0.08/0.14	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.15	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.15/0.36	% Computer   : n015.cluster.edu
0.15/0.36	% Model      : x86_64 x86_64
0.15/0.36	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.15/0.36	% Memory     : 8042.1875MB
0.15/0.36	% OS         : Linux 3.10.0-693.el7.x86_64
0.15/0.36	% CPULimit   : 1200
0.15/0.36	% WCLimit    : 120
0.15/0.36	% DateTime   : Tue Jul 13 16:20:04 EDT 2021
0.15/0.37	% CPUTime    : 
5.12/1.14	% SZS status Theorem
5.12/1.14	
7.96/1.42	% SZS output start Proof
7.96/1.42	Take the following subset of the input axioms:
10.60/1.75	  fof(ax31, axiom, ![U, V]: (existent(U, V) => ~nonexistent(U, V))).
10.60/1.75	  fof(ax32, axiom, ![U, V]: (nonhuman(U, V) => ~human(U, V))).
10.60/1.75	  fof(ax33, axiom, ![U, V]: (specific(U, V) => ~general(U, V))).
10.60/1.75	  fof(ax34, axiom, ![U, V]: (unisex(U, V) => ~male(U, V))).
10.60/1.75	  fof(ax49, axiom, ![U, V, W]: ((accessible_world(V, W) & man(V, U)) => man(W, U))).
10.60/1.75	  fof(co1, conjecture, ~(~?[X5]: (actual_world(X5) & ?[V, W, X, Y, Z, X6, X7, X8, X9, X1, X2, X10, X11]: (man(X5, X6) & (vincent_forename(X5, X7) & (forename(X5, X7) & (man(X5, X8) & (jules_forename(X5, X9) & (forename(X5, X9) & (vincent_forename(X5, W) & (forename(X5, W) & (agent(X5, X, V) & (theme(X5, X, Y) & (event(X5, X) & (![X3]: (?[X4]: (event(Y, X4) & (present(Y, X4) & (smoke(Y, X4) & agent(Y, X4, X3)))) <= man(Y, X3)) & (of(X5, Z, X1) & (man(X5, X1) & (state(X5, X2) & (agent(X5, X10, X6) & (theme(X5, X10, X11) & (event(X5, X10) & (accessible_world(X5, X11) & (?[X12]: (event(X11, X12) & (smoke(X11, X12) & (present(X11, X12) & agent(X11, X12, X8)))) & (think_believe_consider(X5, X10) & (present(X5, X10) & (proposition(X5, X11) & (be(X5, X2, X1, X1) & (man(X5, X1) & (forename(X5, Z) & (jules_forename(X5, Z) & (accessible_world(X5, Y) & (think_believe_consider(X5, X) & (present(X5, X) & (proposition(X5, Y) & (man(X5, V) & (of(X5, W, V) & (of(X5, X9, X8) & of(X5, X7, X6)))))))))))))))))))))))))))))))))))) & ?[U]: (?[V, W, X, Y, Z, X1, X2]: (of(U, W, V) & (man(U, V) & (present(U, X) & (think_believe_consider(U, X) & (accessible_world(U, Y) & (of(U, Z, X1) & (man(U, X1) & (forename(U, Z) & (be(U, X2, X1, X1) & (state(U, X2) & (man(U, X1) & (jules_forename(U, Z) & (![X3]: (?[X4]: (event(Y, X4) & (present(Y, X4) & (smoke(Y, X4) & agent(Y, X4, X3)))) <= man(Y, X3)) & (event(U, X) & (theme(U, X, Y) & (agent(U, X, V) & (proposition(U, Y) & (forename(U, W) & vincent_forename(U, W))))))))))))))))))) & actual_world(U)))).
10.60/1.75	
10.60/1.75	Now clausify the problem and encode Horn clauses using encoding 3 of
10.60/1.75	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
10.60/1.75	We repeatedly replace C & s=t => u=v by the two clauses:
10.60/1.75	  fresh(y, y, x1...xn) = u
10.60/1.75	  C => fresh(s, t, x1...xn) = v
10.60/1.75	where fresh is a fresh function symbol and x1..xn are the free
10.60/1.75	variables of u and v.
10.60/1.75	A predicate p(X) is encoded as p(X)=true (this is sound, because the
10.60/1.75	input problem has no model of domain size 1).
10.60/1.75	
10.60/1.75	The encoding turns the above axioms into the following unit equations and goals:
10.60/1.75	
10.60/1.75	Axiom 1 (co1_17): actual_world(u) = true2.
10.60/1.75	Axiom 2 (co1_3): accessible_world(u, y) = true2.
10.60/1.75	Axiom 3 (co1_5): man(u, x1) = true2.
10.60/1.75	Axiom 4 (co1_4): man(u, v) = true2.
10.60/1.75	Axiom 5 (co1): forename(u, w) = true2.
10.60/1.75	Axiom 6 (co1_1): forename(u, z) = true2.
10.60/1.75	Axiom 7 (co1_8): event(u, x) = true2.
10.60/1.75	Axiom 8 (co1_6): present(u, x) = true2.
10.60/1.75	Axiom 9 (co1_7): proposition(u, y) = true2.
10.60/1.75	Axiom 10 (co1_10): think_believe_consider(u, x) = true2.
10.60/1.75	Axiom 11 (co1_2): vincent_forename(u, w) = true2.
10.60/1.75	Axiom 12 (co1_16): jules_forename(u, z) = true2.
10.60/1.75	Axiom 13 (co1_9): state(u, x2) = true2.
10.60/1.75	Axiom 14 (co1_14): of(u, w, v) = true2.
