TSTP Solution File: CSR009+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CSR009+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 : Tue Sep 20 14:27:00 EDT 2022
% Result : Theorem 2.17s 1.66s
% Output : Proof 2.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : CSR009+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 16:08:35 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 2.17/1.66 % SZS status Theorem
% 2.17/1.66 % SZS output start Proof
% 2.17/1.66 tff(overflow_type, type, (
% 2.17/1.66 overflow: $i)).
% 2.17/1.66 tff(tptp_fun_Event_7_type, type, (
% 2.17/1.66 tptp_fun_Event_7: ( $i * $i ) > $i)).
% 2.17/1.66 tff(tptp_fun_Height_10_type, type, (
% 2.17/1.66 tptp_fun_Height_10: ( $i * $i ) > $i)).
% 2.17/1.66 tff(tapOn_type, type, (
% 2.17/1.66 tapOn: $i)).
% 2.17/1.66 tff(waterLevel_type, type, (
% 2.17/1.66 waterLevel: $i > $i)).
% 2.17/1.66 tff(filling_type, type, (
% 2.17/1.66 filling: $i)).
% 2.17/1.66 tff(n1_type, type, (
% 2.17/1.66 n1: $i)).
% 2.17/1.66 tff(holdsAt_type, type, (
% 2.17/1.66 holdsAt: ( $i * $i ) > $o)).
% 2.17/1.66 tff(plus_type, type, (
% 2.17/1.66 plus: ( $i * $i ) > $i)).
% 2.17/1.66 tff(n0_type, type, (
% 2.17/1.66 n0: $i)).
% 2.17/1.66 tff(happens_type, type, (
% 2.17/1.66 happens: ( $i * $i ) > $o)).
% 2.17/1.66 tff(stoppedIn_type, type, (
% 2.17/1.66 stoppedIn: ( $i * $i * $i ) > $o)).
% 2.17/1.66 tff(terminates_type, type, (
% 2.17/1.66 terminates: ( $i * $i * $i ) > $o)).
% 2.17/1.66 tff(tptp_fun_Time_0_type, type, (
% 2.17/1.66 tptp_fun_Time_0: ( $i * $i * $i ) > $i)).
% 2.17/1.66 tff(tptp_fun_Event_1_type, type, (
% 2.17/1.66 tptp_fun_Event_1: ( $i * $i * $i ) > $i)).
% 2.17/1.66 tff(less_type, type, (
% 2.17/1.66 less: ( $i * $i ) > $o)).
% 2.17/1.66 tff(less_or_equal_type, type, (
% 2.17/1.66 less_or_equal: ( $i * $i ) > $o)).
% 2.17/1.66 tff(trajectory_type, type, (
% 2.17/1.66 trajectory: ( $i * $i * $i * $i ) > $o)).
% 2.17/1.66 tff(releases_type, type, (
% 2.17/1.66 releases: ( $i * $i * $i ) > $o)).
% 2.17/1.66 tff(initiates_type, type, (
% 2.17/1.66 initiates: ( $i * $i * $i ) > $o)).
% 2.17/1.66 tff(tptp_fun_Event_5_type, type, (
% 2.17/1.66 tptp_fun_Event_5: ( $i * $i ) > $i)).
% 2.17/1.66 tff(tapOff_type, type, (
% 2.17/1.66 tapOff: $i)).
% 2.17/1.66 tff(spilling_type, type, (
% 2.17/1.66 spilling: $i)).
% 2.17/1.66 tff(tptp_fun_Height_9_type, type, (
% 2.17/1.66 tptp_fun_Height_9: ( $i * $i * $i ) > $i)).
% 2.17/1.66 tff(tptp_fun_Height_8_type, type, (
% 2.17/1.66 tptp_fun_Height_8: ( $i * $i * $i ) > $i)).
% 2.17/1.66 tff(n3_type, type, (
% 2.17/1.66 n3: $i)).
% 2.17/1.66 tff(releasedAt_type, type, (
% 2.17/1.66 releasedAt: ( $i * $i ) > $o)).
% 2.17/1.66 tff(n5_type, type, (
% 2.17/1.66 n5: $i)).
% 2.17/1.66 tff(n6_type, type, (
% 2.17/1.66 n6: $i)).
% 2.17/1.66 tff(n2_type, type, (
% 2.17/1.66 n2: $i)).
% 2.17/1.66 tff(n4_type, type, (
% 2.17/1.66 n4: $i)).
% 2.17/1.66 tff(tptp_fun_Event_4_type, type, (
% 2.17/1.66 tptp_fun_Event_4: ( $i * $i ) > $i)).
% 2.17/1.66 tff(1,plain,
% 2.17/1.66 ((plus(n0, n1) = n1) <=> (plus(n0, n1) = n1)),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(2,axiom,(plus(n0, n1) = n1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','plus0_1')).
% 2.17/1.66 tff(3,plain,
% 2.17/1.66 (plus(n0, n1) = n1),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[2, 1])).
% 2.17/1.66 tff(4,plain,
% 2.17/1.66 (n1 = plus(n0, n1)),
% 2.17/1.66 inference(symmetry,[status(thm)],[3])).
% 2.17/1.66 tff(5,plain,
% 2.17/1.66 (stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), n1) <=> stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))),
% 2.17/1.66 inference(monotonicity,[status(thm)],[4])).
% 2.17/1.66 tff(6,plain,
% 2.17/1.66 (stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) <=> stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), n1)),
% 2.17/1.66 inference(symmetry,[status(thm)],[5])).
% 2.17/1.66 tff(7,assumption,(stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))), introduced(assumption)).
% 2.17/1.66 tff(8,plain,
% 2.17/1.66 (stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), n1)),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[7, 6])).
% 2.17/1.66 tff(9,plain,
% 2.17/1.66 (^[Time1: $i, Fluent: $i, Time2: $i] : refl((~((~((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))) | (~(stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time))))))) <=> (~((~((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))) | (~(stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time))))))))),
% 2.17/1.66 inference(bind,[status(th)],[])).
% 2.17/1.66 tff(10,plain,
% 2.17/1.66 (![Time1: $i, Fluent: $i, Time2: $i] : (~((~((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))) | (~(stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time))))))) <=> ![Time1: $i, Fluent: $i, Time2: $i] : (~((~((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))) | (~(stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time)))))))),
% 2.17/1.66 inference(quant_intro,[status(thm)],[9])).
% 2.17/1.66 tff(11,plain,
% 2.17/1.66 (^[Time1: $i, Fluent: $i, Time2: $i] : rewrite((~((~((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))) | (~(stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time))))))) <=> (~((~((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))) | (~(stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time))))))))),
% 2.17/1.66 inference(bind,[status(th)],[])).
% 2.17/1.66 tff(12,plain,
% 2.17/1.66 (![Time1: $i, Fluent: $i, Time2: $i] : (~((~((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))) | (~(stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time))))))) <=> ![Time1: $i, Fluent: $i, Time2: $i] : (~((~((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))) | (~(stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time)))))))),
% 2.17/1.66 inference(quant_intro,[status(thm)],[11])).
% 2.17/1.66 tff(13,plain,
% 2.17/1.66 (![Time1: $i, Fluent: $i, Time2: $i] : (~((~((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))) | (~(stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time))))))) <=> ![Time1: $i, Fluent: $i, Time2: $i] : (~((~((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))) | (~(stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time)))))))),
% 2.17/1.66 inference(transitivity,[status(thm)],[12, 10])).
% 2.17/1.66 tff(14,plain,
% 2.17/1.66 (^[Time1: $i, Fluent: $i, Time2: $i] : trans(monotonicity(rewrite(((~stoppedIn(Time1, Fluent, Time2)) | (happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1)) & less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1)) & less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2) & terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1)))) <=> ((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))), rewrite((stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : (~(happens(Event, Time) & less(Time1, Time) & less(Time, Time2) & terminates(Event, Fluent, Time)))) <=> (stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time))))), ((((~stoppedIn(Time1, Fluent, Time2)) | (happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1)) & less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1)) & less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2) & terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1)))) & (stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : (~(happens(Event, Time) & less(Time1, Time) & less(Time, Time2) & terminates(Event, Fluent, Time))))) <=> (((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1)))))) & (stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time))))))), rewrite((((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1)))))) & (stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time))))) <=> (~((~((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))) | (~(stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time)))))))), ((((~stoppedIn(Time1, Fluent, Time2)) | (happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1)) & less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1)) & less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2) & terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1)))) & (stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : (~(happens(Event, Time) & less(Time1, Time) & less(Time, Time2) & terminates(Event, Fluent, Time))))) <=> (~((~((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))) | (~(stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time)))))))))),
% 2.17/1.66 inference(bind,[status(th)],[])).
% 2.17/1.66 tff(15,plain,
% 2.17/1.66 (![Time1: $i, Fluent: $i, Time2: $i] : (((~stoppedIn(Time1, Fluent, Time2)) | (happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1)) & less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1)) & less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2) & terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1)))) & (stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : (~(happens(Event, Time) & less(Time1, Time) & less(Time, Time2) & terminates(Event, Fluent, Time))))) <=> ![Time1: $i, Fluent: $i, Time2: $i] : (~((~((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))) | (~(stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time)))))))),
% 2.17/1.66 inference(quant_intro,[status(thm)],[14])).
% 2.17/1.66 tff(16,plain,
% 2.17/1.66 (![Time1: $i, Fluent: $i, Time2: $i] : (stoppedIn(Time1, Fluent, Time2) <=> ?[Event: $i, Time: $i] : (happens(Event, Time) & less(Time1, Time) & less(Time, Time2) & terminates(Event, Fluent, Time))) <=> ![Time1: $i, Fluent: $i, Time2: $i] : (stoppedIn(Time1, Fluent, Time2) <=> ?[Event: $i, Time: $i] : (happens(Event, Time) & less(Time1, Time) & less(Time, Time2) & terminates(Event, Fluent, Time)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(17,plain,
% 2.17/1.66 (^[Time1: $i, Fluent: $i, Time2: $i] : rewrite((stoppedIn(Time1, Fluent, Time2) <=> ?[Event: $i, Time: $i] : (((happens(Event, Time) & less(Time1, Time)) & less(Time, Time2)) & terminates(Event, Fluent, Time))) <=> (stoppedIn(Time1, Fluent, Time2) <=> ?[Event: $i, Time: $i] : (happens(Event, Time) & less(Time1, Time) & less(Time, Time2) & terminates(Event, Fluent, Time))))),
% 2.17/1.66 inference(bind,[status(th)],[])).
% 2.17/1.66 tff(18,plain,
% 2.17/1.66 (![Time1: $i, Fluent: $i, Time2: $i] : (stoppedIn(Time1, Fluent, Time2) <=> ?[Event: $i, Time: $i] : (((happens(Event, Time) & less(Time1, Time)) & less(Time, Time2)) & terminates(Event, Fluent, Time))) <=> ![Time1: $i, Fluent: $i, Time2: $i] : (stoppedIn(Time1, Fluent, Time2) <=> ?[Event: $i, Time: $i] : (happens(Event, Time) & less(Time1, Time) & less(Time, Time2) & terminates(Event, Fluent, Time)))),
% 2.17/1.66 inference(quant_intro,[status(thm)],[17])).
% 2.17/1.66 tff(19,axiom,(![Time1: $i, Fluent: $i, Time2: $i] : (stoppedIn(Time1, Fluent, Time2) <=> ?[Event: $i, Time: $i] : (((happens(Event, Time) & less(Time1, Time)) & less(Time, Time2)) & terminates(Event, Fluent, Time)))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax','stoppedin_defn')).
% 2.17/1.66 tff(20,plain,
% 2.17/1.66 (![Time1: $i, Fluent: $i, Time2: $i] : (stoppedIn(Time1, Fluent, Time2) <=> ?[Event: $i, Time: $i] : (happens(Event, Time) & less(Time1, Time) & less(Time, Time2) & terminates(Event, Fluent, Time)))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[19, 18])).
% 2.17/1.66 tff(21,plain,
% 2.17/1.66 (![Time1: $i, Fluent: $i, Time2: $i] : (stoppedIn(Time1, Fluent, Time2) <=> ?[Event: $i, Time: $i] : (happens(Event, Time) & less(Time1, Time) & less(Time, Time2) & terminates(Event, Fluent, Time)))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[20, 16])).
% 2.17/1.66 tff(22,plain,(
% 2.17/1.66 ![Time1: $i, Fluent: $i, Time2: $i] : (((~stoppedIn(Time1, Fluent, Time2)) | (happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1)) & less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1)) & less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2) & terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1)))) & (stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : (~(happens(Event, Time) & less(Time1, Time) & less(Time, Time2) & terminates(Event, Fluent, Time)))))),
% 2.17/1.66 inference(skolemize,[status(sab)],[21])).
% 2.17/1.66 tff(23,plain,
% 2.17/1.66 (![Time1: $i, Fluent: $i, Time2: $i] : (~((~((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))) | (~(stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time)))))))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[22, 15])).
% 2.17/1.66 tff(24,plain,
% 2.17/1.66 (![Time1: $i, Fluent: $i, Time2: $i] : (~((~((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))) | (~(stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time)))))))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[23, 13])).
% 2.17/1.66 tff(25,plain,
% 2.17/1.66 ((~![Time1: $i, Fluent: $i, Time2: $i] : (~((~((~stoppedIn(Time1, Fluent, Time2)) | (~((~happens(tptp_fun_Event_1(Time2, Fluent, Time1), tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(Time1, tptp_fun_Time_0(Time2, Fluent, Time1))) | (~less(tptp_fun_Time_0(Time2, Fluent, Time1), Time2)) | (~terminates(tptp_fun_Event_1(Time2, Fluent, Time1), Fluent, tptp_fun_Time_0(Time2, Fluent, Time1))))))) | (~(stoppedIn(Time1, Fluent, Time2) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(Time1, Time)) | (~less(Time, Time2)) | (~terminates(Event, Fluent, Time)))))))) | (~((~((~stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), n1)) | (~((~happens(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1)) | (~terminates(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))))))) | (~(stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), n1) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(n0, Time)) | (~less(Time, n1)) | (~terminates(Event, tptp_fun_Height_10(waterLevel(filling), tapOn), Time)))))))),
% 2.17/1.66 inference(quant_inst,[status(thm)],[])).
% 2.17/1.66 tff(26,plain,
% 2.17/1.66 (~((~((~stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), n1)) | (~((~happens(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1)) | (~terminates(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))))))) | (~(stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), n1) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(n0, Time)) | (~less(Time, n1)) | (~terminates(Event, tptp_fun_Height_10(waterLevel(filling), tapOn), Time))))))),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[25, 24])).
% 2.17/1.66 tff(27,plain,
% 2.17/1.66 (((~((~stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), n1)) | (~((~happens(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1)) | (~terminates(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))))))) | (~(stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), n1) | ![Event: $i, Time: $i] : ((~happens(Event, Time)) | (~less(n0, Time)) | (~less(Time, n1)) | (~terminates(Event, tptp_fun_Height_10(waterLevel(filling), tapOn), Time)))))) | ((~stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), n1)) | (~((~happens(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1)) | (~terminates(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))))))),
% 2.17/1.66 inference(tautology,[status(thm)],[])).
% 2.17/1.66 tff(28,plain,
% 2.17/1.66 ((~stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), n1)) | (~((~happens(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1)) | (~terminates(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))))),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[27, 26])).
% 2.17/1.66 tff(29,assumption,(~(less_or_equal(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0) <=> ((tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0) = n0) | less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0)))), introduced(assumption)).
% 2.17/1.66 tff(30,plain,
% 2.17/1.66 (^[X: $i, Y: $i] : refl((less_or_equal(X, Y) <=> ((X = Y) | less(X, Y))) <=> (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y))))),
% 2.17/1.66 inference(bind,[status(th)],[])).
% 2.17/1.66 tff(31,plain,
% 2.17/1.66 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y))) <=> ![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 2.17/1.66 inference(quant_intro,[status(thm)],[30])).
% 2.17/1.66 tff(32,plain,
% 2.17/1.66 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y))) <=> ![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(33,plain,
% 2.17/1.66 (^[X: $i, Y: $i] : rewrite((less_or_equal(X, Y) <=> (less(X, Y) | (X = Y))) <=> (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y))))),
% 2.17/1.66 inference(bind,[status(th)],[])).
% 2.17/1.66 tff(34,plain,
% 2.17/1.66 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> (less(X, Y) | (X = Y))) <=> ![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 2.17/1.66 inference(quant_intro,[status(thm)],[33])).
% 2.17/1.66 tff(35,axiom,(![X: $i, Y: $i] : (less_or_equal(X, Y) <=> (less(X, Y) | (X = Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','less_or_equal')).
% 2.17/1.66 tff(36,plain,
% 2.17/1.66 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[35, 34])).
% 2.17/1.66 tff(37,plain,
% 2.17/1.66 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[36, 32])).
% 2.17/1.66 tff(38,plain,(
% 2.17/1.66 ![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 2.17/1.66 inference(skolemize,[status(sab)],[37])).
% 2.17/1.66 tff(39,plain,
% 2.17/1.66 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[38, 31])).
% 2.17/1.66 tff(40,plain,
% 2.17/1.66 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0) <=> ((tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0) = n0) | less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0)))),
% 2.17/1.66 inference(quant_inst,[status(thm)],[])).
% 2.17/1.66 tff(41,plain,
% 2.17/1.66 ($false),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[40, 39, 29])).
% 2.17/1.66 tff(42,plain,(less_or_equal(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0) <=> ((tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0) = n0) | less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.66 tff(43,plain,
% 2.17/1.66 (^[X: $i] : refl((less(X, n1) <=> less_or_equal(X, n0)) <=> (less(X, n1) <=> less_or_equal(X, n0)))),
% 2.17/1.66 inference(bind,[status(th)],[])).
% 2.17/1.66 tff(44,plain,
% 2.17/1.66 (![X: $i] : (less(X, n1) <=> less_or_equal(X, n0)) <=> ![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))),
% 2.17/1.66 inference(quant_intro,[status(thm)],[43])).
% 2.17/1.66 tff(45,plain,
% 2.17/1.66 (![X: $i] : (less(X, n1) <=> less_or_equal(X, n0)) <=> ![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(46,axiom,(![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','less1')).
% 2.17/1.66 tff(47,plain,
% 2.17/1.66 (![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[46, 45])).
% 2.17/1.66 tff(48,plain,(
% 2.17/1.66 ![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))),
% 2.17/1.66 inference(skolemize,[status(sab)],[47])).
% 2.17/1.66 tff(49,plain,
% 2.17/1.66 (![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[48, 44])).
% 2.17/1.66 tff(50,plain,
% 2.17/1.66 ((~![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))) | (less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1) <=> less_or_equal(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0))),
% 2.17/1.66 inference(quant_inst,[status(thm)],[])).
% 2.17/1.66 tff(51,plain,
% 2.17/1.66 (less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1) <=> less_or_equal(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[50, 49])).
% 2.17/1.66 tff(52,assumption,(~((~happens(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1)) | (~terminates(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))))), introduced(assumption)).
% 2.17/1.66 tff(53,plain,
% 2.17/1.66 (((~happens(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1)) | (~terminates(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) | less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1)),
% 2.17/1.66 inference(tautology,[status(thm)],[])).
% 2.17/1.66 tff(54,plain,
% 2.17/1.66 (less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[53, 52])).
% 2.17/1.66 tff(55,plain,
% 2.17/1.66 ((~(less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1) <=> less_or_equal(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0))) | (~less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1)) | less_or_equal(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0)),
% 2.17/1.66 inference(tautology,[status(thm)],[])).
% 2.17/1.66 tff(56,plain,
% 2.17/1.66 ((~(less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1) <=> less_or_equal(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0))) | less_or_equal(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[55, 54])).
% 2.17/1.66 tff(57,plain,
% 2.17/1.66 (less_or_equal(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[56, 51])).
% 2.17/1.66 tff(58,plain,
% 2.17/1.66 (^[X: $i, Y: $i] : refl((less(X, Y) <=> (~((Y = X) | less(Y, X)))) <=> (less(X, Y) <=> (~((Y = X) | less(Y, X)))))),
% 2.17/1.66 inference(bind,[status(th)],[])).
% 2.17/1.66 tff(59,plain,
% 2.17/1.66 (![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X)))) <=> ![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))),
% 2.17/1.66 inference(quant_intro,[status(thm)],[58])).
% 2.17/1.66 tff(60,plain,
% 2.17/1.66 (^[X: $i, Y: $i] : rewrite((less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> (less(X, Y) <=> (~((Y = X) | less(Y, X)))))),
% 2.17/1.66 inference(bind,[status(th)],[])).
% 2.17/1.66 tff(61,plain,
% 2.17/1.66 (![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> ![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))),
% 2.17/1.66 inference(quant_intro,[status(thm)],[60])).
% 2.17/1.66 tff(62,plain,
% 2.17/1.66 (![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> ![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(63,axiom,(![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','less_property')).
% 2.17/1.66 tff(64,plain,
% 2.17/1.66 (![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[63, 62])).
% 2.17/1.66 tff(65,plain,(
% 2.17/1.66 ![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))),
% 2.17/1.66 inference(skolemize,[status(sab)],[64])).
% 2.17/1.66 tff(66,plain,
% 2.17/1.66 (![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[65, 61])).
% 2.17/1.66 tff(67,plain,
% 2.17/1.66 (![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[66, 59])).
% 2.17/1.66 tff(68,plain,
% 2.17/1.66 ((~![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))) | (less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) <=> (~((tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0) = n0) | less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0))))),
% 2.17/1.66 inference(quant_inst,[status(thm)],[])).
% 2.17/1.66 tff(69,plain,
% 2.17/1.66 (less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) <=> (~((tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0) = n0) | less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0)))),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[68, 67])).
% 2.17/1.66 tff(70,plain,
% 2.17/1.66 (((~happens(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1)) | (~terminates(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) | less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))),
% 2.17/1.67 inference(tautology,[status(thm)],[])).
% 2.17/1.67 tff(71,plain,
% 2.17/1.67 (less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[70, 52])).
% 2.17/1.67 tff(72,plain,
% 2.17/1.67 ((~(less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) <=> (~((tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0) = n0) | less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0))))) | (~less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~((tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0) = n0) | less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0)))),
% 2.17/1.67 inference(tautology,[status(thm)],[])).
% 2.17/1.67 tff(73,plain,
% 2.17/1.67 ((~(less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) <=> (~((tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0) = n0) | less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0))))) | (~((tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0) = n0) | less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0)))),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[72, 71])).
% 2.17/1.67 tff(74,plain,
% 2.17/1.67 (~((tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0) = n0) | less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0))),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[73, 69])).
% 2.17/1.67 tff(75,plain,
% 2.17/1.67 ((~(less_or_equal(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0) <=> ((tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0) = n0) | less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0)))) | (~less_or_equal(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0)) | ((tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0) = n0) | less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n0))),
% 2.17/1.67 inference(tautology,[status(thm)],[])).
% 2.17/1.67 tff(76,plain,
% 2.17/1.67 ($false),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[75, 74, 57, 42])).
