TSTP Solution File: CSR023+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CSR023+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 14:27:03 EDT 2022
% Result : Theorem 1.09s 0.97s
% Output : Proof 1.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : CSR023+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n010.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Aug 30 16:13:59 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.33 Usage: tptp [options] [-file:]file
% 0.14/0.33 -h, -? prints this message.
% 0.14/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.33 -m, -model generate model.
% 0.14/0.33 -p, -proof generate proof.
% 0.14/0.33 -c, -core generate unsat core of named formulas.
% 0.14/0.33 -st, -statistics display statistics.
% 0.14/0.33 -t:timeout set timeout (in second).
% 0.14/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.33 -<param>:<value> configuration parameter and value.
% 0.14/0.33 -o:<output-file> file to place output in.
% 1.09/0.97 % SZS status Theorem
% 1.09/0.97 % SZS output start Proof
% 1.09/0.97 tff(initiates_type, type, (
% 1.09/0.97 initiates: ( $i * $i * $i ) > $o)).
% 1.09/0.97 tff(plus_type, type, (
% 1.09/0.97 plus: ( $i * $i ) > $i)).
% 1.09/0.97 tff(n1_type, type, (
% 1.09/0.97 n1: $i)).
% 1.09/0.97 tff(spinning_type, type, (
% 1.09/0.97 spinning: $i)).
% 1.09/0.97 tff(pull_type, type, (
% 1.09/0.97 pull: $i)).
% 1.09/0.97 tff(happens_type, type, (
% 1.09/0.97 happens: ( $i * $i ) > $o)).
% 1.09/0.97 tff(push_type, type, (
% 1.09/0.97 push: $i)).
% 1.09/0.97 tff(backwards_type, type, (
% 1.09/0.97 backwards: $i)).
% 1.09/0.97 tff(forwards_type, type, (
% 1.09/0.97 forwards: $i)).
% 1.09/0.97 tff(n0_type, type, (
% 1.09/0.97 n0: $i)).
% 1.09/0.97 tff(n2_type, type, (
% 1.09/0.97 n2: $i)).
% 1.09/0.97 tff(holdsAt_type, type, (
% 1.09/0.97 holdsAt: ( $i * $i ) > $o)).
% 1.09/0.97 tff(n3_type, type, (
% 1.09/0.97 n3: $i)).
% 1.09/0.97 tff(1,plain,
% 1.09/0.97 (^[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)))))))),
% 1.09/0.97 inference(bind,[status(th)],[])).
% 1.09/0.97 tff(2,plain,
% 1.09/0.97 (![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))))))),
% 1.09/0.97 inference(quant_intro,[status(thm)],[1])).
% 1.09/0.97 tff(3,plain,
% 1.09/0.97 (^[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)))))))),
% 1.09/0.97 inference(bind,[status(th)],[])).
% 1.09/0.97 tff(4,plain,
% 1.09/0.97 (![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))))))),
% 1.09/0.97 inference(quant_intro,[status(thm)],[3])).
% 1.09/0.97 tff(5,plain,
% 1.09/0.97 (![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))))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(6,plain,
% 1.09/0.97 (^[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)))))),
% 1.09/0.98 inference(bind,[status(th)],[])).
% 1.09/0.98 tff(7,plain,
% 1.09/0.98 (![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))))),
% 1.09/0.98 inference(quant_intro,[status(thm)],[6])).
% 1.09/0.98 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')).
% 1.09/0.98 tff(9,plain,
% 1.09/0.98 (![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))))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[8, 7])).
% 1.09/0.98 tff(10,plain,
% 1.09/0.98 (![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))))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[9, 5])).
% 1.09/0.98 tff(11,plain,(
% 1.09/0.98 ![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))))),
% 1.09/0.98 inference(skolemize,[status(sab)],[10])).
% 1.09/0.98 tff(12,plain,
% 1.09/0.98 (![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))))))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[11, 4])).
% 1.09/0.98 tff(13,plain,
% 1.09/0.98 (![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))))))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[12, 2])).
