0.00/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.13	% 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   : n011.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   : 1200
0.13/0.34	% WCLimit    : 120
0.13/0.34	% DateTime   : Wed Jul 14 13:00:10 EDT 2021
0.13/0.34	% CPUTime    : 
85.30/11.10	% SZS status Theorem
85.30/11.10	
85.30/11.15	% SZS output start Proof
85.30/11.15	Take the following subset of the input axioms:
85.30/11.17	  fof(ax1, axiom, ![U]: (![V]: (ssItem(V) => (neq(U, V) <=> U!=V)) <= ssItem(U))).
85.30/11.17	  fof(ax13, axiom, ![U]: ((duplicatefreeP(U) <=> ![V]: (![W]: (![X]: (ssList(X) => ![Y]: (ssList(Y) => ![Z]: (ssList(Z) => (W!=V <= app(app(X, cons(V, Y)), cons(W, Z))=U)))) <= ssItem(W)) <= ssItem(V))) <= ssList(U))).
85.30/11.17	  fof(ax15, axiom, ![U]: (![V]: ((U!=V <=> neq(U, V)) <= ssList(V)) <= ssList(U))).
85.30/11.17	  fof(ax18, axiom, ![U]: (ssList(U) => ![V]: (U!=cons(V, U) <= ssItem(V)))).
85.30/11.17	  fof(ax21, axiom, ![U]: (ssList(U) => ![V]: (nil!=cons(V, U) <= ssItem(V)))).
85.30/11.17	  fof(ax33, axiom, ![U]: (![V]: ((lt(U, V) => ~lt(V, U)) <= ssItem(V)) <= ssItem(U))).
85.30/11.17	  fof(ax38, axiom, ![U]: (~memberP(nil, U) <= ssItem(U))).
85.30/11.17	  fof(ax8, axiom, ![U]: ((cyclefreeP(U) <=> ![V]: (ssItem(V) => ![W]: (![X]: (![Y]: (![Z]: (ssList(Z) => (~(leq(V, W) & leq(W, V)) <= app(app(X, cons(V, Y)), cons(W, Z))=U)) <= ssList(Y)) <= ssList(X)) <= ssItem(W)))) <= ssList(U))).
85.30/11.17	  fof(ax90, axiom, ![U]: (ssItem(U) => ~lt(U, U))).
85.30/11.17	  fof(ax93, axiom, ![U]: (![V]: (((leq(U, V) & V!=U) <=> lt(U, V)) <= ssItem(V)) <= ssItem(U))).
85.30/11.17	  fof(ax94, axiom, ![U]: (ssItem(U) => ![V]: (ssItem(V) => (~gt(V, U) <= gt(U, V))))).
85.30/11.17	  fof(co1, conjecture, ![U]: (![V]: (![W]: (ssList(W) => ![X]: (ssList(X) => (W!=U | (((~neq(V, nil) | (![X3]: (ssItem(X3) => ![X4]: (ssList(X4) => ![X5]: (ssList(X5) => (X!=app(app(X4, cons(X3, nil)), X5) | (app(X4, X5)!=W | ?[X6]: (geq(X6, X3) & (memberP(X, X6) & (X3!=X6 & ssItem(X6))))))))) | ?[Y]: (?[Z]: (?[X1]: (ssList(X1) & (app(app(Z, cons(Y, nil)), X1)=V & (![X2]: ((~memberP(V, X2) | (~geq(X2, Y) | X2=Y)) <= ssItem(X2)) & app(Z, X1)=U))) & ssList(Z)) & ssItem(Y)))) & (neq(X, nil) | ~neq(V, nil))) | V!=X)))) <= ssList(V)) <= ssList(U))).
85.30/11.17	
85.30/11.17	Now clausify the problem and encode Horn clauses using encoding 3 of
85.30/11.17	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
85.30/11.17	We repeatedly replace C & s=t => u=v by the two clauses:
85.30/11.17	  fresh(y, y, x1...xn) = u
85.30/11.17	  C => fresh(s, t, x1...xn) = v
85.30/11.17	where fresh is a fresh function symbol and x1..xn are the free
85.30/11.17	variables of u and v.
85.30/11.17	A predicate p(X) is encoded as p(X)=true (this is sound, because the
85.30/11.17	input problem has no model of domain size 1).
