TSTP Solution File: SWC122+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC122+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 : n013.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 20:53:58 EDT 2023
% Result : Theorem 53.70s 7.22s
% Output : Proof 53.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC122+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.13 % 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 : n013.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 18:51:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 53.70/7.22 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 53.70/7.22
% 53.70/7.22 % SZS status Theorem
% 53.70/7.22
% 53.70/7.23 % SZS output start Proof
% 53.70/7.23 Take the following subset of the input axioms:
% 53.70/7.23 fof(ax17, axiom, ssList(nil)).
% 53.70/7.23 fof(ax6, axiom, ![U]: (ssList(U) => ![V]: (ssList(V) => (rearsegP(U, V) <=> ?[W]: (ssList(W) & app(W, V)=U))))).
% 53.70/7.23 fof(ax7, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => (segmentP(U2, V2) <=> ?[W2]: (ssList(W2) & ?[X]: (ssList(X) & app(app(W2, V2), X)=U2)))))).
% 53.70/7.23 fof(ax84, axiom, ![U2]: (ssList(U2) => app(U2, nil)=U2)).
% 53.70/7.23 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => ![X2]: (ssList(X2) => (V2!=X2 | (U2!=W2 | (~neq(V2, nil) | ((nil!=W2 & nil=X2) | ((neq(U2, nil) & segmentP(V2, U2)) | (neq(X2, nil) & (~neq(W2, nil) | ~rearsegP(X2, W2))))))))))))).
% 53.70/7.23
% 53.70/7.23 Now clausify the problem and encode Horn clauses using encoding 3 of
% 53.70/7.23 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 53.70/7.23 We repeatedly replace C & s=t => u=v by the two clauses:
% 53.70/7.23 fresh(y, y, x1...xn) = u
% 53.70/7.23 C => fresh(s, t, x1...xn) = v
% 53.70/7.23 where fresh is a fresh function symbol and x1..xn are the free
% 53.70/7.23 variables of u and v.
% 53.70/7.23 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 53.70/7.23 input problem has no model of domain size 1).
% 53.70/7.23
% 53.70/7.23 The encoding turns the above axioms into the following unit equations and goals:
% 53.70/7.23
% 53.70/7.23 Axiom 1 (co1_1): v = x.
% 53.70/7.23 Axiom 2 (co1): u = w.
% 53.70/7.23 Axiom 3 (ax17): ssList(nil) = true2.
% 53.70/7.23 Axiom 4 (co1_3): ssList(u) = true2.
% 53.70/7.23 Axiom 5 (co1_4): ssList(v) = true2.
% 53.70/7.23 Axiom 6 (co1_2): neq(v, nil) = true2.
% 53.70/7.23 Axiom 7 (co1_10): fresh16(X, X) = true2.
% 53.70/7.23 Axiom 8 (co1_9): fresh14(X, X) = true2.
% 53.70/7.23 Axiom 9 (ax84): fresh(X, X, Y) = Y.
% 53.70/7.23 Axiom 10 (ax84): fresh(ssList(X), true2, X) = app(X, nil).
% 53.70/7.23 Axiom 11 (ax6_2): fresh269(X, X, Y, Z) = true2.
% 53.70/7.23 Axiom 12 (ax6_1): fresh267(X, X, Y, Z) = Y.
% 53.70/7.23 Axiom 13 (ax6_1): fresh35(X, X, Y, Z) = app(w10(Y, Z), Z).
% 53.70/7.23 Axiom 14 (ax6_2): fresh34(X, X, Y, Z) = ssList(w10(Y, Z)).
% 53.70/7.23 Axiom 15 (ax7): fresh33(X, X, Y, Z) = true2.
% 53.70/7.23 Axiom 16 (co1_10): fresh16(neq(x, nil), true2) = rearsegP(x, w).
% 53.70/7.23 Axiom 17 (co1_9): fresh14(neq(x, nil), true2) = neq(w, nil).
