%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CSR022+1 : TPTP v9.0.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 : Sat Jun 21 05:01:14 AM UTC 2025
% Result : Theorem 0.48s 0.65s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : CSR022+1 : TPTP v9.0.0. Bugfixed v3.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 12:26:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.48/0.65 % SZS status Theorem
% 0.48/0.65 % SZS output start Proof
% 0.48/0.65 tff(terminates_type, type, (
% 0.48/0.65 terminates: ( $i * $i * $i ) > $o)).
% 0.48/0.65 tff(n2_type, type, (
% 0.48/0.65 n2: $i)).
% 0.48/0.65 tff(forwards_type, type, (
% 0.48/0.65 forwards: $i)).
% 0.48/0.65 tff(pull_type, type, (
% 0.48/0.65 pull: $i)).
% 0.48/0.65 tff(happens_type, type, (
% 0.48/0.65 happens: ( $i * $i ) > $o)).
% 0.48/0.65 tff(n0_type, type, (
% 0.48/0.65 n0: $i)).
% 0.48/0.65 tff(push_type, type, (
% 0.48/0.65 push: $i)).
% 0.48/0.65 tff(n1_type, type, (
% 0.48/0.65 n1: $i)).
% 0.48/0.65 tff(holdsAt_type, type, (
% 0.48/0.65 holdsAt: ( $i * $i ) > $o)).
% 0.48/0.65 tff(plus_type, type, (
% 0.48/0.65 plus: ( $i * $i ) > $i)).
% 0.48/0.65 tff(n3_type, type, (
% 0.48/0.65 n3: $i)).
% 0.48/0.65 tff(spinning_type, type, (
% 0.48/0.65 spinning: $i)).
% 0.48/0.65 tff(backwards_type, type, (
% 0.48/0.65 backwards: $i)).
% 0.48/0.65 tff(1,assumption,(~happens(pull, n2)), introduced(assumption)).
% 0.48/0.65 tff(2,plain,
% 0.48/0.65 (^[Event: $i, Time: $i] : refl((happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))))) <=> (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(3,plain,
% 0.48/0.65 (![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[2])).
% 0.48/0.65 tff(4,plain,
% 0.48/0.65 (^[Event: $i, Time: $i] : rewrite((happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)))) <=> (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(5,plain,
% 0.48/0.65 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[4])).
% 0.48/0.65 tff(6,plain,
% 0.48/0.65 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(7,plain,
% 0.48/0.65 (^[Event: $i, Time: $i] : rewrite((happens(Event, Time) <=> (((((Event = push) & (Time = n0)) | ((Event = pull) & (Time = n1))) | ((Event = pull) & (Time = n2))) | ((Event = push) & (Time = n2)))) <=> (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(8,plain,
% 0.48/0.65 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((((Event = push) & (Time = n0)) | ((Event = pull) & (Time = n1))) | ((Event = pull) & (Time = n2))) | ((Event = push) & (Time = n2)))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[7])).
% 0.48/0.65 tff(9,axiom,(![Event: $i, Time: $i] : (happens(Event, Time) <=> (((((Event = push) & (Time = n0)) | ((Event = pull) & (Time = n1))) | ((Event = pull) & (Time = n2))) | ((Event = push) & (Time = n2))))), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax','happens_all_defn')).
% 0.48/0.65 tff(10,plain,
% 0.48/0.65 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.48/0.65 tff(11,plain,
% 0.48/0.65 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.48/0.65 tff(12,plain,(
% 0.48/0.65 ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 0.48/0.65 inference(skolemize,[status(sab)],[11])).
% 0.48/0.65 tff(13,plain,
% 0.48/0.65 (![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.48/0.65 tff(14,plain,
% 0.48/0.65 (![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.48/0.65 tff(15,plain,
% 0.48/0.65 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | happens(pull, n2)) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | happens(pull, n2))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(16,plain,
% 0.48/0.65 ((happens(pull, n2) <=> $true) <=> happens(pull, n2)),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(17,plain,
% 0.48/0.65 (((pull = push) | $true | (n2 = n1) | (~((~(n2 = n0)) | (~(pull = push))))) <=> $true),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(18,plain,
% 0.48/0.65 ((~((~(pull = push)) | (~(n2 = n0)))) <=> (~((~(n2 = n0)) | (~(pull = push))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(19,plain,
% 0.48/0.65 ((~(~(n2 = n1))) <=> (n2 = n1)),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(20,plain,
% 0.48/0.65 (($false | (~(n2 = n1))) <=> (~(n2 = n1))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(21,plain,
% 0.48/0.65 ((~$true) <=> $false),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(22,plain,
% 0.48/0.65 ((pull = pull) <=> $true),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(23,plain,
% 0.48/0.65 ((~(pull = pull)) <=> (~$true)),
% 0.48/0.65 inference(monotonicity,[status(thm)],[22])).