% 2.17/1.67 tff(77,plain,((~happens(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1)) | (~terminates(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.67 tff(78,plain,
% 2.17/1.67 ((~((~stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), n1)) | (~((~happens(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1)) | (~terminates(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))))))) | (~stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), n1)) | (~((~happens(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1)) | (~terminates(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))))),
% 2.17/1.67 inference(tautology,[status(thm)],[])).
% 2.17/1.67 tff(79,plain,
% 2.17/1.67 ((~((~stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), n1)) | (~((~happens(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(n0, tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~less(tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), n1)) | (~terminates(tptp_fun_Event_1(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0), tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Time_0(n1, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))))))) | (~stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), n1))),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[78, 77])).
% 2.17/1.67 tff(80,plain,
% 2.17/1.67 (~stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), n1)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[79, 28])).
% 2.17/1.67 tff(81,plain,
% 2.17/1.67 ($false),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[80, 8])).
% 2.17/1.67 tff(82,plain,(~stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.67 tff(83,plain,
% 2.17/1.67 (((~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))) | $false) <=> (~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height))))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(84,plain,
% 2.17/1.67 ((~$true) <=> $false),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(85,plain,
% 2.17/1.67 ((waterLevel(filling) = waterLevel(filling)) <=> $true),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(86,plain,
% 2.17/1.67 ((~(waterLevel(filling) = waterLevel(filling))) <=> (~$true)),
% 2.17/1.67 inference(monotonicity,[status(thm)],[85])).
% 2.17/1.67 tff(87,plain,
% 2.17/1.67 ((~(waterLevel(filling) = waterLevel(filling))) <=> $false),
% 2.17/1.67 inference(transitivity,[status(thm)],[86, 84])).
% 2.17/1.67 tff(88,plain,
% 2.17/1.67 (((~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))) | (~(waterLevel(filling) = waterLevel(filling)))) <=> ((~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))) | $false)),
% 2.17/1.67 inference(monotonicity,[status(thm)],[87])).
% 2.17/1.67 tff(89,plain,
% 2.17/1.67 (((~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))) | (~(waterLevel(filling) = waterLevel(filling)))) <=> (~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height))))),
% 2.17/1.67 inference(transitivity,[status(thm)],[88, 83])).
% 2.17/1.67 tff(90,plain,
% 2.17/1.67 ((~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))) | (~(waterLevel(filling) = waterLevel(filling)))),
% 2.17/1.67 inference(quant_inst,[status(thm)],[])).
% 2.17/1.67 tff(91,plain,
% 2.17/1.67 (~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[90, 89])).
% 2.17/1.67 tff(92,assumption,(![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))), introduced(assumption)).
% 2.17/1.67 tff(93,plain,
% 2.17/1.67 ($false),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[92, 91])).
% 2.17/1.67 tff(94,plain,(~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.67 tff(95,plain,
% 2.17/1.67 (^[Event: $i, Fluent: $i, Time: $i] : refl((~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height)))))))) <=> (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height)))))))))),
% 2.17/1.67 inference(bind,[status(th)],[])).
% 2.17/1.67 tff(96,plain,
% 2.17/1.67 (![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height)))))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))),
% 2.17/1.67 inference(quant_intro,[status(thm)],[95])).
% 2.17/1.67 tff(97,plain,
% 2.17/1.67 (^[Event: $i, Fluent: $i, Time: $i] : rewrite((~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height)))))))) <=> (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height)))))))))),
% 2.17/1.67 inference(bind,[status(th)],[])).
% 2.17/1.67 tff(98,plain,
% 2.17/1.67 (![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height)))))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))),
% 2.17/1.67 inference(quant_intro,[status(thm)],[97])).
% 2.17/1.67 tff(99,plain,
% 2.17/1.67 (![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height)))))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))),
% 2.17/1.67 inference(transitivity,[status(thm)],[98, 96])).
% 2.17/1.67 tff(100,plain,
% 2.17/1.67 (^[Event: $i, Fluent: $i, Time: $i] : trans(monotonicity(rewrite(((~releases(Event, Fluent, Time)) | ((Event = tapOn) & (Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event))))) <=> ((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))), rewrite((releases(Event, Fluent, Time) | ![Height: $i] : (~((Event = tapOn) & (Fluent = waterLevel(Height))))) <=> (releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height)))))), ((((~releases(Event, Fluent, Time)) | ((Event = tapOn) & (Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event))))) & (releases(Event, Fluent, Time) | ![Height: $i] : (~((Event = tapOn) & (Fluent = waterLevel(Height)))))) <=> (((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event))))))) & (releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height)))))))), rewrite((((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event))))))) & (releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height)))))) <=> (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))), ((((~releases(Event, Fluent, Time)) | ((Event = tapOn) & (Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event))))) & (releases(Event, Fluent, Time) | ![Height: $i] : (~((Event = tapOn) & (Fluent = waterLevel(Height)))))) <=> (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))))),
% 2.17/1.67 inference(bind,[status(th)],[])).
% 2.17/1.67 tff(101,plain,
% 2.17/1.67 (![Event: $i, Fluent: $i, Time: $i] : (((~releases(Event, Fluent, Time)) | ((Event = tapOn) & (Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event))))) & (releases(Event, Fluent, Time) | ![Height: $i] : (~((Event = tapOn) & (Fluent = waterLevel(Height)))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))),
% 2.17/1.67 inference(quant_intro,[status(thm)],[100])).
% 2.17/1.67 tff(102,plain,
% 2.17/1.67 (![Event: $i, Fluent: $i, Time: $i] : (releases(Event, Fluent, Time) <=> ?[Height: $i] : ((Event = tapOn) & (Fluent = waterLevel(Height)))) <=> ![Event: $i, Fluent: $i, Time: $i] : (releases(Event, Fluent, Time) <=> ?[Height: $i] : ((Event = tapOn) & (Fluent = waterLevel(Height))))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(103,axiom,(![Event: $i, Fluent: $i, Time: $i] : (releases(Event, Fluent, Time) <=> ?[Height: $i] : ((Event = tapOn) & (Fluent = waterLevel(Height))))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax','releases_all_defn')).
% 2.17/1.67 tff(104,plain,
% 2.17/1.67 (![Event: $i, Fluent: $i, Time: $i] : (releases(Event, Fluent, Time) <=> ?[Height: $i] : ((Event = tapOn) & (Fluent = waterLevel(Height))))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[103, 102])).
% 2.17/1.67 tff(105,plain,(
% 2.17/1.67 ![Event: $i, Fluent: $i, Time: $i] : (((~releases(Event, Fluent, Time)) | ((Event = tapOn) & (Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event))))) & (releases(Event, Fluent, Time) | ![Height: $i] : (~((Event = tapOn) & (Fluent = waterLevel(Height))))))),
% 2.17/1.67 inference(skolemize,[status(sab)],[104])).
% 2.17/1.67 tff(106,plain,
% 2.17/1.67 (![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[105, 101])).
% 2.17/1.67 tff(107,plain,
% 2.17/1.67 (![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[106, 99])).
% 2.17/1.67 tff(108,plain,
% 2.17/1.67 (((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))) | (~((~((~releases(tapOn, waterLevel(filling), n1)) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))) | (~((~((~releases(tapOn, waterLevel(filling), n1)) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height))))))))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(109,plain,
% 2.17/1.67 ((~((~((~releases(tapOn, waterLevel(filling), n1)) | (~((~(tapOn = tapOn)) | (~(waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)))))))) | (~(releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : ((~(tapOn = tapOn)) | (~(waterLevel(filling) = waterLevel(Height)))))))) <=> (~((~((~releases(tapOn, waterLevel(filling), n1)) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))))))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(110,plain,
% 2.17/1.67 (((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))) | (~((~((~releases(tapOn, waterLevel(filling), n1)) | (~((~(tapOn = tapOn)) | (~(waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)))))))) | (~(releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : ((~(tapOn = tapOn)) | (~(waterLevel(filling) = waterLevel(Height))))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))) | (~((~((~releases(tapOn, waterLevel(filling), n1)) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height))))))))),
% 2.17/1.67 inference(monotonicity,[status(thm)],[109])).
% 2.17/1.67 tff(111,plain,
% 2.17/1.67 (((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))) | (~((~((~releases(tapOn, waterLevel(filling), n1)) | (~((~(tapOn = tapOn)) | (~(waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)))))))) | (~(releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : ((~(tapOn = tapOn)) | (~(waterLevel(filling) = waterLevel(Height))))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))) | (~((~((~releases(tapOn, waterLevel(filling), n1)) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height))))))))),
% 2.17/1.67 inference(transitivity,[status(thm)],[110, 108])).
% 2.17/1.67 tff(112,plain,
% 2.17/1.67 ((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))) | (~((~((~releases(tapOn, waterLevel(filling), n1)) | (~((~(tapOn = tapOn)) | (~(waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)))))))) | (~(releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : ((~(tapOn = tapOn)) | (~(waterLevel(filling) = waterLevel(Height))))))))),
% 2.17/1.67 inference(quant_inst,[status(thm)],[])).
% 2.17/1.67 tff(113,plain,
% 2.17/1.67 ((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))) | (~((~((~releases(tapOn, waterLevel(filling), n1)) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))))))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[112, 111])).
% 2.17/1.67 tff(114,plain,
% 2.17/1.67 (~((~((~releases(tapOn, waterLevel(filling), n1)) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height))))))),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[113, 107])).
% 2.17/1.67 tff(115,plain,
% 2.17/1.67 (((~((~releases(tapOn, waterLevel(filling), n1)) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))))) | (releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height))))),
% 2.17/1.67 inference(tautology,[status(thm)],[])).
% 2.17/1.67 tff(116,plain,
% 2.17/1.67 (releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[115, 114])).
% 2.17/1.67 tff(117,plain,
% 2.17/1.67 ((~(releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height))))) | releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))),
% 2.17/1.67 inference(tautology,[status(thm)],[])).
% 2.17/1.67 tff(118,plain,
% 2.17/1.67 (releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[117, 116])).
% 2.17/1.67 tff(119,plain,
% 2.17/1.67 (releases(tapOn, waterLevel(filling), n1)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[118, 94])).
% 2.17/1.67 tff(120,plain,
% 2.17/1.67 (((~((~releases(tapOn, waterLevel(filling), n1)) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), n1) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))))) | ((~releases(tapOn, waterLevel(filling), n1)) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))),
% 2.17/1.67 inference(tautology,[status(thm)],[])).
% 2.17/1.67 tff(121,plain,
% 2.17/1.67 ((~releases(tapOn, waterLevel(filling), n1)) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)))),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[120, 114])).
% 2.17/1.67 tff(122,plain,
% 2.17/1.67 ((~((~releases(tapOn, waterLevel(filling), n1)) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~releases(tapOn, waterLevel(filling), n1)) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)))),
% 2.17/1.67 inference(tautology,[status(thm)],[])).
% 2.17/1.67 tff(123,plain,
% 2.17/1.67 ((~releases(tapOn, waterLevel(filling), n1)) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)))),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[122, 121])).
% 2.17/1.67 tff(124,plain,
% 2.17/1.67 (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[123, 119])).
% 2.17/1.67 tff(125,assumption,(~((waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))) <=> (filling = tptp_fun_Height_10(waterLevel(filling), tapOn)))), introduced(assumption)).
% 2.17/1.67 tff(126,plain,
% 2.17/1.67 (^[X: $i, Y: $i] : refl(((waterLevel(X) = waterLevel(Y)) <=> (X = Y)) <=> ((waterLevel(X) = waterLevel(Y)) <=> (X = Y)))),
% 2.17/1.67 inference(bind,[status(th)],[])).
% 2.17/1.67 tff(127,plain,
% 2.17/1.67 (![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y))),
% 2.17/1.67 inference(quant_intro,[status(thm)],[126])).
% 2.17/1.67 tff(128,plain,
% 2.17/1.67 (![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(129,axiom,(![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax','distinct_waterLevels')).
% 2.17/1.67 tff(130,plain,
% 2.17/1.67 (![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[129, 128])).
% 2.17/1.67 tff(131,plain,(
% 2.17/1.67 ![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y))),
% 2.17/1.67 inference(skolemize,[status(sab)],[130])).
% 2.17/1.67 tff(132,plain,
% 2.17/1.67 (![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[131, 127])).
% 2.17/1.67 tff(133,plain,
% 2.17/1.67 ((~![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y))) | ((waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))) <=> (filling = tptp_fun_Height_10(waterLevel(filling), tapOn)))),
% 2.17/1.67 inference(quant_inst,[status(thm)],[])).
% 2.17/1.67 tff(134,plain,
% 2.17/1.67 ($false),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[133, 132, 125])).
% 2.17/1.67 tff(135,plain,((waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))) <=> (filling = tptp_fun_Height_10(waterLevel(filling), tapOn))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.67 tff(136,plain,
% 2.17/1.67 ((~((waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))) <=> (filling = tptp_fun_Height_10(waterLevel(filling), tapOn)))) | (~(waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)))) | (filling = tptp_fun_Height_10(waterLevel(filling), tapOn))),
% 2.17/1.67 inference(tautology,[status(thm)],[])).
% 2.17/1.67 tff(137,plain,
% 2.17/1.67 ((~(waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)))) | (filling = tptp_fun_Height_10(waterLevel(filling), tapOn))),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[136, 135])).
% 2.17/1.67 tff(138,plain,
% 2.17/1.67 (filling = tptp_fun_Height_10(waterLevel(filling), tapOn)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[137, 124])).
% 2.17/1.67 tff(139,plain,
% 2.17/1.67 (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling),
% 2.17/1.67 inference(symmetry,[status(thm)],[138])).
% 2.17/1.67 tff(140,plain,
% 2.17/1.67 (trajectory(tptp_fun_Height_10(waterLevel(filling), tapOn), n0, waterLevel(n1), n1) <=> trajectory(filling, n0, waterLevel(n1), n1)),
% 2.17/1.67 inference(monotonicity,[status(thm)],[139])).
% 2.17/1.67 tff(141,plain,
% 2.17/1.67 (trajectory(filling, n0, waterLevel(n1), n1) <=> trajectory(tptp_fun_Height_10(waterLevel(filling), tapOn), n0, waterLevel(n1), n1)),
% 2.17/1.67 inference(symmetry,[status(thm)],[140])).
% 2.17/1.67 tff(142,plain,
% 2.17/1.67 (holdsAt(waterLevel(n0), n0) <=> holdsAt(waterLevel(n0), n0)),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(143,axiom,(holdsAt(waterLevel(n0), n0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','waterLevel_0')).
% 2.17/1.67 tff(144,plain,
% 2.17/1.67 (holdsAt(waterLevel(n0), n0)),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[143, 142])).
% 2.17/1.67 tff(145,plain,
% 2.17/1.67 (^[Height1: $i, Time: $i, Height2: $i, Offset: $i] : refl((trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset)))) <=> (trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset)))))),
% 2.17/1.67 inference(bind,[status(th)],[])).
% 2.17/1.67 tff(146,plain,
% 2.17/1.67 (![Height1: $i, Time: $i, Height2: $i, Offset: $i] : (trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset)))) <=> ![Height1: $i, Time: $i, Height2: $i, Offset: $i] : (trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset))))),
% 2.17/1.67 inference(quant_intro,[status(thm)],[145])).
% 2.17/1.67 tff(147,plain,
% 2.17/1.67 (^[Height1: $i, Time: $i, Height2: $i, Offset: $i] : trans(monotonicity(trans(monotonicity(rewrite((holdsAt(waterLevel(Height1), Time) & (Height2 = plus(Height1, Offset))) <=> (~((~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset)))))), ((~(holdsAt(waterLevel(Height1), Time) & (Height2 = plus(Height1, Offset)))) <=> (~(~((~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset)))))))), rewrite((~(~((~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset)))))) <=> ((~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset))))), ((~(holdsAt(waterLevel(Height1), Time) & (Height2 = plus(Height1, Offset)))) <=> ((~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset)))))), (((~(holdsAt(waterLevel(Height1), Time) & (Height2 = plus(Height1, Offset)))) | trajectory(filling, Time, waterLevel(Height2), Offset)) <=> (((~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset)))) | trajectory(filling, Time, waterLevel(Height2), Offset)))), rewrite((((~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset)))) | trajectory(filling, Time, waterLevel(Height2), Offset)) <=> (trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset))))), (((~(holdsAt(waterLevel(Height1), Time) & (Height2 = plus(Height1, Offset)))) | trajectory(filling, Time, waterLevel(Height2), Offset)) <=> (trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset))))))),
% 2.17/1.67 inference(bind,[status(th)],[])).
% 2.17/1.67 tff(148,plain,
% 2.17/1.67 (![Height1: $i, Time: $i, Height2: $i, Offset: $i] : ((~(holdsAt(waterLevel(Height1), Time) & (Height2 = plus(Height1, Offset)))) | trajectory(filling, Time, waterLevel(Height2), Offset)) <=> ![Height1: $i, Time: $i, Height2: $i, Offset: $i] : (trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset))))),
% 2.17/1.67 inference(quant_intro,[status(thm)],[147])).
% 2.17/1.67 tff(149,plain,
% 2.17/1.67 (![Height1: $i, Time: $i, Height2: $i, Offset: $i] : ((~(holdsAt(waterLevel(Height1), Time) & (Height2 = plus(Height1, Offset)))) | trajectory(filling, Time, waterLevel(Height2), Offset)) <=> ![Height1: $i, Time: $i, Height2: $i, Offset: $i] : ((~(holdsAt(waterLevel(Height1), Time) & (Height2 = plus(Height1, Offset)))) | trajectory(filling, Time, waterLevel(Height2), Offset))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(150,plain,
% 2.17/1.67 (^[Height1: $i, Time: $i, Height2: $i, Offset: $i] : rewrite(((holdsAt(waterLevel(Height1), Time) & (Height2 = plus(Height1, Offset))) => trajectory(filling, Time, waterLevel(Height2), Offset)) <=> ((~(holdsAt(waterLevel(Height1), Time) & (Height2 = plus(Height1, Offset)))) | trajectory(filling, Time, waterLevel(Height2), Offset)))),
% 2.17/1.67 inference(bind,[status(th)],[])).
% 2.17/1.67 tff(151,plain,
% 2.17/1.67 (![Height1: $i, Time: $i, Height2: $i, Offset: $i] : ((holdsAt(waterLevel(Height1), Time) & (Height2 = plus(Height1, Offset))) => trajectory(filling, Time, waterLevel(Height2), Offset)) <=> ![Height1: $i, Time: $i, Height2: $i, Offset: $i] : ((~(holdsAt(waterLevel(Height1), Time) & (Height2 = plus(Height1, Offset)))) | trajectory(filling, Time, waterLevel(Height2), Offset))),
% 2.17/1.67 inference(quant_intro,[status(thm)],[150])).
% 2.17/1.67 tff(152,axiom,(![Height1: $i, Time: $i, Height2: $i, Offset: $i] : ((holdsAt(waterLevel(Height1), Time) & (Height2 = plus(Height1, Offset))) => trajectory(filling, Time, waterLevel(Height2), Offset))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax','change_of_waterLevel')).
% 2.17/1.67 tff(153,plain,
% 2.17/1.67 (![Height1: $i, Time: $i, Height2: $i, Offset: $i] : ((~(holdsAt(waterLevel(Height1), Time) & (Height2 = plus(Height1, Offset)))) | trajectory(filling, Time, waterLevel(Height2), Offset))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[152, 151])).
% 2.17/1.67 tff(154,plain,
% 2.17/1.67 (![Height1: $i, Time: $i, Height2: $i, Offset: $i] : ((~(holdsAt(waterLevel(Height1), Time) & (Height2 = plus(Height1, Offset)))) | trajectory(filling, Time, waterLevel(Height2), Offset))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[153, 149])).
% 2.17/1.67 tff(155,plain,(
% 2.17/1.67 ![Height1: $i, Time: $i, Height2: $i, Offset: $i] : ((~(holdsAt(waterLevel(Height1), Time) & (Height2 = plus(Height1, Offset)))) | trajectory(filling, Time, waterLevel(Height2), Offset))),
% 2.17/1.67 inference(skolemize,[status(sab)],[154])).
% 2.17/1.67 tff(156,plain,
% 2.17/1.67 (![Height1: $i, Time: $i, Height2: $i, Offset: $i] : (trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset))))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[155, 148])).
% 2.17/1.67 tff(157,plain,
% 2.17/1.67 (![Height1: $i, Time: $i, Height2: $i, Offset: $i] : (trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset))))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[156, 146])).
% 2.17/1.67 tff(158,plain,
% 2.17/1.67 (((~![Height1: $i, Time: $i, Height2: $i, Offset: $i] : (trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset))))) | ((~holdsAt(waterLevel(n0), n0)) | (~(n1 = plus(n0, n1))) | trajectory(filling, n0, waterLevel(n1), n1))) <=> ((~![Height1: $i, Time: $i, Height2: $i, Offset: $i] : (trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset))))) | (~holdsAt(waterLevel(n0), n0)) | (~(n1 = plus(n0, n1))) | trajectory(filling, n0, waterLevel(n1), n1))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(159,plain,
% 2.17/1.67 ((trajectory(filling, n0, waterLevel(n1), n1) | (~holdsAt(waterLevel(n0), n0)) | (~(n1 = plus(n0, n1)))) <=> ((~holdsAt(waterLevel(n0), n0)) | (~(n1 = plus(n0, n1))) | trajectory(filling, n0, waterLevel(n1), n1))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(160,plain,
% 2.17/1.67 (((~![Height1: $i, Time: $i, Height2: $i, Offset: $i] : (trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset))))) | (trajectory(filling, n0, waterLevel(n1), n1) | (~holdsAt(waterLevel(n0), n0)) | (~(n1 = plus(n0, n1))))) <=> ((~![Height1: $i, Time: $i, Height2: $i, Offset: $i] : (trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset))))) | ((~holdsAt(waterLevel(n0), n0)) | (~(n1 = plus(n0, n1))) | trajectory(filling, n0, waterLevel(n1), n1)))),
% 2.17/1.67 inference(monotonicity,[status(thm)],[159])).
% 2.17/1.67 tff(161,plain,
% 2.17/1.67 (((~![Height1: $i, Time: $i, Height2: $i, Offset: $i] : (trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset))))) | (trajectory(filling, n0, waterLevel(n1), n1) | (~holdsAt(waterLevel(n0), n0)) | (~(n1 = plus(n0, n1))))) <=> ((~![Height1: $i, Time: $i, Height2: $i, Offset: $i] : (trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset))))) | (~holdsAt(waterLevel(n0), n0)) | (~(n1 = plus(n0, n1))) | trajectory(filling, n0, waterLevel(n1), n1))),
% 2.17/1.67 inference(transitivity,[status(thm)],[160, 158])).
