TSTP Solution File: CSR002+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CSR002+2 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 14:26:58 EDT 2022
% Result : Theorem 18.16s 11.85s
% Output : Proof 18.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : CSR002+2 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.08/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n005.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 30 15:59:18 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.37 Usage: tptp [options] [-file:]file
% 0.14/0.37 -h, -? prints this message.
% 0.14/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.37 -m, -model generate model.
% 0.14/0.37 -p, -proof generate proof.
% 0.14/0.37 -c, -core generate unsat core of named formulas.
% 0.14/0.37 -st, -statistics display statistics.
% 0.14/0.37 -t:timeout set timeout (in second).
% 0.14/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.37 -<param>:<value> configuration parameter and value.
% 0.14/0.37 -o:<output-file> file to place output in.
% 18.16/11.85 % SZS status Theorem
% 18.16/11.85 % SZS output start Proof
% 18.16/11.85 tff(terminates_type, type, (
% 18.16/11.85 terminates: ( $i * $i * $i ) > $o)).
% 18.16/11.85 tff(plus_type, type, (
% 18.16/11.85 plus: ( $i * $i ) > $i)).
% 18.16/11.85 tff(n1_type, type, (
% 18.16/11.85 n1: $i)).
% 18.16/11.85 tff(tptp_fun_Height_10_type, type, (
% 18.16/11.85 tptp_fun_Height_10: ( $i * $i ) > $i)).
% 18.16/11.85 tff(tapOn_type, type, (
% 18.16/11.85 tapOn: $i)).
% 18.16/11.85 tff(waterLevel_type, type, (
% 18.16/11.85 waterLevel: $i > $i)).
% 18.16/11.85 tff(filling_type, type, (
% 18.16/11.85 filling: $i)).
% 18.16/11.85 tff(overflow_type, type, (
% 18.16/11.85 overflow: $i)).
% 18.16/11.85 tff(tapOff_type, type, (
% 18.16/11.85 tapOff: $i)).
% 18.16/11.85 tff(releases_type, type, (
% 18.16/11.85 releases: ( $i * $i * $i ) > $o)).
% 18.16/11.85 tff(holdsAt_type, type, (
% 18.16/11.85 holdsAt: ( $i * $i ) > $o)).
% 18.16/11.85 tff(n4_type, type, (
% 18.16/11.85 n4: $i)).
% 18.16/11.85 tff(n2_type, type, (
% 18.16/11.85 n2: $i)).
% 18.16/11.85 tff(happens_type, type, (
% 18.16/11.85 happens: ( $i * $i ) > $o)).
% 18.16/11.85 tff(n0_type, type, (
% 18.16/11.85 n0: $i)).
% 18.16/11.85 tff(n3_type, type, (
% 18.16/11.85 n3: $i)).
% 18.16/11.85 tff(tptp_fun_Event_5_type, type, (
% 18.16/11.85 tptp_fun_Event_5: ( $i * $i ) > $i)).
% 18.16/11.85 tff(less_type, type, (
% 18.16/11.85 less: ( $i * $i ) > $o)).
% 18.16/11.85 tff(less_or_equal_type, type, (
% 18.16/11.85 less_or_equal: ( $i * $i ) > $o)).
% 18.16/11.85 tff(n7_type, type, (
% 18.16/11.85 n7: $i)).
% 18.16/11.85 tff(n6_type, type, (
% 18.16/11.85 n6: $i)).
% 18.16/11.85 tff(n5_type, type, (
% 18.16/11.85 n5: $i)).
% 18.16/11.85 tff(initiates_type, type, (
% 18.16/11.85 initiates: ( $i * $i * $i ) > $o)).
% 18.16/11.85 tff(tptp_fun_Event_7_type, type, (
% 18.16/11.85 tptp_fun_Event_7: ( $i * $i ) > $i)).
% 18.16/11.85 tff(releasedAt_type, type, (
% 18.16/11.85 releasedAt: ( $i * $i ) > $o)).
% 18.16/11.85 tff(1,assumption,(~(terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))) <=> ((tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~((~(overflow = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling))))))), introduced(assumption)).
% 18.16/11.85 tff(2,plain,
% 18.16/11.85 (^[Event: $i, Fluent: $i, Time: $i] : refl((terminates(Event, Fluent, Time) <=> ((~((~(Event = overflow)) | (~(Fluent = filling)))) | (~((~(Fluent = filling)) | (~(Event = tapOff)))))) <=> (terminates(Event, Fluent, Time) <=> ((~((~(Event = overflow)) | (~(Fluent = filling)))) | (~((~(Fluent = filling)) | (~(Event = tapOff)))))))),
% 18.16/11.85 inference(bind,[status(th)],[])).
% 18.16/11.85 tff(3,plain,
% 18.16/11.85 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~((~(Event = overflow)) | (~(Fluent = filling)))) | (~((~(Fluent = filling)) | (~(Event = tapOff)))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~((~(Event = overflow)) | (~(Fluent = filling)))) | (~((~(Fluent = filling)) | (~(Event = tapOff))))))),
% 18.16/11.85 inference(quant_intro,[status(thm)],[2])).
% 18.16/11.85 tff(4,plain,
% 18.16/11.85 (^[Event: $i, Fluent: $i, Time: $i] : rewrite((terminates(Event, Fluent, Time) <=> (((Event = overflow) & (Fluent = filling)) | ((Event = tapOff) & (Fluent = filling)))) <=> (terminates(Event, Fluent, Time) <=> ((~((~(Event = overflow)) | (~(Fluent = filling)))) | (~((~(Fluent = filling)) | (~(Event = tapOff)))))))),
% 18.16/11.85 inference(bind,[status(th)],[])).
% 18.16/11.85 tff(5,plain,
% 18.16/11.85 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = overflow) & (Fluent = filling)) | ((Event = tapOff) & (Fluent = filling)))) <=> ![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~((~(Event = overflow)) | (~(Fluent = filling)))) | (~((~(Fluent = filling)) | (~(Event = tapOff))))))),
% 18.16/11.85 inference(quant_intro,[status(thm)],[4])).
% 18.16/11.85 tff(6,plain,
% 18.16/11.85 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = overflow) & (Fluent = filling)) | ((Event = tapOff) & (Fluent = filling)))) <=> ![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = overflow) & (Fluent = filling)) | ((Event = tapOff) & (Fluent = filling))))),
% 18.16/11.85 inference(rewrite,[status(thm)],[])).
% 18.16/11.85 tff(7,plain,
% 18.16/11.85 (^[Event: $i, Fluent: $i, Time: $i] : rewrite((terminates(Event, Fluent, Time) <=> (((Event = tapOff) & (Fluent = filling)) | ((Event = overflow) & (Fluent = filling)))) <=> (terminates(Event, Fluent, Time) <=> (((Event = overflow) & (Fluent = filling)) | ((Event = tapOff) & (Fluent = filling)))))),
% 18.16/11.85 inference(bind,[status(th)],[])).
% 18.16/11.85 tff(8,plain,
% 18.16/11.85 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = tapOff) & (Fluent = filling)) | ((Event = overflow) & (Fluent = filling)))) <=> ![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = overflow) & (Fluent = filling)) | ((Event = tapOff) & (Fluent = filling))))),
% 18.16/11.85 inference(quant_intro,[status(thm)],[7])).
% 18.16/11.85 tff(9,axiom,(![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = tapOff) & (Fluent = filling)) | ((Event = overflow) & (Fluent = filling))))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax','terminates_all_defn')).
% 18.16/11.85 tff(10,plain,
% 18.16/11.85 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = overflow) & (Fluent = filling)) | ((Event = tapOff) & (Fluent = filling))))),
% 18.16/11.85 inference(modus_ponens,[status(thm)],[9, 8])).
% 18.16/11.85 tff(11,plain,
% 18.16/11.85 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = overflow) & (Fluent = filling)) | ((Event = tapOff) & (Fluent = filling))))),
% 18.16/11.85 inference(modus_ponens,[status(thm)],[10, 6])).
% 18.16/11.85 tff(12,plain,(
% 18.16/11.85 ![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = overflow) & (Fluent = filling)) | ((Event = tapOff) & (Fluent = filling))))),
% 18.16/11.85 inference(skolemize,[status(sab)],[11])).
% 18.16/11.85 tff(13,plain,
% 18.16/11.85 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~((~(Event = overflow)) | (~(Fluent = filling)))) | (~((~(Fluent = filling)) | (~(Event = tapOff))))))),
% 18.16/11.85 inference(modus_ponens,[status(thm)],[12, 5])).
% 18.16/11.85 tff(14,plain,
% 18.16/11.85 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~((~(Event = overflow)) | (~(Fluent = filling)))) | (~((~(Fluent = filling)) | (~(Event = tapOff))))))),
% 18.16/11.85 inference(modus_ponens,[status(thm)],[13, 3])).
% 18.16/11.85 tff(15,plain,
% 18.16/11.85 (((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~((~(Event = overflow)) | (~(Fluent = filling)))) | (~((~(Fluent = filling)) | (~(Event = tapOff))))))) | (terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))) <=> ((tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~((~(overflow = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~((~(Event = overflow)) | (~(Fluent = filling)))) | (~((~(Fluent = filling)) | (~(Event = tapOff))))))) | (terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))) <=> ((tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~((~(overflow = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)))))))),
% 18.16/11.85 inference(rewrite,[status(thm)],[])).
% 18.16/11.85 tff(16,plain,
% 18.16/11.85 ((terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))) <=> ((~((~(overflow = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)))) | (~((~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)) | (~(overflow = tapOff)))))) <=> (terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))) <=> ((tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~((~(overflow = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling))))))),
% 18.16/11.85 inference(rewrite,[status(thm)],[])).
% 18.16/11.85 tff(17,plain,
% 18.16/11.85 (((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~((~(Event = overflow)) | (~(Fluent = filling)))) | (~((~(Fluent = filling)) | (~(Event = tapOff))))))) | (terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))) <=> ((~((~(overflow = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)))) | (~((~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)) | (~(overflow = tapOff))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~((~(Event = overflow)) | (~(Fluent = filling)))) | (~((~(Fluent = filling)) | (~(Event = tapOff))))))) | (terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))) <=> ((tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~((~(overflow = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)))))))),
% 18.16/11.85 inference(monotonicity,[status(thm)],[16])).
% 18.16/11.85 tff(18,plain,
% 18.16/11.85 (((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~((~(Event = overflow)) | (~(Fluent = filling)))) | (~((~(Fluent = filling)) | (~(Event = tapOff))))))) | (terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))) <=> ((~((~(overflow = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)))) | (~((~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)) | (~(overflow = tapOff))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~((~(Event = overflow)) | (~(Fluent = filling)))) | (~((~(Fluent = filling)) | (~(Event = tapOff))))))) | (terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))) <=> ((tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~((~(overflow = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)))))))),
% 18.16/11.85 inference(transitivity,[status(thm)],[17, 15])).
% 18.16/11.85 tff(19,plain,
% 18.16/11.85 ((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~((~(Event = overflow)) | (~(Fluent = filling)))) | (~((~(Fluent = filling)) | (~(Event = tapOff))))))) | (terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))) <=> ((~((~(overflow = overflow)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)))) | (~((~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)) | (~(overflow = tapOff))))))),
% 18.16/11.85 inference(quant_inst,[status(thm)],[])).
% 18.16/11.85 tff(20,plain,
% 18.16/11.85 ((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~((~(Event = overflow)) | (~(Fluent = filling)))) | (~((~(Fluent = filling)) | (~(Event = tapOff))))))) | (terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))) <=> ((tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~((~(overflow = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling))))))),
% 18.16/11.85 inference(modus_ponens,[status(thm)],[19, 18])).
% 18.16/11.85 tff(21,plain,
% 18.16/11.85 ($false),
% 18.16/11.85 inference(unit_resolution,[status(thm)],[20, 14, 1])).
% 18.16/11.85 tff(22,plain,(terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))) <=> ((tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~((~(overflow = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)))))), inference(lemma,lemma(discharge,[]))).
% 18.16/11.85 tff(23,plain,
% 18.16/11.85 (^[X: $i, Y: $i] : refl(((waterLevel(X) = waterLevel(Y)) <=> (X = Y)) <=> ((waterLevel(X) = waterLevel(Y)) <=> (X = Y)))),
% 18.16/11.85 inference(bind,[status(th)],[])).
% 18.16/11.85 tff(24,plain,
% 18.16/11.85 (![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y))),
% 18.16/11.85 inference(quant_intro,[status(thm)],[23])).
% 18.16/11.85 tff(25,plain,
% 18.16/11.85 (![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y))),
% 18.16/11.85 inference(rewrite,[status(thm)],[])).
% 18.16/11.85 tff(26,axiom,(![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax','distinct_waterLevels')).
% 18.16/11.85 tff(27,plain,
% 18.16/11.85 (![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y))),
% 18.16/11.85 inference(modus_ponens,[status(thm)],[26, 25])).
% 18.16/11.85 tff(28,plain,(
% 18.16/11.85 ![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y))),
% 18.16/11.85 inference(skolemize,[status(sab)],[27])).
% 18.16/11.85 tff(29,plain,
% 18.16/11.85 (![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y))),
% 18.16/11.85 inference(modus_ponens,[status(thm)],[28, 24])).
% 18.16/11.85 tff(30,plain,
% 18.16/11.85 ((~![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))),
% 18.16/11.85 inference(quant_inst,[status(thm)],[])).
% 18.16/11.85 tff(31,plain,
% 18.16/11.85 ((waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)) = waterLevel(filling)) <=> (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling)),
% 18.16/11.85 inference(unit_resolution,[status(thm)],[30, 29])).
% 18.16/11.85 tff(32,plain,
% 18.16/11.85 (((~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))) | $false) <=> (~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height))))),
% 18.16/11.85 inference(rewrite,[status(thm)],[])).
% 18.16/11.85 tff(33,plain,
% 18.16/11.85 ((~$true) <=> $false),
% 18.16/11.85 inference(rewrite,[status(thm)],[])).
% 18.16/11.85 tff(34,plain,
% 18.16/11.85 ((waterLevel(filling) = waterLevel(filling)) <=> $true),
% 18.16/11.85 inference(rewrite,[status(thm)],[])).
% 18.16/11.85 tff(35,plain,
% 18.16/11.85 ((~(waterLevel(filling) = waterLevel(filling))) <=> (~$true)),
% 18.16/11.85 inference(monotonicity,[status(thm)],[34])).
% 18.16/11.85 tff(36,plain,
% 18.16/11.85 ((~(waterLevel(filling) = waterLevel(filling))) <=> $false),
% 18.16/11.85 inference(transitivity,[status(thm)],[35, 33])).
% 18.16/11.85 tff(37,plain,
% 18.16/11.85 (((~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))) | (~(waterLevel(filling) = waterLevel(filling)))) <=> ((~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))) | $false)),
% 18.16/11.85 inference(monotonicity,[status(thm)],[36])).
% 18.16/11.85 tff(38,plain,
% 18.16/11.85 (((~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))) | (~(waterLevel(filling) = waterLevel(filling)))) <=> (~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height))))),
% 18.16/11.85 inference(transitivity,[status(thm)],[37, 32])).
% 18.16/11.85 tff(39,plain,
% 18.16/11.85 ((~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))) | (~(waterLevel(filling) = waterLevel(filling)))),
% 18.16/11.85 inference(quant_inst,[status(thm)],[])).
% 18.16/11.85 tff(40,plain,
% 18.16/11.85 (~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))),
% 18.16/11.85 inference(modus_ponens,[status(thm)],[39, 38])).
% 18.16/11.85 tff(41,assumption,(![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))), introduced(assumption)).
% 18.16/11.85 tff(42,plain,
% 18.16/11.85 ($false),
% 18.16/11.85 inference(unit_resolution,[status(thm)],[41, 40])).
% 18.16/11.85 tff(43,plain,(~![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))), inference(lemma,lemma(discharge,[]))).
% 18.16/11.85 tff(44,plain,
% 18.16/11.85 (^[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)))))))))),
% 18.16/11.85 inference(bind,[status(th)],[])).
% 18.16/11.85 tff(45,plain,
% 18.16/11.85 (![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))))))))),
% 18.16/11.85 inference(quant_intro,[status(thm)],[44])).
% 18.16/11.85 tff(46,plain,
% 18.16/11.85 (^[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)))))))))),
% 18.16/11.85 inference(bind,[status(th)],[])).
% 18.16/11.85 tff(47,plain,
% 18.16/11.85 (![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))))))))),
% 18.16/11.85 inference(quant_intro,[status(thm)],[46])).
% 18.16/11.85 tff(48,plain,
% 18.16/11.85 (![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))))))))),
% 18.16/11.85 inference(transitivity,[status(thm)],[47, 45])).
% 18.16/11.85 tff(49,plain,
% 18.16/11.85 (^[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))))))))))),
% 18.16/11.85 inference(bind,[status(th)],[])).
% 18.16/11.85 tff(50,plain,
% 18.16/11.85 (![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))))))))),
% 18.16/11.85 inference(quant_intro,[status(thm)],[49])).
% 18.16/11.85 tff(51,plain,
% 18.16/11.85 (![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))))),
% 18.16/11.85 inference(rewrite,[status(thm)],[])).
% 18.16/11.85 tff(52,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')).
% 18.16/11.85 tff(53,plain,
% 18.16/11.85 (![Event: $i, Fluent: $i, Time: $i] : (releases(Event, Fluent, Time) <=> ?[Height: $i] : ((Event = tapOn) & (Fluent = waterLevel(Height))))),
% 18.16/11.85 inference(modus_ponens,[status(thm)],[52, 51])).
