TSTP Solution File: SWC189+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC189+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 : n026.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 20:54:20 EDT 2023
% Result : Theorem 7.94s 1.38s
% Output : Proof 7.94s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC189+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 17:47:05 EDT 2023
% 0.13/0.35 % CPUTime :
% 7.94/1.38 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 7.94/1.38
% 7.94/1.38 % SZS status Theorem
% 7.94/1.38
% 7.94/1.39 % SZS output start Proof
% 7.94/1.39 Take the following subset of the input axioms:
% 7.94/1.40 fof(co1, conjecture, ![U]: (ssList(U) => ![V]: (ssList(V) => ![W]: (ssList(W) => ![X]: (ssList(X) => (V!=X | (U!=W | (?[Y]: (ssItem(Y) & ?[Z]: (ssItem(Z) & ?[X1]: (ssList(X1) & ?[X2]: (ssList(X2) & (Y!=Z & app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2)=W))))) | ![X3]: (ssItem(X3) => ![X4]: (ssItem(X4) => ![X5]: (ssList(X5) => ![X6]: (ssList(X6) => (app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6)!=U | X3=X4))))))))))))).
% 7.94/1.40
% 7.94/1.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 7.94/1.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 7.94/1.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 7.94/1.40 fresh(y, y, x1...xn) = u
% 7.94/1.40 C => fresh(s, t, x1...xn) = v
% 7.94/1.40 where fresh is a fresh function symbol and x1..xn are the free
% 7.94/1.40 variables of u and v.
% 7.94/1.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 7.94/1.40 input problem has no model of domain size 1).
% 7.94/1.40
% 7.94/1.40 The encoding turns the above axioms into the following unit equations and goals:
% 7.94/1.40
% 7.94/1.40 Axiom 1 (co1_1): u = w.
% 7.94/1.40 Axiom 2 (co1_9): ssList(x5) = true2.
% 7.94/1.40 Axiom 3 (co1_10): ssList(x6) = true2.
% 7.94/1.40 Axiom 4 (co1_3): ssItem(x3) = true2.
% 7.94/1.40 Axiom 5 (co1_4): ssItem(x4) = true2.
% 7.94/1.40 Axiom 6 (co1_11): fresh(X, X, Y, Z) = Z.
% 7.94/1.40 Axiom 7 (co1_11): fresh93(X, X, Y, Z, W, V) = Y.
% 7.94/1.40 Axiom 8 (co1_11): fresh92(X, X, Y, Z, W, V) = fresh93(ssItem(Y), true2, Y, Z, W, V).
% 7.94/1.40 Axiom 9 (co1_11): fresh91(X, X, Y, Z, W, V) = fresh92(ssItem(Z), true2, Y, Z, W, V).
% 7.94/1.40 Axiom 10 (co1_11): fresh90(X, X, Y, Z, W, V) = fresh91(ssList(W), true2, Y, Z, W, V).
% 7.94/1.40 Axiom 11 (co1): app(app(app(x5, cons(x3, nil)), cons(x4, nil)), x6) = u.
% 7.94/1.40 Axiom 12 (co1_11): fresh90(ssList(X), true2, Y, Z, W, X) = fresh(app(app(app(W, cons(Y, nil)), cons(Z, nil)), X), w, Y, Z).
% 7.94/1.40
% 7.94/1.40 Goal 1 (co1_12): x3 = x4.
% 7.94/1.40 Proof:
% 7.94/1.40 x3
% 7.94/1.40 = { by axiom 7 (co1_11) R->L }
% 7.94/1.40 fresh93(true2, true2, x3, x4, x5, x6)
% 7.94/1.40 = { by axiom 4 (co1_3) R->L }
% 7.94/1.40 fresh93(ssItem(x3), true2, x3, x4, x5, x6)
% 7.94/1.40 = { by axiom 8 (co1_11) R->L }
% 7.94/1.40 fresh92(true2, true2, x3, x4, x5, x6)
% 7.94/1.40 = { by axiom 5 (co1_4) R->L }
% 7.94/1.40 fresh92(ssItem(x4), true2, x3, x4, x5, x6)
% 7.94/1.40 = { by axiom 9 (co1_11) R->L }
% 7.94/1.40 fresh91(true2, true2, x3, x4, x5, x6)
% 7.94/1.40 = { by axiom 2 (co1_9) R->L }
% 7.94/1.40 fresh91(ssList(x5), true2, x3, x4, x5, x6)
% 7.94/1.40 = { by axiom 10 (co1_11) R->L }
% 7.94/1.40 fresh90(true2, true2, x3, x4, x5, x6)
% 7.94/1.40 = { by axiom 3 (co1_10) R->L }
% 7.94/1.40 fresh90(ssList(x6), true2, x3, x4, x5, x6)
% 7.94/1.40 = { by axiom 12 (co1_11) }
% 7.94/1.40 fresh(app(app(app(x5, cons(x3, nil)), cons(x4, nil)), x6), w, x3, x4)
% 7.94/1.40 = { by axiom 1 (co1_1) R->L }
% 7.94/1.40 fresh(app(app(app(x5, cons(x3, nil)), cons(x4, nil)), x6), u, x3, x4)
% 7.94/1.40 = { by axiom 11 (co1) }
% 7.94/1.40 fresh(u, u, x3, x4)
% 7.94/1.40 = { by axiom 6 (co1_11) }
% 7.94/1.40 x4
% 7.94/1.40 % SZS output end Proof
% 7.94/1.40
% 7.94/1.40 RESULT: Theorem (the conjecture is true).
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