TSTP Solution File: SET653+3 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET653+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : n019.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 15:32:53 EDT 2023
% Result : Theorem 0.18s 0.45s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET653+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.33 % Computer : n019.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Sat Aug 26 14:21:28 EDT 2023
% 0.14/0.33 % CPUTime :
% 0.18/0.45 Command-line arguments: --no-flatten-goal
% 0.18/0.45
% 0.18/0.45 % SZS status Theorem
% 0.18/0.45
% 0.18/0.46 % SZS output start Proof
% 0.18/0.46 Take the following subset of the input axioms:
% 0.18/0.46 fof(p1, axiom, ![B]: (ilf_type(B, set_type) => ![C]: (ilf_type(C, set_type) => ![D]: (ilf_type(D, set_type) => ((subset(B, C) & subset(C, D)) => subset(B, D)))))).
% 0.18/0.46 fof(p2, axiom, ![B2]: (ilf_type(B2, set_type) => ![C2]: (ilf_type(C2, set_type) => ![D2]: (ilf_type(D2, relation_type(B2, C2)) => (subset(domain_of(D2), B2) & subset(range_of(D2), C2)))))).
% 0.18/0.46 fof(p22, axiom, ![B2]: ilf_type(B2, set_type)).
% 0.18/0.46 fof(p3, axiom, ![B2]: (ilf_type(B2, set_type) => ![C2]: (ilf_type(C2, set_type) => ![D2]: (ilf_type(D2, set_type) => ![E]: (ilf_type(E, relation_type(B2, D2)) => (subset(domain_of(E), C2) => ilf_type(E, relation_type(C2, D2)))))))).
% 0.18/0.46 fof(prove_relset_1_15, conjecture, ![B2]: (ilf_type(B2, set_type) => ![C2]: (ilf_type(C2, set_type) => ![D2]: (ilf_type(D2, set_type) => ![E2]: (ilf_type(E2, relation_type(B2, D2)) => (subset(B2, C2) => ilf_type(E2, relation_type(C2, D2)))))))).
% 0.18/0.46
% 0.18/0.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.46 fresh(y, y, x1...xn) = u
% 0.18/0.46 C => fresh(s, t, x1...xn) = v
% 0.18/0.46 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.46 variables of u and v.
% 0.18/0.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.46 input problem has no model of domain size 1).
% 0.18/0.46
% 0.18/0.46 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.46
% 0.18/0.46 Axiom 1 (prove_relset_1_15_4): subset(b, c) = true2.
% 0.18/0.46 Axiom 2 (p22): ilf_type(X, set_type) = true2.
% 0.18/0.46 Axiom 3 (p1): fresh76(X, X, Y, Z) = true2.
% 0.18/0.46 Axiom 4 (p1): fresh74(X, X, Y, Z) = subset(Y, Z).
% 0.18/0.46 Axiom 5 (p2): fresh69(X, X, Y, Z) = true2.
% 0.18/0.46 Axiom 6 (p2): fresh14(X, X, Y, Z) = subset(domain_of(Z), Y).
% 0.18/0.46 Axiom 7 (prove_relset_1_15_3): ilf_type(e, relation_type(b, d)) = true2.
% 0.18/0.46 Axiom 8 (p3): fresh67(X, X, Y, Z, W) = true2.
% 0.18/0.46 Axiom 9 (p1): fresh75(X, X, Y, Z, W) = fresh76(ilf_type(Y, set_type), true2, Y, W).
% 0.18/0.46 Axiom 10 (p1): fresh73(X, X, Y, Z, W) = fresh74(ilf_type(Z, set_type), true2, Y, W).
% 0.18/0.46 Axiom 11 (p2): fresh68(X, X, Y, Z, W) = fresh69(ilf_type(Y, set_type), true2, Y, W).
% 0.18/0.46 Axiom 12 (p3): fresh65(X, X, Y, Z, W, V) = ilf_type(V, relation_type(Z, W)).
% 0.18/0.46 Axiom 13 (p1): fresh72(X, X, Y, Z, W) = fresh75(ilf_type(W, set_type), true2, Y, Z, W).
% 0.18/0.46 Axiom 14 (p1): fresh72(subset(X, Y), true2, Z, X, Y) = fresh73(subset(Z, X), true2, Z, X, Y).
% 0.18/0.46 Axiom 15 (p3): fresh66(X, X, Y, Z, W, V) = fresh67(ilf_type(Y, set_type), true2, Z, W, V).
% 0.18/0.46 Axiom 16 (p3): fresh63(X, X, Y, Z, W, V) = fresh66(ilf_type(W, set_type), true2, Y, Z, W, V).
% 0.18/0.46 Axiom 17 (p3): fresh64(X, X, Y, Z, W, V) = fresh65(ilf_type(Z, set_type), true2, Y, Z, W, V).
% 0.18/0.46 Axiom 18 (p2): fresh68(ilf_type(X, relation_type(Y, Z)), true2, Y, Z, X) = fresh14(ilf_type(Z, set_type), true2, Y, X).
% 0.18/0.46 Axiom 19 (p3): fresh63(subset(domain_of(X), Y), true2, Z, Y, W, X) = fresh64(ilf_type(X, relation_type(Z, W)), true2, Z, Y, W, X).
% 0.18/0.46
% 0.18/0.46 Goal 1 (prove_relset_1_15_5): ilf_type(e, relation_type(c, d)) = true2.
