TSTP Solution File: PUZ130+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ130+1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n021.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 13:24:21 EDT 2023
% Result : Theorem 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : PUZ130+1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n021.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 : Sat Aug 26 22:20:12 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.22/0.41 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.22/0.41
% 0.22/0.41 % SZS status Theorem
% 0.22/0.41
% 0.22/0.42 % SZS output start Proof
% 0.22/0.42 Take the following subset of the input axioms:
% 0.22/0.42 fof(cat_chase_axiom, axiom, ![X, Y]: ((cat(X) & dog(Y)) => (chased(Y, X) => hates(owner_of(X), owner_of(Y))))).
% 0.22/0.42 fof(cat_pet_type, axiom, ![A2]: (cat(A2) => pet(A2))).
% 0.22/0.42 fof(dog_pet_type, axiom, ![A2_2]: (dog(A2_2) => pet(A2_2))).
% 0.22/0.42 fof(garfield_type, axiom, cat(garfield)).
% 0.22/0.42 fof(jon_conjecture, conjecture, hates(jon, jon)).
% 0.22/0.42 fof(jon_g_owner_axiom, axiom, owner(jon, garfield)).
% 0.22/0.42 fof(jon_o_owner_axiom, axiom, owner(jon, odie)).
% 0.22/0.42 fof(jon_type, axiom, human(jon)).
% 0.22/0.42 fof(odie_chase_axiom, axiom, chased(odie, garfield)).
% 0.22/0.42 fof(odie_type, axiom, dog(odie)).
% 0.22/0.42 fof(owner_def, axiom, ![X2, Y2]: ((human(X2) & pet(Y2)) => (owner(X2, Y2) <=> X2=owner_of(Y2)))).
% 0.22/0.42
% 0.22/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.42 fresh(y, y, x1...xn) = u
% 0.22/0.42 C => fresh(s, t, x1...xn) = v
% 0.22/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.42 variables of u and v.
% 0.22/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.42 input problem has no model of domain size 1).
% 0.22/0.42
% 0.22/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.42
% 0.22/0.42 Axiom 1 (garfield_type): cat(garfield) = true.
% 0.22/0.42 Axiom 2 (odie_type): dog(odie) = true.
% 0.22/0.42 Axiom 3 (jon_type): human(jon) = true.
% 0.22/0.42 Axiom 4 (odie_chase_axiom): chased(odie, garfield) = true.
% 0.22/0.42 Axiom 5 (jon_g_owner_axiom): owner(jon, garfield) = true.
% 0.22/0.42 Axiom 6 (jon_o_owner_axiom): owner(jon, odie) = true.
% 0.22/0.42 Axiom 7 (cat_pet_type): fresh9(X, X, Y) = true.
% 0.22/0.42 Axiom 8 (dog_pet_type): fresh8(X, X, Y) = true.
% 0.22/0.42 Axiom 9 (cat_chase_axiom): fresh16(X, X, Y, Z) = true.
% 0.22/0.42 Axiom 10 (owner_def_1): fresh14(X, X, Y, Z) = Y.
% 0.22/0.42 Axiom 11 (cat_chase_axiom): fresh10(X, X, Y, Z) = hates(owner_of(Y), owner_of(Z)).
% 0.22/0.42 Axiom 12 (cat_pet_type): fresh9(cat(X), true, X) = pet(X).
% 0.22/0.42 Axiom 13 (dog_pet_type): fresh8(dog(X), true, X) = pet(X).
% 0.22/0.42 Axiom 14 (owner_def_1): fresh4(X, X, Y, Z) = owner_of(Z).
% 0.22/0.42 Axiom 15 (cat_chase_axiom): fresh15(X, X, Y, Z) = fresh16(cat(Y), true, Y, Z).
% 0.22/0.42 Axiom 16 (owner_def_1): fresh13(X, X, Y, Z) = fresh14(pet(Z), true, Y, Z).
% 0.22/0.42 Axiom 17 (cat_chase_axiom): fresh15(chased(X, Y), true, Y, X) = fresh10(dog(X), true, Y, X).
% 0.22/0.42 Axiom 18 (owner_def_1): fresh13(owner(X, Y), true, X, Y) = fresh4(human(X), true, X, Y).
% 0.22/0.42
% 0.22/0.42 Goal 1 (jon_conjecture): hates(jon, jon) = true.