% 53.70/7.23 Axiom 18 (ax6_2): fresh268(X, X, Y, Z) = fresh269(ssList(Y), true2, Y, Z).
% 53.70/7.23 Axiom 19 (ax6_1): fresh266(X, X, Y, Z) = fresh267(ssList(Y), true2, Y, Z).
% 53.70/7.23 Axiom 20 (ax6_2): fresh268(rearsegP(X, Y), true2, X, Y) = fresh34(ssList(Y), true2, X, Y).
% 53.70/7.23 Axiom 21 (ax6_1): fresh266(rearsegP(X, Y), true2, X, Y) = fresh35(ssList(Y), true2, X, Y).
% 53.70/7.23 Axiom 22 (ax7): fresh254(X, X, Y, Z, W, V) = segmentP(Y, Z).
% 53.70/7.23 Axiom 23 (ax7): fresh253(X, X, Y, Z, W, V) = fresh254(ssList(Y), true2, Y, Z, W, V).
% 53.70/7.23 Axiom 24 (ax7): fresh252(X, X, Y, Z, W, V) = fresh253(ssList(Z), true2, Y, Z, W, V).
% 53.70/7.23 Axiom 25 (ax7): fresh251(X, X, Y, Z, W, V) = fresh252(ssList(W), true2, Y, Z, W, V).
% 53.70/7.23 Axiom 26 (ax7): fresh251(ssList(X), true2, Y, Z, W, X) = fresh33(app(app(W, Z), X), Y, Y, Z).
% 53.70/7.23
% 53.70/7.23 Lemma 27: rearsegP(v, u) = true2.
% 53.70/7.23 Proof:
% 53.70/7.23 rearsegP(v, u)
% 53.70/7.23 = { by axiom 2 (co1) }
% 53.70/7.23 rearsegP(v, w)
% 53.70/7.23 = { by axiom 1 (co1_1) }
% 53.70/7.23 rearsegP(x, w)
% 53.70/7.23 = { by axiom 16 (co1_10) R->L }
% 53.70/7.23 fresh16(neq(x, nil), true2)
% 53.70/7.23 = { by axiom 1 (co1_1) R->L }
% 53.70/7.23 fresh16(neq(v, nil), true2)
% 53.70/7.23 = { by axiom 6 (co1_2) }
% 53.70/7.23 fresh16(true2, true2)
% 53.70/7.23 = { by axiom 7 (co1_10) }
% 53.70/7.23 true2
% 53.70/7.23
% 53.70/7.23 Goal 1 (co1_8): tuple2(neq(u, nil), segmentP(v, u)) = tuple2(true2, true2).
% 53.70/7.23 Proof:
% 53.70/7.23 tuple2(neq(u, nil), segmentP(v, u))
% 53.70/7.23 = { by axiom 2 (co1) }
% 53.70/7.23 tuple2(neq(w, nil), segmentP(v, u))
% 53.70/7.23 = { by axiom 17 (co1_9) R->L }
% 53.70/7.23 tuple2(fresh14(neq(x, nil), true2), segmentP(v, u))
% 53.70/7.23 = { by axiom 1 (co1_1) R->L }
% 53.70/7.23 tuple2(fresh14(neq(v, nil), true2), segmentP(v, u))
% 53.70/7.23 = { by axiom 6 (co1_2) }
% 53.70/7.23 tuple2(fresh14(true2, true2), segmentP(v, u))
% 53.70/7.23 = { by axiom 8 (co1_9) }
% 53.70/7.23 tuple2(true2, segmentP(v, u))
% 53.70/7.23 = { by axiom 22 (ax7) R->L }
% 53.70/7.23 tuple2(true2, fresh254(true2, true2, v, u, w10(v, u), nil))
% 53.70/7.23 = { by axiom 5 (co1_4) R->L }
% 53.70/7.23 tuple2(true2, fresh254(ssList(v), true2, v, u, w10(v, u), nil))
% 53.70/7.23 = { by axiom 23 (ax7) R->L }
% 53.70/7.23 tuple2(true2, fresh253(true2, true2, v, u, w10(v, u), nil))
% 53.70/7.23 = { by axiom 9 (ax84) R->L }
% 53.70/7.23 tuple2(true2, fresh253(true2, true2, fresh(true2, true2, v), u, w10(v, u), nil))
% 53.70/7.23 = { by axiom 5 (co1_4) R->L }
% 53.70/7.23 tuple2(true2, fresh253(true2, true2, fresh(ssList(v), true2, v), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 10 (ax84) }
% 53.70/7.24 tuple2(true2, fresh253(true2, true2, app(v, nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 4 (co1_3) R->L }
