TSTP Solution File: CSR017+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CSR017+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : CSR017+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n014.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 30 16:13:48 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.35 Usage: tptp [options] [-file:]file
% 0.15/0.35 -h, -? prints this message.
% 0.15/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.35 -m, -model generate model.
% 0.15/0.35 -p, -proof generate proof.
% 0.15/0.35 -c, -core generate unsat core of named formulas.
% 0.15/0.35 -st, -statistics display statistics.
% 0.15/0.35 -t:timeout set timeout (in second).
% 0.15/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.35 -<param>:<value> configuration parameter and value.
% 0.15/0.35 -o:<output-file> file to place output in.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 tff(less_type, type, (
% 0.21/0.45 less: ( $i * $i ) > $o)).
% 0.21/0.45 tff(plus_type, type, (
% 0.21/0.45 plus: ( $i * $i ) > $i)).
% 0.21/0.45 tff(n1_type, type, (
% 0.21/0.45 n1: $i)).
% 0.21/0.45 tff(n0_type, type, (
% 0.21/0.45 n0: $i)).
% 0.21/0.45 tff(initiates_type, type, (
% 0.21/0.45 initiates: ( $i * $i * $i ) > $o)).
% 0.21/0.45 tff(spinning_type, type, (
% 0.21/0.45 spinning: $i)).
% 0.21/0.45 tff(tptp_fun_Event_5_type, type, (
% 0.21/0.45 tptp_fun_Event_5: ( $i * $i ) > $i)).
% 0.21/0.45 tff(happens_type, type, (
% 0.21/0.45 happens: ( $i * $i ) > $o)).
% 0.21/0.45 tff(releasedAt_type, type, (
% 0.21/0.45 releasedAt: ( $i * $i ) > $o)).
% 0.21/0.45 tff(holdsAt_type, type, (
% 0.21/0.45 holdsAt: ( $i * $i ) > $o)).
% 0.21/0.45 tff(pull_type, type, (
% 0.21/0.45 pull: $i)).
% 0.21/0.45 tff(push_type, type, (
% 0.21/0.45 push: $i)).
% 0.21/0.45 tff(backwards_type, type, (
% 0.21/0.45 backwards: $i)).
% 0.21/0.45 tff(forwards_type, type, (
% 0.21/0.45 forwards: $i)).
% 0.21/0.45 tff(n2_type, type, (
% 0.21/0.45 n2: $i)).
% 0.21/0.45 tff(less_or_equal_type, type, (
% 0.21/0.45 less_or_equal: ( $i * $i ) > $o)).
% 0.21/0.45 tff(n3_type, type, (
% 0.21/0.45 n3: $i)).
% 0.21/0.45 tff(n4_type, type, (
% 0.21/0.45 n4: $i)).
% 0.21/0.45 tff(1,plain,
% 0.21/0.45 ((plus(n0, n1) = n1) <=> (plus(n0, n1) = n1)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(2,axiom,(plus(n0, n1) = n1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus0_1')).
% 0.21/0.45 tff(3,plain,
% 0.21/0.45 (plus(n0, n1) = n1),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.21/0.45 tff(4,plain,
% 0.21/0.45 (n1 = plus(n0, n1)),
% 0.21/0.45 inference(symmetry,[status(thm)],[3])).
% 0.21/0.45 tff(5,plain,
% 0.21/0.45 (releasedAt(spinning, n1) <=> releasedAt(spinning, plus(n0, n1))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[4])).
% 0.21/0.45 tff(6,plain,
% 0.21/0.45 ((~releasedAt(spinning, n1)) <=> (~releasedAt(spinning, plus(n0, n1)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[5])).
% 0.21/0.45 tff(7,assumption,(releasedAt(spinning, n1)), introduced(assumption)).
% 0.21/0.45 tff(8,plain,
% 0.21/0.45 (^[Fluent: $i, Time: $i] : refl((~releasedAt(Fluent, Time)) <=> (~releasedAt(Fluent, Time)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(9,plain,
% 0.21/0.45 (![Fluent: $i, Time: $i] : (~releasedAt(Fluent, Time)) <=> ![Fluent: $i, Time: $i] : (~releasedAt(Fluent, Time))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.45 tff(10,plain,
% 0.21/0.45 (![Fluent: $i, Time: $i] : (~releasedAt(Fluent, Time)) <=> ![Fluent: $i, Time: $i] : (~releasedAt(Fluent, Time))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(11,axiom,(![Fluent: $i, Time: $i] : (~releasedAt(Fluent, Time))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_releasedAt')).
% 0.21/0.45 tff(12,plain,
% 0.21/0.45 (![Fluent: $i, Time: $i] : (~releasedAt(Fluent, Time))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.45 tff(13,plain,(
% 0.21/0.45 ![Fluent: $i, Time: $i] : (~releasedAt(Fluent, Time))),
% 0.21/0.45 inference(skolemize,[status(sab)],[12])).
% 0.21/0.45 tff(14,plain,
% 0.21/0.45 (![Fluent: $i, Time: $i] : (~releasedAt(Fluent, Time))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.21/0.45 tff(15,plain,
% 0.21/0.45 ((~![Fluent: $i, Time: $i] : (~releasedAt(Fluent, Time))) | (~releasedAt(spinning, n1))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(16,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[15, 14, 7])).