% 18.16/11.85 tff(54,plain,(
% 18.16/11.85 ![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))))))),
% 18.16/11.85 inference(skolemize,[status(sab)],[53])).
% 18.16/11.85 tff(55,plain,
% 18.16/11.85 (![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))))))))),
% 18.16/11.85 inference(modus_ponens,[status(thm)],[54, 50])).
% 18.16/11.85 tff(56,plain,
% 18.16/11.85 (![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))))))))),
% 18.16/11.85 inference(modus_ponens,[status(thm)],[55, 48])).
% 18.16/11.85 tff(57,plain,
% 18.16/11.85 (((~![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), waterLevel(filling))) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![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), waterLevel(filling))) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height))))))))),
% 18.16/11.85 inference(rewrite,[status(thm)],[])).
% 18.16/11.85 tff(58,plain,
% 18.16/11.85 ((~((~((~releases(tapOn, waterLevel(filling), waterLevel(filling))) | (~((~(tapOn = tapOn)) | (~(waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)))))))) | (~(releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![Height: $i] : ((~(tapOn = tapOn)) | (~(waterLevel(filling) = waterLevel(Height)))))))) <=> (~((~((~releases(tapOn, waterLevel(filling), waterLevel(filling))) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))))))),
% 18.16/11.85 inference(rewrite,[status(thm)],[])).
% 18.16/11.85 tff(59,plain,
% 18.16/11.85 (((~![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), waterLevel(filling))) | (~((~(tapOn = tapOn)) | (~(waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)))))))) | (~(releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![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), waterLevel(filling))) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height))))))))),
% 18.16/11.85 inference(monotonicity,[status(thm)],[58])).
% 18.16/11.85 tff(60,plain,
% 18.16/11.85 (((~![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), waterLevel(filling))) | (~((~(tapOn = tapOn)) | (~(waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)))))))) | (~(releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![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), waterLevel(filling))) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height))))))))),
% 18.16/11.85 inference(transitivity,[status(thm)],[59, 57])).
% 18.16/11.85 tff(61,plain,
% 18.16/11.85 ((~![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), waterLevel(filling))) | (~((~(tapOn = tapOn)) | (~(waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)))))))) | (~(releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![Height: $i] : ((~(tapOn = tapOn)) | (~(waterLevel(filling) = waterLevel(Height))))))))),
% 18.16/11.85 inference(quant_inst,[status(thm)],[])).
% 18.16/11.85 tff(62,plain,
% 18.16/11.85 ((~![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), waterLevel(filling))) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))))))),
% 18.16/11.85 inference(modus_ponens,[status(thm)],[61, 60])).
% 18.16/11.85 tff(63,plain,
% 18.16/11.85 (~((~((~releases(tapOn, waterLevel(filling), waterLevel(filling))) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height))))))),
% 18.16/11.85 inference(unit_resolution,[status(thm)],[62, 56])).
% 18.16/11.85 tff(64,plain,
% 18.16/11.85 (((~((~releases(tapOn, waterLevel(filling), waterLevel(filling))) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))))) | (releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height))))),
% 18.16/11.85 inference(tautology,[status(thm)],[])).
% 18.16/11.85 tff(65,plain,
% 18.16/11.85 (releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))),
% 18.16/11.85 inference(unit_resolution,[status(thm)],[64, 63])).
% 18.16/11.85 tff(66,plain,
% 18.16/11.85 ((~(releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height))))) | releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))),
% 18.16/11.86 inference(tautology,[status(thm)],[])).
% 18.16/11.86 tff(67,plain,
% 18.16/11.86 (releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))),
% 18.16/11.86 inference(unit_resolution,[status(thm)],[66, 65])).
% 18.16/11.86 tff(68,plain,
% 18.16/11.86 (releases(tapOn, waterLevel(filling), waterLevel(filling))),
% 18.16/11.86 inference(unit_resolution,[status(thm)],[67, 43])).
% 18.16/11.86 tff(69,plain,
% 18.16/11.86 (((~((~releases(tapOn, waterLevel(filling), waterLevel(filling))) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~(releases(tapOn, waterLevel(filling), waterLevel(filling)) | ![Height: $i] : (~(waterLevel(filling) = waterLevel(Height)))))) | ((~releases(tapOn, waterLevel(filling), waterLevel(filling))) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))),
% 18.16/11.86 inference(tautology,[status(thm)],[])).
% 18.16/11.86 tff(70,plain,
% 18.16/11.86 ((~releases(tapOn, waterLevel(filling), waterLevel(filling))) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)))),
% 18.16/11.86 inference(unit_resolution,[status(thm)],[69, 63])).
% 18.16/11.86 tff(71,plain,
% 18.16/11.86 ((~((~releases(tapOn, waterLevel(filling), waterLevel(filling))) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))))) | (~releases(tapOn, waterLevel(filling), waterLevel(filling))) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)))),
% 18.16/11.86 inference(tautology,[status(thm)],[])).
% 18.16/11.86 tff(72,plain,
% 18.16/11.86 ((~releases(tapOn, waterLevel(filling), waterLevel(filling))) | (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)))),
% 18.16/11.86 inference(unit_resolution,[status(thm)],[71, 70])).
% 18.16/11.86 tff(73,plain,
% 18.16/11.86 (waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))),
% 18.16/11.86 inference(unit_resolution,[status(thm)],[72, 68])).
% 18.16/11.86 tff(74,plain,
% 18.16/11.86 (waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn)) = waterLevel(filling)),
% 18.16/11.86 inference(symmetry,[status(thm)],[73])).
% 18.16/11.86 tff(75,plain,
% 18.16/11.86 ((~((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)),
% 18.16/11.86 inference(tautology,[status(thm)],[])).
% 18.16/11.86 tff(76,plain,
% 18.16/11.86 ((~((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)),
% 18.16/11.86 inference(unit_resolution,[status(thm)],[75, 74])).
% 18.16/11.86 tff(77,plain,
% 18.16/11.86 (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling),
% 18.16/11.86 inference(unit_resolution,[status(thm)],[76, 31])).
% 18.16/11.86 tff(78,plain,
% 18.16/11.86 (((tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~((~(overflow = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling))))) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling))),
% 18.16/11.86 inference(tautology,[status(thm)],[])).
% 18.16/11.86 tff(79,plain,
% 18.16/11.86 ((tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~((~(overflow = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling))))),
% 18.16/11.86 inference(unit_resolution,[status(thm)],[78, 77])).
% 18.16/11.86 tff(80,plain,
% 18.16/11.86 ((~(terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))) <=> ((tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~((~(overflow = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling))))))) | terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))) | (~((tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~((~(overflow = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling))))))),
% 18.16/11.86 inference(tautology,[status(thm)],[])).
% 18.16/11.86 tff(81,plain,
% 18.16/11.86 ((~(terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))) <=> ((tptp_fun_Height_10(waterLevel(filling), tapOn) = filling) | (~((~(overflow = tapOff)) | (~(tptp_fun_Height_10(waterLevel(filling), tapOn) = filling))))))) | terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1)))),
% 18.16/11.86 inference(unit_resolution,[status(thm)],[80, 79])).
% 18.16/11.86 tff(82,plain,
% 18.16/11.86 (terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1)))),
% 18.16/11.86 inference(unit_resolution,[status(thm)],[81, 22])).
% 18.16/11.86 tff(83,plain,
% 18.16/11.86 ((plus(n2, n2) = n4) <=> (plus(plus(n1, n1), plus(n1, n1)) = plus(n1, plus(n1, plus(n1, n1))))),
% 18.16/11.86 inference(rewrite,[status(thm)],[])).
% 18.16/11.86 tff(84,plain,
% 18.16/11.86 ((plus(n2, n2) = n4) <=> (plus(n2, n2) = n4)),
% 18.16/11.86 inference(rewrite,[status(thm)],[])).
% 18.16/11.86 tff(85,axiom,(plus(n2, n2) = n4), file('/export/starexec/sandbox/benchmark/theBenchmark.p','plus2_2')).
% 18.16/11.86 tff(86,plain,
% 18.16/11.86 (plus(n2, n2) = n4),
% 18.16/11.86 inference(modus_ponens,[status(thm)],[85, 84])).
% 18.16/11.86 tff(87,plain,
% 18.16/11.86 (plus(plus(n1, n1), plus(n1, n1)) = plus(n1, plus(n1, plus(n1, n1)))),
% 18.16/11.86 inference(modus_ponens,[status(thm)],[86, 83])).
% 18.16/11.86 tff(88,plain,
% 18.16/11.86 (plus(n1, plus(n1, plus(n1, n1))) = plus(plus(n1, n1), plus(n1, n1))),
% 18.16/11.86 inference(symmetry,[status(thm)],[87])).
% 18.16/11.86 tff(89,plain,
% 18.16/11.86 (^[X: $i, Y: $i] : refl((plus(X, Y) = plus(Y, X)) <=> (plus(X, Y) = plus(Y, X)))),
% 18.16/11.86 inference(bind,[status(th)],[])).
% 18.16/11.86 tff(90,plain,
% 18.16/11.86 (![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X)) <=> ![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 18.16/11.86 inference(quant_intro,[status(thm)],[89])).
% 18.16/11.86 tff(91,plain,
% 18.16/11.86 (![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X)) <=> ![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 18.16/11.86 inference(rewrite,[status(thm)],[])).
% 18.16/11.86 tff(92,axiom,(![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_of_plus')).
% 18.16/11.86 tff(93,plain,
% 18.16/11.86 (![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 18.16/11.86 inference(modus_ponens,[status(thm)],[92, 91])).
% 18.16/11.86 tff(94,plain,(
% 18.16/11.86 ![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 18.16/11.86 inference(skolemize,[status(sab)],[93])).
% 18.16/11.86 tff(95,plain,
% 18.16/11.86 (![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 18.16/11.86 inference(modus_ponens,[status(thm)],[94, 90])).
% 18.16/11.86 tff(96,plain,
% 18.16/11.86 ((~![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))) | (plus(n1, plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), n1))),
% 18.16/11.86 inference(quant_inst,[status(thm)],[])).
% 18.16/11.86 tff(97,plain,
% 18.16/11.86 (plus(n1, plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), n1)),
% 18.16/11.86 inference(unit_resolution,[status(thm)],[96, 95])).
% 18.16/11.86 tff(98,plain,
% 18.16/11.86 (plus(plus(n1, plus(n1, n1)), n1) = plus(n1, plus(n1, plus(n1, n1)))),
% 18.16/11.86 inference(symmetry,[status(thm)],[97])).
% 18.16/11.86 tff(99,plain,
% 18.16/11.86 (plus(plus(n1, plus(n1, n1)), n1) = plus(plus(n1, n1), plus(n1, n1))),
% 18.16/11.86 inference(transitivity,[status(thm)],[98, 88])).
% 18.16/11.86 tff(100,assumption,(~((waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))) <=> (filling = tptp_fun_Height_10(waterLevel(filling), tapOn)))), introduced(assumption)).
% 18.16/11.86 tff(101,plain,
% 18.16/11.86 ((~![X: $i, Y: $i] : ((waterLevel(X) = waterLevel(Y)) <=> (X = Y))) | ((waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))) <=> (filling = tptp_fun_Height_10(waterLevel(filling), tapOn)))),
% 18.16/11.86 inference(quant_inst,[status(thm)],[])).
% 18.16/11.86 tff(102,plain,
% 18.16/11.86 ($false),
% 18.16/11.86 inference(unit_resolution,[status(thm)],[101, 29, 100])).
% 18.16/11.86 tff(103,plain,((waterLevel(filling) = waterLevel(tptp_fun_Height_10(waterLevel(filling), tapOn))) <=> (filling = tptp_fun_Height_10(waterLevel(filling), tapOn))), inference(lemma,lemma(discharge,[]))).
% 18.16/11.86 tff(104,plain,
% 18.16/11.86 ((~((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))),
% 18.16/11.86 inference(tautology,[status(thm)],[])).
% 18.16/11.86 tff(105,plain,
% 18.16/11.86 (filling = tptp_fun_Height_10(waterLevel(filling), tapOn)),
% 18.16/11.86 inference(unit_resolution,[status(thm)],[104, 73, 103])).
% 18.16/11.86 tff(106,plain,
% 18.16/11.86 (tptp_fun_Height_10(waterLevel(filling), tapOn) = filling),
% 18.16/11.86 inference(symmetry,[status(thm)],[105])).
% 18.16/11.86 tff(107,plain,
% 18.16/11.86 (holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(plus(n1, plus(n1, n1)), n1)) <=> holdsAt(filling, plus(plus(n1, n1), plus(n1, n1)))),
% 18.16/11.86 inference(monotonicity,[status(thm)],[106, 99])).
% 18.16/11.86 tff(108,plain,
% 18.16/11.86 (holdsAt(filling, plus(plus(n1, n1), plus(n1, n1))) <=> holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(plus(n1, plus(n1, n1)), n1))),
% 18.16/11.86 inference(symmetry,[status(thm)],[107])).
% 18.16/11.86 tff(109,plain,
% 18.16/11.86 (holdsAt(filling, plus(n1, plus(n1, plus(n1, n1)))) <=> holdsAt(filling, plus(plus(n1, n1), plus(n1, n1)))),
% 18.16/11.86 inference(rewrite,[status(thm)],[])).
% 18.16/11.86 tff(110,plain,
% 18.16/11.86 (holdsAt(filling, n4) <=> holdsAt(filling, plus(n1, plus(n1, plus(n1, n1))))),
% 18.16/11.86 inference(rewrite,[status(thm)],[])).
% 18.16/11.86 tff(111,plain,
% 18.16/11.86 (holdsAt(filling, n4) <=> holdsAt(filling, n4)),
% 18.16/11.86 inference(rewrite,[status(thm)],[])).
% 18.16/11.86 tff(112,plain,
% 18.16/11.86 ((~(~holdsAt(filling, n4))) <=> holdsAt(filling, n4)),
% 18.16/11.86 inference(rewrite,[status(thm)],[])).
% 18.16/11.86 tff(113,axiom,(~(~holdsAt(filling, n4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_filling_4')).
% 18.16/11.86 tff(114,plain,
% 18.16/11.86 (holdsAt(filling, n4)),
% 18.16/11.86 inference(modus_ponens,[status(thm)],[113, 112])).
% 18.16/11.86 tff(115,plain,
% 18.16/11.86 (holdsAt(filling, n4)),
% 18.16/11.86 inference(modus_ponens,[status(thm)],[114, 111])).
% 18.16/11.86 tff(116,plain,
% 18.16/11.86 (holdsAt(filling, plus(n1, plus(n1, plus(n1, n1))))),
% 18.16/11.86 inference(modus_ponens,[status(thm)],[115, 110])).
% 18.16/11.86 tff(117,plain,
% 18.16/11.86 (holdsAt(filling, plus(plus(n1, n1), plus(n1, n1)))),
% 18.16/11.86 inference(modus_ponens,[status(thm)],[116, 109])).
% 18.16/11.86 tff(118,plain,
% 18.16/11.86 (holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(plus(n1, plus(n1, n1)), n1))),
% 18.16/11.86 inference(modus_ponens,[status(thm)],[117, 108])).
% 18.16/11.86 tff(119,plain,
% 18.16/11.86 (^[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)))))))),
% 18.16/11.86 inference(bind,[status(th)],[])).
% 18.16/11.86 tff(120,plain,
% 18.16/11.86 (![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))))))),
% 18.16/11.86 inference(quant_intro,[status(thm)],[119])).
% 18.16/11.86 tff(121,plain,
% 18.16/11.86 (^[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)))))))),
% 18.16/11.86 inference(bind,[status(th)],[])).
% 18.16/11.86 tff(122,plain,
% 18.16/11.86 (![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))))))),
% 18.16/11.86 inference(quant_intro,[status(thm)],[121])).
% 18.16/11.86 tff(123,plain,
% 18.16/11.86 (^[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)))))),
% 18.16/11.86 inference(bind,[status(th)],[])).
% 18.16/11.86 tff(124,plain,
% 18.16/11.86 (![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))))),
% 18.16/11.86 inference(quant_intro,[status(thm)],[123])).
% 18.16/11.86 tff(125,plain,
% 18.16/11.86 (![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))))),
% 18.16/11.86 inference(rewrite,[status(thm)],[])).
% 18.16/11.86 tff(126,plain,
% 18.16/11.86 (^[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)))))),
% 18.16/11.86 inference(bind,[status(th)],[])).
% 18.16/11.86 tff(127,plain,
% 18.16/11.86 (![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))))),
% 18.16/11.86 inference(quant_intro,[status(thm)],[126])).
% 18.16/11.86 tff(128,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')).
% 18.16/11.86 tff(129,plain,
% 18.16/11.86 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(n3), Time) & holdsAt(filling, Time) & (Event = overflow))))),
% 18.16/11.86 inference(modus_ponens,[status(thm)],[128, 127])).
% 18.16/11.86 tff(130,plain,
% 18.16/11.86 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(n3), Time) & holdsAt(filling, Time) & (Event = overflow))))),
% 18.16/11.86 inference(modus_ponens,[status(thm)],[129, 125])).
% 18.16/11.86 tff(131,plain,
% 18.16/11.86 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time) & holdsAt(filling, Time) & (Event = overflow))))),
% 18.16/11.86 inference(modus_ponens,[status(thm)],[130, 124])).
