TSTP Solution File: SWC373+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC373+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 : n019.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 20:55:14 EDT 2023
% Result : Theorem 48.27s 6.60s
% Output : Proof 48.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC373+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % 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 : n019.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 18:21:13 EDT 2023
% 0.14/0.35 % CPUTime :
% 48.27/6.60 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 48.27/6.60
% 48.27/6.60 % SZS status Theorem
% 48.27/6.60
% 48.67/6.60 % SZS output start Proof
% 48.67/6.60 Take the following subset of the input axioms:
% 48.67/6.61 fof(ax17, axiom, ssList(nil)).
% 48.67/6.61 fof(ax6, axiom, ![U]: (ssList(U) => ![V]: (ssList(V) => (rearsegP(U, V) <=> ?[W]: (ssList(W) & app(W, V)=U))))).
% 48.67/6.61 fof(ax7, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => (segmentP(U2, V2) <=> ?[W2]: (ssList(W2) & ?[X]: (ssList(X) & app(app(W2, V2), X)=U2)))))).
% 48.67/6.61 fof(ax84, axiom, ![U2]: (ssList(U2) => app(U2, nil)=U2)).
% 48.67/6.61 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => ![X2]: (ssList(X2) => (V2!=X2 | (U2!=W2 | (~rearsegP(X2, W2) | segmentP(V2, U2))))))))).
% 48.67/6.61
% 48.67/6.61 Now clausify the problem and encode Horn clauses using encoding 3 of
% 48.67/6.61 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 48.67/6.61 We repeatedly replace C & s=t => u=v by the two clauses:
% 48.67/6.61 fresh(y, y, x1...xn) = u
% 48.67/6.61 C => fresh(s, t, x1...xn) = v
% 48.67/6.61 where fresh is a fresh function symbol and x1..xn are the free
% 48.67/6.61 variables of u and v.
% 48.67/6.61 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 48.67/6.61 input problem has no model of domain size 1).
% 48.67/6.61
% 48.67/6.61 The encoding turns the above axioms into the following unit equations and goals:
% 48.67/6.61
% 48.67/6.61 Axiom 1 (co1): u = w.
% 48.67/6.61 Axiom 2 (co1_1): v = x.
% 48.67/6.61 Axiom 3 (ax17): ssList(nil) = true2.
% 48.67/6.61 Axiom 4 (co1_2): ssList(u) = true2.
% 48.67/6.61 Axiom 5 (co1_3): ssList(v) = true2.
% 48.67/6.61 Axiom 6 (co1_6): rearsegP(x, w) = true2.
% 48.67/6.61 Axiom 7 (ax84): fresh(X, X, Y) = Y.
% 48.67/6.61 Axiom 8 (ax84): fresh(ssList(X), true2, X) = app(X, nil).
% 48.67/6.61 Axiom 9 (ax6_2): fresh266(X, X, Y, Z) = true2.
% 48.67/6.61 Axiom 10 (ax6_1): fresh264(X, X, Y, Z) = Y.
% 48.67/6.61 Axiom 11 (ax6_1): fresh32(X, X, Y, Z) = app(w10(Y, Z), Z).
% 48.67/6.61 Axiom 12 (ax6_2): fresh31(X, X, Y, Z) = ssList(w10(Y, Z)).
% 48.67/6.61 Axiom 13 (ax7): fresh30(X, X, Y, Z) = true2.
% 48.67/6.61 Axiom 14 (ax6_2): fresh265(X, X, Y, Z) = fresh266(ssList(Y), true2, Y, Z).
% 48.67/6.61 Axiom 15 (ax6_1): fresh263(X, X, Y, Z) = fresh264(ssList(Y), true2, Y, Z).
% 48.67/6.61 Axiom 16 (ax6_2): fresh265(rearsegP(X, Y), true2, X, Y) = fresh31(ssList(Y), true2, X, Y).
% 48.67/6.61 Axiom 17 (ax6_1): fresh263(rearsegP(X, Y), true2, X, Y) = fresh32(ssList(Y), true2, X, Y).
% 48.67/6.61 Axiom 18 (ax7): fresh251(X, X, Y, Z, W, V) = segmentP(Y, Z).
% 48.67/6.61 Axiom 19 (ax7): fresh250(X, X, Y, Z, W, V) = fresh251(ssList(Y), true2, Y, Z, W, V).
% 48.67/6.61 Axiom 20 (ax7): fresh249(X, X, Y, Z, W, V) = fresh250(ssList(Z), true2, Y, Z, W, V).
% 48.67/6.61 Axiom 21 (ax7): fresh248(X, X, Y, Z, W, V) = fresh249(ssList(W), true2, Y, Z, W, V).