% 0.21/0.45 tff(17,plain,(~releasedAt(spinning, n1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(18,plain,
% 0.21/0.45 (~releasedAt(spinning, plus(n0, n1))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[17, 6])).
% 0.21/0.45 tff(19,plain,
% 0.21/0.45 (holdsAt(spinning, plus(n0, n1)) <=> holdsAt(spinning, n1)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[3])).
% 0.21/0.45 tff(20,plain,
% 0.21/0.45 (holdsAt(spinning, n1) <=> holdsAt(spinning, plus(n0, n1))),
% 0.21/0.45 inference(symmetry,[status(thm)],[19])).
% 0.21/0.45 tff(21,plain,
% 0.21/0.45 (holdsAt(spinning, n1) <=> holdsAt(spinning, n1)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(22,plain,
% 0.21/0.45 ((~(~holdsAt(spinning, n1))) <=> holdsAt(spinning, n1)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(23,axiom,(~(~holdsAt(spinning, n1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_spinning_1')).
% 0.21/0.45 tff(24,plain,
% 0.21/0.45 (holdsAt(spinning, n1)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.45 tff(25,plain,
% 0.21/0.45 (holdsAt(spinning, n1)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.21/0.45 tff(26,plain,
% 0.21/0.45 (holdsAt(spinning, plus(n0, n1))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.21/0.45 tff(27,plain,
% 0.21/0.45 ((~holdsAt(spinning, n0)) <=> (~holdsAt(spinning, n0))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(28,axiom,(~holdsAt(spinning, n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_splinning_0')).
% 0.21/0.45 tff(29,plain,
% 0.21/0.45 (~holdsAt(spinning, n0)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.45 tff(30,plain,
% 0.21/0.45 (^[Fluent: $i, Time: $i] : refl((releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))))) <=> (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(31,plain,
% 0.21/0.45 (![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))))) <=> ![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.45 tff(32,plain,
% 0.21/0.45 (^[Fluent: $i, Time: $i] : trans(monotonicity(rewrite((happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)) <=> (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))))), ((releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))) <=> (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))))))), rewrite((releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))))) <=> (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))), ((releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))) <=> (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(33,plain,
% 0.21/0.45 (![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))) <=> ![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.45 tff(34,plain,
% 0.21/0.45 (^[Fluent: $i, Time: $i] : trans(monotonicity(rewrite(((~(~holdsAt(Fluent, Time))) | (~(~releasedAt(Fluent, plus(Time, n1)))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))) <=> (holdsAt(Fluent, Time) | releasedAt(Fluent, plus(Time, n1)) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))), (((~holdsAt(Fluent, plus(Time, n1))) | ((~(~holdsAt(Fluent, Time))) | (~(~releasedAt(Fluent, plus(Time, n1)))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))) <=> ((~holdsAt(Fluent, plus(Time, n1))) | (holdsAt(Fluent, Time) | releasedAt(Fluent, plus(Time, n1)) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))), rewrite(((~holdsAt(Fluent, plus(Time, n1))) | (holdsAt(Fluent, Time) | releasedAt(Fluent, plus(Time, n1)) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))) <=> (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))), (((~holdsAt(Fluent, plus(Time, n1))) | ((~(~holdsAt(Fluent, Time))) | (~(~releasedAt(Fluent, plus(Time, n1)))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))) <=> (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(35,plain,
% 0.21/0.45 (![Fluent: $i, Time: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | ((~(~holdsAt(Fluent, Time))) | (~(~releasedAt(Fluent, plus(Time, n1)))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))) <=> ![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.45 tff(36,plain,
% 0.21/0.45 (![Fluent: $i, Time: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))))) <=> ![Fluent: $i, Time: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(37,plain,
% 0.21/0.45 (^[Fluent: $i, Time: $i] : trans(monotonicity(trans(monotonicity(rewrite((~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time))) <=> (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))), ((((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) <=> (((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))))), rewrite((((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) <=> ((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time))))), ((((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) <=> ((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))))), (((((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) => (~holdsAt(Fluent, plus(Time, n1)))) <=> (((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) => (~holdsAt(Fluent, plus(Time, n1)))))), rewrite((((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) => (~holdsAt(Fluent, plus(Time, n1)))) <=> ((~holdsAt(Fluent, plus(Time, n1))) | (~((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time))))))), (((((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) => (~holdsAt(Fluent, plus(Time, n1)))) <=> ((~holdsAt(Fluent, plus(Time, n1))) | (~((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(38,plain,
% 0.21/0.46 (![Fluent: $i, Time: $i] : ((((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) => (~holdsAt(Fluent, plus(Time, n1)))) <=> ![Fluent: $i, Time: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.46 tff(39,axiom,(![Fluent: $i, Time: $i] : ((((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1)))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time)))) => (~holdsAt(Fluent, plus(Time, n1))))), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+0.ax','keep_not_holding')).
% 0.21/0.46 tff(40,plain,
% 0.21/0.46 (![Fluent: $i, Time: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.46 tff(41,plain,
% 0.21/0.46 (![Fluent: $i, Time: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | (~((~holdsAt(Fluent, Time)) & (~releasedAt(Fluent, plus(Time, n1))) & (~?[Event: $i] : (happens(Event, Time) & initiates(Event, Fluent, Time))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.21/0.46 tff(42,plain,(
% 0.21/0.46 ![Fluent: $i, Time: $i] : ((~holdsAt(Fluent, plus(Time, n1))) | ((~(~holdsAt(Fluent, Time))) | (~(~releasedAt(Fluent, plus(Time, n1)))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[41])).