% 1.09/0.98 tff(14,plain,
% 1.09/0.98 (((~![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, spinning, plus(n1, n1)) <=> ((~((~(spinning = forwards)) | (~(pull = push)) | happens(pull, plus(n1, n1)))) | happens(push, plus(n1, n1)) | (~((~(spinning = backwards)) | happens(push, plus(n1, n1))))))) <=> ((~![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, spinning, plus(n1, n1)) <=> ((~((~(spinning = forwards)) | (~(pull = push)) | happens(pull, plus(n1, n1)))) | happens(push, plus(n1, n1)) | (~((~(spinning = backwards)) | happens(push, plus(n1, n1)))))))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(15,plain,
% 1.09/0.98 ((initiates(pull, spinning, plus(n1, n1)) <=> ((~(happens(pull, plus(n1, n1)) | (~(pull = push)) | (~(spinning = forwards)))) | (~(happens(push, plus(n1, n1)) | (~(pull = pull)) | (~(spinning = backwards)))) | (~((~happens(push, plus(n1, n1))) | (~(pull = pull)) | (~(spinning = spinning)))))) <=> (initiates(pull, spinning, plus(n1, n1)) <=> ((~((~(spinning = forwards)) | (~(pull = push)) | happens(pull, plus(n1, n1)))) | happens(push, plus(n1, n1)) | (~((~(spinning = backwards)) | happens(push, plus(n1, n1))))))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(16,plain,
% 1.09/0.98 (((~![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, spinning, plus(n1, n1)) <=> ((~(happens(pull, plus(n1, n1)) | (~(pull = push)) | (~(spinning = forwards)))) | (~(happens(push, plus(n1, n1)) | (~(pull = pull)) | (~(spinning = backwards)))) | (~((~happens(push, plus(n1, n1))) | (~(pull = pull)) | (~(spinning = 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, spinning, plus(n1, n1)) <=> ((~((~(spinning = forwards)) | (~(pull = push)) | happens(pull, plus(n1, n1)))) | happens(push, plus(n1, n1)) | (~((~(spinning = backwards)) | happens(push, plus(n1, n1)))))))),
% 1.09/0.98 inference(monotonicity,[status(thm)],[15])).
% 1.09/0.98 tff(17,plain,
% 1.09/0.98 (((~![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, spinning, plus(n1, n1)) <=> ((~(happens(pull, plus(n1, n1)) | (~(pull = push)) | (~(spinning = forwards)))) | (~(happens(push, plus(n1, n1)) | (~(pull = pull)) | (~(spinning = backwards)))) | (~((~happens(push, plus(n1, n1))) | (~(pull = pull)) | (~(spinning = 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, spinning, plus(n1, n1)) <=> ((~((~(spinning = forwards)) | (~(pull = push)) | happens(pull, plus(n1, n1)))) | happens(push, plus(n1, n1)) | (~((~(spinning = backwards)) | happens(push, plus(n1, n1)))))))),
% 1.09/0.98 inference(transitivity,[status(thm)],[16, 14])).
% 1.09/0.98 tff(18,plain,
% 1.09/0.98 ((~![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, spinning, plus(n1, n1)) <=> ((~(happens(pull, plus(n1, n1)) | (~(pull = push)) | (~(spinning = forwards)))) | (~(happens(push, plus(n1, n1)) | (~(pull = pull)) | (~(spinning = backwards)))) | (~((~happens(push, plus(n1, n1))) | (~(pull = pull)) | (~(spinning = spinning))))))),
% 1.09/0.98 inference(quant_inst,[status(thm)],[])).
% 1.09/0.98 tff(19,plain,
% 1.09/0.98 ((~![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, spinning, plus(n1, n1)) <=> ((~((~(spinning = forwards)) | (~(pull = push)) | happens(pull, plus(n1, n1)))) | happens(push, plus(n1, n1)) | (~((~(spinning = backwards)) | happens(push, plus(n1, n1))))))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.09/0.98 tff(20,plain,
% 1.09/0.98 (initiates(pull, spinning, plus(n1, n1)) <=> ((~((~(spinning = forwards)) | (~(pull = push)) | happens(pull, plus(n1, n1)))) | happens(push, plus(n1, n1)) | (~((~(spinning = backwards)) | happens(push, plus(n1, n1)))))),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[19, 13])).
% 1.09/0.98 tff(21,assumption,(~happens(push, plus(n1, n1))), introduced(assumption)).
% 1.09/0.98 tff(22,plain,
% 1.09/0.98 (^[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))))))))),
% 1.09/0.98 inference(bind,[status(th)],[])).
% 1.09/0.98 tff(23,plain,
% 1.09/0.98 (![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)))))))),
% 1.09/0.98 inference(quant_intro,[status(thm)],[22])).
% 1.09/0.98 tff(24,plain,
% 1.09/0.98 (^[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))))))))),
% 1.09/0.98 inference(bind,[status(th)],[])).
% 1.09/0.98 tff(25,plain,
% 1.09/0.98 (![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)))))))),
% 1.09/0.98 inference(quant_intro,[status(thm)],[24])).
% 1.09/0.98 tff(26,plain,
% 1.09/0.98 (^[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))))))),
% 1.09/0.98 inference(bind,[status(th)],[])).
% 1.09/0.98 tff(27,plain,
% 1.09/0.98 (![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)))))),
% 1.09/0.98 inference(quant_intro,[status(thm)],[26])).
