0.02/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.09 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.09/0.30 % Computer : n003.cluster.edu 0.09/0.30 % Model : x86_64 x86_64 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.30 % Memory : 8042.1875MB 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.30 % CPULimit : 960 0.09/0.30 % WCLimit : 120 0.09/0.30 % DateTime : Thu Jul 2 07:56:11 EDT 2020 0.09/0.30 % CPUTime : 3.14/0.75 % SZS status Theorem 3.14/0.75 3.14/0.75 % SZS output start Proof 3.14/0.75 Take the following subset of the input axioms: 36.00/4.84 fof(happens_all_defn, axiom, ![Time, Event]: (happens(Event, Time) <=> ((Event=push(agent1, trolley1) & n0=Time) | ((push(agent3, trolley3)=Event & n0=Time) | ((Time=n0 & Event=pull(agent4, trolley4)) | ((Time=n0 & Event=pull(agent6, trolley6)) | ((Event=push(agent6, trolley6) & n0=Time) | ((n0=Time & Event=pull(agent7, trolley7)) | ((n0=Time & Event=pull(agent8, trolley8)) | ((push(agent8, trolley8)=Event & n0=Time) | ((pull(agent9, trolley9)=Event & n0=Time) | ((Event=push(agent9, trolley9) & Time=n0) | ((n0=Time & Event=pull(agent10, trolley10)) | ((Time=n0 & push(agent10, trolley10)=Event) | ((push(agent7, trolley7)=Event & n0=Time) | ((Time=n0 & push(agent5, trolley5)=Event) | ((Time=n0 & Event=pull(agent5, trolley5)) | ((Time=n0 & push(agent4, trolley4)=Event) | ((Event=pull(agent3, trolley3) & Time=n0) | ((n0=Time & push(agent2, trolley2)=Event) | ((Time=n0 & Event=pull(agent2, trolley2)) | (Event=pull(agent1, trolley1) & Time=n0)))))))))))))))))))))). 36.00/4.84 fof(happens_holds, axiom, ![Fluent, Time, Event]: ((initiates(Event, Fluent, Time) & happens(Event, Time)) => holdsAt(Fluent, plus(Time, n1)))). 36.00/4.84 fof(initiates_all_defn, axiom, ![Fluent, Time, Event]: (?[Trolley, Agent]: ((pull(Agent, Trolley)=Event & (~happens(push(Agent, Trolley), Time) & backwards(Trolley)=Fluent)) | ((happens(push(Agent, Trolley), Time) & (Event=pull(Agent, Trolley) & spinning(Trolley)=Fluent)) | (Fluent=forwards(Trolley) & (~happens(pull(Agent, Trolley), Time) & push(Agent, Trolley)=Event)))) <=> initiates(Event, Fluent, Time))). 36.00/4.84 fof(plus0_1, axiom, n1=plus(n0, n1)). 36.00/4.84 fof(spinning_3, conjecture, holdsAt(spinning(trolley1), n1) & (holdsAt(spinning(trolley2), n1) & (holdsAt(spinning(trolley4), n1) & (holdsAt(spinning(trolley10), n1) & (holdsAt(spinning(trolley9), n1) & (holdsAt(spinning(trolley8), n1) & (holdsAt(spinning(trolley7), n1) & (holdsAt(spinning(trolley6), n1) & (holdsAt(spinning(trolley5), n1) & holdsAt(spinning(trolley3), n1)))))))))). 36.00/4.84 fof(symmetry_of_plus, axiom, ![X, Y]: plus(X, Y)=plus(Y, X)). 36.00/4.84 36.00/4.84 Now clausify the problem and encode Horn clauses using encoding 3 of 36.00/4.84 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 36.00/4.84 We repeatedly replace C & s=t => u=v by the two clauses: 36.00/4.84 fresh(y, y, x1...xn) = u 36.00/4.84 C => fresh(s, t, x1...xn) = v 36.00/4.84 where fresh is a fresh function symbol and x1..xn are the free 36.00/4.84 variables of u and v. 36.00/4.84 A predicate p(X) is encoded as p(X)=true (this is sound, because the 36.00/4.84 input problem has no model of domain size 1). 36.00/4.84 36.00/4.84 The encoding turns the above axioms into the following unit equations and goals: 36.00/4.84 36.00/4.84 Axiom 1 (happens_all_defn): fresh86(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 2 (happens_all_defn): fresh87(X, X, Y, Z) = true2. 36.00/4.84 Axiom 3 (happens_all_defn_1): fresh85(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 4 (happens_all_defn_1): fresh84(X, X, Y, Z) = true2. 36.00/4.84 Axiom 5 (happens_all_defn_10): fresh83(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 6 (happens_all_defn_10): fresh82(X, X, Y, Z) = true2. 36.00/4.84 Axiom 7 (happens_all_defn_11): fresh81(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 8 (happens_all_defn_11): fresh80(X, X, Y, Z) = true2. 36.00/4.84 Axiom 9 (happens_all_defn_12): fresh79(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 10 (happens_all_defn_12): fresh78(X, X, Y, Z) = true2. 36.00/4.84 Axiom 11 (happens_all_defn_13): fresh77(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 12 (happens_all_defn_13): fresh76(X, X, Y, Z) = true2. 36.00/4.84 Axiom 13 (happens_all_defn_14): fresh75(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 14 (happens_all_defn_14): fresh74(X, X, Y, Z) = true2. 36.00/4.84 Axiom 15 (happens_all_defn_15): fresh73(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 16 (happens_all_defn_15): fresh72(X, X, Y, Z) = true2. 36.00/4.84 Axiom 17 (happens_all_defn_16): fresh71(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 18 (happens_all_defn_16): fresh70(X, X, Y, Z) = true2. 36.00/4.84 Axiom 19 (happens_all_defn_17): fresh69(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 20 (happens_all_defn_17): fresh68(X, X, Y, Z) = true2. 36.00/4.84 Axiom 21 (happens_all_defn_18): fresh67(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 22 (happens_all_defn_18): fresh66(X, X, Y, Z) = true2. 