10.60/1.75	Axiom 15 (co1_15): of(u, z, x1) = true2.
10.60/1.75	Axiom 16 (co1_12): agent(u, x, v) = true2.
10.60/1.75	Axiom 17 (co1_11): theme(u, x, y) = true2.
10.60/1.75	Axiom 18 (co1_19): fresh140(X, X, Y) = true2.
10.60/1.75	Axiom 19 (co1_20): fresh5(X, X, Y) = true2.
10.60/1.75	Axiom 20 (co1_21): fresh4(X, X, Y) = true2.
10.60/1.75	Axiom 21 (co1_22): fresh3(X, X, Y) = true2.
10.60/1.75	Axiom 22 (co1_23): fresh2(X, X, Y) = true2.
10.60/1.75	Axiom 23 (co1_13): be(u, x2, x1, x1) = true2.
10.60/1.75	Axiom 24 (ax49): fresh49(X, X, Y, Z) = true2.
10.60/1.75	Axiom 25 (co1_19): fresh138(X, X, Y, Z, W) = man(W, x3(W)).
10.60/1.75	Axiom 26 (ax49): fresh50(X, X, Y, Z, W) = man(W, Y).
10.60/1.75	Axiom 27 (co1_20): fresh5(man(y, X), true2, X) = present(y, x4(X)).
10.60/1.75	Axiom 28 (co1_21): fresh4(man(y, X), true2, X) = smoke(y, x4(X)).
10.60/1.75	Axiom 29 (co1_22): fresh3(man(y, X), true2, X) = event(y, x4(X)).
10.60/1.75	Axiom 30 (co1_23): fresh2(man(y, X), true2, X) = agent(y, x4(X), X).
10.60/1.75	Axiom 31 (co1_19): fresh139(X, X, Y, Z, W, V) = fresh140(forename(Y, Z), true2, V).
10.60/1.75	Axiom 32 (co1_19): fresh137(X, X, Y, Z, W, V, U) = fresh138(forename(Y, W), true2, Y, Z, U).
10.60/1.75	Axiom 33 (ax49): fresh50(man(X, Y), true2, Y, X, Z) = fresh49(accessible_world(X, Z), true2, Y, Z).
10.60/1.75	Axiom 34 (co1_19): fresh136(X, X, Y, Z, W, V, U, T) = fresh139(forename(Y, V), true2, Y, Z, W, U).
10.60/1.75	Axiom 35 (co1_19): fresh135(X, X, Y, Z, W, V, U, T) = fresh137(forename(Y, T), true2, Y, Z, W, V, U).
10.60/1.75	Axiom 36 (co1_19): fresh134(X, X, Y, Z, W, V, U, T) = fresh136(vincent_forename(Y, Z), true2, Y, Z, W, V, U, T).
10.60/1.75	Axiom 37 (co1_19): fresh133(X, X, Y, Z, W, V, U, T) = fresh135(vincent_forename(Y, V), true2, Y, Z, W, V, U, T).
10.60/1.75	Axiom 38 (co1_19): fresh132(X, X, Y, Z, W, V, U, T, S) = fresh134(accessible_world(Y, U), true2, Y, Z, W, V, U, S).
10.60/1.75	Axiom 39 (co1_19): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = fresh133(accessible_world(Y, S), true2, Y, W, V, U, T, X2).
10.60/1.75	Axiom 40 (co1_19): fresh130(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh132(man(Y, Z), true2, Y, W, U, T, S, X2, Y2).
10.60/1.75	Axiom 41 (co1_19): fresh129(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2) = fresh131(man(Y, V), true2, Y, Z, W, U, S, X2, Y2, Z2).
10.60/1.75	Axiom 42 (co1_19): fresh128(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = fresh130(man(Y, T), true2, Y, Z, W, V, U, S, X2, Y2, W2).
10.60/1.75	Axiom 43 (co1_19): fresh127(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = fresh129(man(Y, W2), true2, Y, Z, W, V, U, T, S, Y2, Z2, V2).
10.60/1.76	Axiom 44 (co1_19): fresh126(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2) = fresh128(present(Y, X2), true2, Y, Z, W, V, U, T, S, Y2, W2, V2, U2).
10.60/1.76	Axiom 45 (co1_19): fresh125(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh127(present(Y, Z2), true2, Y, Z, W, V, U, T, S, X2, Y2, W2, U2, T2).
10.60/1.76	Axiom 46 (co1_19): fresh124(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh126(present(W2, V2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, U2, T2).
10.60/1.76	Axiom 47 (co1_19): fresh123(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh125(proposition(Y, Y2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
10.60/1.76	Axiom 48 (co1_19): fresh122(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh124(proposition(Y, W2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
10.60/1.76	Axiom 49 (co1_19): fresh121(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh123(smoke(W2, V2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
10.60/1.76	Axiom 50 (co1_19): fresh120(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh122(event(Y, X2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
10.60/1.76	Axiom 51 (co1_19): fresh119(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh121(event(Y, Z2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
10.60/1.76	Axiom 52 (co1_19): fresh118(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2) = fresh120(event(W2, V2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, S2).
10.60/1.76	Axiom 53 (co1_19): fresh117(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2) = fresh119(state(Y, T2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, S2).
10.60/1.76	Axiom 54 (co1_19): fresh116(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2) = fresh118(think_believe_consider(Y, X2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2).
10.60/1.76	Axiom 55 (co1_19): fresh115(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2) = fresh117(think_believe_consider(Y, Z2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2).
10.60/1.76	Axiom 56 (co1_19): fresh105(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2) = fresh106(jules_forename(Y, U), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2).