% 1.09/0.98 tff(28,plain,
% 1.09/0.98 (![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))))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(29,plain,
% 1.09/0.98 (^[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)))))),
% 1.09/0.98 inference(bind,[status(th)],[])).
% 1.09/0.98 tff(30,plain,
% 1.09/0.98 (![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))))),
% 1.09/0.98 inference(quant_intro,[status(thm)],[29])).
% 1.09/0.98 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')).
% 1.09/0.98 tff(32,plain,
% 1.09/0.98 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[31, 30])).
% 1.09/0.98 tff(33,plain,
% 1.09/0.98 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[32, 28])).
% 1.09/0.98 tff(34,plain,
% 1.09/0.98 (![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)))))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[33, 27])).
% 1.09/0.98 tff(35,plain,(
% 1.09/0.98 ![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)))))),
% 1.09/0.98 inference(skolemize,[status(sab)],[34])).
% 1.09/0.98 tff(36,plain,
% 1.09/0.98 (![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)))))))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[35, 25])).
% 1.09/0.98 tff(37,plain,
% 1.09/0.98 (![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)))))))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[36, 23])).
% 1.09/0.98 tff(38,plain,
% 1.09/0.98 (((~![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, 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, plus(n1, n1)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(39,plain,
% 1.09/0.98 ((happens(push, plus(n1, n1)) <=> $true) <=> happens(push, plus(n1, n1))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(40,plain,
% 1.09/0.98 (((~((~(push = pull)) | (~(plus(n1, n1) = n1)))) | (plus(n1, n1) = n0) | $true | (push = pull)) <=> $true),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(41,plain,
% 1.09/0.98 ((~(~(push = pull))) <=> (push = pull)),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(42,plain,
% 1.09/0.98 (((~(push = pull)) | $false) <=> (~(push = pull))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(43,plain,
% 1.09/0.98 ((~$true) <=> $false),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(44,plain,
% 1.09/0.98 ((plus(n1, n1) = plus(n1, n1)) <=> $true),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(45,plain,
% 1.09/0.98 ((~(plus(n1, n1) = plus(n1, n1))) <=> (~$true)),
% 1.09/0.98 inference(monotonicity,[status(thm)],[44])).
% 1.09/0.98 tff(46,plain,
% 1.09/0.99 ((~(plus(n1, n1) = plus(n1, n1))) <=> $false),
% 1.09/0.99 inference(transitivity,[status(thm)],[45, 43])).
% 1.09/0.99 tff(47,plain,
% 1.09/0.99 (((~(push = pull)) | (~(plus(n1, n1) = plus(n1, n1)))) <=> ((~(push = pull)) | $false)),
% 1.09/0.99 inference(monotonicity,[status(thm)],[46])).
% 1.09/0.99 tff(48,plain,
% 1.09/0.99 (((~(push = pull)) | (~(plus(n1, n1) = plus(n1, n1)))) <=> (~(push = pull))),
% 1.09/0.99 inference(transitivity,[status(thm)],[47, 42])).
% 1.09/0.99 tff(49,plain,
% 1.09/0.99 ((~((~(push = pull)) | (~(plus(n1, n1) = plus(n1, n1))))) <=> (~(~(push = pull)))),
% 1.09/0.99 inference(monotonicity,[status(thm)],[48])).
% 1.09/0.99 tff(50,plain,
% 1.09/0.99 ((~((~(push = pull)) | (~(plus(n1, n1) = plus(n1, n1))))) <=> (push = pull)),
% 1.09/0.99 inference(transitivity,[status(thm)],[49, 41])).
% 1.09/0.99 tff(51,plain,
% 1.09/0.99 ((~$false) <=> $true),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(52,plain,
% 1.09/0.99 (($false | $false) <=> $false),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(53,plain,
% 1.09/0.99 ((push = push) <=> $true),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(54,plain,
% 1.09/0.99 ((~(push = push)) <=> (~$true)),
% 1.09/0.99 inference(monotonicity,[status(thm)],[53])).
% 1.09/0.99 tff(55,plain,
% 1.09/0.99 ((~(push = push)) <=> $false),
% 1.09/0.99 inference(transitivity,[status(thm)],[54, 43])).
% 1.09/0.99 tff(56,plain,
% 1.09/0.99 (((~(push = push)) | (~(plus(n1, n1) = plus(n1, n1)))) <=> ($false | $false)),
% 1.09/0.99 inference(monotonicity,[status(thm)],[55, 46])).
% 1.09/0.99 tff(57,plain,
% 1.09/0.99 (((~(push = push)) | (~(plus(n1, n1) = plus(n1, n1)))) <=> $false),
% 1.09/0.99 inference(transitivity,[status(thm)],[56, 52])).
% 1.09/0.99 tff(58,plain,
% 1.09/0.99 ((~((~(push = push)) | (~(plus(n1, n1) = plus(n1, n1))))) <=> (~$false)),
% 1.09/0.99 inference(monotonicity,[status(thm)],[57])).
