%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT056+1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:24:08 AM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT056+1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 7 13:28:47 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.14/0.42 % SZS status Theorem
% 0.14/0.42 % SZS output start Proof
% 0.14/0.42 tff(has_immunity_type, type, (
% 0.14/0.42 has_immunity: ( $i * $i ) > $o)).
% 0.14/0.42 tff(tptp_fun_T1_2_type, type, (
% 0.14/0.42 tptp_fun_T1_2: $i)).
% 0.14/0.42 tff(tptp_fun_X_4_type, type, (
% 0.14/0.42 tptp_fun_X_4: $i)).
% 0.14/0.42 tff(smaller_or_equal_type, type, (
% 0.14/0.42 smaller_or_equal: ( $i * $i ) > $o)).
% 0.14/0.42 tff(eta_type, type, (
% 0.14/0.42 eta: $i)).
% 0.14/0.42 tff(age_type, type, (
% 0.14/0.42 age: ( $i * $i ) > $i)).
% 0.14/0.42 tff(greater_type, type, (
% 0.14/0.42 greater: ( $i * $i ) > $o)).
% 0.14/0.42 tff(organization_type, type, (
% 0.14/0.42 organization: $i > $o)).
% 0.14/0.42 tff(has_endowment_type, type, (
% 0.14/0.42 has_endowment: $i > $o)).
% 0.14/0.42 tff(tptp_fun_T_0_type, type, (
% 0.14/0.42 tptp_fun_T_0: $i > $i)).
% 0.14/0.42 tff(zero_type, type, (
% 0.14/0.42 zero: $i)).
% 0.14/0.42 tff(sigma_type, type, (
% 0.14/0.42 sigma: $i)).
% 0.14/0.42 tff(greater_or_equal_type, type, (
% 0.14/0.42 greater_or_equal: ( $i * $i ) > $o)).
% 0.14/0.42 tff(tptp_fun_T2_1_type, type, (
% 0.14/0.42 tptp_fun_T2_1: $i)).
% 0.14/0.42 tff(tptp_fun_T0_3_type, type, (
% 0.14/0.42 tptp_fun_T0_3: $i)).
% 0.14/0.42 tff(hazard_of_mortality_type, type, (
% 0.14/0.42 hazard_of_mortality: ( $i * $i ) > $i)).
% 0.14/0.42 tff(smaller_type, type, (
% 0.14/0.42 smaller: ( $i * $i ) > $o)).
% 0.14/0.42 tff(1,plain,
% 0.14/0.42 (^[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)))))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(2,plain,
% 0.14/0.42 (![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))))))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.42 tff(3,plain,
% 0.14/0.42 (^[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)))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(4,plain,
% 0.14/0.42 (![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))))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.42 tff(5,plain,
% 0.14/0.42 (^[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)))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(6,plain,
% 0.14/0.42 (![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))))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[5])).
% 0.14/0.42 tff(7,plain,
% 0.14/0.42 (![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))))))))),
% 0.14/0.42 inference(transitivity,[status(thm)],[6, 4])).
% 0.14/0.42 tff(8,plain,
% 0.14/0.42 (^[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))))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(9,plain,
% 0.14/0.42 (![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))))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[8])).
% 0.14/0.42 tff(10,plain,
% 0.14/0.42 (![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)))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(11,plain,
% 0.14/0.42 (^[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))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(12,plain,
% 0.14/0.42 (![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)))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[11])).
% 0.14/0.42 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/sandbox2/benchmark/theBenchmark.p','definition_1')).
% 0.14/0.42 tff(14,plain,
% 0.14/0.42 (![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)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.14/0.42 tff(15,plain,
% 0.14/0.42 (![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)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.14/0.42 tff(16,plain,(
% 0.14/0.42 ![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)))))))),
% 0.14/0.42 inference(skolemize,[status(sab)],[15])).