10.60/1.76	Axiom 57 (co1_19): fresh104(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2) = fresh105(jules_forename(Y, S2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2).
10.60/1.76	Axiom 58 (co1_19): fresh114(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2) = fresh116(theme(Y, X2, Y2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2).
10.60/1.76	Axiom 59 (co1_19): fresh113(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2) = fresh115(theme(Y, Z2, W2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2).
10.60/1.76	Axiom 60 (co1_19): fresh112(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2) = fresh114(agent(Y, X2, T), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2).
10.60/1.76	Axiom 61 (co1_19): fresh111(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2) = fresh113(agent(Y, Z2, Z), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2).
10.60/1.76	Axiom 62 (co1_19): fresh110(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2) = fresh112(agent(W2, V2, V), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2).
10.60/1.76	Axiom 63 (co1_19): fresh109(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2) = fresh110(of(Y, W, Z), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2).
10.60/1.76	Axiom 64 (co1_19): fresh108(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2) = fresh109(of(Y, U, V), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2).
10.60/1.76	Axiom 65 (co1_19): fresh107(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2) = fresh108(of(Y, S, T), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2).
10.60/1.76	Axiom 66 (co1_19): fresh106(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2) = fresh107(of(Y, S2, U2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2).
10.60/1.76	Axiom 67 (co1_19): fresh104(actual_world(X), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh111(be(X, U2, V2, V2), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
10.60/1.76	
10.60/1.76	Lemma 68: man(y, x1) = true2.
10.60/1.76	Proof:
10.60/1.76	  man(y, x1)
10.60/1.76	= { by axiom 26 (ax49) R->L }
10.60/1.76	  fresh50(true2, true2, x1, u, y)
10.60/1.76	= { by axiom 3 (co1_5) R->L }
10.60/1.76	  fresh50(man(u, x1), true2, x1, u, y)
10.60/1.76	= { by axiom 33 (ax49) }
10.60/1.76	  fresh49(accessible_world(u, y), true2, x1, y)
10.60/1.76	= { by axiom 2 (co1_3) }
10.60/1.76	  fresh49(true2, true2, x1, y)
10.60/1.76	= { by axiom 24 (ax49) }
10.60/1.76	  true2
10.60/1.76	
10.60/1.76	Lemma 69: smoke(y, x4(x1)) = true2.
10.60/1.76	Proof:
10.60/1.76	  smoke(y, x4(x1))
10.60/1.76	= { by axiom 28 (co1_21) R->L }
10.60/1.76	  fresh4(man(y, x1), true2, x1)
10.60/1.76	= { by lemma 68 }
10.60/1.76	  fresh4(true2, true2, x1)
10.60/1.76	= { by axiom 20 (co1_21) }
10.60/1.76	  true2
10.60/1.76	
10.60/1.76	Lemma 70: agent(y, x4(x1), x1) = true2.
10.60/1.76	Proof:
10.60/1.76	  agent(y, x4(x1), x1)
10.60/1.76	= { by axiom 30 (co1_23) R->L }
10.60/1.76	  fresh2(man(y, x1), true2, x1)
10.60/1.76	= { by lemma 68 }
10.60/1.76	  fresh2(true2, true2, x1)
10.60/1.76	= { by axiom 22 (co1_23) }
10.60/1.76	  true2
10.60/1.76	
10.60/1.76	Lemma 71: event(y, x4(x1)) = true2.
10.60/1.76	Proof:
10.60/1.76	  event(y, x4(x1))
10.60/1.76	= { by axiom 29 (co1_22) R->L }
10.60/1.76	  fresh3(man(y, x1), true2, x1)
10.60/1.76	= { by lemma 68 }
10.60/1.76	  fresh3(true2, true2, x1)
10.60/1.76	= { by axiom 21 (co1_22) }
10.60/1.76	  true2
10.60/1.76	
10.60/1.76	Lemma 72: present(y, x4(x1)) = true2.
10.60/1.76	Proof:
10.60/1.76	  present(y, x4(x1))
10.60/1.76	= { by axiom 27 (co1_20) R->L }
10.60/1.76	  fresh5(man(y, x1), true2, x1)
10.60/1.76	= { by lemma 68 }
10.60/1.76	  fresh5(true2, true2, x1)
10.60/1.76	= { by axiom 19 (co1_20) }
10.60/1.76	  true2
10.60/1.76	
10.60/1.76	Lemma 73: man(y, x3(y)) = true2.
