TSTP Solution File: CSR018+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CSR018+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 14:27:02 EDT 2022
% Result : Theorem 272.53s 175.74s
% Output : Proof 272.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : CSR018+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.03/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n027.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Aug 30 16:26:46 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 272.53/175.74 % SZS status Theorem
% 272.53/175.74 % SZS output start Proof
% 272.53/175.74 tff(initiates_type, type, (
% 272.53/175.74 initiates: ( $i * $i * $i ) > $o)).
% 272.53/175.74 tff(n1_type, type, (
% 272.53/175.74 n1: $i)).
% 272.53/175.74 tff(backwards_type, type, (
% 272.53/175.74 backwards: $i)).
% 272.53/175.74 tff(pull_type, type, (
% 272.53/175.74 pull: $i)).
% 272.53/175.74 tff(spinning_type, type, (
% 272.53/175.74 spinning: $i)).
% 272.53/175.74 tff(happens_type, type, (
% 272.53/175.74 happens: ( $i * $i ) > $o)).
% 272.53/175.74 tff(push_type, type, (
% 272.53/175.74 push: $i)).
% 272.53/175.74 tff(forwards_type, type, (
% 272.53/175.74 forwards: $i)).
% 272.53/175.74 tff(plus_type, type, (
% 272.53/175.74 plus: ( $i * $i ) > $i)).
% 272.53/175.74 tff(n0_type, type, (
% 272.53/175.74 n0: $i)).
% 272.53/175.74 tff(n2_type, type, (
% 272.53/175.74 n2: $i)).
% 272.53/175.74 tff(less_type, type, (
% 272.53/175.74 less: ( $i * $i ) > $o)).
% 272.53/175.74 tff(less_or_equal_type, type, (
% 272.53/175.74 less_or_equal: ( $i * $i ) > $o)).
% 272.53/175.74 tff(holdsAt_type, type, (
% 272.53/175.74 holdsAt: ( $i * $i ) > $o)).
% 272.53/175.74 tff(1,plain,
% 272.53/175.74 (^[Event: $i, Fluent: $i, Time: $i] : refl((initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning)))))) <=> (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning)))))))),
% 272.53/175.74 inference(bind,[status(th)],[])).
% 272.53/175.74 tff(2,plain,
% 272.53/175.74 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning)))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))),
% 272.53/175.74 inference(quant_intro,[status(thm)],[1])).
% 272.53/175.74 tff(3,plain,
% 272.53/175.74 (^[Event: $i, Fluent: $i, Time: $i] : rewrite((initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time)))) <=> (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning)))))))),
% 272.53/175.74 inference(bind,[status(th)],[])).
% 272.53/175.74 tff(4,plain,
% 272.53/175.74 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time)))) <=> ![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))),
% 272.53/175.74 inference(quant_intro,[status(thm)],[3])).
% 272.53/175.74 tff(5,plain,
% 272.53/175.74 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time)))) <=> ![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time))))),
% 272.53/175.74 inference(rewrite,[status(thm)],[])).
% 272.53/175.74 tff(6,plain,
% 272.53/175.74 (^[Event: $i, Fluent: $i, Time: $i] : rewrite((initiates(Event, Fluent, Time) <=> (((((Event = push) & (Fluent = forwards)) & (~happens(pull, Time))) | (((Event = pull) & (Fluent = backwards)) & (~happens(push, Time)))) | (((Event = pull) & (Fluent = spinning)) & happens(push, Time)))) <=> (initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time)))))),
% 272.53/175.74 inference(bind,[status(th)],[])).
% 272.53/175.74 tff(7,plain,
% 272.53/175.74 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((((Event = push) & (Fluent = forwards)) & (~happens(pull, Time))) | (((Event = pull) & (Fluent = backwards)) & (~happens(push, Time)))) | (((Event = pull) & (Fluent = spinning)) & happens(push, Time)))) <=> ![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time))))),
% 272.53/175.74 inference(quant_intro,[status(thm)],[6])).
% 272.53/175.74 tff(8,axiom,(![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((((Event = push) & (Fluent = forwards)) & (~happens(pull, Time))) | (((Event = pull) & (Fluent = backwards)) & (~happens(push, Time)))) | (((Event = pull) & (Fluent = spinning)) & happens(push, Time))))), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax','initiates_all_defn')).
% 272.53/175.74 tff(9,plain,
% 272.53/175.74 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time))))),
% 272.53/175.74 inference(modus_ponens,[status(thm)],[8, 7])).
% 272.53/175.74 tff(10,plain,
% 272.53/175.74 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time))))),
% 272.53/175.74 inference(modus_ponens,[status(thm)],[9, 5])).
% 272.53/175.74 tff(11,plain,(
% 272.53/175.74 ![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time))))),
% 272.53/175.74 inference(skolemize,[status(sab)],[10])).
% 272.53/175.74 tff(12,plain,
% 272.53/175.74 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))),
% 272.53/175.74 inference(modus_ponens,[status(thm)],[11, 4])).
% 272.53/175.74 tff(13,plain,
% 272.53/175.74 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))),
% 272.53/175.74 inference(modus_ponens,[status(thm)],[12, 2])).
% 272.53/175.74 tff(14,plain,
% 272.53/175.74 (((~![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (initiates(pull, backwards, n1) <=> ((~happens(push, n1)) | (~((~(pull = push)) | happens(pull, n1) | (~(backwards = forwards)))) | (~((~happens(push, n1)) | (~(backwards = spinning))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (initiates(pull, backwards, n1) <=> ((~happens(push, n1)) | (~((~(pull = push)) | happens(pull, n1) | (~(backwards = forwards)))) | (~((~happens(push, n1)) | (~(backwards = spinning)))))))),
% 272.53/175.74 inference(rewrite,[status(thm)],[])).
% 272.53/175.75 tff(15,plain,
% 272.53/175.75 ((initiates(pull, backwards, n1) <=> ((~(happens(pull, n1) | (~(pull = push)) | (~(backwards = forwards)))) | (~(happens(push, n1) | (~(pull = pull)) | (~(backwards = backwards)))) | (~((~happens(push, n1)) | (~(pull = pull)) | (~(backwards = spinning)))))) <=> (initiates(pull, backwards, n1) <=> ((~happens(push, n1)) | (~((~(pull = push)) | happens(pull, n1) | (~(backwards = forwards)))) | (~((~happens(push, n1)) | (~(backwards = spinning))))))),
% 272.53/175.75 inference(rewrite,[status(thm)],[])).
% 272.53/175.75 tff(16,plain,
% 272.53/175.75 (((~![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (initiates(pull, backwards, n1) <=> ((~(happens(pull, n1) | (~(pull = push)) | (~(backwards = forwards)))) | (~(happens(push, n1) | (~(pull = pull)) | (~(backwards = backwards)))) | (~((~happens(push, n1)) | (~(pull = pull)) | (~(backwards = spinning))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (initiates(pull, backwards, n1) <=> ((~happens(push, n1)) | (~((~(pull = push)) | happens(pull, n1) | (~(backwards = forwards)))) | (~((~happens(push, n1)) | (~(backwards = spinning)))))))),
% 272.53/175.75 inference(monotonicity,[status(thm)],[15])).