% 0.48/0.65 tff(24,plain,
% 0.48/0.65 ((~(pull = pull)) <=> $false),
% 0.48/0.65 inference(transitivity,[status(thm)],[23, 21])).
% 0.48/0.65 tff(25,plain,
% 0.48/0.65 (((~(pull = pull)) | (~(n2 = n1))) <=> ($false | (~(n2 = n1)))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[24])).
% 0.48/0.65 tff(26,plain,
% 0.48/0.65 (((~(pull = pull)) | (~(n2 = n1))) <=> (~(n2 = n1))),
% 0.48/0.65 inference(transitivity,[status(thm)],[25, 20])).
% 0.48/0.65 tff(27,plain,
% 0.48/0.65 ((~((~(pull = pull)) | (~(n2 = n1)))) <=> (~(~(n2 = n1)))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[26])).
% 0.48/0.65 tff(28,plain,
% 0.48/0.65 ((~((~(pull = pull)) | (~(n2 = n1)))) <=> (n2 = n1)),
% 0.48/0.65 inference(transitivity,[status(thm)],[27, 19])).
% 0.48/0.65 tff(29,plain,
% 0.48/0.65 ((~$false) <=> $true),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(30,plain,
% 0.48/0.65 (($false | $false) <=> $false),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(31,plain,
% 0.48/0.65 ((n2 = n2) <=> $true),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(32,plain,
% 0.48/0.65 ((~(n2 = n2)) <=> (~$true)),
% 0.48/0.65 inference(monotonicity,[status(thm)],[31])).
% 0.48/0.65 tff(33,plain,
% 0.48/0.65 ((~(n2 = n2)) <=> $false),
% 0.48/0.65 inference(transitivity,[status(thm)],[32, 21])).
% 0.48/0.65 tff(34,plain,
% 0.48/0.65 (((~(n2 = n2)) | (~(pull = pull))) <=> ($false | $false)),
% 0.48/0.65 inference(monotonicity,[status(thm)],[33, 24])).
% 0.48/0.65 tff(35,plain,
% 0.48/0.65 (((~(n2 = n2)) | (~(pull = pull))) <=> $false),
% 0.48/0.65 inference(transitivity,[status(thm)],[34, 30])).
% 0.48/0.65 tff(36,plain,
% 0.48/0.65 ((~((~(n2 = n2)) | (~(pull = pull)))) <=> (~$false)),
% 0.48/0.65 inference(monotonicity,[status(thm)],[35])).
% 0.48/0.65 tff(37,plain,
% 0.48/0.65 ((~((~(n2 = n2)) | (~(pull = pull)))) <=> $true),
% 0.48/0.65 inference(transitivity,[status(thm)],[36, 29])).
% 0.48/0.65 tff(38,plain,
% 0.48/0.65 ((~(~(pull = push))) <=> (pull = push)),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(39,plain,
% 0.48/0.65 (((~(pull = push)) | $false) <=> (~(pull = push))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(40,plain,
% 0.48/0.65 (((~(pull = push)) | (~(n2 = n2))) <=> ((~(pull = push)) | $false)),
% 0.48/0.65 inference(monotonicity,[status(thm)],[33])).
% 0.48/0.65 tff(41,plain,
% 0.48/0.65 (((~(pull = push)) | (~(n2 = n2))) <=> (~(pull = push))),
% 0.48/0.65 inference(transitivity,[status(thm)],[40, 39])).
% 0.48/0.65 tff(42,plain,
% 0.48/0.65 ((~((~(pull = push)) | (~(n2 = n2)))) <=> (~(~(pull = push)))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[41])).