10.60/1.76	Proof:
10.60/1.76	  man(y, x3(y))
10.60/1.76	= { by axiom 25 (co1_19) R->L }
10.60/1.76	  fresh138(true2, true2, u, w, y)
10.60/1.76	= { by axiom 6 (co1_1) R->L }
10.60/1.76	  fresh138(forename(u, z), true2, u, w, y)
10.60/1.76	= { by axiom 32 (co1_19) R->L }
10.60/1.76	  fresh137(true2, true2, u, w, z, w, y)
10.60/1.76	= { by axiom 6 (co1_1) R->L }
10.60/1.76	  fresh137(forename(u, z), true2, u, w, z, w, y)
10.60/1.76	= { by axiom 35 (co1_19) R->L }
10.60/1.76	  fresh135(true2, true2, u, w, z, w, y, z)
10.60/1.76	= { by axiom 11 (co1_2) R->L }
10.60/1.76	  fresh135(vincent_forename(u, w), true2, u, w, z, w, y, z)
10.60/1.76	= { by axiom 37 (co1_19) R->L }
10.60/1.76	  fresh133(true2, true2, u, w, z, w, y, z)
10.60/1.76	= { by axiom 2 (co1_3) R->L }
10.60/1.76	  fresh133(accessible_world(u, y), true2, u, w, z, w, y, z)
10.60/1.76	= { by axiom 39 (co1_19) R->L }
10.60/1.76	  fresh131(true2, true2, u, v, w, z, w, y, y, z)
10.60/1.76	= { by axiom 3 (co1_5) R->L }
10.60/1.76	  fresh131(man(u, x1), true2, u, v, w, z, w, y, y, z)
10.60/1.76	= { by axiom 41 (co1_19) R->L }
10.60/1.76	  fresh129(true2, true2, u, v, w, x1, z, v, w, y, y, z)
10.60/1.76	= { by axiom 3 (co1_5) R->L }
10.60/1.76	  fresh129(man(u, x1), true2, u, v, w, x1, z, v, w, y, y, z)
10.60/1.76	= { by axiom 43 (co1_19) R->L }
10.60/1.76	  fresh127(true2, true2, u, v, w, x1, z, v, w, x, y, y, x1, z)
10.60/1.76	= { by axiom 8 (co1_6) R->L }
10.60/1.76	  fresh127(present(u, x), true2, u, v, w, x1, z, v, w, x, y, y, x1, z)
10.60/1.76	= { by axiom 45 (co1_19) R->L }
10.60/1.76	  fresh125(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, z)
10.60/1.76	= { by axiom 9 (co1_7) R->L }
10.60/1.76	  fresh125(proposition(u, y), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, z)
10.60/1.76	= { by axiom 47 (co1_19) R->L }
10.60/1.76	  fresh123(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, z)
10.60/1.76	= { by lemma 69 R->L }
10.60/1.76	  fresh123(smoke(y, x4(x1)), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, z)
10.60/1.76	= { by axiom 49 (co1_19) R->L }
10.60/1.76	  fresh121(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, z)
10.60/1.76	= { by axiom 7 (co1_8) R->L }
10.60/1.76	  fresh121(event(u, x), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, z)
10.60/1.76	= { by axiom 51 (co1_19) R->L }
10.60/1.76	  fresh119(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, z)
10.60/1.76	= { by axiom 13 (co1_9) R->L }
10.60/1.76	  fresh119(state(u, x2), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, z)
10.60/1.76	= { by axiom 53 (co1_19) R->L }
10.60/1.76	  fresh117(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 10 (co1_10) R->L }
10.60/1.76	  fresh117(think_believe_consider(u, x), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 55 (co1_19) R->L }
10.60/1.76	  fresh115(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 17 (co1_11) R->L }
10.60/1.76	  fresh115(theme(u, x, y), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 59 (co1_19) R->L }
10.60/1.76	  fresh113(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 16 (co1_12) R->L }
10.60/1.76	  fresh113(agent(u, x, v), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 61 (co1_19) R->L }
10.60/1.76	  fresh111(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 23 (co1_13) R->L }
10.60/1.76	  fresh111(be(u, x2, x1, x1), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 67 (co1_19) R->L }
10.60/1.76	  fresh104(actual_world(u), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 1 (co1_17) }
10.60/1.76	  fresh104(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 57 (co1_19) }
10.60/1.76	  fresh105(jules_forename(u, z), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 12 (co1_16) }
10.60/1.76	  fresh105(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 56 (co1_19) }
10.60/1.76	  fresh106(jules_forename(u, z), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 12 (co1_16) }
10.60/1.76	  fresh106(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 66 (co1_19) }
10.60/1.76	  fresh107(of(u, z, x1), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 15 (co1_15) }
10.60/1.76	  fresh107(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 65 (co1_19) }
10.60/1.76	  fresh108(of(u, w, v), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 14 (co1_14) }
10.60/1.76	  fresh108(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 64 (co1_19) }
10.60/1.76	  fresh109(of(u, z, x1), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 15 (co1_15) }
10.60/1.76	  fresh109(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 63 (co1_19) }
10.60/1.76	  fresh110(of(u, w, v), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 14 (co1_14) }
10.60/1.76	  fresh110(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 62 (co1_19) }
10.60/1.76	  fresh112(agent(y, x4(x1), x1), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by lemma 70 }
10.60/1.76	  fresh112(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 60 (co1_19) }
10.60/1.76	  fresh114(agent(u, x, v), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 16 (co1_12) }
10.60/1.76	  fresh114(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 58 (co1_19) }
10.60/1.76	  fresh116(theme(u, x, y), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 17 (co1_11) }
10.60/1.76	  fresh116(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 54 (co1_19) }
10.60/1.76	  fresh118(think_believe_consider(u, x), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 10 (co1_10) }
10.60/1.76	  fresh118(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, x2, z)
10.60/1.76	= { by axiom 52 (co1_19) }
10.60/1.76	  fresh120(event(y, x4(x1)), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, z)
10.60/1.76	= { by lemma 71 }
10.60/1.76	  fresh120(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, z)
10.60/1.76	= { by axiom 50 (co1_19) }
10.60/1.76	  fresh122(event(u, x), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, z)
10.60/1.76	= { by axiom 7 (co1_8) }
10.60/1.76	  fresh122(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, z)
10.60/1.76	= { by axiom 48 (co1_19) }
10.60/1.76	  fresh124(proposition(u, y), true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, z)