% 18.16/11.86 tff(132,plain,(
% 18.16/11.86 ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = tapOn) & (Time = n0)) | (holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time) & holdsAt(filling, Time) & (Event = overflow))))),
% 18.16/11.86 inference(skolemize,[status(sab)],[131])).
% 18.16/11.86 tff(133,plain,
% 18.16/11.86 (![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))),
% 18.16/11.86 inference(modus_ponens,[status(thm)],[132, 122])).
% 18.16/11.86 tff(134,plain,
% 18.16/11.86 (![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))),
% 18.16/11.86 inference(modus_ponens,[status(thm)],[133, 120])).
% 18.16/11.86 tff(135,plain,
% 18.16/11.86 (((~![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(overflow, plus(n1, plus(n1, n1))) <=> ((~((~(overflow = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))))))) <=> ((~![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(overflow, plus(n1, plus(n1, n1))) <=> ((~((~(overflow = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))))))))),
% 18.16/11.86 inference(rewrite,[status(thm)],[])).
% 18.16/11.86 tff(136,plain,
% 18.16/11.86 ((happens(overflow, plus(n1, plus(n1, n1))) <=> ((~((~(overflow = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(overflow = overflow)))))) <=> (happens(overflow, plus(n1, plus(n1, n1))) <=> ((~((~(overflow = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))))))),
% 18.16/11.86 inference(rewrite,[status(thm)],[])).
% 18.16/11.86 tff(137,plain,
% 18.16/11.86 (((~![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(overflow, plus(n1, plus(n1, n1))) <=> ((~((~(overflow = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(overflow = 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(overflow, plus(n1, plus(n1, n1))) <=> ((~((~(overflow = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))))))))),
% 18.16/11.86 inference(monotonicity,[status(thm)],[136])).
% 18.16/11.86 tff(138,plain,
% 18.16/11.86 (((~![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(overflow, plus(n1, plus(n1, n1))) <=> ((~((~(overflow = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(overflow = 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(overflow, plus(n1, plus(n1, n1))) <=> ((~((~(overflow = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))))))))),
% 18.16/11.86 inference(transitivity,[status(thm)],[137, 135])).
% 18.16/11.86 tff(139,plain,
% 18.16/11.86 ((~![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(overflow, plus(n1, plus(n1, n1))) <=> ((~((~(overflow = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(overflow = overflow))))))),
% 18.16/11.86 inference(quant_inst,[status(thm)],[])).
% 18.16/11.86 tff(140,plain,
% 18.16/11.86 ((~![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(overflow, plus(n1, plus(n1, n1))) <=> ((~((~(overflow = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))))))),
% 18.16/11.86 inference(modus_ponens,[status(thm)],[139, 138])).
% 18.16/11.86 tff(141,plain,
% 18.16/11.86 (happens(overflow, plus(n1, plus(n1, n1))) <=> ((~((~(overflow = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))))))),
% 18.16/11.87 inference(unit_resolution,[status(thm)],[140, 134])).
% 18.16/11.87 tff(142,assumption,(~holdsAt(filling, plus(n1, plus(n1, n1)))), introduced(assumption)).
% 18.16/11.87 tff(143,plain,
% 18.16/11.87 (((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))) | holdsAt(filling, plus(n1, plus(n1, n1)))),
% 18.16/11.87 inference(tautology,[status(thm)],[])).
% 18.16/11.87 tff(144,plain,
% 18.16/11.87 ((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))),
% 18.16/11.87 inference(unit_resolution,[status(thm)],[143, 142])).
% 18.16/11.87 tff(145,assumption,(plus(n1, plus(n1, n1)) = n0), introduced(assumption)).
% 18.16/11.87 tff(146,plain,
% 18.16/11.87 (plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = plus(n0, n0)),
% 18.16/11.87 inference(monotonicity,[status(thm)],[145, 145])).
% 18.16/11.87 tff(147,plain,
% 18.16/11.87 (plus(n0, n0) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))),
% 18.16/11.87 inference(symmetry,[status(thm)],[146])).
% 18.16/11.87 tff(148,plain,
% 18.16/11.87 ((plus(n0, n0) = n0) <=> (plus(n0, n0) = n0)),
% 18.16/11.87 inference(rewrite,[status(thm)],[])).
% 18.16/11.87 tff(149,axiom,(plus(n0, n0) = n0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','plus0_0')).
% 18.16/11.87 tff(150,plain,
% 18.16/11.87 (plus(n0, n0) = n0),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[149, 148])).
% 18.16/11.87 tff(151,plain,
% 18.16/11.87 (n0 = plus(n0, n0)),
% 18.16/11.87 inference(symmetry,[status(thm)],[150])).
% 18.16/11.87 tff(152,plain,
% 18.16/11.87 (n0 = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))),
% 18.16/11.87 inference(transitivity,[status(thm)],[151, 147])).
% 18.16/11.87 tff(153,plain,
% 18.16/11.87 (less(plus(n1, plus(n1, plus(n1, n1))), n0) <=> less(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 18.16/11.87 inference(monotonicity,[status(thm)],[152])).
% 18.16/11.87 tff(154,plain,
% 18.16/11.87 (less(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less(plus(n1, plus(n1, plus(n1, n1))), n0)),
% 18.16/11.87 inference(symmetry,[status(thm)],[153])).
% 18.16/11.87 tff(155,plain,
% 18.16/11.87 (^[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))))),
% 18.16/11.87 inference(bind,[status(th)],[])).
% 18.16/11.87 tff(156,plain,
% 18.16/11.87 (![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)))),
% 18.16/11.87 inference(quant_intro,[status(thm)],[155])).
% 18.16/11.87 tff(157,plain,
% 18.16/11.87 (![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)))),
% 18.16/11.87 inference(rewrite,[status(thm)],[])).
% 18.16/11.87 tff(158,plain,
% 18.16/11.87 (^[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))))),
% 18.16/11.87 inference(bind,[status(th)],[])).
% 18.16/11.87 tff(159,plain,
% 18.16/11.87 (![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)))),
% 18.16/11.87 inference(quant_intro,[status(thm)],[158])).
% 18.16/11.87 tff(160,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')).
% 18.16/11.87 tff(161,plain,
% 18.16/11.87 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[160, 159])).
% 18.16/11.87 tff(162,plain,
% 18.16/11.87 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[161, 157])).
% 18.16/11.87 tff(163,plain,(
% 18.16/11.87 ![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 18.16/11.87 inference(skolemize,[status(sab)],[162])).
% 18.16/11.87 tff(164,plain,
% 18.16/11.87 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[163, 156])).
% 18.16/11.87 tff(165,plain,
% 18.16/11.87 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> ((plus(n1, plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))))),
% 18.16/11.87 inference(quant_inst,[status(thm)],[])).
% 18.16/11.87 tff(166,plain,
% 18.16/11.87 (less_or_equal(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> ((plus(n1, plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.87 inference(unit_resolution,[status(thm)],[165, 164])).
% 18.16/11.87 tff(167,plain,
% 18.16/11.87 (^[X: $i] : refl((less(X, n7) <=> less_or_equal(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) <=> (less(X, n7) <=> less_or_equal(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))))),
% 18.16/11.87 inference(bind,[status(th)],[])).
% 18.16/11.87 tff(168,plain,
% 18.16/11.87 (![X: $i] : (less(X, n7) <=> less_or_equal(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) <=> ![X: $i] : (less(X, n7) <=> less_or_equal(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.87 inference(quant_intro,[status(thm)],[167])).
% 18.16/11.87 tff(169,plain,
% 18.16/11.87 (^[X: $i] : rewrite((less(X, n7) <=> less_or_equal(X, n6)) <=> (less(X, n7) <=> less_or_equal(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))))),
% 18.16/11.87 inference(bind,[status(th)],[])).
% 18.16/11.87 tff(170,plain,
% 18.16/11.87 (![X: $i] : (less(X, n7) <=> less_or_equal(X, n6)) <=> ![X: $i] : (less(X, n7) <=> less_or_equal(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.87 inference(quant_intro,[status(thm)],[169])).
% 18.16/11.87 tff(171,plain,
% 18.16/11.87 (![X: $i] : (less(X, n7) <=> less_or_equal(X, n6)) <=> ![X: $i] : (less(X, n7) <=> less_or_equal(X, n6))),
% 18.16/11.87 inference(rewrite,[status(thm)],[])).
% 18.16/11.87 tff(172,axiom,(![X: $i] : (less(X, n7) <=> less_or_equal(X, n6))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','less7')).
% 18.16/11.87 tff(173,plain,
% 18.16/11.87 (![X: $i] : (less(X, n7) <=> less_or_equal(X, n6))),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[172, 171])).
% 18.16/11.87 tff(174,plain,
% 18.16/11.87 (![X: $i] : (less(X, n7) <=> less_or_equal(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[173, 170])).
% 18.16/11.87 tff(175,plain,(
% 18.16/11.87 ![X: $i] : (less(X, n7) <=> less_or_equal(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.87 inference(skolemize,[status(sab)],[174])).
% 18.16/11.87 tff(176,plain,
% 18.16/11.87 (![X: $i] : (less(X, n7) <=> less_or_equal(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[175, 168])).
% 18.16/11.87 tff(177,plain,
% 18.16/11.87 ((~![X: $i] : (less(X, n7) <=> less_or_equal(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))) | (less(plus(n1, plus(n1, plus(n1, n1))), n7) <=> less_or_equal(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.87 inference(quant_inst,[status(thm)],[])).
% 18.16/11.87 tff(178,plain,
% 18.16/11.87 (less(plus(n1, plus(n1, plus(n1, n1))), n7) <=> less_or_equal(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 18.16/11.87 inference(unit_resolution,[status(thm)],[177, 176])).
% 18.16/11.87 tff(179,plain,
% 18.16/11.87 (^[X: $i, Y: $i] : refl((less(X, Y) <=> (~((Y = X) | less(Y, X)))) <=> (less(X, Y) <=> (~((Y = X) | less(Y, X)))))),
% 18.16/11.87 inference(bind,[status(th)],[])).
% 18.16/11.87 tff(180,plain,
% 18.16/11.87 (![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X)))) <=> ![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))),
% 18.16/11.87 inference(quant_intro,[status(thm)],[179])).
% 18.16/11.87 tff(181,plain,
% 18.16/11.87 (^[X: $i, Y: $i] : rewrite((less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> (less(X, Y) <=> (~((Y = X) | less(Y, X)))))),
% 18.16/11.87 inference(bind,[status(th)],[])).
% 18.16/11.87 tff(182,plain,
% 18.16/11.87 (![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> ![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))),
% 18.16/11.87 inference(quant_intro,[status(thm)],[181])).
% 18.16/11.87 tff(183,plain,
% 18.16/11.87 (![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> ![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))),
% 18.16/11.87 inference(rewrite,[status(thm)],[])).
% 18.16/11.87 tff(184,axiom,(![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','less_property')).
% 18.16/11.87 tff(185,plain,
% 18.16/11.87 (![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[184, 183])).
% 18.16/11.87 tff(186,plain,(
% 18.16/11.87 ![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))),
% 18.16/11.87 inference(skolemize,[status(sab)],[185])).
% 18.16/11.87 tff(187,plain,
% 18.16/11.87 (![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[186, 182])).
% 18.16/11.87 tff(188,plain,
% 18.16/11.87 (![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[187, 180])).
% 18.16/11.87 tff(189,plain,
% 18.16/11.87 ((~![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))) | (less(plus(n1, plus(n1, plus(n1, n1))), n7) <=> (~((n7 = plus(n1, plus(n1, plus(n1, n1)))) | less(n7, plus(n1, plus(n1, plus(n1, n1)))))))),
% 18.16/11.87 inference(quant_inst,[status(thm)],[])).
% 18.16/11.87 tff(190,plain,
% 18.16/11.87 (less(plus(n1, plus(n1, plus(n1, n1))), n7) <=> (~((n7 = plus(n1, plus(n1, plus(n1, n1)))) | less(n7, plus(n1, plus(n1, plus(n1, n1))))))),
% 18.16/11.87 inference(unit_resolution,[status(thm)],[189, 188])).
% 18.16/11.87 tff(191,plain,
% 18.16/11.87 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(n7, plus(n1, plus(n1, plus(n1, n1)))) <=> ((n7 = plus(n1, plus(n1, plus(n1, n1)))) | less(n7, plus(n1, plus(n1, plus(n1, n1))))))),
% 18.16/11.87 inference(quant_inst,[status(thm)],[])).
% 18.16/11.87 tff(192,plain,
% 18.16/11.87 (less_or_equal(n7, plus(n1, plus(n1, plus(n1, n1)))) <=> ((n7 = plus(n1, plus(n1, plus(n1, n1)))) | less(n7, plus(n1, plus(n1, plus(n1, n1)))))),
% 18.16/11.87 inference(unit_resolution,[status(thm)],[191, 164])).
% 18.16/11.87 tff(193,plain,
% 18.16/11.87 (less_or_equal(n7, plus(n1, plus(n1, plus(n1, n1)))) <=> less_or_equal(n7, plus(plus(n1, n1), plus(n1, n1)))),
% 18.16/11.87 inference(monotonicity,[status(thm)],[88])).
% 18.16/11.87 tff(194,plain,
% 18.16/11.87 (less_or_equal(n7, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(n7, plus(n1, plus(n1, plus(n1, n1))))),
% 18.16/11.87 inference(symmetry,[status(thm)],[193])).
% 18.16/11.87 tff(195,plain,
% 18.16/11.87 ((~less_or_equal(n7, plus(plus(n1, n1), plus(n1, n1)))) <=> (~less_or_equal(n7, plus(n1, plus(n1, plus(n1, n1)))))),
% 18.16/11.87 inference(monotonicity,[status(thm)],[194])).
% 18.16/11.87 tff(196,plain,
% 18.16/11.87 (^[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)))))),
% 18.16/11.87 inference(bind,[status(th)],[])).
% 18.16/11.87 tff(197,plain,
% 18.16/11.87 (![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))))),
% 18.16/11.87 inference(quant_intro,[status(thm)],[196])).
% 18.16/11.87 tff(198,plain,
% 18.16/11.87 (^[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)))))),
% 18.16/11.87 inference(bind,[status(th)],[])).
% 18.16/11.87 tff(199,plain,
% 18.16/11.87 (![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))))),
% 18.16/11.87 inference(quant_intro,[status(thm)],[198])).
% 18.16/11.87 tff(200,plain,
% 18.16/11.87 (^[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))))))),
% 18.16/11.87 inference(bind,[status(th)],[])).
% 18.16/11.87 tff(201,plain,
% 18.16/11.87 (![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)))))),
% 18.16/11.87 inference(quant_intro,[status(thm)],[200])).
% 18.16/11.87 tff(202,plain,
% 18.16/11.87 (![X: $i] : (less(X, n5) <=> less_or_equal(X, n4)) <=> ![X: $i] : (less(X, n5) <=> less_or_equal(X, n4))),
% 18.16/11.87 inference(rewrite,[status(thm)],[])).
% 18.16/11.87 tff(203,axiom,(![X: $i] : (less(X, n5) <=> less_or_equal(X, n4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','less5')).
% 18.16/11.87 tff(204,plain,
% 18.16/11.87 (![X: $i] : (less(X, n5) <=> less_or_equal(X, n4))),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[203, 202])).
% 18.16/11.87 tff(205,plain,
% 18.16/11.87 (![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(n1, plus(n1, plus(n1, n1)))))),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[204, 201])).
% 18.16/11.87 tff(206,plain,
% 18.16/11.87 (![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, n1))))),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[205, 199])).
% 18.16/11.87 tff(207,plain,(
% 18.16/11.87 ![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, n1))))),
% 18.16/11.87 inference(skolemize,[status(sab)],[206])).
% 18.16/11.87 tff(208,plain,
% 18.16/11.87 (![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(plus(n1, n1), plus(n1, n1))))),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[207, 197])).
% 18.16/11.87 tff(209,plain,
% 18.16/11.87 ((~![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(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(n7, plus(plus(n1, n1), plus(n1, n1))))),
% 18.16/11.87 inference(quant_inst,[status(thm)],[])).
% 18.16/11.87 tff(210,plain,
% 18.16/11.87 (less(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(n7, plus(plus(n1, n1), plus(n1, n1)))),
% 18.16/11.87 inference(unit_resolution,[status(thm)],[209, 208])).
% 18.16/11.87 tff(211,plain,
% 18.16/11.87 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> ((n7 = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1))))))),
% 18.16/11.87 inference(quant_inst,[status(thm)],[])).
% 18.16/11.87 tff(212,plain,
% 18.16/11.87 (less_or_equal(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> ((n7 = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 18.16/11.87 inference(unit_resolution,[status(thm)],[211, 164])).
% 18.16/11.87 tff(213,plain,
% 18.16/11.87 (^[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))))))),
% 18.16/11.87 inference(bind,[status(th)],[])).
% 18.16/11.87 tff(214,plain,
% 18.16/11.87 (![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)))))),
% 18.16/11.87 inference(quant_intro,[status(thm)],[213])).
% 18.16/11.87 tff(215,plain,
% 18.16/11.87 (^[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))))))),
% 18.16/11.87 inference(bind,[status(th)],[])).
% 18.16/11.87 tff(216,plain,
% 18.16/11.87 (![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)))))),
% 18.16/11.87 inference(quant_intro,[status(thm)],[215])).
