TSTP Solution File: SWC002+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC002+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 20:53:21 EDT 2023
% Result : Theorem 100.77s 13.13s
% Output : Proof 101.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SWC002+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.31 % Computer : n013.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Aug 28 16:57:01 EDT 2023
% 0.11/0.31 % CPUTime :
% 100.77/13.13 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 100.77/13.13
% 100.77/13.13 % SZS status Theorem
% 100.77/13.13
% 101.02/13.20 % SZS output start Proof
% 101.02/13.20 Take the following subset of the input axioms:
% 101.57/13.24 fof(ax1, axiom, ![U]: (ssItem(U) => ![V]: (ssItem(V) => (neq(U, V) <=> U!=V)))).
% 101.57/13.24 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))))))))).
% 101.57/13.24 fof(ax15, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => (neq(U2, V2) <=> U2!=V2)))).
% 101.57/13.24 fof(ax18, axiom, ![U2]: (ssList(U2) => ![V2]: (ssItem(V2) => cons(V2, U2)!=U2))).
% 101.57/13.24 fof(ax21, axiom, ![U2]: (ssList(U2) => ![V2]: (ssItem(V2) => nil!=cons(V2, U2)))).
% 101.57/13.24 fof(ax33, axiom, ![U2]: (ssItem(U2) => ![V2]: (ssItem(V2) => (lt(U2, V2) => ~lt(V2, U2))))).
% 101.57/13.24 fof(ax38, axiom, ![U2]: (ssItem(U2) => ~memberP(nil, U2))).
% 101.57/13.24 fof(ax8, axiom, ![U2]: (ssList(U2) => (cyclefreeP(U2) <=> ![V2]: (ssItem(V2) => ![W2]: (ssItem(W2) => ![X7]: (ssList(X7) => ![Y2]: (ssList(Y2) => ![Z2]: (ssList(Z2) => (app(app(X7, cons(V2, Y2)), cons(W2, Z2))=U2 => ~(leq(V2, W2) & leq(W2, V2))))))))))).
% 101.57/13.24 fof(ax90, axiom, ![U2]: (ssItem(U2) => ~lt(U2, U2))).
% 101.57/13.24 fof(ax93, axiom, ![U2]: (ssItem(U2) => ![V2]: (ssItem(V2) => (lt(U2, V2) <=> (U2!=V2 & leq(U2, V2)))))).
% 101.57/13.24 fof(ax94, axiom, ![U2]: (ssItem(U2) => ![V2]: (ssItem(V2) => (gt(U2, V2) => ~gt(V2, U2))))).
% 101.57/13.24 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => ![X7]: (ssList(X7) => (V2!=X7 | (U2!=W2 | ((~neq(V2, nil) | (?[Y2]: (ssItem(Y2) & ?[Z2]: (ssList(Z2) & ?[X1]: (ssList(X1) & (app(app(Z2, cons(Y2, nil)), X1)=V2 & (app(Z2, X1)=U2 & ![X2]: (ssItem(X2) => (~memberP(V2, X2) | (~geq(X2, Y2) | Y2=X2)))))))) | ![X3]: (ssItem(X3) => ![X4]: (ssList(X4) => ![X5]: (ssList(X5) => (app(app(X4, cons(X3, nil)), X5)!=X7 | (app(X4, X5)!=W2 | ?[X6]: (ssItem(X6) & (X3!=X6 & (memberP(X7, X6) & geq(X6, X3))))))))))) & (~neq(V2, nil) | neq(X7, nil)))))))))).
% 101.57/13.24
% 101.57/13.24 Now clausify the problem and encode Horn clauses using encoding 3 of
% 101.57/13.24 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 101.57/13.24 We repeatedly replace C & s=t => u=v by the two clauses:
% 101.57/13.24 fresh(y, y, x1...xn) = u
% 101.57/13.24 C => fresh(s, t, x1...xn) = v
% 101.57/13.24 where fresh is a fresh function symbol and x1..xn are the free
% 101.57/13.24 variables of u and v.
% 101.57/13.24 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 101.57/13.24 input problem has no model of domain size 1).
