0.08/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.14	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.14/0.36	% Computer   : n005.cluster.edu
0.14/0.36	% Model      : x86_64 x86_64
0.14/0.36	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.36	% Memory     : 8042.1875MB
0.14/0.36	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.36	% CPULimit   : 1200
0.14/0.36	% WCLimit    : 120
0.14/0.36	% DateTime   : Tue Jul 13 12:11:03 EDT 2021
0.14/0.36	% CPUTime    : 
3.52/0.88	% SZS status Theorem
3.52/0.88	
5.17/1.01	% SZS output start Proof
5.17/1.01	Take the following subset of the input axioms:
5.17/1.04	  fof(happens_all_defn, axiom, ![Event, Time]: (happens(Event, Time) <=> ((push(agent2, trolley2)=Event & Time=n0) | ((Time=n0 & Event=pull(agent4, trolley4)) | ((n0=Time & push(agent6, trolley6)=Event) | ((Event=pull(agent7, trolley7) & Time=n0) | ((n0=Time & Event=push(agent7, trolley7)) | ((n0=Time & Event=push(agent8, trolley8)) | ((push(agent9, trolley9)=Event & Time=n0) | ((Event=pull(agent9, trolley9) & n0=Time) | ((Time=n0 & pull(agent8, trolley8)=Event) | ((pull(agent6, trolley6)=Event & n0=Time) | ((n0=Time & push(agent5, trolley5)=Event) | ((Time=n0 & Event=pull(agent5, trolley5)) | ((Event=push(agent4, trolley4) & Time=n0) | ((push(agent3, trolley3)=Event & Time=n0) | ((Time=n0 & Event=pull(agent3, trolley3)) | ((Event=pull(agent2, trolley2) & n0=Time) | ((n0=Time & Event=push(agent1, trolley1)) | (pull(agent1, trolley1)=Event & n0=Time)))))))))))))))))))).
5.17/1.04	  fof(happens_holds, axiom, ![Fluent, Event, Time]: (holdsAt(Fluent, plus(Time, n1)) <= (initiates(Event, Fluent, Time) & happens(Event, Time)))).
5.17/1.04	  fof(initiates_all_defn, axiom, ![Fluent, Event, Time]: (?[Agent, Trolley]: ((~happens(push(Agent, Trolley), Time) & (backwards(Trolley)=Fluent & pull(Agent, Trolley)=Event)) | ((Event=pull(Agent, Trolley) & (spinning(Trolley)=Fluent & happens(push(Agent, Trolley), Time))) | (push(Agent, Trolley)=Event & (~happens(pull(Agent, Trolley), Time) & Fluent=forwards(Trolley))))) <=> initiates(Event, Fluent, Time))).
5.17/1.04	  fof(plus0_1, axiom, n1=plus(n0, n1)).
5.17/1.04	  fof(spinning_3, conjecture, holdsAt(spinning(trolley2), n1) & (holdsAt(spinning(trolley3), n1) & (holdsAt(spinning(trolley4), n1) & (holdsAt(spinning(trolley5), n1) & (holdsAt(spinning(trolley6), n1) & (holdsAt(spinning(trolley7), n1) & (holdsAt(spinning(trolley9), n1) & (holdsAt(spinning(trolley8), n1) & holdsAt(spinning(trolley1), n1))))))))).
5.17/1.04	
5.17/1.04	Now clausify the problem and encode Horn clauses using encoding 3 of
5.17/1.04	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
5.17/1.04	We repeatedly replace C & s=t => u=v by the two clauses:
5.17/1.04	  fresh(y, y, x1...xn) = u
5.17/1.04	  C => fresh(s, t, x1...xn) = v
5.17/1.04	where fresh is a fresh function symbol and x1..xn are the free
5.17/1.04	variables of u and v.
5.17/1.04	A predicate p(X) is encoded as p(X)=true (this is sound, because the
5.17/1.04	input problem has no model of domain size 1).
