TSTP Solution File: SWC080+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC080+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 : n020.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 20:53:46 EDT 2023
% Result : Theorem 25.39s 3.66s
% Output : Proof 26.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC080+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.13 % 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 : n020.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 16:42:29 EDT 2023
% 0.14/0.35 % CPUTime :
% 25.39/3.66 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 25.39/3.66
% 25.39/3.66 % SZS status Theorem
% 25.39/3.66
% 25.39/3.67 % SZS output start Proof
% 25.39/3.67 Take the following subset of the input axioms:
% 25.39/3.69 fof(ax1, axiom, ![U]: (ssItem(U) => ![V]: (ssItem(V) => (neq(U, V) <=> U!=V)))).
% 25.39/3.69 fof(ax13, axiom, ![U2]: (ssList(U2) => (duplicatefreeP(U2) <=> ![V2]: (ssItem(V2) => ![W]: (ssItem(W) => ![X]: (ssList(X) => ![Y]: (ssList(Y) => ![Z]: (ssList(Z) => (app(app(X, cons(V2, Y)), cons(W, Z))=U2 => V2!=W))))))))).
% 25.39/3.69 fof(ax15, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => (neq(U2, V2) <=> U2!=V2)))).
% 25.39/3.69 fof(ax17, axiom, ssList(nil)).
% 25.39/3.69 fof(ax18, axiom, ![U2]: (ssList(U2) => ![V2]: (ssItem(V2) => cons(V2, U2)!=U2))).
% 25.39/3.69 fof(ax21, axiom, ![U2]: (ssList(U2) => ![V2]: (ssItem(V2) => nil!=cons(V2, U2)))).
% 25.39/3.69 fof(ax28, axiom, ![U2]: (ssList(U2) => app(nil, U2)=U2)).
% 25.39/3.69 fof(ax33, axiom, ![U2]: (ssItem(U2) => ![V2]: (ssItem(V2) => (lt(U2, V2) => ~lt(V2, U2))))).
% 25.39/3.69 fof(ax38, axiom, ![U2]: (ssItem(U2) => ~memberP(nil, U2))).
% 25.39/3.69 fof(ax5, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => (frontsegP(U2, V2) <=> ?[W2]: (ssList(W2) & app(V2, W2)=U2))))).
% 25.39/3.69 fof(ax7, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => (segmentP(U2, V2) <=> ?[W2]: (ssList(W2) & ?[X2]: (ssList(X2) & app(app(W2, V2), X2)=U2)))))).
% 25.39/3.69 fof(ax8, axiom, ![U2]: (ssList(U2) => (cyclefreeP(U2) <=> ![V2]: (ssItem(V2) => ![W2]: (ssItem(W2) => ![X2]: (ssList(X2) => ![Y2]: (ssList(Y2) => ![Z2]: (ssList(Z2) => (app(app(X2, cons(V2, Y2)), cons(W2, Z2))=U2 => ~(leq(V2, W2) & leq(W2, V2))))))))))).
% 25.39/3.69 fof(ax90, axiom, ![U2]: (ssItem(U2) => ~lt(U2, U2))).
% 25.39/3.69 fof(ax93, axiom, ![U2]: (ssItem(U2) => ![V2]: (ssItem(V2) => (lt(U2, V2) <=> (U2!=V2 & leq(U2, V2)))))).
% 25.39/3.69 fof(ax94, axiom, ![U2]: (ssItem(U2) => ![V2]: (ssItem(V2) => (gt(U2, V2) => ~gt(V2, U2))))).
% 25.39/3.69 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => ![X2]: (~ssList(X2) | (V2!=X2 | (U2!=W2 | ((~neq(V2, nil) | (?[Y2]: (ssList(Y2) & (neq(Y2, nil) & (segmentP(V2, Y2) & segmentP(U2, Y2)))) | ![Z2]: (~ssList(Z2) | (~neq(Z2, nil) | (~frontsegP(X2, Z2) | ~frontsegP(W2, Z2)))))) & (~neq(V2, nil) | neq(X2, nil)))))))))).
