TSTP Solution File: NLP257+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NLP257+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 : n011.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 10:08:20 EDT 2023
% Result : Theorem 5.38s 1.07s
% Output : Proof 7.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NLP257+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.13 % 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 : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 12:37:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 5.38/1.07 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 5.38/1.07
% 5.38/1.07 % SZS status Theorem
% 5.38/1.07
% 6.23/1.26 % SZS output start Proof
% 6.23/1.26 Take the following subset of the input axioms:
% 7.69/1.43 fof(ax31, axiom, ![U, V]: (existent(U, V) => ~nonexistent(U, V))).
% 7.69/1.43 fof(ax32, axiom, ![V2, U2]: (nonhuman(U2, V2) => ~human(U2, V2))).
% 7.69/1.43 fof(ax33, axiom, ![V2, U2]: (specific(U2, V2) => ~general(U2, V2))).
% 7.69/1.43 fof(ax34, axiom, ![V2, U2]: (unisex(U2, V2) => ~male(U2, V2))).
% 7.69/1.43 fof(ax49, axiom, ![W, V2, U2]: ((accessible_world(V2, W) & man(V2, U2)) => man(W, U2))).
% 7.69/1.43 fof(co1, conjecture, ~(?[U2]: (actual_world(U2) & ?[X, Y, Z, X1, X2, V2, W2]: (of(U2, W2, V2) & (man(U2, V2) & (vincent_forename(U2, W2) & (forename(U2, W2) & (proposition(U2, Y) & (agent(U2, X, V2) & (theme(U2, X, Y) & (event(U2, X) & (present(U2, X) & (think_believe_consider(U2, X) & (accessible_world(U2, Y) & (![X3]: (man(Y, X3) => ?[X4]: (event(Y, X4) & (agent(Y, X4, X3) & (present(Y, X4) & smoke(Y, X4))))) & (of(U2, Z, X1) & (man(U2, X1) & (jules_forename(U2, Z) & (forename(U2, Z) & (man(U2, X1) & (state(U2, X2) & be(U2, X2, X1, X1)))))))))))))))))))) & ~?[X5]: (actual_world(X5) & ?[X6, X7, X8, X9, X10, V2, W2, X12, Y2, Z2, X1_2, X2_2]: (of(X5, X7, X6) & (man(X5, X6) & (jules_forename(X5, X7) & (forename(X5, X7) & (of(X5, X8, V2) & (vincent_forename(X5, X8) & (forename(X5, X8) & (of(X5, W2, V2) & (man(X5, V2) & (vincent_forename(X5, W2) & (forename(X5, W2) & (proposition(X5, Y2) & (agent(X5, X12, V2) & (theme(X5, X12, Y2) & (event(X5, X12) & (present(X5, X12) & (think_believe_consider(X5, X12) & (accessible_world(X5, Y2) & (![X3_2]: (man(Y2, X3_2) => ?[X4_2]: (event(Y2, X4_2) & (agent(Y2, X4_2, X3_2) & (present(Y2, X4_2) & smoke(Y2, X4_2))))) & (of(X5, Z2, X1_2) & (man(X5, X1_2) & (jules_forename(X5, Z2) & (forename(X5, Z2) & (man(X5, X1_2) & (state(X5, X2_2) & (be(X5, X2_2, X1_2, X1_2) & (proposition(X5, X10) & (agent(X5, X9, V2) & (theme(X5, X9, X10) & (event(X5, X9) & (present(X5, X9) & (think_believe_consider(X5, X9) & (accessible_world(X5, X10) & ?[X11]: (event(X10, X11) & (agent(X10, X11, X6) & (present(X10, X11) & smoke(X10, X11)))))))))))))))))))))))))))))))))))))))).
% 7.69/1.43
% 7.69/1.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 7.69/1.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 7.69/1.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 7.69/1.43 fresh(y, y, x1...xn) = u
% 7.69/1.43 C => fresh(s, t, x1...xn) = v
% 7.69/1.43 where fresh is a fresh function symbol and x1..xn are the free
% 7.69/1.43 variables of u and v.
% 7.69/1.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 7.69/1.43 input problem has no model of domain size 1).
% 7.69/1.43
% 7.69/1.43 The encoding turns the above axioms into the following unit equations and goals:
% 7.69/1.43
% 7.69/1.43 Axiom 1 (co1_9): accessible_world(u, y) = true2.
% 7.69/1.43 Axiom 2 (co1_1): forename(u, w) = true2.
% 7.69/1.43 Axiom 3 (co1_2): forename(u, z) = true2.
% 7.69/1.43 Axiom 4 (co1_5): man(u, x1) = true2.
% 7.69/1.43 Axiom 5 (co1_4): man(u, v) = true2.
% 7.69/1.43 Axiom 6 (co1_7): event(u, x) = true2.