5.17/1.04	
5.17/1.04	The encoding turns the above axioms into the following unit equations and goals:
5.17/1.04	
5.17/1.04	Axiom 1 (plus0_1): n1 = plus(n0, n1).
5.17/1.04	Axiom 2 (happens_all_defn): fresh93(X, X, Y, Z) = true2.
5.17/1.04	Axiom 3 (happens_all_defn): fresh92(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 4 (happens_all_defn_1): fresh91(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 5 (happens_all_defn_1): fresh90(X, X, Y, Z) = true2.
5.17/1.04	Axiom 6 (happens_all_defn_10): fresh89(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 7 (happens_all_defn_10): fresh88(X, X, Y, Z) = true2.
5.17/1.04	Axiom 8 (happens_all_defn_11): fresh87(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 9 (happens_all_defn_11): fresh86(X, X, Y, Z) = true2.
5.17/1.04	Axiom 10 (happens_all_defn_12): fresh85(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 11 (happens_all_defn_12): fresh84(X, X, Y, Z) = true2.
5.17/1.04	Axiom 12 (happens_all_defn_13): fresh83(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 13 (happens_all_defn_13): fresh82(X, X, Y, Z) = true2.
5.17/1.04	Axiom 14 (happens_all_defn_14): fresh81(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 15 (happens_all_defn_14): fresh80(X, X, Y, Z) = true2.
5.17/1.04	Axiom 16 (happens_all_defn_15): fresh79(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 17 (happens_all_defn_15): fresh78(X, X, Y, Z) = true2.
5.17/1.04	Axiom 18 (happens_all_defn_16): fresh77(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 19 (happens_all_defn_16): fresh76(X, X, Y, Z) = true2.
5.17/1.04	Axiom 20 (happens_all_defn_17): fresh75(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 21 (happens_all_defn_17): fresh74(X, X, Y, Z) = true2.
5.17/1.04	Axiom 22 (happens_all_defn_2): fresh73(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 23 (happens_all_defn_2): fresh72(X, X, Y, Z) = true2.
5.17/1.04	Axiom 24 (happens_all_defn_3): fresh71(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 25 (happens_all_defn_3): fresh70(X, X, Y, Z) = true2.
5.17/1.04	Axiom 26 (happens_all_defn_4): fresh69(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 27 (happens_all_defn_4): fresh68(X, X, Y, Z) = true2.
5.17/1.04	Axiom 28 (happens_all_defn_5): fresh67(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 29 (happens_all_defn_5): fresh66(X, X, Y, Z) = true2.
5.17/1.04	Axiom 30 (happens_all_defn_6): fresh65(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 31 (happens_all_defn_6): fresh64(X, X, Y, Z) = true2.
5.17/1.04	Axiom 32 (happens_all_defn_7): fresh63(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 33 (happens_all_defn_7): fresh62(X, X, Y, Z) = true2.
5.17/1.04	Axiom 34 (happens_all_defn_8): fresh61(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 35 (happens_all_defn_8): fresh60(X, X, Y, Z) = true2.
5.17/1.04	Axiom 36 (happens_all_defn_9): fresh59(X, X, Y, Z) = happens(Y, Z).
5.17/1.04	Axiom 37 (happens_all_defn_9): fresh58(X, X, Y, Z) = true2.
5.17/1.04	Axiom 38 (happens_holds): fresh56(X, X, Y, Z) = true2.
5.17/1.04	Axiom 39 (initiates_all_defn_2): fresh113(X, X, Y, Z, W) = true2.
5.17/1.04	Axiom 40 (happens_holds): fresh57(X, X, Y, Z, W) = holdsAt(W, plus(Z, n1)).
5.17/1.04	Axiom 41 (happens_all_defn): fresh92(X, n0, Y, X) = fresh93(push(agent2, trolley2), Y, Y, X).
5.17/1.04	Axiom 42 (happens_all_defn_1): fresh91(X, n0, Y, X) = fresh90(Y, push(agent4, trolley4), Y, X).
