TSTP Solution File: CSR019+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CSR019+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 14:27:02 EDT 2022
% Result : Theorem 0.62s 0.68s
% Output : Proof 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CSR019+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 16:15:50 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.62/0.68 % SZS status Theorem
% 0.62/0.68 % SZS output start Proof
% 0.62/0.68 tff(terminates_type, type, (
% 0.62/0.68 terminates: ( $i * $i * $i ) > $o)).
% 0.62/0.68 tff(n1_type, type, (
% 0.62/0.68 n1: $i)).
% 0.62/0.68 tff(forwards_type, type, (
% 0.62/0.68 forwards: $i)).
% 0.62/0.68 tff(pull_type, type, (
% 0.62/0.68 pull: $i)).
% 0.62/0.68 tff(spinning_type, type, (
% 0.62/0.68 spinning: $i)).
% 0.62/0.68 tff(happens_type, type, (
% 0.62/0.68 happens: ( $i * $i ) > $o)).
% 0.62/0.68 tff(push_type, type, (
% 0.62/0.68 push: $i)).
% 0.62/0.68 tff(backwards_type, type, (
% 0.62/0.68 backwards: $i)).
% 0.62/0.68 tff(plus_type, type, (
% 0.62/0.68 plus: ( $i * $i ) > $i)).
% 0.62/0.68 tff(n0_type, type, (
% 0.62/0.68 n0: $i)).
% 0.62/0.68 tff(n2_type, type, (
% 0.62/0.68 n2: $i)).
% 0.62/0.68 tff(holdsAt_type, type, (
% 0.62/0.68 holdsAt: ( $i * $i ) > $o)).
% 0.62/0.68 tff(1,assumption,(~terminates(pull, forwards, n1)), introduced(assumption)).
% 0.62/0.68 tff(2,plain,
% 0.62/0.68 (^[Event: $i, Fluent: $i, Time: $i] : refl((terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning)))))) <=> (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning)))))))),
% 0.62/0.68 inference(bind,[status(th)],[])).
% 0.62/0.68 tff(3,plain,
% 0.62/0.68 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning)))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))),
% 0.62/0.68 inference(quant_intro,[status(thm)],[2])).
% 0.62/0.68 tff(4,plain,
% 0.62/0.68 (^[Event: $i, Fluent: $i, Time: $i] : rewrite((terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time))))) <=> (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning)))))))),
% 0.62/0.68 inference(bind,[status(th)],[])).
% 0.62/0.68 tff(5,plain,
% 0.62/0.68 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))),
% 0.62/0.68 inference(quant_intro,[status(thm)],[4])).
% 0.62/0.68 tff(6,plain,
% 0.62/0.68 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time)))))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(7,plain,
% 0.62/0.68 (^[Event: $i, Fluent: $i, Time: $i] : rewrite((terminates(Event, Fluent, Time) <=> ((((((((Event = push) & (Fluent = backwards)) & (~happens(pull, Time))) | (((Event = pull) & (Fluent = forwards)) & (~happens(push, Time)))) | (((Event = pull) & (Fluent = forwards)) & happens(push, Time))) | (((Event = pull) & (Fluent = backwards)) & happens(push, Time))) | (((Event = push) & (Fluent = spinning)) & (~happens(pull, Time)))) | (((Event = pull) & (Fluent = spinning)) & (~happens(push, Time))))) <=> (terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time))))))),
% 0.62/0.68 inference(bind,[status(th)],[])).
% 0.62/0.68 tff(8,plain,
% 0.62/0.68 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((((((((Event = push) & (Fluent = backwards)) & (~happens(pull, Time))) | (((Event = pull) & (Fluent = forwards)) & (~happens(push, Time)))) | (((Event = pull) & (Fluent = forwards)) & happens(push, Time))) | (((Event = pull) & (Fluent = backwards)) & happens(push, Time))) | (((Event = push) & (Fluent = spinning)) & (~happens(pull, Time)))) | (((Event = pull) & (Fluent = spinning)) & (~happens(push, Time))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time)))))),
% 0.62/0.68 inference(quant_intro,[status(thm)],[7])).
