TSTP Solution File: MGT041+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT041+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 : Sun Sep 18 05:22:09 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT041+2 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri Sep 2 02:50:34 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(first_mover_type, type, (
% 0.12/0.39 first_mover: $i > $o)).
% 0.12/0.39 tff(tptp_fun_X_1_type, type, (
% 0.12/0.39 tptp_fun_X_1: $i)).
% 0.12/0.39 tff(efficient_producer_type, type, (
% 0.12/0.39 efficient_producer: $i > $o)).
% 0.12/0.39 tff(has_elaborated_routines_type, type, (
% 0.12/0.39 has_elaborated_routines: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_T_0_type, type, (
% 0.12/0.39 tptp_fun_T_0: $i)).
% 0.12/0.39 tff(number_of_routines_type, type, (
% 0.12/0.39 number_of_routines: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(high_type, type, (
% 0.12/0.39 high: $i)).
% 0.12/0.39 tff(founding_time_type, type, (
% 0.12/0.39 founding_time: ( $i * $i ) > $o)).
% 0.12/0.39 tff(organisation_at_time_type, type, (
% 0.12/0.39 organisation_at_time: ( $i * $i ) > $o)).
% 0.12/0.39 tff(low_type, type, (
% 0.12/0.39 low: $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (?[X: $i, T: $i] : (organisation_at_time(X, T) & founding_time(X, T) & number_of_routines(X, T, high) & (~has_elaborated_routines(X, T))) <=> ?[X: $i, T: $i] : (organisation_at_time(X, T) & founding_time(X, T) & number_of_routines(X, T, high) & (~has_elaborated_routines(X, T)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (^[X: $i, T: $i] : trans(monotonicity(rewrite(((organisation_at_time(X, T) & founding_time(X, T)) & number_of_routines(X, T, high)) <=> (organisation_at_time(X, T) & founding_time(X, T) & number_of_routines(X, T, high))), ((((organisation_at_time(X, T) & founding_time(X, T)) & number_of_routines(X, T, high)) & (~has_elaborated_routines(X, T))) <=> ((organisation_at_time(X, T) & founding_time(X, T) & number_of_routines(X, T, high)) & (~has_elaborated_routines(X, T))))), rewrite(((organisation_at_time(X, T) & founding_time(X, T) & number_of_routines(X, T, high)) & (~has_elaborated_routines(X, T))) <=> (organisation_at_time(X, T) & founding_time(X, T) & number_of_routines(X, T, high) & (~has_elaborated_routines(X, T)))), ((((organisation_at_time(X, T) & founding_time(X, T)) & number_of_routines(X, T, high)) & (~has_elaborated_routines(X, T))) <=> (organisation_at_time(X, T) & founding_time(X, T) & number_of_routines(X, T, high) & (~has_elaborated_routines(X, T)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (?[X: $i, T: $i] : (((organisation_at_time(X, T) & founding_time(X, T)) & number_of_routines(X, T, high)) & (~has_elaborated_routines(X, T))) <=> ?[X: $i, T: $i] : (organisation_at_time(X, T) & founding_time(X, T) & number_of_routines(X, T, high) & (~has_elaborated_routines(X, T)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.39 tff(4,axiom,(?[X: $i, T: $i] : (((organisation_at_time(X, T) & founding_time(X, T)) & number_of_routines(X, T, high)) & (~has_elaborated_routines(X, T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a16')).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (?[X: $i, T: $i] : (organisation_at_time(X, T) & founding_time(X, T) & number_of_routines(X, T, high) & (~has_elaborated_routines(X, T)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (?[X: $i, T: $i] : (organisation_at_time(X, T) & founding_time(X, T) & number_of_routines(X, T, high) & (~has_elaborated_routines(X, T)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.39 tff(7,plain,(
% 0.12/0.39 organisation_at_time(X!1, T!0) & founding_time(X!1, T!0) & number_of_routines(X!1, T!0, high) & (~has_elaborated_routines(X!1, T!0))),
% 0.12/0.39 inference(skolemize,[status(sab)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (~has_elaborated_routines(X!1, T!0)),
% 0.12/0.39 inference(and_elim,[status(thm)],[7])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (founding_time(X!1, T!0)),
% 0.12/0.39 inference(and_elim,[status(thm)],[7])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (organisation_at_time(X!1, T!0)),
% 0.12/0.39 inference(and_elim,[status(thm)],[7])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (^[X: $i, T: $i] : refl((has_elaborated_routines(X, T) | (~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))) <=> (has_elaborated_routines(X, T) | (~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (![X: $i, T: $i] : (has_elaborated_routines(X, T) | (~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))) <=> ![X: $i, T: $i] : (has_elaborated_routines(X, T) | (~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (^[X: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T)) <=> (~((~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))))), ((~(organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T))) <=> (~(~((~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))))))), rewrite((~(~((~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))))) <=> ((~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))), ((~(organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T))) <=> ((~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))))), (((~(organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T))) | has_elaborated_routines(X, T)) <=> (((~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))) | has_elaborated_routines(X, T)))), rewrite((((~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))) | has_elaborated_routines(X, T)) <=> (has_elaborated_routines(X, T) | (~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))), (((~(organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T))) | has_elaborated_routines(X, T)) <=> (has_elaborated_routines(X, T) | (~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (![X: $i, T: $i] : ((~(organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T))) | has_elaborated_routines(X, T)) <=> ![X: $i, T: $i] : (has_elaborated_routines(X, T) | (~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (![X: $i, T: $i] : ((~(organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T))) | has_elaborated_routines(X, T)) <=> ![X: $i, T: $i] : ((~(organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T))) | has_elaborated_routines(X, T))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (^[X: $i, T: $i] : trans(monotonicity(rewrite(((organisation_at_time(X, T) & efficient_producer(X)) & founding_time(X, T)) <=> (organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T))), ((((organisation_at_time(X, T) & efficient_producer(X)) & founding_time(X, T)) => has_elaborated_routines(X, T)) <=> ((organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T)) => has_elaborated_routines(X, T)))), rewrite(((organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T)) => has_elaborated_routines(X, T)) <=> ((~(organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T))) | has_elaborated_routines(X, T))), ((((organisation_at_time(X, T) & efficient_producer(X)) & founding_time(X, T)) => has_elaborated_routines(X, T)) <=> ((~(organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T))) | has_elaborated_routines(X, T))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![X: $i, T: $i] : (((organisation_at_time(X, T) & efficient_producer(X)) & founding_time(X, T)) => has_elaborated_routines(X, T)) <=> ![X: $i, T: $i] : ((~(organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T))) | has_elaborated_routines(X, T))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.39 tff(18,axiom,(![X: $i, T: $i] : (((organisation_at_time(X, T) & efficient_producer(X)) & founding_time(X, T)) => has_elaborated_routines(X, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a14')).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (![X: $i, T: $i] : ((~(organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T))) | has_elaborated_routines(X, T))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (![X: $i, T: $i] : ((~(organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T))) | has_elaborated_routines(X, T))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.12/0.40 tff(21,plain,(
% 0.12/0.40 ![X: $i, T: $i] : ((~(organisation_at_time(X, T) & efficient_producer(X) & founding_time(X, T))) | has_elaborated_routines(X, T))),
% 0.12/0.40 inference(skolemize,[status(sab)],[20])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (![X: $i, T: $i] : (has_elaborated_routines(X, T) | (~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (![X: $i, T: $i] : (has_elaborated_routines(X, T) | (~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 (((~![X: $i, T: $i] : (has_elaborated_routines(X, T) | (~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))) | (has_elaborated_routines(X!1, T!0) | (~efficient_producer(X!1)) | (~organisation_at_time(X!1, T!0)) | (~founding_time(X!1, T!0)))) <=> ((~![X: $i, T: $i] : (has_elaborated_routines(X, T) | (~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))) | has_elaborated_routines(X!1, T!0) | (~efficient_producer(X!1)) | (~organisation_at_time(X!1, T!0)) | (~founding_time(X!1, T!0)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 ((~![X: $i, T: $i] : (has_elaborated_routines(X, T) | (~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))) | (has_elaborated_routines(X!1, T!0) | (~efficient_producer(X!1)) | (~organisation_at_time(X!1, T!0)) | (~founding_time(X!1, T!0)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 ((~![X: $i, T: $i] : (has_elaborated_routines(X, T) | (~efficient_producer(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))) | has_elaborated_routines(X!1, T!0) | (~efficient_producer(X!1)) | (~organisation_at_time(X!1, T!0)) | (~founding_time(X!1, T!0))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (~efficient_producer(X!1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[26, 23, 10, 9, 8])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (^[X: $i, T: $i] : refl((efficient_producer(X) | first_mover(X) | (~organisation_at_time(X, T))) <=> (efficient_producer(X) | first_mover(X) | (~organisation_at_time(X, T))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (![X: $i, T: $i] : (efficient_producer(X) | first_mover(X) | (~organisation_at_time(X, T))) <=> ![X: $i, T: $i] : (efficient_producer(X) | first_mover(X) | (~organisation_at_time(X, T)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 (^[X: $i, T: $i] : trans(monotonicity(rewrite((organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X))) <=> (~(efficient_producer(X) | first_mover(X) | (~organisation_at_time(X, T))))), ((~(organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X)))) <=> (~(~(efficient_producer(X) | first_mover(X) | (~organisation_at_time(X, T))))))), rewrite((~(~(efficient_producer(X) | first_mover(X) | (~organisation_at_time(X, T))))) <=> (efficient_producer(X) | first_mover(X) | (~organisation_at_time(X, T)))), ((~(organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X)))) <=> (efficient_producer(X) | first_mover(X) | (~organisation_at_time(X, T)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (![X: $i, T: $i] : (~(organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X)))) <=> ![X: $i, T: $i] : (efficient_producer(X) | first_mover(X) | (~organisation_at_time(X, T)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 ((~?[X: $i, T: $i] : (organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X)))) <=> (~?[X: $i, T: $i] : (organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 ((~?[X: $i, T: $i] : ((organisation_at_time(X, T) & (~first_mover(X))) & (~efficient_producer(X)))) <=> (~?[X: $i, T: $i] : (organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(34,axiom,(~?[X: $i, T: $i] : ((organisation_at_time(X, T) & (~first_mover(X))) & (~efficient_producer(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t10')).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 (~?[X: $i, T: $i] : (organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (~?[X: $i, T: $i] : (organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[35, 32])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 (~?[X: $i, T: $i] : (organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 (~?[X: $i, T: $i] : (organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[37, 32])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 (~?[X: $i, T: $i] : (organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[38, 32])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 (~?[X: $i, T: $i] : (organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (~?[X: $i, T: $i] : (organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[40, 32])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 (^[X: $i, T: $i] : refl($oeq((~(organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X)))), (~(organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(43,plain,(
% 0.12/0.40 ![X: $i, T: $i] : (~(organisation_at_time(X, T) & (~first_mover(X)) & (~efficient_producer(X))))),
% 0.12/0.40 inference(nnf-neg,[status(sab)],[41, 42])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (![X: $i, T: $i] : (efficient_producer(X) | first_mover(X) | (~organisation_at_time(X, T)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[43, 31])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (![X: $i, T: $i] : (efficient_producer(X) | first_mover(X) | (~organisation_at_time(X, T)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[44, 29])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 (((~![X: $i, T: $i] : (efficient_producer(X) | first_mover(X) | (~organisation_at_time(X, T)))) | (efficient_producer(X!1) | first_mover(X!1) | (~organisation_at_time(X!1, T!0)))) <=> ((~![X: $i, T: $i] : (efficient_producer(X) | first_mover(X) | (~organisation_at_time(X, T)))) | efficient_producer(X!1) | first_mover(X!1) | (~organisation_at_time(X!1, T!0)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 ((~![X: $i, T: $i] : (efficient_producer(X) | first_mover(X) | (~organisation_at_time(X, T)))) | (efficient_producer(X!1) | first_mover(X!1) | (~organisation_at_time(X!1, T!0)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 ((~![X: $i, T: $i] : (efficient_producer(X) | first_mover(X) | (~organisation_at_time(X, T)))) | efficient_producer(X!1) | first_mover(X!1) | (~organisation_at_time(X!1, T!0))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (first_mover(X!1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[48, 10, 45, 27])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (number_of_routines(X!1, T!0, high)),
