TSTP Solution File: SWC385+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC385+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 : n021.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 20:55:18 EDT 2023
% Result : Theorem 3.49s 0.82s
% Output : Proof 3.76s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC385+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13 % 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 : n021.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 17:30:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.49/0.82 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.49/0.82
% 3.49/0.82 % SZS status Theorem
% 3.49/0.82
% 3.49/0.82 % SZS output start Proof
% 3.49/0.82 Take the following subset of the input axioms:
% 3.49/0.82 fof(co1, conjecture, ![U]: (ssList(U) => ![V]: (ssList(V) => ![W]: (ssList(W) => ![X]: (ssList(X) => (V!=X | (U!=W | (~neq(V, nil) | (~segmentP(X, W) | ((~singletonP(W) & neq(X, nil)) | (singletonP(U) & segmentP(V, U)))))))))))).
% 3.49/0.82
% 3.49/0.82 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.49/0.82 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.49/0.82 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.49/0.82 fresh(y, y, x1...xn) = u
% 3.49/0.82 C => fresh(s, t, x1...xn) = v
% 3.49/0.82 where fresh is a fresh function symbol and x1..xn are the free
% 3.49/0.82 variables of u and v.
% 3.49/0.82 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.49/0.82 input problem has no model of domain size 1).
% 3.49/0.82
% 3.49/0.82 The encoding turns the above axioms into the following unit equations and goals:
% 3.49/0.82
% 3.49/0.82 Axiom 1 (co1): u = w.
% 3.49/0.82 Axiom 2 (co1_1): v = x.
% 3.76/0.82 Axiom 3 (co1_7): segmentP(x, w) = true2.
% 3.76/0.82 Axiom 4 (co1_2): neq(v, nil) = true2.
% 3.76/0.82 Axiom 5 (co1_8): fresh14(X, X) = true2.
% 3.76/0.82 Axiom 6 (co1_8): fresh14(neq(x, nil), true2) = singletonP(w).
% 3.76/0.82
% 3.76/0.82 Goal 1 (co1_9): tuple2(singletonP(u), segmentP(v, u)) = tuple2(true2, true2).
% 3.76/0.82 Proof:
% 3.76/0.82 tuple2(singletonP(u), segmentP(v, u))
% 3.76/0.82 = { by axiom 1 (co1) }
% 3.76/0.82 tuple2(singletonP(w), segmentP(v, u))
% 3.76/0.82 = { by axiom 6 (co1_8) R->L }
% 3.76/0.82 tuple2(fresh14(neq(x, nil), true2), segmentP(v, u))
% 3.76/0.82 = { by axiom 2 (co1_1) R->L }
% 3.76/0.82 tuple2(fresh14(neq(v, nil), true2), segmentP(v, u))
% 3.76/0.82 = { by axiom 4 (co1_2) }
% 3.76/0.82 tuple2(fresh14(true2, true2), segmentP(v, u))
% 3.76/0.82 = { by axiom 5 (co1_8) }
% 3.76/0.82 tuple2(true2, segmentP(v, u))
% 3.76/0.82 = { by axiom 1 (co1) }
% 3.76/0.82 tuple2(true2, segmentP(v, w))
% 3.76/0.82 = { by axiom 2 (co1_1) }
% 3.76/0.82 tuple2(true2, segmentP(x, w))
% 3.76/0.82 = { by axiom 3 (co1_7) }
% 3.76/0.82 tuple2(true2, true2)
% 3.76/0.82 % SZS output end Proof
% 3.76/0.82
% 3.76/0.82 RESULT: Theorem (the conjecture is true).
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