TSTP Solution File: CSR024+1.009 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : CSR024+1.009 : TPTP v8.1.2. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 21:40:59 EDT 2023
% Result : Theorem 3.82s 0.87s
% Output : Proof 5.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CSR024+1.009 : TPTP v8.1.2. Bugfixed v3.1.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 12:13:05 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.82/0.87 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.82/0.87
% 3.82/0.87 % SZS status Theorem
% 3.82/0.87
% 4.88/1.00 % SZS output start Proof
% 4.88/1.00 Take the following subset of the input axioms:
% 4.88/1.02 fof(happens_all_defn, axiom, ![Event, Time]: (happens(Event, Time) <=> ((Event=pull(agent1, trolley1) & Time=n0) | ((Event=push(agent1, trolley1) & Time=n0) | ((Event=pull(agent2, trolley2) & Time=n0) | ((Event=push(agent2, trolley2) & Time=n0) | ((Event=pull(agent3, trolley3) & Time=n0) | ((Event=push(agent3, trolley3) & Time=n0) | ((Event=pull(agent4, trolley4) & Time=n0) | ((Event=push(agent4, trolley4) & Time=n0) | ((Event=pull(agent5, trolley5) & Time=n0) | ((Event=push(agent5, trolley5) & Time=n0) | ((Event=pull(agent6, trolley6) & Time=n0) | ((Event=push(agent6, trolley6) & Time=n0) | ((Event=pull(agent7, trolley7) & Time=n0) | ((Event=push(agent7, trolley7) & Time=n0) | ((Event=pull(agent8, trolley8) & Time=n0) | ((Event=push(agent8, trolley8) & Time=n0) | ((Event=pull(agent9, trolley9) & Time=n0) | (Event=push(agent9, trolley9) & Time=n0)))))))))))))))))))).
% 4.88/1.02 fof(happens_holds, axiom, ![Fluent, Time2, Event2]: ((happens(Event2, Time2) & initiates(Event2, Fluent, Time2)) => holdsAt(Fluent, plus(Time2, n1)))).
% 4.88/1.02 fof(initiates_all_defn, axiom, ![Time2, Fluent2, Event2]: (initiates(Event2, Fluent2, Time2) <=> ?[Agent, Trolley]: ((Event2=push(Agent, Trolley) & (Fluent2=forwards(Trolley) & ~happens(pull(Agent, Trolley), Time2))) | ((Event2=pull(Agent, Trolley) & (Fluent2=backwards(Trolley) & ~happens(push(Agent, Trolley), Time2))) | (Event2=pull(Agent, Trolley) & (Fluent2=spinning(Trolley) & happens(push(Agent, Trolley), Time2))))))).
% 4.88/1.02 fof(plus0_1, axiom, plus(n0, n1)=n1).
% 4.88/1.02 fof(spinning_3, conjecture, 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(trolley8), n1) & holdsAt(spinning(trolley9), n1))))))))).
% 4.88/1.02
% 4.88/1.02 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.88/1.02 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.88/1.02 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.88/1.02 fresh(y, y, x1...xn) = u
% 4.88/1.02 C => fresh(s, t, x1...xn) = v
% 4.88/1.02 where fresh is a fresh function symbol and x1..xn are the free
% 4.88/1.02 variables of u and v.
% 4.88/1.02 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.88/1.02 input problem has no model of domain size 1).
% 4.88/1.02
% 4.88/1.02 The encoding turns the above axioms into the following unit equations and goals:
% 4.88/1.02
% 4.88/1.02 Axiom 1 (plus0_1): plus(n0, n1) = n1.
% 4.88/1.02 Axiom 2 (happens_all_defn): fresh92(X, X, Y, Z) = true2.
% 4.88/1.02 Axiom 3 (happens_all_defn): fresh91(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.02 Axiom 4 (happens_all_defn_1): fresh90(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.02 Axiom 5 (happens_all_defn_1): fresh89(X, X, Y, Z) = true2.
% 4.88/1.02 Axiom 6 (happens_all_defn_10): fresh88(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.02 Axiom 7 (happens_all_defn_10): fresh87(X, X, Y, Z) = true2.
% 4.88/1.02 Axiom 8 (happens_all_defn_11): fresh86(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.02 Axiom 9 (happens_all_defn_11): fresh85(X, X, Y, Z) = true2.
% 4.88/1.02 Axiom 10 (happens_all_defn_12): fresh84(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.02 Axiom 11 (happens_all_defn_12): fresh83(X, X, Y, Z) = true2.
% 4.88/1.03 Axiom 12 (happens_all_defn_13): fresh82(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.03 Axiom 13 (happens_all_defn_13): fresh81(X, X, Y, Z) = true2.
