TSTP Solution File: MGT056+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT056+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 05:22:16 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT056+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 03:16:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(has_immunity_type, type, (
% 0.20/0.40 has_immunity: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_T1_2_type, type, (
% 0.20/0.40 tptp_fun_T1_2: $i)).
% 0.20/0.40 tff(tptp_fun_X_4_type, type, (
% 0.20/0.40 tptp_fun_X_4: $i)).
% 0.20/0.40 tff(smaller_or_equal_type, type, (
% 0.20/0.40 smaller_or_equal: ( $i * $i ) > $o)).
% 0.20/0.40 tff(eta_type, type, (
% 0.20/0.40 eta: $i)).
% 0.20/0.40 tff(age_type, type, (
% 0.20/0.40 age: ( $i * $i ) > $i)).
% 0.20/0.40 tff(greater_type, type, (
% 0.20/0.40 greater: ( $i * $i ) > $o)).
% 0.20/0.40 tff(organization_type, type, (
% 0.20/0.40 organization: $i > $o)).
% 0.20/0.40 tff(has_endowment_type, type, (
% 0.20/0.40 has_endowment: $i > $o)).
% 0.20/0.40 tff(tptp_fun_T_0_type, type, (
% 0.20/0.40 tptp_fun_T_0: $i > $i)).
% 0.20/0.40 tff(zero_type, type, (
% 0.20/0.40 zero: $i)).
% 0.20/0.40 tff(sigma_type, type, (
% 0.20/0.40 sigma: $i)).
% 0.20/0.40 tff(greater_or_equal_type, type, (
% 0.20/0.40 greater_or_equal: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_T2_1_type, type, (
% 0.20/0.40 tptp_fun_T2_1: $i)).
% 0.20/0.40 tff(tptp_fun_T0_3_type, type, (
% 0.20/0.40 tptp_fun_T0_3: $i)).
% 0.20/0.40 tff(hazard_of_mortality_type, type, (
% 0.20/0.40 hazard_of_mortality: ( $i * $i ) > $i)).
% 0.20/0.40 tff(smaller_type, type, (
% 0.20/0.40 smaller: ( $i * $i ) > $o)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[X: $i] : rewrite((~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))))) <=> (~((~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))) | (~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![X: $i] : (~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))))) <=> ![X: $i] : (~((~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))) | (~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta))))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (^[X: $i] : refl((~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))))) <=> (~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![X: $i] : (~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))))) <=> ![X: $i] : (~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (^[X: $i] : rewrite((~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))))) <=> (~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (![X: $i] : (~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))))) <=> ![X: $i] : (~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![X: $i] : (~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))))) <=> ![X: $i] : (~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[6, 4])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (^[X: $i] : trans(monotonicity(rewrite(((~has_endowment(X)) | ![T: $i] : (organization(X) & ((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T)) & ((~has_immunity(X, T)) | (~greater(age(X, T), eta))))) <=> ((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))), trans(monotonicity(trans(monotonicity(rewrite((organization(X) & ((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X))) & ((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))) <=> (~((~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))))), ((~(organization(X) & ((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X))) & ((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))) <=> (~(~((~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))))))), rewrite((~(~((~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))))) <=> ((~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))), ((~(organization(X) & ((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X))) & ((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))) <=> ((~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))))), ((has_endowment(X) | (~(organization(X) & ((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X))) & ((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))) <=> (has_endowment(X) | ((~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))))), rewrite((has_endowment(X) | ((~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))) <=> (has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))), ((has_endowment(X) | (~(organization(X) & ((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X))) & ((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))) <=> (has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))))), ((((~has_endowment(X)) | ![T: $i] : (organization(X) & ((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T)) & ((~has_immunity(X, T)) | (~greater(age(X, T), eta))))) & (has_endowment(X) | (~(organization(X) & ((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X))) & ((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))))) <=> (((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta))))))) & (has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))))), rewrite((((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta))))))) & (has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))) <=> (~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))))))), ((((~has_endowment(X)) | ![T: $i] : (organization(X) & ((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T)) & ((~has_immunity(X, T)) | (~greater(age(X, T), eta))))) & (has_endowment(X) | (~(organization(X) & ((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X))) & ((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))))) <=> (~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (![X: $i] : (((~has_endowment(X)) | ![T: $i] : (organization(X) & ((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T)) & ((~has_immunity(X, T)) | (~greater(age(X, T), eta))))) & (has_endowment(X) | (~(organization(X) & ((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X))) & ((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))))) <=> ![X: $i] : (~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (![X: $i] : (has_endowment(X) <=> ![T: $i] : (organization(X) & ((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T)) & ((~has_immunity(X, T)) | (~greater(age(X, T), eta))))) <=> ![X: $i] : (has_endowment(X) <=> ![T: $i] : (organization(X) & ((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T)) & ((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (^[X: $i] : rewrite((has_endowment(X) <=> ![T: $i] : ((organization(X) & (smaller_or_equal(age(X, T), eta) => has_immunity(X, T))) & (greater(age(X, T), eta) => (~has_immunity(X, T))))) <=> (has_endowment(X) <=> ![T: $i] : (organization(X) & ((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T)) & ((~has_immunity(X, T)) | (~greater(age(X, T), eta))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (![X: $i] : (has_endowment(X) <=> ![T: $i] : ((organization(X) & (smaller_or_equal(age(X, T), eta) => has_immunity(X, T))) & (greater(age(X, T), eta) => (~has_immunity(X, T))))) <=> ![X: $i] : (has_endowment(X) <=> ![T: $i] : (organization(X) & ((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T)) & ((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.40 tff(13,axiom,(![X: $i] : (has_endowment(X) <=> ![T: $i] : ((organization(X) & (smaller_or_equal(age(X, T), eta) => has_immunity(X, T))) & (greater(age(X, T), eta) => (~has_immunity(X, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','definition_1')).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![X: $i] : (has_endowment(X) <=> ![T: $i] : (organization(X) & ((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T)) & ((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (![X: $i] : (has_endowment(X) <=> ![T: $i] : (organization(X) & ((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T)) & ((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.20/0.40 tff(16,plain,(