% 0.62/0.68 tff(9,axiom,(![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((((((((Event = push) & (Fluent = backwards)) & (~happens(pull, Time))) | (((Event = pull) & (Fluent = forwards)) & (~happens(push, Time)))) | (((Event = pull) & (Fluent = forwards)) & happens(push, Time))) | (((Event = pull) & (Fluent = backwards)) & happens(push, Time))) | (((Event = push) & (Fluent = spinning)) & (~happens(pull, Time)))) | (((Event = pull) & (Fluent = spinning)) & (~happens(push, Time)))))), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax','terminates_all_defn')).
% 0.62/0.68 tff(10,plain,
% 0.62/0.68 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time)))))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.62/0.68 tff(11,plain,
% 0.62/0.68 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time)))))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.62/0.68 tff(12,plain,(
% 0.62/0.68 ![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = backwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = forwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = forwards) & happens(push, Time)) | ((Event = pull) & (Fluent = backwards) & happens(push, Time)) | ((Event = push) & (Fluent = spinning) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = spinning) & (~happens(push, Time)))))),
% 0.62/0.68 inference(skolemize,[status(sab)],[11])).
% 0.62/0.68 tff(13,plain,
% 0.62/0.68 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.62/0.68 tff(14,plain,
% 0.62/0.68 (![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.62/0.68 tff(15,plain,
% 0.62/0.68 (((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))) | terminates(pull, forwards, n1)) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))) | terminates(pull, forwards, n1))),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(16,plain,
% 0.71/0.69 ((terminates(pull, forwards, n1) <=> $true) <=> terminates(pull, forwards, n1)),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(17,plain,
% 0.71/0.69 (((~((~(forwards = backwards)) | (~(pull = push)) | happens(pull, n1))) | (~happens(push, n1)) | happens(push, n1) | (~((~(forwards = backwards)) | (~happens(push, n1)))) | (~((~(forwards = spinning)) | (~(pull = push)) | happens(pull, n1))) | (~((~(forwards = spinning)) | happens(push, n1)))) <=> $true),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(18,plain,
% 0.71/0.69 ((~(happens(push, n1) | (~(pull = pull)) | (~(forwards = spinning)))) <=> (~((~(forwards = spinning)) | happens(push, n1)))),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(19,plain,
% 0.71/0.69 ((~(happens(pull, n1) | (~(pull = push)) | (~(forwards = spinning)))) <=> (~((~(forwards = spinning)) | (~(pull = push)) | happens(pull, n1)))),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(20,plain,
% 0.71/0.69 ((~((~happens(push, n1)) | (~(pull = pull)) | (~(forwards = backwards)))) <=> (~((~(forwards = backwards)) | (~happens(push, n1))))),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(21,plain,
% 0.71/0.69 ((~(~happens(push, n1))) <=> happens(push, n1)),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(22,plain,
% 0.71/0.69 (((~happens(push, n1)) | $false | $false) <=> (~happens(push, n1))),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(23,plain,
% 0.71/0.69 ((~$true) <=> $false),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(24,plain,
% 0.71/0.69 ((pull = pull) <=> $true),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(25,plain,
% 0.71/0.69 ((~(pull = pull)) <=> (~$true)),
% 0.71/0.69 inference(monotonicity,[status(thm)],[24])).
% 0.71/0.69 tff(26,plain,
% 0.71/0.69 ((~(pull = pull)) <=> $false),
% 0.71/0.69 inference(transitivity,[status(thm)],[25, 23])).
% 0.71/0.69 tff(27,plain,
% 0.71/0.69 ((forwards = forwards) <=> $true),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(28,plain,
% 0.71/0.69 ((~(forwards = forwards)) <=> (~$true)),
% 0.71/0.69 inference(monotonicity,[status(thm)],[27])).
% 0.71/0.69 tff(29,plain,
% 0.71/0.69 ((~(forwards = forwards)) <=> $false),
% 0.71/0.69 inference(transitivity,[status(thm)],[28, 23])).
% 0.71/0.69 tff(30,plain,
% 0.71/0.69 (((~happens(push, n1)) | (~(forwards = forwards)) | (~(pull = pull))) <=> ((~happens(push, n1)) | $false | $false)),
% 0.71/0.69 inference(monotonicity,[status(thm)],[29, 26])).
% 0.71/0.69 tff(31,plain,
% 0.71/0.69 (((~happens(push, n1)) | (~(forwards = forwards)) | (~(pull = pull))) <=> (~happens(push, n1))),
% 0.71/0.69 inference(transitivity,[status(thm)],[30, 22])).