% 4.88/1.03 Axiom 14 (happens_all_defn_14): fresh80(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.03 Axiom 15 (happens_all_defn_14): fresh79(X, X, Y, Z) = true2.
% 4.88/1.03 Axiom 16 (happens_all_defn_15): fresh78(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.03 Axiom 17 (happens_all_defn_15): fresh77(X, X, Y, Z) = true2.
% 4.88/1.03 Axiom 18 (happens_all_defn_16): fresh76(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.03 Axiom 19 (happens_all_defn_16): fresh75(X, X, Y, Z) = true2.
% 4.88/1.03 Axiom 20 (happens_all_defn_17): fresh74(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.03 Axiom 21 (happens_all_defn_17): fresh73(X, X, Y, Z) = true2.
% 4.88/1.03 Axiom 22 (happens_all_defn_2): fresh72(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.03 Axiom 23 (happens_all_defn_2): fresh71(X, X, Y, Z) = true2.
% 4.88/1.03 Axiom 24 (happens_all_defn_3): fresh70(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.03 Axiom 25 (happens_all_defn_3): fresh69(X, X, Y, Z) = true2.
% 4.88/1.03 Axiom 26 (happens_all_defn_4): fresh68(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.03 Axiom 27 (happens_all_defn_4): fresh67(X, X, Y, Z) = true2.
% 4.88/1.03 Axiom 28 (happens_all_defn_5): fresh66(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.03 Axiom 29 (happens_all_defn_5): fresh65(X, X, Y, Z) = true2.
% 4.88/1.03 Axiom 30 (happens_all_defn_6): fresh63(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.03 Axiom 31 (happens_all_defn_6): fresh62(X, X, Y, Z) = true2.
% 4.88/1.03 Axiom 32 (happens_all_defn_7): fresh61(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.03 Axiom 33 (happens_all_defn_7): fresh60(X, X, Y, Z) = true2.
% 4.88/1.03 Axiom 34 (happens_all_defn_8): fresh59(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.03 Axiom 35 (happens_all_defn_8): fresh58(X, X, Y, Z) = true2.
% 4.88/1.03 Axiom 36 (happens_all_defn_9): fresh57(X, X, Y, Z) = happens(Y, Z).
% 4.88/1.03 Axiom 37 (happens_all_defn_9): fresh56(X, X, Y, Z) = true2.
% 4.88/1.03 Axiom 38 (happens_holds): fresh54(X, X, Y, Z) = true2.
% 4.88/1.03 Axiom 39 (initiates_all_defn_2): fresh116(X, X, Y, Z, W) = true2.
% 4.88/1.03 Axiom 40 (happens_holds): fresh55(X, X, Y, Z, W) = holdsAt(W, plus(Z, n1)).
% 4.88/1.03 Axiom 41 (happens_all_defn): fresh91(X, n0, Y, X) = fresh92(Y, push(agent1, trolley1), Y, X).
% 4.88/1.03 Axiom 42 (happens_all_defn_1): fresh90(X, n0, Y, X) = fresh89(Y, push(agent2, trolley2), Y, X).
% 4.88/1.03 Axiom 43 (happens_all_defn_10): fresh88(X, n0, Y, X) = fresh87(Y, pull(agent2, trolley2), Y, X).
% 4.88/1.03 Axiom 44 (happens_all_defn_11): fresh86(X, n0, Y, X) = fresh85(Y, pull(agent3, trolley3), Y, X).
% 4.88/1.03 Axiom 45 (happens_all_defn_12): fresh84(X, n0, Y, X) = fresh83(Y, pull(agent4, trolley4), Y, X).
% 4.88/1.03 Axiom 46 (happens_all_defn_13): fresh82(X, n0, Y, X) = fresh81(Y, pull(agent5, trolley5), Y, X).
% 4.88/1.03 Axiom 47 (happens_all_defn_14): fresh80(X, n0, Y, X) = fresh79(Y, pull(agent6, trolley6), Y, X).
% 4.88/1.03 Axiom 48 (happens_all_defn_15): fresh78(X, n0, Y, X) = fresh77(Y, pull(agent7, trolley7), Y, X).
% 4.88/1.03 Axiom 49 (happens_all_defn_16): fresh76(X, n0, Y, X) = fresh75(Y, pull(agent8, trolley8), Y, X).
% 4.88/1.03 Axiom 50 (happens_all_defn_17): fresh74(X, n0, Y, X) = fresh73(Y, pull(agent9, trolley9), Y, X).
% 4.88/1.03 Axiom 51 (happens_all_defn_2): fresh72(X, n0, Y, X) = fresh71(Y, push(agent3, trolley3), Y, X).