% 18.16/11.87 tff(217,plain,
% 18.16/11.87 (![X: $i] : (less(X, n6) <=> less_or_equal(X, n5)) <=> ![X: $i] : (less(X, n6) <=> less_or_equal(X, n5))),
% 18.16/11.87 inference(rewrite,[status(thm)],[])).
% 18.16/11.87 tff(218,axiom,(![X: $i] : (less(X, n6) <=> less_or_equal(X, n5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','less6')).
% 18.16/11.87 tff(219,plain,
% 18.16/11.87 (![X: $i] : (less(X, n6) <=> less_or_equal(X, n5))),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[218, 217])).
% 18.16/11.87 tff(220,plain,
% 18.16/11.87 (![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)))))),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[219, 216])).
% 18.16/11.87 tff(221,plain,(
% 18.16/11.87 ![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)))))),
% 18.16/11.87 inference(skolemize,[status(sab)],[220])).
% 18.16/11.87 tff(222,plain,
% 18.16/11.87 (![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)))))),
% 18.16/11.87 inference(modus_ponens,[status(thm)],[221, 214])).
% 18.16/11.87 tff(223,plain,
% 18.16/11.87 ((~![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(n7, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 18.16/11.87 inference(quant_inst,[status(thm)],[])).
% 18.16/11.87 tff(224,plain,
% 18.16/11.87 (less(n7, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1))))),
% 18.16/11.87 inference(unit_resolution,[status(thm)],[223, 222])).
% 18.16/11.87 tff(225,plain,
% 18.16/11.87 ((~![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))) | (less(n7, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> (~((plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = n7) | less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), n7))))),
% 18.16/11.87 inference(quant_inst,[status(thm)],[])).
% 18.16/11.87 tff(226,plain,
% 18.16/11.87 (less(n7, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> (~((plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = n7) | less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), n7)))),
% 18.16/11.87 inference(unit_resolution,[status(thm)],[225, 188])).
% 18.16/11.87 tff(227,plain,
% 18.16/11.87 ((~![X: $i] : (less(X, n7) <=> less_or_equal(X, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))) | (less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), n7) <=> less_or_equal(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.87 inference(quant_inst,[status(thm)],[])).
% 18.16/11.87 tff(228,plain,
% 18.16/11.87 (less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), n7) <=> less_or_equal(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 18.16/11.87 inference(unit_resolution,[status(thm)],[227, 176])).
% 18.16/11.87 tff(229,plain,
% 18.16/11.87 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(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(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.87 inference(rewrite,[status(thm)],[])).
% 18.16/11.87 tff(230,plain,
% 18.16/11.87 ((less_or_equal(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> $true) <=> less_or_equal(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 18.16/11.87 inference(rewrite,[status(thm)],[])).
% 18.16/11.87 tff(231,plain,
% 18.16/11.87 (($true | less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) <=> $true),
% 18.16/11.87 inference(rewrite,[status(thm)],[])).
% 18.16/11.87 tff(232,plain,
% 18.16/11.87 ((plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> $true),
% 18.16/11.87 inference(rewrite,[status(thm)],[])).
% 18.16/11.87 tff(233,plain,
% 18.16/11.87 (((plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) <=> ($true | less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.87 inference(monotonicity,[status(thm)],[232])).
% 18.16/11.87 tff(234,plain,
% 18.16/11.87 (((plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) <=> $true),
% 18.16/11.87 inference(transitivity,[status(thm)],[233, 231])).
% 18.16/11.87 tff(235,plain,
% 18.16/11.87 ((less_or_equal(plus(plus(n1, plus(n1, n1)), plus(n1, 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(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, 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, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> $true)),
% 18.16/11.88 inference(monotonicity,[status(thm)],[234])).
% 18.16/11.88 tff(236,plain,
% 18.16/11.88 ((less_or_equal(plus(plus(n1, plus(n1, n1)), plus(n1, 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(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, 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, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 18.16/11.88 inference(transitivity,[status(thm)],[235, 230])).
% 18.16/11.88 tff(237,plain,
% 18.16/11.88 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(plus(plus(n1, plus(n1, n1)), plus(n1, 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(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(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(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.88 inference(monotonicity,[status(thm)],[236])).
% 18.16/11.88 tff(238,plain,
% 18.16/11.88 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(plus(plus(n1, plus(n1, n1)), plus(n1, 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(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(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(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.88 inference(transitivity,[status(thm)],[237, 229])).
% 18.16/11.88 tff(239,plain,
% 18.16/11.88 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(plus(plus(n1, plus(n1, n1)), plus(n1, 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(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))))),
% 18.16/11.88 inference(quant_inst,[status(thm)],[])).
% 18.16/11.88 tff(240,plain,
% 18.16/11.88 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 18.16/11.88 inference(modus_ponens,[status(thm)],[239, 238])).
% 18.16/11.88 tff(241,plain,
% 18.16/11.88 (less_or_equal(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[240, 164])).
% 18.16/11.88 tff(242,plain,
% 18.16/11.88 ((~(less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), n7) <=> less_or_equal(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))) | less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), n7) | (~less_or_equal(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.88 inference(tautology,[status(thm)],[])).
% 18.16/11.88 tff(243,plain,
% 18.16/11.88 ((~(less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), n7) <=> less_or_equal(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))) | less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), n7)),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[242, 241])).
% 18.16/11.88 tff(244,plain,
% 18.16/11.88 (less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), n7)),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[243, 228])).
% 18.16/11.88 tff(245,plain,
% 18.16/11.88 (((plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = n7) | less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), n7)) | (~less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), n7))),
% 18.16/11.88 inference(tautology,[status(thm)],[])).
% 18.16/11.88 tff(246,plain,
% 18.16/11.88 ((plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = n7) | less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), n7)),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[245, 244])).
% 18.16/11.88 tff(247,plain,
% 18.16/11.88 ((~(less(n7, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> (~((plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = n7) | less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), n7))))) | (~less(n7, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) | (~((plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = n7) | less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), n7)))),
% 18.16/11.88 inference(tautology,[status(thm)],[])).
% 18.16/11.88 tff(248,plain,
% 18.16/11.88 ((~(less(n7, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> (~((plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = n7) | less(plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))), n7))))) | (~less(n7, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[247, 246])).
% 18.16/11.88 tff(249,plain,
% 18.16/11.88 (~less(n7, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[248, 226])).
% 18.16/11.88 tff(250,plain,
% 18.16/11.88 ((~(less(n7, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))))) | less(n7, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | (~less_or_equal(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 18.16/11.88 inference(tautology,[status(thm)],[])).
% 18.16/11.88 tff(251,plain,
% 18.16/11.88 ((~(less(n7, plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))))) | (~less_or_equal(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[250, 249])).
% 18.16/11.88 tff(252,plain,
% 18.16/11.88 (~less_or_equal(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1))))),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[251, 224])).
% 18.16/11.88 tff(253,plain,
% 18.16/11.88 ((~(less_or_equal(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> ((n7 = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1))))))) | less_or_equal(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | (~((n7 = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1))))))),
% 18.16/11.88 inference(tautology,[status(thm)],[])).
% 18.16/11.88 tff(254,plain,
% 18.16/11.88 ((~(less_or_equal(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> ((n7 = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1))))))) | (~((n7 = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1))))))),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[253, 252])).
% 18.16/11.88 tff(255,plain,
% 18.16/11.88 (~((n7 = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[254, 212])).
% 18.16/11.88 tff(256,plain,
% 18.16/11.88 (((n7 = plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | less(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1))))) | (~less(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))))),
% 18.16/11.88 inference(tautology,[status(thm)],[])).
% 18.16/11.88 tff(257,plain,
% 18.16/11.88 (~less(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1))))),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[256, 255])).
% 18.16/11.88 tff(258,plain,
% 18.16/11.88 ((~(less(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(n7, plus(plus(n1, n1), plus(n1, n1))))) | less(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) | (~less_or_equal(n7, plus(plus(n1, n1), plus(n1, n1))))),
% 18.16/11.88 inference(tautology,[status(thm)],[])).
% 18.16/11.88 tff(259,plain,
% 18.16/11.88 ((~(less(n7, plus(plus(n1, n1), plus(n1, plus(n1, n1)))) <=> less_or_equal(n7, plus(plus(n1, n1), plus(n1, n1))))) | (~less_or_equal(n7, plus(plus(n1, n1), plus(n1, n1))))),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[258, 257])).
% 18.16/11.88 tff(260,plain,
% 18.16/11.88 (~less_or_equal(n7, plus(plus(n1, n1), plus(n1, n1)))),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[259, 210])).
% 18.16/11.88 tff(261,plain,
% 18.16/11.88 (~less_or_equal(n7, plus(n1, plus(n1, plus(n1, n1))))),
% 18.16/11.88 inference(modus_ponens,[status(thm)],[260, 195])).
% 18.16/11.88 tff(262,plain,
% 18.16/11.88 ((~(less_or_equal(n7, plus(n1, plus(n1, plus(n1, n1)))) <=> ((n7 = plus(n1, plus(n1, plus(n1, n1)))) | less(n7, plus(n1, plus(n1, plus(n1, n1))))))) | less_or_equal(n7, plus(n1, plus(n1, plus(n1, n1)))) | (~((n7 = plus(n1, plus(n1, plus(n1, n1)))) | less(n7, plus(n1, plus(n1, plus(n1, n1))))))),
% 18.16/11.88 inference(tautology,[status(thm)],[])).
% 18.16/11.88 tff(263,plain,
% 18.16/11.88 (~((n7 = plus(n1, plus(n1, plus(n1, n1)))) | less(n7, plus(n1, plus(n1, plus(n1, n1)))))),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[262, 261, 192])).
% 18.16/11.88 tff(264,plain,
% 18.16/11.88 ((~(less(plus(n1, plus(n1, plus(n1, n1))), n7) <=> (~((n7 = plus(n1, plus(n1, plus(n1, n1)))) | less(n7, plus(n1, plus(n1, plus(n1, n1)))))))) | less(plus(n1, plus(n1, plus(n1, n1))), n7) | ((n7 = plus(n1, plus(n1, plus(n1, n1)))) | less(n7, plus(n1, plus(n1, plus(n1, n1)))))),
% 18.16/11.88 inference(tautology,[status(thm)],[])).
% 18.16/11.88 tff(265,plain,
% 18.16/11.88 ((~(less(plus(n1, plus(n1, plus(n1, n1))), n7) <=> (~((n7 = plus(n1, plus(n1, plus(n1, n1)))) | less(n7, plus(n1, plus(n1, plus(n1, n1)))))))) | less(plus(n1, plus(n1, plus(n1, n1))), n7)),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[264, 263])).
% 18.16/11.88 tff(266,plain,
% 18.16/11.88 (less(plus(n1, plus(n1, plus(n1, n1))), n7)),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[265, 190])).
% 18.16/11.88 tff(267,plain,
% 18.16/11.88 ((~(less(plus(n1, plus(n1, plus(n1, n1))), n7) <=> less_or_equal(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))) | (~less(plus(n1, plus(n1, plus(n1, n1))), n7)) | less_or_equal(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 18.16/11.88 inference(tautology,[status(thm)],[])).
% 18.16/11.88 tff(268,plain,
% 18.16/11.88 ((~(less(plus(n1, plus(n1, plus(n1, n1))), n7) <=> less_or_equal(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))) | less_or_equal(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[267, 266])).
% 18.16/11.88 tff(269,plain,
% 18.16/11.88 (less_or_equal(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[268, 178])).
% 18.16/11.88 tff(270,plain,
% 18.16/11.88 ((~(less_or_equal(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> ((plus(n1, plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))))) | (~less_or_equal(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) | ((plus(n1, plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.88 inference(tautology,[status(thm)],[])).
% 18.16/11.88 tff(271,plain,
% 18.16/11.88 ((~(less_or_equal(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> ((plus(n1, plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))))) | ((plus(n1, plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[270, 269])).
% 18.16/11.88 tff(272,plain,
% 18.16/11.88 ((plus(n1, plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 18.16/11.88 inference(unit_resolution,[status(thm)],[271, 166])).
% 18.16/11.89 tff(273,plain,
% 18.16/11.89 (n0 = plus(n1, plus(n1, n1))),
% 18.16/11.89 inference(symmetry,[status(thm)],[145])).
% 18.16/11.89 tff(274,plain,
% 18.16/11.89 (plus(n0, n1) = plus(plus(n1, plus(n1, n1)), n1)),
% 18.16/11.89 inference(monotonicity,[status(thm)],[273])).
% 18.16/11.89 tff(275,plain,
% 18.16/11.89 ((plus(n0, n1) = n1) <=> (plus(n0, n1) = n1)),
% 18.16/11.89 inference(rewrite,[status(thm)],[])).
% 18.16/11.89 tff(276,axiom,(plus(n0, n1) = n1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','plus0_1')).
% 18.16/11.89 tff(277,plain,
% 18.16/11.89 (plus(n0, n1) = n1),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[276, 275])).
% 18.16/11.89 tff(278,plain,
% 18.16/11.89 (n1 = plus(n0, n1)),
% 18.16/11.89 inference(symmetry,[status(thm)],[277])).
% 18.16/11.89 tff(279,plain,
% 18.16/11.89 (n1 = plus(n1, plus(n1, plus(n1, n1)))),
% 18.16/11.89 inference(transitivity,[status(thm)],[278, 274, 98])).
% 18.16/11.89 tff(280,plain,
% 18.16/11.89 ((n1 = n0) <=> (plus(n1, plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 18.16/11.89 inference(monotonicity,[status(thm)],[279, 152])).
% 18.16/11.89 tff(281,plain,
% 18.16/11.89 ((~(n1 = n0)) <=> (~(plus(n1, plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 18.16/11.89 inference(monotonicity,[status(thm)],[280])).
% 18.16/11.89 tff(282,assumption,(n1 = n0), introduced(assumption)).
% 18.16/11.89 tff(283,plain,
% 18.16/11.89 (plus(n1, n1) = plus(n0, n0)),
% 18.16/11.89 inference(monotonicity,[status(thm)],[282, 282])).
% 18.16/11.89 tff(284,plain,
% 18.16/11.89 (plus(n1, n1) = n0),
% 18.16/11.89 inference(transitivity,[status(thm)],[283, 150])).
% 18.16/11.89 tff(285,assumption,(plus(n1, n1) = n0), introduced(assumption)).
% 18.16/11.89 tff(286,plain,
% 18.16/11.89 (n0 = plus(n1, n1)),
% 18.16/11.89 inference(symmetry,[status(thm)],[285])).
% 18.16/11.89 tff(287,plain,
% 18.16/11.89 (plus(plus(n1, n1), plus(n1, n1)) = plus(n0, n0)),
% 18.16/11.89 inference(monotonicity,[status(thm)],[285, 285])).
% 18.16/11.89 tff(288,plain,
% 18.16/11.89 (plus(plus(n1, n1), plus(n1, n1)) = plus(n1, n1)),
% 18.16/11.89 inference(transitivity,[status(thm)],[287, 150, 286])).
% 18.16/11.89 tff(289,plain,
% 18.16/11.89 (holdsAt(filling, plus(plus(n1, n1), plus(n1, n1))) <=> holdsAt(filling, plus(n1, n1))),
% 18.16/11.89 inference(monotonicity,[status(thm)],[288])).
% 18.16/11.89 tff(290,plain,
% 18.16/11.89 (holdsAt(filling, plus(n1, n1)) <=> holdsAt(filling, plus(plus(n1, n1), plus(n1, n1)))),
% 18.16/11.89 inference(symmetry,[status(thm)],[289])).
% 18.16/11.89 tff(291,plain,
% 18.16/11.89 ((~holdsAt(filling, plus(n1, n1))) <=> (~holdsAt(filling, plus(plus(n1, n1), plus(n1, n1))))),
% 18.16/11.89 inference(monotonicity,[status(thm)],[290])).
% 18.16/11.89 tff(292,plain,
% 18.16/11.89 (holdsAt(filling, n0) <=> holdsAt(filling, plus(n1, n1))),
% 18.16/11.89 inference(monotonicity,[status(thm)],[286])).
% 18.16/11.89 tff(293,plain,
% 18.16/11.89 ((~holdsAt(filling, n0)) <=> (~holdsAt(filling, plus(n1, n1)))),
% 18.16/11.89 inference(monotonicity,[status(thm)],[292])).
% 18.16/11.89 tff(294,plain,
% 18.16/11.89 ((~holdsAt(filling, n0)) <=> (~holdsAt(filling, n0))),
% 18.16/11.89 inference(rewrite,[status(thm)],[])).
% 18.16/11.89 tff(295,axiom,(~holdsAt(filling, n0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_filling_0')).
% 18.16/11.89 tff(296,plain,
% 18.16/11.89 (~holdsAt(filling, n0)),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[295, 294])).
% 18.16/11.89 tff(297,plain,
% 18.16/11.89 (~holdsAt(filling, plus(n1, n1))),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[296, 293])).
% 18.16/11.89 tff(298,plain,
% 18.16/11.89 (~holdsAt(filling, plus(plus(n1, n1), plus(n1, n1)))),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[297, 291])).
% 18.16/11.89 tff(299,plain,
% 18.16/11.89 ($false),
% 18.16/11.89 inference(unit_resolution,[status(thm)],[117, 298])).
% 18.16/11.89 tff(300,plain,(~(plus(n1, n1) = n0)), inference(lemma,lemma(discharge,[]))).
% 18.16/11.89 tff(301,plain,
% 18.16/11.89 ($false),
% 18.16/11.89 inference(unit_resolution,[status(thm)],[300, 284])).