% 2.17/1.67 tff(162,plain,
% 2.17/1.67 ((~![Height1: $i, Time: $i, Height2: $i, Offset: $i] : (trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset))))) | (trajectory(filling, n0, waterLevel(n1), n1) | (~holdsAt(waterLevel(n0), n0)) | (~(n1 = plus(n0, n1))))),
% 2.17/1.67 inference(quant_inst,[status(thm)],[])).
% 2.17/1.67 tff(163,plain,
% 2.17/1.67 ((~![Height1: $i, Time: $i, Height2: $i, Offset: $i] : (trajectory(filling, Time, waterLevel(Height2), Offset) | (~holdsAt(waterLevel(Height1), Time)) | (~(Height2 = plus(Height1, Offset))))) | (~holdsAt(waterLevel(n0), n0)) | (~(n1 = plus(n0, n1))) | trajectory(filling, n0, waterLevel(n1), n1)),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[162, 161])).
% 2.17/1.67 tff(164,plain,
% 2.17/1.67 (trajectory(filling, n0, waterLevel(n1), n1)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[163, 157, 144, 4])).
% 2.17/1.67 tff(165,plain,
% 2.17/1.67 (trajectory(tptp_fun_Height_10(waterLevel(filling), tapOn), n0, waterLevel(n1), n1)),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[164, 141])).
% 2.17/1.67 tff(166,plain,
% 2.17/1.67 (holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) <=> holdsAt(filling, n0)),
% 2.17/1.67 inference(monotonicity,[status(thm)],[139])).
% 2.17/1.67 tff(167,plain,
% 2.17/1.67 (holdsAt(filling, n0) <=> holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0)),
% 2.17/1.67 inference(symmetry,[status(thm)],[166])).
% 2.17/1.67 tff(168,plain,
% 2.17/1.67 ((~holdsAt(filling, n0)) <=> (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0))),
% 2.17/1.67 inference(monotonicity,[status(thm)],[167])).
% 2.17/1.67 tff(169,plain,
% 2.17/1.67 ((~holdsAt(filling, n0)) <=> (~holdsAt(filling, n0))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(170,axiom,(~holdsAt(filling, n0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_filling_0')).
% 2.17/1.67 tff(171,plain,
% 2.17/1.67 (~holdsAt(filling, n0)),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[170, 169])).
% 2.17/1.67 tff(172,plain,
% 2.17/1.67 (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0)),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[171, 168])).
% 2.17/1.67 tff(173,plain,
% 2.17/1.67 (holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) <=> holdsAt(filling, n1)),
% 2.17/1.67 inference(monotonicity,[status(thm)],[139, 3])).
% 2.17/1.67 tff(174,plain,
% 2.17/1.67 (holdsAt(filling, n1) <=> holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))),
% 2.17/1.67 inference(symmetry,[status(thm)],[173])).
% 2.17/1.67 tff(175,assumption,((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))) | (~holdsAt(waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)))) | (~((~(tapOn = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))))) | (~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~![Height: $i] : ((~(tapOn = tapOff)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~(tapOn = overflow)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))) | initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))), introduced(assumption)).
% 2.17/1.67 tff(176,plain,
% 2.17/1.67 (^[Event: $i, Fluent: $i, Time: $i] : refl((~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow)))))))))) <=> (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow)))))))))))),
% 2.17/1.67 inference(bind,[status(th)],[])).
% 2.17/1.67 tff(177,plain,
% 2.17/1.67 (![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow)))))))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))))),
% 2.17/1.68 inference(quant_intro,[status(thm)],[176])).
% 2.17/1.68 tff(178,plain,
% 2.17/1.68 (^[Event: $i, Fluent: $i, Time: $i] : rewrite((~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow)))))))))) <=> (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow)))))))))))),
% 2.17/1.68 inference(bind,[status(th)],[])).
% 2.17/1.68 tff(179,plain,
% 2.17/1.68 (![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow)))))))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))))),
% 2.17/1.68 inference(quant_intro,[status(thm)],[178])).
% 2.17/1.68 tff(180,plain,
% 2.17/1.68 (![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow)))))))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))))),
% 2.17/1.68 inference(transitivity,[status(thm)],[179, 177])).
% 2.17/1.68 tff(181,plain,
% 2.17/1.68 (^[Event: $i, Fluent: $i, Time: $i] : trans(monotonicity(trans(monotonicity(rewrite(((Event = overflow) & (Fluent = spilling)) <=> (~((~(Event = overflow)) | (~(Fluent = spilling))))), rewrite(((Event = tapOn) & (Fluent = filling)) <=> (~((~(Event = tapOn)) | (~(Fluent = filling))))), rewrite((holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time) & (Event = tapOff) & (Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))) <=> (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event))))))), rewrite((holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time) & (Event = overflow) & (Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))) <=> (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event))))))), ((((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | (~initiates(Event, Fluent, Time)) | (holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time) & (Event = tapOff) & (Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))) | (holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time) & (Event = overflow) & (Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event))))) <=> ((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~initiates(Event, Fluent, Time)) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event))))))))), rewrite(((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~initiates(Event, Fluent, Time)) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event))))))) <=> ((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))), ((((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | (~initiates(Event, Fluent, Time)) | (holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time) & (Event = tapOff) & (Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))) | (holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time) & (Event = overflow) & (Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event))))) <=> ((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((Event = overflow) & (Fluent = spilling)) <=> (~((~(Event = overflow)) | (~(Fluent = spilling))))), ((~((Event = overflow) & (Fluent = spilling))) <=> (~(~((~(Event = overflow)) | (~(Fluent = spilling))))))), rewrite((~(~((~(Event = overflow)) | (~(Fluent = spilling))))) <=> ((~(Event = overflow)) | (~(Fluent = spilling)))), ((~((Event = overflow) & (Fluent = spilling))) <=> ((~(Event = overflow)) | (~(Fluent = spilling))))), trans(monotonicity(rewrite(((Event = tapOn) & (Fluent = filling)) <=> (~((~(Event = tapOn)) | (~(Fluent = filling))))), ((~((Event = tapOn) & (Fluent = filling))) <=> (~(~((~(Event = tapOn)) | (~(Fluent = filling))))))), rewrite((~(~((~(Event = tapOn)) | (~(Fluent = filling))))) <=> ((~(Event = tapOn)) | (~(Fluent = filling)))), ((~((Event = tapOn) & (Fluent = filling))) <=> ((~(Event = tapOn)) | (~(Fluent = filling))))), quant_intro(proof_bind(^[Height: $i] : trans(monotonicity(rewrite((holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height))) <=> (~((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height)))))), ((~(holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height)))) <=> (~(~((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height)))))))), rewrite((~(~((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height)))))) <=> ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))), ((~(holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height)))) <=> ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))))), (![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height)))) <=> ![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height)))))), quant_intro(proof_bind(^[Height: $i] : trans(monotonicity(rewrite((holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height))) <=> (~((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))), ((~(holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height)))) <=> (~(~((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))), rewrite((~(~((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))) <=> ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow)))), ((~(holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height)))) <=> ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow)))))), (![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height)))) <=> ![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))), (((~((Event = overflow) & (Fluent = spilling))) & (~((Event = tapOn) & (Fluent = filling))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height)))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height))))) <=> (((~(Event = overflow)) | (~(Fluent = spilling))) & ((~(Event = tapOn)) | (~(Fluent = filling))) & ![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height)))) & ![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow)))))), rewrite((((~(Event = overflow)) | (~(Fluent = spilling))) & ((~(Event = tapOn)) | (~(Fluent = filling))) & ![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height)))) & ![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow)))) <=> (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))), (((~((Event = overflow) & (Fluent = spilling))) & (~((Event = tapOn) & (Fluent = filling))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height)))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height))))) <=> (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow)))))))), ((initiates(Event, Fluent, Time) | ((~((Event = overflow) & (Fluent = spilling))) & (~((Event = tapOn) & (Fluent = filling))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height)))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height)))))) <=> (initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))), rewrite((initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))) <=> (initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow)))))))), ((initiates(Event, Fluent, Time) | ((~((Event = overflow) & (Fluent = spilling))) & (~((Event = tapOn) & (Fluent = filling))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height)))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height)))))) <=> (initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))), (((((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | (~initiates(Event, Fluent, Time)) | (holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time) & (Event = tapOff) & (Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))) | (holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time) & (Event = overflow) & (Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event))))) & (initiates(Event, Fluent, Time) | ((~((Event = overflow) & (Fluent = spilling))) & (~((Event = tapOn) & (Fluent = filling))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height)))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height))))))) <=> (((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event))))))) & (initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow)))))))))), rewrite((((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event))))))) & (initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow)))))))) <=> (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))))), (((((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | (~initiates(Event, Fluent, Time)) | (holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time) & (Event = tapOff) & (Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))) | (holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time) & (Event = overflow) & (Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event))))) & (initiates(Event, Fluent, Time) | ((~((Event = overflow) & (Fluent = spilling))) & (~((Event = tapOn) & (Fluent = filling))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height)))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height))))))) <=> (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))))))),
% 2.17/1.68 inference(bind,[status(th)],[])).
% 2.17/1.68 tff(182,plain,
% 2.17/1.68 (![Event: $i, Fluent: $i, Time: $i] : ((((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | (~initiates(Event, Fluent, Time)) | (holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time) & (Event = tapOff) & (Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))) | (holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time) & (Event = overflow) & (Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event))))) & (initiates(Event, Fluent, Time) | ((~((Event = overflow) & (Fluent = spilling))) & (~((Event = tapOn) & (Fluent = filling))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height)))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height))))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))))),
% 2.17/1.68 inference(quant_intro,[status(thm)],[181])).
% 2.17/1.68 tff(183,plain,
% 2.17/1.68 (^[Event: $i, Fluent: $i, Time: $i] : rewrite((((~initiates(Event, Fluent, Time)) | (((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | (holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time) & (Event = tapOff) & (Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))) | (holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time) & (Event = overflow) & (Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))) & (initiates(Event, Fluent, Time) | ((~((Event = overflow) & (Fluent = spilling))) & (~((Event = tapOn) & (Fluent = filling))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height)))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height))))))) <=> ((((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | (~initiates(Event, Fluent, Time)) | (holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time) & (Event = tapOff) & (Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))) | (holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time) & (Event = overflow) & (Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event))))) & (initiates(Event, Fluent, Time) | ((~((Event = overflow) & (Fluent = spilling))) & (~((Event = tapOn) & (Fluent = filling))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height)))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height))))))))),
% 2.17/1.68 inference(bind,[status(th)],[])).
% 2.17/1.68 tff(184,plain,
% 2.17/1.68 (![Event: $i, Fluent: $i, Time: $i] : (((~initiates(Event, Fluent, Time)) | (((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | (holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time) & (Event = tapOff) & (Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))) | (holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time) & (Event = overflow) & (Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))) & (initiates(Event, Fluent, Time) | ((~((Event = overflow) & (Fluent = spilling))) & (~((Event = tapOn) & (Fluent = filling))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height)))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height))))))) <=> ![Event: $i, Fluent: $i, Time: $i] : ((((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | (~initiates(Event, Fluent, Time)) | (holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time) & (Event = tapOff) & (Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))) | (holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time) & (Event = overflow) & (Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event))))) & (initiates(Event, Fluent, Time) | ((~((Event = overflow) & (Fluent = spilling))) & (~((Event = tapOn) & (Fluent = filling))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height)))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height)))))))),
% 2.17/1.68 inference(quant_intro,[status(thm)],[183])).
% 2.17/1.68 tff(185,plain,
% 2.17/1.68 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | ?[Height: $i] : (holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height))) | ?[Height: $i] : (holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | ?[Height: $i] : (holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height))) | ?[Height: $i] : (holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height)))))),
% 2.17/1.68 inference(rewrite,[status(thm)],[])).
% 2.17/1.68 tff(186,plain,
% 2.17/1.68 (^[Event: $i, Fluent: $i, Time: $i] : rewrite((initiates(Event, Fluent, Time) <=> (((((Event = tapOn) & (Fluent = filling)) | ((Event = overflow) & (Fluent = spilling))) | ?[Height: $i] : ((holdsAt(waterLevel(Height), Time) & (Event = tapOff)) & (Fluent = waterLevel(Height)))) | ?[Height: $i] : ((holdsAt(waterLevel(Height), Time) & (Event = overflow)) & (Fluent = waterLevel(Height))))) <=> (initiates(Event, Fluent, Time) <=> (((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | ?[Height: $i] : (holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height))) | ?[Height: $i] : (holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height))))))),
% 2.17/1.68 inference(bind,[status(th)],[])).
% 2.17/1.68 tff(187,plain,
% 2.17/1.68 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((((Event = tapOn) & (Fluent = filling)) | ((Event = overflow) & (Fluent = spilling))) | ?[Height: $i] : ((holdsAt(waterLevel(Height), Time) & (Event = tapOff)) & (Fluent = waterLevel(Height)))) | ?[Height: $i] : ((holdsAt(waterLevel(Height), Time) & (Event = overflow)) & (Fluent = waterLevel(Height))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | ?[Height: $i] : (holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height))) | ?[Height: $i] : (holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height)))))),
% 2.17/1.68 inference(quant_intro,[status(thm)],[186])).
% 2.17/1.68 tff(188,axiom,(![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((((Event = tapOn) & (Fluent = filling)) | ((Event = overflow) & (Fluent = spilling))) | ?[Height: $i] : ((holdsAt(waterLevel(Height), Time) & (Event = tapOff)) & (Fluent = waterLevel(Height)))) | ?[Height: $i] : ((holdsAt(waterLevel(Height), Time) & (Event = overflow)) & (Fluent = waterLevel(Height)))))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax','initiates_all_defn')).
% 2.17/1.68 tff(189,plain,
% 2.17/1.68 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | ?[Height: $i] : (holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height))) | ?[Height: $i] : (holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height)))))),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[188, 187])).
% 2.17/1.68 tff(190,plain,
% 2.17/1.68 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | ?[Height: $i] : (holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height))) | ?[Height: $i] : (holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height)))))),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[189, 185])).
% 2.17/1.68 tff(191,plain,(
% 2.17/1.68 ![Event: $i, Fluent: $i, Time: $i] : (((~initiates(Event, Fluent, Time)) | (((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | (holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time) & (Event = tapOff) & (Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))) | (holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time) & (Event = overflow) & (Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))) & (initiates(Event, Fluent, Time) | ((~((Event = overflow) & (Fluent = spilling))) & (~((Event = tapOn) & (Fluent = filling))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height)))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height)))))))),
% 2.17/1.68 inference(skolemize,[status(sab)],[190])).
% 2.17/1.68 tff(192,plain,
% 2.17/1.68 (![Event: $i, Fluent: $i, Time: $i] : ((((Event = overflow) & (Fluent = spilling)) | ((Event = tapOn) & (Fluent = filling)) | (~initiates(Event, Fluent, Time)) | (holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time) & (Event = tapOff) & (Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))) | (holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time) & (Event = overflow) & (Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event))))) & (initiates(Event, Fluent, Time) | ((~((Event = overflow) & (Fluent = spilling))) & (~((Event = tapOn) & (Fluent = filling))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = tapOff) & (Fluent = waterLevel(Height)))) & ![Height: $i] : (~(holdsAt(waterLevel(Height), Time) & (Event = overflow) & (Fluent = waterLevel(Height)))))))),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[191, 184])).
% 2.17/1.68 tff(193,plain,
% 2.17/1.68 (![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))))),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[192, 182])).
% 2.17/1.68 tff(194,plain,
% 2.17/1.68 (![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))))),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[193, 180])).
% 2.17/1.68 tff(195,plain,
% 2.17/1.68 (((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))))) | (~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))) | (~holdsAt(waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)))) | (~((~(tapOn = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))))) | (~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~![Height: $i] : ((~(tapOn = tapOff)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~(tapOn = overflow)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))) | initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))))) | (~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))) | (~holdsAt(waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)))) | (~((~(tapOn = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))))) | (~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~![Height: $i] : ((~(tapOn = tapOff)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~(tapOn = overflow)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))) | initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))))))),
% 2.17/1.68 inference(rewrite,[status(thm)],[])).
% 2.17/1.68 tff(196,plain,
% 2.17/1.68 ((~((~((~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (~((~(tapOn = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))) | (~((~(tapOn = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))))) | (~(initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (~((~(tapOn = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), n0)) | (~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))) | (~(tapOn = overflow)))))))))) <=> (~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))) | (~holdsAt(waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)))) | (~((~(tapOn = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))))) | (~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~![Height: $i] : ((~(tapOn = tapOff)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~(tapOn = overflow)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))) | initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))))),
% 2.17/1.68 inference(rewrite,[status(thm)],[])).
% 2.17/1.68 tff(197,plain,
% 2.17/1.68 (((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))))) | (~((~((~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (~((~(tapOn = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))) | (~((~(tapOn = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))))) | (~(initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (~((~(tapOn = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), n0)) | (~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))) | (~(tapOn = overflow))))))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))))) | (~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))) | (~holdsAt(waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)))) | (~((~(tapOn = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))))) | (~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~![Height: $i] : ((~(tapOn = tapOff)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~(tapOn = overflow)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))) | initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))))))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[196])).
% 2.17/1.69 tff(198,plain,
% 2.17/1.69 (((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))))) | (~((~((~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (~((~(tapOn = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))) | (~((~(tapOn = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))))) | (~(initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (~((~(tapOn = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), n0)) | (~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))) | (~(tapOn = overflow))))))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))))) | (~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))) | (~holdsAt(waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)))) | (~((~(tapOn = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))))) | (~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~![Height: $i] : ((~(tapOn = tapOff)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~(tapOn = overflow)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))) | initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))))))),
% 2.17/1.69 inference(transitivity,[status(thm)],[197, 195])).
% 2.17/1.69 tff(199,plain,
% 2.17/1.69 ((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))))) | (~((~((~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (~((~(tapOn = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))) | (~((~(tapOn = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))))) | (~(initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (~((~(tapOn = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), n0)) | (~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))) | (~(tapOn = overflow))))))))))),
% 2.17/1.69 inference(quant_inst,[status(thm)],[])).
% 2.17/1.69 tff(200,plain,
% 2.17/1.69 ((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~initiates(Event, Fluent, Time)) | (~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~((~holdsAt(waterLevel(tptp_fun_Height_8(Time, Fluent, Event)), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(tptp_fun_Height_8(Time, Fluent, Event)))))) | (~((~(Event = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(Time, Fluent, Event)), Time)) | (~(Fluent = waterLevel(tptp_fun_Height_9(Time, Fluent, Event)))))))) | (~(initiates(Event, Fluent, Time) | (~((~((~(Event = overflow)) | (~(Fluent = spilling)))) | (~((~(Event = tapOn)) | (~(Fluent = filling)))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Event = tapOff)) | (~(Fluent = waterLevel(Height))))) | (~![Height: $i] : ((~holdsAt(waterLevel(Height), Time)) | (~(Fluent = waterLevel(Height))) | (~(Event = overflow))))))))))) | (~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))) | (~holdsAt(waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)))) | (~((~(tapOn = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))))) | (~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~![Height: $i] : ((~(tapOn = tapOff)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~(tapOn = overflow)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))) | initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[199, 198])).
% 2.17/1.69 tff(201,plain,
% 2.17/1.69 ($false),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[200, 194, 175])).
% 2.17/1.69 tff(202,plain,(~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))) | (~holdsAt(waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)))) | (~((~(tapOn = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))))) | (~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~![Height: $i] : ((~(tapOn = tapOff)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~(tapOn = overflow)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))) | initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.69 tff(203,plain,
% 2.17/1.69 (((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tapOn = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))) | (~holdsAt(waterLevel(tptp_fun_Height_8(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)))) | (~((~(tapOn = overflow)) | (~holdsAt(waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_9(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), tapOn)))))))) | (~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~![Height: $i] : ((~(tapOn = tapOff)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~(tapOn = overflow)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))) | initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) | ((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~![Height: $i] : ((~(tapOn = tapOff)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~(tapOn = overflow)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))) | initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))),
% 2.17/1.69 inference(tautology,[status(thm)],[])).
% 2.17/1.69 tff(204,plain,
% 2.17/1.69 ((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~![Height: $i] : ((~(tapOn = tapOff)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~(tapOn = overflow)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))) | initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[203, 202])).
% 2.17/1.69 tff(205,plain,
% 2.17/1.69 ((~![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y))) | ((waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)) = waterLevel(filling)) <=> (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling))),
% 2.17/1.69 inference(quant_inst,[status(thm)],[])).
% 2.17/1.69 tff(206,plain,
% 2.17/1.69 ((waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)) = waterLevel(filling)) <=> (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[205, 132])).
% 2.17/1.69 tff(207,plain,
% 2.17/1.69 (waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)) = waterLevel(filling)),
% 2.17/1.69 inference(symmetry,[status(thm)],[124])).
% 2.17/1.69 tff(208,plain,
% 2.17/1.69 ((~((waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)) = waterLevel(filling)) <=> (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling))) | (~(waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)) = waterLevel(filling))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)),
% 2.17/1.69 inference(tautology,[status(thm)],[])).
% 2.17/1.69 tff(209,plain,
% 2.17/1.69 ((~((waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)) = waterLevel(filling)) <=> (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[208, 207])).
% 2.17/1.69 tff(210,plain,
% 2.17/1.69 (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[209, 206])).
% 2.17/1.69 tff(211,plain,
% 2.17/1.69 (((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~![Height: $i] : ((~(tapOn = tapOff)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~(tapOn = overflow)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height)))))) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling))),
% 2.17/1.69 inference(tautology,[status(thm)],[])).
% 2.17/1.69 tff(212,plain,
% 2.17/1.69 ((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~![Height: $i] : ((~(tapOn = tapOff)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~(tapOn = overflow)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height)))))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[211, 210])).
% 2.17/1.69 tff(213,plain,
% 2.17/1.69 ((~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~![Height: $i] : ((~(tapOn = tapOff)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~(tapOn = overflow)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))) | initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | (~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~![Height: $i] : ((~(tapOn = tapOff)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~(tapOn = overflow)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))) | initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)),
% 2.17/1.69 inference(tautology,[status(thm)],[])).
% 2.17/1.69 tff(214,plain,
% 2.17/1.69 ((~((~((~((~(tapOn = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = spilling)))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~![Height: $i] : ((~(tapOn = tapOff)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))) | (~![Height: $i] : ((~(tapOn = overflow)) | (~holdsAt(waterLevel(Height), n0)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))) | initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[213, 212])).
% 2.17/1.69 tff(215,plain,
% 2.17/1.69 (initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[214, 204])).
% 2.17/1.69 tff(216,assumption,(initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)), introduced(assumption)).
% 2.17/1.69 tff(217,plain,
% 2.17/1.69 ((~holdsAt(filling, n1)) <=> (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[174])).
% 2.17/1.69 tff(218,assumption,(~holdsAt(filling, n1)), introduced(assumption)).
% 2.17/1.69 tff(219,plain,
% 2.17/1.69 (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[218, 217])).