% 4.88/1.03 Axiom 52 (happens_all_defn_3): fresh70(X, n0, Y, X) = fresh69(Y, push(agent4, trolley4), Y, X).
% 4.88/1.03 Axiom 53 (happens_all_defn_4): fresh68(X, n0, Y, X) = fresh67(Y, push(agent5, trolley5), Y, X).
% 4.88/1.03 Axiom 54 (happens_all_defn_5): fresh66(X, n0, Y, X) = fresh65(Y, push(agent6, trolley6), Y, X).
% 4.88/1.03 Axiom 55 (happens_all_defn_6): fresh63(X, n0, Y, X) = fresh62(Y, push(agent7, trolley7), Y, X).
% 4.88/1.03 Axiom 56 (happens_all_defn_7): fresh61(X, n0, Y, X) = fresh60(Y, push(agent8, trolley8), Y, X).
% 4.88/1.03 Axiom 57 (happens_all_defn_8): fresh59(X, n0, Y, X) = fresh58(Y, push(agent9, trolley9), Y, X).
% 4.88/1.03 Axiom 58 (happens_all_defn_9): fresh57(X, n0, Y, X) = fresh56(Y, pull(agent1, trolley1), Y, X).
% 4.88/1.03 Axiom 59 (initiates_all_defn_2): fresh115(X, X, Y, Z, W, V, U) = fresh116(Y, pull(U, V), Y, Z, W).
% 4.88/1.03 Axiom 60 (initiates_all_defn_2): fresh51(X, X, Y, Z, W, V, U) = initiates(Y, Z, W).
% 4.88/1.03 Axiom 61 (happens_holds): fresh55(initiates(X, Y, Z), true2, X, Z, Y) = fresh54(happens(X, Z), true2, Z, Y).
% 4.88/1.03 Axiom 62 (initiates_all_defn_2): fresh115(happens(push(X, Y), Z), true2, W, V, Z, Y, X) = fresh51(V, spinning(Y), W, V, Z, Y, X).
% 4.88/1.03
% 4.88/1.03 Lemma 63: fresh115(X, X, pull(Y, Z), W, V, Z, Y) = true2.
% 4.88/1.03 Proof:
% 4.88/1.03 fresh115(X, X, pull(Y, Z), W, V, Z, Y)
% 4.88/1.03 = { by axiom 59 (initiates_all_defn_2) }
% 4.88/1.03 fresh116(pull(Y, Z), pull(Y, Z), pull(Y, Z), W, V)
% 4.88/1.03 = { by axiom 39 (initiates_all_defn_2) }
% 4.88/1.03 true2
% 4.88/1.03
% 4.88/1.03 Lemma 64: fresh115(happens(push(X, Y), Z), true2, W, spinning(Y), Z, Y, X) = initiates(W, spinning(Y), Z).
% 4.88/1.03 Proof:
% 4.88/1.03 fresh115(happens(push(X, Y), Z), true2, W, spinning(Y), Z, Y, X)
% 4.88/1.03 = { by axiom 62 (initiates_all_defn_2) }
% 4.88/1.03 fresh51(spinning(Y), spinning(Y), W, spinning(Y), Z, Y, X)
% 4.88/1.03 = { by axiom 60 (initiates_all_defn_2) }
% 4.88/1.03 initiates(W, spinning(Y), Z)
% 4.88/1.03
% 4.88/1.03 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(trolley8), n1), holdsAt(spinning(trolley9), n1)) = tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2).