% 0.12/0.40 inference(and_elim,[status(thm)],[7])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (^[X: $i, T: $i] : refl(((~number_of_routines(X, T, low)) | (~number_of_routines(X, T, high))) <=> ((~number_of_routines(X, T, low)) | (~number_of_routines(X, T, high))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (![X: $i, T: $i] : ((~number_of_routines(X, T, low)) | (~number_of_routines(X, T, high))) <=> ![X: $i, T: $i] : ((~number_of_routines(X, T, low)) | (~number_of_routines(X, T, high)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (^[X: $i, T: $i] : trans(monotonicity(rewrite((number_of_routines(X, T, low) & number_of_routines(X, T, high)) <=> (~((~number_of_routines(X, T, low)) | (~number_of_routines(X, T, high))))), ((~(number_of_routines(X, T, low) & number_of_routines(X, T, high))) <=> (~(~((~number_of_routines(X, T, low)) | (~number_of_routines(X, T, high))))))), rewrite((~(~((~number_of_routines(X, T, low)) | (~number_of_routines(X, T, high))))) <=> ((~number_of_routines(X, T, low)) | (~number_of_routines(X, T, high)))), ((~(number_of_routines(X, T, low) & number_of_routines(X, T, high))) <=> ((~number_of_routines(X, T, low)) | (~number_of_routines(X, T, high)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (![X: $i, T: $i] : (~(number_of_routines(X, T, low) & number_of_routines(X, T, high))) <=> ![X: $i, T: $i] : ((~number_of_routines(X, T, low)) | (~number_of_routines(X, T, high)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (![X: $i, T: $i] : (~(number_of_routines(X, T, low) & number_of_routines(X, T, high))) <=> ![X: $i, T: $i] : (~(number_of_routines(X, T, low) & number_of_routines(X, T, high)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(56,axiom,(![X: $i, T: $i] : (~(number_of_routines(X, T, low) & number_of_routines(X, T, high)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_not_high_and_low')).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (![X: $i, T: $i] : (~(number_of_routines(X, T, low) & number_of_routines(X, T, high)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.40 tff(58,plain,(
% 0.20/0.40 ![X: $i, T: $i] : (~(number_of_routines(X, T, low) & number_of_routines(X, T, high)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[57])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (![X: $i, T: $i] : ((~number_of_routines(X, T, low)) | (~number_of_routines(X, T, high)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (![X: $i, T: $i] : ((~number_of_routines(X, T, low)) | (~number_of_routines(X, T, high)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (((~![X: $i, T: $i] : ((~number_of_routines(X, T, low)) | (~number_of_routines(X, T, high)))) | ((~number_of_routines(X!1, T!0, low)) | (~number_of_routines(X!1, T!0, high)))) <=> ((~![X: $i, T: $i] : ((~number_of_routines(X, T, low)) | (~number_of_routines(X, T, high)))) | (~number_of_routines(X!1, T!0, low)) | (~number_of_routines(X!1, T!0, high)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 ((~![X: $i, T: $i] : ((~number_of_routines(X, T, low)) | (~number_of_routines(X, T, high)))) | ((~number_of_routines(X!1, T!0, low)) | (~number_of_routines(X!1, T!0, high)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 ((~![X: $i, T: $i] : ((~number_of_routines(X, T, low)) | (~number_of_routines(X, T, high)))) | (~number_of_routines(X!1, T!0, low)) | (~number_of_routines(X!1, T!0, high))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (~number_of_routines(X!1, T!0, low)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[63, 60, 50])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (^[X: $i, T: $i] : refl((number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))) <=> (number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (![X: $i, T: $i] : (number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))) <=> ![X: $i, T: $i] : (number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (^[X: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((organisation_at_time(X, T) & first_mover(X) & founding_time(X, T)) <=> (~((~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))))), ((~(organisation_at_time(X, T) & first_mover(X) & founding_time(X, T))) <=> (~(~((~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))))))), rewrite((~(~((~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))))) <=> ((~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))), ((~(organisation_at_time(X, T) & first_mover(X) & founding_time(X, T))) <=> ((~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))))), (((~(organisation_at_time(X, T) & first_mover(X) & founding_time(X, T))) | number_of_routines(X, T, low)) <=> (((~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))) | number_of_routines(X, T, low)))), rewrite((((~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T))) | number_of_routines(X, T, low)) <=> (number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))), (((~(organisation_at_time(X, T) & first_mover(X) & founding_time(X, T))) | number_of_routines(X, T, low)) <=> (number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (![X: $i, T: $i] : ((~(organisation_at_time(X, T) & first_mover(X) & founding_time(X, T))) | number_of_routines(X, T, low)) <=> ![X: $i, T: $i] : (number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (![X: $i, T: $i] : ((~(organisation_at_time(X, T) & first_mover(X) & founding_time(X, T))) | number_of_routines(X, T, low)) <=> ![X: $i, T: $i] : ((~(organisation_at_time(X, T) & first_mover(X) & founding_time(X, T))) | number_of_routines(X, T, low))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (^[X: $i, T: $i] : trans(monotonicity(rewrite(((organisation_at_time(X, T) & first_mover(X)) & founding_time(X, T)) <=> (organisation_at_time(X, T) & first_mover(X) & founding_time(X, T))), ((((organisation_at_time(X, T) & first_mover(X)) & founding_time(X, T)) => number_of_routines(X, T, low)) <=> ((organisation_at_time(X, T) & first_mover(X) & founding_time(X, T)) => number_of_routines(X, T, low)))), rewrite(((organisation_at_time(X, T) & first_mover(X) & founding_time(X, T)) => number_of_routines(X, T, low)) <=> ((~(organisation_at_time(X, T) & first_mover(X) & founding_time(X, T))) | number_of_routines(X, T, low))), ((((organisation_at_time(X, T) & first_mover(X)) & founding_time(X, T)) => number_of_routines(X, T, low)) <=> ((~(organisation_at_time(X, T) & first_mover(X) & founding_time(X, T))) | number_of_routines(X, T, low))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (![X: $i, T: $i] : (((organisation_at_time(X, T) & first_mover(X)) & founding_time(X, T)) => number_of_routines(X, T, low)) <=> ![X: $i, T: $i] : ((~(organisation_at_time(X, T) & first_mover(X) & founding_time(X, T))) | number_of_routines(X, T, low))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.40 tff(72,axiom,(![X: $i, T: $i] : (((organisation_at_time(X, T) & first_mover(X)) & founding_time(X, T)) => number_of_routines(X, T, low))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a15')).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (![X: $i, T: $i] : ((~(organisation_at_time(X, T) & first_mover(X) & founding_time(X, T))) | number_of_routines(X, T, low))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (![X: $i, T: $i] : ((~(organisation_at_time(X, T) & first_mover(X) & founding_time(X, T))) | number_of_routines(X, T, low))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.40 tff(75,plain,(
% 0.20/0.40 ![X: $i, T: $i] : ((~(organisation_at_time(X, T) & first_mover(X) & founding_time(X, T))) | number_of_routines(X, T, low))),
% 0.20/0.40 inference(skolemize,[status(sab)],[74])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (![X: $i, T: $i] : (number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (![X: $i, T: $i] : (number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[76, 66])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (((~![X: $i, T: $i] : (number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))) | (number_of_routines(X!1, T!0, low) | (~organisation_at_time(X!1, T!0)) | (~founding_time(X!1, T!0)) | (~first_mover(X!1)))) <=> ((~![X: $i, T: $i] : (number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))) | number_of_routines(X!1, T!0, low) | (~organisation_at_time(X!1, T!0)) | (~founding_time(X!1, T!0)) | (~first_mover(X!1)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 ((number_of_routines(X!1, T!0, low) | (~first_mover(X!1)) | (~organisation_at_time(X!1, T!0)) | (~founding_time(X!1, T!0))) <=> (number_of_routines(X!1, T!0, low) | (~organisation_at_time(X!1, T!0)) | (~founding_time(X!1, T!0)) | (~first_mover(X!1)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (((~![X: $i, T: $i] : (number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))) | (number_of_routines(X!1, T!0, low) | (~first_mover(X!1)) | (~organisation_at_time(X!1, T!0)) | (~founding_time(X!1, T!0)))) <=> ((~![X: $i, T: $i] : (number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))) | (number_of_routines(X!1, T!0, low) | (~organisation_at_time(X!1, T!0)) | (~founding_time(X!1, T!0)) | (~first_mover(X!1))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[79])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (((~![X: $i, T: $i] : (number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))) | (number_of_routines(X!1, T!0, low) | (~first_mover(X!1)) | (~organisation_at_time(X!1, T!0)) | (~founding_time(X!1, T!0)))) <=> ((~![X: $i, T: $i] : (number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))) | number_of_routines(X!1, T!0, low) | (~organisation_at_time(X!1, T!0)) | (~founding_time(X!1, T!0)) | (~first_mover(X!1)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[80, 78])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 ((~![X: $i, T: $i] : (number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))) | (number_of_routines(X!1, T!0, low) | (~first_mover(X!1)) | (~organisation_at_time(X!1, T!0)) | (~founding_time(X!1, T!0)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 ((~![X: $i, T: $i] : (number_of_routines(X, T, low) | (~first_mover(X)) | (~organisation_at_time(X, T)) | (~founding_time(X, T)))) | number_of_routines(X!1, T!0, low) | (~organisation_at_time(X!1, T!0)) | (~founding_time(X!1, T!0)) | (~first_mover(X!1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[83, 77, 10, 9, 64, 49])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------