% 1.09/0.99 tff(59,plain,
% 1.09/0.99 ((~((~(push = push)) | (~(plus(n1, n1) = plus(n1, n1))))) <=> $true),
% 1.09/0.99 inference(transitivity,[status(thm)],[58, 51])).
% 1.09/0.99 tff(60,plain,
% 1.09/0.99 ((~(~(plus(n1, n1) = n0))) <=> (plus(n1, n1) = n0)),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(61,plain,
% 1.09/0.99 (($false | (~(plus(n1, n1) = n0))) <=> (~(plus(n1, n1) = n0))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(62,plain,
% 1.09/0.99 (((~(push = push)) | (~(plus(n1, n1) = n0))) <=> ($false | (~(plus(n1, n1) = n0)))),
% 1.09/0.99 inference(monotonicity,[status(thm)],[55])).
% 1.09/0.99 tff(63,plain,
% 1.09/0.99 (((~(push = push)) | (~(plus(n1, n1) = n0))) <=> (~(plus(n1, n1) = n0))),
% 1.09/0.99 inference(transitivity,[status(thm)],[62, 61])).
% 1.09/0.99 tff(64,plain,
% 1.09/0.99 ((~((~(push = push)) | (~(plus(n1, n1) = n0)))) <=> (~(~(plus(n1, n1) = n0)))),
% 1.09/0.99 inference(monotonicity,[status(thm)],[63])).
% 1.09/0.99 tff(65,plain,
% 1.09/0.99 ((~((~(push = push)) | (~(plus(n1, n1) = n0)))) <=> (plus(n1, n1) = n0)),
% 1.09/0.99 inference(transitivity,[status(thm)],[64, 60])).
% 1.09/0.99 tff(66,plain,
% 1.09/0.99 (((~((~(push = pull)) | (~(plus(n1, n1) = n1)))) | (~((~(push = push)) | (~(plus(n1, n1) = n0)))) | (~((~(push = push)) | (~(plus(n1, n1) = plus(n1, n1))))) | (~((~(push = pull)) | (~(plus(n1, n1) = plus(n1, n1)))))) <=> ((~((~(push = pull)) | (~(plus(n1, n1) = n1)))) | (plus(n1, n1) = n0) | $true | (push = pull))),
% 1.09/0.99 inference(monotonicity,[status(thm)],[65, 59, 50])).
% 1.09/0.99 tff(67,plain,
% 1.09/0.99 (((~((~(push = pull)) | (~(plus(n1, n1) = n1)))) | (~((~(push = push)) | (~(plus(n1, n1) = n0)))) | (~((~(push = push)) | (~(plus(n1, n1) = plus(n1, n1))))) | (~((~(push = pull)) | (~(plus(n1, n1) = plus(n1, n1)))))) <=> $true),
% 1.09/0.99 inference(transitivity,[status(thm)],[66, 40])).
% 1.09/0.99 tff(68,plain,
% 1.09/0.99 ((happens(push, plus(n1, n1)) <=> ((~((~(push = pull)) | (~(plus(n1, n1) = n1)))) | (~((~(push = push)) | (~(plus(n1, n1) = n0)))) | (~((~(push = push)) | (~(plus(n1, n1) = plus(n1, n1))))) | (~((~(push = pull)) | (~(plus(n1, n1) = plus(n1, n1))))))) <=> (happens(push, plus(n1, n1)) <=> $true)),
% 1.09/0.99 inference(monotonicity,[status(thm)],[67])).
% 1.09/0.99 tff(69,plain,
% 1.09/0.99 ((happens(push, plus(n1, n1)) <=> ((~((~(push = pull)) | (~(plus(n1, n1) = n1)))) | (~((~(push = push)) | (~(plus(n1, n1) = n0)))) | (~((~(push = push)) | (~(plus(n1, n1) = plus(n1, n1))))) | (~((~(push = pull)) | (~(plus(n1, n1) = plus(n1, n1))))))) <=> happens(push, plus(n1, n1))),
% 1.09/0.99 inference(transitivity,[status(thm)],[68, 39])).
% 1.09/0.99 tff(70,plain,
% 1.09/0.99 (((~![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, plus(n1, n1)) <=> ((~((~(push = pull)) | (~(plus(n1, n1) = n1)))) | (~((~(push = push)) | (~(plus(n1, n1) = n0)))) | (~((~(push = push)) | (~(plus(n1, n1) = plus(n1, n1))))) | (~((~(push = pull)) | (~(plus(n1, 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, plus(n1, n1)))),
% 1.09/0.99 inference(monotonicity,[status(thm)],[69])).