% 4.88/1.03 Proof:
% 4.88/1.03 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(trolley8), n1), holdsAt(spinning(trolley9), n1))
% 4.88/1.03 = { by axiom 1 (plus0_1) R->L }
% 4.88/1.03 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(trolley8), n1), holdsAt(spinning(trolley9), plus(n0, n1)))
% 4.88/1.03 = { by axiom 40 (happens_holds) R->L }
% 4.88/1.03 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(trolley8), n1), fresh55(true2, true2, pull(agent9, trolley9), n0, spinning(trolley9)))
% 4.88/1.03 = { by lemma 63 R->L }
% 4.88/1.03 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(trolley8), n1), fresh55(fresh115(true2, true2, pull(agent9, trolley9), spinning(trolley9), n0, trolley9, agent9), true2, pull(agent9, trolley9), n0, spinning(trolley9)))
% 4.88/1.03 = { by axiom 35 (happens_all_defn_8) R->L }
% 4.88/1.03 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(trolley8), n1), fresh55(fresh115(fresh58(push(agent9, trolley9), push(agent9, trolley9), push(agent9, trolley9), n0), true2, pull(agent9, trolley9), spinning(trolley9), n0, trolley9, agent9), true2, pull(agent9, trolley9), n0, spinning(trolley9)))
% 4.88/1.03 = { by axiom 57 (happens_all_defn_8) R->L }
% 4.88/1.03 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(trolley8), n1), fresh55(fresh115(fresh59(n0, n0, push(agent9, trolley9), n0), true2, pull(agent9, trolley9), spinning(trolley9), n0, trolley9, agent9), true2, pull(agent9, trolley9), n0, spinning(trolley9)))
% 4.88/1.03 = { by axiom 34 (happens_all_defn_8) }
% 4.88/1.03 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(trolley8), n1), fresh55(fresh115(happens(push(agent9, trolley9), n0), true2, pull(agent9, trolley9), spinning(trolley9), n0, trolley9, agent9), true2, pull(agent9, trolley9), n0, spinning(trolley9)))
% 4.88/1.03 = { by lemma 64 }
% 4.88/1.03 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(trolley8), n1), fresh55(initiates(pull(agent9, trolley9), spinning(trolley9), n0), true2, pull(agent9, trolley9), n0, spinning(trolley9)))
% 4.88/1.03 = { by axiom 61 (happens_holds) }
% 4.88/1.03 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(trolley8), n1), fresh54(happens(pull(agent9, trolley9), n0), true2, n0, spinning(trolley9)))
% 4.88/1.03 = { by axiom 20 (happens_all_defn_17) R->L }
% 4.88/1.03 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(trolley8), n1), fresh54(fresh74(n0, n0, pull(agent9, trolley9), n0), true2, n0, spinning(trolley9)))
% 4.88/1.03 = { by axiom 50 (happens_all_defn_17) }
% 4.88/1.03 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(trolley8), n1), fresh54(fresh73(pull(agent9, trolley9), pull(agent9, trolley9), pull(agent9, trolley9), n0), true2, n0, spinning(trolley9)))
% 4.88/1.03 = { by axiom 21 (happens_all_defn_17) }
% 4.88/1.03 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(trolley8), n1), fresh54(true2, true2, n0, spinning(trolley9)))
% 4.88/1.03 = { by axiom 38 (happens_holds) }
% 4.88/1.03 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(trolley8), n1), true2)
% 4.88/1.03 = { by axiom 1 (plus0_1) R->L }
% 4.88/1.03 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(trolley8), n1), true2)
% 4.88/1.03 = { by axiom 40 (happens_holds) R->L }
% 4.88/1.03 tuple(fresh55(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(trolley8), n1), true2)
% 4.88/1.03 = { by lemma 63 R->L }
% 4.88/1.03 tuple(fresh55(fresh115(true2, true2, pull(agent1, trolley1), spinning(trolley1), n0, trolley1, agent1), 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(trolley8), n1), true2)
% 4.88/1.03 = { by axiom 2 (happens_all_defn) R->L }
% 4.88/1.03 tuple(fresh55(fresh115(fresh92(push(agent1, trolley1), push(agent1, trolley1), push(agent1, trolley1), n0), true2, pull(agent1, trolley1), spinning(trolley1), n0, trolley1, agent1), 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(trolley8), n1), true2)
% 4.88/1.03 = { by axiom 41 (happens_all_defn) R->L }
% 4.88/1.03 tuple(fresh55(fresh115(fresh91(n0, n0, push(agent1, trolley1), n0), true2, pull(agent1, trolley1), spinning(trolley1), n0, trolley1, agent1), 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(trolley8), n1), true2)
% 4.88/1.03 = { by axiom 3 (happens_all_defn) }
% 4.88/1.03 tuple(fresh55(fresh115(happens(push(agent1, trolley1), n0), true2, pull(agent1, trolley1), spinning(trolley1), n0, trolley1, agent1), 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(trolley8), n1), true2)
% 4.88/1.03 = { by lemma 64 }
% 4.88/1.03 tuple(fresh55(initiates(pull(agent1, trolley1), spinning(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(trolley8), n1), true2)
% 4.88/1.03 = { by axiom 61 (happens_holds) }
% 4.88/1.03 tuple(fresh54(happens(pull(agent1, 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(trolley8), n1), true2)
% 4.88/1.03 = { by axiom 36 (happens_all_defn_9) R->L }