% 0.71/0.69 tff(32,plain,
% 0.71/0.69 ((~((~happens(push, n1)) | (~(forwards = forwards)) | (~(pull = pull)))) <=> (~(~happens(push, n1)))),
% 0.71/0.69 inference(monotonicity,[status(thm)],[31])).
% 0.71/0.69 tff(33,plain,
% 0.71/0.69 ((~((~happens(push, n1)) | (~(forwards = forwards)) | (~(pull = pull)))) <=> happens(push, n1)),
% 0.71/0.69 inference(transitivity,[status(thm)],[32, 21])).
% 0.71/0.69 tff(34,plain,
% 0.71/0.69 ((~(happens(push, n1) | (~(forwards = forwards)) | (~(pull = pull)))) <=> (~happens(push, n1))),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(35,plain,
% 0.71/0.69 ((~(happens(pull, n1) | (~(pull = push)) | (~(forwards = backwards)))) <=> (~((~(forwards = backwards)) | (~(pull = push)) | happens(pull, n1)))),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(36,plain,
% 0.71/0.69 (((~(happens(pull, n1) | (~(pull = push)) | (~(forwards = backwards)))) | (~(happens(push, n1) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n1)) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n1)) | (~(pull = pull)) | (~(forwards = backwards)))) | (~(happens(pull, n1) | (~(pull = push)) | (~(forwards = spinning)))) | (~(happens(push, n1) | (~(pull = pull)) | (~(forwards = spinning))))) <=> ((~((~(forwards = backwards)) | (~(pull = push)) | happens(pull, n1))) | (~happens(push, n1)) | happens(push, n1) | (~((~(forwards = backwards)) | (~happens(push, n1)))) | (~((~(forwards = spinning)) | (~(pull = push)) | happens(pull, n1))) | (~((~(forwards = spinning)) | happens(push, n1))))),
% 0.71/0.69 inference(monotonicity,[status(thm)],[35, 34, 33, 20, 19, 18])).
% 0.71/0.69 tff(37,plain,
% 0.71/0.69 (((~(happens(pull, n1) | (~(pull = push)) | (~(forwards = backwards)))) | (~(happens(push, n1) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n1)) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n1)) | (~(pull = pull)) | (~(forwards = backwards)))) | (~(happens(pull, n1) | (~(pull = push)) | (~(forwards = spinning)))) | (~(happens(push, n1) | (~(pull = pull)) | (~(forwards = spinning))))) <=> $true),
% 0.71/0.69 inference(transitivity,[status(thm)],[36, 17])).
% 0.71/0.69 tff(38,plain,
% 0.71/0.69 ((terminates(pull, forwards, n1) <=> ((~(happens(pull, n1) | (~(pull = push)) | (~(forwards = backwards)))) | (~(happens(push, n1) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n1)) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n1)) | (~(pull = pull)) | (~(forwards = backwards)))) | (~(happens(pull, n1) | (~(pull = push)) | (~(forwards = spinning)))) | (~(happens(push, n1) | (~(pull = pull)) | (~(forwards = spinning)))))) <=> (terminates(pull, forwards, n1) <=> $true)),
% 0.71/0.69 inference(monotonicity,[status(thm)],[37])).
% 0.71/0.69 tff(39,plain,
% 0.71/0.69 ((terminates(pull, forwards, n1) <=> ((~(happens(pull, n1) | (~(pull = push)) | (~(forwards = backwards)))) | (~(happens(push, n1) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n1)) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n1)) | (~(pull = pull)) | (~(forwards = backwards)))) | (~(happens(pull, n1) | (~(pull = push)) | (~(forwards = spinning)))) | (~(happens(push, n1) | (~(pull = pull)) | (~(forwards = spinning)))))) <=> terminates(pull, forwards, n1)),
% 0.71/0.69 inference(transitivity,[status(thm)],[38, 16])).
% 0.71/0.69 tff(40,plain,
% 0.71/0.69 (((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (terminates(pull, forwards, n1) <=> ((~(happens(pull, n1) | (~(pull = push)) | (~(forwards = backwards)))) | (~(happens(push, n1) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n1)) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n1)) | (~(pull = pull)) | (~(forwards = backwards)))) | (~(happens(pull, n1) | (~(pull = push)) | (~(forwards = spinning)))) | (~(happens(push, n1) | (~(pull = pull)) | (~(forwards = spinning))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))) | terminates(pull, forwards, n1))),
% 0.71/0.69 inference(monotonicity,[status(thm)],[39])).