% 272.53/175.75 tff(17,plain,
% 272.53/175.75 (((~![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (initiates(pull, backwards, n1) <=> ((~(happens(pull, n1) | (~(pull = push)) | (~(backwards = forwards)))) | (~(happens(push, n1) | (~(pull = pull)) | (~(backwards = backwards)))) | (~((~happens(push, n1)) | (~(pull = pull)) | (~(backwards = spinning))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (initiates(pull, backwards, n1) <=> ((~happens(push, n1)) | (~((~(pull = push)) | happens(pull, n1) | (~(backwards = forwards)))) | (~((~happens(push, n1)) | (~(backwards = spinning)))))))),
% 272.53/175.75 inference(transitivity,[status(thm)],[16, 14])).
% 272.53/175.75 tff(18,plain,
% 272.53/175.75 ((~![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (initiates(pull, backwards, n1) <=> ((~(happens(pull, n1) | (~(pull = push)) | (~(backwards = forwards)))) | (~(happens(push, n1) | (~(pull = pull)) | (~(backwards = backwards)))) | (~((~happens(push, n1)) | (~(pull = pull)) | (~(backwards = spinning))))))),
% 272.53/175.75 inference(quant_inst,[status(thm)],[])).
% 272.53/175.75 tff(19,plain,
% 272.53/175.75 ((~![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (initiates(pull, backwards, n1) <=> ((~happens(push, n1)) | (~((~(pull = push)) | happens(pull, n1) | (~(backwards = forwards)))) | (~((~happens(push, n1)) | (~(backwards = spinning))))))),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[18, 17])).
% 272.53/175.75 tff(20,plain,
% 272.53/175.75 (initiates(pull, backwards, n1) <=> ((~happens(push, n1)) | (~((~(pull = push)) | happens(pull, n1) | (~(backwards = forwards)))) | (~((~happens(push, n1)) | (~(backwards = spinning)))))),
% 272.53/175.75 inference(unit_resolution,[status(thm)],[19, 13])).
% 272.53/175.75 tff(21,assumption,(~(happens(push, n1) <=> ((push = pull) | (n1 = plus(n1, n1)) | (n1 = n0) | (~((~(push = pull)) | (~(n1 = plus(n1, n1)))))))), introduced(assumption)).
% 272.53/175.75 tff(22,plain,
% 272.53/175.75 (^[Event: $i, Time: $i] : refl((happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1))))))) <=> (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1))))))))),
% 272.53/175.75 inference(bind,[status(th)],[])).
% 272.53/175.75 tff(23,plain,
% 272.53/175.75 (![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1))))))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))),
% 272.53/175.75 inference(quant_intro,[status(thm)],[22])).
% 272.53/175.75 tff(24,plain,
% 272.53/175.75 (^[Event: $i, Time: $i] : rewrite((happens(Event, Time) <=> (((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)) | ((Event = push) & (Time = plus(n1, n1))) | ((Event = pull) & (Time = plus(n1, n1))))) <=> (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1))))))))),
% 272.53/175.75 inference(bind,[status(th)],[])).
% 272.53/175.75 tff(25,plain,
% 272.53/175.75 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)) | ((Event = push) & (Time = plus(n1, n1))) | ((Event = pull) & (Time = plus(n1, n1))))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))),
% 272.53/175.75 inference(quant_intro,[status(thm)],[24])).
% 272.53/175.75 tff(26,plain,
% 272.53/175.75 (^[Event: $i, Time: $i] : rewrite((happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)))) <=> (happens(Event, Time) <=> (((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)) | ((Event = push) & (Time = plus(n1, n1))) | ((Event = pull) & (Time = plus(n1, n1))))))),
% 272.53/175.75 inference(bind,[status(th)],[])).
% 272.53/175.75 tff(27,plain,
% 272.53/175.75 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)) | ((Event = push) & (Time = plus(n1, n1))) | ((Event = pull) & (Time = plus(n1, n1)))))),
% 272.53/175.75 inference(quant_intro,[status(thm)],[26])).
% 272.53/175.75 tff(28,plain,
% 272.53/175.75 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 272.53/175.75 inference(rewrite,[status(thm)],[])).
% 272.53/175.75 tff(29,plain,
% 272.53/175.75 (^[Event: $i, Time: $i] : rewrite((happens(Event, Time) <=> (((((Event = push) & (Time = n0)) | ((Event = pull) & (Time = n1))) | ((Event = pull) & (Time = n2))) | ((Event = push) & (Time = n2)))) <=> (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)))))),
% 272.53/175.75 inference(bind,[status(th)],[])).
% 272.53/175.75 tff(30,plain,
% 272.53/175.75 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((((Event = push) & (Time = n0)) | ((Event = pull) & (Time = n1))) | ((Event = pull) & (Time = n2))) | ((Event = push) & (Time = n2)))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 272.53/175.75 inference(quant_intro,[status(thm)],[29])).
% 272.53/175.75 tff(31,axiom,(![Event: $i, Time: $i] : (happens(Event, Time) <=> (((((Event = push) & (Time = n0)) | ((Event = pull) & (Time = n1))) | ((Event = pull) & (Time = n2))) | ((Event = push) & (Time = n2))))), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax','happens_all_defn')).
% 272.53/175.75 tff(32,plain,
% 272.53/175.75 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[31, 30])).
% 272.53/175.75 tff(33,plain,
% 272.53/175.75 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[32, 28])).
% 272.53/175.75 tff(34,plain,
% 272.53/175.75 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)) | ((Event = push) & (Time = plus(n1, n1))) | ((Event = pull) & (Time = plus(n1, n1)))))),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[33, 27])).
% 272.53/175.75 tff(35,plain,(
% 272.53/175.75 ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)) | ((Event = push) & (Time = plus(n1, n1))) | ((Event = pull) & (Time = plus(n1, n1)))))),
% 272.53/175.75 inference(skolemize,[status(sab)],[34])).
% 272.53/175.75 tff(36,plain,
% 272.53/175.75 (![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[35, 25])).
% 272.53/175.75 tff(37,plain,
% 272.53/175.75 (![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[36, 23])).
% 272.53/175.75 tff(38,plain,
% 272.53/175.75 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | (happens(push, n1) <=> ((push = pull) | (n1 = plus(n1, n1)) | (n1 = n0) | (~((~(push = pull)) | (~(n1 = plus(n1, n1)))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | (happens(push, n1) <=> ((push = pull) | (n1 = plus(n1, n1)) | (n1 = n0) | (~((~(push = pull)) | (~(n1 = plus(n1, n1))))))))),
% 272.53/175.75 inference(rewrite,[status(thm)],[])).