% 0.20/0.40 ![X: $i] : (((~has_endowment(X)) | ![T: $i] : (organization(X) & ((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T)) & ((~has_immunity(X, T)) | (~greater(age(X, T), eta))))) & (has_endowment(X) | (~(organization(X) & ((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X))) & ((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![X: $i] : (~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (![X: $i] : (~((~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta)))))))) | (~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![X: $i] : (~((~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))) | (~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta))))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 ((~![X: $i] : (~((~(has_endowment(X) | (~organization(X)) | (~((~smaller_or_equal(age(X, tptp_fun_T_0(X)), eta)) | has_immunity(X, tptp_fun_T_0(X)))) | (~((~has_immunity(X, tptp_fun_T_0(X))) | (~greater(age(X, tptp_fun_T_0(X)), eta)))))) | (~((~has_endowment(X)) | ![T: $i] : (~((~organization(X)) | (~((~smaller_or_equal(age(X, T), eta)) | has_immunity(X, T))) | (~((~has_immunity(X, T)) | (~greater(age(X, T), eta))))))))))) | (~((~(has_endowment(X!4) | (~organization(X!4)) | (~((~smaller_or_equal(age(X!4, tptp_fun_T_0(X!4)), eta)) | has_immunity(X!4, tptp_fun_T_0(X!4)))) | (~((~has_immunity(X!4, tptp_fun_T_0(X!4))) | (~greater(age(X!4, tptp_fun_T_0(X!4)), eta)))))) | (~((~has_endowment(X!4)) | ![T: $i] : (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T), eta)) | has_immunity(X!4, T))) | (~((~has_immunity(X!4, T)) | (~greater(age(X!4, T), eta))))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (~((~(has_endowment(X!4) | (~organization(X!4)) | (~((~smaller_or_equal(age(X!4, tptp_fun_T_0(X!4)), eta)) | has_immunity(X!4, tptp_fun_T_0(X!4)))) | (~((~has_immunity(X!4, tptp_fun_T_0(X!4))) | (~greater(age(X!4, tptp_fun_T_0(X!4)), eta)))))) | (~((~has_endowment(X!4)) | ![T: $i] : (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T), eta)) | has_immunity(X!4, T))) | (~((~has_immunity(X!4, T)) | (~greater(age(X!4, T), eta)))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (((~(has_endowment(X!4) | (~organization(X!4)) | (~((~smaller_or_equal(age(X!4, tptp_fun_T_0(X!4)), eta)) | has_immunity(X!4, tptp_fun_T_0(X!4)))) | (~((~has_immunity(X!4, tptp_fun_T_0(X!4))) | (~greater(age(X!4, tptp_fun_T_0(X!4)), eta)))))) | (~((~has_endowment(X!4)) | ![T: $i] : (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T), eta)) | has_immunity(X!4, T))) | (~((~has_immunity(X!4, T)) | (~greater(age(X!4, T), eta))))))))) | ((~has_endowment(X!4)) | ![T: $i] : (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T), eta)) | has_immunity(X!4, T))) | (~((~has_immunity(X!4, T)) | (~greater(age(X!4, T), eta)))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 ((~has_endowment(X!4)) | ![T: $i] : (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T), eta)) | has_immunity(X!4, T))) | (~((~has_immunity(X!4, T)) | (~greater(age(X!4, T), eta))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 ((~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & has_endowment(X) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), eta) & greater(age(X, T2), eta) & greater_or_equal(eta, sigma) & greater(sigma, zero))) | (greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)) & (hazard_of_mortality(X, T1) = hazard_of_mortality(X, T0))))) <=> (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & has_endowment(X) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), eta) & greater(age(X, T2), eta) & greater_or_equal(eta, sigma) & greater(sigma, zero))) | (greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)) & (hazard_of_mortality(X, T1) = hazard_of_mortality(X, T0)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 ((~![X: $i, T0: $i, T1: $i, T2: $i] : (((((((organization(X) & has_endowment(X)) & (age(X, T0) = zero)) & smaller_or_equal(age(X, T1), eta)) & greater(age(X, T2), eta)) & greater_or_equal(eta, sigma)) & greater(sigma, zero)) => (greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)) & (hazard_of_mortality(X, T1) = hazard_of_mortality(X, T0))))) <=> (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & has_endowment(X) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), eta) & greater(age(X, T2), eta) & greater_or_equal(eta, sigma) & greater(sigma, zero))) | (greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)) & (hazard_of_mortality(X, T1) = hazard_of_mortality(X, T0)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(26,axiom,(~![X: $i, T0: $i, T1: $i, T2: $i] : (((((((organization(X) & has_endowment(X)) & (age(X, T0) = zero)) & smaller_or_equal(age(X, T1), eta)) & greater(age(X, T2), eta)) & greater_or_equal(eta, sigma)) & greater(sigma, zero)) => (greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)) & (hazard_of_mortality(X, T1) = hazard_of_mortality(X, T0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_9')).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & has_endowment(X) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), eta) & greater(age(X, T2), eta) & greater_or_equal(eta, sigma) & greater(sigma, zero))) | (greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)) & (hazard_of_mortality(X, T1) = hazard_of_mortality(X, T0))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & has_endowment(X) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), eta) & greater(age(X, T2), eta) & greater_or_equal(eta, sigma) & greater(sigma, zero))) | (greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)) & (hazard_of_mortality(X, T1) = hazard_of_mortality(X, T0))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & has_endowment(X) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), eta) & greater(age(X, T2), eta) & greater_or_equal(eta, sigma) & greater(sigma, zero))) | (greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)) & (hazard_of_mortality(X, T1) = hazard_of_mortality(X, T0))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & has_endowment(X) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), eta) & greater(age(X, T2), eta) & greater_or_equal(eta, sigma) & greater(sigma, zero))) | (greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)) & (hazard_of_mortality(X, T1) = hazard_of_mortality(X, T0))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & has_endowment(X) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), eta) & greater(age(X, T2), eta) & greater_or_equal(eta, sigma) & greater(sigma, zero))) | (greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)) & (hazard_of_mortality(X, T1) = hazard_of_mortality(X, T0))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & has_endowment(X) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), eta) & greater(age(X, T2), eta) & greater_or_equal(eta, sigma) & greater(sigma, zero))) | (greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)) & (hazard_of_mortality(X, T1) = hazard_of_mortality(X, T0))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & has_endowment(X) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), eta) & greater(age(X, T2), eta) & greater_or_equal(eta, sigma) & greater(sigma, zero))) | (greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)) & (hazard_of_mortality(X, T1) = hazard_of_mortality(X, T0))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[32, 24])).