% 0.21/0.46 tff(43,plain,
% 0.21/0.46 (![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (happens(tptp_fun_Event_5(Time, Fluent), Time) & initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.21/0.46 tff(44,plain,
% 0.21/0.46 (![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.21/0.46 tff(45,plain,
% 0.21/0.46 (![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[44, 31])).
% 0.21/0.46 tff(46,plain,
% 0.21/0.46 (((~![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))) | (holdsAt(spinning, n0) | releasedAt(spinning, plus(n0, n1)) | (~holdsAt(spinning, plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0)))))) <=> ((~![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))) | holdsAt(spinning, n0) | releasedAt(spinning, plus(n0, n1)) | (~holdsAt(spinning, plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(47,plain,
% 0.21/0.46 ((releasedAt(spinning, plus(n0, n1)) | holdsAt(spinning, n0) | (~holdsAt(spinning, plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0))))) <=> (holdsAt(spinning, n0) | releasedAt(spinning, plus(n0, n1)) | (~holdsAt(spinning, plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(48,plain,
% 0.21/0.46 (((~![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))) | (releasedAt(spinning, plus(n0, n1)) | holdsAt(spinning, n0) | (~holdsAt(spinning, plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0)))))) <=> ((~![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))) | (holdsAt(spinning, n0) | releasedAt(spinning, plus(n0, n1)) | (~holdsAt(spinning, plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[47])).
% 0.21/0.46 tff(49,plain,
% 0.21/0.46 (((~![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))) | (releasedAt(spinning, plus(n0, n1)) | holdsAt(spinning, n0) | (~holdsAt(spinning, plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0)))))) <=> ((~![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))) | holdsAt(spinning, n0) | releasedAt(spinning, plus(n0, n1)) | (~holdsAt(spinning, plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0)))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[48, 46])).
% 0.21/0.46 tff(50,plain,
% 0.21/0.46 ((~![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))) | (releasedAt(spinning, plus(n0, n1)) | holdsAt(spinning, n0) | (~holdsAt(spinning, plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(51,plain,
% 0.21/0.46 ((~![Fluent: $i, Time: $i] : (releasedAt(Fluent, plus(Time, n1)) | holdsAt(Fluent, Time) | (~holdsAt(Fluent, plus(Time, n1))) | (~((~happens(tptp_fun_Event_5(Time, Fluent), Time)) | (~initiates(tptp_fun_Event_5(Time, Fluent), Fluent, Time)))))) | holdsAt(spinning, n0) | releasedAt(spinning, plus(n0, n1)) | (~holdsAt(spinning, plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.46 tff(52,plain,
% 0.21/0.46 (releasedAt(spinning, plus(n0, n1)) | (~holdsAt(spinning, plus(n0, n1))) | (~((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[51, 45, 29])).
% 0.21/0.46 tff(53,plain,
% 0.21/0.46 (releasedAt(spinning, plus(n0, n1)) | (~((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[52, 26])).
% 0.21/0.46 tff(54,plain,
% 0.21/0.46 (~((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[53, 18])).
% 0.21/0.46 tff(55,plain,
% 0.21/0.46 (^[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)))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(56,plain,
% 0.21/0.46 (![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))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[55])).
% 0.21/0.46 tff(57,plain,
% 0.21/0.46 (^[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)))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(58,plain,
% 0.21/0.46 (![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))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[57])).
% 0.21/0.46 tff(59,plain,
% 0.21/0.46 (![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))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(60,plain,
% 0.21/0.46 (^[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)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(61,plain,
% 0.21/0.46 (![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))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.47 tff(62,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')).
% 0.21/0.47 tff(63,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.21/0.47 tff(64,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.21/0.47 tff(65,plain,(
% 0.21/0.47 ![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))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[64])).
% 0.21/0.47 tff(66,plain,
% 0.21/0.47 (![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))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.21/0.47 tff(67,plain,
% 0.21/0.47 (![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))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.21/0.47 tff(68,plain,
% 0.21/0.47 (((~![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(tptp_fun_Event_5(n0, spinning), spinning, n0) <=> ((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0))))))) <=> ((~![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(tptp_fun_Event_5(n0, spinning), spinning, n0) <=> ((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0)))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(69,plain,
% 0.21/0.47 ((initiates(tptp_fun_Event_5(n0, spinning), spinning, n0) <=> ((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~(happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(spinning = backwards)))) | (~((~happens(push, n0)) | (~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(spinning = spinning)))))) <=> (initiates(tptp_fun_Event_5(n0, spinning), spinning, n0) <=> ((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(70,plain,
% 0.21/0.47 (((~![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(tptp_fun_Event_5(n0, spinning), spinning, n0) <=> ((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~(happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(spinning = backwards)))) | (~((~happens(push, n0)) | (~(tptp_fun_Event_5(n0, spinning) = 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(tptp_fun_Event_5(n0, spinning), spinning, n0) <=> ((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0)))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[69])).
% 0.21/0.47 tff(71,plain,
% 0.21/0.47 (((~![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(tptp_fun_Event_5(n0, spinning), spinning, n0) <=> ((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~(happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(spinning = backwards)))) | (~((~happens(push, n0)) | (~(tptp_fun_Event_5(n0, spinning) = 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(tptp_fun_Event_5(n0, spinning), spinning, n0) <=> ((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0)))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[70, 68])).
