TSTP Solution File: SWC404+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC404+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 20:55:24 EDT 2023
% Result : Theorem 164.00s 21.01s
% Output : Proof 164.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC404+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % 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 : n016.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 : Mon Aug 28 17:53:14 EDT 2023
% 0.14/0.36 % CPUTime :
% 164.00/21.01 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 164.00/21.01
% 164.00/21.01 % SZS status Theorem
% 164.00/21.01
% 164.00/21.02 % SZS output start Proof
% 164.00/21.02 Take the following subset of the input axioms:
% 164.00/21.03 fof(ax26, axiom, ![U]: (ssList(U) => ![V]: (ssList(V) => ssList(app(U, V))))).
% 164.00/21.04 fof(ax36, axiom, ![U2]: (ssItem(U2) => ![V2]: (ssList(V2) => ![W]: (ssList(W) => (memberP(app(V2, W), U2) <=> (memberP(V2, U2) | memberP(W, U2))))))).
% 164.00/21.04 fof(ax82, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => app(app(U2, V2), W2)=app(U2, app(V2, W2)))))).
% 164.00/21.04 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 | (~strictorderedP(W2) | (?[X1]: (ssItem(X1) & ?[X2]: (ssList(X2) & (app(X2, cons(X1, nil))=Y & ?[X3]: (ssItem(X3) & ?[X4]: (ssList(X4) & (app(cons(X3, nil), X4)=W2 & lt(X1, X3))))))) | ?[X5]: (ssItem(X5) & ?[X6]: (ssList(X6) & (app(cons(X5, nil), X6)=Z & ?[X7]: (ssItem(X7) & ?[X8]: (ssList(X8) & (app(X8, cons(X7, nil))=W2 & lt(X7, X5)))))))))))) | (![X9]: (ssItem(X9) => (~memberP(U2, X9) | memberP(V2, X9))) | (nil!=X & nil=W2)))))))))).
% 164.00/21.04
% 164.00/21.04 Now clausify the problem and encode Horn clauses using encoding 3 of
% 164.00/21.04 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 164.00/21.04 We repeatedly replace C & s=t => u=v by the two clauses:
% 164.00/21.04 fresh(y, y, x1...xn) = u
% 164.00/21.04 C => fresh(s, t, x1...xn) = v
% 164.00/21.04 where fresh is a fresh function symbol and x1..xn are the free
% 164.00/21.04 variables of u and v.
% 164.00/21.04 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 164.00/21.04 input problem has no model of domain size 1).
% 164.00/21.04
% 164.00/21.04 The encoding turns the above axioms into the following unit equations and goals:
% 164.00/21.04
% 164.00/21.04 Axiom 1 (co1_2): v = x.
% 164.00/21.04 Axiom 2 (co1_1): u = w.
% 164.00/21.04 Axiom 3 (co1_6): ssList(w) = true2.
% 164.00/21.04 Axiom 4 (co1_8): ssList(y) = true2.
% 164.00/21.04 Axiom 5 (co1_9): ssList(z) = true2.
% 164.00/21.04 Axiom 6 (co1_3): ssItem(x9) = true2.
% 164.00/21.04 Axiom 7 (co1_10): memberP(u, x9) = true2.
% 164.00/21.04 Axiom 8 (co1): app(app(y, w), z) = x.
% 164.00/21.04 Axiom 9 (ax26): fresh73(X, X, Y, Z) = ssList(app(Y, Z)).
% 164.00/21.04 Axiom 10 (ax26): fresh72(X, X, Y, Z) = true2.
% 164.00/21.04 Axiom 11 (ax36_1): fresh196(X, X, Y, Z, W) = true2.
% 164.00/21.04 Axiom 12 (ax36_1): fresh194(X, X, Y, Z, W) = memberP(app(Z, W), Y).
% 164.00/21.04 Axiom 13 (ax36): fresh192(X, X, Y, Z, W) = true2.
% 164.00/21.04 Axiom 14 (ax36): fresh190(X, X, Y, Z, W) = memberP(app(Z, W), Y).
% 164.00/21.04 Axiom 15 (ax82): fresh120(X, X, Y, Z, W) = app(Y, app(Z, W)).
% 164.00/21.04 Axiom 16 (ax26): fresh73(ssList(X), true2, Y, X) = fresh72(ssList(Y), true2, Y, X).
% 164.00/21.04 Axiom 17 (ax82): fresh23(X, X, Y, Z, W) = app(app(Y, Z), W).
% 164.00/21.04 Axiom 18 (ax36_1): fresh195(X, X, Y, Z, W) = fresh196(ssItem(Y), true2, Y, Z, W).
% 164.00/21.04 Axiom 19 (ax36_1): fresh193(X, X, Y, Z, W) = fresh194(ssList(Z), true2, Y, Z, W).
% 164.00/21.04 Axiom 20 (ax36): fresh191(X, X, Y, Z, W) = fresh192(ssItem(Y), true2, Y, Z, W).