% 0.14/0.42 tff(17,plain,
% 0.14/0.42 (![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))))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.14/0.42 tff(18,plain,
% 0.14/0.42 (![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))))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.14/0.42 tff(19,plain,
% 0.14/0.42 (![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))))))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.14/0.42 tff(20,plain,
% 0.14/0.42 (((~![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)) | (~((~has_immunity(X!4, tptp_fun_T_0(X!4))) | (~greater(age(X!4, tptp_fun_T_0(X!4)), eta)))) | (~((~smaller_or_equal(age(X!4, tptp_fun_T_0(X!4)), eta)) | has_immunity(X!4, tptp_fun_T_0(X!4)))))) | (~((~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))))))))))) <=> ((~![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)) | (~((~has_immunity(X!4, tptp_fun_T_0(X!4))) | (~greater(age(X!4, tptp_fun_T_0(X!4)), eta)))) | (~((~smaller_or_equal(age(X!4, tptp_fun_T_0(X!4)), eta)) | has_immunity(X!4, tptp_fun_T_0(X!4)))))) | (~((~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)))))))))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(21,plain,
% 0.14/0.42 ((~((~(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) | (~organization(X!4)) | (~((~has_immunity(X!4, tptp_fun_T_0(X!4))) | (~greater(age(X!4, tptp_fun_T_0(X!4)), eta)))) | (~((~smaller_or_equal(age(X!4, tptp_fun_T_0(X!4)), eta)) | has_immunity(X!4, tptp_fun_T_0(X!4)))))) | (~((~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))))))))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(22,plain,
% 0.14/0.43 (((~![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))))))))))) <=> ((~![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)) | (~((~has_immunity(X!4, tptp_fun_T_0(X!4))) | (~greater(age(X!4, tptp_fun_T_0(X!4)), eta)))) | (~((~smaller_or_equal(age(X!4, tptp_fun_T_0(X!4)), eta)) | has_immunity(X!4, tptp_fun_T_0(X!4)))))) | (~((~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)))))))))))),
% 0.14/0.43 inference(monotonicity,[status(thm)],[21])).
% 0.14/0.43 tff(23,plain,
% 0.14/0.43 (((~![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))))))))))) <=> ((~![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)) | (~((~has_immunity(X!4, tptp_fun_T_0(X!4))) | (~greater(age(X!4, tptp_fun_T_0(X!4)), eta)))) | (~((~smaller_or_equal(age(X!4, tptp_fun_T_0(X!4)), eta)) | has_immunity(X!4, tptp_fun_T_0(X!4)))))) | (~((~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)))))))))))),
% 0.14/0.43 inference(transitivity,[status(thm)],[22, 20])).
% 0.14/0.43 tff(24,plain,
% 0.14/0.43 ((~![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))))))))))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(25,plain,
% 0.14/0.43 ((~![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)) | (~((~has_immunity(X!4, tptp_fun_T_0(X!4))) | (~greater(age(X!4, tptp_fun_T_0(X!4)), eta)))) | (~((~smaller_or_equal(age(X!4, tptp_fun_T_0(X!4)), eta)) | has_immunity(X!4, tptp_fun_T_0(X!4)))))) | (~((~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))))))))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.14/0.43 tff(26,plain,
% 0.14/0.43 (~((~(has_endowment(X!4) | (~organization(X!4)) | (~((~has_immunity(X!4, tptp_fun_T_0(X!4))) | (~greater(age(X!4, tptp_fun_T_0(X!4)), eta)))) | (~((~smaller_or_equal(age(X!4, tptp_fun_T_0(X!4)), eta)) | has_immunity(X!4, tptp_fun_T_0(X!4)))))) | (~((~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)))))))))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[25, 19])).