% 25.39/3.69
% 25.39/3.69 Now clausify the problem and encode Horn clauses using encoding 3 of
% 25.39/3.69 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 25.39/3.69 We repeatedly replace C & s=t => u=v by the two clauses:
% 25.39/3.69 fresh(y, y, x1...xn) = u
% 25.39/3.69 C => fresh(s, t, x1...xn) = v
% 25.39/3.69 where fresh is a fresh function symbol and x1..xn are the free
% 25.39/3.69 variables of u and v.
% 25.39/3.69 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 25.39/3.69 input problem has no model of domain size 1).
% 25.39/3.69
% 25.39/3.69 The encoding turns the above axioms into the following unit equations and goals:
% 25.39/3.69
% 25.39/3.69 Axiom 1 (co1_1): v = x.
% 25.39/3.69 Axiom 2 (co1): u = w.
% 25.39/3.69 Axiom 3 (ax17): ssList(nil) = true2.
% 25.39/3.69 Axiom 4 (co1_10): ssList(x) = true2.
% 25.39/3.69 Axiom 5 (co1_7): ssList(u) = true2.
% 25.39/3.69 Axiom 6 (co1_2): neq(v, nil) = true2.
% 25.39/3.69 Axiom 7 (co1_14): fresh17(X, X) = true2.
% 25.39/3.69 Axiom 8 (co1_15): fresh16(X, X) = true2.
% 25.39/3.69 Axiom 9 (co1_16): fresh15(X, X) = true2.
% 25.39/3.69 Axiom 10 (co1_17): fresh14(X, X) = true2.
% 25.39/3.69 Axiom 11 (ax28): fresh7(X, X, Y) = Y.
% 25.39/3.69 Axiom 12 (ax5_2): fresh283(X, X, Y, Z) = true2.
% 25.39/3.69 Axiom 13 (ax5_1): fresh281(X, X, Y, Z) = Y.
% 25.39/3.69 Axiom 14 (ax5_1): fresh44(X, X, Y, Z) = app(Z, w11(Y, Z)).
% 25.39/3.69 Axiom 15 (ax5_2): fresh43(X, X, Y, Z) = ssList(w11(Y, Z)).
% 25.39/3.69 Axiom 16 (ax7): fresh35(X, X, Y, Z) = true2.
% 25.39/3.69 Axiom 17 (co1_14): fresh17(neq(x, nil), true2) = neq(z, nil).
% 25.39/3.69 Axiom 18 (co1_15): fresh16(neq(x, nil), true2) = ssList(z).
% 25.39/3.69 Axiom 19 (co1_16): fresh15(neq(x, nil), true2) = frontsegP(w, z).
% 25.39/3.69 Axiom 20 (co1_17): fresh14(neq(x, nil), true2) = frontsegP(x, z).
% 25.39/3.69 Axiom 21 (ax28): fresh7(ssList(X), true2, X) = app(nil, X).
% 25.39/3.69 Axiom 22 (ax5_2): fresh282(X, X, Y, Z) = fresh283(ssList(Y), true2, Y, Z).
% 25.39/3.69 Axiom 23 (ax5_1): fresh280(X, X, Y, Z) = fresh281(ssList(Y), true2, Y, Z).
% 25.39/3.69 Axiom 24 (ax5_2): fresh282(frontsegP(X, Y), true2, X, Y) = fresh43(ssList(Y), true2, X, Y).
% 25.39/3.69 Axiom 25 (ax5_1): fresh280(frontsegP(X, Y), true2, X, Y) = fresh44(ssList(Y), true2, X, Y).
% 25.39/3.69 Axiom 26 (ax7): fresh260(X, X, Y, Z, W, V) = segmentP(Y, Z).
