TSTP Solution File: SWC339+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC339+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 : n006.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 20:55:03 EDT 2023
% Result : Theorem 11.22s 1.85s
% Output : Proof 11.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWC339+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.14 % 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 : n006.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 15:54:21 EDT 2023
% 0.14/0.35 % CPUTime :
% 11.22/1.85 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 11.22/1.85
% 11.22/1.85 % SZS status Theorem
% 11.22/1.85
% 11.22/1.85 % SZS output start Proof
% 11.22/1.85 Take the following subset of the input axioms:
% 11.22/1.87 fof(ax7, axiom, ![U]: (ssList(U) => ![V]: (ssList(V) => (segmentP(U, V) <=> ?[W]: (ssList(W) & ?[X]: (ssList(X) & app(app(W, V), X)=U)))))).
% 11.22/1.87 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => ![X9]: (ssList(X9) => (V2!=X9 | (U2!=W2 | (![Y]: (ssList(Y) => ![Z]: (ssList(Z) => (app(app(Y, W2), Z)!=X9 | (~totalorderedP(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 & leq(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 & leq(X7, X5)))))))))))) | ((nil!=X9 & nil=W2) | (segmentP(V2, U2) & totalorderedP(U2))))))))))).
% 11.22/1.87
% 11.22/1.87 Now clausify the problem and encode Horn clauses using encoding 3 of
% 11.22/1.87 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 11.22/1.87 We repeatedly replace C & s=t => u=v by the two clauses:
% 11.22/1.87 fresh(y, y, x1...xn) = u
% 11.22/1.87 C => fresh(s, t, x1...xn) = v
% 11.22/1.87 where fresh is a fresh function symbol and x1..xn are the free
% 11.22/1.87 variables of u and v.
% 11.22/1.87 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 11.22/1.87 input problem has no model of domain size 1).
% 11.22/1.87
% 11.22/1.87 The encoding turns the above axioms into the following unit equations and goals:
% 11.22/1.87
% 11.22/1.87 Axiom 1 (co1_1): u = w.
% 11.22/1.87 Axiom 2 (co1_2): v = x.
% 11.22/1.87 Axiom 3 (co1_5): ssList(w) = true2.
% 11.22/1.87 Axiom 4 (co1_4): ssList(v) = true2.
% 11.22/1.87 Axiom 5 (co1_7): ssList(y) = true2.
% 11.22/1.87 Axiom 6 (co1_8): ssList(z) = true2.
% 11.22/1.87 Axiom 7 (co1_9): totalorderedP(w) = true2.
% 11.22/1.87 Axiom 8 (co1): app(app(y, w), z) = x.
% 11.22/1.87 Axiom 9 (ax7): fresh31(X, X, Y, Z) = true2.
% 11.22/1.87 Axiom 10 (ax7): fresh252(X, X, Y, Z, W, V) = segmentP(Y, Z).
% 11.22/1.87 Axiom 11 (ax7): fresh251(X, X, Y, Z, W, V) = fresh252(ssList(Y), true2, Y, Z, W, V).
% 11.22/1.87 Axiom 12 (ax7): fresh250(X, X, Y, Z, W, V) = fresh251(ssList(Z), true2, Y, Z, W, V).
% 11.22/1.87 Axiom 13 (ax7): fresh249(X, X, Y, Z, W, V) = fresh250(ssList(W), true2, Y, Z, W, V).
% 11.22/1.87 Axiom 14 (ax7): fresh249(ssList(X), true2, Y, Z, W, X) = fresh31(app(app(W, Z), X), Y, Y, Z).
% 11.22/1.87
% 11.22/1.87 Goal 1 (co1_13): tuple2(segmentP(v, u), totalorderedP(u)) = tuple2(true2, true2).
% 11.22/1.87 Proof:
% 11.22/1.87 tuple2(segmentP(v, u), totalorderedP(u))
% 11.22/1.87 = { by axiom 1 (co1_1) }
% 11.22/1.87 tuple2(segmentP(v, u), totalorderedP(w))
% 11.22/1.87 = { by axiom 7 (co1_9) }
% 11.22/1.87 tuple2(segmentP(v, u), true2)
% 11.22/1.87 = { by axiom 1 (co1_1) }
% 11.22/1.87 tuple2(segmentP(v, w), true2)
% 11.22/1.87 = { by axiom 10 (ax7) R->L }
% 11.22/1.87 tuple2(fresh252(true2, true2, v, w, y, z), true2)
% 11.22/1.87 = { by axiom 4 (co1_4) R->L }
% 11.22/1.87 tuple2(fresh252(ssList(v), true2, v, w, y, z), true2)
% 11.22/1.87 = { by axiom 11 (ax7) R->L }
% 11.22/1.87 tuple2(fresh251(true2, true2, v, w, y, z), true2)
% 11.22/1.87 = { by axiom 3 (co1_5) R->L }
% 11.22/1.87 tuple2(fresh251(ssList(w), true2, v, w, y, z), true2)
% 11.22/1.87 = { by axiom 12 (ax7) R->L }
% 11.22/1.87 tuple2(fresh250(true2, true2, v, w, y, z), true2)
% 11.22/1.87 = { by axiom 5 (co1_7) R->L }
% 11.22/1.87 tuple2(fresh250(ssList(y), true2, v, w, y, z), true2)
% 11.22/1.87 = { by axiom 13 (ax7) R->L }
% 11.22/1.87 tuple2(fresh249(true2, true2, v, w, y, z), true2)
% 11.22/1.87 = { by axiom 6 (co1_8) R->L }
% 11.22/1.87 tuple2(fresh249(ssList(z), true2, v, w, y, z), true2)
% 11.22/1.87 = { by axiom 14 (ax7) }
% 11.22/1.87 tuple2(fresh31(app(app(y, w), z), v, v, w), true2)
% 11.22/1.87 = { by axiom 8 (co1) }
% 11.22/1.87 tuple2(fresh31(x, v, v, w), true2)
% 11.22/1.87 = { by axiom 2 (co1_2) R->L }
% 11.22/1.87 tuple2(fresh31(v, v, v, w), true2)
% 11.22/1.87 = { by axiom 9 (ax7) }
% 11.22/1.87 tuple2(true2, true2)
% 11.22/1.87 % SZS output end Proof
% 11.22/1.87
% 11.22/1.87 RESULT: Theorem (the conjecture is true).
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