5.17/1.04	Axiom 43 (happens_all_defn_10): fresh89(X, n0, Y, X) = fresh88(Y, pull(agent4, trolley4), Y, X).
5.17/1.04	Axiom 44 (happens_all_defn_11): fresh87(n0, X, Y, X) = fresh86(pull(agent6, trolley6), Y, Y, X).
5.17/1.04	Axiom 45 (happens_all_defn_12): fresh85(X, n0, Y, X) = fresh84(Y, pull(agent7, trolley7), Y, X).
5.17/1.04	Axiom 46 (happens_all_defn_13): fresh83(X, n0, Y, X) = fresh82(pull(agent8, trolley8), Y, Y, X).
5.17/1.04	Axiom 47 (happens_all_defn_14): fresh81(n0, X, Y, X) = fresh80(Y, pull(agent9, trolley9), Y, X).
5.17/1.04	Axiom 48 (happens_all_defn_15): fresh79(X, n0, Y, X) = fresh78(Y, pull(agent5, trolley5), Y, X).
5.17/1.04	Axiom 49 (happens_all_defn_16): fresh77(X, n0, Y, X) = fresh76(Y, pull(agent3, trolley3), Y, X).
5.17/1.04	Axiom 50 (happens_all_defn_17): fresh75(n0, X, Y, X) = fresh74(pull(agent1, trolley1), Y, Y, X).
5.17/1.04	Axiom 51 (happens_all_defn_2): fresh73(n0, X, Y, X) = fresh72(push(agent6, trolley6), Y, Y, X).
5.17/1.04	Axiom 52 (happens_all_defn_3): fresh71(n0, X, Y, X) = fresh70(Y, push(agent7, trolley7), Y, X).
5.17/1.04	Axiom 53 (happens_all_defn_4): fresh69(n0, X, Y, X) = fresh68(Y, push(agent8, trolley8), Y, X).
5.17/1.04	Axiom 54 (happens_all_defn_5): fresh67(X, n0, Y, X) = fresh66(push(agent9, trolley9), Y, Y, X).
5.17/1.04	Axiom 55 (happens_all_defn_6): fresh65(n0, X, Y, X) = fresh64(push(agent5, trolley5), Y, Y, X).
5.17/1.04	Axiom 56 (happens_all_defn_7): fresh63(X, n0, Y, X) = fresh62(push(agent3, trolley3), Y, Y, X).
5.17/1.04	Axiom 57 (happens_all_defn_8): fresh61(n0, X, Y, X) = fresh60(Y, push(agent1, trolley1), Y, X).
5.17/1.04	Axiom 58 (happens_all_defn_9): fresh59(n0, X, Y, X) = fresh58(Y, pull(agent2, trolley2), Y, X).
5.17/1.04	Axiom 59 (initiates_all_defn_2): fresh112(X, X, Y, Z, W, V, U) = fresh113(Y, pull(U, V), Y, Z, W).
5.17/1.04	Axiom 60 (happens_holds): fresh57(happens(X, Y), true2, X, Y, Z) = fresh56(initiates(X, Z, Y), true2, Y, Z).
5.17/1.04	Axiom 61 (initiates_all_defn_2): fresh52(X, X, Y, Z, W, V, U) = initiates(Y, Z, W).
5.17/1.04	Axiom 62 (initiates_all_defn_2): fresh112(happens(push(X, Y), Z), true2, W, V, Z, Y, X) = fresh52(spinning(Y), V, W, V, Z, Y, X).
5.17/1.04	
5.17/1.04	Lemma 63: fresh112(X, X, pull(Y, Z), W, V, Z, Y) = true2.