% 4.88/1.03 tuple(fresh54(fresh57(n0, n0, pull(agent1, 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(trolley8), n1), true2)
% 4.88/1.03 = { by axiom 58 (happens_all_defn_9) }
% 4.88/1.03 tuple(fresh54(fresh56(pull(agent1, trolley1), pull(agent1, trolley1), pull(agent1, 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(trolley8), n1), true2)
% 4.88/1.03 = { by axiom 37 (happens_all_defn_9) }
% 4.88/1.03 tuple(fresh54(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(trolley8), n1), true2)
% 4.88/1.03 = { by axiom 38 (happens_holds) }
% 4.88/1.03 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(trolley8), n1), true2)
% 4.88/1.03 = { by axiom 1 (plus0_1) R->L }
% 4.88/1.03 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(trolley8), n1), true2)
% 4.88/1.03 = { by axiom 40 (happens_holds) R->L }
% 4.88/1.03 tuple(true2, fresh55(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(trolley8), n1), true2)
% 4.88/1.04 = { by lemma 63 R->L }
% 4.88/1.04 tuple(true2, fresh55(fresh115(true2, true2, pull(agent2, trolley2), spinning(trolley2), n0, trolley2, agent2), 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(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 5 (happens_all_defn_1) R->L }
% 4.88/1.04 tuple(true2, fresh55(fresh115(fresh89(push(agent2, trolley2), push(agent2, trolley2), push(agent2, trolley2), n0), true2, pull(agent2, trolley2), spinning(trolley2), n0, trolley2, agent2), 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(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 42 (happens_all_defn_1) R->L }
% 4.88/1.04 tuple(true2, fresh55(fresh115(fresh90(n0, n0, push(agent2, trolley2), n0), true2, pull(agent2, trolley2), spinning(trolley2), n0, trolley2, agent2), 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(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 4 (happens_all_defn_1) }
% 4.88/1.04 tuple(true2, fresh55(fresh115(happens(push(agent2, trolley2), n0), true2, pull(agent2, trolley2), spinning(trolley2), n0, trolley2, agent2), 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(trolley8), n1), true2)
% 4.88/1.04 = { by lemma 64 }
% 4.88/1.04 tuple(true2, fresh55(initiates(pull(agent2, trolley2), spinning(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(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 61 (happens_holds) }
% 4.88/1.04 tuple(true2, fresh54(happens(pull(agent2, 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(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 6 (happens_all_defn_10) R->L }
% 4.88/1.04 tuple(true2, fresh54(fresh88(n0, n0, pull(agent2, 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(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 43 (happens_all_defn_10) }
% 4.88/1.04 tuple(true2, fresh54(fresh87(pull(agent2, trolley2), pull(agent2, trolley2), pull(agent2, 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(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 7 (happens_all_defn_10) }
% 4.88/1.04 tuple(true2, fresh54(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(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 38 (happens_holds) }
% 4.88/1.04 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(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 1 (plus0_1) R->L }
% 4.88/1.04 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(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 40 (happens_holds) R->L }
% 4.88/1.04 tuple(true2, true2, fresh55(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(trolley8), n1), true2)
% 4.88/1.04 = { by lemma 63 R->L }
% 4.88/1.04 tuple(true2, true2, fresh55(fresh115(true2, true2, pull(agent3, trolley3), spinning(trolley3), n0, trolley3, agent3), 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(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 23 (happens_all_defn_2) R->L }
% 4.88/1.04 tuple(true2, true2, fresh55(fresh115(fresh71(push(agent3, trolley3), push(agent3, trolley3), push(agent3, trolley3), n0), true2, pull(agent3, trolley3), spinning(trolley3), n0, trolley3, agent3), 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(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 51 (happens_all_defn_2) R->L }
% 4.88/1.04 tuple(true2, true2, fresh55(fresh115(fresh72(n0, n0, push(agent3, trolley3), n0), true2, pull(agent3, trolley3), spinning(trolley3), n0, trolley3, agent3), 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(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 22 (happens_all_defn_2) }
% 4.88/1.04 tuple(true2, true2, fresh55(fresh115(happens(push(agent3, trolley3), n0), true2, pull(agent3, trolley3), spinning(trolley3), n0, trolley3, agent3), 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(trolley8), n1), true2)
% 4.88/1.04 = { by lemma 64 }
% 4.88/1.04 tuple(true2, true2, fresh55(initiates(pull(agent3, trolley3), spinning(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(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 61 (happens_holds) }