% 18.16/11.89 tff(302,plain,(~(n1 = n0)), inference(lemma,lemma(discharge,[]))).
% 18.16/11.89 tff(303,plain,
% 18.16/11.89 (~(plus(n1, plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[302, 281])).
% 18.16/11.89 tff(304,plain,
% 18.16/11.89 ((~((plus(n1, plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))) | (plus(n1, plus(n1, plus(n1, n1))) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) | less(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 18.16/11.89 inference(tautology,[status(thm)],[])).
% 18.16/11.89 tff(305,plain,
% 18.16/11.89 (less(plus(n1, plus(n1, plus(n1, n1))), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 18.16/11.89 inference(unit_resolution,[status(thm)],[304, 303, 272])).
% 18.16/11.89 tff(306,plain,
% 18.16/11.89 (less(plus(n1, plus(n1, plus(n1, n1))), n0)),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[305, 154])).
% 18.16/11.89 tff(307,plain,
% 18.16/11.89 (^[X: $i] : refl((~less(X, n0)) <=> (~less(X, n0)))),
% 18.16/11.89 inference(bind,[status(th)],[])).
% 18.16/11.89 tff(308,plain,
% 18.16/11.89 (![X: $i] : (~less(X, n0)) <=> ![X: $i] : (~less(X, n0))),
% 18.16/11.89 inference(quant_intro,[status(thm)],[307])).
% 18.16/11.89 tff(309,plain,
% 18.16/11.89 ((~?[X: $i] : less(X, n0)) <=> (~?[X: $i] : less(X, n0))),
% 18.16/11.89 inference(rewrite,[status(thm)],[])).
% 18.16/11.89 tff(310,axiom,(~?[X: $i] : less(X, n0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','less0')).
% 18.16/11.89 tff(311,plain,
% 18.16/11.89 (~?[X: $i] : less(X, n0)),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[310, 309])).
% 18.16/11.89 tff(312,plain,
% 18.16/11.89 (~?[X: $i] : less(X, n0)),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[311, 309])).
% 18.16/11.89 tff(313,plain,
% 18.16/11.89 (~?[X: $i] : less(X, n0)),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[312, 309])).
% 18.16/11.89 tff(314,plain,
% 18.16/11.89 (~?[X: $i] : less(X, n0)),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[313, 309])).
% 18.16/11.89 tff(315,plain,
% 18.16/11.89 (~?[X: $i] : less(X, n0)),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[314, 309])).
% 18.16/11.89 tff(316,plain,
% 18.16/11.89 (~?[X: $i] : less(X, n0)),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[315, 309])).
% 18.16/11.89 tff(317,plain,
% 18.16/11.89 (~?[X: $i] : less(X, n0)),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[316, 309])).
% 18.16/11.89 tff(318,plain,
% 18.16/11.89 (~?[X: $i] : less(X, n0)),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[317, 309])).
% 18.16/11.89 tff(319,plain,
% 18.16/11.89 (~?[X: $i] : less(X, n0)),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[318, 309])).
% 18.16/11.89 tff(320,plain,
% 18.16/11.89 (~?[X: $i] : less(X, n0)),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[319, 309])).
% 18.16/11.89 tff(321,plain,
% 18.16/11.89 (^[X: $i] : refl($oeq((~less(X, n0)), (~less(X, n0))))),
% 18.16/11.89 inference(bind,[status(th)],[])).
% 18.16/11.89 tff(322,plain,(
% 18.16/11.89 ![X: $i] : (~less(X, n0))),
% 18.16/11.89 inference(nnf-neg,[status(sab)],[320, 321])).
% 18.16/11.89 tff(323,plain,
% 18.16/11.89 (![X: $i] : (~less(X, n0))),
% 18.16/11.89 inference(modus_ponens,[status(thm)],[322, 308])).
% 18.16/11.89 tff(324,plain,
% 18.16/11.89 ((~![X: $i] : (~less(X, n0))) | (~less(plus(n1, plus(n1, plus(n1, n1))), n0))),
% 18.16/11.89 inference(quant_inst,[status(thm)],[])).
% 18.16/11.89 tff(325,plain,
% 18.16/11.89 (~less(plus(n1, plus(n1, plus(n1, n1))), n0)),
% 18.16/11.89 inference(unit_resolution,[status(thm)],[324, 323])).
% 18.16/11.89 tff(326,plain,
% 18.16/11.89 ($false),
% 18.16/11.89 inference(unit_resolution,[status(thm)],[325, 306])).
% 18.16/11.89 tff(327,plain,(~(plus(n1, plus(n1, n1)) = n0)), inference(lemma,lemma(discharge,[]))).
% 18.16/11.89 tff(328,plain,
% 18.16/11.89 (((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn))) | (plus(n1, plus(n1, n1)) = n0)),
% 18.16/11.89 inference(tautology,[status(thm)],[])).
% 18.16/11.89 tff(329,plain,
% 18.16/11.89 ((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn))),
% 18.16/11.89 inference(unit_resolution,[status(thm)],[328, 327])).
% 18.16/11.89 tff(330,plain,
% 18.16/11.89 ((~((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))))))) | (~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))))),
% 18.16/11.89 inference(tautology,[status(thm)],[])).
% 18.16/11.89 tff(331,plain,
% 18.16/11.89 ((~((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))))))) | (~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))))),
% 18.16/11.89 inference(unit_resolution,[status(thm)],[330, 329])).
% 18.16/11.89 tff(332,plain,
% 18.16/11.89 (~((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))))))),
% 18.16/11.89 inference(unit_resolution,[status(thm)],[331, 144])).
% 18.16/11.89 tff(333,plain,
% 18.16/11.89 (((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn))) | (plus(n1, plus(n1, n1)) = n0)),
% 18.16/11.89 inference(tautology,[status(thm)],[])).
% 18.16/11.89 tff(334,plain,
% 18.16/11.89 ((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn))),
% 18.16/11.89 inference(unit_resolution,[status(thm)],[333, 327])).
% 18.16/11.89 tff(335,assumption,((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn))), introduced(assumption)).
% 18.16/11.89 tff(336,plain,
% 18.16/11.89 (((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow))) | holdsAt(filling, plus(n1, plus(n1, n1)))),
% 18.16/11.89 inference(tautology,[status(thm)],[])).
% 18.16/11.89 tff(337,plain,
% 18.16/11.89 ((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow))),
% 18.16/11.89 inference(unit_resolution,[status(thm)],[336, 142])).
% 18.16/11.89 tff(338,plain,
% 18.16/11.89 ((~((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow)))))) | (~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow))))),
% 18.16/11.89 inference(tautology,[status(thm)],[])).
% 18.16/11.89 tff(339,plain,
% 18.16/11.89 (~((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow)))))),
% 18.16/11.89 inference(unit_resolution,[status(thm)],[338, 337, 335])).
% 18.16/11.89 tff(340,assumption,(~(happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow))))))), introduced(assumption)).
% 18.16/11.89 tff(341,plain,
% 18.16/11.89 (((~![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(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, 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_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow)))))))),
% 18.16/11.89 inference(rewrite,[status(thm)],[])).
% 18.16/11.89 tff(342,plain,
% 18.16/11.89 ((happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow)))))) <=> (happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow))))))),
% 18.16/11.89 inference(rewrite,[status(thm)],[])).
% 18.16/11.89 tff(343,plain,
% 18.16/11.89 (((~![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(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, 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_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow)))))))),
% 18.16/11.89 inference(monotonicity,[status(thm)],[342])).
% 18.16/11.89 tff(344,plain,
% 18.16/11.89 (((~![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(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, 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_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow)))))))),
% 18.16/11.89 inference(transitivity,[status(thm)],[343, 341])).
% 18.16/11.89 tff(345,plain,
% 18.16/11.89 ((~![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(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow))))))),
% 18.16/11.89 inference(quant_inst,[status(thm)],[])).
% 18.16/11.90 tff(346,plain,
% 18.16/11.90 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow))))))),
% 18.16/11.90 inference(modus_ponens,[status(thm)],[345, 344])).
% 18.16/11.90 tff(347,plain,
% 18.16/11.90 ($false),
% 18.16/11.90 inference(unit_resolution,[status(thm)],[346, 134, 340])).
% 18.16/11.90 tff(348,plain,(happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow)))))), inference(lemma,lemma(discharge,[]))).
% 18.16/11.90 tff(349,plain,
% 18.16/11.90 ((~(happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow))))))) | (~happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow)))))),
% 18.16/11.90 inference(tautology,[status(thm)],[])).
% 18.16/11.90 tff(350,plain,
% 18.16/11.90 ((~happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = overflow)))))),
% 18.16/11.90 inference(unit_resolution,[status(thm)],[349, 348])).
% 18.16/11.90 tff(351,plain,
% 18.16/11.90 (~happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))),
% 18.16/11.90 inference(unit_resolution,[status(thm)],[350, 339])).
% 18.16/11.90 tff(352,plain,
% 18.16/11.90 (((~happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~releases(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1))))) | happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))),
% 18.16/11.90 inference(tautology,[status(thm)],[])).
% 18.16/11.90 tff(353,plain,
% 18.16/11.90 ((~happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~releases(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1))))),
% 18.16/11.90 inference(unit_resolution,[status(thm)],[352, 351])).
% 18.16/11.90 tff(354,plain,
% 18.16/11.90 ((~![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))) | (plus(n1, plus(n1, n1)) = plus(plus(n1, n1), n1))),
% 18.16/11.90 inference(quant_inst,[status(thm)],[])).
% 18.16/11.90 tff(355,plain,
% 18.16/11.90 (plus(n1, plus(n1, n1)) = plus(plus(n1, n1), n1)),
% 18.16/11.90 inference(unit_resolution,[status(thm)],[354, 95])).
% 18.16/11.90 tff(356,plain,
% 18.16/11.90 (plus(plus(n1, n1), n1) = plus(n1, plus(n1, n1))),
% 18.16/11.90 inference(symmetry,[status(thm)],[355])).
% 18.16/11.90 tff(357,plain,
% 18.16/11.90 (releasedAt(filling, plus(plus(n1, n1), n1)) <=> releasedAt(filling, plus(n1, plus(n1, n1)))),
% 18.16/11.90 inference(monotonicity,[status(thm)],[356])).
% 18.16/11.90 tff(358,plain,
% 18.16/11.90 (releasedAt(filling, plus(n1, plus(n1, n1))) <=> releasedAt(filling, plus(plus(n1, n1), n1))),
% 18.16/11.90 inference(symmetry,[status(thm)],[357])).
% 18.16/11.90 tff(359,assumption,(releasedAt(filling, plus(n1, plus(n1, n1)))), introduced(assumption)).
% 18.29/11.90 tff(360,plain,
% 18.29/11.90 (releasedAt(filling, plus(plus(n1, n1), n1))),
% 18.29/11.90 inference(modus_ponens,[status(thm)],[359, 358])).
% 18.29/11.90 tff(361,assumption,((~((~releases(tptp_fun_Event_7(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))))))) | (~(releases(tptp_fun_Event_7(n1, filling), filling, n1) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n1, filling) = tapOn)))))), introduced(assumption)).
% 18.29/11.90 tff(362,plain,
% 18.29/11.90 (((~![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(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))))))) | (~(releases(tptp_fun_Event_7(n1, filling), filling, n1) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n1, 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(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))))))) | (~(releases(tptp_fun_Event_7(n1, filling), filling, n1) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n1, filling) = tapOn))))))))),
% 18.29/11.90 inference(rewrite,[status(thm)],[])).
% 18.29/11.90 tff(363,plain,
% 18.29/11.90 ((~((~((~releases(tptp_fun_Event_7(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))))))) | (~(releases(tptp_fun_Event_7(n1, filling), filling, n1) | ![Height: $i] : ((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(Height)))))))) <=> (~((~((~releases(tptp_fun_Event_7(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))))))) | (~(releases(tptp_fun_Event_7(n1, filling), filling, n1) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n1, filling) = tapOn)))))))),
% 18.29/11.90 inference(rewrite,[status(thm)],[])).
% 18.29/11.90 tff(364,plain,
% 18.29/11.90 (((~![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(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))))))) | (~(releases(tptp_fun_Event_7(n1, filling), filling, n1) | ![Height: $i] : ((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(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(tptp_fun_Event_7(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))))))) | (~(releases(tptp_fun_Event_7(n1, filling), filling, n1) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n1, filling) = tapOn))))))))),
% 18.29/11.90 inference(monotonicity,[status(thm)],[363])).
% 18.29/11.90 tff(365,plain,
% 18.29/11.90 (((~![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(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))))))) | (~(releases(tptp_fun_Event_7(n1, filling), filling, n1) | ![Height: $i] : ((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(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(tptp_fun_Event_7(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))))))) | (~(releases(tptp_fun_Event_7(n1, filling), filling, n1) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n1, filling) = tapOn))))))))),
% 18.29/11.90 inference(transitivity,[status(thm)],[364, 362])).
% 18.29/11.90 tff(366,plain,
% 18.29/11.90 ((~![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(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))))))) | (~(releases(tptp_fun_Event_7(n1, filling), filling, n1) | ![Height: $i] : ((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(Height))))))))),
% 18.29/11.90 inference(quant_inst,[status(thm)],[])).
% 18.29/11.90 tff(367,plain,
% 18.29/11.90 ((~![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(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))))))) | (~(releases(tptp_fun_Event_7(n1, filling), filling, n1) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n1, filling) = tapOn)))))))),
% 18.29/11.90 inference(modus_ponens,[status(thm)],[366, 365])).
% 18.29/11.90 tff(368,plain,
% 18.29/11.90 ($false),
% 18.29/11.90 inference(unit_resolution,[status(thm)],[367, 56, 361])).
% 18.29/11.90 tff(369,plain,(~((~((~releases(tptp_fun_Event_7(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))))))) | (~(releases(tptp_fun_Event_7(n1, filling), filling, n1) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n1, filling) = tapOn))))))), inference(lemma,lemma(discharge,[]))).
% 18.29/11.90 tff(370,plain,
% 18.29/11.90 (((~((~releases(tptp_fun_Event_7(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))))))) | (~(releases(tptp_fun_Event_7(n1, filling), filling, n1) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n1, filling) = tapOn)))))) | ((~releases(tptp_fun_Event_7(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))))))),
% 18.29/11.90 inference(tautology,[status(thm)],[])).
% 18.29/11.90 tff(371,plain,
% 18.29/11.90 ((~releases(tptp_fun_Event_7(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling)))))))),
% 18.29/11.90 inference(unit_resolution,[status(thm)],[370, 369])).
% 18.29/11.90 tff(372,assumption,(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling)))), introduced(assumption)).
% 18.29/11.90 tff(373,plain,
% 18.29/11.90 (^[X: $i] : refl((~(filling = waterLevel(X))) <=> (~(filling = waterLevel(X))))),
% 18.29/11.90 inference(bind,[status(th)],[])).
% 18.29/11.90 tff(374,plain,
% 18.29/11.90 (![X: $i] : (~(filling = waterLevel(X))) <=> ![X: $i] : (~(filling = waterLevel(X)))),
% 18.29/11.90 inference(quant_intro,[status(thm)],[373])).
% 18.29/11.90 tff(375,plain,
% 18.29/11.90 (![X: $i] : (~(filling = waterLevel(X))) <=> ![X: $i] : (~(filling = waterLevel(X)))),
% 18.29/11.90 inference(rewrite,[status(thm)],[])).
% 18.29/11.90 tff(376,axiom,(![X: $i] : (~(filling = waterLevel(X)))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax','filling_not_waterLevel')).
% 18.29/11.90 tff(377,plain,
% 18.29/11.90 (![X: $i] : (~(filling = waterLevel(X)))),
% 18.29/11.90 inference(modus_ponens,[status(thm)],[376, 375])).
% 18.29/11.90 tff(378,plain,(
% 18.29/11.90 ![X: $i] : (~(filling = waterLevel(X)))),
% 18.29/11.90 inference(skolemize,[status(sab)],[377])).
% 18.29/11.90 tff(379,plain,
% 18.29/11.90 (![X: $i] : (~(filling = waterLevel(X)))),
% 18.29/11.90 inference(modus_ponens,[status(thm)],[378, 374])).
% 18.29/11.90 tff(380,plain,
% 18.29/11.90 ((~![X: $i] : (~(filling = waterLevel(X)))) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling)))))),
% 18.29/11.90 inference(quant_inst,[status(thm)],[])).
% 18.29/11.90 tff(381,plain,
% 18.29/11.90 ($false),
% 18.29/11.90 inference(unit_resolution,[status(thm)],[380, 379, 372])).
% 18.29/11.90 tff(382,plain,(~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))), inference(lemma,lemma(discharge,[]))).
% 18.29/11.90 tff(383,plain,
% 18.29/11.90 (((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling)))))) | (filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))),
% 18.29/11.90 inference(tautology,[status(thm)],[])).
% 18.29/11.90 tff(384,plain,
% 18.29/11.90 ((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling)))))),
% 18.29/11.90 inference(unit_resolution,[status(thm)],[383, 382])).
% 18.29/11.90 tff(385,plain,
% 18.29/11.90 ((~((~releases(tptp_fun_Event_7(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))))))) | (~releases(tptp_fun_Event_7(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling)))))))),
% 18.29/11.90 inference(tautology,[status(thm)],[])).