36.00/4.84 Axiom 23 (happens_all_defn_19): fresh65(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 24 (happens_all_defn_19): fresh64(X, X, Y, Z) = true2. 36.00/4.84 Axiom 25 (happens_all_defn_2): fresh63(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 26 (happens_all_defn_2): fresh62(X, X, Y, Z) = true2. 36.00/4.84 Axiom 27 (happens_all_defn_3): fresh61(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 28 (happens_all_defn_3): fresh60(X, X, Y, Z) = true2. 36.00/4.84 Axiom 29 (happens_all_defn_4): fresh59(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 30 (happens_all_defn_4): fresh58(X, X, Y, Z) = true2. 36.00/4.84 Axiom 31 (happens_all_defn_5): fresh57(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 32 (happens_all_defn_5): fresh56(X, X, Y, Z) = true2. 36.00/4.84 Axiom 33 (happens_all_defn_6): fresh54(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 34 (happens_all_defn_6): fresh53(X, X, Y, Z) = true2. 36.00/4.84 Axiom 35 (happens_all_defn_7): fresh52(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 36 (happens_all_defn_7): fresh51(X, X, Y, Z) = true2. 36.00/4.84 Axiom 37 (happens_all_defn_8): fresh50(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 38 (happens_all_defn_8): fresh49(X, X, Y, Z) = true2. 36.00/4.84 Axiom 39 (happens_all_defn_9): fresh48(X, X, Y, Z) = happens(Y, Z). 36.00/4.84 Axiom 40 (happens_all_defn_9): fresh47(X, X, Y, Z) = true2. 36.00/4.84 Axiom 41 (happens_holds): fresh46(X, X, Y, Z, W) = holdsAt(W, plus(Z, n1)). 36.00/4.84 Axiom 42 (happens_holds): fresh45(X, X, Y, Z) = true2. 36.00/4.84 Axiom 43 (initiates_all_defn_1): fresh42(X, X, Y, Z, W, V, U) = initiates(Y, Z, W). 36.00/4.84 Axiom 44 (initiates_all_defn_1): fresh93(X, X, Y, Z, W) = true2. 36.00/4.84 Axiom 45 (initiates_all_defn_1): fresh92(X, X, Y, Z, W, V, U) = fresh93(Y, pull(U, V), Y, Z, W). 36.00/4.84 Axiom 46 (happens_holds): fresh46(happens(X, Y), true2, X, Y, Z) = fresh45(initiates(X, Z, Y), true2, Y, Z). 36.00/4.84 Axiom 47 (initiates_all_defn_1): fresh92(happens(push(X, Y), Z), true2, W, V, Z, Y, X) = fresh42(spinning(Y), V, W, V, Z, Y, X). 36.00/4.84 Axiom 48 (symmetry_of_plus): plus(X, Y) = plus(Y, X). 36.00/4.84 Axiom 49 (happens_all_defn_19): fresh65(X, n0, Y, X) = fresh64(push(agent5, trolley5), Y, Y, X). 36.00/4.84 Axiom 50 (happens_all_defn_18): fresh67(X, n0, Y, X) = fresh66(Y, push(agent9, trolley9), Y, X). 36.00/4.84 Axiom 51 (happens_all_defn_17): fresh69(n0, X, Y, X) = fresh68(push(agent8, trolley8), Y, Y, X). 36.00/4.84 Axiom 52 (happens_all_defn_16): fresh71(n0, X, Y, X) = fresh70(Y, push(agent6, trolley6), Y, X). 36.00/4.84 Axiom 53 (happens_all_defn_15): fresh73(n0, X, Y, X) = fresh72(push(agent3, trolley3), Y, Y, X). 36.00/4.84 Axiom 54 (happens_all_defn_14): fresh75(n0, X, Y, X) = fresh74(push(agent2, trolley2), Y, Y, X). 36.00/4.84 Axiom 55 (happens_all_defn_13): fresh77(X, n0, Y, X) = fresh76(push(agent10, trolley10), Y, Y, X). 36.00/4.84 Axiom 56 (happens_all_defn_12): fresh79(n0, X, Y, X) = fresh78(push(agent7, trolley7), Y, Y, X). 36.00/4.84 Axiom 57 (happens_all_defn_11): fresh81(X, n0, Y, X) = fresh80(push(agent4, trolley4), Y, Y, X). 36.00/4.84 Axiom 58 (happens_all_defn_10): fresh83(n0, X, Y, X) = fresh82(Y, push(agent1, trolley1), Y, X). 36.00/4.84 Axiom 59 (happens_all_defn_9): fresh48(X, n0, Y, X) = fresh47(Y, pull(agent5, trolley5), Y, X). 36.00/4.84 Axiom 60 (happens_all_defn_8): fresh50(n0, X, Y, X) = fresh49(pull(agent9, trolley9), Y, Y, X). 36.00/4.84 Axiom 61 (happens_all_defn_7): fresh52(n0, X, Y, X) = fresh51(Y, pull(agent8, trolley8), Y, X). 36.00/4.84 Axiom 62 (happens_all_defn_6): fresh54(X, n0, Y, X) = fresh53(Y, pull(agent6, trolley6), Y, X). 36.00/4.84 Axiom 63 (happens_all_defn_5): fresh57(X, n0, Y, X) = fresh56(Y, pull(agent3, trolley3), Y, X). 36.00/4.84 Axiom 64 (happens_all_defn_4): fresh59(X, n0, Y, X) = fresh58(Y, pull(agent2, trolley2), Y, X). 36.00/4.84 Axiom 65 (happens_all_defn_3): fresh61(n0, X, Y, X) = fresh60(Y, pull(agent10, trolley10), Y, X). 36.00/4.84 Axiom 66 (happens_all_defn_2): fresh63(n0, X, Y, X) = fresh62(Y, pull(agent7, trolley7), Y, X). 36.00/4.84 Axiom 67 (happens_all_defn_1): fresh85(X, n0, Y, X) = fresh84(Y, pull(agent4, trolley4), Y, X). 36.00/4.84 Axiom 68 (happens_all_defn): fresh86(X, n0, Y, X) = fresh87(Y, pull(agent1, trolley1), Y, X). 36.00/4.84 Axiom 69 (plus0_1): n1 = plus(n0, n1). 36.00/4.84 36.00/4.84 Lemma 70: plus(n1, n0) = n1. 36.00/4.84 Proof: 36.00/4.84 plus(n1, n0) 36.00/4.84 = { by axiom 48 (symmetry_of_plus) } 36.00/4.84 plus(n0, n1) 36.00/4.84 = { by axiom 69 (plus0_1) } 36.00/4.84 n1 36.00/4.84 36.00/4.84 Lemma 71: fresh92(X, X, Y, Z, W, V, U) = fresh92(?, ?, Y, Z, W, V, U). 36.00/4.84 Proof: 36.00/4.84 fresh92(X, X, Y, Z, W, V, U) 36.00/4.84 = { by axiom 45 (initiates_all_defn_1) } 36.00/4.84 fresh93(Y, pull(U, V), Y, Z, W) 36.00/4.84 = { by axiom 45 (initiates_all_defn_1) } 36.00/4.84 fresh92(?, ?, Y, Z, W, V, U) 36.00/4.84 36.00/4.84 Lemma 72: fresh92(happens(push(W, Z), Y), true2, X, spinning(Z), Y, Z, W) = initiates(X, spinning(Z), Y). 