% 7.69/1.43 Axiom 7 (co1_16): present(u, x) = true2.
% 7.69/1.43 Axiom 8 (co1_8): proposition(u, y) = true2.
% 7.69/1.43 Axiom 9 (co1_14): think_believe_consider(u, x) = true2.
% 7.69/1.43 Axiom 10 (co1): jules_forename(u, z) = true2.
% 7.69/1.43 Axiom 11 (co1_3): vincent_forename(u, w) = true2.
% 7.69/1.43 Axiom 12 (co1_6): state(u, x2) = true2.
% 7.69/1.43 Axiom 13 (co1_17): actual_world(u) = true2.
% 7.69/1.43 Axiom 14 (co1_10): of(u, w, v) = true2.
% 7.69/1.43 Axiom 15 (co1_11): of(u, z, x1) = true2.
% 7.69/1.43 Axiom 16 (co1_15): agent(u, x, v) = true2.
% 7.69/1.43 Axiom 17 (co1_13): theme(u, x, y) = true2.
% 7.69/1.43 Axiom 18 (co1_19): fresh139(X, X, Y) = true2.
% 7.69/1.43 Axiom 19 (co1_20): fresh5(X, X, Y) = true2.
% 7.69/1.43 Axiom 20 (co1_21): fresh4(X, X, Y) = true2.
% 7.69/1.43 Axiom 21 (co1_22): fresh3(X, X, Y) = true2.
% 7.69/1.43 Axiom 22 (co1_23): fresh2(X, X, Y) = true2.
% 7.69/1.43 Axiom 23 (co1_12): be(u, x2, x1, x1) = true2.
% 7.69/1.43 Axiom 24 (ax49): fresh49(X, X, Y, Z) = true2.
% 7.69/1.43 Axiom 25 (co1_20): fresh5(man(y, X), true2, X) = event(y, x4(X)).
% 7.69/1.43 Axiom 26 (co1_21): fresh4(man(y, X), true2, X) = smoke(y, x4(X)).
% 7.69/1.43 Axiom 27 (co1_22): fresh3(man(y, X), true2, X) = agent(y, x4(X), X).
% 7.69/1.43 Axiom 28 (co1_23): fresh2(man(y, X), true2, X) = present(y, x4(X)).
% 7.69/1.43 Axiom 29 (co1_19): fresh137(X, X, Y, Z, W) = man(W, x3(W)).
% 7.69/1.43 Axiom 30 (ax49): fresh50(X, X, Y, Z, W) = man(W, Y).
% 7.69/1.43 Axiom 31 (co1_19): fresh138(X, X, Y, Z, W, V) = fresh139(jules_forename(Y, Z), true2, W).
% 7.69/1.43 Axiom 32 (co1_19): fresh136(X, X, Y, Z, W, V) = fresh137(jules_forename(Y, V), true2, Y, Z, W).
% 7.69/1.43 Axiom 33 (ax49): fresh50(accessible_world(X, Y), true2, Z, X, Y) = fresh49(man(X, Z), true2, Z, Y).
% 7.69/1.43 Axiom 34 (co1_19): fresh135(X, X, Y, Z, W, V, U) = fresh138(forename(Y, Z), true2, Y, Z, V, U).
% 7.69/1.43 Axiom 35 (co1_19): fresh134(X, X, Y, Z, W, V, U, T) = fresh136(forename(Y, W), true2, Y, Z, U, T).
% 7.69/1.43 Axiom 36 (co1_19): fresh133(X, X, Y, Z, W, V, U, T) = fresh135(forename(Y, V), true2, Y, Z, W, U, T).
% 7.69/1.43 Axiom 37 (co1_19): fresh132(X, X, Y, Z, W, V, U, T) = fresh134(forename(Y, T), true2, Y, Z, W, V, U, T).
% 7.69/1.43 Axiom 38 (co1_19): fresh131(X, X, Y, Z, W, V, U, T) = fresh133(vincent_forename(Y, W), true2, Y, Z, W, V, U, T).
% 7.69/1.43 Axiom 39 (co1_19): fresh130(X, X, Y, Z, W, V, U, T, S) = fresh132(vincent_forename(Y, U), true2, Y, W, V, U, T, S).
% 7.69/1.43 Axiom 40 (co1_19): fresh129(X, X, Y, Z, W, V, U, T, S, X2) = fresh131(man(Y, Z), true2, Y, W, V, T, S, X2).
% 7.69/1.43 Axiom 41 (co1_19): fresh128(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh130(man(Y, U), true2, Y, Z, W, V, T, S, X2).
% 7.69/1.43 Axiom 42 (co1_19): fresh127(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2) = fresh129(man(Y, Y2), true2, Y, Z, W, V, U, T, S, X2).