% 18.29/11.90 tff(386,plain,
% 18.29/11.90 ((~((~releases(tptp_fun_Event_7(n1, filling), filling, n1)) | (~((~(tptp_fun_Event_7(n1, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n1, filling))))))))) | (~releases(tptp_fun_Event_7(n1, filling), filling, n1))),
% 18.29/11.90 inference(unit_resolution,[status(thm)],[385, 384])).
% 18.29/11.90 tff(387,plain,
% 18.29/11.90 (~releases(tptp_fun_Event_7(n1, filling), filling, n1)),
% 18.29/11.90 inference(unit_resolution,[status(thm)],[386, 371])).
% 18.29/11.90 tff(388,plain,
% 18.29/11.90 (((~happens(tptp_fun_Event_7(n1, filling), n1)) | (~releases(tptp_fun_Event_7(n1, filling), filling, n1))) | releases(tptp_fun_Event_7(n1, filling), filling, n1)),
% 18.29/11.90 inference(tautology,[status(thm)],[])).
% 18.29/11.90 tff(389,plain,
% 18.29/11.90 ((~happens(tptp_fun_Event_7(n1, filling), n1)) | (~releases(tptp_fun_Event_7(n1, filling), filling, n1))),
% 18.29/11.90 inference(unit_resolution,[status(thm)],[388, 387])).
% 18.29/11.90 tff(390,assumption,(releasedAt(filling, plus(n1, n1))), introduced(assumption)).
% 18.29/11.90 tff(391,plain,
% 18.29/11.90 (releasedAt(filling, plus(n0, n1)) <=> releasedAt(filling, n1)),
% 18.29/11.90 inference(monotonicity,[status(thm)],[277])).
% 18.29/11.90 tff(392,plain,
% 18.29/11.90 (releasedAt(filling, n1) <=> releasedAt(filling, plus(n0, n1))),
% 18.29/11.90 inference(symmetry,[status(thm)],[391])).
% 18.29/11.90 tff(393,assumption,(releasedAt(filling, n1)), introduced(assumption)).
% 18.29/11.90 tff(394,plain,
% 18.29/11.90 (releasedAt(filling, plus(n0, n1))),
% 18.29/11.90 inference(modus_ponens,[status(thm)],[393, 392])).
% 18.29/11.90 tff(395,assumption,((~((~releases(tptp_fun_Event_7(n0, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))))))) | (~(releases(tptp_fun_Event_7(n0, filling), filling, n0) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, filling) = tapOn)))))), introduced(assumption)).
% 18.29/11.90 tff(396,plain,
% 18.29/11.90 (((~![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, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))))))) | (~(releases(tptp_fun_Event_7(n0, filling), filling, n0) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, 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, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))))))) | (~(releases(tptp_fun_Event_7(n0, filling), filling, n0) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, filling) = tapOn))))))))),
% 18.29/11.90 inference(rewrite,[status(thm)],[])).
% 18.29/11.90 tff(397,plain,
% 18.29/11.90 ((~((~((~releases(tptp_fun_Event_7(n0, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))))))) | (~(releases(tptp_fun_Event_7(n0, filling), filling, n0) | ![Height: $i] : ((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(Height)))))))) <=> (~((~((~releases(tptp_fun_Event_7(n0, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))))))) | (~(releases(tptp_fun_Event_7(n0, filling), filling, n0) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, filling) = tapOn)))))))),
% 18.29/11.90 inference(rewrite,[status(thm)],[])).
% 18.29/11.90 tff(398,plain,
% 18.29/11.90 (((~![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, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))))))) | (~(releases(tptp_fun_Event_7(n0, filling), filling, n0) | ![Height: $i] : ((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(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(tptp_fun_Event_7(n0, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))))))) | (~(releases(tptp_fun_Event_7(n0, filling), filling, n0) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, filling) = tapOn))))))))),
% 18.29/11.90 inference(monotonicity,[status(thm)],[397])).
% 18.29/11.90 tff(399,plain,
% 18.29/11.90 (((~![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, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))))))) | (~(releases(tptp_fun_Event_7(n0, filling), filling, n0) | ![Height: $i] : ((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(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(tptp_fun_Event_7(n0, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))))))) | (~(releases(tptp_fun_Event_7(n0, filling), filling, n0) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, filling) = tapOn))))))))),
% 18.29/11.90 inference(transitivity,[status(thm)],[398, 396])).
% 18.29/11.90 tff(400,plain,
% 18.29/11.90 ((~![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, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))))))) | (~(releases(tptp_fun_Event_7(n0, filling), filling, n0) | ![Height: $i] : ((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(Height))))))))),
% 18.29/11.90 inference(quant_inst,[status(thm)],[])).
% 18.29/11.90 tff(401,plain,
% 18.29/11.90 ((~![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, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))))))) | (~(releases(tptp_fun_Event_7(n0, filling), filling, n0) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, filling) = tapOn)))))))),
% 18.29/11.90 inference(modus_ponens,[status(thm)],[400, 399])).
% 18.29/11.90 tff(402,plain,
% 18.29/11.90 ($false),
% 18.29/11.90 inference(unit_resolution,[status(thm)],[401, 56, 395])).
% 18.29/11.90 tff(403,plain,(~((~((~releases(tptp_fun_Event_7(n0, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))))))) | (~(releases(tptp_fun_Event_7(n0, filling), filling, n0) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, filling) = tapOn))))))), inference(lemma,lemma(discharge,[]))).
% 18.29/11.90 tff(404,plain,
% 18.29/11.90 (((~((~releases(tptp_fun_Event_7(n0, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))))))) | (~(releases(tptp_fun_Event_7(n0, filling), filling, n0) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(n0, filling) = tapOn)))))) | ((~releases(tptp_fun_Event_7(n0, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))))))),
% 18.29/11.90 inference(tautology,[status(thm)],[])).
% 18.29/11.90 tff(405,plain,
% 18.29/11.90 ((~releases(tptp_fun_Event_7(n0, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling)))))))),
% 18.29/11.90 inference(unit_resolution,[status(thm)],[404, 403])).
% 18.29/11.90 tff(406,assumption,(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling)))), introduced(assumption)).
% 18.29/11.90 tff(407,plain,
% 18.29/11.90 ((~![X: $i] : (~(filling = waterLevel(X)))) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling)))))),
% 18.29/11.91 inference(quant_inst,[status(thm)],[])).
% 18.29/11.91 tff(408,plain,
% 18.29/11.91 ($false),
% 18.29/11.91 inference(unit_resolution,[status(thm)],[407, 379, 406])).
% 18.29/11.91 tff(409,plain,(~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))), inference(lemma,lemma(discharge,[]))).
% 18.29/11.91 tff(410,plain,
% 18.29/11.91 (((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling)))))) | (filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))),
% 18.29/11.91 inference(tautology,[status(thm)],[])).
% 18.29/11.91 tff(411,plain,
% 18.29/11.91 ((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling)))))),
% 18.29/11.91 inference(unit_resolution,[status(thm)],[410, 409])).
% 18.29/11.91 tff(412,plain,
% 18.29/11.91 ((~((~releases(tptp_fun_Event_7(n0, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))))))) | (~releases(tptp_fun_Event_7(n0, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling)))))))),
% 18.29/11.91 inference(tautology,[status(thm)],[])).
% 18.29/11.91 tff(413,plain,
% 18.29/11.91 ((~((~releases(tptp_fun_Event_7(n0, filling), filling, n0)) | (~((~(tptp_fun_Event_7(n0, filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(n0, filling))))))))) | (~releases(tptp_fun_Event_7(n0, filling), filling, n0))),
% 18.29/11.91 inference(unit_resolution,[status(thm)],[412, 411])).
% 18.29/11.91 tff(414,plain,
% 18.29/11.91 (~releases(tptp_fun_Event_7(n0, filling), filling, n0)),
% 18.29/11.91 inference(unit_resolution,[status(thm)],[413, 405])).
% 18.29/11.91 tff(415,plain,
% 18.29/11.91 (((~happens(tptp_fun_Event_7(n0, filling), n0)) | (~releases(tptp_fun_Event_7(n0, filling), filling, n0))) | releases(tptp_fun_Event_7(n0, filling), filling, n0)),
% 18.29/11.91 inference(tautology,[status(thm)],[])).
% 18.29/11.91 tff(416,plain,
% 18.29/11.91 ((~happens(tptp_fun_Event_7(n0, filling), n0)) | (~releases(tptp_fun_Event_7(n0, filling), filling, n0))),
% 18.29/11.91 inference(unit_resolution,[status(thm)],[415, 414])).
% 18.29/11.91 tff(417,plain,
% 18.29/11.91 ((~releasedAt(filling, n0)) <=> (~releasedAt(filling, n0))),
% 18.29/11.91 inference(rewrite,[status(thm)],[])).
% 18.29/11.91 tff(418,axiom,(~releasedAt(filling, n0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_released_filling_0')).
% 18.29/11.91 tff(419,plain,
% 18.29/11.91 (~releasedAt(filling, n0)),
% 18.29/11.91 inference(modus_ponens,[status(thm)],[418, 417])).
% 18.29/11.91 tff(420,plain,
% 18.29/11.91 (^[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))))))),
% 18.29/11.91 inference(bind,[status(th)],[])).
% 18.29/11.91 tff(421,plain,
% 18.29/11.91 (![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)))))),
% 18.29/11.91 inference(quant_intro,[status(thm)],[420])).
% 18.29/11.91 tff(422,plain,
% 18.29/11.91 (^[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)))))))),
% 18.29/11.91 inference(bind,[status(th)],[])).
% 18.29/11.91 tff(423,plain,
% 18.29/11.91 (![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)))))),
% 18.29/11.91 inference(quant_intro,[status(thm)],[422])).
% 18.29/11.91 tff(424,plain,
% 18.29/11.91 (^[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)))))),
% 18.29/11.91 inference(bind,[status(th)],[])).
% 18.29/11.91 tff(425,plain,
% 18.29/11.91 (![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)))),
% 18.29/11.91 inference(quant_intro,[status(thm)],[424])).
% 18.29/11.91 tff(426,plain,
% 18.29/11.91 (![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))))))),
% 18.29/11.91 inference(rewrite,[status(thm)],[])).
% 18.29/11.91 tff(427,plain,
% 18.29/11.91 (^[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))))))))),
% 18.29/11.91 inference(bind,[status(th)],[])).
% 18.29/11.91 tff(428,plain,
% 18.29/11.91 (![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))))))),
% 18.29/11.91 inference(quant_intro,[status(thm)],[427])).
% 18.29/11.91 tff(429,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')).
% 18.29/11.91 tff(430,plain,
% 18.29/11.91 (![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | (~((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time))))))),
% 18.29/11.91 inference(modus_ponens,[status(thm)],[429, 428])).
% 18.29/11.91 tff(431,plain,
% 18.29/11.91 (![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | (~((~releasedAt(Fluent, Time)) & (~?[Event: $i] : (happens(Event, Time) & releases(Event, Fluent, Time))))))),
% 18.29/11.91 inference(modus_ponens,[status(thm)],[430, 426])).
% 18.29/11.91 tff(432,plain,(
% 18.29/11.91 ![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))))),
% 18.29/11.91 inference(skolemize,[status(sab)],[431])).
% 18.29/11.91 tff(433,plain,
% 18.29/11.91 (![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)))),
% 18.29/11.91 inference(modus_ponens,[status(thm)],[432, 425])).
% 18.29/11.91 tff(434,plain,
% 18.29/11.91 (![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)))))),
% 18.29/11.91 inference(modus_ponens,[status(thm)],[433, 423])).
% 18.29/11.91 tff(435,plain,
% 18.29/11.91 (![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)))))),
% 18.29/11.91 inference(modus_ponens,[status(thm)],[434, 421])).
% 18.29/11.91 tff(436,plain,
% 18.29/11.91 (((~![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(filling, n0) | (~releasedAt(filling, plus(n0, n1))) | (~((~happens(tptp_fun_Event_7(n0, filling), n0)) | (~releases(tptp_fun_Event_7(n0, filling), filling, 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(filling, n0) | (~releasedAt(filling, plus(n0, n1))) | (~((~happens(tptp_fun_Event_7(n0, filling), n0)) | (~releases(tptp_fun_Event_7(n0, filling), filling, n0)))))),
% 18.29/11.91 inference(rewrite,[status(thm)],[])).
% 18.29/11.91 tff(437,plain,
% 18.29/11.91 (((~releasedAt(filling, plus(n0, n1))) | releasedAt(filling, n0) | (~((~happens(tptp_fun_Event_7(n0, filling), n0)) | (~releases(tptp_fun_Event_7(n0, filling), filling, n0))))) <=> (releasedAt(filling, n0) | (~releasedAt(filling, plus(n0, n1))) | (~((~happens(tptp_fun_Event_7(n0, filling), n0)) | (~releases(tptp_fun_Event_7(n0, filling), filling, n0)))))),
% 18.29/11.91 inference(rewrite,[status(thm)],[])).
% 18.29/11.91 tff(438,plain,
% 18.29/11.91 (((~![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(filling, plus(n0, n1))) | releasedAt(filling, n0) | (~((~happens(tptp_fun_Event_7(n0, filling), n0)) | (~releases(tptp_fun_Event_7(n0, filling), filling, 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(filling, n0) | (~releasedAt(filling, plus(n0, n1))) | (~((~happens(tptp_fun_Event_7(n0, filling), n0)) | (~releases(tptp_fun_Event_7(n0, filling), filling, n0))))))),
% 18.29/11.91 inference(monotonicity,[status(thm)],[437])).
% 18.29/11.91 tff(439,plain,
% 18.29/11.91 (((~![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(filling, plus(n0, n1))) | releasedAt(filling, n0) | (~((~happens(tptp_fun_Event_7(n0, filling), n0)) | (~releases(tptp_fun_Event_7(n0, filling), filling, 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(filling, n0) | (~releasedAt(filling, plus(n0, n1))) | (~((~happens(tptp_fun_Event_7(n0, filling), n0)) | (~releases(tptp_fun_Event_7(n0, filling), filling, n0)))))),
% 18.29/11.91 inference(transitivity,[status(thm)],[438, 436])).
% 18.29/11.91 tff(440,plain,
% 18.29/11.91 ((~![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(filling, plus(n0, n1))) | releasedAt(filling, n0) | (~((~happens(tptp_fun_Event_7(n0, filling), n0)) | (~releases(tptp_fun_Event_7(n0, filling), filling, n0)))))),
% 18.29/11.91 inference(quant_inst,[status(thm)],[])).
% 18.29/11.91 tff(441,plain,
% 18.29/11.91 ((~![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))) | releasedAt(filling, n0) | (~releasedAt(filling, plus(n0, n1))) | (~((~happens(tptp_fun_Event_7(n0, filling), n0)) | (~releases(tptp_fun_Event_7(n0, filling), filling, n0))))),
% 18.29/11.91 inference(modus_ponens,[status(thm)],[440, 439])).
% 18.29/11.91 tff(442,plain,
% 18.29/11.91 (~releasedAt(filling, plus(n0, n1))),
% 18.29/11.91 inference(unit_resolution,[status(thm)],[441, 435, 419, 416])).
% 18.29/11.91 tff(443,plain,
% 18.29/11.91 ($false),
% 18.29/11.91 inference(unit_resolution,[status(thm)],[442, 394])).
% 18.29/11.91 tff(444,plain,(~releasedAt(filling, n1)), inference(lemma,lemma(discharge,[]))).
% 18.29/11.91 tff(445,plain,
% 18.29/11.91 (((~![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(filling, plus(n1, n1))) | releasedAt(filling, n1) | (~((~happens(tptp_fun_Event_7(n1, filling), n1)) | (~releases(tptp_fun_Event_7(n1, filling), filling, 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(filling, plus(n1, n1))) | releasedAt(filling, n1) | (~((~happens(tptp_fun_Event_7(n1, filling), n1)) | (~releases(tptp_fun_Event_7(n1, filling), filling, n1)))))),
% 18.29/11.91 inference(rewrite,[status(thm)],[])).
% 18.29/11.91 tff(446,plain,
% 18.29/11.91 ((~![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(filling, plus(n1, n1))) | releasedAt(filling, n1) | (~((~happens(tptp_fun_Event_7(n1, filling), n1)) | (~releases(tptp_fun_Event_7(n1, filling), filling, n1)))))),
% 18.29/11.91 inference(quant_inst,[status(thm)],[])).
% 18.29/11.91 tff(447,plain,
% 18.29/11.91 ((~![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))) | (~releasedAt(filling, plus(n1, n1))) | releasedAt(filling, n1) | (~((~happens(tptp_fun_Event_7(n1, filling), n1)) | (~releases(tptp_fun_Event_7(n1, filling), filling, n1))))),
% 18.29/11.91 inference(modus_ponens,[status(thm)],[446, 445])).
% 18.29/11.91 tff(448,plain,
% 18.29/11.91 ($false),
% 18.29/11.91 inference(unit_resolution,[status(thm)],[447, 435, 444, 390, 389])).
% 18.29/11.91 tff(449,plain,(~releasedAt(filling, plus(n1, n1))), inference(lemma,lemma(discharge,[]))).
% 18.29/11.91 tff(450,plain,
% 18.29/11.91 (((~![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(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling))))))))) | (~(releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(plus(n1, n1), 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(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling))))))))) | (~(releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn))))))))),
% 18.29/11.91 inference(rewrite,[status(thm)],[])).
% 18.29/11.91 tff(451,plain,
% 18.29/11.91 ((~((~((~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling))))))))) | (~(releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)) | ![Height: $i] : ((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(Height)))))))) <=> (~((~((~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling))))))))) | (~(releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))))))),
% 18.29/11.91 inference(rewrite,[status(thm)],[])).