% 0.20/0.41 tff(34,plain,(
% 0.20/0.41 ~((~(organization(X!4) & has_endowment(X!4) & (age(X!4, T0!3) = zero) & smaller_or_equal(age(X!4, T1!2), eta) & greater(age(X!4, T2!1), eta) & greater_or_equal(eta, sigma) & greater(sigma, zero))) | (greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2)) & (hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[33])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (organization(X!4) & has_endowment(X!4) & (age(X!4, T0!3) = zero) & smaller_or_equal(age(X!4, T1!2), eta) & greater(age(X!4, T2!1), eta) & greater_or_equal(eta, sigma) & greater(sigma, zero)),
% 0.20/0.41 inference(or_elim,[status(thm)],[34])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (has_endowment(X!4)),
% 0.20/0.41 inference(and_elim,[status(thm)],[35])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 ((~((~has_endowment(X!4)) | ![T: $i] : (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T), eta)) | has_immunity(X!4, T))) | (~((~has_immunity(X!4, T)) | (~greater(age(X!4, T), eta)))))))) | (~has_endowment(X!4)) | ![T: $i] : (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T), eta)) | has_immunity(X!4, T))) | (~((~has_immunity(X!4, T)) | (~greater(age(X!4, T), eta))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 ((~((~has_endowment(X!4)) | ![T: $i] : (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T), eta)) | has_immunity(X!4, T))) | (~((~has_immunity(X!4, T)) | (~greater(age(X!4, T), eta)))))))) | ![T: $i] : (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T), eta)) | has_immunity(X!4, T))) | (~((~has_immunity(X!4, T)) | (~greater(age(X!4, T), eta))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (![T: $i] : (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T), eta)) | has_immunity(X!4, T))) | (~((~has_immunity(X!4, T)) | (~greater(age(X!4, T), eta))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[38, 23])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 ((~![T: $i] : (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T), eta)) | has_immunity(X!4, T))) | (~((~has_immunity(X!4, T)) | (~greater(age(X!4, T), eta))))))) | (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T1!2), eta)) | has_immunity(X!4, T1!2))) | (~((~has_immunity(X!4, T1!2)) | (~greater(age(X!4, T1!2), eta))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T1!2), eta)) | has_immunity(X!4, T1!2))) | (~((~has_immunity(X!4, T1!2)) | (~greater(age(X!4, T1!2), eta)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T1!2), eta)) | has_immunity(X!4, T1!2))) | (~((~has_immunity(X!4, T1!2)) | (~greater(age(X!4, T1!2), eta))))) | ((~smaller_or_equal(age(X!4, T1!2), eta)) | has_immunity(X!4, T1!2))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 ((~smaller_or_equal(age(X!4, T1!2), eta)) | has_immunity(X!4, T1!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (smaller_or_equal(age(X!4, T1!2), eta)),
% 0.20/0.41 inference(and_elim,[status(thm)],[35])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 ((~((~smaller_or_equal(age(X!4, T1!2), eta)) | has_immunity(X!4, T1!2))) | (~smaller_or_equal(age(X!4, T1!2), eta)) | has_immunity(X!4, T1!2)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 ((~((~smaller_or_equal(age(X!4, T1!2), eta)) | has_immunity(X!4, T1!2))) | has_immunity(X!4, T1!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (has_immunity(X!4, T1!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : refl((smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y))) <=> (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y))) <=> ![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y))) <=> ![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : rewrite((smaller_or_equal(X, Y) <=> (smaller(X, Y) | (X = Y))) <=> (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> (smaller(X, Y) | (X = Y))) <=> ![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.41 tff(53,axiom,(![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> (smaller(X, Y) | (X = Y)))), file('/export/starexec/sandbox/benchmark/Axioms/MGT001+0.ax','definition_smaller_or_equal')).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.41 tff(56,plain,(
% 0.20/0.41 ![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[55])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))) | (smaller_or_equal(zero, eta) <=> ((zero = eta) | smaller(zero, eta)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (smaller_or_equal(zero, eta) <=> ((zero = eta) | smaller(zero, eta))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (age(X!4, T0!3) = zero),
% 0.20/0.41 inference(and_elim,[status(thm)],[35])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (zero = age(X!4, T0!3)),
% 0.20/0.41 inference(symmetry,[status(thm)],[60])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (smaller_or_equal(zero, eta) <=> smaller_or_equal(age(X!4, T0!3), eta)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[61])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (smaller_or_equal(age(X!4, T0!3), eta) <=> smaller_or_equal(zero, eta)),
% 0.20/0.41 inference(symmetry,[status(thm)],[62])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 ((~smaller_or_equal(age(X!4, T0!3), eta)) <=> (~smaller_or_equal(zero, eta))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[63])).