10.60/1.76	= { by axiom 9 (co1_7) }
10.60/1.76	  fresh124(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x4(x1), x1, z)
10.60/1.76	= { by axiom 46 (co1_19) }
10.60/1.76	  fresh126(present(y, x4(x1)), true2, u, v, w, x1, z, v, w, x, y, x, y, x1, z)
10.60/1.76	= { by lemma 72 }
10.60/1.76	  fresh126(true2, true2, u, v, w, x1, z, v, w, x, y, x, y, x1, z)
10.60/1.76	= { by axiom 44 (co1_19) }
10.60/1.76	  fresh128(present(u, x), true2, u, v, w, x1, z, v, w, y, y, x1, z)
10.60/1.76	= { by axiom 8 (co1_6) }
10.60/1.76	  fresh128(true2, true2, u, v, w, x1, z, v, w, y, y, x1, z)
10.60/1.76	= { by axiom 42 (co1_19) }
10.60/1.76	  fresh130(man(u, v), true2, u, v, w, x1, z, w, y, y, z)
10.60/1.76	= { by axiom 4 (co1_4) }
10.60/1.76	  fresh130(true2, true2, u, v, w, x1, z, w, y, y, z)
10.60/1.76	= { by axiom 40 (co1_19) }
10.60/1.76	  fresh132(man(u, v), true2, u, w, z, w, y, y, z)
10.60/1.76	= { by axiom 4 (co1_4) }
10.60/1.76	  fresh132(true2, true2, u, w, z, w, y, y, z)
10.60/1.76	= { by axiom 38 (co1_19) }
10.60/1.76	  fresh134(accessible_world(u, y), true2, u, w, z, w, y, z)
10.60/1.76	= { by axiom 2 (co1_3) }
10.60/1.76	  fresh134(true2, true2, u, w, z, w, y, z)
10.60/1.76	= { by axiom 36 (co1_19) }
10.60/1.76	  fresh136(vincent_forename(u, w), true2, u, w, z, w, y, z)
10.80/1.76	= { by axiom 11 (co1_2) }
10.80/1.76	  fresh136(true2, true2, u, w, z, w, y, z)
10.80/1.76	= { by axiom 34 (co1_19) }
10.80/1.76	  fresh139(forename(u, w), true2, u, w, z, y)
10.80/1.76	= { by axiom 5 (co1) }
10.80/1.76	  fresh139(true2, true2, u, w, z, y)
10.80/1.76	= { by axiom 31 (co1_19) }
10.80/1.76	  fresh140(forename(u, w), true2, y)
10.80/1.76	= { by axiom 5 (co1) }
10.80/1.76	  fresh140(true2, true2, y)
10.80/1.76	= { by axiom 18 (co1_19) }
10.80/1.77	  true2
10.80/1.77	
10.80/1.77	Goal 1 (co1_18): tuple(forename(X, Y), forename(X, Z), forename(X, W), forename(X, V), vincent_forename(X, Y), vincent_forename(X, W), accessible_world(X, U), accessible_world(X, T), man(X, S), man(X, X2), man(X, Y2), man(X, Z2), present(X, W2), present(X, V2), present(U, U2), present(T, T2), proposition(X, U), proposition(X, T), smoke(U, U2), smoke(T, T2), event(X, W2), event(X, V2), event(U, U2), event(T, T2), state(X, S2), think_believe_consider(X, W2), think_believe_consider(X, V2), theme(X, W2, U), theme(X, V2, T), agent(X, W2, Y2), agent(X, V2, S), agent(U, U2, x3(U)), agent(T, T2, X2), be(X, S2, Z2, Z2), of(X, Y, S), of(X, Z, X2), of(X, W, Y2), of(X, V, Z2), jules_forename(X, Z), jules_forename(X, V), actual_world(X)) = tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2).
10.80/1.77	The goal is true when:
10.80/1.77	  X = u
10.80/1.77	  Y = w
10.80/1.77	  Z = z
10.80/1.77	  W = w
10.80/1.77	  V = z
10.80/1.77	  U = y
10.80/1.77	  T = y
10.80/1.77	  S = v
10.80/1.77	  X2 = x1
10.80/1.77	  Y2 = v
10.80/1.77	  Z2 = x1
10.80/1.77	  W2 = x
10.80/1.77	  V2 = x
10.80/1.77	  U2 = x4(x3(y))
10.80/1.77	  T2 = x4(x1)
10.80/1.77	  S2 = x2
10.80/1.77	
10.80/1.77	Proof:
10.80/1.77	  tuple(forename(u, w), forename(u, z), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), accessible_world(u, y), accessible_world(u, y), man(u, v), man(u, x1), man(u, v), man(u, x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), proposition(u, y), proposition(u, y), smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), event(u, x), event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), think_believe_consider(u, x), theme(u, x, y), theme(u, x, y), agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), of(u, w, v), of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), actual_world(u))
10.80/1.77	= { by axiom 17 (co1_11) }
10.80/1.77	  tuple(forename(u, w), forename(u, z), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), accessible_world(u, y), accessible_world(u, y), man(u, v), man(u, x1), man(u, v), man(u, x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), proposition(u, y), proposition(u, y), smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), event(u, x), event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), think_believe_consider(u, x), theme(u, x, y), true2, agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), of(u, w, v), of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), actual_world(u))
10.80/1.77	= { by axiom 2 (co1_3) }
10.80/1.77	  tuple(forename(u, w), forename(u, z), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), accessible_world(u, y), true2, man(u, v), man(u, x1), man(u, v), man(u, x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), proposition(u, y), proposition(u, y), smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), event(u, x), event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), think_believe_consider(u, x), theme(u, x, y), true2, agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), of(u, w, v), of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), actual_world(u))
10.80/1.77	= { by axiom 8 (co1_6) }
10.80/1.77	  tuple(forename(u, w), forename(u, z), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), accessible_world(u, y), true2, man(u, v), man(u, x1), man(u, v), man(u, x1), present(u, x), true2, present(y, x4(x3(y))), present(y, x4(x1)), proposition(u, y), proposition(u, y), smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), event(u, x), event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), think_believe_consider(u, x), theme(u, x, y), true2, agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), of(u, w, v), of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), actual_world(u))
10.80/1.77	= { by axiom 9 (co1_7) }
10.80/1.77	  tuple(forename(u, w), forename(u, z), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), accessible_world(u, y), true2, man(u, v), man(u, x1), man(u, v), man(u, x1), present(u, x), true2, present(y, x4(x3(y))), present(y, x4(x1)), proposition(u, y), true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), event(u, x), event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), think_believe_consider(u, x), theme(u, x, y), true2, agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), of(u, w, v), of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), actual_world(u))