36.00/4.84 Proof: 36.00/4.84 fresh92(happens(push(W, Z), Y), true2, X, spinning(Z), Y, Z, W) 36.00/4.84 = { by axiom 47 (initiates_all_defn_1) } 36.00/4.84 fresh42(spinning(Z), spinning(Z), X, spinning(Z), Y, Z, W) 36.00/4.84 = { by axiom 43 (initiates_all_defn_1) } 36.00/4.84 initiates(X, spinning(Z), Y) 36.00/4.84 36.00/4.84 Lemma 73: fresh92(?, ?, pull(W, Z), Y, X, Z, W) = true2. 36.00/4.84 Proof: 36.00/4.84 fresh92(?, ?, pull(W, Z), Y, X, Z, W) 36.00/4.84 = { by axiom 45 (initiates_all_defn_1) } 36.00/4.84 fresh93(pull(W, Z), pull(W, Z), pull(W, Z), Y, X) 36.00/4.84 = { by axiom 44 (initiates_all_defn_1) } 65.63/8.56 true2 65.63/8.56 65.63/8.56 Goal 1 (spinning_3): tuple(holdsAt(spinning(trolley1), n1), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) = tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2). 65.63/8.56 Proof: 65.63/8.56 tuple(holdsAt(spinning(trolley1), n1), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.56 = { by lemma 70 } 65.63/8.57 tuple(holdsAt(spinning(trolley1), plus(n1, n0)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 48 (symmetry_of_plus) } 65.63/8.57 tuple(holdsAt(spinning(trolley1), plus(n0, n1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 41 (happens_holds) } 65.63/8.57 tuple(fresh46(true2, true2, pull(agent1, trolley1), n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 2 (happens_all_defn) } 65.63/8.57 tuple(fresh46(fresh87(pull(agent1, trolley1), pull(agent1, trolley1), pull(agent1, trolley1), n0), true2, pull(agent1, trolley1), n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 68 (happens_all_defn) } 65.63/8.57 tuple(fresh46(fresh86(n0, n0, pull(agent1, trolley1), n0), true2, pull(agent1, trolley1), n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 1 (happens_all_defn) } 65.63/8.57 tuple(fresh46(happens(pull(agent1, trolley1), n0), true2, pull(agent1, trolley1), n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 46 (happens_holds) } 65.63/8.57 tuple(fresh45(initiates(pull(agent1, trolley1), spinning(trolley1), n0), true2, n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by lemma 72 } 65.63/8.57 tuple(fresh45(fresh92(happens(push(agent1, trolley1), n0), true2, pull(agent1, trolley1), spinning(trolley1), n0, trolley1, agent1), true2, n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 5 (happens_all_defn_10) } 65.63/8.57 tuple(fresh45(fresh92(fresh83(n0, n0, push(agent1, trolley1), n0), true2, pull(agent1, trolley1), spinning(trolley1), n0, trolley1, agent1), true2, n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 58 (happens_all_defn_10) } 65.63/8.57 tuple(fresh45(fresh92(fresh82(push(agent1, trolley1), push(agent1, trolley1), push(agent1, trolley1), n0), true2, pull(agent1, trolley1), spinning(trolley1), n0, trolley1, agent1), true2, n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 6 (happens_all_defn_10) } 65.63/8.57 tuple(fresh45(fresh92(true2, true2, pull(agent1, trolley1), spinning(trolley1), n0, trolley1, agent1), true2, n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by lemma 71 } 65.63/8.57 tuple(fresh45(fresh92(?, ?, pull(agent1, trolley1), spinning(trolley1), n0, trolley1, agent1), true2, n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by lemma 73 } 65.63/8.57 tuple(fresh45(true2, true2, n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 42 (happens_holds) } 65.63/8.57 tuple(true2, holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by lemma 70 } 65.63/8.57 tuple(true2, holdsAt(spinning(trolley2), plus(n1, n0)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 48 (symmetry_of_plus) } 65.63/8.57 tuple(true2, holdsAt(spinning(trolley2), plus(n0, n1)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 41 (happens_holds) } 65.63/8.57 tuple(true2, fresh46(true2, true2, pull(agent2, trolley2), n0, spinning(trolley2)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 30 (happens_all_defn_4) } 65.63/8.57 tuple(true2, fresh46(fresh58(pull(agent2, trolley2), pull(agent2, trolley2), pull(agent2, trolley2), n0), true2, pull(agent2, trolley2), n0, spinning(trolley2)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 64 (happens_all_defn_4) } 65.63/8.57 tuple(true2, fresh46(fresh59(n0, n0, pull(agent2, trolley2), n0), true2, pull(agent2, trolley2), n0, spinning(trolley2)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 29 (happens_all_defn_4) } 65.63/8.57 tuple(true2, fresh46(happens(pull(agent2, trolley2), n0), true2, pull(agent2, trolley2), n0, spinning(trolley2)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 46 (happens_holds) } 65.63/8.57 tuple(true2, fresh45(initiates(pull(agent2, trolley2), spinning(trolley2), n0), true2, n0, spinning(trolley2)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by lemma 72 } 65.63/8.57 tuple(true2, fresh45(fresh92(happens(push(agent2, trolley2), n0), true2, pull(agent2, trolley2), spinning(trolley2), n0, trolley2, agent2), true2, n0, spinning(trolley2)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 