% 1.09/0.99 tff(71,plain,
% 1.09/0.99 (((~![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, plus(n1, n1)) <=> ((~((~(push = pull)) | (~(plus(n1, n1) = n1)))) | (~((~(push = push)) | (~(plus(n1, n1) = n0)))) | (~((~(push = push)) | (~(plus(n1, n1) = plus(n1, n1))))) | (~((~(push = pull)) | (~(plus(n1, 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, plus(n1, n1)))),
% 1.09/0.99 inference(transitivity,[status(thm)],[70, 38])).
% 1.09/0.99 tff(72,plain,
% 1.09/0.99 ((~![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, plus(n1, n1)) <=> ((~((~(push = pull)) | (~(plus(n1, n1) = n1)))) | (~((~(push = push)) | (~(plus(n1, n1) = n0)))) | (~((~(push = push)) | (~(plus(n1, n1) = plus(n1, n1))))) | (~((~(push = pull)) | (~(plus(n1, n1) = plus(n1, n1)))))))),
% 1.09/0.99 inference(quant_inst,[status(thm)],[])).
% 1.09/0.99 tff(73,plain,
% 1.09/0.99 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))) | (~((~(Event = push)) | (~(Time = plus(n1, n1))))) | (~((~(Event = pull)) | (~(Time = plus(n1, n1)))))))) | happens(push, plus(n1, n1))),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[72, 71])).
% 1.09/0.99 tff(74,plain,
% 1.09/0.99 ($false),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[73, 37, 21])).
% 1.09/0.99 tff(75,plain,(happens(push, plus(n1, n1))), inference(lemma,lemma(discharge,[]))).
% 1.09/0.99 tff(76,plain,
% 1.09/0.99 (((~((~(spinning = forwards)) | (~(pull = push)) | happens(pull, plus(n1, n1)))) | happens(push, plus(n1, n1)) | (~((~(spinning = backwards)) | happens(push, plus(n1, n1))))) | (~happens(push, plus(n1, n1)))),
% 1.09/0.99 inference(tautology,[status(thm)],[])).
% 1.09/0.99 tff(77,plain,
% 1.09/0.99 ((~((~(spinning = forwards)) | (~(pull = push)) | happens(pull, plus(n1, n1)))) | happens(push, plus(n1, n1)) | (~((~(spinning = backwards)) | happens(push, plus(n1, n1))))),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[76, 75])).
% 1.09/0.99 tff(78,plain,
% 1.09/0.99 ((~(initiates(pull, spinning, plus(n1, n1)) <=> ((~((~(spinning = forwards)) | (~(pull = push)) | happens(pull, plus(n1, n1)))) | happens(push, plus(n1, n1)) | (~((~(spinning = backwards)) | happens(push, plus(n1, n1))))))) | initiates(pull, spinning, plus(n1, n1)) | (~((~((~(spinning = forwards)) | (~(pull = push)) | happens(pull, plus(n1, n1)))) | happens(push, plus(n1, n1)) | (~((~(spinning = backwards)) | happens(push, plus(n1, n1))))))),
% 1.09/0.99 inference(tautology,[status(thm)],[])).
% 1.09/0.99 tff(79,plain,
% 1.09/0.99 ((~(initiates(pull, spinning, plus(n1, n1)) <=> ((~((~(spinning = forwards)) | (~(pull = push)) | happens(pull, plus(n1, n1)))) | happens(push, plus(n1, n1)) | (~((~(spinning = backwards)) | happens(push, plus(n1, n1))))))) | initiates(pull, spinning, plus(n1, n1))),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[78, 77])).
% 1.09/0.99 tff(80,plain,
% 1.09/0.99 (initiates(pull, spinning, plus(n1, n1))),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[79, 20])).
% 1.09/0.99 tff(81,plain,
% 1.09/0.99 (((~![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, 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, plus(n1, n1)))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(82,plain,
% 1.09/0.99 ((happens(pull, plus(n1, n1)) <=> $true) <=> happens(pull, plus(n1, n1))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(83,plain,
% 1.09/0.99 (((plus(n1, n1) = n1) | (~((~(pull = push)) | (~(plus(n1, n1) = n0)))) | (pull = push) | $true) <=> $true),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(84,plain,
% 1.09/0.99 ((pull = pull) <=> $true),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(85,plain,
% 1.09/0.99 ((~(pull = pull)) <=> (~$true)),
% 1.09/0.99 inference(monotonicity,[status(thm)],[84])).
% 1.09/0.99 tff(86,plain,
% 1.09/0.99 ((~(pull = pull)) <=> $false),
% 1.09/0.99 inference(transitivity,[status(thm)],[85, 43])).
% 1.09/0.99 tff(87,plain,
% 1.09/0.99 (((~(pull = pull)) | (~(plus(n1, n1) = plus(n1, n1)))) <=> ($false | $false)),
% 1.09/0.99 inference(monotonicity,[status(thm)],[86, 46])).