% 272.53/175.75 tff(39,plain,
% 272.53/175.75 ((happens(push, n1) <=> ((~((~(push = pull)) | (~(n1 = n1)))) | (~((~(push = push)) | (~(n1 = n0)))) | (~((~(push = push)) | (~(n1 = plus(n1, n1))))) | (~((~(push = pull)) | (~(n1 = plus(n1, n1))))))) <=> (happens(push, n1) <=> ((push = pull) | (n1 = plus(n1, n1)) | (n1 = n0) | (~((~(push = pull)) | (~(n1 = plus(n1, n1)))))))),
% 272.53/175.75 inference(rewrite,[status(thm)],[])).
% 272.53/175.75 tff(40,plain,
% 272.53/175.75 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | (happens(push, n1) <=> ((~((~(push = pull)) | (~(n1 = n1)))) | (~((~(push = push)) | (~(n1 = n0)))) | (~((~(push = push)) | (~(n1 = plus(n1, n1))))) | (~((~(push = pull)) | (~(n1 = plus(n1, n1)))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | (happens(push, n1) <=> ((push = pull) | (n1 = plus(n1, n1)) | (n1 = n0) | (~((~(push = pull)) | (~(n1 = plus(n1, n1))))))))),
% 272.53/175.75 inference(monotonicity,[status(thm)],[39])).
% 272.53/175.75 tff(41,plain,
% 272.53/175.75 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | (happens(push, n1) <=> ((~((~(push = pull)) | (~(n1 = n1)))) | (~((~(push = push)) | (~(n1 = n0)))) | (~((~(push = push)) | (~(n1 = plus(n1, n1))))) | (~((~(push = pull)) | (~(n1 = plus(n1, n1)))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | (happens(push, n1) <=> ((push = pull) | (n1 = plus(n1, n1)) | (n1 = n0) | (~((~(push = pull)) | (~(n1 = plus(n1, n1))))))))),
% 272.53/175.75 inference(transitivity,[status(thm)],[40, 38])).
% 272.53/175.75 tff(42,plain,
% 272.53/175.75 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | (happens(push, n1) <=> ((~((~(push = pull)) | (~(n1 = n1)))) | (~((~(push = push)) | (~(n1 = n0)))) | (~((~(push = push)) | (~(n1 = plus(n1, n1))))) | (~((~(push = pull)) | (~(n1 = plus(n1, n1)))))))),
% 272.53/175.75 inference(quant_inst,[status(thm)],[])).
% 272.53/175.75 tff(43,plain,
% 272.53/175.75 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | (happens(push, n1) <=> ((push = pull) | (n1 = plus(n1, n1)) | (n1 = n0) | (~((~(push = pull)) | (~(n1 = plus(n1, n1)))))))),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[42, 41])).
% 272.53/175.75 tff(44,plain,
% 272.53/175.75 ($false),
% 272.53/175.75 inference(unit_resolution,[status(thm)],[43, 37, 21])).
% 272.53/175.75 tff(45,plain,(happens(push, n1) <=> ((push = pull) | (n1 = plus(n1, n1)) | (n1 = n0) | (~((~(push = pull)) | (~(n1 = plus(n1, n1))))))), inference(lemma,lemma(discharge,[]))).
% 272.53/175.75 tff(46,plain,
% 272.53/175.75 ((~(push = pull)) <=> (~(push = pull))),
% 272.53/175.75 inference(rewrite,[status(thm)],[])).
% 272.53/175.75 tff(47,axiom,(~(push = pull)), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax','push_not_pull')).
% 272.53/175.75 tff(48,plain,
% 272.53/175.75 (~(push = pull)),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[47, 46])).
% 272.53/175.75 tff(49,plain,
% 272.53/175.75 (((~(push = pull)) | (~(n1 = plus(n1, n1)))) | (push = pull)),
% 272.53/175.75 inference(tautology,[status(thm)],[])).
% 272.53/175.75 tff(50,plain,
% 272.53/175.75 ((~(push = pull)) | (~(n1 = plus(n1, n1)))),
% 272.53/175.75 inference(unit_resolution,[status(thm)],[49, 48])).
% 272.53/175.75 tff(51,plain,
% 272.53/175.75 (^[X: $i, Y: $i] : refl((less(X, Y) <=> (~((Y = X) | less(Y, X)))) <=> (less(X, Y) <=> (~((Y = X) | less(Y, X)))))),
% 272.53/175.75 inference(bind,[status(th)],[])).
% 272.53/175.75 tff(52,plain,
% 272.53/175.75 (![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X)))) <=> ![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))),
% 272.53/175.75 inference(quant_intro,[status(thm)],[51])).
% 272.53/175.75 tff(53,plain,
% 272.53/175.75 (^[X: $i, Y: $i] : rewrite((less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> (less(X, Y) <=> (~((Y = X) | less(Y, X)))))),
% 272.53/175.75 inference(bind,[status(th)],[])).
% 272.53/175.75 tff(54,plain,
% 272.53/175.75 (![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> ![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))),
% 272.53/175.75 inference(quant_intro,[status(thm)],[53])).
% 272.53/175.75 tff(55,plain,
% 272.53/175.75 (![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> ![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))),
% 272.53/175.75 inference(rewrite,[status(thm)],[])).
% 272.53/175.75 tff(56,axiom,(![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','less_property')).
% 272.53/175.75 tff(57,plain,
% 272.53/175.75 (![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[56, 55])).
% 272.53/175.75 tff(58,plain,(
% 272.53/175.75 ![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))),
% 272.53/175.75 inference(skolemize,[status(sab)],[57])).
% 272.53/175.75 tff(59,plain,
% 272.53/175.75 (![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[58, 54])).
% 272.53/175.75 tff(60,plain,
% 272.53/175.75 (![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[59, 52])).
% 272.53/175.75 tff(61,plain,
% 272.53/175.75 ((~![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))) | (less(n0, n1) <=> (~((n1 = n0) | less(n1, n0))))),
% 272.53/175.75 inference(quant_inst,[status(thm)],[])).
% 272.53/175.75 tff(62,plain,
% 272.53/175.75 (less(n0, n1) <=> (~((n1 = n0) | less(n1, n0)))),
% 272.53/175.75 inference(unit_resolution,[status(thm)],[61, 60])).
% 272.53/175.75 tff(63,plain,
% 272.53/175.75 (^[X: $i] : refl((less(X, n1) <=> less_or_equal(X, n0)) <=> (less(X, n1) <=> less_or_equal(X, n0)))),
% 272.53/175.75 inference(bind,[status(th)],[])).
% 272.53/175.75 tff(64,plain,
% 272.53/175.75 (![X: $i] : (less(X, n1) <=> less_or_equal(X, n0)) <=> ![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))),
% 272.53/175.75 inference(quant_intro,[status(thm)],[63])).