% 0.20/0.41 tff(65,assumption,(~smaller_or_equal(age(X!4, T0!3), eta)), introduced(assumption)).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (~smaller_or_equal(zero, eta)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 ((~(smaller_or_equal(zero, eta) <=> ((zero = eta) | smaller(zero, eta)))) | smaller_or_equal(zero, eta) | (~((zero = eta) | smaller(zero, eta)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (~((zero = eta) | smaller(zero, eta))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[67, 66, 59])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 (((zero = eta) | smaller(zero, eta)) | (~smaller(zero, eta))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (~smaller(zero, eta)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (((zero = eta) | smaller(zero, eta)) | (~(zero = eta))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (~(zero = eta)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : refl(((X = Y) | smaller(X, Y) | greater(X, Y)) <=> ((X = Y) | smaller(X, Y) | greater(X, Y)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y)) <=> ![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y)) <=> ![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((smaller(X, Y) | (X = Y)) <=> ((X = Y) | smaller(X, Y))), (((smaller(X, Y) | (X = Y)) | greater(X, Y)) <=> (((X = Y) | smaller(X, Y)) | greater(X, Y)))), rewrite((((X = Y) | smaller(X, Y)) | greater(X, Y)) <=> ((X = Y) | smaller(X, Y) | greater(X, Y))), (((smaller(X, Y) | (X = Y)) | greater(X, Y)) <=> ((X = Y) | smaller(X, Y) | greater(X, Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((smaller(X, Y) | (X = Y)) | greater(X, Y)) <=> ![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.42 tff(78,axiom,(![X: $i, Y: $i] : ((smaller(X, Y) | (X = Y)) | greater(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/MGT001+0.ax','meaning_postulate_greater_comparable')).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.20/0.42 tff(81,plain,(
% 0.20/0.42 ![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))),
% 0.20/0.42 inference(skolemize,[status(sab)],[80])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))) | ((zero = eta) | smaller(zero, eta) | greater(zero, eta))) <=> ((~![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))) | (zero = eta) | smaller(zero, eta) | greater(zero, eta))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))) | ((zero = eta) | smaller(zero, eta) | greater(zero, eta))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))) | (zero = eta) | smaller(zero, eta) | greater(zero, eta)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (greater(zero, eta)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[85, 82, 72, 70])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (greater(sigma, zero)),
% 0.20/0.42 inference(and_elim,[status(thm)],[35])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((greater(X, Y) & greater(Y, Z)) <=> (~((~greater(Y, Z)) | (~greater(X, Y))))), ((~(greater(X, Y) & greater(Y, Z))) <=> (~(~((~greater(Y, Z)) | (~greater(X, Y))))))), rewrite((~(~((~greater(Y, Z)) | (~greater(X, Y))))) <=> ((~greater(Y, Z)) | (~greater(X, Y)))), ((~(greater(X, Y) & greater(Y, Z))) <=> ((~greater(Y, Z)) | (~greater(X, Y))))), (((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> (((~greater(Y, Z)) | (~greater(X, Y))) | greater(X, Z)))), rewrite((((~greater(Y, Z)) | (~greater(X, Y))) | greater(X, Z)) <=> (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))), (((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (^[X: $i, Y: $i, Z: $i] : rewrite(((greater(X, Y) & greater(Y, Z)) => greater(X, Z)) <=> ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : ((greater(X, Y) & greater(Y, Z)) => greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.42 tff(94,axiom,(![X: $i, Y: $i, Z: $i] : ((greater(X, Y) & greater(Y, Z)) => greater(X, Z))), file('/export/starexec/sandbox/benchmark/Axioms/MGT001+0.ax','meaning_postulate_greater_transitive')).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.20/0.42 tff(97,plain,(
% 0.20/0.42 ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.20/0.42 inference(skolemize,[status(sab)],[96])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[98, 88])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))) | ((~greater(sigma, zero)) | greater(sigma, eta) | (~greater(zero, eta)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))) | (~greater(sigma, zero)) | greater(sigma, eta) | (~greater(zero, eta)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 ((greater(sigma, eta) | (~greater(zero, eta)) | (~greater(sigma, zero))) <=> ((~greater(sigma, zero)) | greater(sigma, eta) | (~greater(zero, eta)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))) | (greater(sigma, eta) | (~greater(zero, eta)) | (~greater(sigma, zero)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))) | ((~greater(sigma, zero)) | greater(sigma, eta) | (~greater(zero, eta))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[101])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))) | (greater(sigma, eta) | (~greater(zero, eta)) | (~greater(sigma, zero)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))) | (~greater(sigma, zero)) | greater(sigma, eta) | (~greater(zero, eta)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[102, 100])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))) | (greater(sigma, eta) | (~greater(zero, eta)) | (~greater(sigma, zero)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))) | (~greater(sigma, zero)) | greater(sigma, eta) | (~greater(zero, eta))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (greater(sigma, eta)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[105, 99, 87, 86])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : refl(((~greater(X, Y)) | (~greater(Y, X))) <=> ((~greater(X, Y)) | (~greater(Y, X))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X))) <=> ![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((greater(X, Y) & greater(Y, X)) <=> (~((~greater(X, Y)) | (~greater(Y, X))))), ((~(greater(X, Y) & greater(Y, X))) <=> (~(~((~greater(X, Y)) | (~greater(Y, X))))))), rewrite((~(~((~greater(X, Y)) | (~greater(Y, X))))) <=> ((~greater(X, Y)) | (~greater(Y, X)))), ((~(greater(X, Y) & greater(Y, X))) <=> ((~greater(X, Y)) | (~greater(Y, X)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X))) <=> ![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X))) <=> ![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(112,axiom,(![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/MGT001+0.ax','meaning_postulate_greater_strict')).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.42 tff(114,plain,(
% 0.20/0.42 ![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[113])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))) | ((~greater(eta, sigma)) | (~greater(sigma, eta)))) <=> ((~![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))) | (~greater(eta, sigma)) | (~greater(sigma, eta)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))) | ((~greater(eta, sigma)) | (~greater(sigma, eta)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))) | (~greater(eta, sigma)) | (~greater(sigma, eta))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 (~greater(eta, sigma)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[119, 116, 106])).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : refl((greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(122,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[121])).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : rewrite((greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y))) <=> (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.42 tff(126,axiom,(![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y)))), file('/export/starexec/sandbox/benchmark/Axioms/MGT001+0.ax','definition_greater_or_equal')).