% 4.88/1.04 tuple(true2, true2, fresh54(happens(pull(agent3, trolley3), n0), true2, n0, spinning(trolley3)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 8 (happens_all_defn_11) R->L }
% 4.88/1.04 tuple(true2, true2, fresh54(fresh86(n0, n0, pull(agent3, trolley3), n0), true2, n0, spinning(trolley3)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 44 (happens_all_defn_11) }
% 4.88/1.04 tuple(true2, true2, fresh54(fresh85(pull(agent3, trolley3), pull(agent3, trolley3), pull(agent3, trolley3), n0), true2, n0, spinning(trolley3)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 9 (happens_all_defn_11) }
% 4.88/1.04 tuple(true2, true2, fresh54(true2, true2, n0, spinning(trolley3)), holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 38 (happens_holds) }
% 4.88/1.04 tuple(true2, true2, true2, holdsAt(spinning(trolley4), n1), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 1 (plus0_1) R->L }
% 4.88/1.04 tuple(true2, true2, true2, holdsAt(spinning(trolley4), plus(n0, n1)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 40 (happens_holds) R->L }
% 4.88/1.04 tuple(true2, true2, true2, fresh55(true2, true2, pull(agent4, trolley4), n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by lemma 63 R->L }
% 4.88/1.04 tuple(true2, true2, true2, fresh55(fresh115(true2, true2, pull(agent4, trolley4), spinning(trolley4), n0, trolley4, agent4), true2, pull(agent4, trolley4), n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 25 (happens_all_defn_3) R->L }
% 4.88/1.04 tuple(true2, true2, true2, fresh55(fresh115(fresh69(push(agent4, trolley4), push(agent4, trolley4), push(agent4, trolley4), n0), true2, pull(agent4, trolley4), spinning(trolley4), n0, trolley4, agent4), true2, pull(agent4, trolley4), n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 52 (happens_all_defn_3) R->L }
% 4.88/1.04 tuple(true2, true2, true2, fresh55(fresh115(fresh70(n0, n0, push(agent4, trolley4), n0), true2, pull(agent4, trolley4), spinning(trolley4), n0, trolley4, agent4), true2, pull(agent4, trolley4), n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 24 (happens_all_defn_3) }
% 4.88/1.04 tuple(true2, true2, true2, fresh55(fresh115(happens(push(agent4, trolley4), n0), true2, pull(agent4, trolley4), spinning(trolley4), n0, trolley4, agent4), true2, pull(agent4, trolley4), n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by lemma 64 }
% 4.88/1.04 tuple(true2, true2, true2, fresh55(initiates(pull(agent4, trolley4), spinning(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), true2)
% 4.88/1.04 = { by axiom 61 (happens_holds) }
% 4.88/1.04 tuple(true2, true2, true2, fresh54(happens(pull(agent4, trolley4), n0), true2, n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 10 (happens_all_defn_12) R->L }
% 4.88/1.04 tuple(true2, true2, true2, fresh54(fresh84(n0, n0, pull(agent4, trolley4), n0), true2, n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 45 (happens_all_defn_12) }
% 4.88/1.04 tuple(true2, true2, true2, fresh54(fresh83(pull(agent4, trolley4), pull(agent4, trolley4), pull(agent4, trolley4), n0), true2, n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 11 (happens_all_defn_12) }
% 4.88/1.04 tuple(true2, true2, true2, fresh54(true2, true2, n0, spinning(trolley4)), holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 38 (happens_holds) }
% 4.88/1.04 tuple(true2, true2, true2, true2, holdsAt(spinning(trolley5), n1), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 1 (plus0_1) R->L }
% 4.88/1.04 tuple(true2, true2, true2, true2, holdsAt(spinning(trolley5), plus(n0, n1)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 40 (happens_holds) R->L }
% 4.88/1.04 tuple(true2, true2, true2, true2, fresh55(true2, true2, pull(agent5, trolley5), n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by lemma 63 R->L }
% 4.88/1.04 tuple(true2, true2, true2, true2, fresh55(fresh115(true2, true2, pull(agent5, trolley5), spinning(trolley5), n0, trolley5, agent5), true2, pull(agent5, trolley5), n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 27 (happens_all_defn_4) R->L }
% 4.88/1.04 tuple(true2, true2, true2, true2, fresh55(fresh115(fresh67(push(agent5, trolley5), push(agent5, trolley5), push(agent5, trolley5), n0), true2, pull(agent5, trolley5), spinning(trolley5), n0, trolley5, agent5), true2, pull(agent5, trolley5), n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 53 (happens_all_defn_4) R->L }
% 4.88/1.04 tuple(true2, true2, true2, true2, fresh55(fresh115(fresh68(n0, n0, push(agent5, trolley5), n0), true2, pull(agent5, trolley5), spinning(trolley5), n0, trolley5, agent5), true2, pull(agent5, trolley5), n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 26 (happens_all_defn_4) }
