TSTP Solution File: SWC408+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC408+1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n020.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 20:55:26 EDT 2023
% Result : Theorem 5.78s 1.19s
% Output : Proof 5.78s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWC408+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.32 % Computer : n020.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Aug 28 17:42:13 EDT 2023
% 0.12/0.32 % CPUTime :
% 5.78/1.19 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 5.78/1.19
% 5.78/1.19 % SZS status Theorem
% 5.78/1.19
% 5.78/1.19 % SZS output start Proof
% 5.78/1.19 Take the following subset of the input axioms:
% 5.78/1.19 fof(ax36, axiom, ![U]: (ssItem(U) => ![V]: (ssList(V) => ![W]: (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))))).
% 5.78/1.19 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => ![X]: (ssList(X) => (app(X, X)!=W2 | (V2!=X | (U2!=W2 | ![Y]: (ssItem(Y) => (~memberP(V2, Y) | memberP(U2, Y))))))))))).
% 5.78/1.19
% 5.78/1.19 Now clausify the problem and encode Horn clauses using encoding 3 of
% 5.78/1.19 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 5.78/1.19 We repeatedly replace C & s=t => u=v by the two clauses:
% 5.78/1.19 fresh(y, y, x1...xn) = u
% 5.78/1.19 C => fresh(s, t, x1...xn) = v
% 5.78/1.19 where fresh is a fresh function symbol and x1..xn are the free
% 5.78/1.19 variables of u and v.
% 5.78/1.19 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 5.78/1.19 input problem has no model of domain size 1).
% 5.78/1.19
% 5.78/1.19 The encoding turns the above axioms into the following unit equations and goals:
% 5.78/1.19
% 5.78/1.19 Axiom 1 (co1_2): v = x.
% 5.78/1.19 Axiom 2 (co1_1): u = w.
% 5.78/1.19 Axiom 3 (co1_7): ssList(x) = true2.
% 5.78/1.19 Axiom 4 (co1_3): ssItem(y) = true2.
% 5.78/1.19 Axiom 5 (co1): app(x, x) = w.
% 5.78/1.19 Axiom 6 (co1_8): memberP(v, y) = true2.
% 5.78/1.19 Axiom 7 (ax36_1): fresh195(X, X, Y, Z, W) = true2.
% 5.78/1.19 Axiom 8 (ax36_1): fresh193(X, X, Y, Z, W) = memberP(app(Z, W), Y).
% 5.78/1.19 Axiom 9 (ax36_1): fresh194(X, X, Y, Z, W) = fresh195(ssItem(Y), true2, Y, Z, W).
% 5.78/1.19 Axiom 10 (ax36_1): fresh192(X, X, Y, Z, W) = fresh193(ssList(Z), true2, Y, Z, W).
% 5.78/1.19 Axiom 11 (ax36_1): fresh192(memberP(X, Y), true2, Y, Z, X) = fresh194(ssList(X), true2, Y, Z, X).
% 5.78/1.19
% 5.78/1.19 Goal 1 (co1_9): memberP(u, y) = true2.
% 5.78/1.19 Proof:
% 5.78/1.19 memberP(u, y)
% 5.78/1.19 = { by axiom 2 (co1_1) }
% 5.78/1.19 memberP(w, y)
% 5.78/1.19 = { by axiom 5 (co1) R->L }
% 5.78/1.19 memberP(app(x, x), y)
% 5.78/1.19 = { by axiom 8 (ax36_1) R->L }
% 5.78/1.19 fresh193(true2, true2, y, x, x)
% 5.78/1.19 = { by axiom 3 (co1_7) R->L }
% 5.78/1.19 fresh193(ssList(x), true2, y, x, x)
% 5.78/1.19 = { by axiom 10 (ax36_1) R->L }
% 5.78/1.19 fresh192(true2, true2, y, x, x)
% 5.78/1.19 = { by axiom 6 (co1_8) R->L }
% 5.78/1.19 fresh192(memberP(v, y), true2, y, x, x)
% 5.78/1.19 = { by axiom 1 (co1_2) }
% 5.78/1.19 fresh192(memberP(x, y), true2, y, x, x)
% 5.78/1.19 = { by axiom 11 (ax36_1) }
% 5.78/1.19 fresh194(ssList(x), true2, y, x, x)
% 5.78/1.19 = { by axiom 3 (co1_7) }
% 5.78/1.19 fresh194(true2, true2, y, x, x)
% 5.78/1.19 = { by axiom 9 (ax36_1) }
% 5.78/1.19 fresh195(ssItem(y), true2, y, x, x)
% 5.78/1.19 = { by axiom 4 (co1_3) }
% 5.78/1.19 fresh195(true2, true2, y, x, x)
% 5.78/1.19 = { by axiom 7 (ax36_1) }
% 5.78/1.19 true2
% 5.78/1.19 % SZS output end Proof
% 5.78/1.19
% 5.78/1.19 RESULT: Theorem (the conjecture is true).
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