% 25.39/3.69 Axiom 27 (ax7): fresh259(X, X, Y, Z, W, V) = fresh260(ssList(Y), true2, Y, Z, W, V).
% 25.39/3.69 Axiom 28 (ax7): fresh258(X, X, Y, Z, W, V) = fresh259(ssList(Z), true2, Y, Z, W, V).
% 25.39/3.69 Axiom 29 (ax7): fresh257(X, X, Y, Z, W, V) = fresh258(ssList(W), true2, Y, Z, W, V).
% 25.39/3.69 Axiom 30 (ax7): fresh257(ssList(X), true2, Y, Z, W, X) = fresh35(app(app(W, Z), X), Y, Y, Z).
% 25.39/3.69
% 25.39/3.69 Lemma 31: neq(x, nil) = true2.
% 25.39/3.69 Proof:
% 26.26/3.69 neq(x, nil)
% 26.26/3.69 = { by axiom 1 (co1_1) R->L }
% 26.26/3.69 neq(v, nil)
% 26.26/3.69 = { by axiom 6 (co1_2) }
% 26.26/3.69 true2
% 26.26/3.69
% 26.26/3.69 Lemma 32: ssList(z) = true2.
% 26.26/3.69 Proof:
% 26.26/3.69 ssList(z)
% 26.26/3.69 = { by axiom 18 (co1_15) R->L }
% 26.26/3.69 fresh16(neq(x, nil), true2)
% 26.26/3.69 = { by lemma 31 }
% 26.26/3.69 fresh16(true2, true2)
% 26.26/3.69 = { by axiom 8 (co1_15) }
% 26.26/3.69 true2
% 26.26/3.69
% 26.26/3.69 Lemma 33: frontsegP(u, z) = true2.
% 26.26/3.69 Proof:
% 26.26/3.69 frontsegP(u, z)
% 26.26/3.69 = { by axiom 2 (co1) }
% 26.26/3.69 frontsegP(w, z)
% 26.26/3.69 = { by axiom 19 (co1_16) R->L }
% 26.26/3.69 fresh15(neq(x, nil), true2)
% 26.26/3.69 = { by lemma 31 }
% 26.26/3.69 fresh15(true2, true2)
% 26.26/3.69 = { by axiom 9 (co1_16) }
% 26.26/3.69 true2
% 26.26/3.69
% 26.26/3.69 Lemma 34: frontsegP(x, z) = true2.
% 26.26/3.69 Proof:
% 26.26/3.69 frontsegP(x, z)
% 26.26/3.69 = { by axiom 20 (co1_17) R->L }
% 26.26/3.69 fresh14(neq(x, nil), true2)
% 26.26/3.69 = { by lemma 31 }
% 26.26/3.69 fresh14(true2, true2)
% 26.26/3.69 = { by axiom 10 (co1_17) }
% 26.26/3.69 true2
% 26.26/3.69
% 26.26/3.69 Lemma 35: fresh258(X, X, Y, z, Z, W) = fresh259(V, V, Y, z, Z, W).
% 26.26/3.69 Proof:
% 26.26/3.69 fresh258(X, X, Y, z, Z, W)
% 26.26/3.69 = { by axiom 28 (ax7) }
% 26.26/3.69 fresh259(ssList(z), true2, Y, z, Z, W)
% 26.26/3.69 = { by lemma 32 }
% 26.26/3.69 fresh259(true2, true2, Y, z, Z, W)
% 26.26/3.69 = { by axiom 27 (ax7) }
% 26.26/3.69 fresh260(ssList(Y), true2, Y, z, Z, W)
% 26.26/3.69 = { by axiom 27 (ax7) R->L }
% 26.26/3.69 fresh259(V, V, Y, z, Z, W)
% 26.26/3.69
% 26.26/3.69 Lemma 36: fresh257(X, X, Y, Z, nil, W) = fresh258(V, V, Y, Z, nil, W).