% 0.20/0.42 tff(127,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.20/0.42 tff(129,plain,(
% 0.20/0.42 ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[128])).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(eta, sigma) <=> ((eta = sigma) | greater(eta, sigma)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (greater_or_equal(eta, sigma) <=> ((eta = sigma) | greater(eta, sigma))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (greater_or_equal(eta, sigma)),
% 0.20/0.42 inference(and_elim,[status(thm)],[35])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 ((~(greater_or_equal(eta, sigma) <=> ((eta = sigma) | greater(eta, sigma)))) | (~greater_or_equal(eta, sigma)) | ((eta = sigma) | greater(eta, sigma))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 ((~(greater_or_equal(eta, sigma) <=> ((eta = sigma) | greater(eta, sigma)))) | ((eta = sigma) | greater(eta, sigma))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 ((eta = sigma) | greater(eta, sigma)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[135, 132])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 ((~((eta = sigma) | greater(eta, sigma))) | (eta = sigma) | greater(eta, sigma)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(138,plain,
% 0.20/0.42 ((eta = sigma) | greater(eta, sigma)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.20/0.42 tff(139,plain,
% 0.20/0.42 (eta = sigma),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[138, 120])).
% 0.20/0.42 tff(140,plain,
% 0.20/0.42 (sigma = eta),
% 0.20/0.42 inference(symmetry,[status(thm)],[139])).
% 0.20/0.42 tff(141,plain,
% 0.20/0.42 (smaller_or_equal(zero, sigma) <=> smaller_or_equal(age(X!4, T0!3), eta)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[61, 140])).
% 0.20/0.42 tff(142,plain,
% 0.20/0.42 (smaller_or_equal(age(X!4, T0!3), eta) <=> smaller_or_equal(zero, sigma)),
% 0.20/0.42 inference(symmetry,[status(thm)],[141])).
% 0.20/0.42 tff(143,plain,
% 0.20/0.42 ((~smaller_or_equal(age(X!4, T0!3), eta)) <=> (~smaller_or_equal(zero, sigma))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.42 tff(144,plain,
% 0.20/0.42 (~smaller_or_equal(zero, sigma)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[65, 143])).
% 0.20/0.42 tff(145,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))) | (smaller_or_equal(zero, sigma) <=> ((zero = sigma) | smaller(zero, sigma)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(146,plain,
% 0.20/0.42 (smaller_or_equal(zero, sigma) <=> ((zero = sigma) | smaller(zero, sigma))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[145, 57])).
% 0.20/0.42 tff(147,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : refl((smaller(X, Y) <=> greater(Y, X)) <=> (smaller(X, Y) <=> greater(Y, X)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(148,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X)) <=> ![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[147])).
% 0.20/0.42 tff(149,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X)) <=> ![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(150,axiom,(![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/MGT001+0.ax','definition_smaller')).
% 0.20/0.42 tff(151,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.20/0.42 tff(152,plain,(
% 0.20/0.42 ![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.20/0.42 inference(skolemize,[status(sab)],[151])).
% 0.20/0.42 tff(153,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.20/0.42 tff(154,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))) | (smaller(zero, sigma) <=> greater(sigma, zero))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(155,plain,
% 0.20/0.42 (smaller(zero, sigma) <=> greater(sigma, zero)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.20/0.42 tff(156,plain,
% 0.20/0.42 ((~(smaller(zero, sigma) <=> greater(sigma, zero))) | smaller(zero, sigma) | (~greater(sigma, zero))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(157,plain,
% 0.20/0.42 ((~(smaller(zero, sigma) <=> greater(sigma, zero))) | smaller(zero, sigma)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[156, 87])).
% 0.20/0.42 tff(158,plain,
% 0.20/0.42 (smaller(zero, sigma)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[157, 155])).