5.17/1.04	Proof:
5.17/1.04	  fresh112(X, X, pull(Y, Z), W, V, Z, Y)
5.17/1.04	= { by axiom 59 (initiates_all_defn_2) }
5.17/1.04	  fresh113(pull(Y, Z), pull(Y, Z), pull(Y, Z), W, V)
5.17/1.04	= { by axiom 39 (initiates_all_defn_2) }
5.17/1.04	  true2
5.17/1.04	
5.17/1.04	Lemma 64: fresh112(happens(push(X, Y), Z), true2, W, spinning(Y), Z, Y, X) = initiates(W, spinning(Y), Z).
5.17/1.04	Proof:
5.17/1.04	  fresh112(happens(push(X, Y), Z), true2, W, spinning(Y), Z, Y, X)
5.17/1.04	= { by axiom 62 (initiates_all_defn_2) }
5.17/1.04	  fresh52(spinning(Y), spinning(Y), W, spinning(Y), Z, Y, X)
5.17/1.04	= { by axiom 61 (initiates_all_defn_2) }
5.17/1.04	  initiates(W, spinning(Y), Z)
5.17/1.04	
5.17/1.04	Goal 1 (spinning_3): tuple(holdsAt(spinning(trolley1), n1), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1)) = tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2).
5.17/1.04	Proof:
5.17/1.04	  tuple(holdsAt(spinning(trolley1), n1), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by axiom 1 (plus0_1) }
5.17/1.04	  tuple(holdsAt(spinning(trolley1), plus(n0, n1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by axiom 40 (happens_holds) R->L }
5.17/1.04	  tuple(fresh57(true2, true2, pull(agent1, trolley1), n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by axiom 21 (happens_all_defn_17) R->L }
5.17/1.04	  tuple(fresh57(fresh74(pull(agent1, trolley1), pull(agent1, trolley1), pull(agent1, trolley1), n0), true2, pull(agent1, trolley1), n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by axiom 50 (happens_all_defn_17) R->L }
5.17/1.04	  tuple(fresh57(fresh75(n0, n0, pull(agent1, trolley1), n0), true2, pull(agent1, trolley1), n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by axiom 20 (happens_all_defn_17) }
5.17/1.04	  tuple(fresh57(happens(pull(agent1, trolley1), n0), true2, pull(agent1, trolley1), n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by axiom 60 (happens_holds) }
5.17/1.04	  tuple(fresh56(initiates(pull(agent1, trolley1), spinning(trolley1), n0), true2, n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by lemma 64 R->L }
5.17/1.04	  tuple(fresh56(fresh112(happens(push(agent1, trolley1), n0), true2, pull(agent1, trolley1), spinning(trolley1), n0, trolley1, agent1), true2, n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by axiom 34 (happens_all_defn_8) R->L }
5.17/1.04	  tuple(fresh56(fresh112(fresh61(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(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by axiom 57 (happens_all_defn_8) }
5.17/1.04	  tuple(fresh56(fresh112(fresh60(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(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by axiom 35 (happens_all_defn_8) }
5.17/1.04	  tuple(fresh56(fresh112(true2, true2, pull(agent1, trolley1), spinning(trolley1), n0, trolley1, agent1), true2, n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by lemma 63 }
5.17/1.04	  tuple(fresh56(true2, true2, n0, spinning(trolley1)), holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by axiom 38 (happens_holds) }
5.17/1.04	  tuple(true2, holdsAt(spinning(trolley2), n1), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by axiom 1 (plus0_1) }
5.17/1.04	  tuple(true2, holdsAt(spinning(trolley2), plus(n0, n1)), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by axiom 40 (happens_holds) R->L }
5.17/1.04	  tuple(true2, fresh57(true2, true2, pull(agent2, trolley2), n0, spinning(trolley2)), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by axiom 37 (happens_all_defn_9) R->L }
5.17/1.04	  tuple(true2, fresh57(fresh58(pull(agent2, trolley2), pull(agent2, trolley2), pull(agent2, trolley2), n0), true2, pull(agent2, trolley2), n0, spinning(trolley2)), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by axiom 58 (happens_all_defn_9) R->L }
5.17/1.04	  tuple(true2, fresh57(fresh59(n0, n0, pull(agent2, trolley2), n0), true2, pull(agent2, trolley2), n0, spinning(trolley2)), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by axiom 36 (happens_all_defn_9) }
5.17/1.04	  tuple(true2, fresh57(happens(pull(agent2, trolley2), n0), true2, pull(agent2, trolley2), n0, spinning(trolley2)), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.04	= { by axiom 60 (happens_holds) }
5.17/1.05	  tuple(true2, fresh56(initiates(pull(agent2, trolley2), spinning(trolley2), n0), true2, n0, spinning(trolley2)), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by lemma 64 R->L }