% 0.14/0.43 tff(27,plain,
% 0.14/0.43 (((~(has_endowment(X!4) | (~organization(X!4)) | (~((~has_immunity(X!4, tptp_fun_T_0(X!4))) | (~greater(age(X!4, tptp_fun_T_0(X!4)), eta)))) | (~((~smaller_or_equal(age(X!4, tptp_fun_T_0(X!4)), eta)) | has_immunity(X!4, tptp_fun_T_0(X!4)))))) | (~((~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)))))))),
% 0.14/0.43 inference(tautology,[status(thm)],[])).
% 0.14/0.43 tff(28,plain,
% 0.14/0.43 ((~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))))))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.14/0.43 tff(29,plain,
% 0.14/0.43 ((~![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)))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(30,plain,
% 0.14/0.43 ((~![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)))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(31,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/sandbox2/benchmark/theBenchmark.p','lemma_9')).
% 0.14/0.43 tff(32,plain,
% 0.14/0.43 (~![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))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.14/0.43 tff(33,plain,
% 0.14/0.43 (~![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))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.14/0.43 tff(34,plain,
% 0.14/0.43 (~![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))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.14/0.43 tff(35,plain,
% 0.14/0.43 (~![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))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[34, 29])).
% 0.14/0.43 tff(36,plain,(
% 0.14/0.43 ~((~(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))))),
% 0.14/0.43 inference(skolemize,[status(sab)],[35])).
% 0.14/0.43 tff(37,plain,
% 0.14/0.43 (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)),
% 0.14/0.43 inference(or_elim,[status(thm)],[36])).
% 0.14/0.43 tff(38,plain,
% 0.14/0.43 (has_endowment(X!4)),
% 0.14/0.43 inference(and_elim,[status(thm)],[37])).
% 0.14/0.43 tff(39,plain,
% 0.14/0.43 ((~((~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))))))),
% 0.14/0.43 inference(tautology,[status(thm)],[])).
% 0.14/0.43 tff(40,plain,
% 0.14/0.43 ((~((~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))))))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.14/0.43 tff(41,plain,
% 0.14/0.43 (![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))))))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[40, 28])).
% 0.14/0.43 tff(42,plain,
% 0.14/0.43 ((~![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, T1!2), eta)) | has_immunity(X!4, T1!2))) | (~((~has_immunity(X!4, T1!2)) | (~greater(age(X!4, T1!2), eta))))))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(43,plain,
% 0.14/0.43 (~((~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)))))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.14/0.43 tff(44,plain,
% 0.14/0.43 (((~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))),
% 0.14/0.43 inference(tautology,[status(thm)],[])).
% 0.14/0.43 tff(45,plain,
% 0.14/0.43 ((~smaller_or_equal(age(X!4, T1!2), eta)) | has_immunity(X!4, T1!2)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.14/0.43 tff(46,plain,
% 0.14/0.43 (smaller_or_equal(age(X!4, T1!2), eta)),
% 0.14/0.43 inference(and_elim,[status(thm)],[37])).
% 0.14/0.43 tff(47,plain,
% 0.14/0.43 ((~((~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)),
% 0.14/0.43 inference(tautology,[status(thm)],[])).
% 0.14/0.43 tff(48,plain,
% 0.14/0.43 ((~((~smaller_or_equal(age(X!4, T1!2), eta)) | has_immunity(X!4, T1!2))) | has_immunity(X!4, T1!2)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.14/0.43 tff(49,plain,
% 0.14/0.43 (has_immunity(X!4, T1!2)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.14/0.43 tff(50,plain,
% 0.14/0.43 (^[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))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(51,plain,
% 0.14/0.43 (![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)))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[50])).
% 0.14/0.43 tff(52,plain,
% 0.14/0.43 (![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)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(53,plain,
% 0.14/0.43 (^[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))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(54,plain,
% 0.14/0.43 (![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)))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[53])).
% 0.14/0.43 tff(55,axiom,(![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> (smaller(X, Y) | (X = Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax','definition_smaller_or_equal')).