% 2.17/1.69 tff(220,plain,
% 2.17/1.69 (^[Event: $i, Time: $i] : refl((happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow)))))) <=> (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow)))))))),
% 2.17/1.69 inference(bind,[status(th)],[])).
% 2.17/1.69 tff(221,plain,
% 2.17/1.69 (![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow)))))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))),
% 2.17/1.69 inference(quant_intro,[status(thm)],[220])).
% 2.17/1.69 tff(222,plain,
% 2.17/1.69 (^[Event: $i, Time: $i] : rewrite((happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time) & holdsAt(filling, Time) & (Event = overflow)))) <=> (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow)))))))),
% 2.17/1.69 inference(bind,[status(th)],[])).
% 2.17/1.69 tff(223,plain,
% 2.17/1.69 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time) & holdsAt(filling, Time) & (Event = overflow)))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))),
% 2.17/1.69 inference(quant_intro,[status(thm)],[222])).
% 2.17/1.69 tff(224,plain,
% 2.17/1.69 (^[Event: $i, Time: $i] : rewrite((happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(n3), Time) & holdsAt(filling, Time) & (Event = overflow)))) <=> (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time) & holdsAt(filling, Time) & (Event = overflow)))))),
% 2.17/1.69 inference(bind,[status(th)],[])).
% 2.17/1.69 tff(225,plain,
% 2.17/1.69 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(n3), Time) & holdsAt(filling, Time) & (Event = overflow)))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time) & holdsAt(filling, Time) & (Event = overflow))))),
% 2.17/1.69 inference(quant_intro,[status(thm)],[224])).
% 2.17/1.69 tff(226,plain,
% 2.17/1.69 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(n3), Time) & holdsAt(filling, Time) & (Event = overflow)))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(n3), Time) & holdsAt(filling, Time) & (Event = overflow))))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(227,plain,
% 2.17/1.69 (^[Event: $i, Time: $i] : rewrite((happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | ((holdsAt(waterLevel(n3), Time) & holdsAt(filling, Time)) & (Event = overflow)))) <=> (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(n3), Time) & holdsAt(filling, Time) & (Event = overflow)))))),
% 2.17/1.69 inference(bind,[status(th)],[])).
% 2.17/1.69 tff(228,plain,
% 2.17/1.69 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | ((holdsAt(waterLevel(n3), Time) & holdsAt(filling, Time)) & (Event = overflow)))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(n3), Time) & holdsAt(filling, Time) & (Event = overflow))))),
% 2.17/1.69 inference(quant_intro,[status(thm)],[227])).
% 2.17/1.69 tff(229,axiom,(![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | ((holdsAt(waterLevel(n3), Time) & holdsAt(filling, Time)) & (Event = overflow))))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax','happens_all_defn')).
% 2.17/1.69 tff(230,plain,
% 2.17/1.69 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(n3), Time) & holdsAt(filling, Time) & (Event = overflow))))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[229, 228])).
% 2.17/1.69 tff(231,plain,
% 2.17/1.69 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(n3), Time) & holdsAt(filling, Time) & (Event = overflow))))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[230, 226])).
% 2.17/1.69 tff(232,plain,
% 2.17/1.69 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time) & holdsAt(filling, Time) & (Event = overflow))))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[231, 225])).
% 2.17/1.69 tff(233,plain,(
% 2.17/1.69 ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time) & holdsAt(filling, Time) & (Event = overflow))))),
% 2.17/1.69 inference(skolemize,[status(sab)],[232])).
% 2.17/1.69 tff(234,plain,
% 2.17/1.69 (![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[233, 223])).
% 2.17/1.69 tff(235,plain,
% 2.17/1.69 (![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[234, 221])).
% 2.17/1.69 tff(236,plain,
% 2.17/1.69 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | happens(tapOn, n0)) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | happens(tapOn, n0))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(237,plain,
% 2.17/1.69 ((happens(tapOn, n0) <=> $true) <=> happens(tapOn, n0)),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(238,plain,
% 2.17/1.69 (($true | (~((~holdsAt(filling, n0)) | (~(tapOn = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n0))))) <=> $true),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(239,plain,
% 2.17/1.69 ((~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n0)) | (~holdsAt(filling, n0)) | (~(tapOn = overflow)))) <=> (~((~holdsAt(filling, n0)) | (~(tapOn = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n0))))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(240,plain,
% 2.17/1.69 ((~$false) <=> $true),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(241,plain,
% 2.17/1.69 (($false | $false) <=> $false),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(242,plain,
% 2.17/1.69 ((n0 = n0) <=> $true),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(243,plain,
% 2.17/1.69 ((~(n0 = n0)) <=> (~$true)),
% 2.17/1.69 inference(monotonicity,[status(thm)],[242])).
% 2.17/1.69 tff(244,plain,
% 2.17/1.69 ((~(n0 = n0)) <=> $false),
% 2.17/1.69 inference(transitivity,[status(thm)],[243, 84])).
% 2.17/1.69 tff(245,plain,
% 2.17/1.69 ((tapOn = tapOn) <=> $true),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(246,plain,
% 2.17/1.69 ((~(tapOn = tapOn)) <=> (~$true)),
% 2.17/1.70 inference(monotonicity,[status(thm)],[245])).
% 2.17/1.70 tff(247,plain,
% 2.17/1.70 ((~(tapOn = tapOn)) <=> $false),
% 2.17/1.70 inference(transitivity,[status(thm)],[246, 84])).
% 2.17/1.70 tff(248,plain,
% 2.17/1.70 (((~(tapOn = tapOn)) | (~(n0 = n0))) <=> ($false | $false)),
% 2.17/1.70 inference(monotonicity,[status(thm)],[247, 244])).
% 2.17/1.70 tff(249,plain,
% 2.17/1.70 (((~(tapOn = tapOn)) | (~(n0 = n0))) <=> $false),
% 2.17/1.70 inference(transitivity,[status(thm)],[248, 241])).
% 2.17/1.70 tff(250,plain,
% 2.17/1.70 ((~((~(tapOn = tapOn)) | (~(n0 = n0)))) <=> (~$false)),
% 2.17/1.70 inference(monotonicity,[status(thm)],[249])).
% 2.17/1.70 tff(251,plain,
% 2.17/1.70 ((~((~(tapOn = tapOn)) | (~(n0 = n0)))) <=> $true),
% 2.17/1.70 inference(transitivity,[status(thm)],[250, 240])).
% 2.17/1.70 tff(252,plain,
% 2.17/1.70 (((~((~(tapOn = tapOn)) | (~(n0 = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n0)) | (~holdsAt(filling, n0)) | (~(tapOn = overflow))))) <=> ($true | (~((~holdsAt(filling, n0)) | (~(tapOn = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n0)))))),
% 2.17/1.70 inference(monotonicity,[status(thm)],[251, 239])).
% 2.17/1.70 tff(253,plain,
% 2.17/1.70 (((~((~(tapOn = tapOn)) | (~(n0 = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n0)) | (~holdsAt(filling, n0)) | (~(tapOn = overflow))))) <=> $true),
% 2.17/1.70 inference(transitivity,[status(thm)],[252, 238])).
% 2.17/1.70 tff(254,plain,
% 2.17/1.70 ((happens(tapOn, n0) <=> ((~((~(tapOn = tapOn)) | (~(n0 = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n0)) | (~holdsAt(filling, n0)) | (~(tapOn = overflow)))))) <=> (happens(tapOn, n0) <=> $true)),
% 2.17/1.70 inference(monotonicity,[status(thm)],[253])).
% 2.17/1.70 tff(255,plain,
% 2.17/1.70 ((happens(tapOn, n0) <=> ((~((~(tapOn = tapOn)) | (~(n0 = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n0)) | (~holdsAt(filling, n0)) | (~(tapOn = overflow)))))) <=> happens(tapOn, n0)),
% 2.17/1.70 inference(transitivity,[status(thm)],[254, 237])).
% 2.17/1.70 tff(256,plain,
% 2.17/1.70 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tapOn, n0) <=> ((~((~(tapOn = tapOn)) | (~(n0 = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n0)) | (~holdsAt(filling, n0)) | (~(tapOn = overflow))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | happens(tapOn, n0))),
% 2.17/1.70 inference(monotonicity,[status(thm)],[255])).
% 2.17/1.70 tff(257,plain,
% 2.17/1.70 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tapOn, n0) <=> ((~((~(tapOn = tapOn)) | (~(n0 = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n0)) | (~holdsAt(filling, n0)) | (~(tapOn = overflow))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | happens(tapOn, n0))),
% 2.17/1.70 inference(transitivity,[status(thm)],[256, 236])).
% 2.17/1.70 tff(258,plain,
% 2.17/1.70 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tapOn, n0) <=> ((~((~(tapOn = tapOn)) | (~(n0 = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n0)) | (~holdsAt(filling, n0)) | (~(tapOn = overflow))))))),
% 2.17/1.70 inference(quant_inst,[status(thm)],[])).
% 2.17/1.70 tff(259,plain,
% 2.17/1.70 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | happens(tapOn, n0)),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[258, 257])).
% 2.17/1.70 tff(260,plain,
% 2.17/1.70 (happens(tapOn, n0)),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[259, 235])).
% 2.17/1.70 tff(261,plain,
% 2.17/1.70 (^[Event: $i, Time: $i, Fluent: $i] : refl((holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time))) <=> (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time))))),
% 2.17/1.70 inference(bind,[status(th)],[])).
% 2.17/1.70 tff(262,plain,
% 2.17/1.70 (![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time))) <=> ![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))),
% 2.17/1.70 inference(quant_intro,[status(thm)],[261])).
% 2.17/1.70 tff(263,plain,
% 2.17/1.70 (^[Event: $i, Time: $i, Fluent: $i] : trans(monotonicity(trans(monotonicity(rewrite((happens(Event, Time) & initiates(Event, Fluent, Time)) <=> (~((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))))), ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) <=> (~(~((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))))))), rewrite((~(~((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))))) <=> ((~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))), ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) <=> ((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))))), (((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> (((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))))), rewrite((((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))), (((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))))),
% 2.17/1.70 inference(bind,[status(th)],[])).
% 2.17/1.70 tff(264,plain,
% 2.17/1.70 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> ![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))),
% 2.17/1.70 inference(quant_intro,[status(thm)],[263])).
% 2.17/1.70 tff(265,plain,
% 2.17/1.70 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 2.17/1.70 inference(rewrite,[status(thm)],[])).
% 2.17/1.70 tff(266,plain,
% 2.17/1.70 (^[Event: $i, Time: $i, Fluent: $i] : rewrite(((happens(Event, Time) & initiates(Event, Fluent, Time)) => holdsAt(Fluent, plus(Time, n1))) <=> ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))))),
% 2.17/1.70 inference(bind,[status(th)],[])).
% 2.17/1.70 tff(267,plain,
% 2.17/1.70 (![Event: $i, Time: $i, Fluent: $i] : ((happens(Event, Time) & initiates(Event, Fluent, Time)) => holdsAt(Fluent, plus(Time, n1))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 2.17/1.70 inference(quant_intro,[status(thm)],[266])).
% 2.17/1.70 tff(268,axiom,(![Event: $i, Time: $i, Fluent: $i] : ((happens(Event, Time) & initiates(Event, Fluent, Time)) => holdsAt(Fluent, plus(Time, n1)))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax','happens_holds')).
% 2.17/1.70 tff(269,plain,
% 2.17/1.70 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[268, 267])).
% 2.17/1.70 tff(270,plain,
% 2.17/1.70 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[269, 265])).
% 2.17/1.70 tff(271,plain,(
% 2.17/1.70 ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 2.17/1.70 inference(skolemize,[status(sab)],[270])).
% 2.17/1.70 tff(272,plain,
% 2.17/1.70 (![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[271, 264])).
% 2.17/1.70 tff(273,plain,
% 2.17/1.70 (![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[272, 262])).
% 2.17/1.70 tff(274,plain,
% 2.17/1.70 (((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | ((~happens(tapOn, n0)) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) <=> ((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | (~happens(tapOn, n0)) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))),
% 2.17/1.70 inference(rewrite,[status(thm)],[])).
% 2.17/1.70 tff(275,plain,
% 2.17/1.70 ((holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~happens(tapOn, n0)) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) <=> ((~happens(tapOn, n0)) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))),
% 2.17/1.70 inference(rewrite,[status(thm)],[])).
% 2.17/1.70 tff(276,plain,
% 2.17/1.70 (((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | (holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~happens(tapOn, n0)) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) <=> ((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | ((~happens(tapOn, n0)) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))))),
% 2.17/1.70 inference(monotonicity,[status(thm)],[275])).
% 2.17/1.70 tff(277,plain,
% 2.17/1.70 (((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | (holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~happens(tapOn, n0)) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) <=> ((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | (~happens(tapOn, n0)) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))),
% 2.17/1.70 inference(transitivity,[status(thm)],[276, 274])).
% 2.17/1.70 tff(278,plain,
% 2.17/1.70 ((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | (holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~happens(tapOn, n0)) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))),
% 2.17/1.70 inference(quant_inst,[status(thm)],[])).
% 2.17/1.70 tff(279,plain,
% 2.17/1.70 ((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | (~happens(tapOn, n0)) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[278, 277])).
% 2.17/1.70 tff(280,plain,
% 2.17/1.70 (holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[279, 273, 260])).
% 2.17/1.70 tff(281,plain,
% 2.17/1.70 ($false),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[280, 219, 216])).
% 2.17/1.70 tff(282,plain,((~initiates(tapOn, tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | holdsAt(filling, n1)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.70 tff(283,plain,
% 2.17/1.70 (holdsAt(filling, n1)),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[282, 215])).
% 2.17/1.70 tff(284,plain,
% 2.17/1.70 (holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[283, 174])).
% 2.17/1.70 tff(285,assumption,((~(releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | ![Height: $i] : ((~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn))))) | (~((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn))))))))))), introduced(assumption)).
% 2.17/1.70 tff(286,plain,
% 2.17/1.70 (((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))) | (~((~(releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | ![Height: $i] : ((~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn))))) | (~((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn))))))))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))) | (~((~(releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | ![Height: $i] : ((~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn))))) | (~((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)))))))))))))),
% 2.17/1.70 inference(rewrite,[status(thm)],[])).
% 2.17/1.70 tff(287,plain,
% 2.17/1.70 ((~((~((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)))))))))) | (~(releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | ![Height: $i] : ((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height)))))))) <=> (~((~(releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | ![Height: $i] : ((~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn))))) | (~((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn))))))))))))),
% 2.17/1.70 inference(rewrite,[status(thm)],[])).
% 2.17/1.70 tff(288,plain,
% 2.17/1.70 (((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))) | (~((~((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)))))))))) | (~(releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | ![Height: $i] : ((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))) | (~((~(releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | ![Height: $i] : ((~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn))))) | (~((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)))))))))))))),
% 2.17/1.70 inference(monotonicity,[status(thm)],[287])).
% 2.17/1.70 tff(289,plain,
% 2.17/1.70 (((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))) | (~((~((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)))))))))) | (~(releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | ![Height: $i] : ((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))) | (~((~(releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | ![Height: $i] : ((~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn))))) | (~((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)))))))))))))),
% 2.27/1.70 inference(transitivity,[status(thm)],[288, 286])).
% 2.27/1.70 tff(290,plain,
% 2.27/1.70 ((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))) | (~((~((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)))))))))) | (~(releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | ![Height: $i] : ((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))))))))),
% 2.27/1.70 inference(quant_inst,[status(thm)],[])).
% 2.27/1.70 tff(291,plain,
% 2.27/1.70 ((~![Event: $i, Fluent: $i, Time: $i] : (~((~((~releases(Event, Fluent, Time)) | (~((~(Event = tapOn)) | (~(Fluent = waterLevel(tptp_fun_Height_10(Fluent, Event)))))))) | (~(releases(Event, Fluent, Time) | ![Height: $i] : ((~(Event = tapOn)) | (~(Fluent = waterLevel(Height))))))))) | (~((~(releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | ![Height: $i] : ((~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn))))) | (~((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn))))))))))))),
% 2.27/1.70 inference(modus_ponens,[status(thm)],[290, 289])).
% 2.27/1.70 tff(292,plain,
% 2.27/1.70 ($false),
% 2.27/1.70 inference(unit_resolution,[status(thm)],[291, 107, 285])).
% 2.27/1.70 tff(293,plain,(~((~(releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | ![Height: $i] : ((~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn))))) | (~((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)))))))))))), inference(lemma,lemma(discharge,[]))).
% 2.27/1.70 tff(294,plain,
% 2.27/1.70 (((~(releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | ![Height: $i] : ((~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn))))) | (~((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn))))))))))) | ((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)))))))))),
% 2.27/1.70 inference(tautology,[status(thm)],[])).
% 2.27/1.70 tff(295,plain,
% 2.27/1.70 ((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn))))))))),
% 2.27/1.70 inference(unit_resolution,[status(thm)],[294, 293])).
% 2.27/1.70 tff(296,assumption,(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn))))), introduced(assumption)).
% 2.27/1.70 tff(297,plain,
% 2.27/1.70 (filling = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn))))),
% 2.27/1.70 inference(transitivity,[status(thm)],[138, 296])).
% 2.27/1.70 tff(298,assumption,(filling = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn))))), introduced(assumption)).
% 2.27/1.70 tff(299,plain,
% 2.27/1.70 (^[X: $i] : refl((~(filling = waterLevel(X))) <=> (~(filling = waterLevel(X))))),
% 2.27/1.70 inference(bind,[status(th)],[])).
% 2.27/1.70 tff(300,plain,
% 2.27/1.70 (![X: $i] : (~(filling = waterLevel(X))) <=> ![X: $i] : (~(filling = waterLevel(X)))),
% 2.27/1.70 inference(quant_intro,[status(thm)],[299])).
% 2.27/1.70 tff(301,plain,
% 2.27/1.70 (![X: $i] : (~(filling = waterLevel(X))) <=> ![X: $i] : (~(filling = waterLevel(X)))),
% 2.27/1.70 inference(rewrite,[status(thm)],[])).
% 2.27/1.70 tff(302,axiom,(![X: $i] : (~(filling = waterLevel(X)))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax','filling_not_waterLevel')).
% 2.27/1.70 tff(303,plain,
% 2.27/1.70 (![X: $i] : (~(filling = waterLevel(X)))),
% 2.27/1.70 inference(modus_ponens,[status(thm)],[302, 301])).
% 2.27/1.70 tff(304,plain,(
% 2.27/1.70 ![X: $i] : (~(filling = waterLevel(X)))),
% 2.27/1.70 inference(skolemize,[status(sab)],[303])).
% 2.27/1.70 tff(305,plain,
% 2.27/1.70 (![X: $i] : (~(filling = waterLevel(X)))),
% 2.27/1.70 inference(modus_ponens,[status(thm)],[304, 300])).
% 2.27/1.70 tff(306,plain,
% 2.27/1.70 ((~![X: $i] : (~(filling = waterLevel(X)))) | (~(filling = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn))))))),
% 2.27/1.70 inference(quant_inst,[status(thm)],[])).
% 2.27/1.70 tff(307,plain,
% 2.27/1.70 ($false),
% 2.27/1.70 inference(unit_resolution,[status(thm)],[306, 305, 298])).
% 2.27/1.70 tff(308,plain,(~(filling = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)))))), inference(lemma,lemma(discharge,[]))).
% 2.27/1.70 tff(309,plain,
% 2.27/1.70 ($false),
% 2.27/1.70 inference(unit_resolution,[status(thm)],[308, 297])).
% 2.27/1.70 tff(310,plain,(~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)))))), inference(lemma,lemma(discharge,[]))).
% 2.27/1.70 tff(311,plain,
% 2.27/1.70 (((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn))))))) | (tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)))))),
% 2.27/1.70 inference(tautology,[status(thm)],[])).
% 2.27/1.70 tff(312,plain,
% 2.27/1.70 ((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn))))))),
% 2.27/1.70 inference(unit_resolution,[status(thm)],[311, 310])).
% 2.27/1.70 tff(313,plain,
% 2.27/1.70 ((~((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)))))))))) | (~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn))))))))),
% 2.27/1.70 inference(tautology,[status(thm)],[])).
% 2.27/1.70 tff(314,plain,
% 2.27/1.70 ((~((~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~((~(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = waterLevel(tptp_fun_Height_10(tptp_fun_Height_10(waterLevel(filling), tapOn), tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)))))))))) | (~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0))),
% 2.27/1.70 inference(unit_resolution,[status(thm)],[313, 312])).
% 2.27/1.70 tff(315,plain,
% 2.27/1.70 (~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)),
% 2.27/1.70 inference(unit_resolution,[status(thm)],[314, 295])).
% 2.27/1.70 tff(316,plain,
% 2.27/1.70 (((~happens(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)),
% 2.27/1.70 inference(tautology,[status(thm)],[])).
% 2.27/1.70 tff(317,plain,
% 2.27/1.70 ((~happens(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0))),
% 2.27/1.70 inference(unit_resolution,[status(thm)],[316, 315])).
% 2.27/1.70 tff(318,assumption,(releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))), introduced(assumption)).
% 2.27/1.70 tff(319,plain,
% 2.27/1.70 (releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) <=> releasedAt(filling, n0)),
% 2.27/1.70 inference(monotonicity,[status(thm)],[139])).
% 2.27/1.70 tff(320,plain,
% 2.27/1.70 (releasedAt(filling, n0) <=> releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0)),
% 2.27/1.70 inference(symmetry,[status(thm)],[319])).
% 2.27/1.70 tff(321,plain,
% 2.27/1.70 ((~releasedAt(filling, n0)) <=> (~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0))),
% 2.27/1.70 inference(monotonicity,[status(thm)],[320])).
% 2.27/1.70 tff(322,plain,
% 2.27/1.70 ((~releasedAt(filling, n0)) <=> (~releasedAt(filling, n0))),
% 2.27/1.70 inference(rewrite,[status(thm)],[])).
% 2.27/1.70 tff(323,axiom,(~releasedAt(filling, n0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_released_filling_0')).
% 2.27/1.70 tff(324,plain,
% 2.27/1.70 (~releasedAt(filling, n0)),
% 2.27/1.70 inference(modus_ponens,[status(thm)],[323, 322])).
% 2.27/1.70 tff(325,plain,
% 2.27/1.70 (~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0)),
% 2.27/1.70 inference(modus_ponens,[status(thm)],[324, 321])).
% 2.27/1.70 tff(326,assumption,(releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0)), introduced(assumption)).
% 2.27/1.70 tff(327,plain,
% 2.27/1.70 ($false),
% 2.27/1.70 inference(unit_resolution,[status(thm)],[326, 325])).
% 2.27/1.70 tff(328,plain,(~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0)), inference(lemma,lemma(discharge,[]))).
% 2.27/1.70 tff(329,plain,
% 2.27/1.70 (^[Fluent: $i, Time: $i] : refl(((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time))))) <=> ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time))))))),
% 2.27/1.70 inference(bind,[status(th)],[])).
% 2.27/1.70 tff(330,plain,
% 2.27/1.70 (![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time))))) <=> ![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))),
% 2.27/1.70 inference(quant_intro,[status(thm)],[329])).