5.17/1.05	  tuple(true2, fresh56(fresh112(happens(push(agent2, trolley2), n0), true2, pull(agent2, trolley2), spinning(trolley2), n0, trolley2, agent2), true2, n0, spinning(trolley2)), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 3 (happens_all_defn) R->L }
5.17/1.05	  tuple(true2, fresh56(fresh112(fresh92(n0, n0, push(agent2, trolley2), n0), true2, pull(agent2, trolley2), spinning(trolley2), n0, trolley2, agent2), true2, n0, spinning(trolley2)), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 41 (happens_all_defn) }
5.17/1.05	  tuple(true2, fresh56(fresh112(fresh93(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(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 2 (happens_all_defn) }
5.17/1.05	  tuple(true2, fresh56(fresh112(true2, true2, pull(agent2, trolley2), spinning(trolley2), n0, trolley2, agent2), true2, n0, spinning(trolley2)), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by lemma 63 }
5.17/1.05	  tuple(true2, fresh56(true2, true2, n0, spinning(trolley2)), holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 38 (happens_holds) }
5.17/1.05	  tuple(true2, true2, holdsAt(spinning(trolley3), n1), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 1 (plus0_1) }
5.17/1.05	  tuple(true2, true2, holdsAt(spinning(trolley3), plus(n0, n1)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 40 (happens_holds) R->L }
5.17/1.05	  tuple(true2, true2, fresh57(true2, true2, pull(agent3, trolley3), n0, spinning(trolley3)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 19 (happens_all_defn_16) R->L }
5.17/1.05	  tuple(true2, true2, fresh57(fresh76(pull(agent3, trolley3), pull(agent3, trolley3), pull(agent3, trolley3), n0), true2, pull(agent3, trolley3), n0, spinning(trolley3)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 49 (happens_all_defn_16) R->L }
5.17/1.05	  tuple(true2, true2, fresh57(fresh77(n0, n0, pull(agent3, trolley3), n0), true2, pull(agent3, trolley3), n0, spinning(trolley3)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 18 (happens_all_defn_16) }
5.17/1.05	  tuple(true2, true2, fresh57(happens(pull(agent3, trolley3), n0), true2, pull(agent3, trolley3), n0, spinning(trolley3)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 60 (happens_holds) }
5.17/1.05	  tuple(true2, true2, fresh56(initiates(pull(agent3, trolley3), spinning(trolley3), n0), true2, n0, spinning(trolley3)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by lemma 64 R->L }
5.17/1.05	  tuple(true2, true2, fresh56(fresh112(happens(push(agent3, trolley3), n0), true2, pull(agent3, trolley3), spinning(trolley3), n0, trolley3, agent3), true2, n0, spinning(trolley3)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 32 (happens_all_defn_7) R->L }
5.17/1.05	  tuple(true2, true2, fresh56(fresh112(fresh63(n0, n0, push(agent3, trolley3), n0), true2, pull(agent3, trolley3), spinning(trolley3), n0, trolley3, agent3), true2, n0, spinning(trolley3)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 56 (happens_all_defn_7) }
5.17/1.05	  tuple(true2, true2, fresh56(fresh112(fresh62(push(agent3, trolley3), push(agent3, trolley3), push(agent3, trolley3), n0), true2, pull(agent3, trolley3), spinning(trolley3), n0, trolley3, agent3), true2, n0, spinning(trolley3)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 33 (happens_all_defn_7) }
5.17/1.05	  tuple(true2, true2, fresh56(fresh112(true2, true2, pull(agent3, trolley3), spinning(trolley3), n0, trolley3, agent3), true2, n0, spinning(trolley3)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by lemma 63 }
5.17/1.05	  tuple(true2, true2, fresh56(true2, true2, n0, spinning(trolley3)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 38 (happens_holds) }
5.17/1.05	  tuple(true2, true2, true2, holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 1 (plus0_1) }
5.17/1.05	  tuple(true2, true2, true2, holdsAt(spinning(trolley4), plus(n0, n1)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 40 (happens_holds) R->L }
5.17/1.05	  tuple(true2, true2, true2, fresh57(true2, true2, pull(agent4, trolley4), n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 7 (happens_all_defn_10) R->L }
5.17/1.05	  tuple(true2, true2, true2, fresh57(fresh88(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(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 43 (happens_all_defn_10) R->L }
5.17/1.05	  tuple(true2, true2, true2, fresh57(fresh89(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(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 6 (happens_all_defn_10) }
5.17/1.05	  tuple(true2, true2, true2, fresh57(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(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 60 (happens_holds) }