% 53.70/7.24 tuple2(true2, fresh253(ssList(u), true2, app(v, nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 24 (ax7) R->L }
% 53.70/7.24 tuple2(true2, fresh252(true2, true2, app(v, nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 11 (ax6_2) R->L }
% 53.70/7.24 tuple2(true2, fresh252(fresh269(true2, true2, v, u), true2, app(v, nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 5 (co1_4) R->L }
% 53.70/7.24 tuple2(true2, fresh252(fresh269(ssList(v), true2, v, u), true2, app(v, nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 18 (ax6_2) R->L }
% 53.70/7.24 tuple2(true2, fresh252(fresh268(true2, true2, v, u), true2, app(v, nil), u, w10(v, u), nil))
% 53.70/7.24 = { by lemma 27 R->L }
% 53.70/7.24 tuple2(true2, fresh252(fresh268(rearsegP(v, u), true2, v, u), true2, app(v, nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 20 (ax6_2) }
% 53.70/7.24 tuple2(true2, fresh252(fresh34(ssList(u), true2, v, u), true2, app(v, nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 4 (co1_3) }
% 53.70/7.24 tuple2(true2, fresh252(fresh34(true2, true2, v, u), true2, app(v, nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 14 (ax6_2) }
% 53.70/7.24 tuple2(true2, fresh252(ssList(w10(v, u)), true2, app(v, nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 25 (ax7) R->L }
% 53.70/7.24 tuple2(true2, fresh251(true2, true2, app(v, nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 12 (ax6_1) R->L }
% 53.70/7.24 tuple2(true2, fresh251(true2, true2, app(fresh267(true2, true2, v, u), nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 5 (co1_4) R->L }
% 53.70/7.24 tuple2(true2, fresh251(true2, true2, app(fresh267(ssList(v), true2, v, u), nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 19 (ax6_1) R->L }
% 53.70/7.24 tuple2(true2, fresh251(true2, true2, app(fresh266(true2, true2, v, u), nil), u, w10(v, u), nil))
% 53.70/7.24 = { by lemma 27 R->L }
% 53.70/7.24 tuple2(true2, fresh251(true2, true2, app(fresh266(rearsegP(v, u), true2, v, u), nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 21 (ax6_1) }
% 53.70/7.24 tuple2(true2, fresh251(true2, true2, app(fresh35(ssList(u), true2, v, u), nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 4 (co1_3) }
% 53.70/7.24 tuple2(true2, fresh251(true2, true2, app(fresh35(true2, true2, v, u), nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 13 (ax6_1) }
% 53.70/7.24 tuple2(true2, fresh251(true2, true2, app(app(w10(v, u), u), nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 3 (ax17) R->L }
% 53.70/7.24 tuple2(true2, fresh251(ssList(nil), true2, app(app(w10(v, u), u), nil), u, w10(v, u), nil))
% 53.70/7.24 = { by axiom 26 (ax7) }
% 53.70/7.24 tuple2(true2, fresh33(app(app(w10(v, u), u), nil), app(app(w10(v, u), u), nil), app(app(w10(v, u), u), nil), u))
% 53.70/7.24 = { by axiom 15 (ax7) }
% 53.70/7.24 tuple2(true2, true2)
% 53.70/7.24 % SZS output end Proof
% 53.70/7.24
% 53.70/7.24 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------