% 7.69/1.43 Axiom 43 (co1_19): fresh126(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = fresh128(state(Y, W2), true2, Y, Z, W, V, U, T, X2, Y2, Z2).
% 7.69/1.43 Axiom 44 (co1_19): fresh125(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = fresh127(event(Y, S), true2, Y, Z, W, V, U, T, X2, Y2, Z2, W2).
% 7.69/1.43 Axiom 45 (co1_19): fresh124(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh126(event(Y, V2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2).
% 7.69/1.43 Axiom 46 (co1_19): fresh123(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh125(event(U2, T2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2).
% 7.69/1.43 Axiom 47 (co1_19): fresh122(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh124(proposition(Y, X2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 48 (co1_19): fresh121(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh123(proposition(Y, U2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 49 (co1_19): fresh120(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh122(smoke(U2, T2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 50 (co1_19): fresh119(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh121(accessible_world(Y, X2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 51 (co1_19): fresh118(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh120(accessible_world(Y, U2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 52 (co1_19): fresh111(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh112(think_believe_consider(Y, S), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 53 (co1_19): fresh110(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh111(think_believe_consider(Y, V2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 54 (co1_19): fresh106(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh107(present(Y, S), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 55 (co1_19): fresh105(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh106(present(Y, V2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 56 (co1_19): fresh104(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh105(present(U2, T2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 57 (co1_19): fresh117(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh119(of(Y, W, Z), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 58 (co1_19): fresh116(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh118(of(Y, V, U), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 59 (co1_19): fresh115(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh117(of(Y, T, U), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 60 (co1_19): fresh114(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh116(of(Y, Y2, Z2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 61 (co1_19): fresh113(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh114(theme(Y, S, X2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 62 (co1_19): fresh112(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh113(theme(Y, V2, U2), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 63 (co1_19): fresh109(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh110(agent(Y, S, U), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 64 (co1_19): fresh108(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh109(agent(Y, V2, U), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 65 (co1_19): fresh107(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = fresh108(agent(U2, T2, Z), true2, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2).
% 7.69/1.43 Axiom 66 (co1_19): fresh104(actual_world(X), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2) = fresh115(be(X, Z2, Y2, Y2), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2).
% 7.69/1.43
% 7.69/1.43 Lemma 67: man(y, x1) = true2.
% 7.69/1.43 Proof:
% 7.69/1.43 man(y, x1)
% 7.69/1.43 = { by axiom 30 (ax49) R->L }
% 7.69/1.43 fresh50(true2, true2, x1, u, y)
% 7.69/1.43 = { by axiom 1 (co1_9) R->L }
% 7.69/1.43 fresh50(accessible_world(u, y), true2, x1, u, y)
% 7.69/1.43 = { by axiom 33 (ax49) }
% 7.69/1.43 fresh49(man(u, x1), true2, x1, y)
% 7.69/1.43 = { by axiom 4 (co1_5) }
% 7.69/1.43 fresh49(true2, true2, x1, y)
% 7.69/1.43 = { by axiom 24 (ax49) }
% 7.69/1.43 true2
% 7.69/1.43
% 7.69/1.43 Lemma 68: smoke(y, x4(x1)) = true2.
% 7.69/1.43 Proof:
% 7.69/1.43 smoke(y, x4(x1))
% 7.69/1.43 = { by axiom 26 (co1_21) R->L }
% 7.69/1.43 fresh4(man(y, x1), true2, x1)
% 7.69/1.43 = { by lemma 67 }
% 7.69/1.43 fresh4(true2, true2, x1)
% 7.69/1.43 = { by axiom 20 (co1_21) }
% 7.69/1.43 true2
% 7.69/1.43
% 7.69/1.43 Lemma 69: agent(y, x4(x1), x1) = true2.
% 7.69/1.43 Proof:
% 7.69/1.43 agent(y, x4(x1), x1)
% 7.69/1.43 = { by axiom 27 (co1_22) R->L }
% 7.69/1.43 fresh3(man(y, x1), true2, x1)
% 7.69/1.43 = { by lemma 67 }
% 7.69/1.43 fresh3(true2, true2, x1)
% 7.69/1.43 = { by axiom 21 (co1_22) }
% 7.69/1.43 true2
% 7.69/1.43
% 7.69/1.43 Lemma 70: present(y, x4(x1)) = true2.
% 7.69/1.43 Proof:
% 7.69/1.43 present(y, x4(x1))
% 7.69/1.43 = { by axiom 28 (co1_23) R->L }
% 7.69/1.43 fresh2(man(y, x1), true2, x1)
% 7.69/1.43 = { by lemma 67 }
% 7.69/1.43 fresh2(true2, true2, x1)
% 7.69/1.43 = { by axiom 22 (co1_23) }
% 7.69/1.43 true2
% 7.69/1.43
% 7.69/1.43 Lemma 71: event(y, x4(x1)) = true2.