% 0.71/0.69 tff(41,plain,
% 0.71/0.69 (((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (terminates(pull, forwards, n1) <=> ((~(happens(pull, n1) | (~(pull = push)) | (~(forwards = backwards)))) | (~(happens(push, n1) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n1)) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n1)) | (~(pull = pull)) | (~(forwards = backwards)))) | (~(happens(pull, n1) | (~(pull = push)) | (~(forwards = spinning)))) | (~(happens(push, n1) | (~(pull = pull)) | (~(forwards = spinning))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))) | terminates(pull, forwards, n1))),
% 0.71/0.69 inference(transitivity,[status(thm)],[40, 15])).
% 0.71/0.69 tff(42,plain,
% 0.71/0.69 ((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (terminates(pull, forwards, n1) <=> ((~(happens(pull, n1) | (~(pull = push)) | (~(forwards = backwards)))) | (~(happens(push, n1) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n1)) | (~(forwards = forwards)) | (~(pull = pull)))) | (~((~happens(push, n1)) | (~(pull = pull)) | (~(forwards = backwards)))) | (~(happens(pull, n1) | (~(pull = push)) | (~(forwards = spinning)))) | (~(happens(push, n1) | (~(pull = pull)) | (~(forwards = spinning))))))),
% 0.71/0.69 inference(quant_inst,[status(thm)],[])).
% 0.71/0.69 tff(43,plain,
% 0.71/0.69 ((~![Event: $i, Fluent: $i, Time: $i] : (terminates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = backwards)))) | (~(happens(push, Time) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Fluent = forwards)) | (~(Event = pull)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = spinning)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = spinning))))))) | terminates(pull, forwards, n1)),
% 0.71/0.69 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.71/0.69 tff(44,plain,
% 0.71/0.69 ($false),
% 0.71/0.69 inference(unit_resolution,[status(thm)],[43, 14, 1])).
% 0.71/0.69 tff(45,plain,(terminates(pull, forwards, n1)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.69 tff(46,plain,
% 0.71/0.69 (^[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))))))))),
% 0.71/0.69 inference(bind,[status(th)],[])).
% 0.71/0.69 tff(47,plain,
% 0.71/0.69 (![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)))))))),
% 0.71/0.69 inference(quant_intro,[status(thm)],[46])).
% 0.71/0.69 tff(48,plain,
% 0.71/0.69 (^[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))))))))),
% 0.71/0.69 inference(bind,[status(th)],[])).
% 0.71/0.69 tff(49,plain,
% 0.71/0.69 (![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)))))))),
% 0.71/0.69 inference(quant_intro,[status(thm)],[48])).
% 0.71/0.69 tff(50,plain,
% 0.71/0.69 (^[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))))))),
% 0.71/0.69 inference(bind,[status(th)],[])).
% 0.71/0.69 tff(51,plain,
% 0.71/0.69 (![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)))))),
% 0.71/0.69 inference(quant_intro,[status(thm)],[50])).
% 0.71/0.69 tff(52,plain,
% 0.71/0.69 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(53,plain,
% 0.71/0.69 (^[Event: $i, Time: $i] : rewrite((happens(Event, Time) <=> (((((Event = push) & (Time = n0)) | ((Event = pull) & (Time = n1))) | ((Event = pull) & (Time = n2))) | ((Event = push) & (Time = n2)))) <=> (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)))))),
% 0.71/0.69 inference(bind,[status(th)],[])).
% 0.71/0.69 tff(54,plain,
% 0.71/0.69 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((((Event = push) & (Time = n0)) | ((Event = pull) & (Time = n1))) | ((Event = pull) & (Time = n2))) | ((Event = push) & (Time = n2)))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 0.71/0.69 inference(quant_intro,[status(thm)],[53])).
% 0.71/0.69 tff(55,axiom,(![Event: $i, Time: $i] : (happens(Event, Time) <=> (((((Event = push) & (Time = n0)) | ((Event = pull) & (Time = n1))) | ((Event = pull) & (Time = n2))) | ((Event = push) & (Time = n2))))), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax','happens_all_defn')).