13 (happens_all_defn_14) } 65.63/8.57 tuple(true2, fresh45(fresh92(fresh75(n0, n0, push(agent2, trolley2), n0), true2, pull(agent2, trolley2), spinning(trolley2), n0, trolley2, agent2), true2, n0, spinning(trolley2)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 54 (happens_all_defn_14) } 65.63/8.57 tuple(true2, fresh45(fresh92(fresh74(push(agent2, trolley2), push(agent2, trolley2), push(agent2, trolley2), n0), true2, pull(agent2, trolley2), spinning(trolley2), n0, trolley2, agent2), true2, n0, spinning(trolley2)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 14 (happens_all_defn_14) } 65.63/8.57 tuple(true2, fresh45(fresh92(true2, true2, pull(agent2, trolley2), spinning(trolley2), n0, trolley2, agent2), true2, n0, spinning(trolley2)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by lemma 71 } 65.63/8.57 tuple(true2, fresh45(fresh92(?, ?, pull(agent2, trolley2), spinning(trolley2), n0, trolley2, agent2), true2, n0, spinning(trolley2)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by lemma 73 } 65.63/8.57 tuple(true2, fresh45(true2, true2, n0, spinning(trolley2)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 42 (happens_holds) } 65.63/8.57 tuple(true2, true2, holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by lemma 70 } 65.63/8.57 tuple(true2, true2, holdsAt(spinning(trolley4), plus(n1, n0)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 48 (symmetry_of_plus) } 65.63/8.57 tuple(true2, true2, holdsAt(spinning(trolley4), plus(n0, n1)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 41 (happens_holds) } 65.63/8.57 tuple(true2, true2, fresh46(true2, true2, pull(agent4, trolley4), n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 4 (happens_all_defn_1) } 65.63/8.57 tuple(true2, true2, fresh46(fresh84(pull(agent4, trolley4), pull(agent4, trolley4), pull(agent4, trolley4), n0), true2, pull(agent4, trolley4), n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 67 (happens_all_defn_1) } 65.63/8.57 tuple(true2, true2, fresh46(fresh85(n0, n0, pull(agent4, trolley4), n0), true2, pull(agent4, trolley4), n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 3 (happens_all_defn_1) } 65.63/8.57 tuple(true2, true2, fresh46(happens(pull(agent4, trolley4), n0), true2, pull(agent4, trolley4), n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 46 (happens_holds) } 65.63/8.57 tuple(true2, true2, fresh45(initiates(pull(agent4, trolley4), spinning(trolley4), n0), true2, n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by lemma 72 } 65.63/8.57 tuple(true2, true2, fresh45(fresh92(happens(push(agent4, trolley4), n0), true2, pull(agent4, trolley4), spinning(trolley4), n0, trolley4, agent4), true2, n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.57 = { by axiom 7 (happens_all_defn_11) } 65.63/8.58 tuple(true2, true2, fresh45(fresh92(fresh81(n0, n0, push(agent4, trolley4), n0), true2, pull(agent4, trolley4), spinning(trolley4), n0, trolley4, agent4), true2, n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 57 (happens_all_defn_11) } 65.63/8.58 tuple(true2, true2, fresh45(fresh92(fresh80(push(agent4, trolley4), push(agent4, trolley4), push(agent4, trolley4), n0), true2, pull(agent4, trolley4), spinning(trolley4), n0, trolley4, agent4), true2, n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 8 (happens_all_defn_11) } 65.63/8.58 tuple(true2, true2, fresh45(fresh92(true2, true2, pull(agent4, trolley4), spinning(trolley4), n0, trolley4, agent4), true2, n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by lemma 71 } 65.63/8.58 tuple(true2, true2, fresh45(fresh92(?, ?, pull(agent4, trolley4), spinning(trolley4), n0, trolley4, agent4), true2, n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by lemma 73 } 65.63/8.58 tuple(true2, true2, fresh45(true2, true2, n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 42 (happens_holds) } 65.63/8.58 tuple(true2, true2, true2, holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by lemma 70 } 65.63/8.58 tuple(true2, true2, true2, holdsAt(spinning(trolley5), plus(n1, n0)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 48 (symmetry_of_plus) } 65.63/8.58 tuple(true2, true2, true2, holdsAt(spinning(trolley5), plus(n0, n1)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 41 (happens_holds) } 65.63/8.58 tuple(true2, true2, true2, fresh46(true2, true2, pull(agent5, trolley5), n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 40 (happens_all_defn_9) } 65.63/8.58 tuple(true2, true2, true2, fresh46(fresh47(pull(agent5, trolley5), pull(agent5, trolley5), pull(agent5, trolley5), n0), true2, pull(agent5, trolley5), n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 59 (happens_all_defn_9) } 65.63/8.58 tuple(true2, true2, true2, fresh46(fresh48(n0, n0, pull(agent5, trolley5), n0), true2, pull(agent5, trolley5), n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 39 (happens_all_defn_9) } 65.63/8.58 tuple(true2, true2, true2, fresh46(happens(pull(agent5, trolley5), n0), true2, pull(agent5, trolley5), n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 