% 0.14/0.43 tff(56,plain,
% 0.14/0.43 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.14/0.43 tff(57,plain,
% 0.14/0.43 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.14/0.43 tff(58,plain,(
% 0.14/0.43 ![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.14/0.43 inference(skolemize,[status(sab)],[57])).
% 0.14/0.44 tff(59,plain,
% 0.14/0.44 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.14/0.44 tff(60,plain,
% 0.14/0.44 ((~![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))) | (smaller_or_equal(zero, eta) <=> ((zero = eta) | smaller(zero, eta)))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(61,plain,
% 0.14/0.44 (smaller_or_equal(zero, eta) <=> ((zero = eta) | smaller(zero, eta))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.14/0.44 tff(62,plain,
% 0.14/0.44 (age(X!4, T0!3) = zero),
% 0.14/0.44 inference(and_elim,[status(thm)],[37])).
% 0.14/0.44 tff(63,plain,
% 0.14/0.44 (zero = age(X!4, T0!3)),
% 0.14/0.44 inference(symmetry,[status(thm)],[62])).
% 0.14/0.44 tff(64,plain,
% 0.14/0.44 (smaller_or_equal(zero, eta) <=> smaller_or_equal(age(X!4, T0!3), eta)),
% 0.14/0.44 inference(monotonicity,[status(thm)],[63])).
% 0.14/0.44 tff(65,plain,
% 0.14/0.44 (smaller_or_equal(age(X!4, T0!3), eta) <=> smaller_or_equal(zero, eta)),
% 0.14/0.44 inference(symmetry,[status(thm)],[64])).
% 0.14/0.44 tff(66,plain,
% 0.14/0.44 ((~smaller_or_equal(age(X!4, T0!3), eta)) <=> (~smaller_or_equal(zero, eta))),
% 0.14/0.44 inference(monotonicity,[status(thm)],[65])).
% 0.14/0.44 tff(67,assumption,(~smaller_or_equal(age(X!4, T0!3), eta)), introduced(assumption)).
% 0.14/0.44 tff(68,plain,
% 0.14/0.44 (~smaller_or_equal(zero, eta)),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.14/0.44 tff(69,plain,
% 0.14/0.44 ((~(smaller_or_equal(zero, eta) <=> ((zero = eta) | smaller(zero, eta)))) | smaller_or_equal(zero, eta) | (~((zero = eta) | smaller(zero, eta)))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(70,plain,
% 0.14/0.44 (~((zero = eta) | smaller(zero, eta))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[69, 68, 61])).
% 0.14/0.44 tff(71,plain,
% 0.14/0.44 (((zero = eta) | smaller(zero, eta)) | (~smaller(zero, eta))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(72,plain,
% 0.14/0.44 (~smaller(zero, eta)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.14/0.44 tff(73,plain,
% 0.14/0.44 (((zero = eta) | smaller(zero, eta)) | (~(zero = eta))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(74,plain,
% 0.14/0.44 (~(zero = eta)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[73, 70])).
% 0.14/0.44 tff(75,plain,
% 0.14/0.44 (^[X: $i, Y: $i] : refl(((X = Y) | smaller(X, Y) | greater(X, Y)) <=> ((X = Y) | smaller(X, Y) | greater(X, Y)))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(76,plain,
% 0.14/0.44 (![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y)) <=> ![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[75])).
% 0.14/0.44 tff(77,plain,
% 0.14/0.44 (![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y)) <=> ![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(78,plain,
% 0.14/0.44 (^[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))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(79,plain,
% 0.14/0.44 (![X: $i, Y: $i] : ((smaller(X, Y) | (X = Y)) | greater(X, Y)) <=> ![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[78])).
% 0.14/0.44 tff(80,axiom,(![X: $i, Y: $i] : ((smaller(X, Y) | (X = Y)) | greater(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax','meaning_postulate_greater_comparable')).