5.17/1.05	  tuple(true2, true2, true2, fresh56(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(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by lemma 64 R->L }
5.17/1.05	  tuple(true2, true2, true2, fresh56(fresh112(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(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 4 (happens_all_defn_1) R->L }
5.17/1.05	  tuple(true2, true2, true2, fresh56(fresh112(fresh91(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(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 42 (happens_all_defn_1) }
5.17/1.05	  tuple(true2, true2, true2, fresh56(fresh112(fresh90(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(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 5 (happens_all_defn_1) }
5.17/1.05	  tuple(true2, true2, true2, fresh56(fresh112(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(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by lemma 63 }
5.17/1.05	  tuple(true2, true2, true2, fresh56(true2, true2, n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 38 (happens_holds) }
5.17/1.05	  tuple(true2, true2, true2, true2, holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 1 (plus0_1) }
5.17/1.05	  tuple(true2, true2, true2, true2, holdsAt(spinning(trolley5), plus(n0, n1)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 40 (happens_holds) R->L }
5.17/1.05	  tuple(true2, true2, true2, true2, fresh57(true2, true2, pull(agent5, trolley5), n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 17 (happens_all_defn_15) R->L }
5.17/1.05	  tuple(true2, true2, true2, true2, fresh57(fresh78(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(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 48 (happens_all_defn_15) R->L }
5.17/1.05	  tuple(true2, true2, true2, true2, fresh57(fresh79(n0, n0, pull(agent5, trolley5), n0), true2, pull(agent5, trolley5), n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 16 (happens_all_defn_15) }
5.17/1.05	  tuple(true2, true2, true2, true2, fresh57(happens(pull(agent5, trolley5), n0), true2, pull(agent5, trolley5), n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 60 (happens_holds) }
5.17/1.05	  tuple(true2, true2, true2, true2, fresh56(initiates(pull(agent5, trolley5), spinning(trolley5), n0), true2, n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by lemma 64 R->L }
5.17/1.05	  tuple(true2, true2, true2, true2, fresh56(fresh112(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(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 30 (happens_all_defn_6) R->L }
5.17/1.05	  tuple(true2, true2, true2, true2, fresh56(fresh112(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(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.05	= { by axiom 55 (happens_all_defn_6) }
5.17/1.05	  tuple(true2, true2, true2, true2, fresh56(fresh112(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(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 31 (happens_all_defn_6) }
5.17/1.06	  tuple(true2, true2, true2, true2, fresh56(fresh112(true2, true2, pull(agent5, trolley5), spinning(trolley5), n0, trolley5, agent5), true2, n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by lemma 63 }
5.17/1.06	  tuple(true2, true2, true2, true2, fresh56(true2, true2, n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 38 (happens_holds) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 1 (plus0_1) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, holdsAt(spinning(trolley6), plus(n0, n1)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 40 (happens_holds) R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, fresh57(true2, true2, pull(agent6, trolley6), n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 9 (happens_all_defn_11) R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, fresh57(fresh86(pull(agent6, trolley6), pull(agent6, trolley6), pull(agent6, trolley6), n0), true2, pull(agent6, trolley6), n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 44 (happens_all_defn_11) R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, fresh57(fresh87(n0, n0, pull(agent6, trolley6), n0), true2, pull(agent6, trolley6), n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 8 (happens_all_defn_11) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, fresh57(happens(pull(agent6, trolley6), n0), true2, pull(agent6, trolley6), n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 60 (happens_holds) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, fresh56(initiates(pull(agent6, trolley6), spinning(trolley6), n0), true2, n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by lemma 64 R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, fresh56(fresh112(happens(push(agent6, trolley6), n0), true2, pull(agent6, trolley6), spinning(trolley6), n0, trolley6, agent6), true2, n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 22 (happens_all_defn_2) R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, fresh56(fresh112(fresh73(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(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 51 (happens_all_defn_2) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, fresh56(fresh112(fresh72(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(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 23 (happens_all_defn_2) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, fresh56(fresh112(true2, true2, pull(agent6, trolley6), spinning(trolley6), n0, trolley6, agent6), true2, n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by lemma 63 }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, fresh56(true2, true2, n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 38 (happens_holds) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 1 (plus0_1) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley7), plus(n0, n1)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 40 (happens_holds) R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, fresh57(true2, true2, pull(agent7, trolley7), n0, spinning(trolley7)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 11 (happens_all_defn_12) R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, fresh57(fresh84(pull(agent7, trolley7), pull(agent7, trolley7), pull(agent7, trolley7), n0), true2, pull(agent7, trolley7), n0, spinning(trolley7)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 45 (happens_all_defn_12) R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, fresh57(fresh85(n0, n0, pull(agent7, trolley7), n0), true2, pull(agent7, trolley7), n0, spinning(trolley7)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 10 (happens_all_defn_12) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, fresh57(happens(pull(agent7, trolley7), n0), true2, pull(agent7, trolley7), n0, spinning(trolley7)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 60 (happens_holds) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, fresh56(initiates(pull(agent7, trolley7), spinning(trolley7), n0), true2, n0, spinning(trolley7)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by lemma 64 R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, fresh56(fresh112(happens(push(agent7, trolley7), n0), true2, pull(agent7, trolley7), spinning(trolley7), n0, trolley7, agent7), true2, n0, spinning(trolley7)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 24 (happens_all_defn_3) R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, fresh56(fresh112(fresh71(n0, n0, push(agent7, trolley7), n0), true2, pull(agent7, trolley7), spinning(trolley7), n0, trolley7, agent7), true2, n0, spinning(trolley7)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 52 (happens_all_defn_3) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, fresh56(fresh112(fresh70(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(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 25 (happens_all_defn_3) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, fresh56(fresh112(true2, true2, pull(agent7, trolley7), spinning(trolley7), n0, trolley7, agent7), true2, n0, spinning(trolley7)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by lemma 63 }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, fresh56(true2, true2, n0, spinning(trolley7)), holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 38 (happens_holds) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley9), n1), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 1 (plus0_1) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley9), plus(n0, n1)), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 40 (happens_holds) R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, fresh57(true2, true2, pull(agent9, trolley9), n0, spinning(trolley9)), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 15 (happens_all_defn_14) R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, fresh57(fresh80(pull(agent9, trolley9), pull(agent9, trolley9), pull(agent9, trolley9), n0), true2, pull(agent9, trolley9), n0, spinning(trolley9)), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 