46 (happens_holds) } 65.63/8.58 tuple(true2, true2, true2, fresh45(initiates(pull(agent5, trolley5), spinning(trolley5), n0), true2, n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by lemma 72 } 65.63/8.58 tuple(true2, true2, true2, fresh45(fresh92(happens(push(agent5, trolley5), n0), true2, pull(agent5, trolley5), spinning(trolley5), n0, trolley5, agent5), true2, n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 23 (happens_all_defn_19) } 65.63/8.58 tuple(true2, true2, true2, fresh45(fresh92(fresh65(n0, n0, push(agent5, trolley5), n0), true2, pull(agent5, trolley5), spinning(trolley5), n0, trolley5, agent5), true2, n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 49 (happens_all_defn_19) } 65.63/8.58 tuple(true2, true2, true2, fresh45(fresh92(fresh64(push(agent5, trolley5), push(agent5, trolley5), push(agent5, trolley5), n0), true2, pull(agent5, trolley5), spinning(trolley5), n0, trolley5, agent5), true2, n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 24 (happens_all_defn_19) } 65.63/8.58 tuple(true2, true2, true2, fresh45(fresh92(true2, true2, pull(agent5, trolley5), spinning(trolley5), n0, trolley5, agent5), true2, n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by lemma 71 } 65.63/8.58 tuple(true2, true2, true2, fresh45(fresh92(?, ?, pull(agent5, trolley5), spinning(trolley5), n0, trolley5, agent5), true2, n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by lemma 73 } 65.63/8.58 tuple(true2, true2, true2, fresh45(true2, true2, n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 42 (happens_holds) } 65.63/8.58 tuple(true2, true2, true2, true2, holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by lemma 70 } 65.63/8.58 tuple(true2, true2, true2, true2, holdsAt(spinning(trolley6), plus(n1, n0)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 48 (symmetry_of_plus) } 65.63/8.58 tuple(true2, true2, true2, true2, holdsAt(spinning(trolley6), plus(n0, n1)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 41 (happens_holds) } 65.63/8.58 tuple(true2, true2, true2, true2, fresh46(true2, true2, pull(agent6, trolley6), n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 34 (happens_all_defn_6) } 65.63/8.58 tuple(true2, true2, true2, true2, fresh46(fresh53(pull(agent6, trolley6), pull(agent6, trolley6), pull(agent6, trolley6), n0), true2, pull(agent6, trolley6), n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 62 (happens_all_defn_6) } 65.63/8.58 tuple(true2, true2, true2, true2, fresh46(fresh54(n0, n0, pull(agent6, trolley6), n0), true2, pull(agent6, trolley6), n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 33 (happens_all_defn_6) } 65.63/8.58 tuple(true2, true2, true2, true2, fresh46(happens(pull(agent6, trolley6), n0), true2, pull(agent6, trolley6), n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 46 (happens_holds) } 65.63/8.58 tuple(true2, true2, true2, true2, fresh45(initiates(pull(agent6, trolley6), spinning(trolley6), n0), true2, n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by lemma 72 } 65.63/8.58 tuple(true2, true2, true2, true2, fresh45(fresh92(happens(push(agent6, trolley6), n0), true2, pull(agent6, trolley6), spinning(trolley6), n0, trolley6, agent6), true2, n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 17 (happens_all_defn_16) } 65.63/8.58 tuple(true2, true2, true2, true2, fresh45(fresh92(fresh71(n0, n0, push(agent6, trolley6), n0), true2, pull(agent6, trolley6), spinning(trolley6), n0, trolley6, agent6), true2, n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 52 (happens_all_defn_16) } 65.63/8.58 tuple(true2, true2, true2, true2, fresh45(fresh92(fresh70(push(agent6, trolley6), push(agent6, trolley6), push(agent6, trolley6), n0), true2, pull(agent6, trolley6), spinning(trolley6), n0, trolley6, agent6), true2, n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 18 (happens_all_defn_16) } 65.63/8.58 tuple(true2, true2, true2, true2, fresh45(fresh92(true2, true2, pull(agent6, trolley6), spinning(trolley6), n0, trolley6, agent6), true2, n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by lemma 71 } 65.63/8.58 tuple(true2, true2, true2, true2, fresh45(fresh92(?, ?, pull(agent6, trolley6), spinning(trolley6), n0, trolley6, agent6), true2, n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by lemma 73 } 65.63/8.58 tuple(true2, true2, true2, true2, fresh45(true2, true2, n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 42 (happens_holds) } 65.63/8.58 tuple(true2, true2, true2, true2, true2, holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by lemma 70 } 65.63/8.58 tuple(true2, true2, true2, true2, true2, holdsAt(spinning(trolley7), plus(n1, n0)), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 48 (symmetry_of_plus) } 65.63/8.58 tuple(true2, true2, true2, true2, true2, holdsAt(spinning(trolley7), plus(n0, n1)), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 41 (happens_holds) } 65.63/8.58 tuple(true2, true2, true2, true2, true2, fresh46(true2, true2, pull(agent7, trolley7), n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 