% 2.27/1.70 tff(331,plain,
% 2.27/1.70 (^[Fluent: $i, Time: $i] : trans(monotonicity(rewrite((happens(tptp_fun_Event_7(Time, Fluent), Time) & releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)) <=> (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time))))), (((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (happens(tptp_fun_Event_7(Time, Fluent), Time) & releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time))) <=> ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time))))))), rewrite(((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time))))) <=> ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))), (((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (happens(tptp_fun_Event_7(Time, Fluent), Time) & releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time))) <=> ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))))),
% 2.27/1.70 inference(bind,[status(th)],[])).
% 2.27/1.70 tff(332,plain,
% 2.27/1.70 (![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (happens(tptp_fun_Event_7(Time, Fluent), Time) & releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time))) <=> ![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))),
% 2.27/1.70 inference(quant_intro,[status(thm)],[331])).
% 2.27/1.70 tff(333,plain,
% 2.27/1.70 (^[Fluent: $i, Time: $i] : trans(monotonicity(rewrite(((~(~releasedAt(Fluent, Time))) | (happens(tptp_fun_Event_7(Time, Fluent), Time) & releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time))) <=> (releasedAt(Fluent, Time) | (happens(tptp_fun_Event_7(Time, Fluent), Time) & releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))), (((~releasedAt(Fluent, plus(Time, n1))) | ((~(~releasedAt(Fluent, Time))) | (happens(tptp_fun_Event_7(Time, Fluent), Time) & releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))) <=> ((~releasedAt(Fluent, plus(Time, n1))) | (releasedAt(Fluent, Time) | (happens(tptp_fun_Event_7(Time, Fluent), Time) & releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))), rewrite(((~releasedAt(Fluent, plus(Time, n1))) | (releasedAt(Fluent, Time) | (happens(tptp_fun_Event_7(Time, Fluent), Time) & releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))) <=> ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (happens(tptp_fun_Event_7(Time, Fluent), Time) & releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))), (((~releasedAt(Fluent, plus(Time, n1))) | ((~(~releasedAt(Fluent, Time))) | (happens(tptp_fun_Event_7(Time, Fluent), Time) & releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))) <=> ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (happens(tptp_fun_Event_7(Time, Fluent), Time) & releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))),
% 2.27/1.71 inference(bind,[status(th)],[])).
% 2.27/1.71 tff(334,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | ((~(~releasedAt(Fluent, Time))) | (happens(tptp_fun_Event_7(Time, Fluent), Time) & releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))) <=> ![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (happens(tptp_fun_Event_7(Time, Fluent), Time) & releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))),
% 2.27/1.71 inference(quant_intro,[status(thm)],[333])).
% 2.27/1.71 tff(335,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | (~((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time)))))) <=> ![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | (~((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time))))))),
% 2.27/1.71 inference(rewrite,[status(thm)],[])).
% 2.27/1.71 tff(336,plain,
% 2.27/1.71 (^[Fluent: $i, Time: $i] : trans(monotonicity(monotonicity(rewrite((~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time))) <=> (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time)))), (((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time)))) <=> ((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time)))))), ((((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time)))) => (~releasedAt(Fluent, plus(Time, n1)))) <=> (((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time)))) => (~releasedAt(Fluent, plus(Time, n1)))))), rewrite((((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time)))) => (~releasedAt(Fluent, plus(Time, n1)))) <=> ((~releasedAt(Fluent, plus(Time, n1))) | (~((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time))))))), ((((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time)))) => (~releasedAt(Fluent, plus(Time, n1)))) <=> ((~releasedAt(Fluent, plus(Time, n1))) | (~((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time))))))))),
% 2.27/1.71 inference(bind,[status(th)],[])).
% 2.27/1.71 tff(337,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : (((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time)))) => (~releasedAt(Fluent, plus(Time, n1)))) <=> ![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | (~((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time))))))),
% 2.27/1.71 inference(quant_intro,[status(thm)],[336])).
% 2.27/1.71 tff(338,axiom,(![Fluent: $i, Time: $i] : (((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time)))) => (~releasedAt(Fluent, plus(Time, n1))))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax','keep_not_released')).
% 2.27/1.71 tff(339,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | (~((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time))))))),
% 2.27/1.71 inference(modus_ponens,[status(thm)],[338, 337])).
% 2.27/1.71 tff(340,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | (~((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time))))))),
% 2.27/1.71 inference(modus_ponens,[status(thm)],[339, 335])).
% 2.27/1.71 tff(341,plain,(
% 2.27/1.71 ![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | ((~(~releasedAt(Fluent, Time))) | (happens(tptp_fun_Event_7(Time, Fluent), Time) & releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time))))),
% 2.27/1.71 inference(skolemize,[status(sab)],[340])).
% 2.27/1.71 tff(342,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (happens(tptp_fun_Event_7(Time, Fluent), Time) & releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))),
% 2.27/1.71 inference(modus_ponens,[status(thm)],[341, 334])).
% 2.27/1.71 tff(343,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))),
% 2.27/1.71 inference(modus_ponens,[status(thm)],[342, 332])).
% 2.27/1.71 tff(344,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))),
% 2.27/1.71 inference(modus_ponens,[status(thm)],[343, 330])).
% 2.27/1.71 tff(345,plain,
% 2.27/1.71 (((~![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))) | (releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~((~happens(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) | (~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))))) <=> ((~![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~((~happens(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) | (~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))))),
% 2.27/1.71 inference(rewrite,[status(thm)],[])).
% 2.27/1.71 tff(346,plain,
% 2.27/1.71 (((~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~((~happens(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0))))) <=> (releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~((~happens(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) | (~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))))),
% 2.27/1.71 inference(rewrite,[status(thm)],[])).
% 2.27/1.71 tff(347,plain,
% 2.27/1.71 (((~![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))) | ((~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~((~happens(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))))) <=> ((~![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))) | (releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~((~happens(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) | (~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)))))),
% 2.27/1.71 inference(monotonicity,[status(thm)],[346])).
% 2.27/1.71 tff(348,plain,
% 2.27/1.71 (((~![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))) | ((~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~((~happens(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))))) <=> ((~![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~((~happens(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) | (~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))))),
% 2.27/1.71 inference(transitivity,[status(thm)],[347, 345])).
% 2.27/1.71 tff(349,plain,
% 2.27/1.71 ((~![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))) | ((~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~((~happens(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))))),
% 2.27/1.71 inference(quant_inst,[status(thm)],[])).
% 2.27/1.71 tff(350,plain,
% 2.27/1.71 ((~![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~((~happens(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~releases(tptp_fun_Event_7(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) | (~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)))),
% 2.27/1.71 inference(modus_ponens,[status(thm)],[349, 348])).
% 2.27/1.71 tff(351,plain,
% 2.27/1.71 ($false),
% 2.27/1.71 inference(unit_resolution,[status(thm)],[350, 344, 328, 318, 317])).
% 2.27/1.71 tff(352,plain,(~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))), inference(lemma,lemma(discharge,[]))).
% 2.27/1.71 tff(353,plain,
% 2.27/1.71 (^[Fluent: $i, Time: $i] : refl((releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))))) <=> (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))))))),
% 2.27/1.71 inference(bind,[status(th)],[])).
% 2.27/1.71 tff(354,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))))) <=> ![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))),
% 2.27/1.71 inference(quant_intro,[status(thm)],[353])).
% 2.27/1.71 tff(355,plain,
% 2.27/1.71 (^[Fluent: $i, Time: $i] : trans(monotonicity(rewrite((happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)) <=> (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))))), ((releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))) <=> (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))))))), rewrite((releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))))) <=> (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))), ((releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))) <=> (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))))),
% 2.27/1.71 inference(bind,[status(th)],[])).
% 2.27/1.71 tff(356,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))) <=> ![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))),
% 2.27/1.71 inference(quant_intro,[status(thm)],[355])).
% 2.27/1.71 tff(357,plain,
% 2.27/1.71 (^[Fluent: $i, Time: $i] : trans(monotonicity(rewrite(((~(~holdsAt(Fluent, Time))) | (~(~releasedAt(Fluent, plus(Time, n1)))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))) <=> (holdsAt(Fluent, Time) | releasedAt(Fluent, plus(Time, n1)) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))), (((~holdsAt(Fluent, plus(Time, n1))) | ((~(~holdsAt(Fluent, Time))) | (~(~releasedAt(Fluent, plus(Time, n1)))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))) <=> ((~holdsAt(Fluent, plus(Time, n1))) | (holdsAt(Fluent, Time) | releasedAt(Fluent, plus(Time, n1)) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))), rewrite(((~holdsAt(Fluent, plus(Time, n1))) | (holdsAt(Fluent, Time) | releasedAt(Fluent, plus(Time, n1)) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))) <=> (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))), (((~holdsAt(Fluent, plus(Time, n1))) | ((~(~holdsAt(Fluent, Time))) | (~(~releasedAt(Fluent, plus(Time, n1)))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))) <=> (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))),
% 2.27/1.71 inference(bind,[status(th)],[])).
% 2.27/1.71 tff(358,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | ((~(~holdsAt(Fluent, Time))) | (~(~releasedAt(Fluent, plus(Time, n1)))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))) <=> ![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))),
% 2.27/1.71 inference(quant_intro,[status(thm)],[357])).
% 2.27/1.71 tff(359,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))))) <=> ![Fluent: $i, Time: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time))))))),
% 2.27/1.71 inference(rewrite,[status(thm)],[])).
% 2.27/1.71 tff(360,plain,
% 2.27/1.71 (^[Fluent: $i, Time: $i] : trans(monotonicity(trans(monotonicity(rewrite((~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time))) <=> (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))), ((((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) <=> (((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))))), rewrite((((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) <=> ((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time))))), ((((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) <=> ((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))))), (((((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) => (~holdsAt(Fluent, plus(Time, n1)))) <=> (((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) => (~holdsAt(Fluent, plus(Time, n1)))))), rewrite((((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) => (~holdsAt(Fluent, plus(Time, n1)))) <=> ((~holdsAt(Fluent, plus(Time, n1))) | (~((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time))))))), (((((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) => (~holdsAt(Fluent, plus(Time, n1)))) <=> ((~holdsAt(Fluent, plus(Time, n1))) | (~((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time))))))))),
% 2.27/1.71 inference(bind,[status(th)],[])).
% 2.27/1.71 tff(361,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : ((((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) => (~holdsAt(Fluent, plus(Time, n1)))) <=> ![Fluent: $i, Time: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time))))))),
% 2.27/1.71 inference(quant_intro,[status(thm)],[360])).
% 2.27/1.71 tff(362,axiom,(![Fluent: $i, Time: $i] : ((((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) => (~holdsAt(Fluent, plus(Time, n1))))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax','keep_not_holding')).
% 2.27/1.71 tff(363,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time))))))),
% 2.27/1.71 inference(modus_ponens,[status(thm)],[362, 361])).
% 2.27/1.71 tff(364,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time))))))),
% 2.27/1.71 inference(modus_ponens,[status(thm)],[363, 359])).
% 2.27/1.71 tff(365,plain,(
% 2.27/1.71 ![Fluent: $i, Time: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | ((~(~holdsAt(Fluent, Time))) | (~(~releasedAt(Fluent, plus(Time, n1)))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))))),
% 2.27/1.71 inference(skolemize,[status(sab)],[364])).
% 2.27/1.71 tff(366,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))),
% 2.27/1.71 inference(modus_ponens,[status(thm)],[365, 358])).
% 2.27/1.71 tff(367,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))),
% 2.27/1.71 inference(modus_ponens,[status(thm)],[366, 356])).
% 2.27/1.71 tff(368,plain,
% 2.27/1.71 (![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))),
% 2.27/1.71 inference(modus_ponens,[status(thm)],[367, 354])).
% 2.27/1.71 tff(369,plain,
% 2.27/1.71 (((~![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))) | ((~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)))) <=> ((~![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))) | (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)))),
% 2.27/1.71 inference(rewrite,[status(thm)],[])).
% 2.27/1.71 tff(370,plain,
% 2.27/1.71 ((releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0))))) <=> ((~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)))),
% 2.27/1.71 inference(rewrite,[status(thm)],[])).
% 2.27/1.71 tff(371,plain,
% 2.27/1.71 (((~![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))) | (releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))))) <=> ((~![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))) | ((~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))))),
% 2.27/1.71 inference(monotonicity,[status(thm)],[370])).
% 2.27/1.71 tff(372,plain,
% 2.27/1.71 (((~![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))) | (releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))))) <=> ((~![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))) | (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)))),
% 2.27/1.71 inference(transitivity,[status(thm)],[371, 369])).
% 2.27/1.71 tff(373,plain,
% 2.27/1.71 ((~![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))) | (releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))))),
% 2.27/1.71 inference(quant_inst,[status(thm)],[])).
% 2.27/1.71 tff(374,plain,
% 2.27/1.71 ((~![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))) | (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))),
% 2.27/1.71 inference(modus_ponens,[status(thm)],[373, 372])).
% 2.27/1.71 tff(375,plain,
% 2.27/1.71 ((~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))) | holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n0)),
% 2.27/1.71 inference(unit_resolution,[status(thm)],[374, 368, 352])).
% 2.27/1.71 tff(376,plain,
% 2.27/1.71 (~((~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)))),
% 2.27/1.71 inference(unit_resolution,[status(thm)],[375, 284, 172])).
% 2.27/1.71 tff(377,plain,
% 2.27/1.71 (((~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)),
% 2.27/1.71 inference(tautology,[status(thm)],[])).
% 2.27/1.71 tff(378,plain,
% 2.27/1.71 (initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)),
% 2.27/1.71 inference(unit_resolution,[status(thm)],[377, 376])).
% 2.27/1.71 tff(379,plain,
% 2.27/1.71 (((~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0))) | happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)),
% 2.27/1.71 inference(tautology,[status(thm)],[])).
% 2.27/1.71 tff(380,plain,
% 2.27/1.71 (happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)),
% 2.27/1.71 inference(unit_resolution,[status(thm)],[379, 376])).
% 2.27/1.71 tff(381,plain,
% 2.27/1.71 ((~![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))) | (less(n0, n1) <=> less_or_equal(n0, n0))),
% 2.27/1.71 inference(quant_inst,[status(thm)],[])).
% 2.27/1.71 tff(382,plain,
% 2.27/1.71 (less(n0, n1) <=> less_or_equal(n0, n0)),
% 2.27/1.71 inference(unit_resolution,[status(thm)],[381, 49])).
% 2.27/1.71 tff(383,plain,
% 2.27/1.71 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n0, n0)) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n0, n0))),
% 2.27/1.71 inference(rewrite,[status(thm)],[])).
% 2.27/1.71 tff(384,plain,
% 2.27/1.71 ((less_or_equal(n0, n0) <=> $true) <=> less_or_equal(n0, n0)),
% 2.27/1.71 inference(rewrite,[status(thm)],[])).
% 2.27/1.71 tff(385,plain,
% 2.27/1.71 (($true | less(n0, n0)) <=> $true),
% 2.27/1.71 inference(rewrite,[status(thm)],[])).
% 2.27/1.71 tff(386,plain,
% 2.27/1.71 (((n0 = n0) | less(n0, n0)) <=> ($true | less(n0, n0))),
% 2.27/1.71 inference(monotonicity,[status(thm)],[242])).
% 2.27/1.71 tff(387,plain,
% 2.27/1.71 (((n0 = n0) | less(n0, n0)) <=> $true),
% 2.27/1.71 inference(transitivity,[status(thm)],[386, 385])).
% 2.27/1.71 tff(388,plain,
% 2.27/1.71 ((less_or_equal(n0, n0) <=> ((n0 = n0) | less(n0, n0))) <=> (less_or_equal(n0, n0) <=> $true)),
% 2.27/1.71 inference(monotonicity,[status(thm)],[387])).
% 2.27/1.71 tff(389,plain,
% 2.27/1.71 ((less_or_equal(n0, n0) <=> ((n0 = n0) | less(n0, n0))) <=> less_or_equal(n0, n0)),
% 2.27/1.71 inference(transitivity,[status(thm)],[388, 384])).
% 2.27/1.71 tff(390,plain,
% 2.27/1.71 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(n0, n0) <=> ((n0 = n0) | less(n0, n0)))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n0, n0))),
% 2.27/1.71 inference(monotonicity,[status(thm)],[389])).
% 2.27/1.71 tff(391,plain,
% 2.27/1.71 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(n0, n0) <=> ((n0 = n0) | less(n0, n0)))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n0, n0))),
% 2.27/1.71 inference(transitivity,[status(thm)],[390, 383])).
% 2.27/1.71 tff(392,plain,
% 2.27/1.71 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(n0, n0) <=> ((n0 = n0) | less(n0, n0)))),
% 2.27/1.71 inference(quant_inst,[status(thm)],[])).
% 2.27/1.71 tff(393,plain,
% 2.27/1.71 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n0, n0)),
% 2.27/1.71 inference(modus_ponens,[status(thm)],[392, 391])).
% 2.27/1.71 tff(394,plain,
% 2.27/1.71 (less_or_equal(n0, n0)),
% 2.27/1.71 inference(unit_resolution,[status(thm)],[393, 39])).
% 2.27/1.71 tff(395,plain,
% 2.27/1.71 ((~(less(n0, n1) <=> less_or_equal(n0, n0))) | less(n0, n1) | (~less_or_equal(n0, n0))),
% 2.27/1.71 inference(tautology,[status(thm)],[])).
% 2.27/1.71 tff(396,plain,
% 2.27/1.71 (less(n0, n1)),
% 2.27/1.71 inference(unit_resolution,[status(thm)],[395, 394, 382])).
% 2.27/1.71 tff(397,plain,
% 2.27/1.71 (^[Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : refl((holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset))) <=> (holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset))))),
% 2.27/1.71 inference(bind,[status(th)],[])).
% 2.27/1.71 tff(398,plain,
% 2.27/1.71 (![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : (holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset))) <=> ![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : (holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset)))),
% 2.27/1.71 inference(quant_intro,[status(thm)],[397])).
% 2.27/1.71 tff(399,plain,
% 2.27/1.71 (^[Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : trans(monotonicity(trans(monotonicity(rewrite((happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset)))) <=> (~(stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset))))), ((~(happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset))))) <=> (~(~(stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset))))))), rewrite((~(~(stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset))))) <=> (stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset)))), ((~(happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset))))) <=> (stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset))))), (((~(happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset))))) | holdsAt(Fluent2, plus(Time, Offset))) <=> ((stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset))) | holdsAt(Fluent2, plus(Time, Offset))))), rewrite(((stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset))) | holdsAt(Fluent2, plus(Time, Offset))) <=> (holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset)))), (((~(happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset))))) | holdsAt(Fluent2, plus(Time, Offset))) <=> (holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset)))))),
% 2.27/1.71 inference(bind,[status(th)],[])).
% 2.27/1.71 tff(400,plain,
% 2.27/1.71 (![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset))))) | holdsAt(Fluent2, plus(Time, Offset))) <=> ![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : (holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset)))),
% 2.27/1.71 inference(quant_intro,[status(thm)],[399])).
% 2.27/1.71 tff(401,plain,
% 2.27/1.71 (![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset))))) | holdsAt(Fluent2, plus(Time, Offset))) <=> ![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset))))) | holdsAt(Fluent2, plus(Time, Offset)))),
% 2.27/1.71 inference(rewrite,[status(thm)],[])).
% 2.27/1.71 tff(402,plain,
% 2.27/1.71 (^[Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((happens(Event, Time) & initiates(Event, Fluent, Time)) & less(n0, Offset)) <=> (happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset))), ((((happens(Event, Time) & initiates(Event, Fluent, Time)) & less(n0, Offset)) & trajectory(Fluent, Time, Fluent2, Offset)) <=> ((happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset)) & trajectory(Fluent, Time, Fluent2, Offset)))), rewrite(((happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset)) & trajectory(Fluent, Time, Fluent2, Offset)) <=> (happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset))), ((((happens(Event, Time) & initiates(Event, Fluent, Time)) & less(n0, Offset)) & trajectory(Fluent, Time, Fluent2, Offset)) <=> (happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset)))), (((((happens(Event, Time) & initiates(Event, Fluent, Time)) & less(n0, Offset)) & trajectory(Fluent, Time, Fluent2, Offset)) & (~stoppedIn(Time, Fluent, plus(Time, Offset)))) <=> ((happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset)) & (~stoppedIn(Time, Fluent, plus(Time, Offset)))))), rewrite(((happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset)) & (~stoppedIn(Time, Fluent, plus(Time, Offset)))) <=> (happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset))))), (((((happens(Event, Time) & initiates(Event, Fluent, Time)) & less(n0, Offset)) & trajectory(Fluent, Time, Fluent2, Offset)) & (~stoppedIn(Time, Fluent, plus(Time, Offset)))) <=> (happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset)))))), ((((((happens(Event, Time) & initiates(Event, Fluent, Time)) & less(n0, Offset)) & trajectory(Fluent, Time, Fluent2, Offset)) & (~stoppedIn(Time, Fluent, plus(Time, Offset)))) => holdsAt(Fluent2, plus(Time, Offset))) <=> ((happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset)))) => holdsAt(Fluent2, plus(Time, Offset))))), rewrite(((happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset)))) => holdsAt(Fluent2, plus(Time, Offset))) <=> ((~(happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset))))) | holdsAt(Fluent2, plus(Time, Offset)))), ((((((happens(Event, Time) & initiates(Event, Fluent, Time)) & less(n0, Offset)) & trajectory(Fluent, Time, Fluent2, Offset)) & (~stoppedIn(Time, Fluent, plus(Time, Offset)))) => holdsAt(Fluent2, plus(Time, Offset))) <=> ((~(happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset))))) | holdsAt(Fluent2, plus(Time, Offset)))))),
% 2.27/1.71 inference(bind,[status(th)],[])).
% 2.27/1.71 tff(403,plain,
% 2.27/1.71 (![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : (((((happens(Event, Time) & initiates(Event, Fluent, Time)) & less(n0, Offset)) & trajectory(Fluent, Time, Fluent2, Offset)) & (~stoppedIn(Time, Fluent, plus(Time, Offset)))) => holdsAt(Fluent2, plus(Time, Offset))) <=> ![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset))))) | holdsAt(Fluent2, plus(Time, Offset)))),
% 2.27/1.71 inference(quant_intro,[status(thm)],[402])).
% 2.27/1.71 tff(404,axiom,(![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : (((((happens(Event, Time) & initiates(Event, Fluent, Time)) & less(n0, Offset)) & trajectory(Fluent, Time, Fluent2, Offset)) & (~stoppedIn(Time, Fluent, plus(Time, Offset)))) => holdsAt(Fluent2, plus(Time, Offset)))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax','change_holding')).
% 2.27/1.71 tff(405,plain,
% 2.27/1.71 (![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset))))) | holdsAt(Fluent2, plus(Time, Offset)))),
% 2.27/1.71 inference(modus_ponens,[status(thm)],[404, 403])).