% 0.71/0.69 tff(56,plain,
% 0.71/0.69 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 0.71/0.69 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.71/0.69 tff(57,plain,
% 0.71/0.69 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 0.71/0.69 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.71/0.69 tff(58,plain,
% 0.71/0.69 (![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)))))),
% 0.71/0.69 inference(modus_ponens,[status(thm)],[57, 51])).
% 0.71/0.69 tff(59,plain,(
% 0.71/0.69 ![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)))))),
% 0.71/0.69 inference(skolemize,[status(sab)],[58])).
% 0.71/0.69 tff(60,plain,
% 0.71/0.69 (![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)))))))),
% 0.71/0.69 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.71/0.69 tff(61,plain,
% 0.71/0.69 (![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)))))))),
% 0.71/0.69 inference(modus_ponens,[status(thm)],[60, 47])).
% 0.71/0.69 tff(62,plain,
% 0.71/0.69 (((~![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))),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(63,plain,
% 0.71/0.69 ((happens(pull, n1) <=> $true) <=> happens(pull, n1)),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(64,plain,
% 0.71/0.69 (($true | (~((~(pull = push)) | (~(n1 = n0)))) | (~((~(pull = push)) | (~(n1 = plus(n1, n1))))) | (n1 = plus(n1, n1))) <=> $true),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(65,plain,
% 0.71/0.69 ((~(~(n1 = plus(n1, n1)))) <=> (n1 = plus(n1, n1))),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(66,plain,
% 0.71/0.69 (($false | (~(n1 = plus(n1, n1)))) <=> (~(n1 = plus(n1, n1)))),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(67,plain,
% 0.71/0.69 (((~(pull = pull)) | (~(n1 = plus(n1, n1)))) <=> ($false | (~(n1 = plus(n1, n1))))),
% 0.71/0.69 inference(monotonicity,[status(thm)],[26])).
% 0.71/0.69 tff(68,plain,
% 0.71/0.69 (((~(pull = pull)) | (~(n1 = plus(n1, n1)))) <=> (~(n1 = plus(n1, n1)))),
% 0.71/0.69 inference(transitivity,[status(thm)],[67, 66])).
% 0.71/0.69 tff(69,plain,
% 0.71/0.69 ((~((~(pull = pull)) | (~(n1 = plus(n1, n1))))) <=> (~(~(n1 = plus(n1, n1))))),
% 0.71/0.69 inference(monotonicity,[status(thm)],[68])).
% 0.71/0.69 tff(70,plain,
% 0.71/0.69 ((~((~(pull = pull)) | (~(n1 = plus(n1, n1))))) <=> (n1 = plus(n1, n1))),
% 0.71/0.69 inference(transitivity,[status(thm)],[69, 65])).
% 0.71/0.69 tff(71,plain,
% 0.71/0.69 ((~((~(pull = push)) | (~(n1 = n0)))) <=> (~((~(pull = push)) | (~(n1 = n0))))),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(72,plain,
% 0.71/0.69 ((~$false) <=> $true),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(73,plain,
% 0.71/0.69 (($false | $false) <=> $false),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(74,plain,
% 0.71/0.69 ((n1 = n1) <=> $true),
% 0.71/0.69 inference(rewrite,[status(thm)],[])).
% 0.71/0.69 tff(75,plain,
% 0.71/0.69 ((~(n1 = n1)) <=> (~$true)),
% 0.71/0.69 inference(monotonicity,[status(thm)],[74])).
% 0.71/0.69 tff(76,plain,
% 0.71/0.69 ((~(n1 = n1)) <=> $false),
% 0.71/0.69 inference(transitivity,[status(thm)],[75, 23])).
% 0.71/0.69 tff(77,plain,
% 0.71/0.69 (((~(pull = pull)) | (~(n1 = n1))) <=> ($false | $false)),
% 0.71/0.69 inference(monotonicity,[status(thm)],[26, 76])).
% 0.71/0.69 tff(78,plain,
% 0.71/0.69 (((~(pull = pull)) | (~(n1 = n1))) <=> $false),
% 0.71/0.69 inference(transitivity,[status(thm)],[77, 73])).