26 (happens_all_defn_2) } 65.63/8.58 tuple(true2, true2, true2, true2, true2, fresh46(fresh62(pull(agent7, trolley7), pull(agent7, trolley7), pull(agent7, trolley7), n0), true2, pull(agent7, trolley7), n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 66 (happens_all_defn_2) } 65.63/8.58 tuple(true2, true2, true2, true2, true2, fresh46(fresh63(n0, n0, pull(agent7, trolley7), n0), true2, pull(agent7, trolley7), n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 25 (happens_all_defn_2) } 65.63/8.58 tuple(true2, true2, true2, true2, true2, fresh46(happens(pull(agent7, trolley7), n0), true2, pull(agent7, trolley7), n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by axiom 46 (happens_holds) } 65.63/8.58 tuple(true2, true2, true2, true2, true2, fresh45(initiates(pull(agent7, trolley7), spinning(trolley7), n0), true2, n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.58 = { by lemma 72 } 65.63/8.59 tuple(true2, true2, true2, true2, true2, fresh45(fresh92(happens(push(agent7, trolley7), n0), true2, pull(agent7, trolley7), spinning(trolley7), n0, trolley7, agent7), true2, n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by axiom 9 (happens_all_defn_12) } 65.63/8.59 tuple(true2, true2, true2, true2, true2, fresh45(fresh92(fresh79(n0, n0, push(agent7, trolley7), n0), true2, pull(agent7, trolley7), spinning(trolley7), n0, trolley7, agent7), true2, n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by axiom 56 (happens_all_defn_12) } 65.63/8.59 tuple(true2, true2, true2, true2, true2, fresh45(fresh92(fresh78(push(agent7, trolley7), push(agent7, trolley7), push(agent7, trolley7), n0), true2, pull(agent7, trolley7), spinning(trolley7), n0, trolley7, agent7), true2, n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by axiom 10 (happens_all_defn_12) } 65.63/8.59 tuple(true2, true2, true2, true2, true2, fresh45(fresh92(true2, true2, pull(agent7, trolley7), spinning(trolley7), n0, trolley7, agent7), true2, n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by lemma 71 } 65.63/8.59 tuple(true2, true2, true2, true2, true2, fresh45(fresh92(?, ?, pull(agent7, trolley7), spinning(trolley7), n0, trolley7, agent7), true2, n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by lemma 73 } 65.63/8.59 tuple(true2, true2, true2, true2, true2, fresh45(true2, true2, n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by axiom 42 (happens_holds) } 65.63/8.59 tuple(true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley8), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by lemma 70 } 65.63/8.59 tuple(true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley8), plus(n1, n0)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by axiom 48 (symmetry_of_plus) } 65.63/8.59 tuple(true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley8), plus(n0, n1)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by axiom 41 (happens_holds) } 65.63/8.59 tuple(true2, true2, true2, true2, true2, true2, fresh46(true2, true2, pull(agent8, trolley8), n0, spinning(trolley8)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by axiom 36 (happens_all_defn_7) } 65.63/8.59 tuple(true2, true2, true2, true2, true2, true2, fresh46(fresh51(pull(agent8, trolley8), pull(agent8, trolley8), pull(agent8, trolley8), n0), true2, pull(agent8, trolley8), n0, spinning(trolley8)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by axiom 61 (happens_all_defn_7) } 65.63/8.59 tuple(true2, true2, true2, true2, true2, true2, fresh46(fresh52(n0, n0, pull(agent8, trolley8), n0), true2, pull(agent8, trolley8), n0, spinning(trolley8)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by axiom 35 (happens_all_defn_7) } 65.63/8.59 tuple(true2, true2, true2, true2, true2, true2, fresh46(happens(pull(agent8, trolley8), n0), true2, pull(agent8, trolley8), n0, spinning(trolley8)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by axiom 46 (happens_holds) } 65.63/8.59 tuple(true2, true2, true2, true2, true2, true2, fresh45(initiates(pull(agent8, trolley8), spinning(trolley8), n0), true2, n0, spinning(trolley8)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by lemma 72 } 65.63/8.59 tuple(true2, true2, true2, true2, true2, true2, fresh45(fresh92(happens(push(agent8, trolley8), n0), true2, pull(agent8, trolley8), spinning(trolley8), n0, trolley8, agent8), true2, n0, spinning(trolley8)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by axiom 19 (happens_all_defn_17) } 65.63/8.59 tuple(true2, true2, true2, true2, true2, true2, fresh45(fresh92(fresh69(n0, n0, push(agent8, trolley8), n0), true2, pull(agent8, trolley8), spinning(trolley8), n0, trolley8, agent8), true2, n0, spinning(trolley8)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by axiom 51 (happens_all_defn_17) } 65.63/8.59 tuple(true2, true2, true2, true2, true2, true2, fresh45(fresh92(fresh68(push(agent8, trolley8), push(agent8, trolley8), push(agent8, trolley8), n0), true2, pull(agent8, trolley8), spinning(trolley8), n0, trolley8, agent8), true2, n0, spinning(trolley8)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by