% 0.14/0.44 tff(81,plain,
% 0.14/0.44 (![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.14/0.44 tff(82,plain,
% 0.14/0.44 (![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.14/0.44 tff(83,plain,(
% 0.14/0.44 ![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))),
% 0.14/0.44 inference(skolemize,[status(sab)],[82])).
% 0.14/0.44 tff(84,plain,
% 0.14/0.44 (![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.14/0.44 tff(85,plain,
% 0.14/0.44 (((~![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))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(86,plain,
% 0.14/0.44 ((~![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))) | ((zero = eta) | smaller(zero, eta) | greater(zero, eta))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(87,plain,
% 0.14/0.44 ((~![X: $i, Y: $i] : ((X = Y) | smaller(X, Y) | greater(X, Y))) | (zero = eta) | smaller(zero, eta) | greater(zero, eta)),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.14/0.44 tff(88,plain,
% 0.14/0.44 (greater(zero, eta)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[87, 84, 74, 72])).
% 0.14/0.44 tff(89,plain,
% 0.14/0.44 (greater(sigma, zero)),
% 0.14/0.44 inference(and_elim,[status(thm)],[37])).
% 0.14/0.44 tff(90,plain,
% 0.14/0.44 (![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)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(91,plain,
% 0.14/0.44 (^[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)))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(92,plain,
% 0.14/0.44 (![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)))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[91])).
% 0.14/0.44 tff(93,plain,
% 0.14/0.44 (![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))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(94,plain,
% 0.14/0.44 (^[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)))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(95,plain,
% 0.14/0.44 (![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))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[94])).
% 0.14/0.44 tff(96,axiom,(![X: $i, Y: $i, Z: $i] : ((greater(X, Y) & greater(Y, Z)) => greater(X, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax','meaning_postulate_greater_transitive')).
% 0.14/0.44 tff(97,plain,
% 0.14/0.44 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.14/0.44 tff(98,plain,
% 0.14/0.44 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.14/0.44 tff(99,plain,(
% 0.14/0.44 ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.14/0.44 inference(skolemize,[status(sab)],[98])).
% 0.14/0.44 tff(100,plain,
% 0.14/0.44 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.14/0.44 tff(101,plain,
% 0.14/0.44 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[100, 90])).
% 0.14/0.44 tff(102,plain,
% 0.14/0.44 (((~![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)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(103,plain,
% 0.14/0.44 ((greater(sigma, eta) | (~greater(zero, eta)) | (~greater(sigma, zero))) <=> ((~greater(sigma, zero)) | greater(sigma, eta) | (~greater(zero, eta)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(104,plain,
% 0.14/0.44 (((~![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))))),
% 0.14/0.44 inference(monotonicity,[status(thm)],[103])).
% 0.14/0.44 tff(105,plain,
% 0.14/0.44 (((~![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)))),
% 0.14/0.44 inference(transitivity,[status(thm)],[104, 102])).
% 0.14/0.44 tff(106,plain,
% 0.14/0.44 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))) | (greater(sigma, eta) | (~greater(zero, eta)) | (~greater(sigma, zero)))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(107,plain,
% 0.14/0.44 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(Y, Z)) | (~greater(X, Y)))) | (~greater(sigma, zero)) | greater(sigma, eta) | (~greater(zero, eta))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.14/0.44 tff(108,plain,
% 0.14/0.44 (greater(sigma, eta)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[107, 101, 89, 88])).
% 0.14/0.44 tff(109,plain,
% 0.14/0.44 (^[X: $i, Y: $i] : refl(((~greater(X, Y)) | (~greater(Y, X))) <=> ((~greater(X, Y)) | (~greater(Y, X))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(110,plain,
% 0.14/0.44 (![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X))) <=> ![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[109])).
% 0.14/0.44 tff(111,plain,
% 0.14/0.44 (^[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)))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(112,plain,
% 0.14/0.44 (![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X))) <=> ![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[111])).