% 0.21/0.47 tff(72,plain,
% 0.21/0.47 ((~![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(tptp_fun_Event_5(n0, spinning), spinning, n0) <=> ((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~(happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(spinning = backwards)))) | (~((~happens(push, n0)) | (~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(spinning = spinning))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(73,plain,
% 0.21/0.47 ((~![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(tptp_fun_Event_5(n0, spinning), spinning, n0) <=> ((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.47 tff(74,plain,
% 0.21/0.47 (initiates(tptp_fun_Event_5(n0, spinning), spinning, n0) <=> ((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[73, 67])).
% 0.21/0.47 tff(75,assumption,(~((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0)))), introduced(assumption)).
% 0.21/0.47 tff(76,plain,
% 0.21/0.47 (((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0))) | initiates(tptp_fun_Event_5(n0, spinning), spinning, n0)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(77,plain,
% 0.21/0.47 (initiates(tptp_fun_Event_5(n0, spinning), spinning, n0)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.21/0.47 tff(78,plain,
% 0.21/0.47 ((~(initiates(tptp_fun_Event_5(n0, spinning), spinning, n0) <=> ((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0))))))) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0)) | ((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0)))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(79,plain,
% 0.21/0.47 ((~(initiates(tptp_fun_Event_5(n0, spinning), spinning, n0) <=> ((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0))))))) | ((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.21/0.47 tff(80,plain,
% 0.21/0.47 ((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[79, 74])).
% 0.21/0.47 tff(81,plain,
% 0.21/0.47 ((~(spinning = backwards)) <=> (~(spinning = backwards))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(82,axiom,(~(spinning = backwards)), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax','spinning_not_backwards')).
% 0.21/0.47 tff(83,plain,
% 0.21/0.47 (~(spinning = backwards)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.47 tff(84,plain,
% 0.21/0.47 (((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull))) | (spinning = backwards)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(85,plain,
% 0.21/0.47 ((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.21/0.47 tff(86,plain,
% 0.21/0.47 ((spinning = forwards) <=> (forwards = spinning)),
% 0.21/0.47 inference(commutativity,[status(thm)],[])).
% 0.21/0.47 tff(87,plain,
% 0.21/0.47 ((forwards = spinning) <=> (spinning = forwards)),
% 0.21/0.47 inference(symmetry,[status(thm)],[86])).
% 0.21/0.48 tff(88,plain,
% 0.21/0.48 ((~(forwards = spinning)) <=> (~(spinning = forwards))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[87])).
% 0.21/0.48 tff(89,plain,
% 0.21/0.48 ((~(forwards = spinning)) <=> (~(forwards = spinning))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(90,axiom,(~(forwards = spinning)), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax','forwards_not_spinning')).
% 0.21/0.48 tff(91,plain,
% 0.21/0.48 (~(forwards = spinning)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.48 tff(92,plain,
% 0.21/0.48 (~(spinning = forwards)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[91, 88])).
% 0.21/0.48 tff(93,plain,
% 0.21/0.48 ((happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards))) | (spinning = forwards)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(94,plain,
% 0.21/0.48 (happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.21/0.48 tff(95,plain,
% 0.21/0.48 ((~((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0)))))) | (~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(96,plain,
% 0.21/0.48 ((~((~(happens(pull, n0) | (~(tptp_fun_Event_5(n0, spinning) = push)) | (~(spinning = forwards)))) | (~((~(spinning = backwards)) | happens(push, n0) | (~(tptp_fun_Event_5(n0, spinning) = pull)))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0)))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[95, 94, 85])).
% 0.21/0.48 tff(97,plain,
% 0.21/0.48 (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[96, 80])).
% 0.21/0.48 tff(98,plain,
% 0.21/0.48 (((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~happens(push, n0))) | (tptp_fun_Event_5(n0, spinning) = pull)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(99,plain,
% 0.21/0.48 (tptp_fun_Event_5(n0, spinning) = pull),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.21/0.48 tff(100,plain,
% 0.21/0.48 (^[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))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(101,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[100])).
% 0.21/0.48 tff(102,plain,
% 0.21/0.48 (^[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))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(103,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[102])).
% 0.21/0.48 tff(104,plain,
% 0.21/0.48 (^[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))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(105,plain,
% 0.21/0.48 (![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)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[104])).
% 0.21/0.48 tff(106,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(107,plain,
% 0.21/0.48 (^[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)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(108,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[107])).
% 0.21/0.48 tff(109,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')).
% 0.21/0.48 tff(110,plain,
% 0.21/0.48 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.48 tff(111,plain,
% 0.21/0.48 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.21/0.48 tff(112,plain,
% 0.21/0.48 (![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)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[111, 105])).
% 0.21/0.48 tff(113,plain,(
% 0.21/0.48 ![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)))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[112])).
% 0.21/0.48 tff(114,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[113, 103])).
% 0.21/0.48 tff(115,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[114, 101])).