axiom 20 (happens_all_defn_17) } 65.63/8.59 tuple(true2, true2, true2, true2, true2, true2, fresh45(fresh92(true2, true2, pull(agent8, trolley8), spinning(trolley8), n0, trolley8, agent8), true2, n0, spinning(trolley8)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by lemma 71 } 65.63/8.59 tuple(true2, true2, true2, true2, true2, true2, fresh45(fresh92(?, ?, pull(agent8, trolley8), spinning(trolley8), n0, trolley8, agent8), true2, n0, spinning(trolley8)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by lemma 73 } 65.63/8.59 tuple(true2, true2, true2, true2, true2, true2, fresh45(true2, true2, n0, spinning(trolley8)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by axiom 42 (happens_holds) } 65.63/8.59 tuple(true2, true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by lemma 70 } 65.63/8.59 tuple(true2, true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley9), plus(n1, n0)), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.59 = { by axiom 48 (symmetry_of_plus) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley9), plus(n0, n1)), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 41 (happens_holds) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, fresh46(true2, true2, pull(agent9, trolley9), n0, spinning(trolley9)), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 38 (happens_all_defn_8) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, fresh46(fresh49(pull(agent9, trolley9), pull(agent9, trolley9), pull(agent9, trolley9), n0), true2, pull(agent9, trolley9), n0, spinning(trolley9)), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 60 (happens_all_defn_8) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, fresh46(fresh50(n0, n0, pull(agent9, trolley9), n0), true2, pull(agent9, trolley9), n0, spinning(trolley9)), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 37 (happens_all_defn_8) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, fresh46(happens(pull(agent9, trolley9), n0), true2, pull(agent9, trolley9), n0, spinning(trolley9)), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 46 (happens_holds) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, fresh45(initiates(pull(agent9, trolley9), spinning(trolley9), n0), true2, n0, spinning(trolley9)), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by lemma 72 } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, fresh45(fresh92(happens(push(agent9, trolley9), n0), true2, pull(agent9, trolley9), spinning(trolley9), n0, trolley9, agent9), true2, n0, spinning(trolley9)), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 21 (happens_all_defn_18) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, fresh45(fresh92(fresh67(n0, n0, push(agent9, trolley9), n0), true2, pull(agent9, trolley9), spinning(trolley9), n0, trolley9, agent9), true2, n0, spinning(trolley9)), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 50 (happens_all_defn_18) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, fresh45(fresh92(fresh66(push(agent9, trolley9), push(agent9, trolley9), push(agent9, trolley9), n0), true2, pull(agent9, trolley9), spinning(trolley9), n0, trolley9, agent9), true2, n0, spinning(trolley9)), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 22 (happens_all_defn_18) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, fresh45(fresh92(true2, true2, pull(agent9, trolley9), spinning(trolley9), n0, trolley9, agent9), true2, n0, spinning(trolley9)), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by lemma 71 } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, fresh45(fresh92(?, ?, pull(agent9, trolley9), spinning(trolley9), n0, trolley9, agent9), true2, n0, spinning(trolley9)), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by lemma 73 } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, fresh45(true2, true2, n0, spinning(trolley9)), holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 42 (happens_holds) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley10), n1), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by lemma 70 } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley10), plus(n1, n0)), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 48 (symmetry_of_plus) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley10), plus(n0, n1)), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 41 (happens_holds) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh46(true2, true2, pull(agent10, trolley10), n0, spinning(trolley10)), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 28 (happens_all_defn_3) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh46(fresh60(pull(agent10, trolley10), pull(agent10, trolley10), pull(agent10, trolley10), n0), true2, pull(agent10, trolley10), n0, spinning(trolley10)), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 65 (happens_all_defn_3) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh46(fresh61(n0, n0, pull(agent10, trolley10), n0), true2, pull(agent10, trolley10), n0, spinning(trolley10)), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 