% 101.57/13.24
% 101.57/13.24 The encoding turns the above axioms into the following unit equations and goals:
% 101.57/13.24
% 101.57/13.24 Axiom 1 (co1_3): v = x.
% 101.57/13.24 Axiom 2 (co1_2): u = w.
% 101.57/13.24 Axiom 3 (co1_5): neq(v, nil) = true2.
% 101.57/13.24 Axiom 4 (co1_22): fresh19(X, X) = x.
% 101.57/13.24 Axiom 5 (co1_23): fresh18(X, X) = w.
% 101.57/13.24 Axiom 6 (co1_24): fresh17(X, X) = true2.
% 101.57/13.24 Axiom 7 (co1_26): fresh15(X, X) = true2.
% 101.57/13.24 Axiom 8 (co1_27): fresh14(X, X) = true2.
% 101.57/13.24 Axiom 9 (co1_14): fresh116(X, X, Y) = true2.
% 101.57/13.24 Axiom 10 (co1_15): fresh111(X, X, Y) = true2.
% 101.57/13.24 Axiom 11 (co1_16): fresh106(X, X, Y) = true2.
% 101.57/13.24 Axiom 12 (co1_20): fresh101(X, X, Y) = Y.
% 101.57/13.24 Axiom 13 (co1_20): fresh99(X, X, Y) = x3.
% 101.57/13.24 Axiom 14 (co1_20): fresh100(X, X, Y) = fresh101(ssItem(Y), true2, Y).
% 101.57/13.24 Axiom 15 (co1_23): fresh18(neq(x, nil), true2) = app(x4, x5).
% 101.57/13.24 Axiom 16 (co1_24): fresh17(neq(x, nil), true2) = ssItem(x3).
% 101.57/13.24 Axiom 17 (co1_26): fresh15(neq(x, nil), true2) = ssList(x4).
% 101.57/13.24 Axiom 18 (co1_27): fresh14(neq(x, nil), true2) = ssList(x5).
% 101.57/13.24 Axiom 19 (co1_14): fresh115(X, X, Y, Z, W) = fresh116(app(Z, W), u, Y).
% 101.57/13.24 Axiom 20 (co1_15): fresh110(X, X, Y, Z, W) = fresh111(app(Z, W), u, Y).
% 101.57/13.24 Axiom 21 (co1_16): fresh105(X, X, Y, Z, W) = fresh106(app(Z, W), u, Y).
% 101.57/13.24 Axiom 22 (co1_20): fresh98(X, X, Y) = fresh99(neq(x, nil), true2, Y).
% 101.57/13.24 Axiom 23 (co1_20): fresh98(geq(X, x3), true2, X) = fresh100(memberP(x, X), true2, X).
% 101.57/13.24 Axiom 24 (co1_14): fresh22(X, X, Y, Z, W) = ssItem(x2(Y)).
% 101.57/13.24 Axiom 25 (co1_15): fresh21(X, X, Y, Z, W) = memberP(v, x2(Y)).
% 101.57/13.24 Axiom 26 (co1_16): fresh20(X, X, Y, Z, W) = geq(x2(Y), Y).
% 101.57/13.24 Axiom 27 (co1_22): fresh19(neq(x, nil), true2) = app(app(x4, cons(x3, nil)), x5).
% 101.57/13.24 Axiom 28 (co1_14): fresh114(X, X, Y, Z, W) = fresh115(ssItem(Y), true2, Y, Z, W).
% 101.57/13.25 Axiom 29 (co1_14): fresh112(X, X, Y, Z, W) = fresh113(ssList(Z), true2, Y, Z, W).
% 101.57/13.25 Axiom 30 (co1_15): fresh109(X, X, Y, Z, W) = fresh110(ssItem(Y), true2, Y, Z, W).
% 101.57/13.25 Axiom 31 (co1_15): fresh107(X, X, Y, Z, W) = fresh108(ssList(Z), true2, Y, Z, W).
% 101.57/13.25 Axiom 32 (co1_16): fresh104(X, X, Y, Z, W) = fresh105(ssItem(Y), true2, Y, Z, W).
