TSTP Solution File: SWC398+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC398+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 20:55:22 EDT 2023
% Result : Theorem 5.55s 1.11s
% Output : Proof 6.01s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC398+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 14:57:44 EDT 2023
% 0.14/0.35 % CPUTime :
% 5.55/1.11 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 5.55/1.11
% 5.55/1.11 % SZS status Theorem
% 5.55/1.11
% 5.55/1.11 % SZS output start Proof
% 5.55/1.11 Take the following subset of the input axioms:
% 6.01/1.12 fof(ax36, axiom, ![U]: (ssItem(U) => ![V]: (ssList(V) => ![W]: (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))))).
% 6.01/1.12 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => ![X]: (ssList(X) => (V2!=X | (U2!=W2 | (![Y]: (ssList(Y) => (app(W2, Y)!=X | (~equalelemsP(W2) | ?[Z]: (ssItem(Z) & ?[X1]: (ssList(X1) & (app(cons(Z, nil), X1)=Y & ?[X2]: (ssList(X2) & app(X2, cons(Z, nil))=W2))))))) | (![X3]: (ssItem(X3) => (~memberP(U2, X3) | memberP(V2, X3))) | (nil!=X & nil=W2)))))))))).
% 6.01/1.12
% 6.01/1.12 Now clausify the problem and encode Horn clauses using encoding 3 of
% 6.01/1.12 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 6.01/1.12 We repeatedly replace C & s=t => u=v by the two clauses:
% 6.01/1.12 fresh(y, y, x1...xn) = u
% 6.01/1.12 C => fresh(s, t, x1...xn) = v
% 6.01/1.12 where fresh is a fresh function symbol and x1..xn are the free
% 6.01/1.12 variables of u and v.
% 6.01/1.12 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 6.01/1.12 input problem has no model of domain size 1).
% 6.01/1.12
% 6.01/1.12 The encoding turns the above axioms into the following unit equations and goals:
% 6.01/1.12
% 6.01/1.12 Axiom 1 (co1_2): v = x.
% 6.01/1.12 Axiom 2 (co1_1): u = w.
% 6.01/1.12 Axiom 3 (co1_6): ssList(w) = true2.
% 6.01/1.12 Axiom 4 (co1_8): ssList(y) = true2.
% 6.01/1.12 Axiom 5 (co1_3): ssItem(x3) = true2.
% 6.01/1.12 Axiom 6 (co1): app(w, y) = x.
% 6.01/1.12 Axiom 7 (co1_9): memberP(u, x3) = true2.
% 6.01/1.12 Axiom 8 (ax36): fresh192(X, X, Y, Z, W) = true2.
% 6.01/1.12 Axiom 9 (ax36): fresh190(X, X, Y, Z, W) = memberP(app(Z, W), Y).
% 6.01/1.12 Axiom 10 (ax36): fresh191(X, X, Y, Z, W) = fresh192(ssItem(Y), true2, Y, Z, W).
% 6.01/1.12 Axiom 11 (ax36): fresh189(X, X, Y, Z, W) = fresh190(ssList(Z), true2, Y, Z, W).
% 6.01/1.12 Axiom 12 (ax36): fresh189(memberP(X, Y), true2, Y, X, Z) = fresh191(ssList(Z), true2, Y, X, Z).
% 6.01/1.12
% 6.01/1.12 Goal 1 (co1_13): memberP(v, x3) = true2.
% 6.01/1.12 Proof:
% 6.01/1.12 memberP(v, x3)
% 6.01/1.12 = { by axiom 1 (co1_2) }
% 6.01/1.12 memberP(x, x3)
% 6.01/1.12 = { by axiom 6 (co1) R->L }
% 6.01/1.12 memberP(app(w, y), x3)
% 6.01/1.12 = { by axiom 9 (ax36) R->L }
% 6.01/1.12 fresh190(true2, true2, x3, w, y)
% 6.01/1.12 = { by axiom 3 (co1_6) R->L }
% 6.01/1.12 fresh190(ssList(w), true2, x3, w, y)
% 6.01/1.12 = { by axiom 11 (ax36) R->L }
% 6.01/1.12 fresh189(true2, true2, x3, w, y)
% 6.01/1.12 = { by axiom 7 (co1_9) R->L }
% 6.01/1.12 fresh189(memberP(u, x3), true2, x3, w, y)
% 6.01/1.12 = { by axiom 2 (co1_1) }
% 6.01/1.12 fresh189(memberP(w, x3), true2, x3, w, y)
% 6.01/1.12 = { by axiom 12 (ax36) }
% 6.01/1.12 fresh191(ssList(y), true2, x3, w, y)
% 6.01/1.12 = { by axiom 4 (co1_8) }
% 6.01/1.12 fresh191(true2, true2, x3, w, y)
% 6.01/1.12 = { by axiom 10 (ax36) }
% 6.01/1.12 fresh192(ssItem(x3), true2, x3, w, y)
% 6.01/1.12 = { by axiom 5 (co1_3) }
% 6.01/1.12 fresh192(true2, true2, x3, w, y)
% 6.01/1.12 = { by axiom 8 (ax36) }
% 6.01/1.12 true2
% 6.01/1.12 % SZS output end Proof
% 6.01/1.12
% 6.01/1.12 RESULT: Theorem (the conjecture is true).
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