TSTP Solution File: NLP145-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NLP145-1 : 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 : n027.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 10:07:39 EDT 2023
% Result : Unsatisfiable 0.21s 0.54s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NLP145-1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n027.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 10:44:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.54 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.54
% 0.21/0.54 % SZS status Unsatisfiable
% 0.21/0.54
% 0.21/0.55 % SZS output start Proof
% 0.21/0.55 Take the following subset of the input axioms:
% 0.21/0.55 fof(clause1, axiom, ![U, V]: ~member(U, V, V)).
% 0.21/0.55 fof(clause11, axiom, ![U2, V2]: (~organism(U2, V2) | living(U2, V2))).
% 0.21/0.55 fof(clause2, axiom, ![U2, V2]: (~fellow(U2, V2) | man(U2, V2))).
% 0.21/0.55 fof(clause3, axiom, ![U2, V2]: (~man(U2, V2) | human_person(U2, V2))).
% 0.21/0.55 fof(clause30, axiom, ![U2, V2]: (~instrumentality(U2, V2) | artifact(U2, V2))).
% 0.21/0.55 fof(clause31, axiom, ![U2, V2]: (~artifact(U2, V2) | object(U2, V2))).
% 0.21/0.55 fof(clause33, axiom, ![U2, V2]: (~object(U2, V2) | nonliving(U2, V2))).
% 0.21/0.55 fof(clause4, axiom, ![U2, V2]: (~human_person(U2, V2) | organism(U2, V2))).
% 0.21/0.55 fof(clause48, axiom, ![U2, V2]: (~frontseat(U2, V2) | seat(U2, V2))).
% 0.21/0.55 fof(clause49, axiom, ![U2, V2]: (~seat(U2, V2) | furniture(U2, V2))).
% 0.21/0.55 fof(clause50, axiom, ![U2, V2]: (~furniture(U2, V2) | instrumentality(U2, V2))).
% 0.21/0.55 fof(clause51, axiom, ![U2, V2]: (~old(U2, V2) | ~young(U2, V2))).
% 0.21/0.55 fof(clause52, axiom, ![U2, V2]: (~male(U2, V2) | ~unisex(U2, V2))).
% 0.21/0.55 fof(clause53, axiom, ![U2, V2]: (~general(U2, V2) | ~specific(U2, V2))).
% 0.21/0.55 fof(clause54, axiom, ![U2, V2]: (~multiple(U2, V2) | ~singleton(U2, V2))).
% 0.21/0.55 fof(clause55, axiom, ![U2, V2]: (~living(U2, V2) | ~nonliving(U2, V2))).
% 0.21/0.55 fof(clause56, axiom, ![U2, V2]: (~human(U2, V2) | ~nonhuman(U2, V2))).
% 0.21/0.55 fof(clause57, axiom, ![U2, V2]: (~nonexistent(U2, V2) | ~existent(U2, V2))).
% 0.21/0.55 fof(clause58, axiom, ![U2, V2]: (~nonliving(U2, V2) | ~animate(U2, V2))).
% 0.21/0.55 fof(clause59, axiom, ![W, X, U2, V2]: (~be(U2, V2, W, X) | W=X)).
% 0.21/0.55 fof(clause60, axiom, ![U2, V2]: (~two(U2, V2) | member(U2, skf10(V2, U2), V2))).
% 0.21/0.55 fof(clause62, axiom, ![U2, V2]: (skf10(U2, V2)!=skf8(U2, V2) | ~two(V2, U2))).
% 0.21/0.55 fof(clause74, negated_conjecture, two(skc7, skc8)).
% 0.21/0.55 fof(clause88, negated_conjecture, ![U2]: (~member(skc7, U2, skc8) | fellow(skc7, U2))).
% 0.21/0.55 fof(clause89, negated_conjecture, ![U2, V2]: (~member(skc7, U2, skc8) | frontseat(skc7, skf5(V2)))).
% 0.21/0.55 fof(clause92, negated_conjecture, ![U2]: (~member(skc7, U2, skc8) | be(skc7, skf6(U2), U2, skf5(U2)))).
% 0.21/0.55
% 0.21/0.55 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.55 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.55 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.55 fresh(y, y, x1...xn) = u
% 0.21/0.55 C => fresh(s, t, x1...xn) = v
% 0.21/0.55 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.55 variables of u and v.
% 0.21/0.55 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.55 input problem has no model of domain size 1).
% 0.21/0.55
% 0.21/0.55 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.55
% 0.21/0.55 Axiom 1 (clause74): two(skc7, skc8) = true2.
% 0.21/0.55 Axiom 2 (clause88): fresh7(X, X, Y) = true2.
% 0.21/0.55 Axiom 3 (clause89): fresh6(X, X, Y) = true2.
% 0.21/0.55 Axiom 4 (clause92): fresh2(X, X, Y) = true2.
% 0.21/0.55 Axiom 5 (clause59): fresh(X, X, Y, Z) = Z.
% 0.21/0.55 Axiom 6 (clause11): fresh58(X, X, Y, Z) = true2.
