresh51(fresh56(fresh59(fresh75(true2, true2, skc12, skc13), true2, skc12, skc13), true2, skc12, skc13), true2, skc12, skc13), living(skc12, skc13))
% 0.20/0.57 = { by axiom 6 (clause11) }
% 0.20/0.57 tuple2(fresh51(fresh56(fresh59(true2, true2, skc12, skc13), true2, skc12, skc13), true2, skc12, skc13), living(skc12, skc13))
% 0.20/0.57 = { by axiom 7 (clause12) }
% 0.20/0.57 tuple2(fresh51(fresh56(true2, true2, skc12, skc13), true2, skc12, skc13), living(skc12, skc13))
% 0.20/0.57 = { by axiom 8 (clause13) }
% 0.20/0.57 tuple2(fresh51(true2, true2, skc12, skc13), living(skc12, skc13))
% 0.20/0.57 = { by axiom 9 (clause18) }
% 0.20/0.57 tuple2(true2, living(skc12, skc13))
% 0.20/0.57 = { by axiom 20 (clause31) R->L }
% 0.20/0.57 tuple2(true2, fresh36(organism(skc12, skc13), true2, skc12, skc13))
% 0.20/0.57 = { by axiom 19 (clause28) R->L }
% 0.20/0.57 tuple2(true2, fresh36(fresh40(human_person(skc12, skc13), true2, skc12, skc13), true2, skc12, skc13))
% 0.20/0.57 = { by axiom 4 (clause67) R->L }
% 0.20/0.57 tuple2(true2, fresh36(fresh40(human_person(skc12, fresh(true2, true2, skc16, skc13)), true2, skc12, skc13), true2, skc12, skc13))
% 0.20/0.57 = { by axiom 3 (clause106) R->L }
% 0.20/0.57 tuple2(true2, fresh36(fresh40(human_person(skc12, fresh(be(skc12, skc14, skc16, skc13), true2, skc16, skc13)), true2, skc12, skc13), true2, skc12, skc13))
% 0.20/0.57 = { by axiom 21 (clause67) }
% 0.20/0.57 tuple2(true2, fresh36(fresh40(human_person(skc12, skc16), true2, skc12, skc13), true2, skc12, skc13))
% 0.20/0.57 = { by axiom 18 (clause27) R->L }
% 0.20/0.57 tuple2(true2, fresh36(fresh40(fresh41(man(skc12, skc16), true2, skc12, skc16), true2, skc12, skc13), true2, skc12, skc13))
% 0.20/0.58 = { by axiom 1 (clause87) }
% 0.20/0.58 tuple2(true2, fresh36(fresh40(fresh41(true2, true2, skc12, skc16), true2, skc12, skc13), true2, skc12, skc13))
% 0.20/0.58 = { by axiom 10 (clause27) }
% 0.20/0.58 tuple2(true2, fresh36(fresh40(true2, true2, skc12, skc13), true2, skc12, skc13))
% 0.20/0.58 = { by axiom 11 (clause28) }
% 0.20/0.58 tuple2(true2, fresh36(true2, true2, skc12, skc13))
% 0.20/0.58 = { by axiom 12 (clause31) }
% 0.20/0.58 tuple2(true2, true2)
% 0.20/0.58 % SZS output end Proof
% 0.20/0.58
% 0.20/0.58 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------