% 0.20/0.42 tff(159,plain,
% 0.20/0.42 (((zero = sigma) | smaller(zero, sigma)) | (~smaller(zero, sigma))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(160,plain,
% 0.20/0.42 ((zero = sigma) | smaller(zero, sigma)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.20/0.43 tff(161,plain,
% 0.20/0.43 ((~(smaller_or_equal(zero, sigma) <=> ((zero = sigma) | smaller(zero, sigma)))) | smaller_or_equal(zero, sigma) | (~((zero = sigma) | smaller(zero, sigma)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(162,plain,
% 0.20/0.43 ((~(smaller_or_equal(zero, sigma) <=> ((zero = sigma) | smaller(zero, sigma)))) | smaller_or_equal(zero, sigma)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.20/0.43 tff(163,plain,
% 0.20/0.43 (smaller_or_equal(zero, sigma)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[162, 146])).
% 0.20/0.43 tff(164,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[163, 144])).
% 0.20/0.43 tff(165,plain,(smaller_or_equal(age(X!4, T0!3), eta)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(166,plain,
% 0.20/0.43 ((~![T: $i] : (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T), eta)) | has_immunity(X!4, T))) | (~((~has_immunity(X!4, T)) | (~greater(age(X!4, T), eta))))))) | (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T0!3), eta)) | has_immunity(X!4, T0!3))) | (~((~has_immunity(X!4, T0!3)) | (~greater(age(X!4, T0!3), eta))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(167,plain,
% 0.20/0.43 (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T0!3), eta)) | has_immunity(X!4, T0!3))) | (~((~has_immunity(X!4, T0!3)) | (~greater(age(X!4, T0!3), eta)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[166, 39])).
% 0.20/0.43 tff(168,plain,
% 0.20/0.43 (((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T0!3), eta)) | has_immunity(X!4, T0!3))) | (~((~has_immunity(X!4, T0!3)) | (~greater(age(X!4, T0!3), eta))))) | ((~smaller_or_equal(age(X!4, T0!3), eta)) | has_immunity(X!4, T0!3))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(169,plain,
% 0.20/0.43 ((~smaller_or_equal(age(X!4, T0!3), eta)) | has_immunity(X!4, T0!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.20/0.43 tff(170,plain,
% 0.20/0.43 ((~((~smaller_or_equal(age(X!4, T0!3), eta)) | has_immunity(X!4, T0!3))) | (~smaller_or_equal(age(X!4, T0!3), eta)) | has_immunity(X!4, T0!3)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(171,plain,
% 0.20/0.43 ((~smaller_or_equal(age(X!4, T0!3), eta)) | has_immunity(X!4, T0!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.20/0.43 tff(172,plain,
% 0.20/0.43 (has_immunity(X!4, T0!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[171, 165])).
% 0.20/0.43 tff(173,plain,
% 0.20/0.43 ((~![T: $i] : (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T), eta)) | has_immunity(X!4, T))) | (~((~has_immunity(X!4, T)) | (~greater(age(X!4, T), eta))))))) | (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T2!1), eta)) | has_immunity(X!4, T2!1))) | (~((~has_immunity(X!4, T2!1)) | (~greater(age(X!4, T2!1), eta))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(174,plain,
% 0.20/0.43 (~((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T2!1), eta)) | has_immunity(X!4, T2!1))) | (~((~has_immunity(X!4, T2!1)) | (~greater(age(X!4, T2!1), eta)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[173, 39])).
% 0.20/0.43 tff(175,plain,
% 0.20/0.43 (((~organization(X!4)) | (~((~smaller_or_equal(age(X!4, T2!1), eta)) | has_immunity(X!4, T2!1))) | (~((~has_immunity(X!4, T2!1)) | (~greater(age(X!4, T2!1), eta))))) | ((~has_immunity(X!4, T2!1)) | (~greater(age(X!4, T2!1), eta)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(176,plain,
% 0.20/0.43 ((~has_immunity(X!4, T2!1)) | (~greater(age(X!4, T2!1), eta))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.20/0.43 tff(177,plain,
% 0.20/0.43 (greater(age(X!4, T2!1), eta)),
% 0.20/0.43 inference(and_elim,[status(thm)],[35])).
% 0.20/0.43 tff(178,plain,
% 0.20/0.43 ((~((~has_immunity(X!4, T2!1)) | (~greater(age(X!4, T2!1), eta)))) | (~has_immunity(X!4, T2!1)) | (~greater(age(X!4, T2!1), eta))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(179,plain,
% 0.20/0.43 ((~((~has_immunity(X!4, T2!1)) | (~greater(age(X!4, T2!1), eta)))) | (~has_immunity(X!4, T2!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.20/0.43 tff(180,plain,
% 0.20/0.43 (~has_immunity(X!4, T2!1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[179, 176])).
% 0.20/0.43 tff(181,assumption,(~greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2))), introduced(assumption)).
% 0.20/0.43 tff(182,plain,
% 0.20/0.43 (organization(X!4)),
% 0.20/0.43 inference(and_elim,[status(thm)],[35])).
% 0.20/0.43 tff(183,plain,
% 0.20/0.43 (^[X: $i, T0: $i, T: $i] : refl((has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0))) <=> (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(184,plain,
% 0.20/0.43 (![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0))) <=> ![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[183])).
% 0.20/0.43 tff(185,plain,
% 0.20/0.43 (^[X: $i, T0: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((organization(X) & has_immunity(X, T0) & (~has_immunity(X, T))) <=> (~((~organization(X)) | (~has_immunity(X, T0)) | has_immunity(X, T)))), ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) <=> (~(~((~organization(X)) | (~has_immunity(X, T0)) | has_immunity(X, T)))))), rewrite((~(~((~organization(X)) | (~has_immunity(X, T0)) | has_immunity(X, T)))) <=> ((~organization(X)) | (~has_immunity(X, T0)) | has_immunity(X, T))), ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) <=> ((~organization(X)) | (~has_immunity(X, T0)) | has_immunity(X, T)))), (((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> (((~organization(X)) | (~has_immunity(X, T0)) | has_immunity(X, T)) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))))), rewrite((((~organization(X)) | (~has_immunity(X, T0)) | has_immunity(X, T)) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0)))), (((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(186,plain,
% 0.20/0.43 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> ![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[185])).
