TSTP Solution File: PUZ129+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ129+2 : TPTP v8.1.2. Released v4.0.0.
% 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 : n014.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 0.21s 0.43s
% 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
% 0.12/0.13 % Problem : PUZ129+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 22:02:47 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.43 Command-line arguments: --no-flatten-goal
% 0.21/0.43
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 Take the following subset of the input axioms:
% 0.21/0.47 fof(prove, conjecture, (![A2]: ((person(A2) & (property1(A2, honest, pos) & property1(A2, industrious, pos))) => ?[B]: (property1(B, healthy, pos) & A2=B)) & (![C]: (grocer(C) => ~?[D]: (property1(D, healthy, pos) & C=D)) & (![E]: ((grocer(E) & property1(E, industrious, pos)) => ?[F]: (property1(F, honest, pos) & E=F)) & (![G]: (cyclist(G) => ?[H]: (property1(H, industrious, pos) & G=H)) & (![I]: ((cyclist(I) & property1(I, unhealthy, pos)) => ?[J]: (property1(J, dishonest, pos) & I=J)) & (![K]: ((person(K) & property1(K, healthy, pos)) => ~?[L]: (property1(L, unhealthy, pos) & K=L)) & (![M]: ((person(M) & property1(M, honest, pos)) => ~?[N]: (property1(N, dishonest, pos) & M=N)) & (![O]: (grocer(O) => ?[P]: (person(P) & O=P)) & ![Q]: (cyclist(Q) => ?[R]: (person(R) & Q=R)))))))))) => ![S]: (grocer(S) => ~?[T]: (cyclist(T) & S=T))).
% 0.21/0.47
% 0.21/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.47 fresh(y, y, x1...xn) = u
% 0.21/0.47 C => fresh(s, t, x1...xn) = v
% 0.21/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.47 variables of u and v.
% 0.21/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.47 input problem has no model of domain size 1).
% 0.21/0.47
% 0.21/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.47
% 0.21/0.47 Axiom 1 (prove): s = t.
% 0.21/0.47 Axiom 2 (prove_1): grocer(s) = true2.
% 0.21/0.47 Axiom 3 (prove_2): cyclist(t) = true2.
% 0.21/0.47 Axiom 4 (prove_3): fresh20(X, X, Y) = Y.
% 0.21/0.47 Axiom 5 (prove_4): fresh18(X, X, Y) = true2.
% 0.21/0.47 Axiom 6 (prove_13): fresh13(X, X, Y) = true2.
% 0.21/0.47 Axiom 7 (prove_15): fresh12(X, X, Y) = true2.
% 0.21/0.47 Axiom 8 (prove_3): fresh10(X, X, Y) = b(Y).
% 0.21/0.47 Axiom 9 (prove_8): fresh8(X, X, Y) = f(Y).
% 0.21/0.47 Axiom 10 (prove_9): fresh6(X, X, Y) = true2.
% 0.21/0.47 Axiom 11 (prove_8): fresh5(X, X, Y) = Y.
% 0.21/0.47 Axiom 12 (prove_12): fresh3(X, X, Y) = Y.
% 0.21/0.47 Axiom 13 (prove_14): fresh2(X, X, Y) = Y.
% 0.21/0.47 Axiom 14 (prove_3): fresh19(X, X, Y) = fresh20(person(Y), true2, Y).
% 0.21/0.47 Axiom 15 (prove_4): fresh17(X, X, Y) = fresh18(person(Y), true2, Y).
% 0.21/0.47 Axiom 16 (prove_13): fresh13(grocer(X), true2, X) = person(p(X)).
% 0.21/0.47 Axiom 17 (prove_12): fresh3(grocer(X), true2, X) = p(X).
% 0.21/0.47 Axiom 18 (prove_14): fresh2(cyclist(X), true2, X) = h(X).
% 0.21/0.47 Axiom 19 (prove_4): fresh9(X, X, Y) = property1(b(Y), healthy, pos).