% 7.69/1.43 Proof:
% 7.69/1.43 event(y, x4(x1))
% 7.69/1.43 = { by axiom 25 (co1_20) R->L }
% 7.69/1.43 fresh5(man(y, x1), true2, x1)
% 7.69/1.43 = { by lemma 67 }
% 7.69/1.43 fresh5(true2, true2, x1)
% 7.69/1.43 = { by axiom 19 (co1_20) }
% 7.69/1.43 true2
% 7.69/1.43
% 7.69/1.43 Lemma 72: man(y, x3(y)) = true2.
% 7.69/1.43 Proof:
% 7.69/1.43 man(y, x3(y))
% 7.69/1.43 = { by axiom 29 (co1_19) R->L }
% 7.69/1.43 fresh137(true2, true2, u, z, y)
% 7.69/1.43 = { by axiom 10 (co1) R->L }
% 7.69/1.43 fresh137(jules_forename(u, z), true2, u, z, y)
% 7.69/1.43 = { by axiom 32 (co1_19) R->L }
% 7.69/1.43 fresh136(true2, true2, u, z, y, z)
% 7.69/1.43 = { by axiom 2 (co1_1) R->L }
% 7.69/1.43 fresh136(forename(u, w), true2, u, z, y, z)
% 7.69/1.43 = { by axiom 35 (co1_19) R->L }
% 7.69/1.43 fresh134(true2, true2, u, z, w, w, y, z)
% 7.69/1.43 = { by axiom 3 (co1_2) R->L }
% 7.69/1.43 fresh134(forename(u, z), true2, u, z, w, w, y, z)
% 7.69/1.43 = { by axiom 37 (co1_19) R->L }
% 7.69/1.43 fresh132(true2, true2, u, z, w, w, y, z)
% 7.69/1.43 = { by axiom 11 (co1_3) R->L }
% 7.69/1.43 fresh132(vincent_forename(u, w), true2, u, z, w, w, y, z)
% 7.69/1.43 = { by axiom 39 (co1_19) R->L }
% 7.69/1.43 fresh130(true2, true2, u, x1, z, w, w, y, z)
% 7.69/1.43 = { by axiom 5 (co1_4) R->L }
% 7.69/1.43 fresh130(man(u, v), true2, u, x1, z, w, w, y, z)
% 7.69/1.43 = { by axiom 41 (co1_19) R->L }
% 7.69/1.43 fresh128(true2, true2, u, x1, z, w, v, w, y, z, x1)
% 7.69/1.43 = { by axiom 12 (co1_6) R->L }
% 7.69/1.43 fresh128(state(u, x2), true2, u, x1, z, w, v, w, y, z, x1)
% 7.69/1.43 = { by axiom 43 (co1_19) R->L }
% 7.69/1.43 fresh126(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2)
% 7.69/1.43 = { by axiom 6 (co1_7) R->L }
% 7.69/1.43 fresh126(event(u, x), true2, u, x1, z, w, v, w, x, y, z, x1, x2)
% 7.69/1.43 = { by axiom 45 (co1_19) R->L }
% 7.69/1.43 fresh124(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 8 (co1_8) R->L }
% 7.69/1.43 fresh124(proposition(u, y), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 47 (co1_19) R->L }
% 7.69/1.43 fresh122(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by lemma 68 R->L }
% 7.69/1.43 fresh122(smoke(y, x4(x1)), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 49 (co1_19) R->L }
% 7.69/1.43 fresh120(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 1 (co1_9) R->L }
% 7.69/1.43 fresh120(accessible_world(u, y), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 51 (co1_19) R->L }
% 7.69/1.43 fresh118(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 14 (co1_10) R->L }
% 7.69/1.43 fresh118(of(u, w, v), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 58 (co1_19) R->L }
% 7.69/1.43 fresh116(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 15 (co1_11) R->L }
% 7.69/1.43 fresh116(of(u, z, x1), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 60 (co1_19) R->L }
% 7.69/1.43 fresh114(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 17 (co1_13) R->L }
% 7.69/1.43 fresh114(theme(u, x, y), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 61 (co1_19) R->L }
% 7.69/1.43 fresh113(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 17 (co1_13) R->L }
% 7.69/1.43 fresh113(theme(u, x, y), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 62 (co1_19) R->L }
% 7.69/1.43 fresh112(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 9 (co1_14) R->L }
% 7.69/1.43 fresh112(think_believe_consider(u, x), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 52 (co1_19) R->L }
% 7.69/1.43 fresh111(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 9 (co1_14) R->L }
% 7.69/1.43 fresh111(think_believe_consider(u, x), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 53 (co1_19) R->L }
% 7.69/1.43 fresh110(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 16 (co1_15) R->L }
% 7.69/1.43 fresh110(agent(u, x, v), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 63 (co1_19) R->L }
% 7.69/1.43 fresh109(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 16 (co1_15) R->L }
% 7.69/1.43 fresh109(agent(u, x, v), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 64 (co1_19) R->L }
% 7.69/1.43 fresh108(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by lemma 69 R->L }
% 7.69/1.43 fresh108(agent(y, x4(x1), x1), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 65 (co1_19) R->L }