% 0.21/0.55 Axiom 7 (clause2): fresh48(X, X, Y, Z) = true2.
% 0.21/0.55 Axiom 8 (clause3): fresh37(X, X, Y, Z) = true2.
% 0.21/0.55 Axiom 9 (clause30): fresh36(X, X, Y, Z) = true2.
% 0.21/0.55 Axiom 10 (clause31): fresh35(X, X, Y, Z) = true2.
% 0.21/0.55 Axiom 11 (clause33): fresh33(X, X, Y, Z) = true2.
% 0.21/0.55 Axiom 12 (clause4): fresh26(X, X, Y, Z) = true2.
% 0.21/0.55 Axiom 13 (clause48): fresh17(X, X, Y, Z) = true2.
% 0.21/0.55 Axiom 14 (clause49): fresh16(X, X, Y, Z) = true2.
% 0.21/0.55 Axiom 15 (clause50): fresh14(X, X, Y, Z) = true2.
% 0.21/0.55 Axiom 16 (clause60): fresh12(X, X, Y, Z) = true2.
% 0.21/0.55 Axiom 17 (clause11): fresh58(organism(X, Y), true2, X, Y) = living(X, Y).
% 0.21/0.55 Axiom 18 (clause2): fresh48(fellow(X, Y), true2, X, Y) = man(X, Y).
% 0.21/0.55 Axiom 19 (clause3): fresh37(man(X, Y), true2, X, Y) = human_person(X, Y).
% 0.21/0.55 Axiom 20 (clause30): fresh36(instrumentality(X, Y), true2, X, Y) = artifact(X, Y).
% 0.21/0.55 Axiom 21 (clause31): fresh35(artifact(X, Y), true2, X, Y) = object(X, Y).
% 0.21/0.55 Axiom 22 (clause33): fresh33(object(X, Y), true2, X, Y) = nonliving(X, Y).
% 0.21/0.55 Axiom 23 (clause4): fresh26(human_person(X, Y), true2, X, Y) = organism(X, Y).
% 0.21/0.55 Axiom 24 (clause48): fresh17(frontseat(X, Y), true2, X, Y) = seat(X, Y).
% 0.21/0.55 Axiom 25 (clause49): fresh16(seat(X, Y), true2, X, Y) = furniture(X, Y).
% 0.21/0.55 Axiom 26 (clause50): fresh14(furniture(X, Y), true2, X, Y) = instrumentality(X, Y).
% 0.21/0.55 Axiom 27 (clause60): fresh12(two(X, Y), true2, X, Y) = member(X, skf10(Y, X), Y).
% 0.21/0.55 Axiom 28 (clause88): fresh7(member(skc7, X, skc8), true2, X) = fellow(skc7, X).
% 0.21/0.55 Axiom 29 (clause89): fresh6(member(skc7, X, skc8), true2, Y) = frontseat(skc7, skf5(Y)).
% 0.21/0.55 Axiom 30 (clause92): fresh2(member(skc7, X, skc8), true2, X) = be(skc7, skf6(X), X, skf5(X)).
% 0.21/0.55 Axiom 31 (clause59): fresh(be(X, Y, Z, W), true2, Z, W) = Z.
% 0.21/0.55
% 0.21/0.55 Lemma 32: member(skc7, skf10(skc8, skc7), skc8) = true2.
% 0.21/0.55 Proof:
% 0.21/0.55 member(skc7, skf10(skc8, skc7), skc8)
% 0.21/0.55 = { by axiom 27 (clause60) R->L }
% 0.21/0.55 fresh12(two(skc7, skc8), true2, skc7, skc8)
% 0.21/0.55 = { by axiom 1 (clause74) }
% 0.21/0.55 fresh12(true2, true2, skc7, skc8)
% 0.21/0.55 = { by axiom 16 (clause60) }
% 0.21/0.56 true2
% 0.21/0.56
% 0.21/0.56 Goal 1 (clause55): tuple(living(X, Y), nonliving(X, Y)) = tuple(true2, true2).
