TSTP Solution File: SWC403+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC403+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 : n029.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 20:55:24 EDT 2023
% Result : Theorem 211.88s 27.09s
% Output : Proof 212.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC403+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 15:13:26 EDT 2023
% 0.12/0.33 % CPUTime :
% 211.88/27.09 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 211.88/27.09
% 211.88/27.09 % SZS status Theorem
% 211.88/27.09
% 211.88/27.10 % SZS output start Proof
% 211.88/27.10 Take the following subset of the input axioms:
% 211.98/27.10 fof(ax26, axiom, ![U]: (ssList(U) => ![V]: (ssList(V) => ssList(app(U, V))))).
% 211.98/27.10 fof(ax36, axiom, ![U2]: (ssItem(U2) => ![V2]: (ssList(V2) => ![W]: (ssList(W) => (memberP(app(V2, W), U2) <=> (memberP(V2, U2) | memberP(W, U2))))))).
% 211.98/27.10 fof(ax7, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => (segmentP(U2, V2) <=> ?[W2]: (ssList(W2) & ?[X]: (ssList(X) & app(app(W2, V2), X)=U2)))))).
% 211.98/27.10 fof(ax82, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => app(app(U2, V2), W2)=app(U2, app(V2, W2)))))).
% 211.98/27.10 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => ![X2]: (ssList(X2) => (V2!=X2 | (U2!=W2 | (~segmentP(X2, W2) | (~strictorderedP(W2) | (?[Y]: (ssList(Y) & (neq(W2, Y) & (segmentP(X2, Y) & (segmentP(Y, W2) & strictorderedP(Y))))) | ![Z]: (ssItem(Z) => (~memberP(U2, Z) | memberP(V2, Z))))))))))))).
% 211.98/27.10
% 211.98/27.10 Now clausify the problem and encode Horn clauses using encoding 3 of
% 211.98/27.10 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 211.98/27.10 We repeatedly replace C & s=t => u=v by the two clauses:
% 211.98/27.10 fresh(y, y, x1...xn) = u
% 211.98/27.10 C => fresh(s, t, x1...xn) = v
% 211.98/27.10 where fresh is a fresh function symbol and x1..xn are the free
% 211.98/27.10 variables of u and v.
% 211.98/27.10 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 211.98/27.10 input problem has no model of domain size 1).
% 211.98/27.10
% 211.98/27.10 The encoding turns the above axioms into the following unit equations and goals:
% 211.98/27.10
% 211.98/27.10 Axiom 1 (co1_1): v = x.
% 211.98/27.10 Axiom 2 (co1): u = w.
% 211.98/27.10 Axiom 3 (co1_5): ssList(w) = true2.
% 211.98/27.10 Axiom 4 (co1_4): ssList(v) = true2.
% 211.98/27.10 Axiom 5 (co1_2): ssItem(z) = true2.
% 211.98/27.10 Axiom 6 (co1_8): segmentP(x, w) = true2.
% 211.98/27.10 Axiom 7 (co1_7): memberP(u, z) = true2.
% 211.98/27.10 Axiom 8 (ax7_3): fresh258(X, X, Y, Z) = true2.
% 211.98/27.10 Axiom 9 (ax7_2): fresh256(X, X, Y, Z) = true2.
% 211.98/27.10 Axiom 10 (ax7_1): fresh254(X, X, Y, Z) = Y.
% 211.98/27.10 Axiom 11 (ax26): fresh72(X, X, Y, Z) = ssList(app(Y, Z)).
% 211.98/27.10 Axiom 12 (ax26): fresh71(X, X, Y, Z) = true2.
% 211.98/27.10 Axiom 13 (ax7_2): fresh26(X, X, Y, Z) = ssList(w9(Y, Z)).
% 211.98/27.10 Axiom 14 (ax7_3): fresh25(X, X, Y, Z) = ssList(x9(Y, Z)).
% 211.98/27.10 Axiom 15 (ax7_3): fresh257(X, X, Y, Z) = fresh258(ssList(Y), true2, Y, Z).
% 211.98/27.10 Axiom 16 (ax7_2): fresh255(X, X, Y, Z) = fresh256(ssList(Y), true2, Y, Z).
% 211.98/27.10 Axiom 17 (ax7_1): fresh253(X, X, Y, Z) = fresh254(ssList(Y), true2, Y, Z).
% 211.98/27.10 Axiom 18 (ax7_1): fresh252(X, X, Y, Z) = fresh253(ssList(Z), true2, Y, Z).
% 211.98/27.10 Axiom 19 (ax36_1): fresh195(X, X, Y, Z, W) = true2.
% 211.98/27.10 Axiom 20 (ax36_1): fresh193(X, X, Y, Z, W) = memberP(app(Z, W), Y).
% 211.98/27.10 Axiom 21 (ax36): fresh191(X, X, Y, Z, W) = true2.
% 211.98/27.10 Axiom 22 (ax36): fresh189(X, X, Y, Z, W) = memberP(app(Z, W), Y).
% 211.98/27.10 Axiom 23 (ax82): fresh119(X, X, Y, Z, W) = app(Y, app(Z, W)).