% 1.09/0.99 tff(88,plain,
% 1.09/0.99 (((~(pull = pull)) | (~(plus(n1, n1) = plus(n1, n1)))) <=> $false),
% 1.09/0.99 inference(transitivity,[status(thm)],[87, 52])).
% 1.09/0.99 tff(89,plain,
% 1.09/0.99 ((~((~(pull = pull)) | (~(plus(n1, n1) = plus(n1, n1))))) <=> (~$false)),
% 1.09/0.99 inference(monotonicity,[status(thm)],[88])).
% 1.09/0.99 tff(90,plain,
% 1.09/0.99 ((~((~(pull = pull)) | (~(plus(n1, n1) = plus(n1, n1))))) <=> $true),
% 1.09/0.99 inference(transitivity,[status(thm)],[89, 51])).
% 1.09/0.99 tff(91,plain,
% 1.09/0.99 ((~(~(pull = push))) <=> (pull = push)),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(92,plain,
% 1.09/0.99 (((~(pull = push)) | $false) <=> (~(pull = push))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(93,plain,
% 1.09/0.99 (((~(pull = push)) | (~(plus(n1, n1) = plus(n1, n1)))) <=> ((~(pull = push)) | $false)),
% 1.09/0.99 inference(monotonicity,[status(thm)],[46])).
% 1.09/0.99 tff(94,plain,
% 1.09/0.99 (((~(pull = push)) | (~(plus(n1, n1) = plus(n1, n1)))) <=> (~(pull = push))),
% 1.09/0.99 inference(transitivity,[status(thm)],[93, 92])).
% 1.09/0.99 tff(95,plain,
% 1.09/0.99 ((~((~(pull = push)) | (~(plus(n1, n1) = plus(n1, n1))))) <=> (~(~(pull = push)))),
% 1.09/0.99 inference(monotonicity,[status(thm)],[94])).
% 1.09/0.99 tff(96,plain,
% 1.09/0.99 ((~((~(pull = push)) | (~(plus(n1, n1) = plus(n1, n1))))) <=> (pull = push)),
% 1.09/0.99 inference(transitivity,[status(thm)],[95, 91])).
% 1.09/0.99 tff(97,plain,
% 1.09/0.99 ((~(~(plus(n1, n1) = n1))) <=> (plus(n1, n1) = n1)),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(98,plain,
% 1.09/0.99 (($false | (~(plus(n1, n1) = n1))) <=> (~(plus(n1, n1) = n1))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(99,plain,
% 1.09/0.99 (((~(pull = pull)) | (~(plus(n1, n1) = n1))) <=> ($false | (~(plus(n1, n1) = n1)))),
% 1.09/0.99 inference(monotonicity,[status(thm)],[86])).
% 1.09/0.99 tff(100,plain,
% 1.09/0.99 (((~(pull = pull)) | (~(plus(n1, n1) = n1))) <=> (~(plus(n1, n1) = n1))),
% 1.09/0.99 inference(transitivity,[status(thm)],[99, 98])).
% 1.09/0.99 tff(101,plain,
% 1.09/0.99 ((~((~(pull = pull)) | (~(plus(n1, n1) = n1)))) <=> (~(~(plus(n1, n1) = n1)))),
% 1.09/0.99 inference(monotonicity,[status(thm)],[100])).
% 1.09/0.99 tff(102,plain,
% 1.09/0.99 ((~((~(pull = pull)) | (~(plus(n1, n1) = n1)))) <=> (plus(n1, n1) = n1)),
% 1.09/0.99 inference(transitivity,[status(thm)],[101, 97])).
% 1.09/0.99 tff(103,plain,
% 1.09/0.99 (((~((~(pull = pull)) | (~(plus(n1, n1) = n1)))) | (~((~(pull = push)) | (~(plus(n1, n1) = n0)))) | (~((~(pull = push)) | (~(plus(n1, n1) = plus(n1, n1))))) | (~((~(pull = pull)) | (~(plus(n1, n1) = plus(n1, n1)))))) <=> ((plus(n1, n1) = n1) | (~((~(pull = push)) | (~(plus(n1, n1) = n0)))) | (pull = push) | $true)),
% 1.09/0.99 inference(monotonicity,[status(thm)],[102, 96, 90])).
% 1.09/0.99 tff(104,plain,
% 1.09/0.99 (((~((~(pull = pull)) | (~(plus(n1, n1) = n1)))) | (~((~(pull = push)) | (~(plus(n1, n1) = n0)))) | (~((~(pull = push)) | (~(plus(n1, n1) = plus(n1, n1))))) | (~((~(pull = pull)) | (~(plus(n1, n1) = plus(n1, n1)))))) <=> $true),
% 1.09/0.99 inference(transitivity,[status(thm)],[103, 83])).