% 0.21/0.47 Axiom 20 (prove_9): fresh7(X, X, Y) = property1(f(Y), honest, pos).
% 0.21/0.47 Axiom 21 (prove_15): fresh12(cyclist(X), true2, X) = property1(h(X), industrious, pos).
% 0.21/0.47 Axiom 22 (prove_3): fresh19(property1(X, industrious, pos), true2, X) = fresh10(property1(X, honest, pos), true2, X).
% 0.21/0.47 Axiom 23 (prove_4): fresh17(property1(X, industrious, pos), true2, X) = fresh9(property1(X, honest, pos), true2, X).
% 0.21/0.47 Axiom 24 (prove_9): fresh7(grocer(X), true2, X) = fresh6(property1(X, industrious, pos), true2, X).
% 0.21/0.47 Axiom 25 (prove_8): fresh8(grocer(X), true2, X) = fresh5(property1(X, industrious, pos), true2, X).
% 0.21/0.47
% 0.21/0.47 Lemma 26: person(s) = true2.
% 0.21/0.47 Proof:
% 0.21/0.47 person(s)
% 0.21/0.47 = { by axiom 12 (prove_12) R->L }
% 0.21/0.47 person(fresh3(true2, true2, s))
% 0.21/0.47 = { by axiom 2 (prove_1) R->L }
% 0.21/0.47 person(fresh3(grocer(s), true2, s))
% 0.21/0.47 = { by axiom 17 (prove_12) }
% 0.21/0.47 person(p(s))
% 0.21/0.47 = { by axiom 16 (prove_13) R->L }
% 0.21/0.47 fresh13(grocer(s), true2, s)
% 0.21/0.47 = { by axiom 2 (prove_1) }
% 0.21/0.47 fresh13(true2, true2, s)
% 0.21/0.47 = { by axiom 6 (prove_13) }
% 0.21/0.47 true2
% 0.21/0.47
% 0.21/0.47 Lemma 27: cyclist(s) = true2.
% 0.21/0.47 Proof:
% 0.21/0.47 cyclist(s)
% 0.21/0.47 = { by axiom 1 (prove) }
% 0.21/0.47 cyclist(t)
% 0.21/0.47 = { by axiom 3 (prove_2) }
% 0.21/0.47 true2
% 0.21/0.47
% 0.21/0.47 Lemma 28: property1(s, industrious, pos) = true2.
% 0.21/0.47 Proof:
% 0.21/0.47 property1(s, industrious, pos)
% 0.21/0.47 = { by axiom 13 (prove_14) R->L }
% 0.21/0.47 property1(fresh2(true2, true2, s), industrious, pos)
% 0.21/0.47 = { by lemma 27 R->L }
% 0.21/0.47 property1(fresh2(cyclist(s), true2, s), industrious, pos)
% 0.21/0.47 = { by axiom 18 (prove_14) }
% 0.21/0.47 property1(h(s), industrious, pos)
% 0.21/0.47 = { by axiom 21 (prove_15) R->L }
% 0.21/0.47 fresh12(cyclist(s), true2, s)
% 0.21/0.47 = { by lemma 27 }
% 0.21/0.47 fresh12(true2, true2, s)
% 0.21/0.47 = { by axiom 7 (prove_15) }
% 0.21/0.47 true2
% 0.21/0.47
% 0.21/0.47 Lemma 29: property1(s, honest, pos) = true2.
