TSTP Solution File: SET575+3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SET575+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 15:32:28 EDT 2023
% Result : Theorem 0.22s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET575+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.14 % 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 : n011.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 12:41:24 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.40 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.22/0.40
% 0.22/0.40 % SZS status Theorem
% 0.22/0.40
% 0.22/0.40 % SZS output start Proof
% 0.22/0.40 Take the following subset of the input axioms:
% 0.22/0.40 fof(intersect_defn, axiom, ![B, C]: (intersect(B, C) <=> ?[D]: (member(D, B) & member(D, C)))).
% 0.22/0.40 fof(prove_th15, conjecture, ![B2, C2]: (intersect(B2, C2) => ?[D2]: (member(D2, B2) & member(D2, C2)))).
% 0.22/0.40
% 0.22/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.41 fresh(y, y, x1...xn) = u
% 0.22/0.41 C => fresh(s, t, x1...xn) = v
% 0.22/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.41 variables of u and v.
% 0.22/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.41 input problem has no model of domain size 1).
% 0.22/0.41
% 0.22/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.41
% 0.22/0.41 Axiom 1 (prove_th15): intersect(b, c) = true2.
% 0.22/0.41 Axiom 2 (intersect_defn_1): fresh5(X, X, Y, Z) = true2.
% 0.22/0.41 Axiom 3 (intersect_defn): fresh4(X, X, Y, Z) = true2.
% 0.22/0.41 Axiom 4 (intersect_defn_1): fresh5(intersect(X, Y), true2, X, Y) = member(d(X, Y), Y).
% 0.22/0.41 Axiom 5 (intersect_defn): fresh4(intersect(X, Y), true2, X, Y) = member(d(X, Y), X).
% 0.22/0.41
% 0.22/0.41 Goal 1 (prove_th15_1): tuple(member(X, b), member(X, c)) = tuple(true2, true2).
% 0.22/0.41 The goal is true when:
% 0.22/0.41 X = d(b, c)
% 0.22/0.41
% 0.22/0.41 Proof:
% 0.22/0.41 tuple(member(d(b, c), b), member(d(b, c), c))
% 0.22/0.41 = { by axiom 5 (intersect_defn) R->L }
% 0.22/0.41 tuple(fresh4(intersect(b, c), true2, b, c), member(d(b, c), c))
% 0.22/0.41 = { by axiom 1 (prove_th15) }
% 0.22/0.41 tuple(fresh4(true2, true2, b, c), member(d(b, c), c))
% 0.22/0.41 = { by axiom 3 (intersect_defn) }
% 0.22/0.41 tuple(true2, member(d(b, c), c))
% 0.22/0.41 = { by axiom 4 (intersect_defn_1) R->L }
% 0.22/0.41 tuple(true2, fresh5(intersect(b, c), true2, b, c))
% 0.22/0.41 = { by axiom 1 (prove_th15) }
% 0.22/0.41 tuple(true2, fresh5(true2, true2, b, c))
% 0.22/0.41 = { by axiom 2 (intersect_defn_1) }
% 0.22/0.41 tuple(true2, true2)
% 0.22/0.41 % SZS output end Proof
% 0.22/0.41
% 0.22/0.41 RESULT: Theorem (the conjecture is true).
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