85.30/11.17	
85.30/11.17	The encoding turns the above axioms into the following unit equations and goals:
85.30/11.17	
85.30/11.17	Axiom 1 (co1_2): w = u.
85.30/11.17	Axiom 2 (co1_3): v = x.
85.30/11.17	Axiom 3 (co1_22): fresh20(X, X) = x.
85.30/11.17	Axiom 4 (co1_23): fresh19(X, X) = w.
85.30/11.17	Axiom 5 (co1_24): fresh18(X, X) = true2.
85.30/11.17	Axiom 6 (co1_25): fresh17(X, X) = true2.
85.30/11.17	Axiom 7 (co1_26): fresh16(X, X) = true2.
85.30/11.17	Axiom 8 (co1_11): neq(v, nil) = true2.
85.30/11.17	Axiom 9 (co1_17): fresh116(X, X, Y) = true2.
85.30/11.17	Axiom 10 (co1_18): fresh111(X, X, Y) = true2.
85.30/11.17	Axiom 11 (co1_19): fresh106(X, X, Y) = true2.
85.30/11.17	Axiom 12 (co1_21): fresh101(X, X, Y) = Y.
85.30/11.17	Axiom 13 (co1_21): fresh99(X, X, Y) = x3.
85.30/11.17	Axiom 14 (co1_23): fresh19(neq(x, nil), true2) = app(x4, x5).
85.30/11.17	Axiom 15 (co1_24): fresh18(neq(x, nil), true2) = ssList(x4).
85.30/11.17	Axiom 16 (co1_25): fresh17(neq(x, nil), true2) = ssList(x5).
85.30/11.17	Axiom 17 (co1_26): fresh16(neq(x, nil), true2) = ssItem(x3).
85.30/11.17	Axiom 18 (co1_21): fresh100(X, X, Y) = fresh101(ssItem(Y), true2, Y).
85.30/11.17	Axiom 19 (co1_21): fresh98(X, X, Y) = fresh99(geq(Y, x3), true2, Y).
85.30/11.17	Axiom 20 (co1_21): fresh98(neq(x, nil), true2, X) = fresh100(memberP(x, X), true2, X).
85.30/11.17	Axiom 21 (co1_22): fresh20(neq(x, nil), true2) = app(app(x4, cons(x3, nil)), x5).
85.30/11.17	Axiom 22 (co1_17): fresh115(X, X, Y, Z, W) = fresh116(app(Z, W), u, Y).
85.30/11.17	Axiom 23 (co1_18): fresh110(X, X, Y, Z, W) = fresh111(app(Z, W), u, Y).
85.30/11.17	Axiom 24 (co1_19): fresh105(X, X, Y, Z, W) = fresh106(app(Z, W), u, Y).
85.30/11.17	Axiom 25 (co1_17): fresh23(X, X, Y, Z, W) = ssItem(x2(Y)).
85.30/11.17	Axiom 26 (co1_18): fresh22(X, X, Y, Z, W) = geq(x2(Y), Y).
85.30/11.17	Axiom 27 (co1_19): fresh21(X, X, Y, Z, W) = memberP(v, x2(Y)).
85.30/11.17	Axiom 28 (co1_17): fresh114(X, X, Y, Z, W) = fresh115(ssList(Z), true2, Y, Z, W).
85.30/11.17	Axiom 29 (co1_17): fresh113(X, X, Y, Z, W) = fresh114(ssList(W), true2, Y, Z, W).
85.30/11.17	Axiom 30 (co1_17): fresh112(X, X, Y, Z, W) = fresh113(ssItem(Y), true2, Y, Z, W).
85.30/11.17	Axiom 31 (co1_18): fresh109(X, X, Y, Z, W) = fresh110(ssList(Z), true2, Y, Z, W).
85.30/11.17	Axiom 32 (co1_18): fresh108(X, X, Y, Z, W) = fresh109(ssList(W), true2, Y, Z, W).
85.30/11.17	Axiom 33 (co1_18): fresh107(X, X, Y, Z, W) = fresh108(ssItem(Y), true2, Y, Z, W).