% 4.88/1.04 tuple(true2, true2, true2, true2, fresh55(fresh115(happens(push(agent5, trolley5), n0), true2, pull(agent5, trolley5), spinning(trolley5), n0, trolley5, agent5), true2, pull(agent5, trolley5), n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by lemma 64 }
% 4.88/1.04 tuple(true2, true2, true2, true2, fresh55(initiates(pull(agent5, trolley5), spinning(trolley5), n0), true2, pull(agent5, trolley5), n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 61 (happens_holds) }
% 4.88/1.04 tuple(true2, true2, true2, true2, fresh54(happens(pull(agent5, trolley5), n0), true2, n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 12 (happens_all_defn_13) R->L }
% 4.88/1.04 tuple(true2, true2, true2, true2, fresh54(fresh82(n0, n0, pull(agent5, trolley5), n0), true2, n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 46 (happens_all_defn_13) }
% 4.88/1.04 tuple(true2, true2, true2, true2, fresh54(fresh81(pull(agent5, trolley5), pull(agent5, trolley5), pull(agent5, trolley5), n0), true2, n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 13 (happens_all_defn_13) }
% 4.88/1.04 tuple(true2, true2, true2, true2, fresh54(true2, true2, n0, spinning(trolley5)), holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 38 (happens_holds) }
% 4.88/1.04 tuple(true2, true2, true2, true2, true2, holdsAt(spinning(trolley6), n1), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 1 (plus0_1) R->L }
% 4.88/1.04 tuple(true2, true2, true2, true2, true2, holdsAt(spinning(trolley6), plus(n0, n1)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 40 (happens_holds) R->L }
% 4.88/1.04 tuple(true2, true2, true2, true2, true2, fresh55(true2, true2, pull(agent6, trolley6), n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by lemma 63 R->L }
% 4.88/1.04 tuple(true2, true2, true2, true2, true2, fresh55(fresh115(true2, true2, pull(agent6, trolley6), spinning(trolley6), n0, trolley6, agent6), true2, pull(agent6, trolley6), n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 4.88/1.04 = { by axiom 29 (happens_all_defn_5) R->L }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, fresh55(fresh115(fresh65(push(agent6, trolley6), push(agent6, trolley6), push(agent6, trolley6), n0), true2, pull(agent6, trolley6), spinning(trolley6), n0, trolley6, agent6), true2, pull(agent6, trolley6), n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 54 (happens_all_defn_5) R->L }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, fresh55(fresh115(fresh66(n0, n0, push(agent6, trolley6), n0), true2, pull(agent6, trolley6), spinning(trolley6), n0, trolley6, agent6), true2, pull(agent6, trolley6), n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 28 (happens_all_defn_5) }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, fresh55(fresh115(happens(push(agent6, trolley6), n0), true2, pull(agent6, trolley6), spinning(trolley6), n0, trolley6, agent6), true2, pull(agent6, trolley6), n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by lemma 64 }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, fresh55(initiates(pull(agent6, trolley6), spinning(trolley6), n0), true2, pull(agent6, trolley6), n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 61 (happens_holds) }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, fresh54(happens(pull(agent6, trolley6), n0), true2, n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 14 (happens_all_defn_14) R->L }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, fresh54(fresh80(n0, n0, pull(agent6, trolley6), n0), true2, n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 47 (happens_all_defn_14) }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, fresh54(fresh79(pull(agent6, trolley6), pull(agent6, trolley6), pull(agent6, trolley6), n0), true2, n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 15 (happens_all_defn_14) }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, fresh54(true2, true2, n0, spinning(trolley6)), holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 38 (happens_holds) }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley7), n1), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 1 (plus0_1) R->L }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley7), plus(n0, n1)), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 40 (happens_holds) R->L }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, true2, fresh55(true2, true2, pull(agent7, trolley7), n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by lemma 63 R->L }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, true2, fresh55(fresh115(true2, true2, pull(agent7, trolley7), spinning(trolley7), n0, trolley7, agent7), true2, pull(agent7, trolley7), n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 31 (happens_all_defn_6) R->L }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, true2, fresh55(fresh115(fresh62(push(agent7, trolley7), push(agent7, trolley7), push(agent7, trolley7), n0), true2, pull(agent7, trolley7), spinning(trolley7), n0, trolley7, agent7), true2, pull(agent7, trolley7), n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 