% 0.14/0.44 tff(113,plain,
% 0.14/0.44 (![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X))) <=> ![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(114,axiom,(![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax','meaning_postulate_greater_strict')).
% 0.14/0.44 tff(115,plain,
% 0.14/0.44 (![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.14/0.44 tff(116,plain,(
% 0.14/0.44 ![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X)))),
% 0.14/0.44 inference(skolemize,[status(sab)],[115])).
% 0.14/0.44 tff(117,plain,
% 0.14/0.44 (![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.14/0.44 tff(118,plain,
% 0.14/0.44 (![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.14/0.44 tff(119,plain,
% 0.14/0.44 (((~![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)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(120,plain,
% 0.14/0.44 ((~![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))) | ((~greater(eta, sigma)) | (~greater(sigma, eta)))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(121,plain,
% 0.14/0.44 ((~![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))) | (~greater(eta, sigma)) | (~greater(sigma, eta))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.14/0.44 tff(122,plain,
% 0.14/0.44 (~greater(eta, sigma)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[121, 118, 108])).
% 0.14/0.44 tff(123,plain,
% 0.14/0.44 (^[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))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(124,plain,
% 0.14/0.44 (![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)))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[123])).
% 0.14/0.44 tff(125,plain,
% 0.14/0.44 (![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)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(126,plain,
% 0.14/0.44 (^[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))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(127,plain,
% 0.14/0.44 (![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)))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[126])).
% 0.14/0.44 tff(128,axiom,(![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax','definition_greater_or_equal')).
% 0.14/0.44 tff(129,plain,
% 0.14/0.44 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.14/0.44 tff(130,plain,
% 0.14/0.44 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.14/0.44 tff(131,plain,(
% 0.14/0.44 ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.14/0.44 inference(skolemize,[status(sab)],[130])).
% 0.14/0.44 tff(132,plain,
% 0.14/0.44 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.14/0.44 tff(133,plain,
% 0.14/0.44 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(eta, sigma) <=> ((eta = sigma) | greater(eta, sigma)))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(134,plain,
% 0.14/0.44 (greater_or_equal(eta, sigma) <=> ((eta = sigma) | greater(eta, sigma))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.14/0.44 tff(135,plain,
% 0.14/0.44 (greater_or_equal(eta, sigma)),
% 0.14/0.44 inference(and_elim,[status(thm)],[37])).
% 0.14/0.44 tff(136,plain,
% 0.14/0.44 ((~(greater_or_equal(eta, sigma) <=> ((eta = sigma) | greater(eta, sigma)))) | (~greater_or_equal(eta, sigma)) | ((eta = sigma) | greater(eta, sigma))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(137,plain,
% 0.14/0.44 ((~(greater_or_equal(eta, sigma) <=> ((eta = sigma) | greater(eta, sigma)))) | ((eta = sigma) | greater(eta, sigma))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.14/0.44 tff(138,plain,
% 0.14/0.44 ((eta = sigma) | greater(eta, sigma)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[137, 134])).
% 0.14/0.44 tff(139,plain,
% 0.14/0.44 ((~((eta = sigma) | greater(eta, sigma))) | (eta = sigma) | greater(eta, sigma)),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(140,plain,
% 0.14/0.44 ((eta = sigma) | greater(eta, sigma)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.14/0.44 tff(141,plain,
% 0.14/0.44 (eta = sigma),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[140, 122])).
% 0.14/0.44 tff(142,plain,
% 0.14/0.44 (sigma = eta),
% 0.14/0.44 inference(symmetry,[status(thm)],[141])).
% 0.14/0.44 tff(143,plain,
% 0.14/0.44 (smaller_or_equal(zero, sigma) <=> smaller_or_equal(age(X!4, T0!3), eta)),
% 0.14/0.44 inference(monotonicity,[status(thm)],[63, 142])).