47 (happens_all_defn_14) R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, fresh57(fresh81(n0, n0, pull(agent9, trolley9), n0), true2, pull(agent9, trolley9), n0, spinning(trolley9)), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 14 (happens_all_defn_14) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, fresh57(happens(pull(agent9, trolley9), n0), true2, pull(agent9, trolley9), n0, spinning(trolley9)), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 60 (happens_holds) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, fresh56(initiates(pull(agent9, trolley9), spinning(trolley9), n0), true2, n0, spinning(trolley9)), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by lemma 64 R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, fresh56(fresh112(happens(push(agent9, trolley9), n0), true2, pull(agent9, trolley9), spinning(trolley9), n0, trolley9, agent9), true2, n0, spinning(trolley9)), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 28 (happens_all_defn_5) R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, fresh56(fresh112(fresh67(n0, n0, push(agent9, trolley9), n0), true2, pull(agent9, trolley9), spinning(trolley9), n0, trolley9, agent9), true2, n0, spinning(trolley9)), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 54 (happens_all_defn_5) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, fresh56(fresh112(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(trolley8), n1))
5.17/1.06	= { by axiom 29 (happens_all_defn_5) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, fresh56(fresh112(true2, true2, pull(agent9, trolley9), spinning(trolley9), n0, trolley9, agent9), true2, n0, spinning(trolley9)), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by lemma 63 }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, fresh56(true2, true2, n0, spinning(trolley9)), holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 38 (happens_holds) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley8), n1))
5.17/1.06	= { by axiom 1 (plus0_1) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley8), plus(n0, n1)))
5.17/1.06	= { by axiom 40 (happens_holds) R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh57(true2, true2, pull(agent8, trolley8), n0, spinning(trolley8)))
5.17/1.06	= { by axiom 13 (happens_all_defn_13) R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh57(fresh82(pull(agent8, trolley8), pull(agent8, trolley8), pull(agent8, trolley8), n0), true2, pull(agent8, trolley8), n0, spinning(trolley8)))
5.17/1.06	= { by axiom 46 (happens_all_defn_13) R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh57(fresh83(n0, n0, pull(agent8, trolley8), n0), true2, pull(agent8, trolley8), n0, spinning(trolley8)))
5.17/1.06	= { by axiom 12 (happens_all_defn_13) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh57(happens(pull(agent8, trolley8), n0), true2, pull(agent8, trolley8), n0, spinning(trolley8)))
5.17/1.06	= { by axiom 60 (happens_holds) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh56(initiates(pull(agent8, trolley8), spinning(trolley8), n0), true2, n0, spinning(trolley8)))
5.17/1.06	= { by lemma 64 R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh56(fresh112(happens(push(agent8, trolley8), n0), true2, pull(agent8, trolley8), spinning(trolley8), n0, trolley8, agent8), true2, n0, spinning(trolley8)))
5.17/1.06	= { by axiom 26 (happens_all_defn_4) R->L }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh56(fresh112(fresh69(n0, n0, push(agent8, trolley8), n0), true2, pull(agent8, trolley8), spinning(trolley8), n0, trolley8, agent8), true2, n0, spinning(trolley8)))
5.17/1.06	= { by axiom 53 (happens_all_defn_4) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh56(fresh112(fresh68(push(agent8, trolley8), push(agent8, trolley8), push(agent8, trolley8), n0), true2, pull(agent8, trolley8), spinning(trolley8), n0, trolley8, agent8), true2, n0, spinning(trolley8)))
5.17/1.06	= { by axiom 27 (happens_all_defn_4) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh56(fresh112(true2, true2, pull(agent8, trolley8), spinning(trolley8), n0, trolley8, agent8), true2, n0, spinning(trolley8)))
5.17/1.06	= { by lemma 63 }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, fresh56(true2, true2, n0, spinning(trolley8)))
5.17/1.06	= { by axiom 38 (happens_holds) }
5.17/1.06	  tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2)
5.17/1.06	% SZS output end Proof
5.17/1.06	
5.17/1.06	RESULT: Theorem (the conjecture is true).
5.17/1.07	EOF