% 101.57/13.25 Axiom 33 (co1_16): fresh102(X, X, Y, Z, W) = fresh103(ssList(Z), true2, Y, Z, W).
% 101.57/13.25 Axiom 34 (co1_14): fresh113(X, X, Y, Z, W) = fresh114(neq(x, nil), true2, Y, Z, W).
% 101.57/13.25 Axiom 35 (co1_15): fresh108(X, X, Y, Z, W) = fresh109(neq(x, nil), true2, Y, Z, W).
% 101.57/13.25 Axiom 36 (co1_16): fresh103(X, X, Y, Z, W) = fresh104(neq(x, nil), true2, Y, Z, W).
% 101.57/13.25 Axiom 37 (co1_14): fresh112(ssList(X), true2, Y, Z, X) = fresh22(app(app(Z, cons(Y, nil)), X), v, Y, Z, X).
% 101.57/13.25 Axiom 38 (co1_15): fresh107(ssList(X), true2, Y, Z, X) = fresh21(app(app(Z, cons(Y, nil)), X), v, Y, Z, X).
% 101.57/13.25 Axiom 39 (co1_16): fresh102(ssList(X), true2, Y, Z, X) = fresh20(app(app(Z, cons(Y, nil)), X), v, Y, Z, X).
% 101.57/13.25
% 101.57/13.25 Lemma 40: neq(x, nil) = true2.
% 101.57/13.25 Proof:
% 101.57/13.25 neq(x, nil)
% 101.57/13.25 = { by axiom 1 (co1_3) R->L }
% 101.57/13.25 neq(v, nil)
% 101.57/13.25 = { by axiom 3 (co1_5) }
% 101.57/13.25 true2
% 101.57/13.25
% 101.57/13.25 Lemma 41: ssItem(x3) = true2.
% 101.57/13.25 Proof:
% 101.57/13.25 ssItem(x3)
% 101.57/13.25 = { by axiom 16 (co1_24) R->L }
% 101.57/13.25 fresh17(neq(x, nil), true2)
% 101.57/13.25 = { by lemma 40 }
% 101.57/13.25 fresh17(true2, true2)
% 101.57/13.25 = { by axiom 6 (co1_24) }
% 101.57/13.25 true2
% 101.57/13.25
% 101.57/13.25 Lemma 42: ssList(x4) = true2.
% 101.57/13.25 Proof:
% 101.57/13.25 ssList(x4)
% 101.57/13.25 = { by axiom 17 (co1_26) R->L }
% 101.57/13.25 fresh15(neq(x, nil), true2)
% 101.57/13.25 = { by lemma 40 }
% 101.57/13.25 fresh15(true2, true2)
% 101.57/13.25 = { by axiom 7 (co1_26) }
% 101.57/13.25 true2
% 101.57/13.25
% 101.57/13.25 Lemma 43: ssList(x5) = true2.
% 101.57/13.25 Proof:
% 101.57/13.25 ssList(x5)
% 101.57/13.25 = { by axiom 18 (co1_27) R->L }
% 101.57/13.25 fresh14(neq(x, nil), true2)
% 101.57/13.25 = { by lemma 40 }
% 101.57/13.25 fresh14(true2, true2)
% 101.57/13.25 = { by axiom 8 (co1_27) }
% 101.57/13.25 true2
% 101.57/13.25
% 101.57/13.25 Lemma 44: app(x4, x5) = u.
% 101.57/13.25 Proof:
% 101.57/13.25 app(x4, x5)
% 101.57/13.25 = { by axiom 15 (co1_23) R->L }
% 101.57/13.25 fresh18(neq(x, nil), true2)
% 101.57/13.25 = { by lemma 40 }
% 101.57/13.25 fresh18(true2, true2)
% 101.57/13.25 = { by axiom 5 (co1_23) }
% 101.57/13.25 w
% 101.57/13.25 = { by axiom 2 (co1_2) R->L }
% 101.57/13.25 u
% 101.57/13.25
% 101.57/13.25 Lemma 45: app(app(x4, cons(x3, nil)), x5) = x.