85.30/11.17	Axiom 34 (co1_19): fresh104(X, X, Y, Z, W) = fresh105(ssList(Z), true2, Y, Z, W).
85.30/11.17	Axiom 35 (co1_19): fresh103(X, X, Y, Z, W) = fresh104(ssList(W), true2, Y, Z, W).
85.30/11.17	Axiom 36 (co1_19): fresh102(X, X, Y, Z, W) = fresh103(ssItem(Y), true2, Y, Z, W).
85.30/11.17	Axiom 37 (co1_17): fresh112(neq(x, nil), true2, X, Y, Z) = fresh23(app(app(Y, cons(X, nil)), Z), v, X, Y, Z).
85.30/11.17	Axiom 38 (co1_18): fresh107(neq(x, nil), true2, X, Y, Z) = fresh22(app(app(Y, cons(X, nil)), Z), v, X, Y, Z).
85.30/11.17	Axiom 39 (co1_19): fresh102(neq(x, nil), true2, X, Y, Z) = fresh21(app(app(Y, cons(X, nil)), Z), v, X, Y, Z).
85.30/11.17	
85.30/11.17	Lemma 40: ssList(x4) = true2.
85.30/11.17	Proof:
85.30/11.17	  ssList(x4)
85.30/11.17	= { by axiom 15 (co1_24) R->L }
85.30/11.17	  fresh18(neq(x, nil), true2)
85.30/11.17	= { by axiom 2 (co1_3) R->L }
85.30/11.17	  fresh18(neq(v, nil), true2)
85.30/11.17	= { by axiom 8 (co1_11) }
85.30/11.17	  fresh18(true2, true2)
85.30/11.17	= { by axiom 5 (co1_24) }
85.30/11.17	  true2
85.30/11.17	
85.30/11.17	Lemma 41: ssList(x5) = true2.
85.30/11.17	Proof:
85.30/11.17	  ssList(x5)
85.30/11.17	= { by axiom 16 (co1_25) R->L }
85.30/11.17	  fresh17(neq(x, nil), true2)
85.30/11.17	= { by axiom 2 (co1_3) R->L }
85.30/11.17	  fresh17(neq(v, nil), true2)
85.30/11.17	= { by axiom 8 (co1_11) }
85.30/11.17	  fresh17(true2, true2)
85.30/11.17	= { by axiom 6 (co1_25) }
85.30/11.17	  true2
85.30/11.17	
85.30/11.17	Lemma 42: ssItem(x3) = true2.
85.30/11.17	Proof:
85.30/11.17	  ssItem(x3)
85.30/11.17	= { by axiom 17 (co1_26) R->L }
85.30/11.17	  fresh16(neq(x, nil), true2)
85.30/11.17	= { by axiom 2 (co1_3) R->L }
85.30/11.17	  fresh16(neq(v, nil), true2)
85.30/11.17	= { by axiom 8 (co1_11) }
85.30/11.17	  fresh16(true2, true2)
85.30/11.17	= { by axiom 7 (co1_26) }
85.30/11.17	  true2
85.30/11.17	
85.30/11.17	Lemma 43: app(x4, x5) = w.
85.30/11.17	Proof:
85.30/11.17	  app(x4, x5)
85.30/11.17	= { by axiom 14 (co1_23) R->L }
85.30/11.17	  fresh19(neq(x, nil), true2)
85.30/11.17	= { by axiom 2 (co1_3) R->L }
85.30/11.17	  fresh19(neq(v, nil), true2)
85.30/11.17	= { by axiom 8 (co1_11) }
85.30/11.17	  fresh19(true2, true2)
85.30/11.17	= { by axiom 4 (co1_23) }
85.30/11.17	  w
85.30/11.17	
85.30/11.17	Lemma 44: app(app(x4, cons(x3, nil)), x5) = v.
