TSTP Solution File: SWC364+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC364+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 : n008.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 20:55:11 EDT 2023
% Result : Theorem 199.03s 25.85s
% Output : Proof 199.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC364+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 : n008.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 16:58:32 EDT 2023
% 0.13/0.35 % CPUTime :
% 199.03/25.85 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 199.03/25.85
% 199.03/25.85 % SZS status Theorem
% 199.03/25.85
% 199.03/25.86 % SZS output start Proof
% 199.03/25.86 Take the following subset of the input axioms:
% 199.03/25.86 fof(ax16, axiom, ![U]: (ssList(U) => ![V]: (ssItem(V) => ssList(cons(V, U))))).
% 199.03/25.86 fof(ax17, axiom, ssList(nil)).
% 199.03/25.87 fof(ax55, axiom, ![U2]: (ssList(U2) => segmentP(U2, U2))).
% 199.03/25.87 fof(ax56, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W]: (ssList(W) => ![X]: (ssList(X) => (segmentP(U2, V2) => segmentP(app(app(W, U2), X), V2))))))).
% 199.03/25.87 fof(ax84, axiom, ![U2]: (ssList(U2) => app(U2, nil)=U2)).
% 199.03/25.87 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => ![X2]: (ssList(X2) => (V2!=X2 | (U2!=W2 | ((~neq(V2, nil) | (![Y]: (ssItem(Y) => app(cons(Y, nil), W2)!=X2) | segmentP(V2, U2))) & (~neq(V2, nil) | neq(X2, nil)))))))))).
% 199.03/25.87
% 199.03/25.87 Now clausify the problem and encode Horn clauses using encoding 3 of
% 199.03/25.87 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 199.03/25.87 We repeatedly replace C & s=t => u=v by the two clauses:
% 199.03/25.87 fresh(y, y, x1...xn) = u
% 199.03/25.87 C => fresh(s, t, x1...xn) = v
% 199.03/25.87 where fresh is a fresh function symbol and x1..xn are the free
% 199.03/25.87 variables of u and v.
% 199.03/25.87 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 199.03/25.87 input problem has no model of domain size 1).
% 199.03/25.87
% 199.03/25.87 The encoding turns the above axioms into the following unit equations and goals:
% 199.03/25.87
% 199.03/25.87 Axiom 1 (co1_2): v = x.
% 199.03/25.87 Axiom 2 (co1_1): u = w.
% 199.03/25.87 Axiom 3 (ax17): ssList(nil) = true2.
% 199.03/25.87 Axiom 4 (co1_6): ssList(v) = true2.
% 199.03/25.87 Axiom 5 (co1_5): ssList(u) = true2.
% 199.03/25.87 Axiom 6 (co1_4): neq(v, nil) = true2.
% 199.03/25.87 Axiom 7 (co1_10): fresh17(X, X) = true2.
% 199.03/25.87 Axiom 8 (co1_9): fresh14(X, X) = x.
% 199.03/25.87 Axiom 9 (ax84): fresh(X, X, Y) = Y.
% 199.03/25.87 Axiom 10 (ax55): fresh49(X, X, Y) = true2.
% 199.03/25.87 Axiom 11 (ax84): fresh(ssList(X), true2, X) = app(X, nil).
% 199.03/25.87 Axiom 12 (ax16): fresh80(X, X, Y, Z) = ssList(cons(Z, Y)).
% 199.03/25.87 Axiom 13 (ax16): fresh79(X, X, Y, Z) = true2.
% 199.03/25.87 Axiom 14 (ax55): fresh49(ssList(X), true2, X) = segmentP(X, X).
% 199.03/25.87 Axiom 15 (co1_10): fresh17(neq(x, nil), true2) = ssItem(y).
% 199.03/25.87 Axiom 16 (co1_9): fresh14(neq(x, nil), true2) = app(cons(y, nil), w).
% 199.03/25.87 Axiom 17 (ax16): fresh80(ssList(X), true2, X, Y) = fresh79(ssItem(Y), true2, X, Y).
% 199.03/25.87 Axiom 18 (ax56): fresh138(X, X, Y, Z, W, V) = true2.
% 199.03/25.87 Axiom 19 (ax56): fresh136(X, X, Y, Z, W, V) = segmentP(app(app(W, Y), V), Z).
% 199.03/25.87 Axiom 20 (ax56): fresh137(X, X, Y, Z, W, V) = fresh138(ssList(Y), true2, Y, Z, W, V).
% 199.03/25.87 Axiom 21 (ax56): fresh134(X, X, Y, Z, W, V) = fresh137(ssList(W), true2, Y, Z, W, V).
% 199.03/25.87 Axiom 22 (ax56): fresh135(X, X, Y, Z, W, V) = fresh136(ssList(Z), true2, Y, Z, W, V).
% 199.03/25.87 Axiom 23 (ax56): fresh134(segmentP(X, Y), true2, X, Y, Z, W) = fresh135(ssList(W), true2, X, Y, Z, W).
% 199.03/25.87
% 199.03/25.87 Goal 1 (co1_12): tuple2(neq(x, nil), segmentP(v, u)) = tuple2(true2, true2).