% 272.53/175.75 tff(65,plain,
% 272.53/175.75 (![X: $i] : (less(X, n1) <=> less_or_equal(X, n0)) <=> ![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))),
% 272.53/175.75 inference(rewrite,[status(thm)],[])).
% 272.53/175.75 tff(66,axiom,(![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','less1')).
% 272.53/175.75 tff(67,plain,
% 272.53/175.75 (![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[66, 65])).
% 272.53/175.75 tff(68,plain,(
% 272.53/175.75 ![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))),
% 272.53/175.75 inference(skolemize,[status(sab)],[67])).
% 272.53/175.75 tff(69,plain,
% 272.53/175.75 (![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[68, 64])).
% 272.53/175.75 tff(70,plain,
% 272.53/175.75 ((~![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))) | (less(n0, n1) <=> less_or_equal(n0, n0))),
% 272.53/175.75 inference(quant_inst,[status(thm)],[])).
% 272.53/175.75 tff(71,plain,
% 272.53/175.75 (less(n0, n1) <=> less_or_equal(n0, n0)),
% 272.53/175.75 inference(unit_resolution,[status(thm)],[70, 69])).
% 272.53/175.75 tff(72,plain,
% 272.53/175.75 (^[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))))),
% 272.53/175.75 inference(bind,[status(th)],[])).
% 272.53/175.75 tff(73,plain,
% 272.53/175.75 (![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)))),
% 272.53/175.75 inference(quant_intro,[status(thm)],[72])).
% 272.53/175.75 tff(74,plain,
% 272.53/175.75 (![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)))),
% 272.53/175.75 inference(rewrite,[status(thm)],[])).
% 272.53/175.75 tff(75,plain,
% 272.53/175.75 (^[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))))),
% 272.53/175.75 inference(bind,[status(th)],[])).
% 272.53/175.75 tff(76,plain,
% 272.53/175.75 (![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)))),
% 272.53/175.75 inference(quant_intro,[status(thm)],[75])).
% 272.53/175.75 tff(77,axiom,(![X: $i, Y: $i] : (less_or_equal(X, Y) <=> (less(X, Y) | (X = Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','less_or_equal')).
% 272.53/175.75 tff(78,plain,
% 272.53/175.75 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[77, 76])).
% 272.53/175.75 tff(79,plain,
% 272.53/175.75 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[78, 74])).
% 272.53/175.75 tff(80,plain,(
% 272.53/175.75 ![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 272.53/175.75 inference(skolemize,[status(sab)],[79])).
% 272.53/175.75 tff(81,plain,
% 272.53/175.75 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[80, 73])).
% 272.53/175.75 tff(82,plain,
% 272.53/175.75 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n0, n0)) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n0, n0))),
% 272.53/175.75 inference(rewrite,[status(thm)],[])).
% 272.53/175.75 tff(83,plain,
% 272.53/175.75 ((less_or_equal(n0, n0) <=> $true) <=> less_or_equal(n0, n0)),
% 272.53/175.75 inference(rewrite,[status(thm)],[])).
% 272.53/175.75 tff(84,plain,
% 272.53/175.75 (($true | less(n0, n0)) <=> $true),
% 272.53/175.75 inference(rewrite,[status(thm)],[])).
% 272.53/175.75 tff(85,plain,
% 272.53/175.75 ((n0 = n0) <=> $true),
% 272.53/175.75 inference(rewrite,[status(thm)],[])).
% 272.53/175.75 tff(86,plain,
% 272.53/175.75 (((n0 = n0) | less(n0, n0)) <=> ($true | less(n0, n0))),
% 272.53/175.75 inference(monotonicity,[status(thm)],[85])).
% 272.53/175.75 tff(87,plain,
% 272.53/175.75 (((n0 = n0) | less(n0, n0)) <=> $true),
% 272.53/175.75 inference(transitivity,[status(thm)],[86, 84])).
% 272.53/175.75 tff(88,plain,
% 272.53/175.75 ((less_or_equal(n0, n0) <=> ((n0 = n0) | less(n0, n0))) <=> (less_or_equal(n0, n0) <=> $true)),
% 272.53/175.75 inference(monotonicity,[status(thm)],[87])).
% 272.53/175.75 tff(89,plain,
% 272.53/175.75 ((less_or_equal(n0, n0) <=> ((n0 = n0) | less(n0, n0))) <=> less_or_equal(n0, n0)),
% 272.53/175.75 inference(transitivity,[status(thm)],[88, 83])).
% 272.53/175.75 tff(90,plain,
% 272.53/175.75 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(n0, n0) <=> ((n0 = n0) | less(n0, n0)))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n0, n0))),
% 272.53/175.75 inference(monotonicity,[status(thm)],[89])).
% 272.53/175.75 tff(91,plain,
% 272.53/175.75 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(n0, n0) <=> ((n0 = n0) | less(n0, n0)))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n0, n0))),
% 272.53/175.75 inference(transitivity,[status(thm)],[90, 82])).
% 272.53/175.75 tff(92,plain,
% 272.53/175.75 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(n0, n0) <=> ((n0 = n0) | less(n0, n0)))),
% 272.53/175.75 inference(quant_inst,[status(thm)],[])).
% 272.53/175.75 tff(93,plain,
% 272.53/175.75 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n0, n0)),
% 272.53/175.75 inference(modus_ponens,[status(thm)],[92, 91])).
% 272.53/175.75 tff(94,plain,
% 272.53/175.75 (less_or_equal(n0, n0)),
% 272.53/175.75 inference(unit_resolution,[status(thm)],[93, 81])).
% 272.53/175.75 tff(95,plain,
% 272.53/175.75 ((~(less(n0, n1) <=> less_or_equal(n0, n0))) | less(n0, n1) | (~less_or_equal(n0, n0))),
% 272.53/175.75 inference(tautology,[status(thm)],[])).
% 272.53/175.75 tff(96,plain,
% 272.53/175.75 ((~(less(n0, n1) <=> less_or_equal(n0, n0))) | less(n0, n1)),
% 272.53/175.75 inference(unit_resolution,[status(thm)],[95, 94])).
% 272.53/175.75 tff(97,plain,
% 272.53/175.75 (less(n0, n1)),
% 272.53/175.75 inference(unit_resolution,[status(thm)],[96, 71])).
% 272.53/175.75 tff(98,plain,
% 272.53/175.75 ((~(less(n0, n1) <=> (~((n1 = n0) | less(n1, n0))))) | (~less(n0, n1)) | (~((n1 = n0) | less(n1, n0)))),
% 272.53/175.75 inference(tautology,[status(thm)],[])).
% 272.53/175.75 tff(99,plain,
% 272.53/175.75 ((~(less(n0, n1) <=> (~((n1 = n0) | less(n1, n0))))) | (~((n1 = n0) | less(n1, n0)))),
% 272.53/175.75 inference(unit_resolution,[status(thm)],[98, 97])).