% 0.48/0.65 tff(43,plain,
% 0.48/0.65 ((~((~(pull = push)) | (~(n2 = n2)))) <=> (pull = push)),
% 0.48/0.65 inference(transitivity,[status(thm)],[42, 38])).
% 0.48/0.65 tff(44,plain,
% 0.48/0.65 (((~((~(pull = push)) | (~(n2 = n2)))) | (~((~(n2 = n2)) | (~(pull = pull)))) | (~((~(pull = pull)) | (~(n2 = n1)))) | (~((~(pull = push)) | (~(n2 = n0))))) <=> ((pull = push) | $true | (n2 = n1) | (~((~(n2 = n0)) | (~(pull = push)))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[43, 37, 28, 18])).
% 0.48/0.65 tff(45,plain,
% 0.48/0.65 (((~((~(pull = push)) | (~(n2 = n2)))) | (~((~(n2 = n2)) | (~(pull = pull)))) | (~((~(pull = pull)) | (~(n2 = n1)))) | (~((~(pull = push)) | (~(n2 = n0))))) <=> $true),
% 0.48/0.65 inference(transitivity,[status(thm)],[44, 17])).
% 0.48/0.65 tff(46,plain,
% 0.48/0.65 ((happens(pull, n2) <=> ((~((~(pull = push)) | (~(n2 = n2)))) | (~((~(n2 = n2)) | (~(pull = pull)))) | (~((~(pull = pull)) | (~(n2 = n1)))) | (~((~(pull = push)) | (~(n2 = n0)))))) <=> (happens(pull, n2) <=> $true)),
% 0.48/0.65 inference(monotonicity,[status(thm)],[45])).
% 0.48/0.65 tff(47,plain,
% 0.48/0.65 ((happens(pull, n2) <=> ((~((~(pull = push)) | (~(n2 = n2)))) | (~((~(n2 = n2)) | (~(pull = pull)))) | (~((~(pull = pull)) | (~(n2 = n1)))) | (~((~(pull = push)) | (~(n2 = n0)))))) <=> happens(pull, n2)),
% 0.48/0.65 inference(transitivity,[status(thm)],[46, 16])).
% 0.48/0.65 tff(48,plain,
% 0.48/0.65 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | (happens(pull, n2) <=> ((~((~(pull = push)) | (~(n2 = n2)))) | (~((~(n2 = n2)) | (~(pull = pull)))) | (~((~(pull = pull)) | (~(n2 = n1)))) | (~((~(pull = push)) | (~(n2 = n0))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | happens(pull, n2))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[47])).
% 0.48/0.65 tff(49,plain,
% 0.48/0.65 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | (happens(pull, n2) <=> ((~((~(pull = push)) | (~(n2 = n2)))) | (~((~(n2 = n2)) | (~(pull = pull)))) | (~((~(pull = pull)) | (~(n2 = n1)))) | (~((~(pull = push)) | (~(n2 = n0))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | happens(pull, n2))),
% 0.48/0.65 inference(transitivity,[status(thm)],[48, 15])).
% 0.48/0.65 tff(50,plain,
% 0.48/0.65 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | (happens(pull, n2) <=> ((~((~(pull = push)) | (~(n2 = n2)))) | (~((~(n2 = n2)) | (~(pull = pull)))) | (~((~(pull = pull)) | (~(n2 = n1)))) | (~((~(pull = push)) | (~(n2 = n0))))))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(51,plain,
% 0.48/0.65 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | happens(pull, n2)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.48/0.65 tff(52,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[51, 14, 1])).
% 0.48/0.65 tff(53,plain,(happens(pull, n2)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(54,plain,
% 0.48/0.65 ((plus(n1, n2) = n3) <=> (plus(n1, n2) = n3)),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(55,axiom,(plus(n1, n2) = n3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus1_2')).
% 0.48/0.65 tff(56,plain,
% 0.48/0.65 (plus(n1, n2) = n3),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.48/0.65 tff(57,plain,
% 0.48/0.65 (^[X: $i, Y: $i] : refl((plus(X, Y) = plus(Y, X)) <=> (plus(X, Y) = plus(Y, X)))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(58,plain,
% 0.48/0.65 (![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X)) <=> ![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[57])).