% 0.21/0.48 tff(116,plain,
% 0.21/0.48 (((~![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(tptp_fun_Event_5(n0, spinning), n0) <=> ((tptp_fun_Event_5(n0, spinning) = push) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = 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(tptp_fun_Event_5(n0, spinning), n0) <=> ((tptp_fun_Event_5(n0, spinning) = push) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1))))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(117,plain,
% 0.21/0.48 ((happens(tptp_fun_Event_5(n0, spinning), n0) <=> ((~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = n0)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1))))))) <=> (happens(tptp_fun_Event_5(n0, spinning), n0) <=> ((tptp_fun_Event_5(n0, spinning) = push) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(118,plain,
% 0.21/0.48 (((~![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(tptp_fun_Event_5(n0, spinning), n0) <=> ((~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = n0)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = 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(tptp_fun_Event_5(n0, spinning), n0) <=> ((tptp_fun_Event_5(n0, spinning) = push) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1))))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.48 tff(119,plain,
% 0.21/0.48 (((~![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(tptp_fun_Event_5(n0, spinning), n0) <=> ((~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = n0)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = 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(tptp_fun_Event_5(n0, spinning), n0) <=> ((tptp_fun_Event_5(n0, spinning) = push) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1))))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[118, 116])).
% 0.21/0.48 tff(120,plain,
% 0.21/0.48 ((~![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(tptp_fun_Event_5(n0, spinning), n0) <=> ((~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = n0)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1)))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(121,plain,
% 0.21/0.48 ((~![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(tptp_fun_Event_5(n0, spinning), n0) <=> ((tptp_fun_Event_5(n0, spinning) = push) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.48 tff(122,plain,
% 0.21/0.48 (happens(tptp_fun_Event_5(n0, spinning), n0) <=> ((tptp_fun_Event_5(n0, spinning) = push) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[121, 115])).
% 0.21/0.48 tff(123,plain,
% 0.21/0.48 (((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0))) | happens(tptp_fun_Event_5(n0, spinning), n0)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(124,plain,
% 0.21/0.48 (happens(tptp_fun_Event_5(n0, spinning), n0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[123, 75])).
% 0.21/0.48 tff(125,plain,
% 0.21/0.48 ((~(happens(tptp_fun_Event_5(n0, spinning), n0) <=> ((tptp_fun_Event_5(n0, spinning) = push) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1)))))))) | (~happens(tptp_fun_Event_5(n0, spinning), n0)) | ((tptp_fun_Event_5(n0, spinning) = push) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1))))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(126,plain,
% 0.21/0.48 ((~(happens(tptp_fun_Event_5(n0, spinning), n0) <=> ((tptp_fun_Event_5(n0, spinning) = push) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1)))))))) | ((tptp_fun_Event_5(n0, spinning) = push) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.21/0.48 tff(127,plain,
% 0.21/0.48 ((tptp_fun_Event_5(n0, spinning) = push) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[126, 122])).
% 0.21/0.48 tff(128,assumption,(~(n0 = plus(n1, n1))), introduced(assumption)).
% 0.21/0.48 tff(129,plain,
% 0.21/0.48 (((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1)))) | (n0 = plus(n1, n1))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(130,plain,
% 0.21/0.48 ((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.21/0.48 tff(131,plain,
% 0.21/0.48 (((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1)))) | (n0 = plus(n1, n1))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(132,plain,
% 0.21/0.48 ((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[131, 128])).
% 0.21/0.48 tff(133,assumption,(n0 = n1), introduced(assumption)).
% 0.21/0.48 tff(134,plain,
% 0.21/0.48 (holdsAt(spinning, n0) <=> holdsAt(spinning, n1)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[133])).
% 0.21/0.49 tff(135,plain,
% 0.21/0.49 (holdsAt(spinning, n1) <=> holdsAt(spinning, n0)),
% 0.21/0.49 inference(symmetry,[status(thm)],[134])).
% 0.21/0.49 tff(136,plain,
% 0.21/0.49 (holdsAt(spinning, n0)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[25, 135])).
% 0.21/0.49 tff(137,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[29, 136])).
% 0.21/0.49 tff(138,plain,(~(n0 = n1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(139,plain,
% 0.21/0.49 (((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1))) | (n0 = n1)),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(140,plain,
% 0.21/0.49 ((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.21/0.49 tff(141,plain,
% 0.21/0.49 ((~((tptp_fun_Event_5(n0, spinning) = push) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1))))))) | (tptp_fun_Event_5(n0, spinning) = push) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1)))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(142,plain,
% 0.21/0.49 ((~((tptp_fun_Event_5(n0, spinning) = push) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = n1)))) | (~((~(tptp_fun_Event_5(n0, spinning) = push)) | (~(n0 = plus(n1, n1))))) | (~((~(tptp_fun_Event_5(n0, spinning) = pull)) | (~(n0 = plus(n1, n1))))))) | (tptp_fun_Event_5(n0, spinning) = push)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[141, 140, 132, 130])).
% 0.21/0.49 tff(143,plain,
% 0.21/0.49 (tptp_fun_Event_5(n0, spinning) = push),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[142, 127])).
% 0.21/0.49 tff(144,plain,
% 0.21/0.49 (push = tptp_fun_Event_5(n0, spinning)),
% 0.21/0.49 inference(symmetry,[status(thm)],[143])).
% 0.21/0.49 tff(145,plain,
% 0.21/0.49 (push = pull),
% 0.21/0.49 inference(transitivity,[status(thm)],[144, 99])).
% 0.21/0.49 tff(146,plain,
% 0.21/0.49 ((~(push = pull)) <=> (~(push = pull))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(147,axiom,(~(push = pull)), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax','push_not_pull')).
% 0.21/0.49 tff(148,plain,
% 0.21/0.49 (~(push = pull)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.21/0.49 tff(149,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[148, 145])).