% 272.53/175.75 tff(100,plain,
% 272.53/175.75 (~((n1 = n0) | less(n1, n0))),
% 272.53/175.75 inference(unit_resolution,[status(thm)],[99, 62])).
% 272.53/175.75 tff(101,plain,
% 272.53/175.75 (((n1 = n0) | less(n1, n0)) | (~(n1 = n0))),
% 272.53/175.75 inference(tautology,[status(thm)],[])).
% 272.53/175.75 tff(102,plain,
% 272.53/175.75 (~(n1 = n0)),
% 272.53/175.75 inference(unit_resolution,[status(thm)],[101, 100])).
% 272.53/175.75 tff(103,plain,
% 272.53/175.75 ((plus(n1, n1) = n1) <=> (n1 = plus(n1, n1))),
% 272.53/175.75 inference(commutativity,[status(thm)],[])).
% 272.53/175.75 tff(104,plain,
% 272.53/175.75 ((~(plus(n1, n1) = n1)) <=> (~(n1 = plus(n1, n1)))),
% 272.53/175.75 inference(monotonicity,[status(thm)],[103])).
% 272.53/175.75 tff(105,plain,
% 272.53/175.75 ((~![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))) | (less(n1, plus(n1, n1)) <=> (~((plus(n1, n1) = n1) | less(plus(n1, n1), n1))))),
% 272.53/175.75 inference(quant_inst,[status(thm)],[])).
% 272.53/175.75 tff(106,plain,
% 272.53/175.75 (less(n1, plus(n1, n1)) <=> (~((plus(n1, n1) = n1) | less(plus(n1, n1), n1)))),
% 272.53/175.75 inference(unit_resolution,[status(thm)],[105, 60])).
% 272.53/175.75 tff(107,plain,
% 272.53/175.75 (^[X: $i] : refl((less(X, plus(n1, n1)) <=> less_or_equal(X, n1)) <=> (less(X, plus(n1, n1)) <=> less_or_equal(X, n1)))),
% 272.53/175.75 inference(bind,[status(th)],[])).
% 272.53/175.75 tff(108,plain,
% 272.53/175.75 (![X: $i] : (less(X, plus(n1, n1)) <=> less_or_equal(X, n1)) <=> ![X: $i] : (less(X, plus(n1, n1)) <=> less_or_equal(X, n1))),
% 272.53/175.75 inference(quant_intro,[status(thm)],[107])).
% 272.53/175.75 tff(109,plain,
% 272.53/175.75 (^[X: $i] : rewrite((less(X, n2) <=> less_or_equal(X, n1)) <=> (less(X, plus(n1, n1)) <=> less_or_equal(X, n1)))),
% 272.53/175.76 inference(bind,[status(th)],[])).
% 272.53/175.76 tff(110,plain,
% 272.53/175.76 (![X: $i] : (less(X, n2) <=> less_or_equal(X, n1)) <=> ![X: $i] : (less(X, plus(n1, n1)) <=> less_or_equal(X, n1))),
% 272.53/175.76 inference(quant_intro,[status(thm)],[109])).
% 272.53/175.76 tff(111,plain,
% 272.53/175.76 (![X: $i] : (less(X, n2) <=> less_or_equal(X, n1)) <=> ![X: $i] : (less(X, n2) <=> less_or_equal(X, n1))),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(112,axiom,(![X: $i] : (less(X, n2) <=> less_or_equal(X, n1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','less2')).
% 272.53/175.76 tff(113,plain,
% 272.53/175.76 (![X: $i] : (less(X, n2) <=> less_or_equal(X, n1))),
% 272.53/175.76 inference(modus_ponens,[status(thm)],[112, 111])).
% 272.53/175.76 tff(114,plain,
% 272.53/175.76 (![X: $i] : (less(X, plus(n1, n1)) <=> less_or_equal(X, n1))),
% 272.53/175.76 inference(modus_ponens,[status(thm)],[113, 110])).
% 272.53/175.76 tff(115,plain,(
% 272.53/175.76 ![X: $i] : (less(X, plus(n1, n1)) <=> less_or_equal(X, n1))),
% 272.53/175.76 inference(skolemize,[status(sab)],[114])).
% 272.53/175.76 tff(116,plain,
% 272.53/175.76 (![X: $i] : (less(X, plus(n1, n1)) <=> less_or_equal(X, n1))),
% 272.53/175.76 inference(modus_ponens,[status(thm)],[115, 108])).
% 272.53/175.76 tff(117,plain,
% 272.53/175.76 ((~![X: $i] : (less(X, plus(n1, n1)) <=> less_or_equal(X, n1))) | (less(n1, plus(n1, n1)) <=> less_or_equal(n1, n1))),
% 272.53/175.76 inference(quant_inst,[status(thm)],[])).
% 272.53/175.76 tff(118,plain,
% 272.53/175.76 (less(n1, plus(n1, n1)) <=> less_or_equal(n1, n1)),
% 272.53/175.76 inference(unit_resolution,[status(thm)],[117, 116])).
% 272.53/175.76 tff(119,plain,
% 272.53/175.76 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n1, n1)) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n1, n1))),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(120,plain,
% 272.53/175.76 ((less_or_equal(n1, n1) <=> $true) <=> less_or_equal(n1, n1)),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(121,plain,
% 272.53/175.76 (($true | less(n1, n1)) <=> $true),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(122,plain,
% 272.53/175.76 ((n1 = n1) <=> $true),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(123,plain,
% 272.53/175.76 (((n1 = n1) | less(n1, n1)) <=> ($true | less(n1, n1))),
% 272.53/175.76 inference(monotonicity,[status(thm)],[122])).
% 272.53/175.76 tff(124,plain,
% 272.53/175.76 (((n1 = n1) | less(n1, n1)) <=> $true),
% 272.53/175.76 inference(transitivity,[status(thm)],[123, 121])).
% 272.53/175.76 tff(125,plain,
% 272.53/175.76 ((less_or_equal(n1, n1) <=> ((n1 = n1) | less(n1, n1))) <=> (less_or_equal(n1, n1) <=> $true)),
% 272.53/175.76 inference(monotonicity,[status(thm)],[124])).
% 272.53/175.76 tff(126,plain,
% 272.53/175.76 ((less_or_equal(n1, n1) <=> ((n1 = n1) | less(n1, n1))) <=> less_or_equal(n1, n1)),
% 272.53/175.76 inference(transitivity,[status(thm)],[125, 120])).
% 272.53/175.76 tff(127,plain,
% 272.53/175.76 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(n1, n1) <=> ((n1 = n1) | less(n1, n1)))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n1, n1))),
% 272.53/175.76 inference(monotonicity,[status(thm)],[126])).
% 272.53/175.76 tff(128,plain,
% 272.53/175.76 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(n1, n1) <=> ((n1 = n1) | less(n1, n1)))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n1, n1))),
% 272.53/175.76 inference(transitivity,[status(thm)],[127, 119])).