% 18.29/11.91 tff(452,plain,
% 18.29/11.91 (((~![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(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling))))))))) | (~(releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)) | ![Height: $i] : ((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(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(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling))))))))) | (~(releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn))))))))),
% 18.29/11.91 inference(monotonicity,[status(thm)],[451])).
% 18.29/11.91 tff(453,plain,
% 18.29/11.91 (((~![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(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling))))))))) | (~(releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)) | ![Height: $i] : ((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(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(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling))))))))) | (~(releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn))))))))),
% 18.29/11.91 inference(transitivity,[status(thm)],[452, 450])).
% 18.29/11.91 tff(454,plain,
% 18.29/11.91 ((~![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(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling))))))))) | (~(releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)) | ![Height: $i] : ((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(Height))))))))),
% 18.29/11.91 inference(quant_inst,[status(thm)],[])).
% 18.29/11.91 tff(455,plain,
% 18.29/11.91 ((~![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(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling))))))))) | (~(releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))))))),
% 18.29/11.91 inference(modus_ponens,[status(thm)],[454, 453])).
% 18.29/11.91 tff(456,plain,
% 18.29/11.91 (~((~((~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling))))))))) | (~(releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn))))))),
% 18.29/11.91 inference(unit_resolution,[status(thm)],[455, 56])).
% 18.29/11.91 tff(457,plain,
% 18.29/11.91 (((~((~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling))))))))) | (~(releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)) | ![Height: $i] : ((~(filling = waterLevel(Height))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))))) | ((~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling))))))))),
% 18.29/11.91 inference(tautology,[status(thm)],[])).
% 18.29/11.91 tff(458,plain,
% 18.29/11.91 ((~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling)))))))),
% 18.29/11.91 inference(unit_resolution,[status(thm)],[457, 456])).
% 18.29/11.91 tff(459,assumption,(~((~happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))) | (~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))))), introduced(assumption)).
% 18.29/11.91 tff(460,plain,
% 18.29/11.91 (((~happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))) | (~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)))) | releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))),
% 18.29/11.91 inference(tautology,[status(thm)],[])).
% 18.29/11.91 tff(461,plain,
% 18.29/11.91 (releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))),
% 18.29/11.91 inference(unit_resolution,[status(thm)],[460, 459])).
% 18.29/11.91 tff(462,plain,
% 18.29/11.91 ((~((~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling))))))))) | (~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling)))))))),
% 18.29/11.91 inference(tautology,[status(thm)],[])).
% 18.29/11.91 tff(463,plain,
% 18.29/11.91 ((~((~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling))))))))) | (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling)))))))),
% 18.29/11.91 inference(unit_resolution,[status(thm)],[462, 461])).
% 18.29/11.91 tff(464,plain,
% 18.29/11.91 (~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling))))))),
% 18.29/11.91 inference(unit_resolution,[status(thm)],[463, 458])).
% 18.29/11.91 tff(465,plain,
% 18.29/11.91 (((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(filling = waterLevel(tptp_fun_Height_10(filling, tptp_fun_Event_7(plus(n1, n1), filling)))))) | (tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)),
% 18.29/11.91 inference(tautology,[status(thm)],[])).
% 18.29/11.91 tff(466,plain,
% 18.29/11.91 (tptp_fun_Event_7(plus(n1, n1), filling) = tapOn),
% 18.29/11.91 inference(unit_resolution,[status(thm)],[465, 464])).
% 18.29/11.92 tff(467,plain,
% 18.29/11.92 (((~![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(plus(n1, n1), filling), plus(n1, n1)) <=> ((~((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, 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_7(plus(n1, n1), filling), plus(n1, n1)) <=> ((~((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow)))))))),
% 18.29/11.92 inference(rewrite,[status(thm)],[])).
% 18.29/11.92 tff(468,plain,
% 18.29/11.92 ((happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1)) <=> ((~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(plus(n1, n1) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow)))))) <=> (happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1)) <=> ((~((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow))))))),
% 18.29/11.92 inference(rewrite,[status(thm)],[])).
% 18.29/11.92 tff(469,plain,
% 18.29/11.92 (((~![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(plus(n1, n1), filling), plus(n1, n1)) <=> ((~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(plus(n1, n1) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, 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_7(plus(n1, n1), filling), plus(n1, n1)) <=> ((~((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow)))))))),
% 18.29/11.92 inference(monotonicity,[status(thm)],[468])).
% 18.29/11.92 tff(470,plain,
% 18.29/11.92 (((~![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(plus(n1, n1), filling), plus(n1, n1)) <=> ((~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(plus(n1, n1) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, 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_7(plus(n1, n1), filling), plus(n1, n1)) <=> ((~((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow)))))))),
% 18.29/11.92 inference(transitivity,[status(thm)],[469, 467])).
% 18.29/11.92 tff(471,plain,
% 18.29/11.92 ((~![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(plus(n1, n1), filling), plus(n1, n1)) <=> ((~((~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)) | (~(plus(n1, n1) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow))))))),
% 18.29/11.92 inference(quant_inst,[status(thm)],[])).
% 18.29/11.92 tff(472,plain,
% 18.29/11.92 ((~![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(plus(n1, n1), filling), plus(n1, n1)) <=> ((~((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow))))))),
% 18.29/11.92 inference(modus_ponens,[status(thm)],[471, 470])).
% 18.29/11.92 tff(473,plain,
% 18.29/11.92 (happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1)) <=> ((~((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow)))))),
% 18.29/11.92 inference(unit_resolution,[status(thm)],[472, 134])).
% 18.29/11.92 tff(474,plain,
% 18.29/11.92 (((~happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))) | (~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)))) | happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))),
% 18.29/11.92 inference(tautology,[status(thm)],[])).
% 18.29/11.92 tff(475,plain,
% 18.29/11.92 (happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))),
% 18.29/11.92 inference(unit_resolution,[status(thm)],[474, 459])).
% 18.29/11.92 tff(476,plain,
% 18.29/11.92 ((~(happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1)) <=> ((~((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow))))))) | (~happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))) | ((~((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow)))))),
% 18.29/11.92 inference(tautology,[status(thm)],[])).
% 18.29/11.92 tff(477,plain,
% 18.29/11.92 ((~(happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1)) <=> ((~((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow))))))) | ((~((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow)))))),
% 18.29/11.92 inference(unit_resolution,[status(thm)],[476, 475])).
% 18.29/11.92 tff(478,plain,
% 18.29/11.92 ((~((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow))))),
% 18.29/11.92 inference(unit_resolution,[status(thm)],[477, 473])).
% 18.29/11.92 tff(479,plain,
% 18.29/11.92 (((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn))) | (plus(n1, n1) = n0)),
% 18.29/11.92 inference(tautology,[status(thm)],[])).
% 18.29/11.92 tff(480,plain,
% 18.29/11.92 ((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn))),
% 18.29/11.92 inference(unit_resolution,[status(thm)],[479, 300])).
% 18.29/11.92 tff(481,plain,
% 18.29/11.92 ((~((~((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow)))))) | (~((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow))))),
% 18.29/11.92 inference(tautology,[status(thm)],[])).
% 18.29/11.92 tff(482,plain,
% 18.29/11.92 ((~((~((~(plus(n1, n1) = n0)) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = tapOn)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow)))))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow))))),
% 18.29/11.92 inference(unit_resolution,[status(thm)],[481, 480])).
% 18.29/11.92 tff(483,plain,
% 18.29/11.92 (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow)))),
% 18.29/11.92 inference(unit_resolution,[status(thm)],[482, 478])).
% 18.29/11.92 tff(484,plain,
% 18.29/11.92 (((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, n1))) | (~holdsAt(filling, plus(n1, n1))) | (~(tptp_fun_Event_7(plus(n1, n1), filling) = overflow))) | (tptp_fun_Event_7(plus(n1, n1), filling) = overflow)),
% 18.29/11.92 inference(tautology,[status(thm)],[])).
% 18.29/11.92 tff(485,plain,
% 18.29/11.92 (tptp_fun_Event_7(plus(n1, n1), filling) = overflow),
% 18.29/11.92 inference(unit_resolution,[status(thm)],[484, 483])).
% 18.29/11.92 tff(486,plain,
% 18.29/11.92 (overflow = tptp_fun_Event_7(plus(n1, n1), filling)),
% 18.29/11.92 inference(symmetry,[status(thm)],[485])).
% 18.29/11.92 tff(487,plain,
% 18.29/11.92 (overflow = tapOn),
% 18.29/11.92 inference(transitivity,[status(thm)],[486, 466])).
% 18.29/11.92 tff(488,plain,
% 18.29/11.92 ((~(overflow = tapOn)) <=> (~(overflow = tapOn))),
% 18.29/11.92 inference(rewrite,[status(thm)],[])).
% 18.29/11.92 tff(489,axiom,(~(overflow = tapOn)), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax','overflow_not_tapOn')).
% 18.29/11.92 tff(490,plain,
% 18.29/11.92 (~(overflow = tapOn)),
% 18.29/11.92 inference(modus_ponens,[status(thm)],[489, 488])).
% 18.29/11.92 tff(491,plain,
% 18.29/11.92 ($false),
% 18.29/11.92 inference(unit_resolution,[status(thm)],[490, 487])).
% 18.29/11.92 tff(492,plain,((~happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))) | (~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)))), inference(lemma,lemma(discharge,[]))).
% 18.29/11.92 tff(493,plain,
% 18.29/11.92 (((~![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(filling, plus(n1, n1)) | (~releasedAt(filling, plus(plus(n1, n1), n1))) | (~((~happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))) | (~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, 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(filling, plus(n1, n1)) | (~releasedAt(filling, plus(plus(n1, n1), n1))) | (~((~happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))) | (~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))))))),
% 18.29/11.92 inference(rewrite,[status(thm)],[])).
% 18.29/11.92 tff(494,plain,
% 18.29/11.92 (((~releasedAt(filling, plus(plus(n1, n1), n1))) | releasedAt(filling, plus(n1, n1)) | (~((~happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))) | (~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)))))) <=> (releasedAt(filling, plus(n1, n1)) | (~releasedAt(filling, plus(plus(n1, n1), n1))) | (~((~happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))) | (~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))))))),
% 18.29/11.92 inference(rewrite,[status(thm)],[])).
% 18.29/11.92 tff(495,plain,
% 18.29/11.92 (((~![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(filling, plus(plus(n1, n1), n1))) | releasedAt(filling, plus(n1, n1)) | (~((~happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))) | (~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, 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(filling, plus(n1, n1)) | (~releasedAt(filling, plus(plus(n1, n1), n1))) | (~((~happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))) | (~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)))))))),
% 18.29/11.92 inference(monotonicity,[status(thm)],[494])).
% 18.29/11.92 tff(496,plain,
% 18.29/11.92 (((~![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(filling, plus(plus(n1, n1), n1))) | releasedAt(filling, plus(n1, n1)) | (~((~happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))) | (~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, 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(filling, plus(n1, n1)) | (~releasedAt(filling, plus(plus(n1, n1), n1))) | (~((~happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))) | (~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))))))),
% 18.29/11.92 inference(transitivity,[status(thm)],[495, 493])).
% 18.29/11.92 tff(497,plain,
% 18.29/11.92 ((~![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(filling, plus(plus(n1, n1), n1))) | releasedAt(filling, plus(n1, n1)) | (~((~happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))) | (~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1))))))),
% 18.29/11.92 inference(quant_inst,[status(thm)],[])).
% 18.29/11.92 tff(498,plain,
% 18.29/11.92 ((~![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))) | releasedAt(filling, plus(n1, n1)) | (~releasedAt(filling, plus(plus(n1, n1), n1))) | (~((~happens(tptp_fun_Event_7(plus(n1, n1), filling), plus(n1, n1))) | (~releases(tptp_fun_Event_7(plus(n1, n1), filling), filling, plus(n1, n1)))))),
% 18.29/11.92 inference(modus_ponens,[status(thm)],[497, 496])).
% 18.29/11.92 tff(499,plain,
% 18.29/11.92 (~releasedAt(filling, plus(plus(n1, n1), n1))),
% 18.29/11.92 inference(unit_resolution,[status(thm)],[498, 435, 492, 449])).
% 18.29/11.92 tff(500,plain,
% 18.29/11.92 ($false),
% 18.29/11.92 inference(unit_resolution,[status(thm)],[499, 360])).
% 18.29/11.92 tff(501,plain,(~releasedAt(filling, plus(n1, plus(n1, n1)))), inference(lemma,lemma(discharge,[]))).
% 18.29/11.92 tff(502,assumption,((~happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~initiates(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1))))), introduced(assumption)).
% 18.29/11.92 tff(503,plain,
% 18.29/11.92 (holdsAt(filling, plus(plus(n1, plus(n1, n1)), n1)) <=> holdsAt(filling, plus(plus(n1, n1), plus(n1, n1)))),
% 18.29/11.92 inference(monotonicity,[status(thm)],[99])).
% 18.29/11.92 tff(504,plain,
% 18.29/11.92 (holdsAt(filling, plus(plus(n1, n1), plus(n1, n1))) <=> holdsAt(filling, plus(plus(n1, plus(n1, n1)), n1))),
% 18.29/11.92 inference(symmetry,[status(thm)],[503])).
% 18.29/11.92 tff(505,plain,
% 18.29/11.92 (holdsAt(filling, plus(plus(n1, plus(n1, n1)), n1))),
% 18.29/11.92 inference(modus_ponens,[status(thm)],[117, 504])).
% 18.29/11.92 tff(506,plain,
% 18.29/11.92 (^[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))))))),
% 18.29/11.92 inference(bind,[status(th)],[])).
% 18.29/11.92 tff(507,plain,
% 18.29/11.92 (![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)))))),
% 18.29/11.92 inference(quant_intro,[status(thm)],[506])).
% 18.29/11.92 tff(508,plain,
% 18.29/11.92 (^[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)))))))),
% 18.29/11.92 inference(bind,[status(th)],[])).
% 18.29/11.92 tff(509,plain,
% 18.29/11.92 (![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)))))),
% 18.29/11.92 inference(quant_intro,[status(thm)],[508])).
% 18.29/11.92 tff(510,plain,
% 18.29/11.92 (^[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)))))),
% 18.29/11.93 inference(bind,[status(th)],[])).
% 18.29/11.93 tff(511,plain,
% 18.29/11.93 (![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)))),
% 18.29/11.93 inference(quant_intro,[status(thm)],[510])).
% 18.29/11.93 tff(512,plain,
% 18.29/11.93 (![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))))))),
% 18.29/11.93 inference(rewrite,[status(thm)],[])).
% 18.29/11.93 tff(513,plain,
% 18.29/11.93 (^[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))))))))),
% 18.29/11.93 inference(bind,[status(th)],[])).
% 18.29/11.93 tff(514,plain,
% 18.29/11.93 (![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))))))),
% 18.29/11.93 inference(quant_intro,[status(thm)],[513])).
% 18.29/11.93 tff(515,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')).
% 18.29/11.93 tff(516,plain,
% 18.29/11.93 (![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))))))),
% 18.29/11.93 inference(modus_ponens,[status(thm)],[515, 514])).
% 18.29/11.93 tff(517,plain,
% 18.29/11.93 (![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))))))),
% 18.29/11.93 inference(modus_ponens,[status(thm)],[516, 512])).
% 18.29/11.93 tff(518,plain,(
% 18.29/11.93 ![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))))),
% 18.29/11.93 inference(skolemize,[status(sab)],[517])).
% 18.29/11.93 tff(519,plain,
% 18.29/11.93 (![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)))),
% 18.29/11.93 inference(modus_ponens,[status(thm)],[518, 511])).
% 18.29/11.93 tff(520,plain,
% 18.29/11.93 (![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)))))),
% 18.29/11.93 inference(modus_ponens,[status(thm)],[519, 509])).
% 18.29/11.93 tff(521,plain,
% 18.29/11.93 (![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)))))),
% 18.29/11.93 inference(modus_ponens,[status(thm)],[520, 507])).
% 18.29/11.93 tff(522,plain,
% 18.29/11.93 (((~![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(filling, plus(plus(n1, plus(n1, n1)), n1)) | holdsAt(filling, plus(n1, plus(n1, n1))) | (~holdsAt(filling, plus(plus(n1, plus(n1, n1)), n1))) | (~((~happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~initiates(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, 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)))))) | releasedAt(filling, plus(plus(n1, plus(n1, n1)), n1)) | holdsAt(filling, plus(n1, plus(n1, n1))) | (~holdsAt(filling, plus(plus(n1, plus(n1, n1)), n1))) | (~((~happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~initiates(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1)))))))),
% 18.29/11.93 inference(rewrite,[status(thm)],[])).
% 18.29/11.93 tff(523,plain,
% 18.29/11.93 ((~![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(filling, plus(plus(n1, plus(n1, n1)), n1)) | holdsAt(filling, plus(n1, plus(n1, n1))) | (~holdsAt(filling, plus(plus(n1, plus(n1, n1)), n1))) | (~((~happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~initiates(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1)))))))),
% 18.29/11.93 inference(quant_inst,[status(thm)],[])).