% 2.27/1.71 tff(406,plain,
% 2.27/1.71 (![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset))))) | holdsAt(Fluent2, plus(Time, Offset)))),
% 2.27/1.71 inference(modus_ponens,[status(thm)],[405, 401])).
% 2.27/1.71 tff(407,plain,(
% 2.27/1.71 ![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time) & less(n0, Offset) & trajectory(Fluent, Time, Fluent2, Offset) & (~stoppedIn(Time, Fluent, plus(Time, Offset))))) | holdsAt(Fluent2, plus(Time, Offset)))),
% 2.27/1.72 inference(skolemize,[status(sab)],[406])).
% 2.27/1.72 tff(408,plain,
% 2.27/1.72 (![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : (holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset)))),
% 2.27/1.72 inference(modus_ponens,[status(thm)],[407, 400])).
% 2.27/1.72 tff(409,plain,
% 2.27/1.72 (![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : (holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset)))),
% 2.27/1.72 inference(modus_ponens,[status(thm)],[408, 398])).
% 2.27/1.72 tff(410,plain,
% 2.27/1.72 (((~![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : (holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset)))) | (stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | holdsAt(waterLevel(n1), plus(n0, n1)) | (~trajectory(tptp_fun_Height_10(waterLevel(filling), tapOn), n0, waterLevel(n1), n1)) | (~less(n0, n1)))) <=> ((~![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : (holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset)))) | stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | holdsAt(waterLevel(n1), plus(n0, n1)) | (~trajectory(tptp_fun_Height_10(waterLevel(filling), tapOn), n0, waterLevel(n1), n1)) | (~less(n0, n1)))),
% 2.27/1.72 inference(rewrite,[status(thm)],[])).
% 2.27/1.72 tff(411,plain,
% 2.27/1.72 ((holdsAt(waterLevel(n1), plus(n0, n1)) | stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~less(n0, n1)) | (~trajectory(tptp_fun_Height_10(waterLevel(filling), tapOn), n0, waterLevel(n1), n1))) <=> (stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | holdsAt(waterLevel(n1), plus(n0, n1)) | (~trajectory(tptp_fun_Height_10(waterLevel(filling), tapOn), n0, waterLevel(n1), n1)) | (~less(n0, n1)))),
% 2.27/1.72 inference(rewrite,[status(thm)],[])).
% 2.27/1.72 tff(412,plain,
% 2.27/1.72 (((~![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : (holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset)))) | (holdsAt(waterLevel(n1), plus(n0, n1)) | stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~less(n0, n1)) | (~trajectory(tptp_fun_Height_10(waterLevel(filling), tapOn), n0, waterLevel(n1), n1)))) <=> ((~![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : (holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset)))) | (stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | holdsAt(waterLevel(n1), plus(n0, n1)) | (~trajectory(tptp_fun_Height_10(waterLevel(filling), tapOn), n0, waterLevel(n1), n1)) | (~less(n0, n1))))),
% 2.27/1.72 inference(monotonicity,[status(thm)],[411])).
% 2.27/1.72 tff(413,plain,
% 2.27/1.72 (((~![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : (holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset)))) | (holdsAt(waterLevel(n1), plus(n0, n1)) | stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~less(n0, n1)) | (~trajectory(tptp_fun_Height_10(waterLevel(filling), tapOn), n0, waterLevel(n1), n1)))) <=> ((~![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : (holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset)))) | stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | holdsAt(waterLevel(n1), plus(n0, n1)) | (~trajectory(tptp_fun_Height_10(waterLevel(filling), tapOn), n0, waterLevel(n1), n1)) | (~less(n0, n1)))),
% 2.27/1.72 inference(transitivity,[status(thm)],[412, 410])).
% 2.27/1.72 tff(414,plain,
% 2.27/1.72 ((~![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : (holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset)))) | (holdsAt(waterLevel(n1), plus(n0, n1)) | stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~less(n0, n1)) | (~trajectory(tptp_fun_Height_10(waterLevel(filling), tapOn), n0, waterLevel(n1), n1)))),
% 2.27/1.72 inference(quant_inst,[status(thm)],[])).
% 2.27/1.72 tff(415,plain,
% 2.27/1.72 ((~![Event: $i, Time: $i, Fluent: $i, Fluent2: $i, Offset: $i] : (holdsAt(Fluent2, plus(Time, Offset)) | stoppedIn(Time, Fluent, plus(Time, Offset)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)) | (~less(n0, Offset)) | (~trajectory(Fluent, Time, Fluent2, Offset)))) | stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | (~initiates(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n0)) | (~happens(tptp_fun_Event_5(n0, tptp_fun_Height_10(waterLevel(filling), tapOn)), n0)) | holdsAt(waterLevel(n1), plus(n0, n1)) | (~trajectory(tptp_fun_Height_10(waterLevel(filling), tapOn), n0, waterLevel(n1), n1)) | (~less(n0, n1))),
% 2.27/1.72 inference(modus_ponens,[status(thm)],[414, 413])).
% 2.27/1.72 tff(416,plain,
% 2.27/1.72 (stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | holdsAt(waterLevel(n1), plus(n0, n1)) | (~trajectory(tptp_fun_Height_10(waterLevel(filling), tapOn), n0, waterLevel(n1), n1))),
% 2.27/1.72 inference(unit_resolution,[status(thm)],[415, 409, 396, 380, 378])).
% 2.27/1.72 tff(417,plain,
% 2.27/1.72 (stoppedIn(n0, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) | holdsAt(waterLevel(n1), plus(n0, n1))),
% 2.27/1.72 inference(unit_resolution,[status(thm)],[416, 165])).
% 2.27/1.72 tff(418,plain,
% 2.27/1.72 (holdsAt(waterLevel(n1), plus(n0, n1))),
% 2.27/1.72 inference(unit_resolution,[status(thm)],[417, 82])).
% 2.27/1.72 tff(419,plain,
% 2.27/1.72 (holdsAt(waterLevel(n1), n1) <=> holdsAt(waterLevel(n1), plus(n0, n1))),
% 2.27/1.72 inference(monotonicity,[status(thm)],[4])).
% 2.27/1.72 tff(420,plain,
% 2.27/1.72 (holdsAt(waterLevel(n1), plus(n0, n1)) <=> holdsAt(waterLevel(n1), n1)),
% 2.27/1.72 inference(symmetry,[status(thm)],[419])).
% 2.27/1.72 tff(421,assumption,(holdsAt(waterLevel(n1), plus(n0, n1))), introduced(assumption)).
% 2.27/1.72 tff(422,plain,
% 2.27/1.72 (holdsAt(waterLevel(n1), n1)),
% 2.27/1.72 inference(modus_ponens,[status(thm)],[421, 420])).
% 2.27/1.72 tff(423,plain,
% 2.27/1.72 ((plus(n1, n1) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> (plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = plus(n1, n1))),
% 2.27/1.72 inference(commutativity,[status(thm)],[])).
% 2.27/1.72 tff(424,plain,
% 2.27/1.72 ((~(plus(n1, n1) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) <=> (~(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = plus(n1, n1)))),
% 2.27/1.72 inference(monotonicity,[status(thm)],[423])).
% 2.27/1.72 tff(425,plain,
% 2.27/1.72 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> ((plus(plus(n1, n1), plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))))),
% 2.27/1.72 inference(quant_inst,[status(thm)],[])).
% 2.27/1.72 tff(426,plain,
% 2.27/1.72 (less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> ((plus(plus(n1, n1), plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 2.27/1.72 inference(unit_resolution,[status(thm)],[425, 39])).
% 2.27/1.72 tff(427,plain,
% 2.27/1.72 (^[X: $i] : refl((less(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, plus(n1, n1))))) <=> (less(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, plus(n1, n1))))))),
% 2.27/1.72 inference(bind,[status(th)],[])).
% 2.27/1.72 tff(428,plain,
% 2.27/1.72 (![X: $i] : (less(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, plus(n1, n1))))) <=> ![X: $i] : (less(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 2.27/1.72 inference(quant_intro,[status(thm)],[427])).
% 2.27/1.72 tff(429,plain,
% 2.27/1.72 (^[X: $i] : rewrite((less(X, n6) <=> less_or_equal(X, n5)) <=> (less(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, plus(n1, n1))))))),
% 2.27/1.72 inference(bind,[status(th)],[])).
% 2.27/1.72 tff(430,plain,
% 2.27/1.72 (![X: $i] : (less(X, n6) <=> less_or_equal(X, n5)) <=> ![X: $i] : (less(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 2.27/1.72 inference(quant_intro,[status(thm)],[429])).
% 2.27/1.72 tff(431,plain,
% 2.27/1.72 (![X: $i] : (less(X, n6) <=> less_or_equal(X, n5)) <=> ![X: $i] : (less(X, n6) <=> less_or_equal(X, n5))),
% 2.27/1.72 inference(rewrite,[status(thm)],[])).
% 2.27/1.72 tff(432,axiom,(![X: $i] : (less(X, n6) <=> less_or_equal(X, n5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','less6')).
% 2.27/1.72 tff(433,plain,
% 2.27/1.72 (![X: $i] : (less(X, n6) <=> less_or_equal(X, n5))),
% 2.27/1.72 inference(modus_ponens,[status(thm)],[432, 431])).
% 2.27/1.72 tff(434,plain,
% 2.27/1.72 (![X: $i] : (less(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 2.27/1.72 inference(modus_ponens,[status(thm)],[433, 430])).
% 2.27/1.72 tff(435,plain,(
% 2.27/1.72 ![X: $i] : (less(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 2.27/1.72 inference(skolemize,[status(sab)],[434])).
% 2.27/1.72 tff(436,plain,
% 2.27/1.72 (![X: $i] : (less(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 2.27/1.72 inference(modus_ponens,[status(thm)],[435, 428])).
% 2.27/1.72 tff(437,plain,
% 2.27/1.72 ((~![X: $i] : (less(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))))) | (less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 2.27/1.72 inference(quant_inst,[status(thm)],[])).
% 2.27/1.72 tff(438,plain,
% 2.27/1.72 (less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1))))),
% 2.27/1.72 inference(unit_resolution,[status(thm)],[437, 436])).
% 2.27/1.72 tff(439,assumption,(~less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1))))), introduced(assumption)).
% 2.27/1.72 tff(440,plain,
% 2.27/1.72 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1))))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 2.27/1.72 inference(rewrite,[status(thm)],[])).
% 2.27/1.72 tff(441,plain,
% 2.27/1.72 ((less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> $true) <=> less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1))))),
% 2.27/1.72 inference(rewrite,[status(thm)],[])).
% 2.27/1.72 tff(442,plain,
% 2.27/1.72 (($true | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1))))) <=> $true),
% 2.27/1.72 inference(rewrite,[status(thm)],[])).
% 2.27/1.72 tff(443,plain,
% 2.27/1.72 ((plus(plus(n1, n1), plus(n1, plus(n1, n1))) = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> $true),
% 2.27/1.72 inference(rewrite,[status(thm)],[])).
% 2.27/1.72 tff(444,plain,
% 2.27/1.72 (((plus(plus(n1, n1), plus(n1, plus(n1, n1))) = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1))))) <=> ($true | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 2.27/1.72 inference(monotonicity,[status(thm)],[443])).
% 2.27/1.72 tff(445,plain,
% 2.27/1.72 (((plus(plus(n1, n1), plus(n1, plus(n1, n1))) = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1))))) <=> $true),
% 2.27/1.72 inference(transitivity,[status(thm)],[444, 442])).
% 2.27/1.72 tff(446,plain,
% 2.27/1.72 ((less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> ((plus(plus(n1, n1), plus(n1, plus(n1, n1))) = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))))) <=> (less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> $true)),
% 2.27/1.72 inference(monotonicity,[status(thm)],[445])).
% 2.27/1.72 tff(447,plain,
% 2.27/1.72 ((less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> ((plus(plus(n1, n1), plus(n1, plus(n1, n1))) = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))))) <=> less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1))))),
% 2.27/1.72 inference(transitivity,[status(thm)],[446, 441])).
% 2.27/1.72 tff(448,plain,
% 2.27/1.72 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> ((plus(plus(n1, n1), plus(n1, plus(n1, n1))) = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1))))))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 2.27/1.72 inference(monotonicity,[status(thm)],[447])).
% 2.27/1.72 tff(449,plain,
% 2.27/1.72 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> ((plus(plus(n1, n1), plus(n1, plus(n1, n1))) = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1))))))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 2.27/1.72 inference(transitivity,[status(thm)],[448, 440])).
% 2.27/1.72 tff(450,plain,
% 2.27/1.72 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> ((plus(plus(n1, n1), plus(n1, plus(n1, n1))) = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1))))))),
% 2.27/1.72 inference(quant_inst,[status(thm)],[])).
% 2.27/1.72 tff(451,plain,
% 2.27/1.72 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1))))),
% 2.27/1.72 inference(modus_ponens,[status(thm)],[450, 449])).
% 2.27/1.72 tff(452,plain,
% 2.27/1.72 ($false),
% 2.27/1.72 inference(unit_resolution,[status(thm)],[451, 39, 439])).
% 2.27/1.72 tff(453,plain,(less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1))))), inference(lemma,lemma(discharge,[]))).
% 2.27/1.72 tff(454,plain,
% 2.27/1.72 ((~(less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | (~less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 2.27/1.72 inference(tautology,[status(thm)],[])).
% 2.27/1.72 tff(455,plain,
% 2.27/1.72 ((~(less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, n1), plus(n1, plus(n1, n1)))))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 2.27/1.72 inference(unit_resolution,[status(thm)],[454, 453])).
% 2.27/1.72 tff(456,plain,
% 2.27/1.72 (less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 2.27/1.72 inference(unit_resolution,[status(thm)],[455, 438])).
% 2.27/1.72 tff(457,plain,
% 2.27/1.72 (((plus(plus(n1, n1), plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) | (~less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 2.27/1.72 inference(tautology,[status(thm)],[])).
% 2.27/1.72 tff(458,plain,
% 2.27/1.72 ((plus(plus(n1, n1), plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 2.27/1.72 inference(unit_resolution,[status(thm)],[457, 456])).
% 2.27/1.72 tff(459,plain,
% 2.27/1.72 ((~(less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> ((plus(plus(n1, n1), plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))))) | less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | (~((plus(plus(n1, n1), plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))))),
% 2.27/1.72 inference(tautology,[status(thm)],[])).
% 2.27/1.72 tff(460,plain,
% 2.27/1.72 ((~(less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> ((plus(plus(n1, n1), plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))))) | less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 2.27/1.72 inference(unit_resolution,[status(thm)],[459, 458])).
% 2.27/1.72 tff(461,plain,
% 2.27/1.72 (less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[460, 426])).
% 2.27/1.73 tff(462,assumption,(plus(n1, n1) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))), introduced(assumption)).
% 2.27/1.73 tff(463,plain,
% 2.27/1.73 (plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = plus(n1, n1)),
% 2.27/1.73 inference(symmetry,[status(thm)],[462])).
% 2.27/1.73 tff(464,plain,
% 2.27/1.73 (less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, n1))),
% 2.27/1.73 inference(monotonicity,[status(thm)],[463])).
% 2.27/1.73 tff(465,plain,
% 2.27/1.73 (less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, n1)) <=> less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(symmetry,[status(thm)],[464])).
% 2.27/1.73 tff(466,plain,
% 2.27/1.73 ((~less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, n1))) <=> (~less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 2.27/1.73 inference(monotonicity,[status(thm)],[465])).
% 2.27/1.73 tff(467,plain,
% 2.27/1.73 (^[X: $i] : refl((less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1))) <=> (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1))))),
% 2.27/1.73 inference(bind,[status(th)],[])).
% 2.27/1.73 tff(468,plain,
% 2.27/1.73 (![X: $i] : (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1))) <=> ![X: $i] : (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1)))),
% 2.27/1.73 inference(quant_intro,[status(thm)],[467])).
% 2.27/1.73 tff(469,plain,
% 2.27/1.73 (^[X: $i] : rewrite((less(X, n3) <=> less_or_equal(X, n2)) <=> (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1))))),
% 2.27/1.73 inference(bind,[status(th)],[])).
% 2.27/1.73 tff(470,plain,
% 2.27/1.73 (![X: $i] : (less(X, n3) <=> less_or_equal(X, n2)) <=> ![X: $i] : (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1)))),
% 2.27/1.73 inference(quant_intro,[status(thm)],[469])).
% 2.27/1.73 tff(471,plain,
% 2.27/1.73 (![X: $i] : (less(X, n3) <=> less_or_equal(X, n2)) <=> ![X: $i] : (less(X, n3) <=> less_or_equal(X, n2))),
% 2.27/1.73 inference(rewrite,[status(thm)],[])).
% 2.27/1.73 tff(472,axiom,(![X: $i] : (less(X, n3) <=> less_or_equal(X, n2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','less3')).
% 2.27/1.73 tff(473,plain,
% 2.27/1.73 (![X: $i] : (less(X, n3) <=> less_or_equal(X, n2))),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[472, 471])).
% 2.27/1.73 tff(474,plain,
% 2.27/1.73 (![X: $i] : (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1)))),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[473, 470])).
% 2.27/1.73 tff(475,plain,(
% 2.27/1.73 ![X: $i] : (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1)))),
% 2.27/1.73 inference(skolemize,[status(sab)],[474])).
% 2.27/1.73 tff(476,plain,
% 2.27/1.73 (![X: $i] : (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1)))),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[475, 468])).
% 2.27/1.73 tff(477,plain,
% 2.27/1.73 ((~![X: $i] : (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1)))) | (less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1))) <=> less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, n1)))),
% 2.27/1.73 inference(quant_inst,[status(thm)],[])).
% 2.27/1.73 tff(478,plain,
% 2.27/1.73 (less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1))) <=> less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, n1))),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[477, 476])).
% 2.27/1.73 tff(479,plain,
% 2.27/1.73 ((~![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))) | (less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1))) <=> (~((plus(n1, plus(n1, n1)) = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, plus(n1, n1)))))))),
% 2.27/1.73 inference(quant_inst,[status(thm)],[])).
% 2.27/1.73 tff(480,plain,
% 2.27/1.73 (less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1))) <=> (~((plus(n1, plus(n1, n1)) = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, plus(n1, n1))))))),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[479, 67])).
% 2.27/1.73 tff(481,plain,
% 2.27/1.73 ((plus(n2, n2) = n4) <=> (plus(plus(n1, n1), plus(n1, n1)) = plus(n1, plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(rewrite,[status(thm)],[])).
% 2.27/1.73 tff(482,plain,
% 2.27/1.73 ((plus(n2, n2) = n4) <=> (plus(n2, n2) = n4)),
% 2.27/1.73 inference(rewrite,[status(thm)],[])).
% 2.27/1.73 tff(483,axiom,(plus(n2, n2) = n4), file('/export/starexec/sandbox/benchmark/theBenchmark.p','plus2_2')).
% 2.27/1.73 tff(484,plain,
% 2.27/1.73 (plus(n2, n2) = n4),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[483, 482])).
% 2.27/1.73 tff(485,plain,
% 2.27/1.73 (plus(plus(n1, n1), plus(n1, n1)) = plus(n1, plus(n1, plus(n1, n1)))),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[484, 481])).
% 2.27/1.73 tff(486,plain,
% 2.27/1.73 (less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))) <=> less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(monotonicity,[status(thm)],[485])).
% 2.27/1.73 tff(487,assumption,(~less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))), introduced(assumption)).
% 2.27/1.73 tff(488,plain,
% 2.27/1.73 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(rewrite,[status(thm)],[])).
% 2.27/1.73 tff(489,plain,
% 2.27/1.73 ((less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> $true) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))),
% 2.27/1.73 inference(rewrite,[status(thm)],[])).
% 2.27/1.73 tff(490,plain,
% 2.27/1.73 (($true | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> $true),
% 2.27/1.73 inference(rewrite,[status(thm)],[])).
% 2.27/1.73 tff(491,plain,
% 2.27/1.73 ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) <=> $true),
% 2.27/1.73 inference(rewrite,[status(thm)],[])).
% 2.27/1.73 tff(492,plain,
% 2.27/1.73 (((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> ($true | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(monotonicity,[status(thm)],[491])).
% 2.27/1.73 tff(493,plain,
% 2.27/1.73 (((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> $true),
% 2.27/1.73 inference(transitivity,[status(thm)],[492, 490])).
% 2.27/1.73 tff(494,plain,
% 2.27/1.73 ((less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) <=> (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> $true)),
% 2.27/1.73 inference(monotonicity,[status(thm)],[493])).
% 2.27/1.73 tff(495,plain,
% 2.27/1.73 ((less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))),
% 2.27/1.73 inference(transitivity,[status(thm)],[494, 489])).
% 2.27/1.73 tff(496,plain,
% 2.27/1.73 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(monotonicity,[status(thm)],[495])).
% 2.27/1.73 tff(497,plain,
% 2.27/1.73 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(transitivity,[status(thm)],[496, 488])).
% 2.27/1.73 tff(498,plain,
% 2.27/1.73 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 2.27/1.73 inference(quant_inst,[status(thm)],[])).
% 2.27/1.73 tff(499,plain,
% 2.27/1.73 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[498, 497])).
% 2.27/1.73 tff(500,plain,
% 2.27/1.73 ($false),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[499, 39, 487])).
% 2.27/1.73 tff(501,plain,(less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))), inference(lemma,lemma(discharge,[]))).
% 2.27/1.73 tff(502,assumption,(~(less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))), introduced(assumption)).
% 2.27/1.73 tff(503,plain,
% 2.27/1.73 (^[X: $i] : refl((less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1)))) <=> (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1)))))),
% 2.27/1.73 inference(bind,[status(th)],[])).
% 2.27/1.73 tff(504,plain,
% 2.27/1.73 (![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1)))) <=> ![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(quant_intro,[status(thm)],[503])).
% 2.27/1.73 tff(505,plain,
% 2.27/1.73 (^[X: $i] : rewrite((less(X, plus(n1, plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(n1, plus(n1, n1)))) <=> (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1)))))),
% 2.27/1.73 inference(bind,[status(th)],[])).
% 2.27/1.73 tff(506,plain,
% 2.27/1.73 (![X: $i] : (less(X, plus(n1, plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(n1, plus(n1, n1)))) <=> ![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(quant_intro,[status(thm)],[505])).
% 2.27/1.73 tff(507,plain,
% 2.27/1.73 (^[X: $i] : rewrite((less(X, n4) <=> less_or_equal(X, n3)) <=> (less(X, plus(n1, plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(n1, plus(n1, n1)))))),
% 2.27/1.73 inference(bind,[status(th)],[])).
% 2.27/1.73 tff(508,plain,
% 2.27/1.73 (![X: $i] : (less(X, n4) <=> less_or_equal(X, n3)) <=> ![X: $i] : (less(X, plus(n1, plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(quant_intro,[status(thm)],[507])).