% 0.21/0.47 Proof:
% 0.21/0.47 property1(s, honest, pos)
% 0.21/0.47 = { by axiom 11 (prove_8) R->L }
% 0.21/0.47 property1(fresh5(true2, true2, s), honest, pos)
% 0.21/0.47 = { by lemma 28 R->L }
% 0.21/0.47 property1(fresh5(property1(s, industrious, pos), true2, s), honest, pos)
% 0.21/0.47 = { by axiom 25 (prove_8) R->L }
% 0.21/0.47 property1(fresh8(grocer(s), true2, s), honest, pos)
% 0.21/0.47 = { by axiom 2 (prove_1) }
% 0.21/0.47 property1(fresh8(true2, true2, s), honest, pos)
% 0.21/0.47 = { by axiom 9 (prove_8) }
% 0.21/0.47 property1(f(s), honest, pos)
% 0.21/0.47 = { by axiom 20 (prove_9) R->L }
% 0.21/0.47 fresh7(true2, true2, s)
% 0.21/0.47 = { by axiom 2 (prove_1) R->L }
% 0.21/0.47 fresh7(grocer(s), true2, s)
% 0.21/0.47 = { by axiom 24 (prove_9) }
% 0.21/0.47 fresh6(property1(s, industrious, pos), true2, s)
% 0.21/0.47 = { by lemma 28 }
% 0.21/0.47 fresh6(true2, true2, s)
% 0.21/0.47 = { by axiom 10 (prove_9) }
% 0.21/0.47 true2
% 0.21/0.47
% 0.21/0.47 Goal 1 (prove_7): tuple2(property1(X, healthy, pos), grocer(X)) = tuple2(true2, true2).
% 0.21/0.47 The goal is true when:
% 0.21/0.47 X = s
% 0.21/0.47
% 0.21/0.47 Proof:
% 0.21/0.47 tuple2(property1(s, healthy, pos), grocer(s))
% 0.21/0.47 = { by axiom 4 (prove_3) R->L }
% 0.21/0.47 tuple2(property1(fresh20(true2, true2, s), healthy, pos), grocer(s))
% 0.21/0.47 = { by lemma 26 R->L }
% 0.21/0.47 tuple2(property1(fresh20(person(s), true2, s), healthy, pos), grocer(s))
% 0.21/0.47 = { by axiom 14 (prove_3) R->L }
% 0.21/0.47 tuple2(property1(fresh19(true2, true2, s), healthy, pos), grocer(s))
% 0.21/0.47 = { by lemma 28 R->L }
% 0.21/0.47 tuple2(property1(fresh19(property1(s, industrious, pos), true2, s), healthy, pos), grocer(s))
% 0.21/0.47 = { by axiom 22 (prove_3) }
% 0.21/0.47 tuple2(property1(fresh10(property1(s, honest, pos), true2, s), healthy, pos), grocer(s))
% 0.21/0.47 = { by lemma 29 }
% 0.21/0.47 tuple2(property1(fresh10(true2, true2, s), healthy, pos), grocer(s))
% 0.21/0.47 = { by axiom 8 (prove_3) }
% 0.21/0.47 tuple2(property1(b(s), healthy, pos), grocer(s))
% 0.21/0.47 = { by axiom 19 (prove_4) R->L }
% 0.21/0.47 tuple2(fresh9(true2, true2, s), grocer(s))
% 0.21/0.47 = { by lemma 29 R->L }
% 0.21/0.47 tuple2(fresh9(property1(s, honest, pos), true2, s), grocer(s))
% 0.21/0.47 = { by axiom 23 (prove_4) R->L }
% 0.21/0.47 tuple2(fresh17(property1(s, industrious, pos), true2, s), grocer(s))
% 0.21/0.47 = { by lemma 28 }
% 0.21/0.47 tuple2(fresh17(true2, true2, s), grocer(s))
% 0.21/0.47 = { by axiom 15 (prove_4) }
% 0.21/0.47 tuple2(fresh18(person(s), true2, s), grocer(s))
% 0.21/0.47 = { by lemma 26 }
% 0.21/0.47 tuple2(fresh18(true2, true2, s), grocer(s))
% 0.21/0.47 = { by axiom 5 (prove_4) }
% 0.21/0.47 tuple2(true2, grocer(s))
% 0.21/0.47 = { by axiom 2 (prove_1) }
% 0.21/0.47 tuple2(true2, true2)
% 0.21/0.47 % SZS output end Proof
% 0.21/0.47
% 0.21/0.47 RESULT: Theorem (the conjecture is true).
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