% 7.69/1.43 fresh107(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 7 (co1_16) R->L }
% 7.69/1.43 fresh107(present(u, x), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 54 (co1_19) R->L }
% 7.69/1.43 fresh106(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 7 (co1_16) R->L }
% 7.69/1.43 fresh106(present(u, x), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 55 (co1_19) R->L }
% 7.69/1.43 fresh105(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by lemma 70 R->L }
% 7.69/1.43 fresh105(present(y, x4(x1)), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 56 (co1_19) R->L }
% 7.69/1.43 fresh104(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 13 (co1_17) R->L }
% 7.69/1.43 fresh104(actual_world(u), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 66 (co1_19) }
% 7.69/1.43 fresh115(be(u, x2, x1, x1), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 23 (co1_12) }
% 7.69/1.43 fresh115(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 59 (co1_19) }
% 7.69/1.43 fresh117(of(u, w, v), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.43 = { by axiom 14 (co1_10) }
% 7.69/1.43 fresh117(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.44 = { by axiom 57 (co1_19) }
% 7.69/1.44 fresh119(of(u, z, x1), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.44 = { by axiom 15 (co1_11) }
% 7.69/1.44 fresh119(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.44 = { by axiom 50 (co1_19) }
% 7.69/1.44 fresh121(accessible_world(u, y), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.44 = { by axiom 1 (co1_9) }
% 7.69/1.44 fresh121(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.44 = { by axiom 48 (co1_19) }
% 7.69/1.44 fresh123(proposition(u, y), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.44 = { by axiom 8 (co1_8) }
% 7.69/1.44 fresh123(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x, y, x4(x1))
% 7.69/1.44 = { by axiom 46 (co1_19) }
% 7.69/1.44 fresh125(event(y, x4(x1)), true2, u, x1, z, w, v, w, x, y, z, x1, x2, x)
% 7.69/1.44 = { by lemma 71 }
% 7.69/1.44 fresh125(true2, true2, u, x1, z, w, v, w, x, y, z, x1, x2, x)
% 7.69/1.44 = { by axiom 44 (co1_19) }
% 7.69/1.44 fresh127(event(u, x), true2, u, x1, z, w, v, w, y, z, x1, x2)
% 7.69/1.44 = { by axiom 6 (co1_7) }
% 7.69/1.44 fresh127(true2, true2, u, x1, z, w, v, w, y, z, x1, x2)
% 7.69/1.44 = { by axiom 42 (co1_19) }
% 7.69/1.44 fresh129(man(u, x1), true2, u, x1, z, w, v, w, y, z)
% 7.69/1.44 = { by axiom 4 (co1_5) }
% 7.69/1.44 fresh129(true2, true2, u, x1, z, w, v, w, y, z)
% 7.69/1.44 = { by axiom 40 (co1_19) }
% 7.69/1.44 fresh131(man(u, x1), true2, u, z, w, w, y, z)
% 7.69/1.44 = { by axiom 4 (co1_5) }
% 7.69/1.44 fresh131(true2, true2, u, z, w, w, y, z)
% 7.69/1.44 = { by axiom 38 (co1_19) }
% 7.69/1.44 fresh133(vincent_forename(u, w), true2, u, z, w, w, y, z)
% 7.69/1.44 = { by axiom 11 (co1_3) }
% 7.69/1.44 fresh133(true2, true2, u, z, w, w, y, z)
% 7.69/1.44 = { by axiom 36 (co1_19) }
% 7.69/1.44 fresh135(forename(u, w), true2, u, z, w, y, z)
% 7.69/1.44 = { by axiom 2 (co1_1) }
% 7.69/1.44 fresh135(true2, true2, u, z, w, y, z)
% 7.69/1.44 = { by axiom 34 (co1_19) }
% 7.69/1.44 fresh138(forename(u, z), true2, u, z, y, z)
% 7.69/1.44 = { by axiom 3 (co1_2) }
% 7.69/1.44 fresh138(true2, true2, u, z, y, z)
% 7.69/1.44 = { by axiom 31 (co1_19) }
% 7.69/1.44 fresh139(jules_forename(u, z), true2, y)
% 7.69/1.44 = { by axiom 10 (co1) }
% 7.69/1.44 fresh139(true2, true2, y)
% 7.69/1.44 = { by axiom 18 (co1_19) }
% 7.69/1.44 true2
% 7.69/1.44
% 7.69/1.44 Goal 1 (co1_18): tuple(jules_forename(X, Y), jules_forename(X, Z), forename(X, Y), forename(X, W), forename(X, V), forename(X, Z), vincent_forename(X, W), vincent_forename(X, V), man(X, U), man(X, T), man(X, S), state(X, X2), event(X, Y2), event(X, Z2), event(W2, V2), event(U2, T2), proposition(X, W2), proposition(X, U2), smoke(W2, V2), smoke(U2, T2), accessible_world(X, W2), accessible_world(X, U2), of(X, Y, U), of(X, W, T), of(X, V, T), of(X, Z, S), be(X, X2, S, S), theme(X, Y2, W2), theme(X, Z2, U2), think_believe_consider(X, Y2), think_believe_consider(X, Z2), agent(X, Y2, T), agent(X, Z2, T), agent(W2, V2, x3(W2)), agent(U2, T2, U), present(X, Y2), present(X, Z2), present(W2, V2), present(U2, T2), 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).