% 0.48/0.65 tff(59,plain,
% 0.48/0.65 (![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X)) <=> ![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(60,axiom,(![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetry_of_plus')).
% 0.48/0.65 tff(61,plain,
% 0.48/0.65 (![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.48/0.65 tff(62,plain,(
% 0.48/0.65 ![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 0.48/0.65 inference(skolemize,[status(sab)],[61])).
% 0.48/0.65 tff(63,plain,
% 0.48/0.65 (![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.48/0.65 tff(64,plain,
% 0.48/0.65 ((~![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))) | (plus(n1, n2) = plus(n2, n1))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(65,plain,
% 0.48/0.65 (plus(n1, n2) = plus(n2, n1)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.48/0.65 tff(66,plain,
% 0.48/0.65 (plus(n2, n1) = plus(n1, n2)),
% 0.48/0.66 inference(symmetry,[status(thm)],[65])).
% 0.48/0.66 tff(67,plain,
% 0.48/0.66 (plus(n2, n1) = n3),
% 0.48/0.66 inference(transitivity,[status(thm)],[66, 56])).
% 0.48/0.66 tff(68,plain,
% 0.48/0.66 (holdsAt(forwards, plus(n2, n1)) <=> holdsAt(forwards, n3)),
% 0.48/0.66 inference(monotonicity,[status(thm)],[67])).
% 0.48/0.66 tff(69,plain,
% 0.48/0.66 (holdsAt(forwards, n3) <=> holdsAt(forwards, plus(n2, n1))),
% 0.48/0.66 inference(symmetry,[status(thm)],[68])).
% 0.48/0.66 tff(70,plain,
% 0.48/0.66 (holdsAt(forwards, n3) <=> holdsAt(forwards, n3)),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(71,plain,
% 0.48/0.66 ((~(~holdsAt(forwards, n3))) <=> holdsAt(forwards, n3)),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(72,axiom,(~(~holdsAt(forwards, n3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_forwards_3')).
% 0.48/0.66 tff(73,plain,
% 0.48/0.66 (holdsAt(forwards, n3)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.48/0.66 tff(74,plain,
% 0.48/0.66 (holdsAt(forwards, n3)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[73, 70])).
% 0.48/0.66 tff(75,plain,
% 0.48/0.66 (holdsAt(forwards, plus(n2, n1))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[74, 69])).
% 0.48/0.66 tff(76,plain,
% 0.48/0.66 (^[Event: $i, Time: $i, Fluent: $i] : refl(((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time))) <=> ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(77,plain,
% 0.48/0.66 (![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[76])).
% 0.48/0.66 tff(78,plain,
% 0.48/0.66 (^[Event: $i, Time: $i, Fluent: $i] : trans(monotonicity(trans(monotonicity(rewrite((happens(Event, Time) & terminates(Event, Fluent, Time)) <=> (~((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))))), ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) <=> (~(~((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))))))), rewrite((~(~((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))))) <=> ((~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))), ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) <=> ((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))))), (((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))) <=> (((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))))), rewrite((((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))) <=> ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))), (((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))) <=> ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(79,plain,
% 0.48/0.66 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[78])).
% 0.48/0.66 tff(80,plain,
% 0.48/0.66 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(81,plain,
% 0.48/0.66 (^[Event: $i, Time: $i, Fluent: $i] : rewrite(((happens(Event, Time) & terminates(Event, Fluent, Time)) => (~holdsAt(Fluent, plus(Time, n1)))) <=> ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(82,plain,
% 0.48/0.66 (![Event: $i, Time: $i, Fluent: $i] : ((happens(Event, Time) & terminates(Event, Fluent, Time)) => (~holdsAt(Fluent, plus(Time, n1)))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1))))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[81])).
% 0.48/0.66 tff(83,axiom,(![Event: $i, Time: $i, Fluent: $i] : ((happens(Event, Time) & terminates(Event, Fluent, Time)) => (~holdsAt(Fluent, plus(Time, n1))))), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+0.ax','happens_terminates_not_holds')).
% 0.48/0.66 tff(84,plain,
% 0.48/0.66 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.48/0.66 tff(85,plain,
% 0.48/0.66 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.48/0.66 tff(86,plain,(
% 0.48/0.66 ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1))))),
% 0.48/0.66 inference(skolemize,[status(sab)],[85])).