% 0.71/0.69 tff(79,plain,
% 0.71/0.69 ((~((~(pull = pull)) | (~(n1 = n1)))) <=> (~$false)),
% 0.71/0.69 inference(monotonicity,[status(thm)],[78])).
% 0.71/0.69 tff(80,plain,
% 0.71/0.69 ((~((~(pull = pull)) | (~(n1 = n1)))) <=> $true),
% 0.71/0.69 inference(transitivity,[status(thm)],[79, 72])).
% 0.71/0.69 tff(81,plain,
% 0.71/0.69 (((~((~(pull = pull)) | (~(n1 = n1)))) | (~((~(pull = push)) | (~(n1 = n0)))) | (~((~(pull = push)) | (~(n1 = plus(n1, n1))))) | (~((~(pull = pull)) | (~(n1 = plus(n1, n1)))))) <=> ($true | (~((~(pull = push)) | (~(n1 = n0)))) | (~((~(pull = push)) | (~(n1 = plus(n1, n1))))) | (n1 = plus(n1, n1)))),
% 0.71/0.69 inference(monotonicity,[status(thm)],[80, 71, 70])).
% 0.71/0.69 tff(82,plain,
% 0.71/0.69 (((~((~(pull = pull)) | (~(n1 = n1)))) | (~((~(pull = push)) | (~(n1 = n0)))) | (~((~(pull = push)) | (~(n1 = plus(n1, n1))))) | (~((~(pull = pull)) | (~(n1 = plus(n1, n1)))))) <=> $true),
% 0.71/0.70 inference(transitivity,[status(thm)],[81, 64])).
% 0.71/0.70 tff(83,plain,
% 0.71/0.70 ((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)),
% 0.71/0.70 inference(monotonicity,[status(thm)],[82])).
% 0.71/0.70 tff(84,plain,
% 0.71/0.70 ((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)),
% 0.71/0.70 inference(transitivity,[status(thm)],[83, 63])).
% 0.71/0.70 tff(85,plain,
% 0.71/0.70 (((~![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))),
% 0.71/0.70 inference(monotonicity,[status(thm)],[84])).
% 0.71/0.70 tff(86,plain,
% 0.71/0.70 (((~![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))),
% 0.71/0.70 inference(transitivity,[status(thm)],[85, 62])).
% 0.71/0.70 tff(87,plain,
% 0.71/0.70 ((~![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)))))))),
% 0.71/0.70 inference(quant_inst,[status(thm)],[])).
% 0.71/0.70 tff(88,plain,
% 0.71/0.70 ((~![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)),
% 0.71/0.70 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.71/0.70 tff(89,plain,
% 0.71/0.70 (happens(pull, n1)),
% 0.71/0.70 inference(unit_resolution,[status(thm)],[88, 61])).
% 0.71/0.70 tff(90,plain,
% 0.71/0.70 (holdsAt(forwards, n2) <=> holdsAt(forwards, plus(n1, n1))),
% 0.71/0.70 inference(rewrite,[status(thm)],[])).
% 0.71/0.70 tff(91,plain,
% 0.71/0.70 (holdsAt(forwards, n2) <=> holdsAt(forwards, n2)),
% 0.71/0.70 inference(rewrite,[status(thm)],[])).
% 0.71/0.70 tff(92,plain,
% 0.71/0.70 ((~(~holdsAt(forwards, n2))) <=> holdsAt(forwards, n2)),
% 0.71/0.70 inference(rewrite,[status(thm)],[])).
% 0.71/0.70 tff(93,axiom,(~(~holdsAt(forwards, n2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_forwards_2')).
% 0.71/0.70 tff(94,plain,
% 0.71/0.70 (holdsAt(forwards, n2)),
% 0.71/0.70 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.71/0.70 tff(95,plain,
% 0.71/0.70 (holdsAt(forwards, n2)),
% 0.71/0.70 inference(modus_ponens,[status(thm)],[94, 91])).
% 0.71/0.70 tff(96,plain,
% 0.71/0.70 (holdsAt(forwards, plus(n1, n1))),
% 0.71/0.70 inference(modus_ponens,[status(thm)],[95, 90])).
% 0.71/0.70 tff(97,plain,
% 0.71/0.70 (^[Event: $i, Time: $i, Fluent: $i] : refl(((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time))) <=> ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time))))),
% 0.71/0.70 inference(bind,[status(th)],[])).