% 26.26/3.69 Proof:
% 26.26/3.69 fresh257(X, X, Y, Z, nil, W)
% 26.26/3.69 = { by axiom 29 (ax7) }
% 26.26/3.69 fresh258(ssList(nil), true2, Y, Z, nil, W)
% 26.26/3.69 = { by axiom 3 (ax17) }
% 26.26/3.69 fresh258(true2, true2, Y, Z, nil, W)
% 26.26/3.69 = { by axiom 28 (ax7) }
% 26.26/3.69 fresh259(ssList(Z), true2, Y, Z, nil, W)
% 26.26/3.69 = { by axiom 28 (ax7) R->L }
% 26.26/3.69 fresh258(V, V, Y, Z, nil, W)
% 26.26/3.69
% 26.26/3.69 Lemma 37: fresh257(ssList(X), true2, app(z, X), z, nil, X) = true2.
% 26.26/3.69 Proof:
% 26.26/3.69 fresh257(ssList(X), true2, app(z, X), z, nil, X)
% 26.26/3.69 = { by axiom 11 (ax28) R->L }
% 26.26/3.69 fresh257(ssList(X), true2, app(fresh7(true2, true2, z), X), z, nil, X)
% 26.26/3.69 = { by lemma 32 R->L }
% 26.26/3.69 fresh257(ssList(X), true2, app(fresh7(ssList(z), true2, z), X), z, nil, X)
% 26.26/3.69 = { by axiom 21 (ax28) }
% 26.26/3.69 fresh257(ssList(X), true2, app(app(nil, z), X), z, nil, X)
% 26.26/3.69 = { by axiom 30 (ax7) }
% 26.26/3.69 fresh35(app(app(nil, z), X), app(app(nil, z), X), app(app(nil, z), X), z)
% 26.26/3.69 = { by axiom 16 (ax7) }
% 26.26/3.69 true2
% 26.26/3.69
% 26.26/3.69 Goal 1 (co1_11): tuple(neq(X, nil), neq(x, nil), ssList(X), segmentP(u, X), segmentP(v, X)) = tuple(true2, true2, true2, true2, true2).
% 26.26/3.69 The goal is true when:
% 26.26/3.69 X = z
% 26.26/3.69
% 26.26/3.69 Proof:
% 26.26/3.69 tuple(neq(z, nil), neq(x, nil), ssList(z), segmentP(u, z), segmentP(v, z))
% 26.26/3.69 = { by lemma 31 }
% 26.26/3.69 tuple(neq(z, nil), true2, ssList(z), segmentP(u, z), segmentP(v, z))
% 26.26/3.69 = { by axiom 1 (co1_1) }
% 26.26/3.69 tuple(neq(z, nil), true2, ssList(z), segmentP(u, z), segmentP(x, z))
% 26.26/3.69 = { by axiom 17 (co1_14) R->L }
% 26.26/3.69 tuple(fresh17(neq(x, nil), true2), true2, ssList(z), segmentP(u, z), segmentP(x, z))
% 26.26/3.69 = { by lemma 31 }
% 26.26/3.69 tuple(fresh17(true2, true2), true2, ssList(z), segmentP(u, z), segmentP(x, z))
% 26.26/3.69 = { by axiom 7 (co1_14) }
% 26.26/3.69 tuple(true2, true2, ssList(z), segmentP(u, z), segmentP(x, z))
% 26.26/3.69 = { by lemma 32 }
% 26.26/3.69 tuple(true2, true2, true2, segmentP(u, z), segmentP(x, z))
% 26.26/3.69 = { by axiom 26 (ax7) R->L }
% 26.26/3.69 tuple(true2, true2, true2, fresh260(true2, true2, u, z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by axiom 5 (co1_7) R->L }
% 26.26/3.69 tuple(true2, true2, true2, fresh260(ssList(u), true2, u, z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by axiom 27 (ax7) R->L }
% 26.26/3.69 tuple(true2, true2, true2, fresh259(W, W, u, z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by axiom 13 (ax5_1) R->L }
% 26.26/3.69 tuple(true2, true2, true2, fresh259(W, W, fresh281(true2, true2, u, z), z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by axiom 5 (co1_7) R->L }