% 0.20/0.43 tff(187,plain,
% 0.20/0.43 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> ![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(188,plain,
% 0.20/0.43 (^[X: $i, T0: $i, T: $i] : trans(monotonicity(rewrite(((organization(X) & has_immunity(X, T0)) & (~has_immunity(X, T))) <=> (organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))), ((((organization(X) & has_immunity(X, T0)) & (~has_immunity(X, T))) => greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> ((organization(X) & has_immunity(X, T0) & (~has_immunity(X, T))) => greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))))), rewrite(((organization(X) & has_immunity(X, T0) & (~has_immunity(X, T))) => greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)))), ((((organization(X) & has_immunity(X, T0)) & (~has_immunity(X, T))) => greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(189,plain,
% 0.20/0.43 (![X: $i, T0: $i, T: $i] : (((organization(X) & has_immunity(X, T0)) & (~has_immunity(X, T))) => greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> ![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[188])).
% 0.20/0.43 tff(190,axiom,(![X: $i, T0: $i, T: $i] : (((organization(X) & has_immunity(X, T0)) & (~has_immunity(X, T))) => greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','assumption_3')).
% 0.20/0.43 tff(191,plain,
% 0.20/0.43 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.20/0.43 tff(192,plain,
% 0.20/0.43 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[191, 187])).
% 0.20/0.43 tff(193,plain,(
% 0.20/0.43 ![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[192])).
% 0.20/0.43 tff(194,plain,
% 0.20/0.43 (![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[193, 186])).
% 0.20/0.43 tff(195,plain,
% 0.20/0.43 (![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[194, 184])).
% 0.20/0.43 tff(196,plain,
% 0.20/0.43 (((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0)))) | (greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2)) | (~organization(X!4)) | (~has_immunity(X!4, T1!2)) | has_immunity(X!4, T2!1))) <=> ((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0)))) | greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2)) | (~organization(X!4)) | (~has_immunity(X!4, T1!2)) | has_immunity(X!4, T2!1))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(197,plain,
% 0.20/0.43 ((has_immunity(X!4, T2!1) | greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2)) | (~organization(X!4)) | (~has_immunity(X!4, T1!2))) <=> (greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2)) | (~organization(X!4)) | (~has_immunity(X!4, T1!2)) | has_immunity(X!4, T2!1))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(198,plain,
% 0.20/0.43 (((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0)))) | (has_immunity(X!4, T2!1) | greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2)) | (~organization(X!4)) | (~has_immunity(X!4, T1!2)))) <=> ((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0)))) | (greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2)) | (~organization(X!4)) | (~has_immunity(X!4, T1!2)) | has_immunity(X!4, T2!1)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[197])).
% 0.20/0.43 tff(199,plain,
% 0.20/0.43 (((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0)))) | (has_immunity(X!4, T2!1) | greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2)) | (~organization(X!4)) | (~has_immunity(X!4, T1!2)))) <=> ((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0)))) | greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2)) | (~organization(X!4)) | (~has_immunity(X!4, T1!2)) | has_immunity(X!4, T2!1))),
% 0.20/0.44 inference(transitivity,[status(thm)],[198, 196])).
% 0.20/0.44 tff(200,plain,
% 0.20/0.44 ((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0)))) | (has_immunity(X!4, T2!1) | greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2)) | (~organization(X!4)) | (~has_immunity(X!4, T1!2)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(201,plain,
% 0.20/0.44 ((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0)))) | greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2)) | (~organization(X!4)) | (~has_immunity(X!4, T1!2)) | has_immunity(X!4, T2!1)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.20/0.44 tff(202,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[201, 195, 182, 181, 47, 180])).
% 0.20/0.44 tff(203,plain,(greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(204,plain,
% 0.20/0.44 ((~(~((~greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2))) | (~(hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)))))) <=> ((~greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2))) | (~(hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(205,plain,
% 0.20/0.44 ((greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2)) & (hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3))) <=> (~((~greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2))) | (~(hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(206,plain,
% 0.20/0.44 ((~(greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2)) & (hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)))) <=> (~(~((~greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2))) | (~(hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[205])).
% 0.20/0.44 tff(207,plain,
% 0.20/0.44 ((~(greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2)) & (hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)))) <=> ((~greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2))) | (~(hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[206, 204])).
% 0.20/0.44 tff(208,plain,
% 0.20/0.44 (~(greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2)) & (hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)))),
% 0.20/0.44 inference(or_elim,[status(thm)],[34])).
% 0.20/0.44 tff(209,plain,
% 0.20/0.44 ((~greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2))) | (~(hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.20/0.44 tff(210,plain,
% 0.20/0.44 (~(hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[209, 203])).
% 0.20/0.44 tff(211,plain,
% 0.20/0.44 (^[X: $i, T0: $i, T: $i] : refl(((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0))) <=> ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(212,plain,
% 0.20/0.44 (![X: $i, T0: $i, T: $i] : ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0))) <=> ![X: $i, T0: $i, T: $i] : ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[211])).