55 (happens_all_defn_6) R->L }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, true2, fresh55(fresh115(fresh63(n0, n0, push(agent7, trolley7), n0), true2, pull(agent7, trolley7), spinning(trolley7), n0, trolley7, agent7), true2, pull(agent7, trolley7), n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 30 (happens_all_defn_6) }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, true2, fresh55(fresh115(happens(push(agent7, trolley7), n0), true2, pull(agent7, trolley7), spinning(trolley7), n0, trolley7, agent7), true2, pull(agent7, trolley7), n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by lemma 64 }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, true2, fresh55(initiates(pull(agent7, trolley7), spinning(trolley7), n0), true2, pull(agent7, trolley7), n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 61 (happens_holds) }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, true2, fresh54(happens(pull(agent7, trolley7), n0), true2, n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 16 (happens_all_defn_15) R->L }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, true2, fresh54(fresh78(n0, n0, pull(agent7, trolley7), n0), true2, n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 48 (happens_all_defn_15) }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, true2, fresh54(fresh77(pull(agent7, trolley7), pull(agent7, trolley7), pull(agent7, trolley7), n0), true2, n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 17 (happens_all_defn_15) }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, true2, fresh54(true2, true2, n0, spinning(trolley7)), holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.04 = { by axiom 38 (happens_holds) }
% 5.36/1.04 tuple(true2, true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley8), n1), true2)
% 5.36/1.05 = { by axiom 1 (plus0_1) R->L }
% 5.36/1.05 tuple(true2, true2, true2, true2, true2, true2, true2, holdsAt(spinning(trolley8), plus(n0, n1)), true2)
% 5.36/1.05 = { by axiom 40 (happens_holds) R->L }
% 5.36/1.05 tuple(true2, true2, true2, true2, true2, true2, true2, fresh55(true2, true2, pull(agent8, trolley8), n0, spinning(trolley8)), true2)
% 5.36/1.05 = { by lemma 63 R->L }
% 5.36/1.05 tuple(true2, true2, true2, true2, true2, true2, true2, fresh55(fresh115(true2, true2, pull(agent8, trolley8), spinning(trolley8), n0, trolley8, agent8), true2, pull(agent8, trolley8), n0, spinning(trolley8)), true2)
% 5.36/1.05 = { by axiom 33 (happens_all_defn_7) R->L }
% 5.36/1.05 tuple(true2, true2, true2, true2, true2, true2, true2, fresh55(fresh115(fresh60(push(agent8, trolley8), push(agent8, trolley8), push(agent8, trolley8), n0), true2, pull(agent8, trolley8), spinning(trolley8), n0, trolley8, agent8), true2, pull(agent8, trolley8), n0, spinning(trolley8)), true2)
% 5.36/1.05 = { by axiom 56 (happens_all_defn_7) R->L }
% 5.36/1.05 tuple(true2, true2, true2, true2, true2, true2, true2, fresh55(fresh115(fresh61(n0, n0, push(agent8, trolley8), n0), true2, pull(agent8, trolley8), spinning(trolley8), n0, trolley8, agent8), true2, pull(agent8, trolley8), n0, spinning(trolley8)), true2)
% 5.36/1.05 = { by axiom 32 (happens_all_defn_7) }
% 5.36/1.05 tuple(true2, true2, true2, true2, true2, true2, true2, fresh55(fresh115(happens(push(agent8, trolley8), n0), true2, pull(agent8, trolley8), spinning(trolley8), n0, trolley8, agent8), true2, pull(agent8, trolley8), n0, spinning(trolley8)), true2)
% 5.36/1.05 = { by lemma 64 }
% 5.36/1.05 tuple(true2, true2, true2, true2, true2, true2, true2, fresh55(initiates(pull(agent8, trolley8), spinning(trolley8), n0), true2, pull(agent8, trolley8), n0, spinning(trolley8)), true2)
% 5.36/1.05 = { by axiom 61 (happens_holds) }
% 5.36/1.05 tuple(true2, true2, true2, true2, true2, true2, true2, fresh54(happens(pull(agent8, trolley8), n0), true2, n0, spinning(trolley8)), true2)
% 5.36/1.05 = { by axiom 18 (happens_all_defn_16) R->L }
% 5.36/1.05 tuple(true2, true2, true2, true2, true2, true2, true2, fresh54(fresh76(n0, n0, pull(agent8, trolley8), n0), true2, n0, spinning(trolley8)), true2)
% 5.36/1.05 = { by axiom 49 (happens_all_defn_16) }
% 5.36/1.05 tuple(true2, true2, true2, true2, true2, true2, true2, fresh54(fresh75(pull(agent8, trolley8), pull(agent8, trolley8), pull(agent8, trolley8), n0), true2, n0, spinning(trolley8)), true2)
% 5.36/1.05 = { by axiom 19 (happens_all_defn_16) }
% 5.36/1.05 tuple(true2, true2, true2, true2, true2, true2, true2, fresh54(true2, true2, n0, spinning(trolley8)), true2)
% 5.36/1.05 = { by axiom 38 (happens_holds) }
% 5.36/1.05 tuple(true2, true2, true2, true2, true2, true2, true2, true2, true2)
% 5.36/1.05 % SZS output end Proof
% 5.36/1.05
% 5.36/1.05 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------