% 211.98/27.10 Axiom 24 (ax26): fresh72(ssList(X), true2, Y, X) = fresh71(ssList(Y), true2, Y, X).
% 211.98/27.11 Axiom 25 (ax82): fresh22(X, X, Y, Z, W) = app(app(Y, Z), W).
% 211.98/27.11 Axiom 26 (ax7_3): fresh257(segmentP(X, Y), true2, X, Y) = fresh25(ssList(Y), true2, X, Y).
% 211.98/27.11 Axiom 27 (ax7_2): fresh255(segmentP(X, Y), true2, X, Y) = fresh26(ssList(Y), true2, X, Y).
% 211.98/27.11 Axiom 28 (ax36_1): fresh194(X, X, Y, Z, W) = fresh195(ssItem(Y), true2, Y, Z, W).
% 211.98/27.11 Axiom 29 (ax36_1): fresh192(X, X, Y, Z, W) = fresh193(ssList(Z), true2, Y, Z, W).
% 211.98/27.11 Axiom 30 (ax36): fresh190(X, X, Y, Z, W) = fresh191(ssItem(Y), true2, Y, Z, W).
% 211.98/27.11 Axiom 31 (ax36): fresh188(X, X, Y, Z, W) = fresh189(ssList(Z), true2, Y, Z, W).
% 211.98/27.11 Axiom 32 (ax82): fresh118(X, X, Y, Z, W) = fresh119(ssList(Y), true2, Y, Z, W).
% 211.98/27.11 Axiom 33 (ax82): fresh118(ssList(X), true2, Y, Z, X) = fresh22(ssList(Z), true2, Y, Z, X).
% 211.98/27.11 Axiom 34 (ax36_1): fresh192(memberP(X, Y), true2, Y, Z, X) = fresh194(ssList(X), true2, Y, Z, X).
% 211.98/27.11 Axiom 35 (ax36): fresh188(memberP(X, Y), true2, Y, X, Z) = fresh190(ssList(Z), true2, Y, X, Z).
% 211.98/27.11 Axiom 36 (ax7_1): fresh252(segmentP(X, Y), true2, X, Y) = app(app(w9(X, Y), Y), x9(X, Y)).
% 211.98/27.11
% 211.98/27.11 Lemma 37: segmentP(v, w) = true2.
% 211.98/27.11 Proof:
% 211.98/27.11 segmentP(v, w)
% 211.98/27.11 = { by axiom 1 (co1_1) }
% 211.98/27.11 segmentP(x, w)
% 211.98/27.11 = { by axiom 6 (co1_8) }
% 211.98/27.11 true2
% 211.98/27.11
% 211.98/27.11 Lemma 38: ssList(w9(v, w)) = true2.
% 211.98/27.11 Proof:
% 211.98/27.11 ssList(w9(v, w))
% 211.98/27.11 = { by axiom 13 (ax7_2) R->L }
% 211.98/27.11 fresh26(true2, true2, v, w)
% 211.98/27.11 = { by axiom 3 (co1_5) R->L }
% 211.98/27.11 fresh26(ssList(w), true2, v, w)
% 211.98/27.11 = { by axiom 27 (ax7_2) R->L }
% 211.98/27.11 fresh255(segmentP(v, w), true2, v, w)
% 211.98/27.11 = { by lemma 37 }
% 211.98/27.11 fresh255(true2, true2, v, w)
% 211.98/27.11 = { by axiom 16 (ax7_2) }
% 211.98/27.11 fresh256(ssList(v), true2, v, w)
% 211.98/27.11 = { by axiom 4 (co1_4) }
% 211.98/27.11 fresh256(true2, true2, v, w)
% 211.98/27.11 = { by axiom 9 (ax7_2) }
% 211.98/27.11 true2
% 211.98/27.11
% 211.98/27.11 Lemma 39: ssList(x9(v, w)) = true2.
% 211.98/27.11 Proof:
% 211.98/27.11 ssList(x9(v, w))
% 211.98/27.11 = { by axiom 14 (ax7_3) R->L }
% 211.98/27.11 fresh25(true2, true2, v, w)
% 211.98/27.11 = { by axiom 3 (co1_5) R->L }
% 211.98/27.11 fresh25(ssList(w), true2, v, w)
% 211.98/27.11 = { by axiom 26 (ax7_3) R->L }
% 211.98/27.11 fresh257(segmentP(v, w), true2, v, w)
% 211.98/27.11 = { by lemma 37 }
% 211.98/27.11 fresh257(true2, true2, v, w)
% 212.04/27.11 = { by axiom 15 (ax7_3) }
% 212.04/27.11 fresh258(ssList(v), true2, v, w)
% 212.04/27.11 = { by axiom 4 (co1_4) }
% 212.04/27.11 fresh258(true2, true2, v, w)
% 212.04/27.11 = { by axiom 8 (ax7_3) }
% 212.04/27.11 true2
% 212.04/27.11
% 212.04/27.11 Goal 1 (co1_11): memberP(v, z) = true2.