% 2.27/1.73 tff(509,plain,
% 2.27/1.73 (![X: $i] : (less(X, n4) <=> less_or_equal(X, n3)) <=> ![X: $i] : (less(X, n4) <=> less_or_equal(X, n3))),
% 2.27/1.73 inference(rewrite,[status(thm)],[])).
% 2.27/1.73 tff(510,axiom,(![X: $i] : (less(X, n4) <=> less_or_equal(X, n3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','less4')).
% 2.27/1.73 tff(511,plain,
% 2.27/1.73 (![X: $i] : (less(X, n4) <=> less_or_equal(X, n3))),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[510, 509])).
% 2.27/1.73 tff(512,plain,
% 2.27/1.73 (![X: $i] : (less(X, plus(n1, plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[511, 508])).
% 2.27/1.73 tff(513,plain,
% 2.27/1.73 (![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[512, 506])).
% 2.27/1.73 tff(514,plain,(
% 2.27/1.73 ![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(skolemize,[status(sab)],[513])).
% 2.27/1.73 tff(515,plain,
% 2.27/1.73 (![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[514, 504])).
% 2.27/1.73 tff(516,plain,
% 2.27/1.73 ((~![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1))))) | (less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(quant_inst,[status(thm)],[])).
% 2.27/1.73 tff(517,plain,
% 2.27/1.73 ($false),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[516, 515, 502])).
% 2.27/1.73 tff(518,plain,(less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))), inference(lemma,lemma(discharge,[]))).
% 2.27/1.73 tff(519,plain,
% 2.27/1.73 ((~(less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) | less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))) | (~less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(tautology,[status(thm)],[])).
% 2.27/1.73 tff(520,plain,
% 2.27/1.73 (less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))) | (~less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[519, 518])).
% 2.27/1.73 tff(521,plain,
% 2.27/1.73 (less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1)))),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[520, 501])).
% 2.27/1.73 tff(522,plain,
% 2.27/1.73 (less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[521, 486])).
% 2.27/1.73 tff(523,plain,
% 2.27/1.73 (((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1))))) | (~less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1)))))),
% 2.27/1.73 inference(tautology,[status(thm)],[])).
% 2.27/1.73 tff(524,plain,
% 2.27/1.73 ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[523, 522])).
% 2.27/1.73 tff(525,assumption,(~(less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1)))) <=> ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1))))))), introduced(assumption)).
% 2.27/1.73 tff(526,plain,
% 2.27/1.73 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1)))) <=> ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1))))))),
% 2.27/1.73 inference(quant_inst,[status(thm)],[])).
% 2.27/1.73 tff(527,plain,
% 2.27/1.73 ($false),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[526, 39, 525])).
% 2.27/1.73 tff(528,plain,(less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1)))) <=> ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1)))))), inference(lemma,lemma(discharge,[]))).
% 2.27/1.73 tff(529,plain,
% 2.27/1.73 ((~(less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1)))) <=> ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1))))))) | less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1)))) | (~((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1))))))),
% 2.27/1.73 inference(tautology,[status(thm)],[])).
% 2.27/1.73 tff(530,plain,
% 2.27/1.73 (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1)))) | (~((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1))))))),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[529, 528])).
% 2.27/1.73 tff(531,plain,
% 2.27/1.73 (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[530, 524])).
% 2.27/1.73 tff(532,plain,
% 2.27/1.73 (plus(n1, plus(n1, plus(n1, n1))) = plus(plus(n1, n1), plus(n1, n1))),
% 2.27/1.73 inference(symmetry,[status(thm)],[485])).
% 2.27/1.73 tff(533,plain,
% 2.27/1.73 (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1)))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1)))),
% 2.27/1.73 inference(monotonicity,[status(thm)],[532])).
% 2.27/1.73 tff(534,plain,
% 2.27/1.73 (less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(symmetry,[status(thm)],[533])).
% 2.27/1.73 tff(535,plain,
% 2.27/1.73 ((~less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1)))) <=> (~less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1)))))),
% 2.27/1.73 inference(monotonicity,[status(thm)],[534])).
% 2.27/1.73 tff(536,assumption,(~less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1)))), introduced(assumption)).
% 2.27/1.73 tff(537,plain,
% 2.27/1.73 (~less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[536, 535])).
% 2.27/1.73 tff(538,assumption,(less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1))))), introduced(assumption)).
% 2.27/1.73 tff(539,plain,
% 2.27/1.73 ($false),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[538, 537])).
% 2.27/1.73 tff(540,plain,((~less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, plus(n1, n1))))) | less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1)))), inference(lemma,lemma(discharge,[]))).
% 2.27/1.73 tff(541,plain,
% 2.27/1.73 (less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1)))),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[540, 531])).
% 2.27/1.73 tff(542,assumption,(~(less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))))), introduced(assumption)).
% 2.27/1.73 tff(543,plain,
% 2.27/1.73 (^[X: $i] : refl((less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, n1)))) <=> (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, n1)))))),
% 2.27/1.73 inference(bind,[status(th)],[])).
% 2.27/1.73 tff(544,plain,
% 2.27/1.73 (![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, n1)))) <=> ![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, n1))))),
% 2.27/1.73 inference(quant_intro,[status(thm)],[543])).
% 2.27/1.73 tff(545,plain,
% 2.27/1.73 (^[X: $i] : rewrite((less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(n1, plus(n1, plus(n1, n1))))) <=> (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, n1)))))),
% 2.27/1.73 inference(bind,[status(th)],[])).
% 2.27/1.73 tff(546,plain,
% 2.27/1.73 (![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(n1, plus(n1, plus(n1, n1))))) <=> ![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, n1))))),
% 2.27/1.73 inference(quant_intro,[status(thm)],[545])).
% 2.27/1.73 tff(547,plain,
% 2.27/1.73 (^[X: $i] : rewrite((less(X, n5) <=> less_or_equal(X, n4)) <=> (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(n1, plus(n1, plus(n1, n1))))))),
% 2.27/1.73 inference(bind,[status(th)],[])).
% 2.27/1.73 tff(548,plain,
% 2.27/1.73 (![X: $i] : (less(X, n5) <=> less_or_equal(X, n4)) <=> ![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(n1, plus(n1, plus(n1, n1)))))),
% 2.27/1.73 inference(quant_intro,[status(thm)],[547])).
% 2.27/1.73 tff(549,plain,
% 2.27/1.73 (![X: $i] : (less(X, n5) <=> less_or_equal(X, n4)) <=> ![X: $i] : (less(X, n5) <=> less_or_equal(X, n4))),
% 2.27/1.73 inference(rewrite,[status(thm)],[])).
% 2.27/1.73 tff(550,axiom,(![X: $i] : (less(X, n5) <=> less_or_equal(X, n4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','less5')).
% 2.27/1.73 tff(551,plain,
% 2.27/1.73 (![X: $i] : (less(X, n5) <=> less_or_equal(X, n4))),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[550, 549])).
% 2.27/1.73 tff(552,plain,
% 2.27/1.73 (![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(n1, plus(n1, plus(n1, n1)))))),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[551, 548])).
% 2.27/1.73 tff(553,plain,
% 2.27/1.73 (![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, n1))))),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[552, 546])).
% 2.27/1.73 tff(554,plain,(
% 2.27/1.73 ![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, n1))))),
% 2.27/1.73 inference(skolemize,[status(sab)],[553])).
% 2.27/1.73 tff(555,plain,
% 2.27/1.73 (![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, n1))))),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[554, 544])).
% 2.27/1.73 tff(556,plain,
% 2.27/1.73 ((~![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, n1))))) | (less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))))),
% 2.27/1.73 inference(quant_inst,[status(thm)],[])).
% 2.27/1.73 tff(557,plain,
% 2.27/1.73 ($false),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[556, 555, 542])).
% 2.27/1.73 tff(558,plain,(less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1)))), inference(lemma,lemma(discharge,[]))).
% 2.27/1.73 tff(559,plain,
% 2.27/1.73 ((~(less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))))) | less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | (~less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))))),
% 2.27/1.73 inference(tautology,[status(thm)],[])).
% 2.27/1.73 tff(560,plain,
% 2.27/1.73 (less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | (~less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))))),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[559, 558])).
% 2.27/1.73 tff(561,plain,
% 2.27/1.73 (less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[560, 541])).
% 2.27/1.73 tff(562,plain,
% 2.27/1.73 (((plus(n1, plus(n1, n1)) = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, plus(n1, n1))))) | (~less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 2.27/1.73 inference(tautology,[status(thm)],[])).
% 2.27/1.73 tff(563,plain,
% 2.27/1.73 ((plus(n1, plus(n1, n1)) = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[562, 561])).
% 2.27/1.73 tff(564,plain,
% 2.27/1.73 ((~(less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1))) <=> (~((plus(n1, plus(n1, n1)) = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, plus(n1, n1)))))))) | (~less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~((plus(n1, plus(n1, n1)) = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, plus(n1, n1))))))),
% 2.27/1.73 inference(tautology,[status(thm)],[])).
% 2.27/1.73 tff(565,plain,
% 2.27/1.73 ((~(less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1))) <=> (~((plus(n1, plus(n1, n1)) = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, plus(n1, n1)))))))) | (~less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[564, 563])).
% 2.27/1.73 tff(566,plain,
% 2.27/1.73 (~less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[565, 480])).
% 2.27/1.73 tff(567,plain,
% 2.27/1.73 ((~(less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1))) <=> less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, n1)))) | less(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1))) | (~less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, n1)))),
% 2.27/1.73 inference(tautology,[status(thm)],[])).
% 2.27/1.73 tff(568,plain,
% 2.27/1.73 (~less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(n1, n1))),
% 2.27/1.73 inference(unit_resolution,[status(thm)],[567, 566, 478])).
% 2.27/1.73 tff(569,plain,
% 2.27/1.73 (~less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 2.27/1.73 inference(modus_ponens,[status(thm)],[568, 466])).
% 2.27/1.73 tff(570,assumption,(less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))), introduced(assumption)).
% 2.27/1.74 tff(571,plain,
% 2.27/1.74 ($false),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[570, 569])).
% 2.27/1.74 tff(572,plain,((~(plus(n1, n1) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) | (~less_or_equal(plus(plus(n1, n1), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))), inference(lemma,lemma(discharge,[]))).
% 2.27/1.74 tff(573,plain,
% 2.27/1.74 (~(plus(n1, n1) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[572, 461])).
% 2.27/1.74 tff(574,plain,
% 2.27/1.74 (~(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = plus(n1, n1))),
% 2.27/1.74 inference(modus_ponens,[status(thm)],[573, 424])).
% 2.27/1.74 tff(575,assumption,(n1 = plus(n1, plus(n1, n1))), introduced(assumption)).
% 2.27/1.74 tff(576,plain,
% 2.27/1.74 (plus(n1, plus(n1, n1)) = n1),
% 2.27/1.74 inference(symmetry,[status(thm)],[575])).
% 2.27/1.74 tff(577,plain,
% 2.27/1.74 (plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = plus(n1, n1)),
% 2.27/1.74 inference(monotonicity,[status(thm)],[576, 576])).
% 2.27/1.74 tff(578,assumption,(~(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = plus(n1, n1))), introduced(assumption)).
% 2.27/1.74 tff(579,plain,
% 2.27/1.74 ($false),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[578, 577])).
% 2.27/1.74 tff(580,plain,((~(n1 = plus(n1, plus(n1, n1)))) | (plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = plus(n1, n1))), inference(lemma,lemma(discharge,[]))).
% 2.27/1.74 tff(581,plain,
% 2.27/1.74 (~(n1 = plus(n1, plus(n1, n1)))),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[580, 574])).
% 2.27/1.74 tff(582,assumption,(holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)), introduced(assumption)).
% 2.27/1.74 tff(583,plain,
% 2.27/1.74 (^[Time: $i, Height1: $i, Height2: $i] : refl(((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time))) <=> ((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time))))),
% 2.27/1.74 inference(bind,[status(th)],[])).
% 2.27/1.74 tff(584,plain,
% 2.27/1.74 (![Time: $i, Height1: $i, Height2: $i] : ((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time))) <=> ![Time: $i, Height1: $i, Height2: $i] : ((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time)))),
% 2.27/1.74 inference(quant_intro,[status(thm)],[583])).
% 2.27/1.74 tff(585,plain,
% 2.27/1.74 (^[Time: $i, Height1: $i, Height2: $i] : trans(monotonicity(trans(monotonicity(rewrite((holdsAt(waterLevel(Height1), Time) & holdsAt(waterLevel(Height2), Time)) <=> (~((~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time))))), ((~(holdsAt(waterLevel(Height1), Time) & holdsAt(waterLevel(Height2), Time))) <=> (~(~((~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time))))))), rewrite((~(~((~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time))))) <=> ((~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time)))), ((~(holdsAt(waterLevel(Height1), Time) & holdsAt(waterLevel(Height2), Time))) <=> ((~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time))))), (((~(holdsAt(waterLevel(Height1), Time) & holdsAt(waterLevel(Height2), Time))) | (Height1 = Height2)) <=> (((~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time))) | (Height1 = Height2)))), rewrite((((~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time))) | (Height1 = Height2)) <=> ((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time)))), (((~(holdsAt(waterLevel(Height1), Time) & holdsAt(waterLevel(Height2), Time))) | (Height1 = Height2)) <=> ((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time)))))),
% 2.27/1.74 inference(bind,[status(th)],[])).
% 2.27/1.74 tff(586,plain,
% 2.27/1.74 (![Time: $i, Height1: $i, Height2: $i] : ((~(holdsAt(waterLevel(Height1), Time) & holdsAt(waterLevel(Height2), Time))) | (Height1 = Height2)) <=> ![Time: $i, Height1: $i, Height2: $i] : ((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time)))),
% 2.27/1.74 inference(quant_intro,[status(thm)],[585])).
% 2.27/1.74 tff(587,plain,
% 2.27/1.74 (![Time: $i, Height1: $i, Height2: $i] : ((~(holdsAt(waterLevel(Height1), Time) & holdsAt(waterLevel(Height2), Time))) | (Height1 = Height2)) <=> ![Time: $i, Height1: $i, Height2: $i] : ((~(holdsAt(waterLevel(Height1), Time) & holdsAt(waterLevel(Height2), Time))) | (Height1 = Height2))),
% 2.27/1.74 inference(rewrite,[status(thm)],[])).
% 2.27/1.74 tff(588,plain,
% 2.27/1.74 (^[Time: $i, Height1: $i, Height2: $i] : rewrite(((holdsAt(waterLevel(Height1), Time) & holdsAt(waterLevel(Height2), Time)) => (Height1 = Height2)) <=> ((~(holdsAt(waterLevel(Height1), Time) & holdsAt(waterLevel(Height2), Time))) | (Height1 = Height2)))),
% 2.27/1.74 inference(bind,[status(th)],[])).
% 2.27/1.74 tff(589,plain,
% 2.27/1.74 (![Time: $i, Height1: $i, Height2: $i] : ((holdsAt(waterLevel(Height1), Time) & holdsAt(waterLevel(Height2), Time)) => (Height1 = Height2)) <=> ![Time: $i, Height1: $i, Height2: $i] : ((~(holdsAt(waterLevel(Height1), Time) & holdsAt(waterLevel(Height2), Time))) | (Height1 = Height2))),
% 2.27/1.74 inference(quant_intro,[status(thm)],[588])).
% 2.27/1.74 tff(590,axiom,(![Time: $i, Height1: $i, Height2: $i] : ((holdsAt(waterLevel(Height1), Time) & holdsAt(waterLevel(Height2), Time)) => (Height1 = Height2))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax','same_waterLevel')).
% 2.27/1.74 tff(591,plain,
% 2.27/1.74 (![Time: $i, Height1: $i, Height2: $i] : ((~(holdsAt(waterLevel(Height1), Time) & holdsAt(waterLevel(Height2), Time))) | (Height1 = Height2))),
% 2.27/1.74 inference(modus_ponens,[status(thm)],[590, 589])).
% 2.27/1.74 tff(592,plain,
% 2.27/1.74 (![Time: $i, Height1: $i, Height2: $i] : ((~(holdsAt(waterLevel(Height1), Time) & holdsAt(waterLevel(Height2), Time))) | (Height1 = Height2))),
% 2.27/1.74 inference(modus_ponens,[status(thm)],[591, 587])).
% 2.27/1.74 tff(593,plain,(
% 2.27/1.74 ![Time: $i, Height1: $i, Height2: $i] : ((~(holdsAt(waterLevel(Height1), Time) & holdsAt(waterLevel(Height2), Time))) | (Height1 = Height2))),
% 2.27/1.74 inference(skolemize,[status(sab)],[592])).
% 2.27/1.74 tff(594,plain,
% 2.27/1.74 (![Time: $i, Height1: $i, Height2: $i] : ((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time)))),
% 2.27/1.74 inference(modus_ponens,[status(thm)],[593, 586])).
% 2.27/1.74 tff(595,plain,
% 2.27/1.74 (![Time: $i, Height1: $i, Height2: $i] : ((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time)))),
% 2.27/1.74 inference(modus_ponens,[status(thm)],[594, 584])).
% 2.27/1.74 tff(596,plain,
% 2.27/1.74 (((~![Time: $i, Height1: $i, Height2: $i] : ((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time)))) | ((n1 = plus(n1, plus(n1, n1))) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~holdsAt(waterLevel(n1), n1)))) <=> ((~![Time: $i, Height1: $i, Height2: $i] : ((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time)))) | (n1 = plus(n1, plus(n1, n1))) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~holdsAt(waterLevel(n1), n1)))),
% 2.27/1.74 inference(rewrite,[status(thm)],[])).
% 2.27/1.74 tff(597,plain,
% 2.27/1.74 (((n1 = plus(n1, plus(n1, n1))) | (~holdsAt(waterLevel(n1), n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1))) <=> ((n1 = plus(n1, plus(n1, n1))) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~holdsAt(waterLevel(n1), n1)))),
% 2.27/1.74 inference(rewrite,[status(thm)],[])).
% 2.27/1.74 tff(598,plain,
% 2.27/1.74 (((~![Time: $i, Height1: $i, Height2: $i] : ((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time)))) | ((n1 = plus(n1, plus(n1, n1))) | (~holdsAt(waterLevel(n1), n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)))) <=> ((~![Time: $i, Height1: $i, Height2: $i] : ((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time)))) | ((n1 = plus(n1, plus(n1, n1))) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~holdsAt(waterLevel(n1), n1))))),
% 2.27/1.74 inference(monotonicity,[status(thm)],[597])).
% 2.27/1.74 tff(599,plain,
% 2.27/1.74 (((~![Time: $i, Height1: $i, Height2: $i] : ((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time)))) | ((n1 = plus(n1, plus(n1, n1))) | (~holdsAt(waterLevel(n1), n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)))) <=> ((~![Time: $i, Height1: $i, Height2: $i] : ((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time)))) | (n1 = plus(n1, plus(n1, n1))) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~holdsAt(waterLevel(n1), n1)))),
% 2.27/1.74 inference(transitivity,[status(thm)],[598, 596])).
% 2.27/1.74 tff(600,plain,
% 2.27/1.74 ((~![Time: $i, Height1: $i, Height2: $i] : ((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time)))) | ((n1 = plus(n1, plus(n1, n1))) | (~holdsAt(waterLevel(n1), n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)))),
% 2.27/1.74 inference(quant_inst,[status(thm)],[])).
% 2.27/1.74 tff(601,plain,
% 2.27/1.74 ((~![Time: $i, Height1: $i, Height2: $i] : ((Height1 = Height2) | (~holdsAt(waterLevel(Height1), Time)) | (~holdsAt(waterLevel(Height2), Time)))) | (n1 = plus(n1, plus(n1, n1))) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~holdsAt(waterLevel(n1), n1))),
% 2.27/1.74 inference(modus_ponens,[status(thm)],[600, 599])).
% 2.27/1.74 tff(602,plain,
% 2.27/1.74 (~holdsAt(waterLevel(n1), n1)),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[601, 595, 582, 581])).
% 2.27/1.74 tff(603,plain,
% 2.27/1.74 ($false),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[602, 422])).
% 2.27/1.74 tff(604,plain,((~holdsAt(waterLevel(n1), plus(n0, n1))) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1))), inference(lemma,lemma(discharge,[]))).
% 2.27/1.74 tff(605,plain,
% 2.27/1.74 (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[604, 418])).
% 2.27/1.74 tff(606,plain,
% 2.27/1.74 (((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow))) | holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)),
% 2.27/1.74 inference(tautology,[status(thm)],[])).
% 2.27/1.74 tff(607,plain,
% 2.27/1.74 ((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow))),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[606, 605])).
% 2.27/1.74 tff(608,plain,
% 2.27/1.74 ((~![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))) | (less(n0, n1) <=> (~((n1 = n0) | less(n1, n0))))),
% 2.27/1.74 inference(quant_inst,[status(thm)],[])).
% 2.27/1.74 tff(609,plain,
% 2.27/1.74 (less(n0, n1) <=> (~((n1 = n0) | less(n1, n0)))),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[608, 67])).
% 2.27/1.74 tff(610,plain,
% 2.27/1.74 ((~(less(n0, n1) <=> (~((n1 = n0) | less(n1, n0))))) | (~less(n0, n1)) | (~((n1 = n0) | less(n1, n0)))),
% 2.27/1.74 inference(tautology,[status(thm)],[])).
% 2.27/1.74 tff(611,plain,
% 2.27/1.74 (~((n1 = n0) | less(n1, n0))),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[610, 396, 609])).
% 2.27/1.74 tff(612,plain,
% 2.27/1.74 (((n1 = n0) | less(n1, n0)) | (~(n1 = n0))),
% 2.27/1.74 inference(tautology,[status(thm)],[])).
% 2.27/1.74 tff(613,plain,
% 2.27/1.74 (~(n1 = n0)),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[612, 611])).
% 2.27/1.74 tff(614,plain,
% 2.27/1.74 (((~(n1 = n0)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn))) | (n1 = n0)),
% 2.27/1.74 inference(tautology,[status(thm)],[])).
% 2.27/1.74 tff(615,plain,
% 2.27/1.74 ((~(n1 = n0)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn))),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[614, 613])).
% 2.27/1.74 tff(616,plain,
% 2.27/1.74 ((~((~((~(n1 = n0)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow)))))) | (~((~(n1 = n0)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow))))),
% 2.27/1.74 inference(tautology,[status(thm)],[])).
% 2.27/1.74 tff(617,plain,
% 2.27/1.74 (~((~((~(n1 = n0)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow)))))),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[616, 615, 607])).
% 2.27/1.74 tff(618,plain,
% 2.27/1.74 (releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, n1)) <=> releasedAt(filling, plus(n1, n1))),
% 2.27/1.74 inference(monotonicity,[status(thm)],[139])).
% 2.27/1.74 tff(619,plain,
% 2.27/1.74 (releasedAt(filling, plus(n1, n1)) <=> releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, n1))),
% 2.27/1.74 inference(symmetry,[status(thm)],[618])).