10.80/1.77	= { by axiom 7 (co1_8) }
10.80/1.77	  tuple(forename(u, w), forename(u, z), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), accessible_world(u, y), true2, man(u, v), man(u, x1), man(u, v), man(u, x1), present(u, x), true2, present(y, x4(x3(y))), present(y, x4(x1)), proposition(u, y), true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), think_believe_consider(u, x), theme(u, x, y), true2, agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), of(u, w, v), of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), actual_world(u))
10.80/1.77	= { by axiom 10 (co1_10) }
10.80/1.77	  tuple(forename(u, w), forename(u, z), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), accessible_world(u, y), true2, man(u, v), man(u, x1), man(u, v), man(u, x1), present(u, x), true2, present(y, x4(x3(y))), present(y, x4(x1)), proposition(u, y), true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), true2, theme(u, x, y), true2, agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), of(u, w, v), of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), actual_world(u))
10.80/1.77	= { by axiom 1 (co1_17) }
10.80/1.77	  tuple(forename(u, w), forename(u, z), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), accessible_world(u, y), true2, man(u, v), man(u, x1), man(u, v), man(u, x1), present(u, x), true2, present(y, x4(x3(y))), present(y, x4(x1)), proposition(u, y), true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), true2, theme(u, x, y), true2, agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), of(u, w, v), of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.77	= { by axiom 14 (co1_14) }
10.80/1.77	  tuple(forename(u, w), forename(u, z), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), accessible_world(u, y), true2, man(u, v), man(u, x1), man(u, v), man(u, x1), present(u, x), true2, present(y, x4(x3(y))), present(y, x4(x1)), proposition(u, y), true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), true2, theme(u, x, y), true2, agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), true2, of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.77	= { by axiom 5 (co1) }
10.80/1.78	  tuple(true2, forename(u, z), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), accessible_world(u, y), true2, man(u, v), man(u, x1), man(u, v), man(u, x1), present(u, x), true2, present(y, x4(x3(y))), present(y, x4(x1)), proposition(u, y), true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), true2, theme(u, x, y), true2, agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), true2, of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 11 (co1_2) }
10.80/1.78	  tuple(true2, forename(u, z), forename(u, w), forename(u, z), true2, vincent_forename(u, w), accessible_world(u, y), true2, man(u, v), man(u, x1), man(u, v), man(u, x1), present(u, x), true2, present(y, x4(x3(y))), present(y, x4(x1)), proposition(u, y), true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), true2, theme(u, x, y), true2, agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), true2, of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 4 (co1_4) }
10.80/1.78	  tuple(true2, forename(u, z), forename(u, w), forename(u, z), true2, vincent_forename(u, w), accessible_world(u, y), true2, true2, man(u, x1), man(u, v), man(u, x1), present(u, x), true2, present(y, x4(x3(y))), present(y, x4(x1)), proposition(u, y), true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), true2, theme(u, x, y), true2, agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), true2, of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 16 (co1_12) }
10.80/1.78	  tuple(true2, forename(u, z), forename(u, w), forename(u, z), true2, vincent_forename(u, w), accessible_world(u, y), true2, true2, man(u, x1), man(u, v), man(u, x1), present(u, x), true2, present(y, x4(x3(y))), present(y, x4(x1)), proposition(u, y), true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), true2, theme(u, x, y), true2, agent(u, x, v), true2, agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), true2, of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 17 (co1_11) }
10.80/1.78	  tuple(true2, forename(u, z), forename(u, w), forename(u, z), true2, vincent_forename(u, w), accessible_world(u, y), true2, true2, man(u, x1), man(u, v), man(u, x1), present(u, x), true2, present(y, x4(x3(y))), present(y, x4(x1)), proposition(u, y), true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), true2, true2, true2, agent(u, x, v), true2, agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), true2, of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 2 (co1_3) }
10.80/1.78	  tuple(true2, forename(u, z), forename(u, w), forename(u, z), true2, vincent_forename(u, w), true2, true2, true2, man(u, x1), man(u, v), man(u, x1), present(u, x), true2, present(y, x4(x3(y))), present(y, x4(x1)), proposition(u, y), true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), true2, true2, true2, agent(u, x, v), true2, agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), true2, of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 8 (co1_6) }
10.80/1.78	  tuple(true2, forename(u, z), forename(u, w), forename(u, z), true2, vincent_forename(u, w), true2, true2, true2, man(u, x1), man(u, v), man(u, x1), true2, true2, present(y, x4(x3(y))), present(y, x4(x1)), proposition(u, y), true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), true2, true2, true2, agent(u, x, v), true2, agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), true2, of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 9 (co1_7) }
10.80/1.78	  tuple(true2, forename(u, z), forename(u, w), forename(u, z), true2, vincent_forename(u, w), true2, true2, true2, man(u, x1), man(u, v), man(u, x1), true2, true2, present(y, x4(x3(y))), present(y, x4(x1)), true2, true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), event(u, x), true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), true2, true2, true2, agent(u, x, v), true2, agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), true2, of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 7 (co1_8) }