% 212.04/27.11 Proof:
% 212.04/27.11 memberP(v, z)
% 212.04/27.11 = { by axiom 10 (ax7_1) R->L }
% 212.04/27.11 memberP(fresh254(true2, true2, v, w), z)
% 212.04/27.11 = { by axiom 4 (co1_4) R->L }
% 212.04/27.11 memberP(fresh254(ssList(v), true2, v, w), z)
% 212.04/27.11 = { by axiom 17 (ax7_1) R->L }
% 212.04/27.11 memberP(fresh253(true2, true2, v, w), z)
% 212.04/27.11 = { by axiom 3 (co1_5) R->L }
% 212.04/27.11 memberP(fresh253(ssList(w), true2, v, w), z)
% 212.04/27.11 = { by axiom 18 (ax7_1) R->L }
% 212.04/27.11 memberP(fresh252(true2, true2, v, w), z)
% 212.04/27.11 = { by lemma 37 R->L }
% 212.04/27.11 memberP(fresh252(segmentP(v, w), true2, v, w), z)
% 212.04/27.11 = { by axiom 36 (ax7_1) }
% 212.04/27.11 memberP(app(app(w9(v, w), w), x9(v, w)), z)
% 212.04/27.11 = { by axiom 25 (ax82) R->L }
% 212.04/27.11 memberP(fresh22(true2, true2, w9(v, w), w, x9(v, w)), z)
% 212.04/27.11 = { by axiom 3 (co1_5) R->L }
% 212.04/27.11 memberP(fresh22(ssList(w), true2, w9(v, w), w, x9(v, w)), z)
% 212.04/27.11 = { by axiom 33 (ax82) R->L }
% 212.04/27.11 memberP(fresh118(ssList(x9(v, w)), true2, w9(v, w), w, x9(v, w)), z)
% 212.04/27.11 = { by lemma 39 }
% 212.04/27.11 memberP(fresh118(true2, true2, w9(v, w), w, x9(v, w)), z)
% 212.04/27.11 = { by axiom 32 (ax82) }
% 212.04/27.11 memberP(fresh119(ssList(w9(v, w)), true2, w9(v, w), w, x9(v, w)), z)
% 212.04/27.11 = { by lemma 38 }
% 212.04/27.11 memberP(fresh119(true2, true2, w9(v, w), w, x9(v, w)), z)
% 212.04/27.11 = { by axiom 23 (ax82) }
% 212.04/27.11 memberP(app(w9(v, w), app(w, x9(v, w))), z)
% 212.04/27.11 = { by axiom 20 (ax36_1) R->L }
% 212.04/27.11 fresh193(true2, true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by lemma 38 R->L }
% 212.04/27.11 fresh193(ssList(w9(v, w)), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 29 (ax36_1) R->L }
% 212.04/27.11 fresh192(true2, true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 21 (ax36) R->L }
% 212.04/27.11 fresh192(fresh191(true2, true2, z, w, x9(v, w)), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 5 (co1_2) R->L }
% 212.04/27.11 fresh192(fresh191(ssItem(z), true2, z, w, x9(v, w)), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 30 (ax36) R->L }
% 212.04/27.11 fresh192(fresh190(true2, true2, z, w, x9(v, w)), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by lemma 39 R->L }
% 212.04/27.11 fresh192(fresh190(ssList(x9(v, w)), true2, z, w, x9(v, w)), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 35 (ax36) R->L }
% 212.04/27.11 fresh192(fresh188(memberP(w, z), true2, z, w, x9(v, w)), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 2 (co1) R->L }
% 212.04/27.11 fresh192(fresh188(memberP(u, z), true2, z, w, x9(v, w)), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 7 (co1_7) }
% 212.04/27.11 fresh192(fresh188(true2, true2, z, w, x9(v, w)), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 31 (ax36) }
% 212.04/27.11 fresh192(fresh189(ssList(w), true2, z, w, x9(v, w)), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 3 (co1_5) }
% 212.04/27.11 fresh192(fresh189(true2, true2, z, w, x9(v, w)), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 22 (ax36) }
% 212.04/27.11 fresh192(memberP(app(w, x9(v, w)), z), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 34 (ax36_1) }
% 212.04/27.11 fresh194(ssList(app(w, x9(v, w))), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 11 (ax26) R->L }
% 212.04/27.11 fresh194(fresh72(true2, true2, w, x9(v, w)), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by lemma 39 R->L }
% 212.04/27.11 fresh194(fresh72(ssList(x9(v, w)), true2, w, x9(v, w)), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 24 (ax26) }
% 212.04/27.11 fresh194(fresh71(ssList(w), true2, w, x9(v, w)), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 3 (co1_5) }
% 212.04/27.11 fresh194(fresh71(true2, true2, w, x9(v, w)), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 12 (ax26) }
% 212.04/27.11 fresh194(true2, true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 28 (ax36_1) }
% 212.04/27.11 fresh195(ssItem(z), true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 5 (co1_2) }
% 212.04/27.11 fresh195(true2, true2, z, w9(v, w), app(w, x9(v, w)))
% 212.04/27.11 = { by axiom 19 (ax36_1) }
% 212.04/27.11 true2
% 212.04/27.11 % SZS output end Proof
% 212.04/27.11
% 212.04/27.11 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------