% 7.69/1.44 The goal is true when:
% 7.69/1.44 X = u
% 7.69/1.44 Y = z
% 7.69/1.44 Z = z
% 7.69/1.44 W = w
% 7.69/1.44 V = w
% 7.69/1.44 U = x1
% 7.69/1.44 T = v
% 7.69/1.44 S = x1
% 7.69/1.44 X2 = x2
% 7.69/1.44 Y2 = x
% 7.69/1.44 Z2 = x
% 7.69/1.44 W2 = y
% 7.69/1.44 V2 = x4(x3(y))
% 7.69/1.44 U2 = y
% 7.69/1.44 T2 = x4(x1)
% 7.69/1.44
% 7.69/1.44 Proof:
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), man(u, x1), state(u, x2), event(u, x), event(u, x), event(y, x4(x3(y))), event(y, x4(x1)), proposition(u, y), proposition(u, y), smoke(y, x4(x3(y))), smoke(y, x4(x1)), accessible_world(u, y), accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), be(u, x2, x1, x1), theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), actual_world(u))
% 7.69/1.44 = { by axiom 23 (co1_12) }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), man(u, x1), state(u, x2), event(u, x), event(u, x), event(y, x4(x3(y))), event(y, x4(x1)), proposition(u, y), proposition(u, y), smoke(y, x4(x3(y))), smoke(y, x4(x1)), accessible_world(u, y), accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), actual_world(u))
% 7.69/1.44 = { by axiom 4 (co1_5) }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, state(u, x2), event(u, x), event(u, x), event(y, x4(x3(y))), event(y, x4(x1)), proposition(u, y), proposition(u, y), smoke(y, x4(x3(y))), smoke(y, x4(x1)), accessible_world(u, y), accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), actual_world(u))
% 7.69/1.44 = { by axiom 12 (co1_6) }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), event(y, x4(x3(y))), event(y, x4(x1)), proposition(u, y), proposition(u, y), smoke(y, x4(x3(y))), smoke(y, x4(x1)), accessible_world(u, y), accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), actual_world(u))
% 7.69/1.44 = { by axiom 13 (co1_17) }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), event(y, x4(x3(y))), event(y, x4(x1)), proposition(u, y), proposition(u, y), smoke(y, x4(x3(y))), smoke(y, x4(x1)), accessible_world(u, y), accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), true2)
% 7.69/1.44 = { by axiom 25 (co1_20) R->L }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), fresh5(man(y, x3(y)), true2, x3(y)), event(y, x4(x1)), proposition(u, y), proposition(u, y), smoke(y, x4(x3(y))), smoke(y, x4(x1)), accessible_world(u, y), accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), true2)
% 7.69/1.44 = { by lemma 72 }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), fresh5(true2, true2, x3(y)), event(y, x4(x1)), proposition(u, y), proposition(u, y), smoke(y, x4(x3(y))), smoke(y, x4(x1)), accessible_world(u, y), accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), true2)
% 7.69/1.44 = { by axiom 19 (co1_20) }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), true2, event(y, x4(x1)), proposition(u, y), proposition(u, y), smoke(y, x4(x3(y))), smoke(y, x4(x1)), accessible_world(u, y), accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), true2)
% 7.69/1.44 = { by axiom 8 (co1_8) }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), true2, event(y, x4(x1)), true2, proposition(u, y), smoke(y, x4(x3(y))), smoke(y, x4(x1)), accessible_world(u, y), accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), true2)
% 7.69/1.44 = { by axiom 26 (co1_21) R->L }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), true2, event(y, x4(x1)), true2, proposition(u, y), fresh4(man(y, x3(y)), true2, x3(y)), smoke(y, x4(x1)), accessible_world(u, y), accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), true2)
% 7.69/1.44 = { by lemma 72 }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), true2, event(y, x4(x1)), true2, proposition(u, y), fresh4(true2, true2, x3(y)), smoke(y, x4(x1)), accessible_world(u, y), accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), true2)
% 7.69/1.44 = { by axiom 20 (co1_21) }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), true2, event(y, x4(x1)), true2, proposition(u, y), true2, smoke(y, x4(x1)), accessible_world(u, y), accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), true2)
% 7.69/1.44 = { by axiom 1 (co1_9) }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), true2, event(y, x4(x1)), true2, proposition(u, y), true2, smoke(y, x4(x1)), true2, accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), agent(y, x4(x3(y)), x3(y)), agent(y, x4(x1), x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), true2)
% 7.69/1.44 = { by axiom 27 (co1_22) R->L }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), true2, event(y, x4(x1)), true2, proposition(u, y), true2, smoke(y, x4(x1)), true2, accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), fresh3(man(y, x3(y)), true2, x3(y)), agent(y, x4(x1), x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), true2)