% 0.48/0.66 tff(87,plain,
% 0.48/0.66 (![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.48/0.66 tff(88,plain,
% 0.48/0.66 (![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[87, 77])).
% 0.48/0.66 tff(89,plain,
% 0.48/0.66 (((~![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))) | ((~holdsAt(forwards, plus(n2, n1))) | (~happens(pull, n2)) | (~terminates(pull, forwards, n2)))) <=> ((~![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))) | (~holdsAt(forwards, plus(n2, n1))) | (~happens(pull, n2)) | (~terminates(pull, forwards, n2)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(90,plain,
% 0.48/0.66 ((~![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))) | ((~holdsAt(forwards, plus(n2, n1))) | (~happens(pull, n2)) | (~terminates(pull, forwards, n2)))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(91,plain,
% 0.48/0.66 ((~![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))) | (~holdsAt(forwards, plus(n2, n1))) | (~happens(pull, n2)) | (~terminates(pull, forwards, n2))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.48/0.66 tff(92,plain,
% 0.48/0.66 (~terminates(pull, forwards, n2)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[91, 88, 75, 53])).
% 0.48/0.66 tff(93,plain,
% 0.48/0.66 (^[Event: $i, Fluent: $i, Time: $i] : refl((terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning)))))) <=> (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning)))))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(94,plain,
% 0.48/0.66 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning)))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[93])).
% 0.48/0.66 tff(95,plain,
% 0.48/0.66 (^[Event: $i, Fluent: $i, Time: $i] : rewrite((terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time))))) <=> (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning)))))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(96,plain,
% 0.48/0.66 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[95])).
% 0.48/0.66 tff(97,plain,
% 0.48/0.66 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time)))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(98,plain,
% 0.48/0.66 (^[Event: $i, Fluent: $i, Time: $i] : rewrite((terminates(Event, Fluent, Time) <=> ((((((((Event = push) & (Fluent = backwards)) & (~happens(pull, Time))) | (((Event = pull) & (Fluent = forwards)) & (~happens(push, Time)))) | (((Event = pull) & (Fluent = forwards)) & happens(push, Time))) | (((Event = pull) & (Fluent = backwards)) & happens(push, Time))) | (((Event = push) & (Fluent = spinning)) & (~happens(pull, Time)))) | (((Event = pull) & (Fluent = spinning)) & (~happens(push, Time))))) <=> (terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time))))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(99,plain,
% 0.48/0.66 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((((((((Event = push) & (Fluent = backwards)) & (~happens(pull, Time))) | (((Event = pull) & (Fluent = forwards)) & (~happens(push, Time)))) | (((Event = pull) & (Fluent = forwards)) & happens(push, Time))) | (((Event = pull) & (Fluent = backwards)) & happens(push, Time))) | (((Event = push) & (Fluent = spinning)) & (~happens(pull, Time)))) | (((Event = pull) & (Fluent = spinning)) & (~happens(push, Time))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time)))))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[98])).
% 0.48/0.66 tff(100,axiom,(![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((((((((Event = push) & (Fluent = backwards)) & (~happens(pull, Time))) | (((Event = pull) & (Fluent = forwards)) & (~happens(push, Time)))) | (((Event = pull) & (Fluent = forwards)) & happens(push, Time))) | (((Event = pull) & (Fluent = backwards)) & happens(push, Time))) | (((Event = push) & (Fluent = spinning)) & (~happens(pull, Time)))) | (((Event = pull) & (Fluent = spinning)) & (~happens(push, Time)))))), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax','terminates_all_defn')).
% 0.48/0.66 tff(101,plain,
% 0.48/0.66 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time)))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.48/0.66 tff(102,plain,
% 0.48/0.66 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time)))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.48/0.66 tff(103,plain,(
% 0.48/0.66 ![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time)))))),
% 0.48/0.66 inference(skolemize,[status(sab)],[102])).
% 0.48/0.66 tff(104,plain,
% 0.48/0.66 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.48/0.66 tff(105,plain,
% 0.48/0.66 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[104, 94])).
