TSTP Solution File: SWC254+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC254+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 20:54:39 EDT 2023
% Result : Theorem 6.99s 1.39s
% Output : Proof 6.99s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SWC254+1 : TPTP v8.1.2. Released v2.4.0.
% 0.05/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.32 % Computer : n020.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 16:11:28 EDT 2023
% 0.11/0.32 % CPUTime :
% 6.99/1.39 Command-line arguments: --no-flatten-goal
% 6.99/1.39
% 6.99/1.39 % SZS status Theorem
% 6.99/1.39
% 6.99/1.40 % SZS output start Proof
% 6.99/1.40 Take the following subset of the input axioms:
% 6.99/1.41 fof(ax4, axiom, ![U]: (ssList(U) => (singletonP(U) <=> ?[V]: (ssItem(V) & cons(V, nil)=U)))).
% 6.99/1.41 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W]: (ssList(W) => ![X]: (ssList(X) => (V2!=X | (U2!=W | ((~neq(V2, nil) | (![Y]: (ssItem(Y) => ![Z]: (ssList(Z) => (cons(Y, nil)!=W | app(Z, cons(Y, nil))!=X))) | singletonP(U2))) & (~neq(V2, nil) | neq(X, nil)))))))))).
% 6.99/1.41
% 6.99/1.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 6.99/1.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 6.99/1.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 6.99/1.41 fresh(y, y, x1...xn) = u
% 6.99/1.41 C => fresh(s, t, x1...xn) = v
% 6.99/1.41 where fresh is a fresh function symbol and x1..xn are the free
% 6.99/1.41 variables of u and v.
% 6.99/1.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 6.99/1.41 input problem has no model of domain size 1).
% 6.99/1.41
% 6.99/1.41 The encoding turns the above axioms into the following unit equations and goals:
% 6.99/1.41
% 6.99/1.41 Axiom 1 (co1_2): u = w.
% 6.99/1.41 Axiom 2 (co1_3): v = x.
% 6.99/1.41 Axiom 3 (co1_9): ssList(w) = true2.
% 6.99/1.41 Axiom 4 (co1_12): fresh18(X, X) = w.
% 6.99/1.41 Axiom 5 (co1_13): fresh17(X, X) = true2.
% 6.99/1.41 Axiom 6 (co1_5): neq(v, nil) = true2.
% 6.99/1.41 Axiom 7 (ax4): fresh282(X, X, Y) = true2.
% 6.99/1.41 Axiom 8 (ax4): fresh65(X, X, Y, Z) = singletonP(Y).
% 6.99/1.41 Axiom 9 (co1_12): fresh18(neq(x, nil), true2) = cons(y, nil).
% 6.99/1.41 Axiom 10 (co1_13): fresh17(neq(x, nil), true2) = ssItem(y).
% 6.99/1.41 Axiom 11 (ax4): fresh281(X, X, Y, Z) = fresh282(cons(Z, nil), Y, Y).
% 6.99/1.41 Axiom 12 (ax4): fresh281(ssList(X), true2, X, Y) = fresh65(ssItem(Y), true2, X, Y).
% 6.99/1.41
% 6.99/1.41 Goal 1 (co1_16): tuple2(neq(x, nil), singletonP(u)) = tuple2(true2, true2).
% 6.99/1.41 Proof:
% 6.99/1.41 tuple2(neq(x, nil), singletonP(u))
% 6.99/1.41 = { by axiom 1 (co1_2) }
% 6.99/1.41 tuple2(neq(x, nil), singletonP(w))
% 6.99/1.41 = { by axiom 2 (co1_3) R->L }
% 6.99/1.41 tuple2(neq(v, nil), singletonP(w))
% 6.99/1.41 = { by axiom 6 (co1_5) }
% 6.99/1.41 tuple2(true2, singletonP(w))
% 6.99/1.41 = { by axiom 8 (ax4) R->L }
% 6.99/1.41 tuple2(true2, fresh65(true2, true2, w, y))
% 6.99/1.41 = { by axiom 5 (co1_13) R->L }
% 6.99/1.41 tuple2(true2, fresh65(fresh17(true2, true2), true2, w, y))
% 6.99/1.41 = { by axiom 6 (co1_5) R->L }
% 6.99/1.41 tuple2(true2, fresh65(fresh17(neq(v, nil), true2), true2, w, y))
% 6.99/1.41 = { by axiom 2 (co1_3) }
% 6.99/1.41 tuple2(true2, fresh65(fresh17(neq(x, nil), true2), true2, w, y))
% 6.99/1.41 = { by axiom 10 (co1_13) }
% 6.99/1.41 tuple2(true2, fresh65(ssItem(y), true2, w, y))
% 6.99/1.41 = { by axiom 12 (ax4) R->L }
% 6.99/1.41 tuple2(true2, fresh281(ssList(w), true2, w, y))
% 6.99/1.41 = { by axiom 3 (co1_9) }
% 6.99/1.41 tuple2(true2, fresh281(true2, true2, w, y))
% 6.99/1.41 = { by axiom 11 (ax4) }
% 6.99/1.41 tuple2(true2, fresh282(cons(y, nil), w, w))
% 6.99/1.41 = { by axiom 9 (co1_12) R->L }
% 6.99/1.41 tuple2(true2, fresh282(fresh18(neq(x, nil), true2), w, w))
% 6.99/1.41 = { by axiom 2 (co1_3) R->L }
% 6.99/1.41 tuple2(true2, fresh282(fresh18(neq(v, nil), true2), w, w))
% 6.99/1.41 = { by axiom 6 (co1_5) }
% 6.99/1.41 tuple2(true2, fresh282(fresh18(true2, true2), w, w))
% 6.99/1.41 = { by axiom 4 (co1_12) }
% 6.99/1.41 tuple2(true2, fresh282(w, w, w))
% 6.99/1.41 = { by axiom 7 (ax4) }
% 6.99/1.41 tuple2(true2, true2)
% 6.99/1.41 % SZS output end Proof
% 6.99/1.41
% 6.99/1.41 RESULT: Theorem (the conjecture is true).
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