% 0.18/0.46 Proof:
% 0.18/0.46 ilf_type(e, relation_type(c, d))
% 0.18/0.46 = { by axiom 12 (p3) R->L }
% 0.18/0.46 fresh65(true2, true2, b, c, d, e)
% 0.18/0.46 = { by axiom 2 (p22) R->L }
% 0.18/0.46 fresh65(ilf_type(c, set_type), true2, b, c, d, e)
% 0.18/0.46 = { by axiom 17 (p3) R->L }
% 0.18/0.46 fresh64(true2, true2, b, c, d, e)
% 0.18/0.46 = { by axiom 7 (prove_relset_1_15_3) R->L }
% 0.18/0.46 fresh64(ilf_type(e, relation_type(b, d)), true2, b, c, d, e)
% 0.18/0.46 = { by axiom 19 (p3) R->L }
% 0.18/0.46 fresh63(subset(domain_of(e), c), true2, b, c, d, e)
% 0.18/0.46 = { by axiom 4 (p1) R->L }
% 0.18/0.46 fresh63(fresh74(true2, true2, domain_of(e), c), true2, b, c, d, e)
% 0.18/0.46 = { by axiom 2 (p22) R->L }
% 0.18/0.46 fresh63(fresh74(ilf_type(b, set_type), true2, domain_of(e), c), true2, b, c, d, e)
% 0.18/0.46 = { by axiom 10 (p1) R->L }
% 0.18/0.46 fresh63(fresh73(true2, true2, domain_of(e), b, c), true2, b, c, d, e)
% 0.18/0.46 = { by axiom 5 (p2) R->L }
% 0.18/0.46 fresh63(fresh73(fresh69(true2, true2, b, e), true2, domain_of(e), b, c), true2, b, c, d, e)
% 0.18/0.46 = { by axiom 2 (p22) R->L }
% 0.18/0.46 fresh63(fresh73(fresh69(ilf_type(b, set_type), true2, b, e), true2, domain_of(e), b, c), true2, b, c, d, e)
% 0.18/0.46 = { by axiom 11 (p2) R->L }
% 0.18/0.46 fresh63(fresh73(fresh68(true2, true2, b, d, e), true2, domain_of(e), b, c), true2, b, c, d, e)
% 0.18/0.46 = { by axiom 7 (prove_relset_1_15_3) R->L }
% 0.18/0.46 fresh63(fresh73(fresh68(ilf_type(e, relation_type(b, d)), true2, b, d, e), true2, domain_of(e), b, c), true2, b, c, d, e)
% 0.18/0.46 = { by axiom 18 (p2) }
% 0.18/0.46 fresh63(fresh73(fresh14(ilf_type(d, set_type), true2, b, e), true2, domain_of(e), b, c), true2, b, c, d, e)
% 0.18/0.46 = { by axiom 2 (p22) }
% 0.18/0.46 fresh63(fresh73(fresh14(true2, true2, b, e), true2, domain_of(e), b, c), true2, b, c, d, e)
% 0.18/0.46 = { by axiom 6 (p2) }
% 0.18/0.46 fresh63(fresh73(subset(domain_of(e), b), true2, domain_of(e), b, c), true2, b, c, d, e)
% 0.18/0.46 = { by axiom 14 (p1) R->L }
% 0.18/0.46 fresh63(fresh72(subset(b, c), true2, domain_of(e), b, c), true2, b, c, d, e)
% 0.18/0.46 = { by axiom 1 (prove_relset_1_15_4) }
% 0.18/0.47 fresh63(fresh72(true2, true2, domain_of(e), b, c), true2, b, c, d, e)
% 0.18/0.47 = { by axiom 13 (p1) }
% 0.18/0.47 fresh63(fresh75(ilf_type(c, set_type), true2, domain_of(e), b, c), true2, b, c, d, e)
% 0.18/0.47 = { by axiom 2 (p22) }
% 0.18/0.47 fresh63(fresh75(true2, true2, domain_of(e), b, c), true2, b, c, d, e)
% 0.18/0.47 = { by axiom 9 (p1) }
% 0.18/0.47 fresh63(fresh76(ilf_type(domain_of(e), set_type), true2, domain_of(e), c), true2, b, c, d, e)
% 0.18/0.47 = { by axiom 2 (p22) }
% 0.18/0.47 fresh63(fresh76(true2, true2, domain_of(e), c), true2, b, c, d, e)
% 0.18/0.47 = { by axiom 3 (p1) }
% 0.18/0.47 fresh63(true2, true2, b, c, d, e)
% 0.18/0.47 = { by axiom 16 (p3) }
% 0.18/0.47 fresh66(ilf_type(d, set_type), true2, b, c, d, e)
% 0.18/0.47 = { by axiom 2 (p22) }
% 0.18/0.47 fresh66(true2, true2, b, c, d, e)
% 0.18/0.47 = { by axiom 15 (p3) }
% 0.18/0.47 fresh67(ilf_type(b, set_type), true2, c, d, e)
% 0.18/0.47 = { by axiom 2 (p22) }
% 0.18/0.47 fresh67(true2, true2, c, d, e)
% 0.18/0.47 = { by axiom 8 (p3) }
% 0.18/0.47 true2
% 0.18/0.47 % SZS output end Proof
% 0.18/0.47
% 0.18/0.47 RESULT: Theorem (the conjecture is true).
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