% 0.21/0.49 tff(150,plain,(((~happens(tptp_fun_Event_5(n0, spinning), n0)) | (~initiates(tptp_fun_Event_5(n0, spinning), spinning, n0))) | (n0 = plus(n1, n1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(151,plain,
% 0.21/0.49 (n0 = plus(n1, n1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[150, 54])).
% 0.21/0.49 tff(152,plain,
% 0.21/0.49 ((plus(n0, n0) = n0) <=> (plus(n0, n0) = n0)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(153,axiom,(plus(n0, n0) = n0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus0_0')).
% 0.21/0.49 tff(154,plain,
% 0.21/0.49 (plus(n0, n0) = n0),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.21/0.49 tff(155,plain,
% 0.21/0.49 (plus(n1, n1) = n0),
% 0.21/0.49 inference(symmetry,[status(thm)],[151])).
% 0.21/0.49 tff(156,plain,
% 0.21/0.49 (plus(plus(n1, n1), plus(n1, n1)) = plus(n0, n0)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[155, 155])).
% 0.21/0.49 tff(157,plain,
% 0.21/0.49 (plus(plus(n1, n1), plus(n1, n1)) = plus(n1, n1)),
% 0.21/0.49 inference(transitivity,[status(thm)],[156, 154, 151])).
% 0.21/0.49 tff(158,plain,
% 0.21/0.49 (less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))) <=> less(plus(n1, plus(n1, n1)), plus(n1, n1))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[157])).
% 0.21/0.49 tff(159,plain,
% 0.21/0.49 (less(plus(n1, plus(n1, n1)), plus(n1, n1)) <=> less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1)))),
% 0.21/0.49 inference(symmetry,[status(thm)],[158])).
% 0.21/0.49 tff(160,plain,
% 0.21/0.49 ((~less(plus(n1, plus(n1, n1)), plus(n1, n1))) <=> (~less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[159])).
% 0.21/0.49 tff(161,plain,
% 0.21/0.49 (^[X: $i, Y: $i] : refl((less_or_equal(X, Y) <=> ((X = Y) | less(X, Y))) <=> (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(162,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y))) <=> ![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[161])).
% 0.21/0.49 tff(163,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y))) <=> ![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(164,plain,
% 0.21/0.49 (^[X: $i, Y: $i] : rewrite((less_or_equal(X, Y) <=> (less(X, Y) | (X = Y))) <=> (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(165,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> (less(X, Y) | (X = Y))) <=> ![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[164])).
% 0.21/0.49 tff(166,axiom,(![X: $i, Y: $i] : (less_or_equal(X, Y) <=> (less(X, Y) | (X = Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','less_or_equal')).
% 0.21/0.49 tff(167,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.21/0.49 tff(168,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.21/0.49 tff(169,plain,(
% 0.21/0.49 ![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[168])).
% 0.21/0.49 tff(170,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.21/0.49 tff(171,plain,
% 0.21/0.49 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, n1)) <=> ((plus(n1, plus(n1, n1)) = plus(n1, n1)) | less(plus(n1, plus(n1, n1)), plus(n1, n1))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(172,plain,
% 0.21/0.49 (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, n1)) <=> ((plus(n1, plus(n1, n1)) = plus(n1, n1)) | less(plus(n1, plus(n1, n1)), plus(n1, n1)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.21/0.49 tff(173,plain,
% 0.21/0.49 (plus(n0, n1) = plus(plus(n1, n1), n1)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[151])).
% 0.21/0.49 tff(174,plain,
% 0.21/0.49 (plus(plus(n1, n1), n1) = plus(n0, n1)),
% 0.21/0.49 inference(symmetry,[status(thm)],[173])).
% 0.21/0.49 tff(175,plain,
% 0.21/0.49 (^[X: $i, Y: $i] : refl((plus(X, Y) = plus(Y, X)) <=> (plus(X, Y) = plus(Y, X)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(176,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X)) <=> ![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[175])).
% 0.21/0.49 tff(177,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X)) <=> ![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(178,axiom,(![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetry_of_plus')).
% 0.21/0.49 tff(179,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.21/0.49 tff(180,plain,(
% 0.21/0.49 ![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 0.21/0.49 inference(skolemize,[status(sab)],[179])).
% 0.21/0.49 tff(181,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[180, 176])).
% 0.21/0.49 tff(182,plain,
% 0.21/0.49 ((~![X: $i, Y: $i] : (plus(X, Y) = plus(Y, X))) | (plus(n1, plus(n1, n1)) = plus(plus(n1, n1), n1))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(183,plain,
% 0.21/0.49 (plus(n1, plus(n1, n1)) = plus(plus(n1, n1), n1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.21/0.49 tff(184,plain,
% 0.21/0.49 (plus(n1, plus(n1, n1)) = n1),
% 0.21/0.49 inference(transitivity,[status(thm)],[183, 174, 3])).
% 0.21/0.49 tff(185,plain,
% 0.21/0.49 (plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) = plus(n1, n1)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[184, 184])).
% 0.21/0.49 tff(186,plain,
% 0.21/0.49 (plus(n1, n1) = plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))),
% 0.21/0.49 inference(symmetry,[status(thm)],[185])).
% 0.21/0.49 tff(187,plain,
% 0.21/0.49 (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, n1)) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[186])).