% 199.03/25.87 Proof:
% 199.03/25.87 tuple2(neq(x, nil), segmentP(v, u))
% 199.03/25.87 = { by axiom 9 (ax84) R->L }
% 199.03/25.87 tuple2(neq(x, nil), segmentP(fresh(true2, true2, v), u))
% 199.03/25.87 = { by axiom 4 (co1_6) R->L }
% 199.03/25.87 tuple2(neq(x, nil), segmentP(fresh(ssList(v), true2, v), u))
% 199.03/25.87 = { by axiom 11 (ax84) }
% 199.03/25.87 tuple2(neq(x, nil), segmentP(app(v, nil), u))
% 199.03/25.87 = { by axiom 1 (co1_2) }
% 199.03/25.87 tuple2(neq(x, nil), segmentP(app(x, nil), u))
% 199.03/25.87 = { by axiom 8 (co1_9) R->L }
% 199.03/25.87 tuple2(neq(x, nil), segmentP(app(fresh14(true2, true2), nil), u))
% 199.03/25.87 = { by axiom 6 (co1_4) R->L }
% 199.03/25.87 tuple2(neq(x, nil), segmentP(app(fresh14(neq(v, nil), true2), nil), u))
% 199.03/25.87 = { by axiom 1 (co1_2) }
% 199.03/25.87 tuple2(neq(x, nil), segmentP(app(fresh14(neq(x, nil), true2), nil), u))
% 199.03/25.87 = { by axiom 16 (co1_9) }
% 199.03/25.87 tuple2(neq(x, nil), segmentP(app(app(cons(y, nil), w), nil), u))
% 199.03/25.87 = { by axiom 2 (co1_1) R->L }
% 199.03/25.87 tuple2(neq(x, nil), segmentP(app(app(cons(y, nil), u), nil), u))
% 199.03/25.87 = { by axiom 19 (ax56) R->L }
% 199.03/25.87 tuple2(neq(x, nil), fresh136(true2, true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 5 (co1_5) R->L }
% 199.03/25.87 tuple2(neq(x, nil), fresh136(ssList(u), true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 22 (ax56) R->L }
% 199.03/25.87 tuple2(neq(x, nil), fresh135(true2, true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 3 (ax17) R->L }
% 199.03/25.87 tuple2(neq(x, nil), fresh135(ssList(nil), true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 23 (ax56) R->L }
% 199.03/25.87 tuple2(neq(x, nil), fresh134(segmentP(u, u), true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 14 (ax55) R->L }
% 199.03/25.87 tuple2(neq(x, nil), fresh134(fresh49(ssList(u), true2, u), true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 5 (co1_5) }
% 199.03/25.87 tuple2(neq(x, nil), fresh134(fresh49(true2, true2, u), true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 10 (ax55) }
% 199.03/25.87 tuple2(neq(x, nil), fresh134(true2, true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 21 (ax56) }
% 199.03/25.87 tuple2(neq(x, nil), fresh137(ssList(cons(y, nil)), true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 12 (ax16) R->L }
% 199.03/25.87 tuple2(neq(x, nil), fresh137(fresh80(true2, true2, nil, y), true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 3 (ax17) R->L }
% 199.03/25.87 tuple2(neq(x, nil), fresh137(fresh80(ssList(nil), true2, nil, y), true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 17 (ax16) }
% 199.03/25.87 tuple2(neq(x, nil), fresh137(fresh79(ssItem(y), true2, nil, y), true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 15 (co1_10) R->L }
% 199.03/25.87 tuple2(neq(x, nil), fresh137(fresh79(fresh17(neq(x, nil), true2), true2, nil, y), true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 1 (co1_2) R->L }
% 199.03/25.87 tuple2(neq(x, nil), fresh137(fresh79(fresh17(neq(v, nil), true2), true2, nil, y), true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 6 (co1_4) }
% 199.03/25.87 tuple2(neq(x, nil), fresh137(fresh79(fresh17(true2, true2), true2, nil, y), true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 7 (co1_10) }
% 199.03/25.87 tuple2(neq(x, nil), fresh137(fresh79(true2, true2, nil, y), true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 13 (ax16) }
% 199.03/25.87 tuple2(neq(x, nil), fresh137(true2, true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 20 (ax56) }
% 199.03/25.87 tuple2(neq(x, nil), fresh138(ssList(u), true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 5 (co1_5) }
% 199.03/25.87 tuple2(neq(x, nil), fresh138(true2, true2, u, u, cons(y, nil), nil))
% 199.03/25.87 = { by axiom 18 (ax56) }
% 199.03/25.87 tuple2(neq(x, nil), true2)
% 199.03/25.87 = { by axiom 1 (co1_2) R->L }
% 199.03/25.87 tuple2(neq(v, nil), true2)
% 199.03/25.87 = { by axiom 6 (co1_4) }
% 199.03/25.87 tuple2(true2, true2)
% 199.03/25.87 % SZS output end Proof
% 199.03/25.87
% 199.03/25.87 RESULT: Theorem (the conjecture is true).
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