TSTP Solution File: SWC399+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC399+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 : n016.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 232.81s 29.68s
% Output : Proof 233.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWC399+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n016.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 17:14:44 EDT 2023
% 0.14/0.35 % CPUTime :
% 232.81/29.68 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 232.81/29.68
% 232.81/29.68 % SZS status Theorem
% 232.81/29.68
% 232.81/29.69 % SZS output start Proof
% 232.81/29.69 Take the following subset of the input axioms:
% 233.08/29.72 fof(ax26, axiom, ![U]: (ssList(U) => ![V]: (ssList(V) => ssList(app(U, V))))).
% 233.08/29.72 fof(ax36, axiom, ![U2]: (ssItem(U2) => ![V2]: (ssList(V2) => ![W]: (ssList(W) => (memberP(app(V2, W), U2) <=> (memberP(V2, U2) | memberP(W, U2))))))).
% 233.08/29.72 fof(ax82, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => app(app(U2, V2), W2)=app(U2, app(V2, W2)))))).
% 233.08/29.72 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => ![X]: (~ssList(X) | (V2!=X | (U2!=W2 | (![Y]: (ssList(Y) => ![Z]: (~ssList(Z) | (app(app(Y, W2), Z)!=X | (~equalelemsP(W2) | (?[X1]: (ssItem(X1) & ?[X2]: (ssList(X2) & (app(X2, cons(X1, nil))=Y & ?[X3]: (ssList(X3) & app(cons(X1, nil), X3)=W2)))) | ?[X4]: (ssItem(X4) & ?[X5]: (ssList(X5) & (app(cons(X4, nil), X5)=Z & ?[X6]: (ssList(X6) & app(X6, cons(X4, nil))=W2))))))))) | (![X7]: (~ssItem(X7) | (~memberP(U2, X7) | memberP(V2, X7))) | (nil!=X & nil=W2)))))))))).
% 233.08/29.72
% 233.08/29.72 Now clausify the problem and encode Horn clauses using encoding 3 of
% 233.08/29.72 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 233.08/29.72 We repeatedly replace C & s=t => u=v by the two clauses:
% 233.08/29.72 fresh(y, y, x1...xn) = u
% 233.08/29.72 C => fresh(s, t, x1...xn) = v
% 233.08/29.72 where fresh is a fresh function symbol and x1..xn are the free
% 233.08/29.72 variables of u and v.
% 233.08/29.72 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 233.08/29.72 input problem has no model of domain size 1).
% 233.08/29.72
% 233.08/29.72 The encoding turns the above axioms into the following unit equations and goals:
% 233.08/29.72
% 233.08/29.72 Axiom 1 (co1_2): v = x.
% 233.08/29.72 Axiom 2 (co1_1): u = w.
% 233.08/29.72 Axiom 3 (co1_6): ssList(w) = true2.
% 233.08/29.72 Axiom 4 (co1_8): ssList(y) = true2.
% 233.08/29.72 Axiom 5 (co1_9): ssList(z) = true2.
% 233.08/29.72 Axiom 6 (co1_3): ssItem(x7) = true2.
% 233.08/29.72 Axiom 7 (co1_10): memberP(u, x7) = true2.
% 233.08/29.72 Axiom 8 (co1): app(app(y, w), z) = x.
% 233.08/29.72 Axiom 9 (ax26): fresh73(X, X, Y, Z) = ssList(app(Y, Z)).
% 233.08/29.72 Axiom 10 (ax26): fresh72(X, X, Y, Z) = true2.
% 233.08/29.72 Axiom 11 (ax36_1): fresh196(X, X, Y, Z, W) = true2.
% 233.08/29.72 Axiom 12 (ax36_1): fresh194(X, X, Y, Z, W) = memberP(app(Z, W), Y).
% 233.08/29.72 Axiom 13 (ax36): fresh192(X, X, Y, Z, W) = true2.
% 233.08/29.72 Axiom 14 (ax36): fresh190(X, X, Y, Z, W) = memberP(app(Z, W), Y).
% 233.08/29.72 Axiom 15 (ax82): fresh120(X, X, Y, Z, W) = app(Y, app(Z, W)).
% 233.08/29.72 Axiom 16 (ax26): fresh73(ssList(X), true2, Y, X) = fresh72(ssList(Y), true2, Y, X).
% 233.08/29.72 Axiom 17 (ax82): fresh23(X, X, Y, Z, W) = app(app(Y, Z), W).
% 233.08/29.72 Axiom 18 (ax36_1): fresh195(X, X, Y, Z, W) = fresh196(ssItem(Y), true2, Y, Z, W).
% 233.08/29.72 Axiom 19 (ax36_1): fresh193(X, X, Y, Z, W) = fresh194(ssList(Z), true2, Y, Z, W).
% 233.08/29.72 Axiom 20 (ax36): fresh191(X, X, Y, Z, W) = fresh192(ssItem(Y), true2, Y, Z, W).