% 101.57/13.25 Proof:
% 101.57/13.25 app(app(x4, cons(x3, nil)), x5)
% 101.57/13.25 = { by axiom 27 (co1_22) R->L }
% 101.57/13.25 fresh19(neq(x, nil), true2)
% 101.57/13.25 = { by lemma 40 }
% 101.57/13.25 fresh19(true2, true2)
% 101.57/13.25 = { by axiom 4 (co1_22) }
% 101.57/13.25 x
% 101.57/13.25
% 101.57/13.25 Goal 1 (co1_12): tuple6(X, app(Y, Z), app(app(Y, cons(X, nil)), Z), ssItem(X), neq(x, nil), ssList(Y), ssList(Z)) = tuple6(x2(X), u, v, true2, true2, true2, true2).
% 101.57/13.25 The goal is true when:
% 101.57/13.25 X = x3
% 101.57/13.25 Y = x4
% 101.57/13.25 Z = x5
% 101.57/13.25
% 101.57/13.25 Proof:
% 101.57/13.25 tuple6(x3, app(x4, x5), app(app(x4, cons(x3, nil)), x5), ssItem(x3), neq(x, nil), ssList(x4), ssList(x5))
% 101.57/13.25 = { by lemma 40 }
% 101.57/13.25 tuple6(x3, app(x4, x5), app(app(x4, cons(x3, nil)), x5), ssItem(x3), true2, ssList(x4), ssList(x5))
% 101.57/13.25 = { by lemma 45 }
% 101.57/13.25 tuple6(x3, app(x4, x5), x, ssItem(x3), true2, ssList(x4), ssList(x5))
% 101.57/13.25 = { by lemma 44 }
% 101.57/13.25 tuple6(x3, u, x, ssItem(x3), true2, ssList(x4), ssList(x5))
% 101.57/13.25 = { by lemma 41 }
% 101.57/13.25 tuple6(x3, u, x, true2, true2, ssList(x4), ssList(x5))
% 101.57/13.25 = { by lemma 42 }
% 101.57/13.25 tuple6(x3, u, x, true2, true2, true2, ssList(x5))
% 101.57/13.25 = { by lemma 43 }
% 101.57/13.25 tuple6(x3, u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 13 (co1_20) R->L }
% 101.57/13.25 tuple6(fresh99(true2, true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by lemma 40 R->L }
% 101.57/13.25 tuple6(fresh99(neq(x, nil), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 22 (co1_20) R->L }
% 101.57/13.25 tuple6(fresh98(true2, true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 11 (co1_16) R->L }
% 101.57/13.25 tuple6(fresh98(fresh106(u, u, x3), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by lemma 44 R->L }
% 101.57/13.25 tuple6(fresh98(fresh106(app(x4, x5), u, x3), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 21 (co1_16) R->L }
% 101.57/13.25 tuple6(fresh98(fresh105(true2, true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by lemma 41 R->L }
% 101.57/13.25 tuple6(fresh98(fresh105(ssItem(x3), true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 32 (co1_16) R->L }
% 101.57/13.25 tuple6(fresh98(fresh104(true2, true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by lemma 40 R->L }
% 101.57/13.25 tuple6(fresh98(fresh104(neq(x, nil), true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 36 (co1_16) R->L }
% 101.57/13.25 tuple6(fresh98(fresh103(true2, true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by lemma 42 R->L }
% 101.57/13.25 tuple6(fresh98(fresh103(ssList(x4), true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 33 (co1_16) R->L }
% 101.57/13.25 tuple6(fresh98(fresh102(true2, true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by lemma 43 R->L }
% 101.57/13.25 tuple6(fresh98(fresh102(ssList(x5), true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 39 (co1_16) }
% 101.57/13.25 tuple6(fresh98(fresh20(app(app(x4, cons(x3, nil)), x5), v, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 1 (co1_3) }
% 101.57/13.25 tuple6(fresh98(fresh20(app(app(x4, cons(x3, nil)), x5), x, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by lemma 45 }
% 101.57/13.25 tuple6(fresh98(fresh20(x, x, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 26 (co1_16) }
% 101.57/13.25 tuple6(fresh98(geq(x2(x3), x3), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 23 (co1_20) }
% 101.57/13.25 tuple6(fresh100(memberP(x, x2(x3)), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 1 (co1_3) R->L }
% 101.57/13.25 tuple6(fresh100(memberP(v, x2(x3)), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 25 (co1_15) R->L }
% 101.57/13.25 tuple6(fresh100(fresh21(x, x, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by lemma 45 R->L }