% 26.26/3.69 tuple(true2, true2, true2, fresh259(W, W, fresh281(ssList(u), true2, u, z), z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by axiom 23 (ax5_1) R->L }
% 26.26/3.69 tuple(true2, true2, true2, fresh259(W, W, fresh280(true2, true2, u, z), z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by lemma 33 R->L }
% 26.26/3.69 tuple(true2, true2, true2, fresh259(W, W, fresh280(frontsegP(u, z), true2, u, z), z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by axiom 25 (ax5_1) }
% 26.26/3.69 tuple(true2, true2, true2, fresh259(W, W, fresh44(ssList(z), true2, u, z), z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by lemma 32 }
% 26.26/3.69 tuple(true2, true2, true2, fresh259(W, W, fresh44(true2, true2, u, z), z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by axiom 14 (ax5_1) }
% 26.26/3.69 tuple(true2, true2, true2, fresh259(W, W, app(z, w11(u, z)), z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by lemma 35 R->L }
% 26.26/3.69 tuple(true2, true2, true2, fresh258(Z, Z, app(z, w11(u, z)), z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by lemma 36 R->L }
% 26.26/3.69 tuple(true2, true2, true2, fresh257(true2, true2, app(z, w11(u, z)), z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by axiom 12 (ax5_2) R->L }
% 26.26/3.69 tuple(true2, true2, true2, fresh257(fresh283(true2, true2, u, z), true2, app(z, w11(u, z)), z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by axiom 5 (co1_7) R->L }
% 26.26/3.69 tuple(true2, true2, true2, fresh257(fresh283(ssList(u), true2, u, z), true2, app(z, w11(u, z)), z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by axiom 22 (ax5_2) R->L }
% 26.26/3.69 tuple(true2, true2, true2, fresh257(fresh282(true2, true2, u, z), true2, app(z, w11(u, z)), z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by lemma 33 R->L }
% 26.26/3.69 tuple(true2, true2, true2, fresh257(fresh282(frontsegP(u, z), true2, u, z), true2, app(z, w11(u, z)), z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by axiom 24 (ax5_2) }
% 26.26/3.69 tuple(true2, true2, true2, fresh257(fresh43(ssList(z), true2, u, z), true2, app(z, w11(u, z)), z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by lemma 32 }
% 26.26/3.69 tuple(true2, true2, true2, fresh257(fresh43(true2, true2, u, z), true2, app(z, w11(u, z)), z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by axiom 15 (ax5_2) }
% 26.26/3.69 tuple(true2, true2, true2, fresh257(ssList(w11(u, z)), true2, app(z, w11(u, z)), z, nil, w11(u, z)), segmentP(x, z))
% 26.26/3.69 = { by lemma 37 }
% 26.26/3.69 tuple(true2, true2, true2, true2, segmentP(x, z))
% 26.26/3.69 = { by axiom 26 (ax7) R->L }
% 26.26/3.69 tuple(true2, true2, true2, true2, fresh260(true2, true2, x, z, nil, w11(x, z)))
% 26.26/3.69 = { by axiom 4 (co1_10) R->L }
% 26.26/3.69 tuple(true2, true2, true2, true2, fresh260(ssList(x), true2, x, z, nil, w11(x, z)))
% 26.26/3.69 = { by axiom 27 (ax7) R->L }