% 272.53/175.76 tff(129,plain,
% 272.53/175.76 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(n1, n1) <=> ((n1 = n1) | less(n1, n1)))),
% 272.53/175.76 inference(quant_inst,[status(thm)],[])).
% 272.53/175.76 tff(130,plain,
% 272.53/175.76 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n1, n1)),
% 272.53/175.76 inference(modus_ponens,[status(thm)],[129, 128])).
% 272.53/175.76 tff(131,plain,
% 272.53/175.76 (less_or_equal(n1, n1)),
% 272.53/175.76 inference(unit_resolution,[status(thm)],[130, 81])).
% 272.53/175.76 tff(132,plain,
% 272.53/175.76 ((~(less(n1, plus(n1, n1)) <=> less_or_equal(n1, n1))) | less(n1, plus(n1, n1)) | (~less_or_equal(n1, n1))),
% 272.53/175.76 inference(tautology,[status(thm)],[])).
% 272.53/175.76 tff(133,plain,
% 272.53/175.76 ((~(less(n1, plus(n1, n1)) <=> less_or_equal(n1, n1))) | less(n1, plus(n1, n1))),
% 272.53/175.76 inference(unit_resolution,[status(thm)],[132, 131])).
% 272.53/175.76 tff(134,plain,
% 272.53/175.76 (less(n1, plus(n1, n1))),
% 272.53/175.76 inference(unit_resolution,[status(thm)],[133, 118])).
% 272.53/175.76 tff(135,plain,
% 272.53/175.76 ((~(less(n1, plus(n1, n1)) <=> (~((plus(n1, n1) = n1) | less(plus(n1, n1), n1))))) | (~less(n1, plus(n1, n1))) | (~((plus(n1, n1) = n1) | less(plus(n1, n1), n1)))),
% 272.53/175.76 inference(tautology,[status(thm)],[])).
% 272.53/175.76 tff(136,plain,
% 272.53/175.76 ((~(less(n1, plus(n1, n1)) <=> (~((plus(n1, n1) = n1) | less(plus(n1, n1), n1))))) | (~((plus(n1, n1) = n1) | less(plus(n1, n1), n1)))),
% 272.53/175.76 inference(unit_resolution,[status(thm)],[135, 134])).
% 272.53/175.76 tff(137,plain,
% 272.53/175.76 (~((plus(n1, n1) = n1) | less(plus(n1, n1), n1))),
% 272.53/175.76 inference(unit_resolution,[status(thm)],[136, 106])).
% 272.53/175.76 tff(138,plain,
% 272.53/175.76 (((plus(n1, n1) = n1) | less(plus(n1, n1), n1)) | (~(plus(n1, n1) = n1))),
% 272.53/175.76 inference(tautology,[status(thm)],[])).
% 272.53/175.76 tff(139,plain,
% 272.53/175.76 (~(plus(n1, n1) = n1)),
% 272.53/175.76 inference(unit_resolution,[status(thm)],[138, 137])).
% 272.53/175.76 tff(140,plain,
% 272.53/175.76 (~(n1 = plus(n1, n1))),
% 272.53/175.76 inference(modus_ponens,[status(thm)],[139, 104])).
% 272.53/175.76 tff(141,plain,
% 272.53/175.76 ((~((push = pull) | (n1 = plus(n1, n1)) | (n1 = n0) | (~((~(push = pull)) | (~(n1 = plus(n1, n1))))))) | (push = pull) | (n1 = plus(n1, n1)) | (n1 = n0) | (~((~(push = pull)) | (~(n1 = plus(n1, n1)))))),
% 272.53/175.76 inference(tautology,[status(thm)],[])).
% 272.53/175.76 tff(142,plain,
% 272.53/175.76 (~((push = pull) | (n1 = plus(n1, n1)) | (n1 = n0) | (~((~(push = pull)) | (~(n1 = plus(n1, n1))))))),
% 272.53/175.76 inference(unit_resolution,[status(thm)],[141, 48, 140, 102, 50])).
% 272.53/175.76 tff(143,plain,
% 272.53/175.76 ((~(happens(push, n1) <=> ((push = pull) | (n1 = plus(n1, n1)) | (n1 = n0) | (~((~(push = pull)) | (~(n1 = plus(n1, n1)))))))) | (~happens(push, n1)) | ((push = pull) | (n1 = plus(n1, n1)) | (n1 = n0) | (~((~(push = pull)) | (~(n1 = plus(n1, n1))))))),
% 272.53/175.76 inference(tautology,[status(thm)],[])).
% 272.53/175.76 tff(144,plain,
% 272.53/175.76 ((~(happens(push, n1) <=> ((push = pull) | (n1 = plus(n1, n1)) | (n1 = n0) | (~((~(push = pull)) | (~(n1 = plus(n1, n1)))))))) | (~happens(push, n1))),
% 272.53/175.76 inference(unit_resolution,[status(thm)],[143, 142])).
% 272.53/175.76 tff(145,plain,
% 272.53/175.76 (~happens(push, n1)),
% 272.53/175.76 inference(unit_resolution,[status(thm)],[144, 45])).
% 272.53/175.76 tff(146,plain,
% 272.53/175.76 (((~happens(push, n1)) | (~((~(pull = push)) | happens(pull, n1) | (~(backwards = forwards)))) | (~((~happens(push, n1)) | (~(backwards = spinning))))) | happens(push, n1)),
% 272.53/175.76 inference(tautology,[status(thm)],[])).
% 272.53/175.76 tff(147,plain,
% 272.53/175.76 ((~happens(push, n1)) | (~((~(pull = push)) | happens(pull, n1) | (~(backwards = forwards)))) | (~((~happens(push, n1)) | (~(backwards = spinning))))),
% 272.53/175.76 inference(unit_resolution,[status(thm)],[146, 145])).
% 272.53/175.76 tff(148,plain,
% 272.53/175.76 ((~(initiates(pull, backwards, n1) <=> ((~happens(push, n1)) | (~((~(pull = push)) | happens(pull, n1) | (~(backwards = forwards)))) | (~((~happens(push, n1)) | (~(backwards = spinning))))))) | initiates(pull, backwards, n1) | (~((~happens(push, n1)) | (~((~(pull = push)) | happens(pull, n1) | (~(backwards = forwards)))) | (~((~happens(push, n1)) | (~(backwards = spinning))))))),
% 272.53/175.76 inference(tautology,[status(thm)],[])).
% 272.53/175.76 tff(149,plain,
% 272.53/175.76 ((~(initiates(pull, backwards, n1) <=> ((~happens(push, n1)) | (~((~(pull = push)) | happens(pull, n1) | (~(backwards = forwards)))) | (~((~happens(push, n1)) | (~(backwards = spinning))))))) | initiates(pull, backwards, n1)),
% 272.53/175.76 inference(unit_resolution,[status(thm)],[148, 147])).