27 (happens_all_defn_3) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh46(happens(pull(agent10, trolley10), n0), true2, pull(agent10, trolley10), n0, spinning(trolley10)), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 46 (happens_holds) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh45(initiates(pull(agent10, trolley10), spinning(trolley10), n0), true2, n0, spinning(trolley10)), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by lemma 72 } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh45(fresh92(happens(push(agent10, trolley10), n0), true2, pull(agent10, trolley10), spinning(trolley10), n0, trolley10, agent10), true2, n0, spinning(trolley10)), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 11 (happens_all_defn_13) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh45(fresh92(fresh77(n0, n0, push(agent10, trolley10), n0), true2, pull(agent10, trolley10), spinning(trolley10), n0, trolley10, agent10), true2, n0, spinning(trolley10)), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 55 (happens_all_defn_13) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh45(fresh92(fresh76(push(agent10, trolley10), push(agent10, trolley10), push(agent10, trolley10), n0), true2, pull(agent10, trolley10), spinning(trolley10), n0, trolley10, agent10), true2, n0, spinning(trolley10)), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 12 (happens_all_defn_13) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh45(fresh92(true2, true2, pull(agent10, trolley10), spinning(trolley10), n0, trolley10, agent10), true2, n0, spinning(trolley10)), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by lemma 71 } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh45(fresh92(?, ?, pull(agent10, trolley10), spinning(trolley10), n0, trolley10, agent10), true2, n0, spinning(trolley10)), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by lemma 73 } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh45(true2, true2, n0, spinning(trolley10)), holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by axiom 42 (happens_holds) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley3), n1)) 65.63/8.60 = { by lemma 70 } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley3), plus(n1, n0))) 65.63/8.60 = { by axiom 48 (symmetry_of_plus) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley3), plus(n0, n1))) 65.63/8.60 = { by axiom 41 (happens_holds) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh46(true2, true2, pull(agent3, trolley3), n0, spinning(trolley3))) 65.63/8.60 = { by axiom 32 (happens_all_defn_5) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh46(fresh56(pull(agent3, trolley3), pull(agent3, trolley3), pull(agent3, trolley3), n0), true2, pull(agent3, trolley3), n0, spinning(trolley3))) 65.63/8.60 = { by axiom 63 (happens_all_defn_5) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh46(fresh57(n0, n0, pull(agent3, trolley3), n0), true2, pull(agent3, trolley3), n0, spinning(trolley3))) 65.63/8.60 = { by axiom 31 (happens_all_defn_5) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh46(happens(pull(agent3, trolley3), n0), true2, pull(agent3, trolley3), n0, spinning(trolley3))) 65.63/8.60 = { by axiom 46 (happens_holds) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh45(initiates(pull(agent3, trolley3), spinning(trolley3), n0), true2, n0, spinning(trolley3))) 65.63/8.60 = { by lemma 72 } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh45(fresh92(happens(push(agent3, trolley3), n0), true2, pull(agent3, trolley3), spinning(trolley3), n0, trolley3, agent3), true2, n0, spinning(trolley3))) 65.63/8.60 = { by axiom 15 (happens_all_defn_15) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh45(fresh92(fresh73(n0, n0, push(agent3, trolley3), n0), true2, pull(agent3, trolley3), spinning(trolley3), n0, trolley3, agent3), true2, n0, spinning(trolley3))) 65.63/8.60 = { by axiom 53 (happens_all_defn_15) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh45(fresh92(fresh72(push(agent3, trolley3), push(agent3, trolley3), push(agent3, trolley3), n0), true2, pull(agent3, trolley3), spinning(trolley3), n0, trolley3, agent3), true2, n0, spinning(trolley3))) 65.63/8.60 = { by axiom 16 (happens_all_defn_15) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh45(fresh92(true2, true2, pull(agent3, trolley3), spinning(trolley3), n0, trolley3, agent3), true2, n0, spinning(trolley3))) 65.63/8.60 = { by lemma 71 } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh45(fresh92(?, ?, pull(agent3, trolley3), spinning(trolley3), n0, trolley3, agent3), true2, n0, spinning(trolley3))) 65.63/8.60 = { by lemma 73 } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, fresh45(true2, true2, n0, spinning(trolley3))) 65.63/8.60 = { by axiom 42 (happens_holds) } 65.63/8.60 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2, true2) 65.63/8.60 % SZS output end Proof 65.63/8.60 65.63/8.60 RESULT: Theorem (the conjecture is true). 65.63/8.61 EOF