% 48.67/6.61 Axiom 22 (ax7): fresh248(ssList(X), true2, Y, Z, W, X) = fresh30(app(app(W, Z), X), Y, Y, Z).
% 48.67/6.61
% 48.67/6.61 Lemma 23: rearsegP(v, u) = true2.
% 48.67/6.61 Proof:
% 48.67/6.61 rearsegP(v, u)
% 48.67/6.61 = { by axiom 1 (co1) }
% 48.67/6.61 rearsegP(v, w)
% 48.67/6.61 = { by axiom 2 (co1_1) }
% 48.67/6.61 rearsegP(x, w)
% 48.67/6.61 = { by axiom 6 (co1_6) }
% 48.67/6.61 true2
% 48.67/6.61
% 48.67/6.61 Goal 1 (co1_7): segmentP(v, u) = true2.
% 48.67/6.61 Proof:
% 48.67/6.61 segmentP(v, u)
% 48.67/6.61 = { by axiom 18 (ax7) R->L }
% 48.67/6.61 fresh251(true2, true2, v, u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 5 (co1_3) R->L }
% 48.67/6.61 fresh251(ssList(v), true2, v, u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 19 (ax7) R->L }
% 48.67/6.61 fresh250(true2, true2, v, u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 7 (ax84) R->L }
% 48.67/6.61 fresh250(true2, true2, fresh(true2, true2, v), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 5 (co1_3) R->L }
% 48.67/6.61 fresh250(true2, true2, fresh(ssList(v), true2, v), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 8 (ax84) }
% 48.67/6.61 fresh250(true2, true2, app(v, nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 4 (co1_2) R->L }
% 48.67/6.61 fresh250(ssList(u), true2, app(v, nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 20 (ax7) R->L }
% 48.67/6.61 fresh249(true2, true2, app(v, nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 9 (ax6_2) R->L }
% 48.67/6.61 fresh249(fresh266(true2, true2, v, u), true2, app(v, nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 5 (co1_3) R->L }
% 48.67/6.61 fresh249(fresh266(ssList(v), true2, v, u), true2, app(v, nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 14 (ax6_2) R->L }
% 48.67/6.61 fresh249(fresh265(true2, true2, v, u), true2, app(v, nil), u, w10(v, u), nil)
% 48.67/6.61 = { by lemma 23 R->L }
% 48.67/6.61 fresh249(fresh265(rearsegP(v, u), true2, v, u), true2, app(v, nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 16 (ax6_2) }
% 48.67/6.61 fresh249(fresh31(ssList(u), true2, v, u), true2, app(v, nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 4 (co1_2) }
% 48.67/6.61 fresh249(fresh31(true2, true2, v, u), true2, app(v, nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 12 (ax6_2) }
% 48.67/6.61 fresh249(ssList(w10(v, u)), true2, app(v, nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 21 (ax7) R->L }
% 48.67/6.61 fresh248(true2, true2, app(v, nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 10 (ax6_1) R->L }
% 48.67/6.61 fresh248(true2, true2, app(fresh264(true2, true2, v, u), nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 5 (co1_3) R->L }
% 48.67/6.61 fresh248(true2, true2, app(fresh264(ssList(v), true2, v, u), nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 15 (ax6_1) R->L }
% 48.67/6.61 fresh248(true2, true2, app(fresh263(true2, true2, v, u), nil), u, w10(v, u), nil)
% 48.67/6.61 = { by lemma 23 R->L }
% 48.67/6.61 fresh248(true2, true2, app(fresh263(rearsegP(v, u), true2, v, u), nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 17 (ax6_1) }
% 48.67/6.61 fresh248(true2, true2, app(fresh32(ssList(u), true2, v, u), nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 4 (co1_2) }
% 48.67/6.61 fresh248(true2, true2, app(fresh32(true2, true2, v, u), nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 11 (ax6_1) }
% 48.67/6.61 fresh248(true2, true2, app(app(w10(v, u), u), nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 3 (ax17) R->L }
% 48.67/6.61 fresh248(ssList(nil), true2, app(app(w10(v, u), u), nil), u, w10(v, u), nil)
% 48.67/6.61 = { by axiom 22 (ax7) }
% 48.67/6.61 fresh30(app(app(w10(v, u), u), nil), app(app(w10(v, u), u), nil), app(app(w10(v, u), u), nil), u)
% 48.67/6.61 = { by axiom 13 (ax7) }
% 48.67/6.61 true2
% 48.67/6.61 % SZS output end Proof
% 48.67/6.61
% 48.67/6.61 RESULT: Theorem (the conjecture is true).
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