% 272.53/175.76 tff(150,plain,
% 272.53/175.76 (initiates(pull, backwards, n1)),
% 272.53/175.76 inference(unit_resolution,[status(thm)],[149, 20])).
% 272.53/175.76 tff(151,assumption,(~happens(pull, n1)), introduced(assumption)).
% 272.53/175.76 tff(152,plain,
% 272.53/175.76 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | happens(pull, n1)) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | happens(pull, n1))),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(153,plain,
% 272.53/175.76 ((happens(pull, n1) <=> $true) <=> happens(pull, n1)),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(154,plain,
% 272.53/175.76 (($true | (~((~(pull = push)) | (~(n1 = n0)))) | (~((~(pull = push)) | (~(n1 = plus(n1, n1))))) | (n1 = plus(n1, n1))) <=> $true),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(155,plain,
% 272.53/175.76 ((~(~(n1 = plus(n1, n1)))) <=> (n1 = plus(n1, n1))),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(156,plain,
% 272.53/175.76 (($false | (~(n1 = plus(n1, n1)))) <=> (~(n1 = plus(n1, n1)))),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(157,plain,
% 272.53/175.76 ((~$true) <=> $false),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(158,plain,
% 272.53/175.76 ((pull = pull) <=> $true),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(159,plain,
% 272.53/175.76 ((~(pull = pull)) <=> (~$true)),
% 272.53/175.76 inference(monotonicity,[status(thm)],[158])).
% 272.53/175.76 tff(160,plain,
% 272.53/175.76 ((~(pull = pull)) <=> $false),
% 272.53/175.76 inference(transitivity,[status(thm)],[159, 157])).
% 272.53/175.76 tff(161,plain,
% 272.53/175.76 (((~(pull = pull)) | (~(n1 = plus(n1, n1)))) <=> ($false | (~(n1 = plus(n1, n1))))),
% 272.53/175.76 inference(monotonicity,[status(thm)],[160])).
% 272.53/175.76 tff(162,plain,
% 272.53/175.76 (((~(pull = pull)) | (~(n1 = plus(n1, n1)))) <=> (~(n1 = plus(n1, n1)))),
% 272.53/175.76 inference(transitivity,[status(thm)],[161, 156])).
% 272.53/175.76 tff(163,plain,
% 272.53/175.76 ((~((~(pull = pull)) | (~(n1 = plus(n1, n1))))) <=> (~(~(n1 = plus(n1, n1))))),
% 272.53/175.76 inference(monotonicity,[status(thm)],[162])).
% 272.53/175.76 tff(164,plain,
% 272.53/175.76 ((~((~(pull = pull)) | (~(n1 = plus(n1, n1))))) <=> (n1 = plus(n1, n1))),
% 272.53/175.76 inference(transitivity,[status(thm)],[163, 155])).
% 272.53/175.76 tff(165,plain,
% 272.53/175.76 ((~((~(pull = push)) | (~(n1 = n0)))) <=> (~((~(pull = push)) | (~(n1 = n0))))),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(166,plain,
% 272.53/175.76 ((~$false) <=> $true),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(167,plain,
% 272.53/175.76 (($false | $false) <=> $false),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(168,plain,
% 272.53/175.76 ((~(n1 = n1)) <=> (~$true)),
% 272.53/175.76 inference(monotonicity,[status(thm)],[122])).
% 272.53/175.76 tff(169,plain,
% 272.53/175.76 ((~(n1 = n1)) <=> $false),
% 272.53/175.76 inference(transitivity,[status(thm)],[168, 157])).
% 272.53/175.76 tff(170,plain,
% 272.53/175.76 (((~(pull = pull)) | (~(n1 = n1))) <=> ($false | $false)),
% 272.53/175.76 inference(monotonicity,[status(thm)],[160, 169])).
% 272.53/175.76 tff(171,plain,
% 272.53/175.76 (((~(pull = pull)) | (~(n1 = n1))) <=> $false),
% 272.53/175.76 inference(transitivity,[status(thm)],[170, 167])).
% 272.53/175.76 tff(172,plain,
% 272.53/175.76 ((~((~(pull = pull)) | (~(n1 = n1)))) <=> (~$false)),
% 272.53/175.76 inference(monotonicity,[status(thm)],[171])).
% 272.53/175.76 tff(173,plain,
% 272.53/175.76 ((~((~(pull = pull)) | (~(n1 = n1)))) <=> $true),
% 272.53/175.76 inference(transitivity,[status(thm)],[172, 166])).
% 272.53/175.76 tff(174,plain,
% 272.53/175.76 (((~((~(pull = pull)) | (~(n1 = n1)))) | (~((~(pull = push)) | (~(n1 = n0)))) | (~((~(pull = push)) | (~(n1 = plus(n1, n1))))) | (~((~(pull = pull)) | (~(n1 = plus(n1, n1)))))) <=> ($true | (~((~(pull = push)) | (~(n1 = n0)))) | (~((~(pull = push)) | (~(n1 = plus(n1, n1))))) | (n1 = plus(n1, n1)))),
% 272.53/175.76 inference(monotonicity,[status(thm)],[173, 165, 164])).
% 272.53/175.76 tff(175,plain,
% 272.53/175.76 (((~((~(pull = pull)) | (~(n1 = n1)))) | (~((~(pull = push)) | (~(n1 = n0)))) | (~((~(pull = push)) | (~(n1 = plus(n1, n1))))) | (~((~(pull = pull)) | (~(n1 = plus(n1, n1)))))) <=> $true),
% 272.53/175.76 inference(transitivity,[status(thm)],[174, 154])).
% 272.53/175.76 tff(176,plain,
% 272.53/175.76 ((happens(pull, n1) <=> ((~((~(pull = pull)) | (~(n1 = n1)))) | (~((~(pull = push)) | (~(n1 = n0)))) | (~((~(pull = push)) | (~(n1 = plus(n1, n1))))) | (~((~(pull = pull)) | (~(n1 = plus(n1, n1))))))) <=> (happens(pull, n1) <=> $true)),
% 272.53/175.76 inference(monotonicity,[status(thm)],[175])).
% 272.53/175.76 tff(177,plain,
% 272.53/175.76 ((happens(pull, n1) <=> ((~((~(pull = pull)) | (~(n1 = n1)))) | (~((~(pull = push)) | (~(n1 = n0)))) | (~((~(pull = push)) | (~(n1 = plus(n1, n1))))) | (~((~(pull = pull)) | (~(n1 = plus(n1, n1))))))) <=> happens(pull, n1)),
% 272.53/175.76 inference(transitivity,[status(thm)],[176, 153])).