85.30/11.17	Proof:
85.30/11.17	  app(app(x4, cons(x3, nil)), x5)
85.30/11.17	= { by axiom 21 (co1_22) R->L }
85.30/11.17	  fresh20(neq(x, nil), true2)
85.30/11.17	= { by axiom 2 (co1_3) R->L }
85.30/11.17	  fresh20(neq(v, nil), true2)
85.30/11.17	= { by axiom 8 (co1_11) }
85.30/11.17	  fresh20(true2, true2)
85.30/11.17	= { by axiom 3 (co1_22) }
85.30/11.17	  x
85.30/11.17	= { by axiom 2 (co1_3) R->L }
85.30/11.17	  v
85.30/11.17	
85.30/11.17	Goal 1 (co1_13): tuple6(x2(X), app(Y, Z), app(app(Y, cons(X, nil)), Z), ssList(Y), ssList(Z), ssItem(X), neq(x, nil)) = tuple6(X, u, v, true2, true2, true2, true2).
85.30/11.17	The goal is true when:
85.30/11.17	  X = x3
85.30/11.17	  Y = x4
85.30/11.17	  Z = x5
85.30/11.17	
85.30/11.17	Proof:
85.30/11.17	  tuple6(x2(x3), app(x4, x5), app(app(x4, cons(x3, nil)), x5), ssList(x4), ssList(x5), ssItem(x3), neq(x, nil))
85.30/11.17	= { by axiom 2 (co1_3) R->L }
85.30/11.17	  tuple6(x2(x3), app(x4, x5), app(app(x4, cons(x3, nil)), x5), ssList(x4), ssList(x5), ssItem(x3), neq(v, nil))
85.30/11.17	= { by axiom 8 (co1_11) }
85.30/11.17	  tuple6(x2(x3), app(x4, x5), app(app(x4, cons(x3, nil)), x5), ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.17	= { by lemma 44 }
85.30/11.17	  tuple6(x2(x3), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.17	= { by axiom 12 (co1_21) R->L }
85.30/11.17	  tuple6(fresh101(true2, true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.17	= { by axiom 9 (co1_17) R->L }
85.30/11.17	  tuple6(fresh101(fresh116(w, w, x3), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.17	= { by lemma 43 R->L }
85.30/11.17	  tuple6(fresh101(fresh116(app(x4, x5), w, x3), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.17	= { by axiom 1 (co1_2) }
85.30/11.17	  tuple6(fresh101(fresh116(app(x4, x5), u, x3), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.17	= { by axiom 22 (co1_17) R->L }
85.30/11.17	  tuple6(fresh101(fresh115(true2, true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.17	= { by lemma 40 R->L }
85.30/11.17	  tuple6(fresh101(fresh115(ssList(x4), true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.17	= { by axiom 28 (co1_17) R->L }
85.30/11.17	  tuple6(fresh101(fresh114(true2, true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.17	= { by lemma 41 R->L }
85.30/11.17	  tuple6(fresh101(fresh114(ssList(x5), true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 29 (co1_17) R->L }
85.30/11.18	  tuple6(fresh101(fresh113(true2, true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by lemma 42 R->L }
85.30/11.18	  tuple6(fresh101(fresh113(ssItem(x3), true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 30 (co1_17) R->L }
85.30/11.18	  tuple6(fresh101(fresh112(true2, true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 8 (co1_11) R->L }
85.30/11.18	  tuple6(fresh101(fresh112(neq(v, nil), true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 2 (co1_3) }
85.30/11.18	  tuple6(fresh101(fresh112(neq(x, nil), true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 37 (co1_17) }
85.30/11.18	  tuple6(fresh101(fresh23(app(app(x4, cons(x3, nil)), x5), v, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by lemma 44 }
85.30/11.18	  tuple6(fresh101(fresh23(v, v, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 25 (co1_17) }
85.30/11.18	  tuple6(fresh101(ssItem(x2(x3)), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 18 (co1_21) R->L }
85.30/11.18	  tuple6(fresh100(true2, true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 11 (co1_19) R->L }
85.30/11.18	  tuple6(fresh100(fresh106(w, w, x3), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by lemma 43 R->L }
85.30/11.18	  tuple6(fresh100(fresh106(app(x4, x5), w, x3), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 1 (co1_2) }
85.30/11.18	  tuple6(fresh100(fresh106(app(x4, x5), u, x3), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 24 (co1_19) R->L }
85.30/11.18	  tuple6(fresh100(fresh105(true2, true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by lemma 40 R->L }
85.30/11.18	  tuple6(fresh100(fresh105(ssList(x4), true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 34 (co1_19) R->L }
85.30/11.18	  tuple6(fresh100(fresh104(true2, true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by lemma 41 R->L }