% 0.21/0.56 The goal is true when:
% 0.21/0.56 X = skc7
% 0.21/0.56 Y = skf10(skc8, skc7)
% 0.21/0.56
% 0.21/0.56 Proof:
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), nonliving(skc7, skf10(skc8, skc7)))
% 0.21/0.56 = { by axiom 31 (clause59) R->L }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), nonliving(skc7, fresh(be(skc7, skf6(skf10(skc8, skc7)), skf10(skc8, skc7), skf5(skf10(skc8, skc7))), true2, skf10(skc8, skc7), skf5(skf10(skc8, skc7)))))
% 0.21/0.56 = { by axiom 30 (clause92) R->L }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), nonliving(skc7, fresh(fresh2(member(skc7, skf10(skc8, skc7), skc8), true2, skf10(skc8, skc7)), true2, skf10(skc8, skc7), skf5(skf10(skc8, skc7)))))
% 0.21/0.56 = { by lemma 32 }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), nonliving(skc7, fresh(fresh2(true2, true2, skf10(skc8, skc7)), true2, skf10(skc8, skc7), skf5(skf10(skc8, skc7)))))
% 0.21/0.56 = { by axiom 4 (clause92) }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), nonliving(skc7, fresh(true2, true2, skf10(skc8, skc7), skf5(skf10(skc8, skc7)))))
% 0.21/0.56 = { by axiom 5 (clause59) }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), nonliving(skc7, skf5(skf10(skc8, skc7))))
% 0.21/0.56 = { by axiom 22 (clause33) R->L }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), fresh33(object(skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))))
% 0.21/0.56 = { by axiom 21 (clause31) R->L }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), fresh33(fresh35(artifact(skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))))
% 0.21/0.56 = { by axiom 20 (clause30) R->L }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), fresh33(fresh35(fresh36(instrumentality(skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))))
% 0.21/0.56 = { by axiom 26 (clause50) R->L }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), fresh33(fresh35(fresh36(fresh14(furniture(skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))))
% 0.21/0.56 = { by axiom 25 (clause49) R->L }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), fresh33(fresh35(fresh36(fresh14(fresh16(seat(skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))))
% 0.21/0.56 = { by axiom 24 (clause48) R->L }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), fresh33(fresh35(fresh36(fresh14(fresh16(fresh17(frontseat(skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))))
% 0.21/0.56 = { by axiom 29 (clause89) R->L }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), fresh33(fresh35(fresh36(fresh14(fresh16(fresh17(fresh6(member(skc7, skf10(skc8, skc7), skc8), true2, skf10(skc8, skc7)), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))))
% 0.21/0.56 = { by lemma 32 }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), fresh33(fresh35(fresh36(fresh14(fresh16(fresh17(fresh6(true2, true2, skf10(skc8, skc7)), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))))
% 0.21/0.56 = { by axiom 3 (clause89) }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), fresh33(fresh35(fresh36(fresh14(fresh16(fresh17(true2, true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))))
% 0.21/0.56 = { by axiom 13 (clause48) }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), fresh33(fresh35(fresh36(fresh14(fresh16(true2, true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))))
% 0.21/0.56 = { by axiom 14 (clause49) }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), fresh33(fresh35(fresh36(fresh14(true2, true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))))
% 0.21/0.56 = { by axiom 15 (clause50) }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), fresh33(fresh35(fresh36(true2, true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))))
% 0.21/0.56 = { by axiom 9 (clause30) }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), fresh33(fresh35(true2, true2, skc7, skf5(skf10(skc8, skc7))), true2, skc7, skf5(skf10(skc8, skc7))))
% 0.21/0.56 = { by axiom 10 (clause31) }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), fresh33(true2, true2, skc7, skf5(skf10(skc8, skc7))))
% 0.21/0.56 = { by axiom 11 (clause33) }
% 0.21/0.56 tuple(living(skc7, skf10(skc8, skc7)), true2)
% 0.21/0.56 = { by axiom 17 (clause11) R->L }
% 0.21/0.56 tuple(fresh58(organism(skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2)
% 0.21/0.56 = { by axiom 23 (clause4) R->L }
% 0.21/0.56 tuple(fresh58(fresh26(human_person(skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2)
% 0.21/0.56 = { by axiom 19 (clause3) R->L }
% 0.21/0.56 tuple(fresh58(fresh26(fresh37(man(skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2)
% 0.21/0.56 = { by axiom 18 (clause2) R->L }
% 0.21/0.56 tuple(fresh58(fresh26(fresh37(fresh48(fellow(skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2)
% 0.21/0.56 = { by axiom 28 (clause88) R->L }
% 0.21/0.56 tuple(fresh58(fresh26(fresh37(fresh48(fresh7(member(skc7, skf10(skc8, skc7), skc8), true2, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2)
% 0.21/0.56 = { by lemma 32 }
% 0.21/0.56 tuple(fresh58(fresh26(fresh37(fresh48(fresh7(true2, true2, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2)
% 0.21/0.56 = { by axiom 2 (clause88) }
% 0.21/0.56 tuple(fresh58(fresh26(fresh37(fresh48(true2, true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2)
% 0.21/0.56 = { by axiom 7 (clause2) }
% 0.21/0.56 tuple(fresh58(fresh26(fresh37(true2, true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2)
% 0.21/0.56 = { by axiom 8 (clause3) }
% 0.21/0.56 tuple(fresh58(fresh26(true2, true2, skc7, skf10(skc8, skc7)), true2, skc7, skf10(skc8, skc7)), true2)
% 0.21/0.56 = { by axiom 12 (clause4) }
% 0.21/0.56 tuple(fresh58(true2, true2, skc7, skf10(skc8, skc7)), true2)
% 0.21/0.56 = { by axiom 6 (clause11) }
% 0.21/0.56 tuple(true2, true2)
% 0.21/0.56 % SZS output end Proof
% 0.21/0.56
% 0.21/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
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