TSTP Solution File: SET658+3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SET658+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 : n011.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 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET658+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 09:13:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.50 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.50
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 Take the following subset of the input axioms:
% 0.20/0.51 fof(p1, axiom, ![B]: (ilf_type(B, set_type) => ![C]: (ilf_type(C, binary_relation_type) => (subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C))))))).
% 0.20/0.51 fof(p15, axiom, ![B2]: (ilf_type(B2, set_type) => subset(B2, B2))).
% 0.20/0.51 fof(p28, axiom, ![B2]: ilf_type(B2, set_type)).
% 0.20/0.51 fof(prove_relset_1_20, conjecture, ![B2]: (ilf_type(B2, binary_relation_type) => ilf_type(B2, relation_type(domain_of(B2), range_of(B2))))).
% 0.20/0.51
% 0.20/0.51 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.51 fresh(y, y, x1...xn) = u
% 0.20/0.51 C => fresh(s, t, x1...xn) = v
% 0.20/0.51 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.51 variables of u and v.
% 0.20/0.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.51 input problem has no model of domain size 1).
% 0.20/0.51
% 0.20/0.51 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.51
% 0.20/0.51 Axiom 1 (p28): ilf_type(X, set_type) = true2.
% 0.20/0.51 Axiom 2 (prove_relset_1_20): ilf_type(b, binary_relation_type) = true2.
% 0.20/0.51 Axiom 3 (p15): fresh24(X, X, Y) = true2.
% 0.20/0.51 Axiom 4 (p1): fresh99(X, X, Y, Z) = true2.
% 0.20/0.51 Axiom 5 (p1): fresh33(X, X, Y, Z) = ilf_type(Z, relation_type(Y, range_of(Z))).
% 0.20/0.51 Axiom 6 (p15): fresh24(ilf_type(X, set_type), true2, X) = subset(X, X).
% 0.20/0.51 Axiom 7 (p1): fresh98(X, X, Y, Z) = fresh99(ilf_type(Y, set_type), true2, Y, Z).
% 0.20/0.51 Axiom 8 (p1): fresh98(subset(domain_of(X), Y), true2, Y, X) = fresh33(ilf_type(X, binary_relation_type), true2, Y, X).
% 0.20/0.51
% 0.20/0.51 Goal 1 (prove_relset_1_20_1): ilf_type(b, relation_type(domain_of(b), range_of(b))) = true2.
% 0.20/0.51 Proof:
% 0.20/0.51 ilf_type(b, relation_type(domain_of(b), range_of(b)))
% 0.20/0.51 = { by axiom 5 (p1) R->L }
% 0.20/0.51 fresh33(true2, true2, domain_of(b), b)
% 0.20/0.51 = { by axiom 2 (prove_relset_1_20) R->L }
% 0.20/0.51 fresh33(ilf_type(b, binary_relation_type), true2, domain_of(b), b)
% 0.20/0.51 = { by axiom 8 (p1) R->L }
% 0.20/0.51 fresh98(subset(domain_of(b), domain_of(b)), true2, domain_of(b), b)
% 0.20/0.51 = { by axiom 6 (p15) R->L }
% 0.20/0.51 fresh98(fresh24(ilf_type(domain_of(b), set_type), true2, domain_of(b)), true2, domain_of(b), b)
% 0.20/0.51 = { by axiom 1 (p28) }
% 0.20/0.51 fresh98(fresh24(true2, true2, domain_of(b)), true2, domain_of(b), b)
% 0.20/0.51 = { by axiom 3 (p15) }
% 0.20/0.51 fresh98(true2, true2, domain_of(b), b)
% 0.20/0.51 = { by axiom 7 (p1) }
% 0.20/0.51 fresh99(ilf_type(domain_of(b), set_type), true2, domain_of(b), b)
% 0.20/0.51 = { by axiom 1 (p28) }
% 0.20/0.51 fresh99(true2, true2, domain_of(b), b)
% 0.20/0.51 = { by axiom 4 (p1) }
% 0.20/0.51 true2
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51
% 0.20/0.51 RESULT: Theorem (the conjecture is true).
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