% 1.09/0.99 tff(105,plain,
% 1.09/0.99 ((happens(pull, plus(n1, n1)) <=> ((~((~(pull = pull)) | (~(plus(n1, n1) = n1)))) | (~((~(pull = push)) | (~(plus(n1, n1) = n0)))) | (~((~(pull = push)) | (~(plus(n1, n1) = plus(n1, n1))))) | (~((~(pull = pull)) | (~(plus(n1, n1) = plus(n1, n1))))))) <=> (happens(pull, plus(n1, n1)) <=> $true)),
% 1.09/0.99 inference(monotonicity,[status(thm)],[104])).
% 1.09/0.99 tff(106,plain,
% 1.09/0.99 ((happens(pull, plus(n1, n1)) <=> ((~((~(pull = pull)) | (~(plus(n1, n1) = n1)))) | (~((~(pull = push)) | (~(plus(n1, n1) = n0)))) | (~((~(pull = push)) | (~(plus(n1, n1) = plus(n1, n1))))) | (~((~(pull = pull)) | (~(plus(n1, n1) = plus(n1, n1))))))) <=> happens(pull, plus(n1, n1))),
% 1.09/0.99 inference(transitivity,[status(thm)],[105, 82])).
% 1.09/0.99 tff(107,plain,
% 1.09/0.99 (((~![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, plus(n1, n1)) <=> ((~((~(pull = pull)) | (~(plus(n1, n1) = n1)))) | (~((~(pull = push)) | (~(plus(n1, n1) = n0)))) | (~((~(pull = push)) | (~(plus(n1, n1) = plus(n1, n1))))) | (~((~(pull = pull)) | (~(plus(n1, 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, plus(n1, n1)))),
% 1.09/0.99 inference(monotonicity,[status(thm)],[106])).
% 1.09/0.99 tff(108,plain,
% 1.09/0.99 (((~![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, plus(n1, n1)) <=> ((~((~(pull = pull)) | (~(plus(n1, n1) = n1)))) | (~((~(pull = push)) | (~(plus(n1, n1) = n0)))) | (~((~(pull = push)) | (~(plus(n1, n1) = plus(n1, n1))))) | (~((~(pull = pull)) | (~(plus(n1, 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, plus(n1, n1)))),
% 1.09/0.99 inference(transitivity,[status(thm)],[107, 81])).
% 1.09/0.99 tff(109,plain,
% 1.09/0.99 ((~![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, plus(n1, n1)) <=> ((~((~(pull = pull)) | (~(plus(n1, n1) = n1)))) | (~((~(pull = push)) | (~(plus(n1, n1) = n0)))) | (~((~(pull = push)) | (~(plus(n1, n1) = plus(n1, n1))))) | (~((~(pull = pull)) | (~(plus(n1, n1) = plus(n1, n1)))))))),
% 1.09/0.99 inference(quant_inst,[status(thm)],[])).
% 1.09/0.99 tff(110,plain,
% 1.09/0.99 ((~![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, plus(n1, n1))),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.09/0.99 tff(111,plain,
% 1.09/0.99 (happens(pull, plus(n1, n1))),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[110, 37])).
% 1.09/0.99 tff(112,plain,
% 1.09/0.99 (^[X: $i, Y: $i] : refl((plus(X, Y) = plus(Y, X)) <=> (plus(X, Y) = plus(Y, X)))),
% 1.09/0.99 inference(bind,[status(th)],[])).
% 1.09/0.99 tff(113,plain,
% 1.09/0.99 (![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X)) <=> ![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 1.09/0.99 inference(quant_intro,[status(thm)],[112])).
% 1.09/0.99 tff(114,plain,
% 1.09/0.99 (![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X)) <=> ![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(115,axiom,(![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetry_of_plus')).
% 1.09/1.00 tff(116,plain,
% 1.09/1.00 (![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[115, 114])).
% 1.09/1.00 tff(117,plain,(
% 1.09/1.00 ![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 1.09/1.00 inference(skolemize,[status(sab)],[116])).
% 1.09/1.00 tff(118,plain,
% 1.09/1.00 (![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[117, 113])).
% 1.09/1.00 tff(119,plain,
% 1.09/1.00 ((~![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))) | (plus(n1, plus(n1, n1)) = plus(plus(n1, n1), n1))),
% 1.09/1.00 inference(quant_inst,[status(thm)],[])).
% 1.09/1.00 tff(120,plain,
% 1.09/1.00 (plus(n1, plus(n1, n1)) = plus(plus(n1, n1), n1)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[119, 118])).
% 1.09/1.00 tff(121,plain,
% 1.09/1.00 (plus(plus(n1, n1), n1) = plus(n1, plus(n1, n1))),
% 1.09/1.00 inference(symmetry,[status(thm)],[120])).