% 0.22/0.42 Proof:
% 0.22/0.42 hates(jon, jon)
% 0.22/0.42 = { by axiom 10 (owner_def_1) R->L }
% 0.22/0.42 hates(jon, fresh14(true, true, jon, odie))
% 0.22/0.42 = { by axiom 8 (dog_pet_type) R->L }
% 0.22/0.42 hates(jon, fresh14(fresh8(true, true, odie), true, jon, odie))
% 0.22/0.42 = { by axiom 2 (odie_type) R->L }
% 0.22/0.42 hates(jon, fresh14(fresh8(dog(odie), true, odie), true, jon, odie))
% 0.22/0.42 = { by axiom 13 (dog_pet_type) }
% 0.22/0.42 hates(jon, fresh14(pet(odie), true, jon, odie))
% 0.22/0.42 = { by axiom 16 (owner_def_1) R->L }
% 0.22/0.42 hates(jon, fresh13(true, true, jon, odie))
% 0.22/0.42 = { by axiom 6 (jon_o_owner_axiom) R->L }
% 0.22/0.42 hates(jon, fresh13(owner(jon, odie), true, jon, odie))
% 0.22/0.42 = { by axiom 18 (owner_def_1) }
% 0.22/0.42 hates(jon, fresh4(human(jon), true, jon, odie))
% 0.22/0.42 = { by axiom 3 (jon_type) }
% 0.22/0.42 hates(jon, fresh4(true, true, jon, odie))
% 0.22/0.42 = { by axiom 14 (owner_def_1) }
% 0.22/0.42 hates(jon, owner_of(odie))
% 0.22/0.42 = { by axiom 10 (owner_def_1) R->L }
% 0.22/0.42 hates(fresh14(true, true, jon, garfield), owner_of(odie))
% 0.22/0.42 = { by axiom 7 (cat_pet_type) R->L }
% 0.22/0.42 hates(fresh14(fresh9(true, true, garfield), true, jon, garfield), owner_of(odie))
% 0.22/0.42 = { by axiom 1 (garfield_type) R->L }
% 0.22/0.42 hates(fresh14(fresh9(cat(garfield), true, garfield), true, jon, garfield), owner_of(odie))
% 0.22/0.42 = { by axiom 12 (cat_pet_type) }
% 0.22/0.42 hates(fresh14(pet(garfield), true, jon, garfield), owner_of(odie))
% 0.22/0.42 = { by axiom 16 (owner_def_1) R->L }
% 0.22/0.42 hates(fresh13(true, true, jon, garfield), owner_of(odie))
% 0.22/0.42 = { by axiom 5 (jon_g_owner_axiom) R->L }
% 0.22/0.42 hates(fresh13(owner(jon, garfield), true, jon, garfield), owner_of(odie))
% 0.22/0.42 = { by axiom 18 (owner_def_1) }
% 0.22/0.42 hates(fresh4(human(jon), true, jon, garfield), owner_of(odie))
% 0.22/0.42 = { by axiom 3 (jon_type) }
% 0.22/0.42 hates(fresh4(true, true, jon, garfield), owner_of(odie))
% 0.22/0.42 = { by axiom 14 (owner_def_1) }
% 0.22/0.42 hates(owner_of(garfield), owner_of(odie))
% 0.22/0.42 = { by axiom 11 (cat_chase_axiom) R->L }
% 0.22/0.42 fresh10(true, true, garfield, odie)
% 0.22/0.42 = { by axiom 2 (odie_type) R->L }
% 0.22/0.42 fresh10(dog(odie), true, garfield, odie)
% 0.22/0.42 = { by axiom 17 (cat_chase_axiom) R->L }
% 0.22/0.42 fresh15(chased(odie, garfield), true, garfield, odie)
% 0.22/0.42 = { by axiom 4 (odie_chase_axiom) }
% 0.22/0.42 fresh15(true, true, garfield, odie)
% 0.22/0.42 = { by axiom 15 (cat_chase_axiom) }
% 0.22/0.42 fresh16(cat(garfield), true, garfield, odie)
% 0.22/0.42 = { by axiom 1 (garfield_type) }
% 0.22/0.42 fresh16(true, true, garfield, odie)
% 0.22/0.42 = { by axiom 9 (cat_chase_axiom) }
% 0.22/0.42 true
% 0.22/0.42 % SZS output end Proof
% 0.22/0.42
% 0.22/0.42 RESULT: Theorem (the conjecture is true).
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