% 164.00/21.04 Axiom 21 (ax36): fresh189(X, X, Y, Z, W) = fresh190(ssList(Z), true2, Y, Z, W).
% 164.00/21.04 Axiom 22 (ax82): fresh119(X, X, Y, Z, W) = fresh120(ssList(Y), true2, Y, Z, W).
% 164.00/21.04 Axiom 23 (ax82): fresh119(ssList(X), true2, Y, Z, X) = fresh23(ssList(Z), true2, Y, Z, X).
% 164.00/21.04 Axiom 24 (ax36_1): fresh193(memberP(X, Y), true2, Y, Z, X) = fresh195(ssList(X), true2, Y, Z, X).
% 164.00/21.04 Axiom 25 (ax36): fresh189(memberP(X, Y), true2, Y, X, Z) = fresh191(ssList(Z), true2, Y, X, Z).
% 164.00/21.04
% 164.00/21.04 Goal 1 (co1_15): memberP(v, x9) = true2.
% 164.00/21.04 Proof:
% 164.00/21.04 memberP(v, x9)
% 164.00/21.04 = { by axiom 1 (co1_2) }
% 164.00/21.04 memberP(x, x9)
% 164.00/21.04 = { by axiom 8 (co1) R->L }
% 164.00/21.04 memberP(app(app(y, w), z), x9)
% 164.00/21.04 = { by axiom 17 (ax82) R->L }
% 164.00/21.04 memberP(fresh23(true2, true2, y, w, z), x9)
% 164.00/21.04 = { by axiom 3 (co1_6) R->L }
% 164.00/21.04 memberP(fresh23(ssList(w), true2, y, w, z), x9)
% 164.00/21.04 = { by axiom 23 (ax82) R->L }
% 164.00/21.04 memberP(fresh119(ssList(z), true2, y, w, z), x9)
% 164.00/21.04 = { by axiom 5 (co1_9) }
% 164.00/21.04 memberP(fresh119(true2, true2, y, w, z), x9)
% 164.00/21.04 = { by axiom 22 (ax82) }
% 164.00/21.04 memberP(fresh120(ssList(y), true2, y, w, z), x9)
% 164.00/21.04 = { by axiom 4 (co1_8) }
% 164.00/21.04 memberP(fresh120(true2, true2, y, w, z), x9)
% 164.00/21.04 = { by axiom 15 (ax82) }
% 164.00/21.04 memberP(app(y, app(w, z)), x9)
% 164.00/21.04 = { by axiom 12 (ax36_1) R->L }
% 164.00/21.04 fresh194(true2, true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 4 (co1_8) R->L }
% 164.00/21.04 fresh194(ssList(y), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 19 (ax36_1) R->L }
% 164.00/21.04 fresh193(true2, true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 13 (ax36) R->L }
% 164.00/21.04 fresh193(fresh192(true2, true2, x9, w, z), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 6 (co1_3) R->L }
% 164.00/21.04 fresh193(fresh192(ssItem(x9), true2, x9, w, z), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 20 (ax36) R->L }
% 164.00/21.04 fresh193(fresh191(true2, true2, x9, w, z), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 5 (co1_9) R->L }
% 164.00/21.04 fresh193(fresh191(ssList(z), true2, x9, w, z), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 25 (ax36) R->L }
% 164.00/21.04 fresh193(fresh189(memberP(w, x9), true2, x9, w, z), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 2 (co1_1) R->L }
% 164.00/21.04 fresh193(fresh189(memberP(u, x9), true2, x9, w, z), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 7 (co1_10) }
% 164.00/21.04 fresh193(fresh189(true2, true2, x9, w, z), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 21 (ax36) }
% 164.00/21.04 fresh193(fresh190(ssList(w), true2, x9, w, z), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 3 (co1_6) }
% 164.00/21.04 fresh193(fresh190(true2, true2, x9, w, z), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 14 (ax36) }
% 164.00/21.04 fresh193(memberP(app(w, z), x9), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 24 (ax36_1) }
% 164.00/21.04 fresh195(ssList(app(w, z)), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 9 (ax26) R->L }
% 164.00/21.04 fresh195(fresh73(true2, true2, w, z), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 5 (co1_9) R->L }
% 164.00/21.04 fresh195(fresh73(ssList(z), true2, w, z), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 16 (ax26) }
% 164.00/21.04 fresh195(fresh72(ssList(w), true2, w, z), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 3 (co1_6) }
% 164.00/21.04 fresh195(fresh72(true2, true2, w, z), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 10 (ax26) }
% 164.00/21.04 fresh195(true2, true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 18 (ax36_1) }
% 164.00/21.04 fresh196(ssItem(x9), true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 6 (co1_3) }
% 164.00/21.04 fresh196(true2, true2, x9, y, app(w, z))
% 164.00/21.04 = { by axiom 11 (ax36_1) }
% 164.00/21.04 true2
% 164.00/21.04 % SZS output end Proof
% 164.00/21.04
% 164.00/21.04 RESULT: Theorem (the conjecture is true).
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