% 0.14/0.44 tff(144,plain,
% 0.14/0.44 (smaller_or_equal(age(X!4, T0!3), eta) <=> smaller_or_equal(zero, sigma)),
% 0.14/0.44 inference(symmetry,[status(thm)],[143])).
% 0.14/0.44 tff(145,plain,
% 0.14/0.44 ((~smaller_or_equal(age(X!4, T0!3), eta)) <=> (~smaller_or_equal(zero, sigma))),
% 0.14/0.44 inference(monotonicity,[status(thm)],[144])).
% 0.14/0.44 tff(146,plain,
% 0.14/0.44 (~smaller_or_equal(zero, sigma)),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[67, 145])).
% 0.14/0.44 tff(147,plain,
% 0.14/0.44 ((~![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))) | (smaller_or_equal(zero, sigma) <=> ((zero = sigma) | smaller(zero, sigma)))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(148,plain,
% 0.14/0.44 (smaller_or_equal(zero, sigma) <=> ((zero = sigma) | smaller(zero, sigma))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[147, 59])).
% 0.14/0.44 tff(149,plain,
% 0.14/0.44 (^[X: $i, Y: $i] : refl((smaller(X, Y) <=> greater(Y, X)) <=> (smaller(X, Y) <=> greater(Y, X)))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(150,plain,
% 0.14/0.44 (![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X)) <=> ![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[149])).
% 0.14/0.44 tff(151,plain,
% 0.14/0.44 (![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X)) <=> ![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(152,axiom,(![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax','definition_smaller')).
% 0.14/0.44 tff(153,plain,
% 0.14/0.44 (![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.14/0.44 tff(154,plain,(
% 0.14/0.44 ![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.14/0.44 inference(skolemize,[status(sab)],[153])).
% 0.14/0.44 tff(155,plain,
% 0.14/0.44 (![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.14/0.44 tff(156,plain,
% 0.14/0.44 ((~![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))) | (smaller(zero, sigma) <=> greater(sigma, zero))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(157,plain,
% 0.14/0.44 (smaller(zero, sigma) <=> greater(sigma, zero)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.14/0.44 tff(158,plain,
% 0.14/0.44 ((~(smaller(zero, sigma) <=> greater(sigma, zero))) | smaller(zero, sigma) | (~greater(sigma, zero))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(159,plain,
% 0.14/0.44 ((~(smaller(zero, sigma) <=> greater(sigma, zero))) | smaller(zero, sigma)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[158, 89])).
% 0.14/0.44 tff(160,plain,
% 0.14/0.44 (smaller(zero, sigma)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[159, 157])).
% 0.14/0.44 tff(161,plain,
% 0.14/0.44 (((zero = sigma) | smaller(zero, sigma)) | (~smaller(zero, sigma))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(162,plain,
% 0.14/0.44 ((zero = sigma) | smaller(zero, sigma)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.14/0.44 tff(163,plain,
% 0.14/0.44 ((~(smaller_or_equal(zero, sigma) <=> ((zero = sigma) | smaller(zero, sigma)))) | smaller_or_equal(zero, sigma) | (~((zero = sigma) | smaller(zero, sigma)))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(164,plain,
% 0.14/0.44 ((~(smaller_or_equal(zero, sigma) <=> ((zero = sigma) | smaller(zero, sigma)))) | smaller_or_equal(zero, sigma)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.14/0.44 tff(165,plain,
% 0.14/0.44 (smaller_or_equal(zero, sigma)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[164, 148])).
% 0.14/0.44 tff(166,plain,
% 0.14/0.44 ($false),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[165, 146])).
% 0.14/0.44 tff(167,plain,(smaller_or_equal(age(X!4, T0!3), eta)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.44 tff(168,plain,
% 0.14/0.44 ((~![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))))))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(169,plain,
% 0.14/0.44 (~((~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)))))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[168, 41])).