% 26.26/3.69 tuple(true2, true2, true2, true2, fresh259(Y, Y, x, z, nil, w11(x, z)))
% 26.26/3.69 = { by axiom 13 (ax5_1) R->L }
% 26.26/3.69 tuple(true2, true2, true2, true2, fresh259(Y, Y, fresh281(true2, true2, x, z), z, nil, w11(x, z)))
% 26.26/3.69 = { by axiom 4 (co1_10) R->L }
% 26.26/3.69 tuple(true2, true2, true2, true2, fresh259(Y, Y, fresh281(ssList(x), true2, x, z), z, nil, w11(x, z)))
% 26.26/3.69 = { by axiom 23 (ax5_1) R->L }
% 26.26/3.69 tuple(true2, true2, true2, true2, fresh259(Y, Y, fresh280(true2, true2, x, z), z, nil, w11(x, z)))
% 26.26/3.69 = { by lemma 34 R->L }
% 26.26/3.69 tuple(true2, true2, true2, true2, fresh259(Y, Y, fresh280(frontsegP(x, z), true2, x, z), z, nil, w11(x, z)))
% 26.26/3.69 = { by axiom 25 (ax5_1) }
% 26.26/3.69 tuple(true2, true2, true2, true2, fresh259(Y, Y, fresh44(ssList(z), true2, x, z), z, nil, w11(x, z)))
% 26.26/3.69 = { by lemma 32 }
% 26.26/3.69 tuple(true2, true2, true2, true2, fresh259(Y, Y, fresh44(true2, true2, x, z), z, nil, w11(x, z)))
% 26.26/3.69 = { by axiom 14 (ax5_1) }
% 26.26/3.70 tuple(true2, true2, true2, true2, fresh259(Y, Y, app(z, w11(x, z)), z, nil, w11(x, z)))
% 26.26/3.70 = { by lemma 35 R->L }
% 26.26/3.70 tuple(true2, true2, true2, true2, fresh258(X, X, app(z, w11(x, z)), z, nil, w11(x, z)))
% 26.26/3.70 = { by lemma 36 R->L }
% 26.26/3.70 tuple(true2, true2, true2, true2, fresh257(true2, true2, app(z, w11(x, z)), z, nil, w11(x, z)))
% 26.26/3.70 = { by axiom 12 (ax5_2) R->L }
% 26.26/3.70 tuple(true2, true2, true2, true2, fresh257(fresh283(true2, true2, x, z), true2, app(z, w11(x, z)), z, nil, w11(x, z)))
% 26.26/3.70 = { by axiom 4 (co1_10) R->L }
% 26.26/3.70 tuple(true2, true2, true2, true2, fresh257(fresh283(ssList(x), true2, x, z), true2, app(z, w11(x, z)), z, nil, w11(x, z)))
% 26.26/3.70 = { by axiom 22 (ax5_2) R->L }
% 26.26/3.70 tuple(true2, true2, true2, true2, fresh257(fresh282(true2, true2, x, z), true2, app(z, w11(x, z)), z, nil, w11(x, z)))
% 26.26/3.70 = { by lemma 34 R->L }
% 26.26/3.70 tuple(true2, true2, true2, true2, fresh257(fresh282(frontsegP(x, z), true2, x, z), true2, app(z, w11(x, z)), z, nil, w11(x, z)))
% 26.26/3.70 = { by axiom 24 (ax5_2) }
% 26.26/3.70 tuple(true2, true2, true2, true2, fresh257(fresh43(ssList(z), true2, x, z), true2, app(z, w11(x, z)), z, nil, w11(x, z)))
% 26.26/3.70 = { by lemma 32 }
% 26.26/3.70 tuple(true2, true2, true2, true2, fresh257(fresh43(true2, true2, x, z), true2, app(z, w11(x, z)), z, nil, w11(x, z)))
% 26.26/3.70 = { by axiom 15 (ax5_2) }
% 26.26/3.70 tuple(true2, true2, true2, true2, fresh257(ssList(w11(x, z)), true2, app(z, w11(x, z)), z, nil, w11(x, z)))
% 26.26/3.70 = { by lemma 37 }
% 26.26/3.70 tuple(true2, true2, true2, true2, true2)
% 26.26/3.70 % SZS output end Proof
% 26.26/3.70
% 26.26/3.70 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------