TSTP Solution File: SWC328+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWC328+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 : n025.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 20:55:00 EDT 2023
% Result : Theorem 0.18s 0.77s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC328+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.12 % 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 : n025.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 16:55:09 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.18/0.77 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.18/0.77
% 0.18/0.77 % SZS status Theorem
% 0.18/0.77
% 0.18/0.78 % SZS output start Proof
% 0.18/0.78 Take the following subset of the input axioms:
% 0.18/0.78 fof(ax57, axiom, ![U]: (ssList(U) => segmentP(U, nil))).
% 0.18/0.78 fof(ax74, axiom, equalelemsP(nil)).
% 0.18/0.78 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V]: (ssList(V) => ![W]: (ssList(W) => ![X]: (ssList(X) => (nil!=W | (V!=X | (U2!=W | (segmentP(V, U2) & equalelemsP(U2)))))))))).
% 0.18/0.78
% 0.18/0.78 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.78 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.78 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.78 fresh(y, y, x1...xn) = u
% 0.18/0.78 C => fresh(s, t, x1...xn) = v
% 0.18/0.78 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.78 variables of u and v.
% 0.18/0.78 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.78 input problem has no model of domain size 1).
% 0.18/0.78
% 0.18/0.78 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.78
% 0.18/0.78 Axiom 1 (co1): nil = w.
% 0.18/0.78 Axiom 2 (co1_1): u = w.
% 0.18/0.78 Axiom 3 (co1_4): ssList(v) = true2.
% 0.18/0.78 Axiom 4 (ax74): equalelemsP(nil) = true2.
% 0.18/0.78 Axiom 5 (ax57): fresh44(X, X, Y) = true2.
% 0.18/0.78 Axiom 6 (ax57): fresh44(ssList(X), true2, X) = segmentP(X, nil).
% 0.18/0.78
% 0.18/0.78 Lemma 7: u = nil.
% 0.18/0.78 Proof:
% 0.18/0.78 u
% 0.18/0.78 = { by axiom 2 (co1_1) }
% 0.18/0.78 w
% 0.18/0.78 = { by axiom 1 (co1) R->L }
% 0.18/0.78 nil
% 0.18/0.78
% 0.18/0.78 Goal 1 (co1_7): tuple2(segmentP(v, u), equalelemsP(u)) = tuple2(true2, true2).
% 0.18/0.78 Proof:
% 0.18/0.78 tuple2(segmentP(v, u), equalelemsP(u))
% 0.18/0.78 = { by lemma 7 }
% 0.18/0.78 tuple2(segmentP(v, u), equalelemsP(nil))
% 0.18/0.78 = { by axiom 4 (ax74) }
% 0.18/0.78 tuple2(segmentP(v, u), true2)
% 0.18/0.78 = { by lemma 7 }
% 0.18/0.78 tuple2(segmentP(v, nil), true2)
% 0.18/0.78 = { by axiom 6 (ax57) R->L }
% 0.18/0.78 tuple2(fresh44(ssList(v), true2, v), true2)
% 0.18/0.78 = { by axiom 3 (co1_4) }
% 0.18/0.78 tuple2(fresh44(true2, true2, v), true2)
% 0.18/0.78 = { by axiom 5 (ax57) }
% 0.18/0.78 tuple2(true2, true2)
% 0.18/0.78 % SZS output end Proof
% 0.18/0.78
% 0.18/0.78 RESULT: Theorem (the conjecture is true).
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