% 0.48/0.66 tff(106,plain,
% 0.48/0.66 (((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))) | terminates(pull, forwards, n2)) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))) | terminates(pull, forwards, n2))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(107,plain,
% 0.48/0.66 ((terminates(pull, forwards, n2) <=> $true) <=> terminates(pull, forwards, n2)),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(108,plain,
% 0.48/0.66 (((~((~(forwards = backwards)) | happens(pull, n2) | (~(pull = push)))) | (~happens(push, n2)) | happens(push, n2) | (~((~(forwards = backwards)) | (~happens(push, n2)))) | (~((~(forwards = spinning)) | happens(pull, n2) | (~(pull = push)))) | (~((~(forwards = spinning)) | happens(push, n2)))) <=> $true),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(109,plain,
% 0.48/0.66 ((~(happens(push, n2) | (~(pull = pull)) | (~(forwards = spinning)))) <=> (~((~(forwards = spinning)) | happens(push, n2)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(110,plain,
% 0.48/0.66 ((~(happens(pull, n2) | (~(pull = push)) | (~(forwards = spinning)))) <=> (~((~(forwards = spinning)) | happens(pull, n2) | (~(pull = push))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(111,plain,
% 0.48/0.66 ((~((~happens(push, n2)) | (~(pull = pull)) | (~(forwards = backwards)))) <=> (~((~(forwards = backwards)) | (~happens(push, n2))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(112,plain,
% 0.48/0.66 ((~(~happens(push, n2))) <=> happens(push, n2)),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(113,plain,
% 0.48/0.66 (((~happens(push, n2)) | $false | $false) <=> (~happens(push, n2))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(114,plain,
% 0.48/0.66 ((forwards = forwards) <=> $true),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(115,plain,
% 0.48/0.66 ((~(forwards = forwards)) <=> (~$true)),
% 0.48/0.66 inference(monotonicity,[status(thm)],[114])).
% 0.48/0.66 tff(116,plain,
% 0.48/0.66 ((~(forwards = forwards)) <=> $false),
% 0.48/0.66 inference(transitivity,[status(thm)],[115, 21])).
% 0.48/0.66 tff(117,plain,
% 0.48/0.66 (((~happens(push, n2)) | (~(forwards = forwards)) | (~(pull = pull))) <=> ((~happens(push, n2)) | $false | $false)),
% 0.48/0.66 inference(monotonicity,[status(thm)],[116, 24])).
% 0.48/0.66 tff(118,plain,
% 0.48/0.66 (((~happens(push, n2)) | (~(forwards = forwards)) | (~(pull = pull))) <=> (~happens(push, n2))),
% 0.48/0.66 inference(transitivity,[status(thm)],[117, 113])).
% 0.48/0.66 tff(119,plain,
% 0.48/0.66 ((~((~happens(push, n2)) | (~(forwards = forwards)) | (~(pull = pull)))) <=> (~(~happens(push, n2)))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[118])).
% 0.48/0.66 tff(120,plain,
% 0.48/0.66 ((~((~happens(push, n2)) | (~(forwards = forwards)) | (~(pull = pull)))) <=> happens(push, n2)),
% 0.48/0.66 inference(transitivity,[status(thm)],[119, 112])).
% 0.48/0.66 tff(121,plain,
% 0.48/0.66 ((~(happens(push, n2) | (~(forwards = forwards)) | (~(pull = pull)))) <=> (~happens(push, n2))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(122,plain,
% 0.48/0.66 ((~(happens(pull, n2) | (~(pull = push)) | (~(forwards = backwards)))) <=> (~((~(forwards = backwards)) | happens(pull, n2) | (~(pull = push))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(123,plain,
% 0.48/0.66 (((~(happens(pull, n2) | (~(pull = push)) | (~(forwards = backwards)))) | (~(happens(push, n2) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n2)) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n2)) | (~(pull = pull)) | (~(forwards = backwards)))) | (~(happens(pull, n2) | (~(pull = push)) | (~(forwards = spinning)))) | (~(happens(push, n2) | (~(pull = pull)) | (~(forwards = spinning))))) <=> ((~((~(forwards = backwards)) | happens(pull, n2) | (~(pull = push)))) | (~happens(push, n2)) | happens(push, n2) | (~((~(forwards = backwards)) | (~happens(push, n2)))) | (~((~(forwards = spinning)) | happens(pull, n2) | (~(pull = push)))) | (~((~(forwards = spinning)) | happens(push, n2))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[122, 121, 120, 111, 110, 109])).