% 0.20/0.44 tff(213,plain,
% 0.20/0.44 (^[X: $i, T0: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((organization(X) & has_immunity(X, T0) & has_immunity(X, T)) <=> (~((~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0))))), ((~(organization(X) & has_immunity(X, T0) & has_immunity(X, T))) <=> (~(~((~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0))))))), rewrite((~(~((~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0))))) <=> ((~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0)))), ((~(organization(X) & has_immunity(X, T0) & has_immunity(X, T))) <=> ((~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0))))), (((~(organization(X) & has_immunity(X, T0) & has_immunity(X, T))) | (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T))) <=> (((~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0))) | (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T))))), rewrite((((~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0))) | (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T))) <=> ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0)))), (((~(organization(X) & has_immunity(X, T0) & has_immunity(X, T))) | (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T))) <=> ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(214,plain,
% 0.20/0.44 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & has_immunity(X, T))) | (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T))) <=> ![X: $i, T0: $i, T: $i] : ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[213])).
% 0.20/0.44 tff(215,plain,
% 0.20/0.44 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & has_immunity(X, T))) | (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T))) <=> ![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & has_immunity(X, T))) | (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(216,plain,
% 0.20/0.44 (^[X: $i, T0: $i, T: $i] : trans(monotonicity(rewrite(((organization(X) & has_immunity(X, T0)) & has_immunity(X, T)) <=> (organization(X) & has_immunity(X, T0) & has_immunity(X, T))), ((((organization(X) & has_immunity(X, T0)) & has_immunity(X, T)) => (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T))) <=> ((organization(X) & has_immunity(X, T0) & has_immunity(X, T)) => (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T))))), rewrite(((organization(X) & has_immunity(X, T0) & has_immunity(X, T)) => (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T))) <=> ((~(organization(X) & has_immunity(X, T0) & has_immunity(X, T))) | (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)))), ((((organization(X) & has_immunity(X, T0)) & has_immunity(X, T)) => (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T))) <=> ((~(organization(X) & has_immunity(X, T0) & has_immunity(X, T))) | (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(217,plain,
% 0.20/0.44 (![X: $i, T0: $i, T: $i] : (((organization(X) & has_immunity(X, T0)) & has_immunity(X, T)) => (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T))) <=> ![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & has_immunity(X, T))) | (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[216])).
% 0.20/0.44 tff(218,axiom,(![X: $i, T0: $i, T: $i] : (((organization(X) & has_immunity(X, T0)) & has_immunity(X, T)) => (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','assumption_2')).
% 0.20/0.44 tff(219,plain,
% 0.20/0.44 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & has_immunity(X, T))) | (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.44 tff(220,plain,
% 0.20/0.44 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & has_immunity(X, T))) | (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[219, 215])).
% 0.20/0.44 tff(221,plain,(
% 0.20/0.44 ![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & has_immunity(X, T))) | (hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[220])).
% 0.20/0.44 tff(222,plain,
% 0.20/0.44 (![X: $i, T0: $i, T: $i] : ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[221, 214])).
% 0.20/0.44 tff(223,plain,
% 0.20/0.44 (![X: $i, T0: $i, T: $i] : ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[222, 212])).
% 0.20/0.44 tff(224,plain,
% 0.20/0.44 (((~![X: $i, T0: $i, T: $i] : ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0)))) | ((hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)) | (~organization(X!4)) | (~has_immunity(X!4, T0!3)) | (~has_immunity(X!4, T1!2)))) <=> ((~![X: $i, T0: $i, T: $i] : ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0)))) | (hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)) | (~organization(X!4)) | (~has_immunity(X!4, T0!3)) | (~has_immunity(X!4, T1!2)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(225,plain,
% 0.20/0.44 (((hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)) | (~has_immunity(X!4, T0!3)) | (~organization(X!4)) | (~has_immunity(X!4, T1!2))) <=> ((hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)) | (~organization(X!4)) | (~has_immunity(X!4, T0!3)) | (~has_immunity(X!4, T1!2)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(226,plain,
% 0.20/0.44 (((~![X: $i, T0: $i, T: $i] : ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0)))) | ((hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)) | (~has_immunity(X!4, T0!3)) | (~organization(X!4)) | (~has_immunity(X!4, T1!2)))) <=> ((~![X: $i, T0: $i, T: $i] : ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0)))) | ((hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)) | (~organization(X!4)) | (~has_immunity(X!4, T0!3)) | (~has_immunity(X!4, T1!2))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[225])).
% 0.20/0.44 tff(227,plain,
% 0.20/0.44 (((~![X: $i, T0: $i, T: $i] : ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0)))) | ((hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)) | (~has_immunity(X!4, T0!3)) | (~organization(X!4)) | (~has_immunity(X!4, T1!2)))) <=> ((~![X: $i, T0: $i, T: $i] : ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0)))) | (hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)) | (~organization(X!4)) | (~has_immunity(X!4, T0!3)) | (~has_immunity(X!4, T1!2)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[226, 224])).
% 0.20/0.44 tff(228,plain,
% 0.20/0.44 ((~![X: $i, T0: $i, T: $i] : ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0)))) | ((hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)) | (~has_immunity(X!4, T0!3)) | (~organization(X!4)) | (~has_immunity(X!4, T1!2)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(229,plain,
% 0.20/0.44 ((~![X: $i, T0: $i, T: $i] : ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0)))) | (hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)) | (~organization(X!4)) | (~has_immunity(X!4, T0!3)) | (~has_immunity(X!4, T1!2))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.20/0.44 tff(230,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[229, 223, 182, 210, 172, 47])).
% 0.20/0.44 % SZS output end Proof
%------------------------------------------------------------------------------