% 0.71/0.70 tff(98,plain,
% 0.71/0.70 (![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))),
% 0.71/0.70 inference(quant_intro,[status(thm)],[97])).
% 0.71/0.70 tff(99,plain,
% 0.71/0.70 (^[Event: $i, Time: $i, Fluent: $i] : trans(monotonicity(trans(monotonicity(rewrite((happens(Event, Time) & terminates(Event, Fluent, Time)) <=> (~((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))))), ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) <=> (~(~((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))))))), rewrite((~(~((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))))) <=> ((~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))), ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) <=> ((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))))), (((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))) <=> (((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))))), rewrite((((~happens(Event, Time)) | (~terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))) <=> ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))), (((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))) <=> ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))))),
% 0.71/0.70 inference(bind,[status(th)],[])).
% 0.71/0.70 tff(100,plain,
% 0.71/0.70 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))),
% 0.71/0.70 inference(quant_intro,[status(thm)],[99])).
% 0.71/0.70 tff(101,plain,
% 0.71/0.70 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1))))),
% 0.71/0.70 inference(rewrite,[status(thm)],[])).
% 0.71/0.70 tff(102,plain,
% 0.71/0.70 (^[Event: $i, Time: $i, Fluent: $i] : rewrite(((happens(Event, Time) & terminates(Event, Fluent, Time)) => (~holdsAt(Fluent, plus(Time, n1)))) <=> ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1)))))),
% 0.71/0.70 inference(bind,[status(th)],[])).
% 0.71/0.70 tff(103,plain,
% 0.71/0.70 (![Event: $i, Time: $i, Fluent: $i] : ((happens(Event, Time) & terminates(Event, Fluent, Time)) => (~holdsAt(Fluent, plus(Time, n1)))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1))))),
% 0.71/0.70 inference(quant_intro,[status(thm)],[102])).
% 0.71/0.70 tff(104,axiom,(![Event: $i, Time: $i, Fluent: $i] : ((happens(Event, Time) & terminates(Event, Fluent, Time)) => (~holdsAt(Fluent, plus(Time, n1))))), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+0.ax','happens_terminates_not_holds')).
% 0.71/0.70 tff(105,plain,
% 0.71/0.70 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1))))),
% 0.71/0.70 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.71/0.70 tff(106,plain,
% 0.71/0.70 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1))))),
% 0.71/0.70 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.71/0.70 tff(107,plain,(
% 0.71/0.70 ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & terminates(Event, Fluent, Time))) | (~holdsAt(Fluent, plus(Time, n1))))),
% 0.71/0.70 inference(skolemize,[status(sab)],[106])).
% 0.71/0.70 tff(108,plain,
% 0.71/0.70 (![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))),
% 0.71/0.70 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.71/0.70 tff(109,plain,
% 0.71/0.70 (![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))),
% 0.71/0.70 inference(modus_ponens,[status(thm)],[108, 98])).
% 0.71/0.70 tff(110,plain,
% 0.71/0.70 (((~![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))) | ((~holdsAt(forwards, plus(n1, n1))) | (~happens(pull, n1)) | (~terminates(pull, forwards, n1)))) <=> ((~![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))) | (~holdsAt(forwards, plus(n1, n1))) | (~happens(pull, n1)) | (~terminates(pull, forwards, n1)))),
% 0.71/0.70 inference(rewrite,[status(thm)],[])).
% 0.71/0.70 tff(111,plain,
% 0.71/0.70 ((~![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))) | ((~holdsAt(forwards, plus(n1, n1))) | (~happens(pull, n1)) | (~terminates(pull, forwards, n1)))),
% 0.71/0.70 inference(quant_inst,[status(thm)],[])).
% 0.71/0.70 tff(112,plain,
% 0.71/0.70 ((~![Event: $i, Time: $i, Fluent: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~happens(Event, Time)) | (~terminates(Event, Fluent, Time)))) | (~holdsAt(forwards, plus(n1, n1))) | (~happens(pull, n1)) | (~terminates(pull, forwards, n1))),
% 0.71/0.70 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.71/0.70 tff(113,plain,
% 0.71/0.70 ($false),
% 0.71/0.70 inference(unit_resolution,[status(thm)],[112, 109, 96, 89, 45])).
% 0.71/0.70 % SZS output end Proof
%------------------------------------------------------------------------------