% 18.29/11.93 tff(524,plain,
% 18.29/11.93 ((~![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(filling, plus(plus(n1, plus(n1, n1)), n1)) | holdsAt(filling, plus(n1, plus(n1, n1))) | (~holdsAt(filling, plus(plus(n1, plus(n1, n1)), n1))) | (~((~happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~initiates(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1))))))),
% 18.29/11.93 inference(modus_ponens,[status(thm)],[523, 522])).
% 18.29/11.93 tff(525,plain,
% 18.29/11.93 (releasedAt(filling, plus(plus(n1, plus(n1, n1)), n1)) | holdsAt(filling, plus(n1, plus(n1, n1))) | (~holdsAt(filling, plus(plus(n1, plus(n1, n1)), n1))) | (~((~happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~initiates(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1))))))),
% 18.29/11.93 inference(unit_resolution,[status(thm)],[524, 521])).
% 18.29/11.93 tff(526,plain,
% 18.29/11.93 (releasedAt(filling, plus(plus(n1, plus(n1, n1)), n1)) | holdsAt(filling, plus(n1, plus(n1, n1))) | (~((~happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~initiates(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1))))))),
% 18.29/11.93 inference(unit_resolution,[status(thm)],[525, 505])).
% 18.29/11.93 tff(527,plain,
% 18.29/11.93 (releasedAt(filling, plus(plus(n1, plus(n1, n1)), n1))),
% 18.29/11.93 inference(unit_resolution,[status(thm)],[526, 142, 502])).
% 18.29/11.93 tff(528,plain,
% 18.29/11.93 (((~![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)))))) | ((~((~happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~releases(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1)))))) | releasedAt(filling, plus(n1, plus(n1, n1))) | (~releasedAt(filling, plus(plus(n1, plus(n1, n1)), 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)))))) | (~((~happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~releases(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1)))))) | releasedAt(filling, plus(n1, plus(n1, n1))) | (~releasedAt(filling, plus(plus(n1, plus(n1, n1)), n1))))),
% 18.29/11.93 inference(rewrite,[status(thm)],[])).
% 18.29/11.93 tff(529,plain,
% 18.29/11.93 (((~releasedAt(filling, plus(plus(n1, plus(n1, n1)), n1))) | releasedAt(filling, plus(n1, plus(n1, n1))) | (~((~happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~releases(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1))))))) <=> ((~((~happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~releases(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1)))))) | releasedAt(filling, plus(n1, plus(n1, n1))) | (~releasedAt(filling, plus(plus(n1, plus(n1, n1)), n1))))),
% 18.29/11.93 inference(rewrite,[status(thm)],[])).
% 18.29/11.93 tff(530,plain,
% 18.29/11.93 (((~![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(filling, plus(plus(n1, plus(n1, n1)), n1))) | releasedAt(filling, plus(n1, plus(n1, n1))) | (~((~happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~releases(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, 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)))))) | ((~((~happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~releases(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1)))))) | releasedAt(filling, plus(n1, plus(n1, n1))) | (~releasedAt(filling, plus(plus(n1, plus(n1, n1)), n1)))))),
% 18.29/11.93 inference(monotonicity,[status(thm)],[529])).
% 18.29/11.93 tff(531,plain,
% 18.29/11.93 (((~![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(filling, plus(plus(n1, plus(n1, n1)), n1))) | releasedAt(filling, plus(n1, plus(n1, n1))) | (~((~happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~releases(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, 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)))))) | (~((~happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~releases(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1)))))) | releasedAt(filling, plus(n1, plus(n1, n1))) | (~releasedAt(filling, plus(plus(n1, plus(n1, n1)), n1))))),
% 18.29/11.93 inference(transitivity,[status(thm)],[530, 528])).
% 18.29/11.93 tff(532,plain,
% 18.29/11.93 ((~![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(filling, plus(plus(n1, plus(n1, n1)), n1))) | releasedAt(filling, plus(n1, plus(n1, n1))) | (~((~happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~releases(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1)))))))),
% 18.29/11.93 inference(quant_inst,[status(thm)],[])).
% 18.29/11.93 tff(533,plain,
% 18.29/11.93 ((~![Fluent: $i, Time: $i] : ((~releasedAt(Fluent, plus(Time, n1))) | releasedAt(Fluent, Time) | (~((~happens(tptp_fun_Event_7(Time, Fluent), Time)) | (~releases(tptp_fun_Event_7(Time, Fluent), Fluent, Time)))))) | (~((~happens(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~releases(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1)))))) | releasedAt(filling, plus(n1, plus(n1, n1))) | (~releasedAt(filling, plus(plus(n1, plus(n1, n1)), n1)))),
% 18.29/11.93 inference(modus_ponens,[status(thm)],[532, 531])).
% 18.29/11.93 tff(534,plain,
% 18.29/11.93 ($false),
% 18.29/11.93 inference(unit_resolution,[status(thm)],[533, 435, 527, 501, 353])).
% 18.29/11.93 tff(535,plain,(holdsAt(filling, plus(n1, plus(n1, n1))) | (~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_7(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~initiates(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1))))))), inference(lemma,lemma(discharge,[]))).
% 18.29/11.93 tff(536,plain,
% 18.29/11.93 (holdsAt(filling, plus(n1, plus(n1, n1))) | (~((~happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~initiates(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1))))))),
% 18.29/11.93 inference(unit_resolution,[status(thm)],[535, 334])).
% 18.29/11.93 tff(537,plain,
% 18.29/11.93 (~((~happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~initiates(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1)))))),
% 18.29/11.93 inference(unit_resolution,[status(thm)],[536, 142])).
% 18.29/11.93 tff(538,plain,
% 18.29/11.93 (((~happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | (~initiates(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), filling, plus(n1, plus(n1, n1))))) | happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))),
% 18.29/11.93 inference(tautology,[status(thm)],[])).
% 18.29/11.93 tff(539,plain,
% 18.29/11.93 (happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))),
% 18.29/11.93 inference(unit_resolution,[status(thm)],[538, 537])).
% 18.29/11.93 tff(540,assumption,(~(happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))))))), introduced(assumption)).
% 18.29/11.93 tff(541,plain,
% 18.29/11.93 (((~![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_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))))))) <=> ((~![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_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))))))))),
% 18.29/11.93 inference(rewrite,[status(thm)],[])).
% 18.29/11.93 tff(542,plain,
% 18.29/11.93 ((happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)))))) <=> (happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))))))),
% 18.29/11.93 inference(rewrite,[status(thm)],[])).
% 18.29/11.93 tff(543,plain,
% 18.29/11.93 (((~![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_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_5(plus(n1, plus(n1, 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_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))))))))),
% 18.29/11.94 inference(monotonicity,[status(thm)],[542])).
% 18.29/11.94 tff(544,plain,
% 18.29/11.94 (((~![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_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_5(plus(n1, plus(n1, 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_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))))))))),
% 18.29/11.94 inference(transitivity,[status(thm)],[543, 541])).
% 18.29/11.94 tff(545,plain,
% 18.29/11.94 ((~![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_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow))))))),
% 18.29/11.94 inference(quant_inst,[status(thm)],[])).
% 18.29/11.94 tff(546,plain,
% 18.29/11.94 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = tapOn)) | (~(Time = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), Time)) | (~holdsAt(filling, Time)) | (~(Event = overflow))))))) | (happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))))))),
% 18.29/11.94 inference(modus_ponens,[status(thm)],[545, 544])).
% 18.29/11.94 tff(547,plain,
% 18.29/11.94 ($false),
% 18.29/11.94 inference(unit_resolution,[status(thm)],[546, 134, 540])).
% 18.29/11.94 tff(548,plain,(happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))))))), inference(lemma,lemma(discharge,[]))).
% 18.29/11.94 tff(549,plain,
% 18.29/11.94 ((~(happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1))) <=> ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))))))) | (~happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))))))),
% 18.29/11.94 inference(tautology,[status(thm)],[])).
% 18.29/11.94 tff(550,plain,
% 18.29/11.94 ((~happens(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling), plus(n1, plus(n1, n1)))) | ((~((~(plus(n1, plus(n1, n1)) = n0)) | (~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = tapOn)))) | (~((~(tptp_fun_Event_5(plus(n1, plus(n1, n1)), filling) = overflow)) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))))))),
% 18.29/11.94 inference(unit_resolution,[status(thm)],[549, 548])).
% 18.29/11.94 tff(551,plain,
% 18.29/11.94 ($false),
% 18.29/11.94 inference(unit_resolution,[status(thm)],[550, 539, 332])).
% 18.29/11.94 tff(552,plain,(holdsAt(filling, plus(n1, plus(n1, n1)))), inference(lemma,lemma(discharge,[]))).
% 18.29/11.94 tff(553,plain,
% 18.29/11.94 (holdsAt(waterLevel(n3), n3) <=> holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))),
% 18.29/11.94 inference(rewrite,[status(thm)],[])).
% 18.29/11.94 tff(554,plain,
% 18.29/11.94 (holdsAt(waterLevel(n3), n3) <=> holdsAt(waterLevel(n3), n3)),
% 18.29/11.94 inference(rewrite,[status(thm)],[])).
% 18.29/11.94 tff(555,axiom,(holdsAt(waterLevel(n3), n3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','waterLevel_3')).
% 18.29/11.94 tff(556,plain,
% 18.29/11.94 (holdsAt(waterLevel(n3), n3)),
% 18.29/11.94 inference(modus_ponens,[status(thm)],[555, 554])).
% 18.29/11.94 tff(557,plain,
% 18.29/11.94 (holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))),
% 18.29/11.94 inference(modus_ponens,[status(thm)],[556, 553])).
% 18.29/11.94 tff(558,plain,
% 18.29/11.94 ((~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))))) | (~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))),
% 18.29/11.94 inference(tautology,[status(thm)],[])).
% 18.29/11.94 tff(559,plain,
% 18.29/11.94 (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))))),
% 18.29/11.94 inference(unit_resolution,[status(thm)],[558, 557, 552])).
% 18.29/11.94 tff(560,plain,
% 18.29/11.94 (((~((~(overflow = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))))) | ((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1)))))),
% 18.29/11.94 inference(tautology,[status(thm)],[])).
% 18.29/11.94 tff(561,plain,
% 18.29/11.94 ((~((~(overflow = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))))),
% 18.29/11.94 inference(unit_resolution,[status(thm)],[560, 559])).
% 18.29/11.94 tff(562,plain,
% 18.29/11.94 ((~(happens(overflow, plus(n1, plus(n1, n1))) <=> ((~((~(overflow = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))))))) | happens(overflow, plus(n1, plus(n1, n1))) | (~((~((~(overflow = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))))))),
% 18.29/11.94 inference(tautology,[status(thm)],[])).
% 18.29/11.94 tff(563,plain,
% 18.29/11.94 ((~(happens(overflow, plus(n1, plus(n1, n1))) <=> ((~((~(overflow = tapOn)) | (~(plus(n1, plus(n1, n1)) = n0)))) | (~((~holdsAt(waterLevel(plus(n1, plus(n1, n1))), plus(n1, plus(n1, n1)))) | (~holdsAt(filling, plus(n1, plus(n1, n1))))))))) | happens(overflow, plus(n1, plus(n1, n1)))),
% 18.29/11.94 inference(unit_resolution,[status(thm)],[562, 561])).
% 18.29/11.94 tff(564,plain,
% 18.29/11.94 (happens(overflow, plus(n1, plus(n1, n1)))),
% 18.29/11.94 inference(unit_resolution,[status(thm)],[563, 141])).
% 18.29/11.94 tff(565,plain,
% 18.29/11.94 (^[Event: $i, Time: $i, Fluent: $i] : refl(((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time))) <=> ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time))))),
% 18.29/11.94 inference(bind,[status(th)],[])).
% 18.29/11.94 tff(566,plain,
% 18.29/11.94 (![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))),
% 18.29/11.94 inference(quant_intro,[status(thm)],[565])).
% 18.29/11.94 tff(567,plain,
% 18.29/11.94 (^[Event: $i, Time: $i, Fluent: $i] : trans(monotonicity(trans(monotonicity(rewrite((happens(Event, Time) & terminates(Event, Fluent, Time)) <=> (~((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))))), ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) <=> (~(~((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))))))), rewrite((~(~((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))))) <=> ((~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))), ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) <=> ((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))))), (((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))) <=> (((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))))), rewrite((((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))) <=> ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))), (((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))) <=> ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))))),
% 18.29/11.94 inference(bind,[status(th)],[])).
% 18.29/11.94 tff(568,plain,
% 18.29/11.94 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))),
% 18.29/11.94 inference(quant_intro,[status(thm)],[567])).
% 18.29/11.94 tff(569,plain,
% 18.29/11.94 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1))))),
% 18.29/11.94 inference(rewrite,[status(thm)],[])).
% 18.29/11.94 tff(570,plain,
% 18.29/11.94 (^[Event: $i, Time: $i, Fluent: $i] : rewrite(((happens(Event, Time) & terminates(Event, Fluent, Time)) => (~holdsAt(Fluent, plus(Time, n1)))) <=> ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))))),
% 18.29/11.94 inference(bind,[status(th)],[])).
% 18.29/11.94 tff(571,plain,
% 18.29/11.94 (![Event: $i, Time: $i, Fluent: $i] : ((happens(Event, Time) & terminates(Event, Fluent, Time)) => (~holdsAt(Fluent, plus(Time, n1)))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1))))),
% 18.29/11.94 inference(quant_intro,[status(thm)],[570])).
% 18.29/11.94 tff(572,axiom,(![Event: $i, Time: $i, Fluent: $i] : ((happens(Event, Time) & terminates(Event, Fluent, Time)) => (~holdsAt(Fluent, plus(Time, n1))))), file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax','happens_terminates_not_holds')).
% 18.29/11.94 tff(573,plain,
% 18.29/11.94 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1))))),
% 18.29/11.94 inference(modus_ponens,[status(thm)],[572, 571])).
% 18.29/11.94 tff(574,plain,
% 18.29/11.94 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1))))),
% 18.29/11.94 inference(modus_ponens,[status(thm)],[573, 569])).
% 18.29/11.94 tff(575,plain,(
% 18.29/11.94 ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1))))),
% 18.29/11.94 inference(skolemize,[status(sab)],[574])).
% 18.29/11.94 tff(576,plain,
% 18.29/11.94 (![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))),
% 18.29/11.94 inference(modus_ponens,[status(thm)],[575, 568])).
% 18.29/11.94 tff(577,plain,
% 18.29/11.94 (![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))),
% 18.29/11.94 inference(modus_ponens,[status(thm)],[576, 566])).
% 18.29/11.94 tff(578,plain,
% 18.29/11.94 (((~![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))) | ((~happens(overflow, plus(n1, plus(n1, n1)))) | (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(plus(n1, plus(n1, n1)), n1))) | (~terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1)))))) <=> ((~![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))) | (~happens(overflow, plus(n1, plus(n1, n1)))) | (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(plus(n1, plus(n1, n1)), n1))) | (~terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1)))))),
% 18.29/11.94 inference(rewrite,[status(thm)],[])).
% 18.29/11.94 tff(579,plain,
% 18.29/11.94 (((~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(plus(n1, plus(n1, n1)), n1))) | (~happens(overflow, plus(n1, plus(n1, n1)))) | (~terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))))) <=> ((~happens(overflow, plus(n1, plus(n1, n1)))) | (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(plus(n1, plus(n1, n1)), n1))) | (~terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1)))))),
% 18.29/11.94 inference(rewrite,[status(thm)],[])).
% 18.29/11.94 tff(580,plain,
% 18.29/11.94 (((~![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))) | ((~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(plus(n1, plus(n1, n1)), n1))) | (~happens(overflow, plus(n1, plus(n1, n1)))) | (~terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1)))))) <=> ((~![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))) | ((~happens(overflow, plus(n1, plus(n1, n1)))) | (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(plus(n1, plus(n1, n1)), n1))) | (~terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))))))),
% 18.29/11.94 inference(monotonicity,[status(thm)],[579])).
% 18.29/11.94 tff(581,plain,
% 18.29/11.94 (((~![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))) | ((~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(plus(n1, plus(n1, n1)), n1))) | (~happens(overflow, plus(n1, plus(n1, n1)))) | (~terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1)))))) <=> ((~![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))) | (~happens(overflow, plus(n1, plus(n1, n1)))) | (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(plus(n1, plus(n1, n1)), n1))) | (~terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1)))))),
% 18.29/11.94 inference(transitivity,[status(thm)],[580, 578])).
% 18.29/11.94 tff(582,plain,
% 18.29/11.94 ((~![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))) | ((~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(plus(n1, plus(n1, n1)), n1))) | (~happens(overflow, plus(n1, plus(n1, n1)))) | (~terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1)))))),
% 18.29/11.94 inference(quant_inst,[status(thm)],[])).
% 18.29/11.94 tff(583,plain,
% 18.29/11.94 ((~![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))) | (~happens(overflow, plus(n1, plus(n1, n1)))) | (~holdsAt(tptp_fun_Height_10(waterLevel(filling), tapOn), plus(plus(n1, plus(n1, n1)), n1))) | (~terminates(overflow, tptp_fun_Height_10(waterLevel(filling), tapOn), plus(n1, plus(n1, n1))))),
% 18.29/11.94 inference(modus_ponens,[status(thm)],[582, 581])).
% 18.29/11.95 tff(584,plain,
% 18.29/11.95 ($false),
% 18.29/11.95 inference(unit_resolution,[status(thm)],[583, 577, 564, 118, 82])).
% 18.29/11.95 % SZS output end Proof
%------------------------------------------------------------------------------