% 272.53/175.76 tff(178,plain,
% 272.53/175.76 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | (happens(pull, n1) <=> ((~((~(pull = pull)) | (~(n1 = n1)))) | (~((~(pull = push)) | (~(n1 = n0)))) | (~((~(pull = push)) | (~(n1 = plus(n1, n1))))) | (~((~(pull = pull)) | (~(n1 = plus(n1, n1)))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | happens(pull, n1))),
% 272.53/175.76 inference(monotonicity,[status(thm)],[177])).
% 272.53/175.76 tff(179,plain,
% 272.53/175.76 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | (happens(pull, n1) <=> ((~((~(pull = pull)) | (~(n1 = n1)))) | (~((~(pull = push)) | (~(n1 = n0)))) | (~((~(pull = push)) | (~(n1 = plus(n1, n1))))) | (~((~(pull = pull)) | (~(n1 = plus(n1, n1)))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | happens(pull, n1))),
% 272.53/175.76 inference(transitivity,[status(thm)],[178, 152])).
% 272.53/175.76 tff(180,plain,
% 272.53/175.76 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | (happens(pull, n1) <=> ((~((~(pull = pull)) | (~(n1 = n1)))) | (~((~(pull = push)) | (~(n1 = n0)))) | (~((~(pull = push)) | (~(n1 = plus(n1, n1))))) | (~((~(pull = pull)) | (~(n1 = plus(n1, n1)))))))),
% 272.53/175.76 inference(quant_inst,[status(thm)],[])).
% 272.53/175.76 tff(181,plain,
% 272.53/175.76 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | happens(pull, n1)),
% 272.53/175.76 inference(modus_ponens,[status(thm)],[180, 179])).
% 272.53/175.76 tff(182,plain,
% 272.53/175.76 ($false),
% 272.53/175.76 inference(unit_resolution,[status(thm)],[181, 37, 151])).
% 272.53/175.76 tff(183,plain,(happens(pull, n1)), inference(lemma,lemma(discharge,[]))).
% 272.53/175.76 tff(184,plain,
% 272.53/175.76 ((~holdsAt(backwards, n2)) <=> (~holdsAt(backwards, plus(n1, n1)))),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(185,plain,
% 272.53/175.76 ((~holdsAt(backwards, n2)) <=> (~holdsAt(backwards, n2))),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(186,axiom,(~holdsAt(backwards, n2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','backwards_2')).
% 272.53/175.76 tff(187,plain,
% 272.53/175.76 (~holdsAt(backwards, n2)),
% 272.53/175.76 inference(modus_ponens,[status(thm)],[186, 185])).
% 272.53/175.76 tff(188,plain,
% 272.53/175.76 (~holdsAt(backwards, plus(n1, n1))),
% 272.53/175.76 inference(modus_ponens,[status(thm)],[187, 184])).
% 272.53/175.76 tff(189,plain,
% 272.53/175.76 (^[Event: $i, Time: $i, Fluent: $i] : refl((holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time))) <=> (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time))))),
% 272.53/175.76 inference(bind,[status(th)],[])).
% 272.53/175.76 tff(190,plain,
% 272.53/175.76 (![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time))) <=> ![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))),
% 272.53/175.76 inference(quant_intro,[status(thm)],[189])).
% 272.53/175.76 tff(191,plain,
% 272.53/175.76 (^[Event: $i, Time: $i, Fluent: $i] : trans(monotonicity(trans(monotonicity(rewrite((happens(Event, Time) & initiates(Event, Fluent, Time)) <=> (~((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))))), ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) <=> (~(~((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))))))), rewrite((~(~((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))))) <=> ((~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))), ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) <=> ((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))))), (((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> (((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))))), rewrite((((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))), (((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))))),
% 272.53/175.76 inference(bind,[status(th)],[])).
% 272.53/175.76 tff(192,plain,
% 272.53/175.76 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> ![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))),
% 272.53/175.76 inference(quant_intro,[status(thm)],[191])).
% 272.53/175.76 tff(193,plain,
% 272.53/175.76 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(194,plain,
% 272.53/175.76 (^[Event: $i, Time: $i, Fluent: $i] : rewrite(((happens(Event, Time) & initiates(Event, Fluent, Time)) => holdsAt(Fluent, plus(Time, n1))) <=> ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))))),
% 272.53/175.76 inference(bind,[status(th)],[])).
% 272.53/175.76 tff(195,plain,
% 272.53/175.76 (![Event: $i, Time: $i, Fluent: $i] : ((happens(Event, Time) & initiates(Event, Fluent, Time)) => holdsAt(Fluent, plus(Time, n1))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 272.53/175.76 inference(quant_intro,[status(thm)],[194])).
% 272.53/175.76 tff(196,axiom,(![Event: $i, Time: $i, Fluent: $i] : ((happens(Event, Time) & initiates(Event, Fluent, Time)) => holdsAt(Fluent, plus(Time, n1)))), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+0.ax','happens_holds')).
% 272.53/175.76 tff(197,plain,
% 272.53/175.76 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 272.53/175.76 inference(modus_ponens,[status(thm)],[196, 195])).
% 272.53/175.76 tff(198,plain,
% 272.53/175.76 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 272.53/175.76 inference(modus_ponens,[status(thm)],[197, 193])).
% 272.53/175.76 tff(199,plain,(
% 272.53/175.76 ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 272.53/175.76 inference(skolemize,[status(sab)],[198])).
% 272.53/175.76 tff(200,plain,
% 272.53/175.76 (![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))),
% 272.53/175.76 inference(modus_ponens,[status(thm)],[199, 192])).
% 272.53/175.76 tff(201,plain,
% 272.53/175.76 (![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))),
% 272.53/175.76 inference(modus_ponens,[status(thm)],[200, 190])).
% 272.53/175.76 tff(202,plain,
% 272.53/175.76 (((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | (holdsAt(backwards, plus(n1, n1)) | (~happens(pull, n1)) | (~initiates(pull, backwards, n1)))) <=> ((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | holdsAt(backwards, plus(n1, n1)) | (~happens(pull, n1)) | (~initiates(pull, backwards, n1)))),
% 272.53/175.76 inference(rewrite,[status(thm)],[])).
% 272.53/175.76 tff(203,plain,
% 272.53/175.76 ((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | (holdsAt(backwards, plus(n1, n1)) | (~happens(pull, n1)) | (~initiates(pull, backwards, n1)))),
% 272.53/175.76 inference(quant_inst,[status(thm)],[])).
% 272.53/175.76 tff(204,plain,
% 272.53/175.76 ((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | holdsAt(backwards, plus(n1, n1)) | (~happens(pull, n1)) | (~initiates(pull, backwards, n1))),
% 272.56/175.76 inference(modus_ponens,[status(thm)],[203, 202])).
% 272.56/175.76 tff(205,plain,
% 272.56/175.76 ($false),
% 272.56/175.76 inference(unit_resolution,[status(thm)],[204, 201, 188, 183, 150])).
% 272.56/175.76 % SZS output end Proof
%------------------------------------------------------------------------------