% 7.69/1.44 = { by lemma 72 }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), true2, event(y, x4(x1)), true2, proposition(u, y), true2, smoke(y, x4(x1)), true2, accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), fresh3(true2, true2, x3(y)), agent(y, x4(x1), x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), true2)
% 7.69/1.44 = { by axiom 21 (co1_22) }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), true2, event(y, x4(x1)), true2, proposition(u, y), true2, smoke(y, x4(x1)), true2, accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), true2, agent(y, x4(x1), x1), present(u, x), present(u, x), present(y, x4(x3(y))), present(y, x4(x1)), true2)
% 7.69/1.44 = { by axiom 28 (co1_23) R->L }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), true2, event(y, x4(x1)), true2, proposition(u, y), true2, smoke(y, x4(x1)), true2, accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), true2, agent(y, x4(x1), x1), present(u, x), present(u, x), fresh2(man(y, x3(y)), true2, x3(y)), present(y, x4(x1)), true2)
% 7.69/1.44 = { by lemma 72 }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), true2, event(y, x4(x1)), true2, proposition(u, y), true2, smoke(y, x4(x1)), true2, accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), true2, agent(y, x4(x1), x1), present(u, x), present(u, x), fresh2(true2, true2, x3(y)), present(y, x4(x1)), true2)
% 7.69/1.44 = { by axiom 22 (co1_23) }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), true2, event(y, x4(x1)), true2, proposition(u, y), true2, smoke(y, x4(x1)), true2, accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), true2, agent(y, x4(x1), x1), present(u, x), present(u, x), true2, present(y, x4(x1)), true2)
% 7.69/1.44 = { by lemma 69 }
% 7.69/1.44 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), man(u, x1), man(u, v), true2, true2, event(u, x), event(u, x), true2, event(y, x4(x1)), true2, proposition(u, y), true2, smoke(y, x4(x1)), true2, accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), true2, true2, present(u, x), present(u, x), true2, present(y, x4(x1)), true2)
% 7.69/1.44 = { by axiom 4 (co1_5) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, man(u, v), true2, true2, event(u, x), event(u, x), true2, event(y, x4(x1)), true2, proposition(u, y), true2, smoke(y, x4(x1)), true2, accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), true2, true2, present(u, x), present(u, x), true2, present(y, x4(x1)), true2)
% 7.69/1.45 = { by lemma 71 }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, man(u, v), true2, true2, event(u, x), event(u, x), true2, true2, true2, proposition(u, y), true2, smoke(y, x4(x1)), true2, accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), true2, true2, present(u, x), present(u, x), true2, present(y, x4(x1)), true2)
% 7.69/1.45 = { by axiom 8 (co1_8) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, man(u, v), true2, true2, event(u, x), event(u, x), true2, true2, true2, true2, true2, smoke(y, x4(x1)), true2, accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), true2, true2, present(u, x), present(u, x), true2, present(y, x4(x1)), true2)
% 7.69/1.45 = { by lemma 68 }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, man(u, v), true2, true2, event(u, x), event(u, x), true2, true2, true2, true2, true2, true2, true2, accessible_world(u, y), of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), true2, true2, present(u, x), present(u, x), true2, present(y, x4(x1)), true2)
% 7.69/1.45 = { by axiom 1 (co1_9) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, man(u, v), true2, true2, event(u, x), event(u, x), true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), true2, true2, present(u, x), present(u, x), true2, present(y, x4(x1)), true2)
% 7.69/1.45 = { by lemma 70 }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, man(u, v), true2, true2, event(u, x), event(u, x), true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), agent(u, x, v), agent(u, x, v), true2, true2, present(u, x), present(u, x), true2, true2, true2)
% 7.69/1.45 = { by axiom 16 (co1_15) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, man(u, v), true2, true2, event(u, x), event(u, x), true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), true2, agent(u, x, v), true2, true2, present(u, x), present(u, x), true2, true2, true2)
% 7.69/1.45 = { by axiom 5 (co1_4) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, true2, true2, true2, event(u, x), event(u, x), true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), true2, agent(u, x, v), true2, true2, present(u, x), present(u, x), true2, true2, true2)
% 7.69/1.45 = { by axiom 6 (co1_7) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, true2, true2, true2, true2, event(u, x), true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, theme(u, x, y), theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), true2, agent(u, x, v), true2, true2, present(u, x), present(u, x), true2, true2, true2)