% 0.21/0.49 tff(188,plain,
% 0.21/0.49 (less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, n1))),
% 0.21/0.49 inference(symmetry,[status(thm)],[187])).
% 0.21/0.49 tff(189,plain,
% 0.21/0.49 ((~less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) <=> (~less_or_equal(plus(n1, plus(n1, n1)), plus(n1, n1)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[188])).
% 0.21/0.49 tff(190,plain,
% 0.21/0.49 (^[X: $i] : refl((less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1))) <=> (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(191,plain,
% 0.21/0.49 (![X: $i] : (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1))) <=> ![X: $i] : (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[190])).
% 0.21/0.49 tff(192,plain,
% 0.21/0.49 (^[X: $i] : rewrite((less(X, n3) <=> less_or_equal(X, n2)) <=> (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(193,plain,
% 0.21/0.49 (![X: $i] : (less(X, n3) <=> less_or_equal(X, n2)) <=> ![X: $i] : (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[192])).
% 0.21/0.49 tff(194,plain,
% 0.21/0.49 (![X: $i] : (less(X, n3) <=> less_or_equal(X, n2)) <=> ![X: $i] : (less(X, n3) <=> less_or_equal(X, n2))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(195,axiom,(![X: $i] : (less(X, n3) <=> less_or_equal(X, n2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','less3')).
% 0.21/0.49 tff(196,plain,
% 0.21/0.49 (![X: $i] : (less(X, n3) <=> less_or_equal(X, n2))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.21/0.49 tff(197,plain,
% 0.21/0.49 (![X: $i] : (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[196, 193])).
% 0.21/0.49 tff(198,plain,(
% 0.21/0.49 ![X: $i] : (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[197])).
% 0.21/0.49 tff(199,plain,
% 0.21/0.49 (![X: $i] : (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[198, 191])).
% 0.21/0.49 tff(200,plain,
% 0.21/0.49 ((~![X: $i] : (less(X, plus(n1, plus(n1, n1))) <=> less_or_equal(X, plus(n1, n1)))) | (less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, n1)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(201,plain,
% 0.21/0.49 (less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, n1))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.21/0.49 tff(202,assumption,(less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))), introduced(assumption)).
% 0.21/0.49 tff(203,plain,
% 0.21/0.49 (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, n1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[202, 188])).
% 0.21/0.49 tff(204,plain,
% 0.21/0.49 (^[X: $i, Y: $i] : refl((less(X, Y) <=> (~((Y = X) | less(Y, X)))) <=> (less(X, Y) <=> (~((Y = X) | less(Y, X)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(205,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X)))) <=> ![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[204])).
% 0.21/0.49 tff(206,plain,
% 0.21/0.49 (^[X: $i, Y: $i] : rewrite((less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> (less(X, Y) <=> (~((Y = X) | less(Y, X)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(207,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> ![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[206])).
% 0.21/0.49 tff(208,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> ![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(209,axiom,(![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','less_property')).
% 0.21/0.49 tff(210,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.21/0.49 tff(211,plain,(
% 0.21/0.49 ![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))),
% 0.21/0.49 inference(skolemize,[status(sab)],[210])).
% 0.21/0.49 tff(212,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.21/0.49 tff(213,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[212, 205])).
% 0.21/0.49 tff(214,plain,
% 0.21/0.49 (((~![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))) | (~less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) <=> ((~![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))) | (~less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(215,plain,
% 0.21/0.49 ((less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> $false) <=> (~less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(216,plain,
% 0.21/0.49 ((~$true) <=> $false),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(217,plain,
% 0.21/0.49 (($true | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> $true),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(218,plain,
% 0.21/0.49 ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) <=> $true),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(219,plain,
% 0.21/0.49 (((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> ($true | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[218])).
% 0.21/0.49 tff(220,plain,
% 0.21/0.49 (((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> $true),
% 0.21/0.49 inference(transitivity,[status(thm)],[219, 217])).
% 0.21/0.49 tff(221,plain,
% 0.21/0.49 ((~((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) <=> (~$true)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[220])).
% 0.21/0.49 tff(222,plain,
% 0.21/0.49 ((~((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) <=> $false),
% 0.21/0.49 inference(transitivity,[status(thm)],[221, 216])).
% 0.21/0.49 tff(223,plain,
% 0.21/0.49 ((less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> (~((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))) <=> (less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> $false)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[222])).
% 0.21/0.49 tff(224,plain,
% 0.21/0.49 ((less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> (~((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))) <=> (~less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[223, 215])).
% 0.21/0.49 tff(225,plain,
% 0.21/0.49 (((~![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))) | (less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> (~((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))))) <=> ((~![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))) | (~less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[224])).
% 0.21/0.49 tff(226,plain,
% 0.21/0.49 (((~![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))) | (less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> (~((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))))) <=> ((~![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))) | (~less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[225, 214])).
% 0.21/0.49 tff(227,plain,
% 0.21/0.49 ((~![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))) | (less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> (~((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(228,plain,
% 0.21/0.49 ((~![X: $i, Y: $i] : (less(X, Y) <=> (~((Y = X) | less(Y, X))))) | (~less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.21/0.49 tff(229,plain,
% 0.21/0.49 (~less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[228, 213])).
% 0.21/0.49 tff(230,plain,
% 0.21/0.49 ((~(less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, n1)))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) | (~less_or_equal(plus(n1, plus(n1, n1)), plus(n1, n1)))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(231,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[230, 229, 203, 201])).