% 2.27/1.74 tff(620,assumption,(~(happens(tptp_fun_Event_4(n1, filling), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_4(n1, filling) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow))))))), introduced(assumption)).
% 2.27/1.74 tff(621,plain,
% 2.27/1.74 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_4(n1, filling), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_4(n1, filling) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_4(n1, filling), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_4(n1, filling) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow)))))))),
% 2.27/1.74 inference(rewrite,[status(thm)],[])).
% 2.27/1.74 tff(622,plain,
% 2.27/1.74 ((happens(tptp_fun_Event_4(n1, filling), n1) <=> ((~((~(tptp_fun_Event_4(n1, filling) = tapOn)) | (~(n1 = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~holdsAt(filling, n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow)))))) <=> (happens(tptp_fun_Event_4(n1, filling), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_4(n1, filling) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow))))))),
% 2.27/1.74 inference(rewrite,[status(thm)],[])).
% 2.27/1.74 tff(623,plain,
% 2.27/1.74 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_4(n1, filling), n1) <=> ((~((~(tptp_fun_Event_4(n1, filling) = tapOn)) | (~(n1 = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~holdsAt(filling, n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_4(n1, filling), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_4(n1, filling) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow)))))))),
% 2.27/1.74 inference(monotonicity,[status(thm)],[622])).
% 2.27/1.74 tff(624,plain,
% 2.27/1.74 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_4(n1, filling), n1) <=> ((~((~(tptp_fun_Event_4(n1, filling) = tapOn)) | (~(n1 = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~holdsAt(filling, n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_4(n1, filling), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_4(n1, filling) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow)))))))),
% 2.27/1.74 inference(transitivity,[status(thm)],[623, 621])).
% 2.27/1.74 tff(625,plain,
% 2.27/1.74 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_4(n1, filling), n1) <=> ((~((~(tptp_fun_Event_4(n1, filling) = tapOn)) | (~(n1 = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~holdsAt(filling, n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow))))))),
% 2.27/1.74 inference(quant_inst,[status(thm)],[])).
% 2.27/1.74 tff(626,plain,
% 2.27/1.74 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_4(n1, filling), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_4(n1, filling) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow))))))),
% 2.27/1.74 inference(modus_ponens,[status(thm)],[625, 624])).
% 2.27/1.74 tff(627,plain,
% 2.27/1.74 ($false),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[626, 235, 620])).
% 2.27/1.74 tff(628,plain,(happens(tptp_fun_Event_4(n1, filling), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_4(n1, filling) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow)))))), inference(lemma,lemma(discharge,[]))).
% 2.27/1.74 tff(629,plain,
% 2.27/1.74 (((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow))) | holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)),
% 2.27/1.74 inference(tautology,[status(thm)],[])).
% 2.27/1.74 tff(630,plain,
% 2.27/1.74 ((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow))),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[629, 605])).
% 2.27/1.74 tff(631,plain,
% 2.27/1.74 (((~(n1 = n0)) | (~(tptp_fun_Event_4(n1, filling) = tapOn))) | (n1 = n0)),
% 2.27/1.74 inference(tautology,[status(thm)],[])).
% 2.27/1.74 tff(632,plain,
% 2.27/1.74 ((~(n1 = n0)) | (~(tptp_fun_Event_4(n1, filling) = tapOn))),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[631, 613])).
% 2.27/1.74 tff(633,plain,
% 2.27/1.74 ((~((~((~(n1 = n0)) | (~(tptp_fun_Event_4(n1, filling) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow)))))) | (~((~(n1 = n0)) | (~(tptp_fun_Event_4(n1, filling) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow))))),
% 2.27/1.74 inference(tautology,[status(thm)],[])).
% 2.27/1.74 tff(634,plain,
% 2.27/1.74 (~((~((~(n1 = n0)) | (~(tptp_fun_Event_4(n1, filling) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow)))))),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[633, 632, 630])).
% 2.27/1.74 tff(635,plain,
% 2.27/1.74 ((~(happens(tptp_fun_Event_4(n1, filling), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_4(n1, filling) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow))))))) | (~happens(tptp_fun_Event_4(n1, filling), n1)) | ((~((~(n1 = n0)) | (~(tptp_fun_Event_4(n1, filling) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow)))))),
% 2.27/1.74 inference(tautology,[status(thm)],[])).
% 2.27/1.74 tff(636,plain,
% 2.27/1.74 ((~(happens(tptp_fun_Event_4(n1, filling), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_4(n1, filling) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_4(n1, filling) = overflow))))))) | (~happens(tptp_fun_Event_4(n1, filling), n1))),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[635, 634])).
% 2.27/1.74 tff(637,plain,
% 2.27/1.74 (~happens(tptp_fun_Event_4(n1, filling), n1)),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[636, 628])).
% 2.27/1.74 tff(638,plain,
% 2.27/1.74 (((~happens(tptp_fun_Event_4(n1, filling), n1)) | (~terminates(tptp_fun_Event_4(n1, filling), filling, n1))) | happens(tptp_fun_Event_4(n1, filling), n1)),
% 2.27/1.74 inference(tautology,[status(thm)],[])).
% 2.27/1.74 tff(639,plain,
% 2.27/1.74 ((~happens(tptp_fun_Event_4(n1, filling), n1)) | (~terminates(tptp_fun_Event_4(n1, filling), filling, n1))),
% 2.27/1.74 inference(unit_resolution,[status(thm)],[638, 637])).
% 2.27/1.74 tff(640,plain,
% 2.27/1.74 ((~holdsAt(filling, n2)) <=> (~holdsAt(filling, plus(n1, n1)))),
% 2.27/1.74 inference(rewrite,[status(thm)],[])).
% 2.27/1.74 tff(641,plain,
% 2.27/1.74 ((~holdsAt(filling, n2)) <=> (~holdsAt(filling, n2))),
% 2.27/1.74 inference(rewrite,[status(thm)],[])).
% 2.27/1.74 tff(642,axiom,(~holdsAt(filling, n2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','filling_2')).
% 2.27/1.74 tff(643,plain,
% 2.27/1.74 (~holdsAt(filling, n2)),
% 2.27/1.74 inference(modus_ponens,[status(thm)],[642, 641])).
% 2.27/1.74 tff(644,plain,
% 2.27/1.74 (~holdsAt(filling, plus(n1, n1))),
% 2.27/1.74 inference(modus_ponens,[status(thm)],[643, 640])).
% 2.27/1.74 tff(645,plain,
% 2.27/1.74 (^[Fluent: $i, Time: $i] : refl((holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (~((~happens(tptp_fun_Event_4(Time, Fluent), Time)) | (~terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time))))) <=> (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (~((~happens(tptp_fun_Event_4(Time, Fluent), Time)) | (~terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time))))))),
% 2.27/1.74 inference(bind,[status(th)],[])).
% 2.27/1.74 tff(646,plain,
% 2.27/1.74 (![Fluent: $i, Time: $i] : (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (~((~happens(tptp_fun_Event_4(Time, Fluent), Time)) | (~terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time))))) <=> ![Fluent: $i, Time: $i] : (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (~((~happens(tptp_fun_Event_4(Time, Fluent), Time)) | (~terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time)))))),
% 2.27/1.74 inference(quant_intro,[status(thm)],[645])).
% 2.27/1.74 tff(647,plain,
% 2.27/1.74 (^[Fluent: $i, Time: $i] : trans(monotonicity(rewrite((happens(tptp_fun_Event_4(Time, Fluent), Time) & terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time)) <=> (~((~happens(tptp_fun_Event_4(Time, Fluent), Time)) | (~terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time))))), ((holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (happens(tptp_fun_Event_4(Time, Fluent), Time) & terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time))) <=> (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (~((~happens(tptp_fun_Event_4(Time, Fluent), Time)) | (~terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time))))))), rewrite((holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (~((~happens(tptp_fun_Event_4(Time, Fluent), Time)) | (~terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time))))) <=> (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (~((~happens(tptp_fun_Event_4(Time, Fluent), Time)) | (~terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time)))))), ((holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (happens(tptp_fun_Event_4(Time, Fluent), Time) & terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time))) <=> (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (~((~happens(tptp_fun_Event_4(Time, Fluent), Time)) | (~terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time)))))))),
% 2.27/1.74 inference(bind,[status(th)],[])).
% 2.27/1.74 tff(648,plain,
% 2.27/1.74 (![Fluent: $i, Time: $i] : (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (happens(tptp_fun_Event_4(Time, Fluent), Time) & terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time))) <=> ![Fluent: $i, Time: $i] : (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (~((~happens(tptp_fun_Event_4(Time, Fluent), Time)) | (~terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time)))))),
% 2.27/1.74 inference(quant_intro,[status(thm)],[647])).
% 2.27/1.74 tff(649,plain,
% 2.27/1.74 (^[Fluent: $i, Time: $i] : trans(monotonicity(rewrite(((~holdsAt(Fluent, Time)) | (~(~releasedAt(Fluent, plus(Time, n1)))) | (happens(tptp_fun_Event_4(Time, Fluent), Time) & terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time))) <=> ((~holdsAt(Fluent, Time)) | releasedAt(Fluent, plus(Time, n1)) | (happens(tptp_fun_Event_4(Time, Fluent), Time) & terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time)))), ((((~holdsAt(Fluent, Time)) | (~(~releasedAt(Fluent, plus(Time, n1)))) | (happens(tptp_fun_Event_4(Time, Fluent), Time) & terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> (((~holdsAt(Fluent, Time)) | releasedAt(Fluent, plus(Time, n1)) | (happens(tptp_fun_Event_4(Time, Fluent), Time) & terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))))), rewrite((((~holdsAt(Fluent, Time)) | releasedAt(Fluent, plus(Time, n1)) | (happens(tptp_fun_Event_4(Time, Fluent), Time) & terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (happens(tptp_fun_Event_4(Time, Fluent), Time) & terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time)))), ((((~holdsAt(Fluent, Time)) | (~(~releasedAt(Fluent, plus(Time, n1)))) | (happens(tptp_fun_Event_4(Time, Fluent), Time) & terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (happens(tptp_fun_Event_4(Time, Fluent), Time) & terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time)))))),
% 2.27/1.74 inference(bind,[status(th)],[])).
% 2.27/1.74 tff(650,plain,
% 2.27/1.74 (![Fluent: $i, Time: $i] : (((~holdsAt(Fluent, Time)) | (~(~releasedAt(Fluent, plus(Time, n1)))) | (happens(tptp_fun_Event_4(Time, Fluent), Time) & terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> ![Fluent: $i, Time: $i] : (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (happens(tptp_fun_Event_4(Time, Fluent), Time) & terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time)))),
% 2.27/1.74 inference(quant_intro,[status(thm)],[649])).
% 2.27/1.74 tff(651,plain,
% 2.27/1.74 (![Fluent: $i, Time: $i] : ((~(holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time))))) | holdsAt(Fluent, plus(Time, n1))) <=> ![Fluent: $i, Time: $i] : ((~(holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time))))) | holdsAt(Fluent, plus(Time, n1)))),
% 2.27/1.74 inference(rewrite,[status(thm)],[])).
% 2.27/1.74 tff(652,plain,
% 2.27/1.74 (^[Fluent: $i, Time: $i] : trans(monotonicity(trans(monotonicity(rewrite((~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time))) <=> (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time)))), (((holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time)))) <=> ((holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time)))))), rewrite(((holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time)))) <=> (holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time))))), (((holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time)))) <=> (holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time)))))), ((((holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time)))) => holdsAt(Fluent, plus(Time, n1))) <=> ((holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time)))) => holdsAt(Fluent, plus(Time, n1))))), rewrite(((holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time)))) => holdsAt(Fluent, plus(Time, n1))) <=> ((~(holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time))))) | holdsAt(Fluent, plus(Time, n1)))), ((((holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time)))) => holdsAt(Fluent, plus(Time, n1))) <=> ((~(holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time))))) | holdsAt(Fluent, plus(Time, n1)))))),
% 2.27/1.74 inference(bind,[status(th)],[])).
% 2.27/1.74 tff(653,plain,
% 2.27/1.74 (![Fluent: $i, Time: $i] : (((holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time)))) => holdsAt(Fluent, plus(Time, n1))) <=> ![Fluent: $i, Time: $i] : ((~(holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time))))) | holdsAt(Fluent, plus(Time, n1)))),
% 2.27/1.74 inference(quant_intro,[status(thm)],[652])).
% 2.27/1.74 tff(654,axiom,(![Fluent: $i, Time: $i] : (((holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time)))) => holdsAt(Fluent, plus(Time, n1)))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax','keep_holding')).
% 2.27/1.74 tff(655,plain,
% 2.27/1.74 (![Fluent: $i, Time: $i] : ((~(holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time))))) | holdsAt(Fluent, plus(Time, n1)))),
% 2.27/1.74 inference(modus_ponens,[status(thm)],[654, 653])).
% 2.27/1.74 tff(656,plain,
% 2.27/1.74 (![Fluent: $i, Time: $i] : ((~(holdsAt(Fluent, Time) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & terminates(Event, Fluent, Time))))) | holdsAt(Fluent, plus(Time, n1)))),
% 2.27/1.74 inference(modus_ponens,[status(thm)],[655, 651])).
% 2.27/1.74 tff(657,plain,(
% 2.27/1.74 ![Fluent: $i, Time: $i] : (((~holdsAt(Fluent, Time)) | (~(~releasedAt(Fluent, plus(Time, n1)))) | (happens(tptp_fun_Event_4(Time, Fluent), Time) & terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 2.27/1.74 inference(skolemize,[status(sab)],[656])).
% 2.27/1.74 tff(658,plain,
% 2.27/1.74 (![Fluent: $i, Time: $i] : (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (happens(tptp_fun_Event_4(Time, Fluent), Time) & terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time)))),
% 2.27/1.74 inference(modus_ponens,[status(thm)],[657, 650])).
% 2.27/1.74 tff(659,plain,
% 2.27/1.74 (![Fluent: $i, Time: $i] : (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (~((~happens(tptp_fun_Event_4(Time, Fluent), Time)) | (~terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time)))))),
% 2.27/1.74 inference(modus_ponens,[status(thm)],[658, 648])).
% 2.27/1.74 tff(660,plain,
% 2.27/1.74 (![Fluent: $i, Time: $i] : (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (~((~happens(tptp_fun_Event_4(Time, Fluent), Time)) | (~terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time)))))),
% 2.27/1.74 inference(modus_ponens,[status(thm)],[659, 646])).
% 2.27/1.74 tff(661,plain,
% 2.27/1.74 (((~![Fluent: $i, Time: $i] : (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (~((~happens(tptp_fun_Event_4(Time, Fluent), Time)) | (~terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time)))))) | (holdsAt(filling, plus(n1, n1)) | releasedAt(filling, plus(n1, n1)) | (~holdsAt(filling, n1)) | (~((~happens(tptp_fun_Event_4(n1, filling), n1)) | (~terminates(tptp_fun_Event_4(n1, filling), filling, n1)))))) <=> ((~![Fluent: $i, Time: $i] : (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (~((~happens(tptp_fun_Event_4(Time, Fluent), Time)) | (~terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time)))))) | holdsAt(filling, plus(n1, n1)) | releasedAt(filling, plus(n1, n1)) | (~holdsAt(filling, n1)) | (~((~happens(tptp_fun_Event_4(n1, filling), n1)) | (~terminates(tptp_fun_Event_4(n1, filling), filling, n1)))))),
% 2.27/1.75 inference(rewrite,[status(thm)],[])).
% 2.27/1.75 tff(662,plain,
% 2.27/1.75 ((~![Fluent: $i, Time: $i] : (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (~((~happens(tptp_fun_Event_4(Time, Fluent), Time)) | (~terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time)))))) | (holdsAt(filling, plus(n1, n1)) | releasedAt(filling, plus(n1, n1)) | (~holdsAt(filling, n1)) | (~((~happens(tptp_fun_Event_4(n1, filling), n1)) | (~terminates(tptp_fun_Event_4(n1, filling), filling, n1)))))),
% 2.27/1.75 inference(quant_inst,[status(thm)],[])).
% 2.27/1.75 tff(663,plain,
% 2.27/1.75 ((~![Fluent: $i, Time: $i] : (holdsAt(Fluent, plus(Time, n1)) | releasedAt(Fluent, plus(Time, n1)) | (~holdsAt(Fluent, Time)) | (~((~happens(tptp_fun_Event_4(Time, Fluent), Time)) | (~terminates(tptp_fun_Event_4(Time, Fluent), Fluent, Time)))))) | holdsAt(filling, plus(n1, n1)) | releasedAt(filling, plus(n1, n1)) | (~holdsAt(filling, n1)) | (~((~happens(tptp_fun_Event_4(n1, filling), n1)) | (~terminates(tptp_fun_Event_4(n1, filling), filling, n1))))),
% 2.27/1.75 inference(modus_ponens,[status(thm)],[662, 661])).
% 2.27/1.75 tff(664,plain,
% 2.27/1.75 (releasedAt(filling, plus(n1, n1)) | (~holdsAt(filling, n1)) | (~((~happens(tptp_fun_Event_4(n1, filling), n1)) | (~terminates(tptp_fun_Event_4(n1, filling), filling, n1))))),
% 2.27/1.75 inference(unit_resolution,[status(thm)],[663, 660, 644])).
% 2.27/1.75 tff(665,plain,
% 2.27/1.75 (releasedAt(filling, plus(n1, n1)) | (~((~happens(tptp_fun_Event_4(n1, filling), n1)) | (~terminates(tptp_fun_Event_4(n1, filling), filling, n1))))),
% 2.27/1.75 inference(unit_resolution,[status(thm)],[664, 283])).
% 2.27/1.75 tff(666,plain,
% 2.27/1.75 (releasedAt(filling, plus(n1, n1))),
% 2.27/1.75 inference(unit_resolution,[status(thm)],[665, 639])).
% 2.27/1.75 tff(667,plain,
% 2.27/1.75 (releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, n1))),
% 2.27/1.75 inference(modus_ponens,[status(thm)],[666, 619])).
% 2.27/1.75 tff(668,plain,
% 2.27/1.75 (releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n1) <=> releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))),
% 2.27/1.75 inference(monotonicity,[status(thm)],[4])).
% 2.27/1.75 tff(669,plain,
% 2.27/1.75 (releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1)) <=> releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n1)),
% 2.27/1.75 inference(symmetry,[status(thm)],[668])).
% 2.27/1.75 tff(670,plain,
% 2.27/1.75 ((~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n0, n1))) <=> (~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n1))),
% 2.27/1.75 inference(monotonicity,[status(thm)],[669])).
% 2.27/1.75 tff(671,plain,
% 2.27/1.75 (~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n1)),
% 2.27/1.75 inference(modus_ponens,[status(thm)],[352, 670])).
% 2.27/1.75 tff(672,plain,
% 2.27/1.75 (((~![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))) | ((~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, n1))) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n1) | (~((~happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1)) | (~releases(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n1)))))) <=> ((~![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))) | (~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, n1))) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n1) | (~((~happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1)) | (~releases(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n1)))))),
% 2.27/1.75 inference(rewrite,[status(thm)],[])).
% 2.27/1.75 tff(673,plain,
% 2.27/1.75 ((~![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))) | ((~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, n1))) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n1) | (~((~happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1)) | (~releases(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n1)))))),
% 2.27/1.75 inference(quant_inst,[status(thm)],[])).
% 2.27/1.75 tff(674,plain,
% 2.27/1.75 ((~![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))) | (~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, n1))) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n1) | (~((~happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1)) | (~releases(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n1))))),
% 2.27/1.75 inference(modus_ponens,[status(thm)],[673, 672])).
% 2.27/1.75 tff(675,plain,
% 2.27/1.75 ((~releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, n1))) | releasedAt(tptp_fun_Height_10(waterLevel(filling), tapOn), n1) | (~((~happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1)) | (~releases(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n1))))),
% 2.27/1.75 inference(unit_resolution,[status(thm)],[674, 344])).
% 2.27/1.75 tff(676,plain,
% 2.27/1.75 (~((~happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1)) | (~releases(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n1)))),
% 2.27/1.75 inference(unit_resolution,[status(thm)],[675, 671, 667])).
% 2.27/1.75 tff(677,plain,
% 2.27/1.75 (((~happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1)) | (~releases(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), tptp_fun_Height_10(waterLevel(filling), tapOn), n1))) | happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1)),
% 2.27/1.75 inference(tautology,[status(thm)],[])).
% 2.27/1.75 tff(678,plain,
% 2.27/1.75 (happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1)),
% 2.27/1.75 inference(unit_resolution,[status(thm)],[677, 676])).
% 2.27/1.75 tff(679,plain,
% 2.27/1.75 ((~(happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow))))))) | (~happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1)) | ((~((~(n1 = n0)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow)))))),
% 2.27/1.75 inference(tautology,[status(thm)],[])).
% 2.27/1.75 tff(680,plain,
% 2.27/1.75 (~(happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow))))))),
% 2.27/1.75 inference(unit_resolution,[status(thm)],[679, 678, 617])).
% 2.27/1.75 tff(681,plain,
% 2.27/1.75 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow)))))))),
% 2.27/1.75 inference(rewrite,[status(thm)],[])).
% 2.27/1.75 tff(682,plain,
% 2.27/1.75 ((happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1) <=> ((~((~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(n1 = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~holdsAt(filling, n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow)))))) <=> (happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow))))))),
% 2.27/1.75 inference(rewrite,[status(thm)],[])).
% 2.27/1.75 tff(683,plain,
% 2.27/1.75 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1) <=> ((~((~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(n1 = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~holdsAt(filling, n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow)))))))),
% 2.27/1.75 inference(monotonicity,[status(thm)],[682])).
% 2.27/1.75 tff(684,plain,
% 2.27/1.75 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1) <=> ((~((~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(n1 = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~holdsAt(filling, n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow)))))))),
% 2.27/1.75 inference(transitivity,[status(thm)],[683, 681])).
% 2.27/1.75 tff(685,plain,
% 2.27/1.75 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1) <=> ((~((~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)) | (~(n1 = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~holdsAt(filling, n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow))))))),
% 2.27/1.75 inference(quant_inst,[status(thm)],[])).
% 2.27/1.75 tff(686,plain,
% 2.27/1.75 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)), n1) <=> ((~((~(n1 = n0)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = tapOn)))) | (~((~holdsAt(filling, n1)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), n1)) | (~(tptp_fun_Event_7(n1, tptp_fun_Height_10(waterLevel(filling), tapOn)) = overflow))))))),
% 2.27/1.75 inference(modus_ponens,[status(thm)],[685, 684])).
% 2.27/1.75 tff(687,plain,
% 2.27/1.75 ($false),
% 2.27/1.75 inference(unit_resolution,[status(thm)],[686, 235, 680])).
% 2.27/1.75 % SZS output end Proof
%------------------------------------------------------------------------------