10.80/1.78	  tuple(true2, forename(u, z), forename(u, w), forename(u, z), true2, vincent_forename(u, w), true2, true2, true2, man(u, x1), man(u, v), man(u, x1), true2, true2, present(y, x4(x3(y))), present(y, x4(x1)), true2, true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), true2, true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), think_believe_consider(u, x), true2, true2, true2, agent(u, x, v), true2, agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), true2, of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 10 (co1_10) }
10.80/1.78	  tuple(true2, forename(u, z), forename(u, w), forename(u, z), true2, vincent_forename(u, w), true2, true2, true2, man(u, x1), man(u, v), man(u, x1), true2, true2, present(y, x4(x3(y))), present(y, x4(x1)), true2, true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), true2, true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), true2, true2, true2, true2, agent(u, x, v), true2, agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), true2, of(u, z, x1), of(u, w, v), of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 14 (co1_14) }
10.80/1.78	  tuple(true2, forename(u, z), forename(u, w), forename(u, z), true2, vincent_forename(u, w), true2, true2, true2, man(u, x1), man(u, v), man(u, x1), true2, true2, present(y, x4(x3(y))), present(y, x4(x1)), true2, true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), true2, true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), true2, true2, true2, true2, agent(u, x, v), true2, agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), true2, of(u, z, x1), true2, of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 5 (co1) }
10.80/1.78	  tuple(true2, forename(u, z), true2, forename(u, z), true2, vincent_forename(u, w), true2, true2, true2, man(u, x1), man(u, v), man(u, x1), true2, true2, present(y, x4(x3(y))), present(y, x4(x1)), true2, true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), true2, true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), true2, true2, true2, true2, agent(u, x, v), true2, agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), true2, of(u, z, x1), true2, of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 11 (co1_2) }
10.80/1.78	  tuple(true2, forename(u, z), true2, forename(u, z), true2, true2, true2, true2, true2, man(u, x1), man(u, v), man(u, x1), true2, true2, present(y, x4(x3(y))), present(y, x4(x1)), true2, true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), true2, true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), true2, true2, true2, true2, agent(u, x, v), true2, agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), true2, of(u, z, x1), true2, of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 4 (co1_4) }
10.80/1.78	  tuple(true2, forename(u, z), true2, forename(u, z), true2, true2, true2, true2, true2, man(u, x1), true2, man(u, x1), true2, true2, present(y, x4(x3(y))), present(y, x4(x1)), true2, true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), true2, true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), true2, true2, true2, true2, agent(u, x, v), true2, agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), true2, of(u, z, x1), true2, of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 16 (co1_12) }
10.80/1.78	  tuple(true2, forename(u, z), true2, forename(u, z), true2, true2, true2, true2, true2, man(u, x1), true2, man(u, x1), true2, true2, present(y, x4(x3(y))), present(y, x4(x1)), true2, true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), true2, true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), be(u, x2, x1, x1), true2, of(u, z, x1), true2, of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by lemma 70 }
10.80/1.78	  tuple(true2, forename(u, z), true2, forename(u, z), true2, true2, true2, true2, true2, man(u, x1), true2, man(u, x1), true2, true2, present(y, x4(x3(y))), present(y, x4(x1)), true2, true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), true2, true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, be(u, x2, x1, x1), true2, of(u, z, x1), true2, of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 3 (co1_5) }
10.80/1.78	  tuple(true2, forename(u, z), true2, forename(u, z), true2, true2, true2, true2, true2, true2, true2, man(u, x1), true2, true2, present(y, x4(x3(y))), present(y, x4(x1)), true2, true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), true2, true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, be(u, x2, x1, x1), true2, of(u, z, x1), true2, of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by lemma 72 }
10.80/1.78	  tuple(true2, forename(u, z), true2, forename(u, z), true2, true2, true2, true2, true2, true2, true2, man(u, x1), true2, true2, present(y, x4(x3(y))), true2, true2, true2, smoke(y, x4(x3(y))), smoke(y, x4(x1)), true2, true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, be(u, x2, x1, x1), true2, of(u, z, x1), true2, of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by lemma 69 }
10.80/1.78	  tuple(true2, forename(u, z), true2, forename(u, z), true2, true2, true2, true2, true2, true2, true2, man(u, x1), true2, true2, present(y, x4(x3(y))), true2, true2, true2, smoke(y, x4(x3(y))), true2, true2, true2, event(y, x4(x3(y))), event(y, x4(x1)), state(u, x2), true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, be(u, x2, x1, x1), true2, of(u, z, x1), true2, of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by lemma 71 }
10.80/1.78	  tuple(true2, forename(u, z), true2, forename(u, z), true2, true2, true2, true2, true2, true2, true2, man(u, x1), true2, true2, present(y, x4(x3(y))), true2, true2, true2, smoke(y, x4(x3(y))), true2, true2, true2, event(y, x4(x3(y))), true2, state(u, x2), true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, be(u, x2, x1, x1), true2, of(u, z, x1), true2, of(u, z, x1), jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 15 (co1_15) }
10.80/1.78	  tuple(true2, forename(u, z), true2, forename(u, z), true2, true2, true2, true2, true2, true2, true2, man(u, x1), true2, true2, present(y, x4(x3(y))), true2, true2, true2, smoke(y, x4(x3(y))), true2, true2, true2, event(y, x4(x3(y))), true2, state(u, x2), true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, be(u, x2, x1, x1), true2, of(u, z, x1), true2, true2, jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 6 (co1_1) }