% 101.57/13.25 tuple6(fresh100(fresh21(app(app(x4, cons(x3, nil)), x5), x, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 1 (co1_3) R->L }
% 101.57/13.25 tuple6(fresh100(fresh21(app(app(x4, cons(x3, nil)), x5), v, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 38 (co1_15) R->L }
% 101.57/13.25 tuple6(fresh100(fresh107(ssList(x5), true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by lemma 43 }
% 101.57/13.25 tuple6(fresh100(fresh107(true2, true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 31 (co1_15) }
% 101.57/13.25 tuple6(fresh100(fresh108(ssList(x4), true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by lemma 42 }
% 101.57/13.25 tuple6(fresh100(fresh108(true2, true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by axiom 35 (co1_15) }
% 101.57/13.25 tuple6(fresh100(fresh109(neq(x, nil), true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.25 = { by lemma 40 }
% 101.57/13.26 tuple6(fresh100(fresh109(true2, true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by axiom 30 (co1_15) }
% 101.57/13.26 tuple6(fresh100(fresh110(ssItem(x3), true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by lemma 41 }
% 101.57/13.26 tuple6(fresh100(fresh110(true2, true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by axiom 20 (co1_15) }
% 101.57/13.26 tuple6(fresh100(fresh111(app(x4, x5), u, x3), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by lemma 44 }
% 101.57/13.26 tuple6(fresh100(fresh111(u, u, x3), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by axiom 10 (co1_15) }
% 101.57/13.26 tuple6(fresh100(true2, true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by axiom 14 (co1_20) }
% 101.57/13.26 tuple6(fresh101(ssItem(x2(x3)), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by axiom 24 (co1_14) R->L }
% 101.57/13.26 tuple6(fresh101(fresh22(x, x, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by lemma 45 R->L }
% 101.57/13.26 tuple6(fresh101(fresh22(app(app(x4, cons(x3, nil)), x5), x, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by axiom 1 (co1_3) R->L }
% 101.57/13.26 tuple6(fresh101(fresh22(app(app(x4, cons(x3, nil)), x5), v, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by axiom 37 (co1_14) R->L }
% 101.57/13.26 tuple6(fresh101(fresh112(ssList(x5), true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by lemma 43 }
% 101.57/13.26 tuple6(fresh101(fresh112(true2, true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by axiom 29 (co1_14) }
% 101.57/13.26 tuple6(fresh101(fresh113(ssList(x4), true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by lemma 42 }
% 101.57/13.26 tuple6(fresh101(fresh113(true2, true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by axiom 34 (co1_14) }
% 101.57/13.26 tuple6(fresh101(fresh114(neq(x, nil), true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by lemma 40 }
% 101.57/13.26 tuple6(fresh101(fresh114(true2, true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by axiom 28 (co1_14) }
% 101.57/13.26 tuple6(fresh101(fresh115(ssItem(x3), true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by lemma 41 }
% 101.57/13.26 tuple6(fresh101(fresh115(true2, true2, x3, x4, x5), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by axiom 19 (co1_14) }
% 101.57/13.26 tuple6(fresh101(fresh116(app(x4, x5), u, x3), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by lemma 44 }
% 101.57/13.26 tuple6(fresh101(fresh116(u, u, x3), true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by axiom 9 (co1_14) }
% 101.57/13.26 tuple6(fresh101(true2, true2, x2(x3)), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by axiom 12 (co1_20) }
% 101.57/13.26 tuple6(x2(x3), u, x, true2, true2, true2, true2)
% 101.57/13.26 = { by axiom 1 (co1_3) R->L }
% 101.57/13.26 tuple6(x2(x3), u, v, true2, true2, true2, true2)
% 101.57/13.26 % SZS output end Proof
% 101.57/13.26
% 101.57/13.26 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------