% 0.48/0.66 tff(124,plain,
% 0.48/0.66 (((~(happens(pull, n2) | (~(pull = push)) | (~(forwards = backwards)))) | (~(happens(push, n2) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n2)) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n2)) | (~(pull = pull)) | (~(forwards = backwards)))) | (~(happens(pull, n2) | (~(pull = push)) | (~(forwards = spinning)))) | (~(happens(push, n2) | (~(pull = pull)) | (~(forwards = spinning))))) <=> $true),
% 0.48/0.67 inference(transitivity,[status(thm)],[123, 108])).
% 0.48/0.67 tff(125,plain,
% 0.48/0.67 ((terminates(pull, forwards, n2) <=> ((~(happens(pull, n2) | (~(pull = push)) | (~(forwards = backwards)))) | (~(happens(push, n2) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n2)) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n2)) | (~(pull = pull)) | (~(forwards = backwards)))) | (~(happens(pull, n2) | (~(pull = push)) | (~(forwards = spinning)))) | (~(happens(push, n2) | (~(pull = pull)) | (~(forwards = spinning)))))) <=> (terminates(pull, forwards, n2) <=> $true)),
% 0.48/0.67 inference(monotonicity,[status(thm)],[124])).
% 0.48/0.67 tff(126,plain,
% 0.48/0.67 ((terminates(pull, forwards, n2) <=> ((~(happens(pull, n2) | (~(pull = push)) | (~(forwards = backwards)))) | (~(happens(push, n2) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n2)) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n2)) | (~(pull = pull)) | (~(forwards = backwards)))) | (~(happens(pull, n2) | (~(pull = push)) | (~(forwards = spinning)))) | (~(happens(push, n2) | (~(pull = pull)) | (~(forwards = spinning)))))) <=> terminates(pull, forwards, n2)),
% 0.48/0.67 inference(transitivity,[status(thm)],[125, 107])).
% 0.48/0.67 tff(127,plain,
% 0.48/0.67 (((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (terminates(pull, forwards, n2) <=> ((~(happens(pull, n2) | (~(pull = push)) | (~(forwards = backwards)))) | (~(happens(push, n2) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n2)) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n2)) | (~(pull = pull)) | (~(forwards = backwards)))) | (~(happens(pull, n2) | (~(pull = push)) | (~(forwards = spinning)))) | (~(happens(push, n2) | (~(pull = pull)) | (~(forwards = spinning))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))) | terminates(pull, forwards, n2))),
% 0.48/0.67 inference(monotonicity,[status(thm)],[126])).
% 0.48/0.67 tff(128,plain,
% 0.48/0.67 (((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (terminates(pull, forwards, n2) <=> ((~(happens(pull, n2) | (~(pull = push)) | (~(forwards = backwards)))) | (~(happens(push, n2) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n2)) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n2)) | (~(pull = pull)) | (~(forwards = backwards)))) | (~(happens(pull, n2) | (~(pull = push)) | (~(forwards = spinning)))) | (~(happens(push, n2) | (~(pull = pull)) | (~(forwards = spinning))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))) | terminates(pull, forwards, n2))),
% 0.48/0.67 inference(transitivity,[status(thm)],[127, 106])).
% 0.48/0.67 tff(129,plain,
% 0.48/0.67 ((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (terminates(pull, forwards, n2) <=> ((~(happens(pull, n2) | (~(pull = push)) | (~(forwards = backwards)))) | (~(happens(push, n2) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n2)) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n2)) | (~(pull = pull)) | (~(forwards = backwards)))) | (~(happens(pull, n2) | (~(pull = push)) | (~(forwards = spinning)))) | (~(happens(push, n2) | (~(pull = pull)) | (~(forwards = spinning))))))),
% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
% 0.48/0.67 tff(130,plain,
% 0.48/0.67 ((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))) | terminates(pull, forwards, n2)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.48/0.67 tff(131,plain,
% 0.48/0.67 ($false),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[130, 105, 92])).
% 0.48/0.67 % SZS output end Proof
% 0.48/0.67 % E exiting
%------------------------------------------------------------------------------