10.80/1.78	  tuple(true2, forename(u, z), true2, true2, true2, true2, true2, true2, true2, true2, true2, man(u, x1), true2, true2, present(y, x4(x3(y))), true2, true2, true2, smoke(y, x4(x3(y))), true2, true2, true2, event(y, x4(x3(y))), true2, state(u, x2), true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, be(u, x2, x1, x1), true2, of(u, z, x1), true2, true2, jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 3 (co1_5) }
10.80/1.78	  tuple(true2, forename(u, z), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, present(y, x4(x3(y))), true2, true2, true2, smoke(y, x4(x3(y))), true2, true2, true2, event(y, x4(x3(y))), true2, state(u, x2), true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, be(u, x2, x1, x1), true2, of(u, z, x1), true2, true2, jules_forename(u, z), jules_forename(u, z), true2)
10.80/1.78	= { by axiom 12 (co1_16) }
10.80/1.78	  tuple(true2, forename(u, z), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, present(y, x4(x3(y))), true2, true2, true2, smoke(y, x4(x3(y))), true2, true2, true2, event(y, x4(x3(y))), true2, state(u, x2), true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, be(u, x2, x1, x1), true2, of(u, z, x1), true2, true2, jules_forename(u, z), true2, true2)
10.80/1.78	= { by axiom 6 (co1_1) }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, present(y, x4(x3(y))), true2, true2, true2, smoke(y, x4(x3(y))), true2, true2, true2, event(y, x4(x3(y))), true2, state(u, x2), true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, be(u, x2, x1, x1), true2, of(u, z, x1), true2, true2, jules_forename(u, z), true2, true2)
10.80/1.78	= { by axiom 15 (co1_15) }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, present(y, x4(x3(y))), true2, true2, true2, smoke(y, x4(x3(y))), true2, true2, true2, event(y, x4(x3(y))), true2, state(u, x2), true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, be(u, x2, x1, x1), true2, true2, true2, true2, jules_forename(u, z), true2, true2)
10.80/1.78	= { by axiom 12 (co1_16) }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, present(y, x4(x3(y))), true2, true2, true2, smoke(y, x4(x3(y))), true2, true2, true2, event(y, x4(x3(y))), true2, state(u, x2), true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, be(u, x2, x1, x1), true2, true2, true2, true2, true2, true2, true2)
10.80/1.78	= { by axiom 13 (co1_9) }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, present(y, x4(x3(y))), true2, true2, true2, smoke(y, x4(x3(y))), true2, true2, true2, event(y, x4(x3(y))), true2, true2, true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, be(u, x2, x1, x1), true2, true2, true2, true2, true2, true2, true2)
10.80/1.78	= { by axiom 23 (co1_13) }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, present(y, x4(x3(y))), true2, true2, true2, smoke(y, x4(x3(y))), true2, true2, true2, event(y, x4(x3(y))), true2, true2, true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, true2, true2, true2, true2, true2, true2, true2, true2)
10.80/1.78	= { by axiom 27 (co1_20) R->L }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh5(man(y, x3(y)), true2, x3(y)), true2, true2, true2, smoke(y, x4(x3(y))), true2, true2, true2, event(y, x4(x3(y))), true2, true2, true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, true2, true2, true2, true2, true2, true2, true2, true2)
10.80/1.78	= { by lemma 73 }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh5(true2, true2, x3(y)), true2, true2, true2, smoke(y, x4(x3(y))), true2, true2, true2, event(y, x4(x3(y))), true2, true2, true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, true2, true2, true2, true2, true2, true2, true2, true2)
10.80/1.78	= { by axiom 19 (co1_20) }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, smoke(y, x4(x3(y))), true2, true2, true2, event(y, x4(x3(y))), true2, true2, true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, true2, true2, true2, true2, true2, true2, true2, true2)
10.80/1.78	= { by axiom 28 (co1_21) R->L }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh4(man(y, x3(y)), true2, x3(y)), true2, true2, true2, event(y, x4(x3(y))), true2, true2, true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, true2, true2, true2, true2, true2, true2, true2, true2)
10.80/1.78	= { by lemma 73 }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh4(true2, true2, x3(y)), true2, true2, true2, event(y, x4(x3(y))), true2, true2, true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, true2, true2, true2, true2, true2, true2, true2, true2)
10.80/1.78	= { by axiom 20 (co1_21) }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, event(y, x4(x3(y))), true2, true2, true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, true2, true2, true2, true2, true2, true2, true2, true2)
10.80/1.78	= { by axiom 29 (co1_22) R->L }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh3(man(y, x3(y)), true2, x3(y)), true2, true2, true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, true2, true2, true2, true2, true2, true2, true2, true2)
10.80/1.78	= { by lemma 73 }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh3(true2, true2, x3(y)), true2, true2, true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, true2, true2, true2, true2, true2, true2, true2, true2)
10.80/1.78	= { by axiom 21 (co1_22) }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, agent(y, x4(x3(y)), x3(y)), true2, true2, true2, true2, true2, true2, true2, true2, true2)
10.80/1.78	= { by axiom 30 (co1_23) R->L }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh2(man(y, x3(y)), true2, x3(y)), true2, true2, true2, true2, true2, true2, true2, true2, true2)
10.80/1.78	= { by lemma 73 }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh2(true2, true2, x3(y)), true2, true2, true2, true2, true2, true2, true2, true2, true2)
10.80/1.78	= { by axiom 22 (co1_23) }
10.80/1.78	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2)
10.80/1.78	% SZS output end Proof
10.80/1.78	
10.80/1.78	RESULT: Theorem (the conjecture is true).
10.80/1.79	EOF