% 0.21/0.49 tff(232,plain,(~less_or_equal(plus(n1, plus(n1, n1)), plus(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(233,plain,
% 0.21/0.49 (~less_or_equal(plus(n1, plus(n1, n1)), plus(n1, n1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[232, 189])).
% 0.21/0.49 tff(234,plain,
% 0.21/0.49 ((~(less_or_equal(plus(n1, plus(n1, n1)), plus(n1, n1)) <=> ((plus(n1, plus(n1, n1)) = plus(n1, n1)) | less(plus(n1, plus(n1, n1)), plus(n1, n1))))) | less_or_equal(plus(n1, plus(n1, n1)), plus(n1, n1)) | (~((plus(n1, plus(n1, n1)) = plus(n1, n1)) | less(plus(n1, plus(n1, n1)), plus(n1, n1))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(235,plain,
% 0.21/0.49 (~((plus(n1, plus(n1, n1)) = plus(n1, n1)) | less(plus(n1, plus(n1, n1)), plus(n1, n1)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[234, 233, 172])).
% 0.21/0.49 tff(236,plain,
% 0.21/0.49 (((plus(n1, plus(n1, n1)) = plus(n1, n1)) | less(plus(n1, plus(n1, n1)), plus(n1, n1))) | (~less(plus(n1, plus(n1, n1)), plus(n1, n1)))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(237,plain,
% 0.21/0.49 (~less(plus(n1, plus(n1, n1)), plus(n1, n1))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.21/0.49 tff(238,plain,
% 0.21/0.49 (~less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[237, 160])).
% 0.21/0.49 tff(239,plain,
% 0.21/0.49 (^[X: $i] : refl((less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1)))) <=> (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(240,plain,
% 0.21/0.49 (![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1)))) <=> ![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[239])).
% 0.21/0.49 tff(241,plain,
% 0.21/0.49 (^[X: $i] : rewrite((less(X, plus(n1, plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(n1, plus(n1, n1)))) <=> (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(242,plain,
% 0.21/0.49 (![X: $i] : (less(X, plus(n1, plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(n1, plus(n1, n1)))) <=> ![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[241])).
% 0.21/0.49 tff(243,plain,
% 0.21/0.49 (^[X: $i] : rewrite((less(X, n4) <=> less_or_equal(X, n3)) <=> (less(X, plus(n1, plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(n1, plus(n1, n1)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(244,plain,
% 0.21/0.50 (![X: $i] : (less(X, n4) <=> less_or_equal(X, n3)) <=> ![X: $i] : (less(X, plus(n1, plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(n1, plus(n1, n1))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[243])).
% 0.21/0.50 tff(245,plain,
% 0.21/0.50 (![X: $i] : (less(X, n4) <=> less_or_equal(X, n3)) <=> ![X: $i] : (less(X, n4) <=> less_or_equal(X, n3))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(246,axiom,(![X: $i] : (less(X, n4) <=> less_or_equal(X, n3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','less4')).
% 0.21/0.50 tff(247,plain,
% 0.21/0.50 (![X: $i] : (less(X, n4) <=> less_or_equal(X, n3))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.21/0.50 tff(248,plain,
% 0.21/0.50 (![X: $i] : (less(X, plus(n1, plus(n1, plus(n1, n1)))) <=> less_or_equal(X, plus(n1, plus(n1, n1))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[247, 244])).
% 0.21/0.50 tff(249,plain,
% 0.21/0.50 (![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[248, 242])).
% 0.21/0.50 tff(250,plain,(
% 0.21/0.50 ![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[249])).
% 0.21/0.50 tff(251,plain,
% 0.21/0.50 (![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[250, 240])).
% 0.21/0.50 tff(252,plain,
% 0.21/0.50 ((~![X: $i] : (less(X, plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(X, plus(n1, plus(n1, n1))))) | (less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(253,plain,
% 0.21/0.50 (less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.21/0.50 tff(254,plain,
% 0.21/0.50 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(255,plain,
% 0.21/0.50 ((less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> $true) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(256,plain,
% 0.21/0.50 ((less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) <=> (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> $true)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[220])).
% 0.21/0.50 tff(257,plain,
% 0.21/0.50 ((less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[256, 255])).
% 0.21/0.50 tff(258,plain,
% 0.21/0.50 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[257])).
% 0.21/0.50 tff(259,plain,
% 0.21/0.50 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[258, 254])).
% 0.21/0.50 tff(260,plain,
% 0.21/0.50 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))) <=> ((plus(n1, plus(n1, n1)) = plus(n1, plus(n1, n1))) | less(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(261,plain,
% 0.21/0.50 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.21/0.50 tff(262,plain,
% 0.21/0.50 (less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[261, 170])).
% 0.21/0.50 tff(263,plain,
% 0.21/0.50 ((~(less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) | less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))) | (~less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(264,plain,
% 0.21/0.50 ((~(less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1))) <=> less_or_equal(plus(n1, plus(n1, n1)), plus(n1, plus(n1, n1))))) | less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[263, 262])).
% 0.21/0.50 tff(265,plain,
% 0.21/0.50 (less(plus(n1, plus(n1, n1)), plus(plus(n1, n1), plus(n1, n1)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[264, 253])).
% 0.21/0.50 tff(266,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[265, 238])).
% 0.21/0.50 % SZS output end Proof
%------------------------------------------------------------------------------