85.30/11.18	  tuple6(fresh100(fresh104(ssList(x5), true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 35 (co1_19) R->L }
85.30/11.18	  tuple6(fresh100(fresh103(true2, true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by lemma 42 R->L }
85.30/11.18	  tuple6(fresh100(fresh103(ssItem(x3), true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 36 (co1_19) R->L }
85.30/11.18	  tuple6(fresh100(fresh102(true2, true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 8 (co1_11) R->L }
85.30/11.18	  tuple6(fresh100(fresh102(neq(v, nil), true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 2 (co1_3) }
85.30/11.18	  tuple6(fresh100(fresh102(neq(x, nil), true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 39 (co1_19) }
85.30/11.18	  tuple6(fresh100(fresh21(app(app(x4, cons(x3, nil)), x5), v, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by lemma 44 }
85.30/11.18	  tuple6(fresh100(fresh21(v, v, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 27 (co1_19) }
85.30/11.18	  tuple6(fresh100(memberP(v, x2(x3)), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 2 (co1_3) }
85.30/11.18	  tuple6(fresh100(memberP(x, x2(x3)), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 20 (co1_21) R->L }
85.30/11.18	  tuple6(fresh98(neq(x, nil), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 2 (co1_3) R->L }
85.30/11.18	  tuple6(fresh98(neq(v, nil), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 8 (co1_11) }
85.30/11.18	  tuple6(fresh98(true2, true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 19 (co1_21) }
85.30/11.18	  tuple6(fresh99(geq(x2(x3), x3), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 26 (co1_18) R->L }
85.30/11.18	  tuple6(fresh99(fresh22(v, v, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by lemma 44 R->L }
85.30/11.18	  tuple6(fresh99(fresh22(app(app(x4, cons(x3, nil)), x5), v, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 38 (co1_18) R->L }
85.30/11.18	  tuple6(fresh99(fresh107(neq(x, nil), true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 2 (co1_3) R->L }
85.30/11.18	  tuple6(fresh99(fresh107(neq(v, nil), true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 8 (co1_11) }
85.30/11.18	  tuple6(fresh99(fresh107(true2, true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 33 (co1_18) }
85.30/11.18	  tuple6(fresh99(fresh108(ssItem(x3), true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by lemma 42 }
85.30/11.18	  tuple6(fresh99(fresh108(true2, true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 32 (co1_18) }
85.30/11.18	  tuple6(fresh99(fresh109(ssList(x5), true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by lemma 41 }
85.30/11.18	  tuple6(fresh99(fresh109(true2, true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 31 (co1_18) }
85.30/11.18	  tuple6(fresh99(fresh110(ssList(x4), true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by lemma 40 }
85.30/11.18	  tuple6(fresh99(fresh110(true2, true2, x3, x4, x5), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 23 (co1_18) }
85.30/11.18	  tuple6(fresh99(fresh111(app(x4, x5), u, x3), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 1 (co1_2) R->L }
85.30/11.18	  tuple6(fresh99(fresh111(app(x4, x5), w, x3), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by lemma 43 }
85.30/11.18	  tuple6(fresh99(fresh111(w, w, x3), true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 10 (co1_18) }
85.30/11.18	  tuple6(fresh99(true2, true2, x2(x3)), app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by axiom 13 (co1_21) }
85.30/11.18	  tuple6(x3, app(x4, x5), v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by lemma 43 }
85.30/11.18	  tuple6(x3, w, v, ssList(x4), ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by lemma 40 }
85.30/11.18	  tuple6(x3, w, v, true2, ssList(x5), ssItem(x3), true2)
85.30/11.18	= { by lemma 41 }
85.30/11.18	  tuple6(x3, w, v, true2, true2, ssItem(x3), true2)
85.30/11.18	= { by lemma 42 }
85.30/11.18	  tuple6(x3, w, v, true2, true2, true2, true2)
85.30/11.18	= { by axiom 1 (co1_2) }
85.30/11.18	  tuple6(x3, u, v, true2, true2, true2, true2)
85.30/11.18	% SZS output end Proof
85.30/11.18	
85.30/11.18	RESULT: Theorem (the conjecture is true).
85.30/11.21	EOF