TSTP Solution File: SWC353+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC353+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 : n022.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 20:55:07 EDT 2023
% Result : Theorem 15.40s 2.34s
% Output : Proof 15.40s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWC353+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 14:33:54 EDT 2023
% 0.13/0.34 % CPUTime :
% 15.40/2.34 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 15.40/2.34
% 15.40/2.34 % SZS status Theorem
% 15.40/2.34
% 15.40/2.35 % SZS output start Proof
% 15.40/2.35 Take the following subset of the input axioms:
% 15.40/2.37 fof(ax42, axiom, ![U]: (ssList(U) => frontsegP(U, U))).
% 15.40/2.37 fof(ax43, axiom, ![U2]: (ssList(U2) => ![V]: (ssList(V) => ![W]: (ssList(W) => (frontsegP(U2, V) => frontsegP(app(U2, W), V)))))).
% 15.40/2.37 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 | (~totalorderedP(W2) | ?[Z]: (ssItem(Z) & ?[X1]: (ssList(X1) & (app(cons(Z, nil), X1)=Y & ?[X2]: (ssItem(X2) & ?[X3]: (ssList(X3) & (app(X3, cons(X2, nil))=W2 & leq(X2, Z)))))))))) | (frontsegP(V2, U2) | (nil!=X & nil=W2)))))))))).
% 15.40/2.37
% 15.40/2.37 Now clausify the problem and encode Horn clauses using encoding 3 of
% 15.40/2.37 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 15.40/2.37 We repeatedly replace C & s=t => u=v by the two clauses:
% 15.40/2.37 fresh(y, y, x1...xn) = u
% 15.40/2.37 C => fresh(s, t, x1...xn) = v
% 15.40/2.37 where fresh is a fresh function symbol and x1..xn are the free
% 15.40/2.37 variables of u and v.
% 15.40/2.37 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 15.40/2.37 input problem has no model of domain size 1).
% 15.40/2.37
% 15.40/2.37 The encoding turns the above axioms into the following unit equations and goals:
% 15.40/2.37
% 15.40/2.37 Axiom 1 (co1_1): u = w.
% 15.40/2.37 Axiom 2 (co1_2): v = x.
% 15.40/2.37 Axiom 3 (co1_5): ssList(w) = true2.
% 15.40/2.37 Axiom 4 (co1_7): ssList(y) = true2.
% 15.40/2.37 Axiom 5 (co1): app(w, y) = x.
% 15.40/2.37 Axiom 6 (ax42): fresh59(X, X, Y) = true2.
% 15.40/2.37 Axiom 7 (ax42): fresh59(ssList(X), true2, X) = frontsegP(X, X).
% 15.40/2.37 Axiom 8 (ax43): fresh175(X, X, Y, Z, W) = true2.
% 15.40/2.37 Axiom 9 (ax43): fresh173(X, X, Y, Z, W) = frontsegP(app(Y, W), Z).
% 15.40/2.37 Axiom 10 (ax43): fresh174(X, X, Y, Z, W) = fresh175(ssList(Y), true2, Y, Z, W).
% 15.40/2.37 Axiom 11 (ax43): fresh172(X, X, Y, Z, W) = fresh173(ssList(Z), true2, Y, Z, W).
% 15.40/2.37 Axiom 12 (ax43): fresh172(frontsegP(X, Y), true2, X, Y, Z) = fresh174(ssList(Z), true2, X, Y, Z).
% 15.40/2.37
% 15.40/2.37 Goal 1 (co1_11): frontsegP(v, u) = true2.
% 15.40/2.37 Proof:
% 15.40/2.37 frontsegP(v, u)
% 15.40/2.37 = { by axiom 1 (co1_1) }
% 15.40/2.37 frontsegP(v, w)
% 15.40/2.37 = { by axiom 2 (co1_2) }
% 15.40/2.37 frontsegP(x, w)
% 15.40/2.37 = { by axiom 5 (co1) R->L }
% 15.40/2.37 frontsegP(app(w, y), w)
% 15.40/2.37 = { by axiom 9 (ax43) R->L }
% 15.40/2.37 fresh173(true2, true2, w, w, y)
% 15.40/2.37 = { by axiom 3 (co1_5) R->L }
% 15.40/2.37 fresh173(ssList(w), true2, w, w, y)
% 15.40/2.37 = { by axiom 11 (ax43) R->L }
% 15.40/2.37 fresh172(true2, true2, w, w, y)
% 15.40/2.37 = { by axiom 6 (ax42) R->L }
% 15.40/2.37 fresh172(fresh59(true2, true2, w), true2, w, w, y)
% 15.40/2.37 = { by axiom 3 (co1_5) R->L }
% 15.40/2.37 fresh172(fresh59(ssList(w), true2, w), true2, w, w, y)
% 15.40/2.37 = { by axiom 7 (ax42) }
% 15.40/2.37 fresh172(frontsegP(w, w), true2, w, w, y)
% 15.40/2.37 = { by axiom 12 (ax43) }
% 15.40/2.37 fresh174(ssList(y), true2, w, w, y)
% 15.40/2.37 = { by axiom 4 (co1_7) }
% 15.40/2.37 fresh174(true2, true2, w, w, y)
% 15.40/2.37 = { by axiom 10 (ax43) }
% 15.40/2.37 fresh175(ssList(w), true2, w, w, y)
% 15.40/2.37 = { by axiom 3 (co1_5) }
% 15.40/2.37 fresh175(true2, true2, w, w, y)
% 15.40/2.37 = { by axiom 8 (ax43) }
% 15.40/2.37 true2
% 15.40/2.37 % SZS output end Proof
% 15.40/2.37
% 15.40/2.37 RESULT: Theorem (the conjecture is true).
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