% 1.09/1.00 tff(122,plain,
% 1.09/1.00 (holdsAt(spinning, plus(plus(n1, n1), n1)) <=> holdsAt(spinning, plus(n1, plus(n1, n1)))),
% 1.09/1.00 inference(monotonicity,[status(thm)],[121])).
% 1.09/1.00 tff(123,plain,
% 1.09/1.00 (holdsAt(spinning, plus(n1, plus(n1, n1))) <=> holdsAt(spinning, plus(plus(n1, n1), n1))),
% 1.09/1.00 inference(symmetry,[status(thm)],[122])).
% 1.09/1.00 tff(124,plain,
% 1.09/1.00 ((~holdsAt(spinning, plus(n1, plus(n1, n1)))) <=> (~holdsAt(spinning, plus(plus(n1, n1), n1)))),
% 1.09/1.00 inference(monotonicity,[status(thm)],[123])).
% 1.09/1.00 tff(125,plain,
% 1.09/1.00 ((~holdsAt(spinning, n3)) <=> (~holdsAt(spinning, plus(n1, plus(n1, n1))))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(126,plain,
% 1.09/1.00 ((~holdsAt(spinning, n3)) <=> (~holdsAt(spinning, n3))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(127,axiom,(~holdsAt(spinning, n3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','spinning_3')).
% 1.09/1.00 tff(128,plain,
% 1.09/1.00 (~holdsAt(spinning, n3)),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[127, 126])).
% 1.09/1.00 tff(129,plain,
% 1.09/1.00 (~holdsAt(spinning, plus(n1, plus(n1, n1)))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[128, 125])).
% 1.09/1.00 tff(130,plain,
% 1.09/1.00 (~holdsAt(spinning, plus(plus(n1, n1), n1))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[129, 124])).
% 1.09/1.00 tff(131,plain,
% 1.09/1.00 (^[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))))),
% 1.09/1.00 inference(bind,[status(th)],[])).
% 1.09/1.00 tff(132,plain,
% 1.09/1.00 (![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)))),
% 1.09/1.00 inference(quant_intro,[status(thm)],[131])).
% 1.09/1.00 tff(133,plain,
% 1.09/1.00 (^[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)))))),
% 1.09/1.00 inference(bind,[status(th)],[])).
% 1.09/1.00 tff(134,plain,
% 1.09/1.00 (![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)))),
% 1.09/1.00 inference(quant_intro,[status(thm)],[133])).
% 1.09/1.00 tff(135,plain,
% 1.09/1.00 (![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)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(136,plain,
% 1.09/1.00 (^[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))))),
% 1.09/1.00 inference(bind,[status(th)],[])).
% 1.09/1.00 tff(137,plain,
% 1.09/1.00 (![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)))),
% 1.09/1.00 inference(quant_intro,[status(thm)],[136])).
% 1.09/1.00 tff(138,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')).
% 1.09/1.00 tff(139,plain,
% 1.09/1.00 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[138, 137])).
% 1.09/1.00 tff(140,plain,
% 1.09/1.00 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[139, 135])).
% 1.09/1.00 tff(141,plain,(
% 1.09/1.00 ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 1.09/1.00 inference(skolemize,[status(sab)],[140])).
% 1.09/1.00 tff(142,plain,
% 1.09/1.00 (![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[141, 134])).
% 1.09/1.00 tff(143,plain,
% 1.09/1.00 (![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[142, 132])).
% 1.09/1.00 tff(144,plain,
% 1.09/1.00 (((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | (holdsAt(spinning, plus(plus(n1, n1), n1)) | (~happens(pull, plus(n1, n1))) | (~initiates(pull, spinning, plus(n1, n1))))) <=> ((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | holdsAt(spinning, plus(plus(n1, n1), n1)) | (~happens(pull, plus(n1, n1))) | (~initiates(pull, spinning, plus(n1, n1))))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(145,plain,
% 1.09/1.00 ((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | (holdsAt(spinning, plus(plus(n1, n1), n1)) | (~happens(pull, plus(n1, n1))) | (~initiates(pull, spinning, plus(n1, n1))))),
% 1.09/1.00 inference(quant_inst,[status(thm)],[])).
% 1.09/1.00 tff(146,plain,
% 1.09/1.00 ((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | holdsAt(spinning, plus(plus(n1, n1), n1)) | (~happens(pull, plus(n1, n1))) | (~initiates(pull, spinning, plus(n1, n1)))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[145, 144])).
% 1.09/1.00 tff(147,plain,
% 1.09/1.00 ($false),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[146, 143, 130, 111, 80])).
% 1.09/1.00 % SZS output end Proof
%------------------------------------------------------------------------------