% 7.69/1.45 = { by axiom 17 (co1_13) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, true2, true2, true2, true2, event(u, x), true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, true2, theme(u, x, y), think_believe_consider(u, x), think_believe_consider(u, x), true2, agent(u, x, v), true2, true2, present(u, x), present(u, x), true2, true2, true2)
% 7.69/1.45 = { by axiom 9 (co1_14) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, true2, true2, true2, true2, event(u, x), true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, true2, theme(u, x, y), true2, think_believe_consider(u, x), true2, agent(u, x, v), true2, true2, present(u, x), present(u, x), true2, true2, true2)
% 7.69/1.45 = { by axiom 7 (co1_16) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, true2, true2, true2, true2, event(u, x), true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, true2, theme(u, x, y), true2, think_believe_consider(u, x), true2, agent(u, x, v), true2, true2, true2, present(u, x), true2, true2, true2)
% 7.69/1.45 = { by axiom 6 (co1_7) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, true2, theme(u, x, y), true2, think_believe_consider(u, x), true2, agent(u, x, v), true2, true2, true2, present(u, x), true2, true2, true2)
% 7.69/1.45 = { by axiom 17 (co1_13) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, true2, true2, true2, think_believe_consider(u, x), true2, agent(u, x, v), true2, true2, true2, present(u, x), true2, true2, true2)
% 7.69/1.45 = { by axiom 9 (co1_14) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, true2, true2, true2, true2, true2, agent(u, x, v), true2, true2, true2, present(u, x), true2, true2, true2)
% 7.69/1.45 = { by axiom 16 (co1_15) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, present(u, x), true2, true2, true2)
% 7.69/1.45 = { by axiom 7 (co1_16) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), forename(u, w), forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2)
% 7.69/1.45 = { by axiom 2 (co1_1) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), true2, forename(u, w), forename(u, z), vincent_forename(u, w), vincent_forename(u, w), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2)
% 7.69/1.45 = { by axiom 11 (co1_3) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), true2, forename(u, w), forename(u, z), true2, vincent_forename(u, w), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), of(u, w, v), of(u, w, v), of(u, z, x1), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2)
% 7.69/1.45 = { by axiom 14 (co1_10) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), true2, forename(u, w), forename(u, z), true2, vincent_forename(u, w), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), true2, of(u, w, v), of(u, z, x1), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2)
% 7.69/1.45 = { by axiom 2 (co1_1) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), true2, true2, forename(u, z), true2, vincent_forename(u, w), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), true2, of(u, w, v), of(u, z, x1), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2)
% 7.69/1.45 = { by axiom 11 (co1_3) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), true2, true2, forename(u, z), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), true2, of(u, w, v), of(u, z, x1), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2)
% 7.69/1.45 = { by axiom 14 (co1_10) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), forename(u, z), true2, true2, forename(u, z), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), true2, true2, of(u, z, x1), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2)
% 7.69/1.45 = { by axiom 3 (co1_2) }
% 7.69/1.45 tuple(jules_forename(u, z), jules_forename(u, z), true2, true2, true2, forename(u, z), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), true2, true2, of(u, z, x1), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2)
% 7.69/1.45 = { by axiom 10 (co1) }
% 7.69/1.45 tuple(true2, jules_forename(u, z), true2, true2, true2, forename(u, z), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), true2, true2, of(u, z, x1), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2)
% 7.69/1.45 = { by axiom 15 (co1_11) }
% 7.69/1.45 tuple(true2, jules_forename(u, z), true2, true2, true2, forename(u, z), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2)
% 7.69/1.45 = { by axiom 3 (co1_2) }
% 7.69/1.45 tuple(true2, jules_forename(u, z), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, of(u, z, x1), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2)
% 7.69/1.45 = { by axiom 10 (co1) }
% 7.69/1.45 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, of(u, z, x1), true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2, true2)
% 7.69/1.45 = { by axiom 15 (co1_11) }
% 7.69/1.45 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)
% 7.69/1.45 % SZS output end Proof
% 7.69/1.45
% 7.69/1.45 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------