% 233.08/29.72 Axiom 21 (ax36): fresh189(X, X, Y, Z, W) = fresh190(ssList(Z), true2, Y, Z, W).
% 233.08/29.72 Axiom 22 (ax82): fresh119(X, X, Y, Z, W) = fresh120(ssList(Y), true2, Y, Z, W).
% 233.08/29.72 Axiom 23 (ax82): fresh119(ssList(X), true2, Y, Z, X) = fresh23(ssList(Z), true2, Y, Z, X).
% 233.08/29.72 Axiom 24 (ax36_1): fresh193(memberP(X, Y), true2, Y, Z, X) = fresh195(ssList(X), true2, Y, Z, X).
% 233.08/29.72 Axiom 25 (ax36): fresh189(memberP(X, Y), true2, Y, X, Z) = fresh191(ssList(Z), true2, Y, X, Z).
% 233.08/29.72
% 233.08/29.72 Goal 1 (co1_15): memberP(v, x7) = true2.
% 233.08/29.72 Proof:
% 233.08/29.72 memberP(v, x7)
% 233.08/29.72 = { by axiom 1 (co1_2) }
% 233.08/29.72 memberP(x, x7)
% 233.08/29.72 = { by axiom 8 (co1) R->L }
% 233.08/29.72 memberP(app(app(y, w), z), x7)
% 233.08/29.72 = { by axiom 17 (ax82) R->L }
% 233.08/29.72 memberP(fresh23(true2, true2, y, w, z), x7)
% 233.08/29.73 = { by axiom 3 (co1_6) R->L }
% 233.08/29.73 memberP(fresh23(ssList(w), true2, y, w, z), x7)
% 233.08/29.73 = { by axiom 23 (ax82) R->L }
% 233.08/29.73 memberP(fresh119(ssList(z), true2, y, w, z), x7)
% 233.08/29.73 = { by axiom 5 (co1_9) }
% 233.08/29.73 memberP(fresh119(true2, true2, y, w, z), x7)
% 233.08/29.73 = { by axiom 22 (ax82) }
% 233.08/29.73 memberP(fresh120(ssList(y), true2, y, w, z), x7)
% 233.08/29.73 = { by axiom 4 (co1_8) }
% 233.08/29.73 memberP(fresh120(true2, true2, y, w, z), x7)
% 233.08/29.73 = { by axiom 15 (ax82) }
% 233.08/29.73 memberP(app(y, app(w, z)), x7)
% 233.08/29.73 = { by axiom 12 (ax36_1) R->L }
% 233.08/29.73 fresh194(true2, true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 4 (co1_8) R->L }
% 233.08/29.73 fresh194(ssList(y), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 19 (ax36_1) R->L }
% 233.08/29.73 fresh193(true2, true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 13 (ax36) R->L }
% 233.08/29.73 fresh193(fresh192(true2, true2, x7, w, z), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 6 (co1_3) R->L }
% 233.08/29.73 fresh193(fresh192(ssItem(x7), true2, x7, w, z), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 20 (ax36) R->L }
% 233.08/29.73 fresh193(fresh191(true2, true2, x7, w, z), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 5 (co1_9) R->L }
% 233.08/29.73 fresh193(fresh191(ssList(z), true2, x7, w, z), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 25 (ax36) R->L }
% 233.08/29.73 fresh193(fresh189(memberP(w, x7), true2, x7, w, z), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 2 (co1_1) R->L }
% 233.08/29.73 fresh193(fresh189(memberP(u, x7), true2, x7, w, z), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 7 (co1_10) }
% 233.08/29.73 fresh193(fresh189(true2, true2, x7, w, z), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 21 (ax36) }
% 233.08/29.73 fresh193(fresh190(ssList(w), true2, x7, w, z), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 3 (co1_6) }
% 233.08/29.73 fresh193(fresh190(true2, true2, x7, w, z), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 14 (ax36) }
% 233.08/29.73 fresh193(memberP(app(w, z), x7), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 24 (ax36_1) }
% 233.08/29.73 fresh195(ssList(app(w, z)), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 9 (ax26) R->L }
% 233.08/29.73 fresh195(fresh73(true2, true2, w, z), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 5 (co1_9) R->L }
% 233.08/29.73 fresh195(fresh73(ssList(z), true2, w, z), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 16 (ax26) }
% 233.08/29.73 fresh195(fresh72(ssList(w), true2, w, z), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 3 (co1_6) }
% 233.08/29.73 fresh195(fresh72(true2, true2, w, z), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 10 (ax26) }
% 233.08/29.73 fresh195(true2, true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 18 (ax36_1) }
% 233.08/29.73 fresh196(ssItem(x7), true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 6 (co1_3) }
% 233.08/29.73 fresh196(true2, true2, x7, y, app(w, z))
% 233.08/29.73 = { by axiom 11 (ax36_1) }
% 233.08/29.73 true2
% 233.08/29.73 % SZS output end Proof
% 233.08/29.73
% 233.08/29.73 RESULT: Theorem (the conjecture is true).
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