% 0.14/0.44 tff(170,plain,
% 0.14/0.44 (((~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))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(171,plain,
% 0.14/0.44 ((~smaller_or_equal(age(X!4, T0!3), eta)) | has_immunity(X!4, T0!3)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.14/0.44 tff(172,plain,
% 0.14/0.44 ((~((~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)),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.45 tff(173,plain,
% 0.14/0.45 ((~smaller_or_equal(age(X!4, T0!3), eta)) | has_immunity(X!4, T0!3)),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.14/0.45 tff(174,plain,
% 0.14/0.45 (has_immunity(X!4, T0!3)),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[173, 167])).
% 0.14/0.45 tff(175,plain,
% 0.14/0.45 ((~![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))))))),
% 0.14/0.45 inference(quant_inst,[status(thm)],[])).
% 0.14/0.45 tff(176,plain,
% 0.14/0.45 (~((~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)))))),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[175, 41])).
% 0.14/0.45 tff(177,plain,
% 0.14/0.45 (((~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)))),
% 0.14/0.45 inference(tautology,[status(thm)],[])).
% 0.14/0.45 tff(178,plain,
% 0.14/0.45 ((~has_immunity(X!4, T2!1)) | (~greater(age(X!4, T2!1), eta))),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.14/0.45 tff(179,plain,
% 0.14/0.45 (greater(age(X!4, T2!1), eta)),
% 0.14/0.45 inference(and_elim,[status(thm)],[37])).
% 0.14/0.45 tff(180,plain,
% 0.14/0.45 ((~((~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))),
% 0.14/0.45 inference(tautology,[status(thm)],[])).
% 0.14/0.45 tff(181,plain,
% 0.14/0.45 ((~((~has_immunity(X!4, T2!1)) | (~greater(age(X!4, T2!1), eta)))) | (~has_immunity(X!4, T2!1))),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.14/0.45 tff(182,plain,
% 0.14/0.45 (~has_immunity(X!4, T2!1)),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[181, 178])).
% 0.14/0.45 tff(183,assumption,(~greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2))), introduced(assumption)).
% 0.14/0.45 tff(184,plain,
% 0.14/0.45 (organization(X!4)),
% 0.14/0.45 inference(and_elim,[status(thm)],[37])).
% 0.14/0.45 tff(185,plain,
% 0.14/0.45 (^[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))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(186,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[185])).
% 0.14/0.45 tff(187,plain,
% 0.14/0.45 (^[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)))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(188,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[187])).
% 0.14/0.45 tff(189,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(190,plain,
% 0.14/0.45 (^[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)))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(191,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[190])).
% 0.14/0.45 tff(192,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/sandbox2/benchmark/theBenchmark.p','assumption_3')).
% 0.14/0.45 tff(193,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.14/0.45 tff(194,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.14/0.45 tff(195,plain,(
% 0.14/0.45 ![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)))),
% 0.14/0.45 inference(skolemize,[status(sab)],[194])).
% 0.14/0.45 tff(196,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[195, 188])).
% 0.14/0.45 tff(197,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[196, 186])).
% 0.14/0.45 tff(198,plain,
% 0.14/0.45 (((~![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))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(199,plain,
% 0.14/0.45 ((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))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(200,plain,
% 0.14/0.45 (((~![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)))),
% 0.14/0.45 inference(monotonicity,[status(thm)],[199])).
% 0.14/0.45 tff(201,plain,
% 0.14/0.45 (((~![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))),
% 0.14/0.45 inference(transitivity,[status(thm)],[200, 198])).
% 0.14/0.45 tff(202,plain,
% 0.14/0.45 ((~![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)))),
% 0.14/0.45 inference(quant_inst,[status(thm)],[])).
% 0.14/0.45 tff(203,plain,
% 0.14/0.45 ((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | (~organization(X)) | (~has_immunity(X, T0)))) | greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2)) | (~organization(X!4)) | (~has_immunity(X!4, T1!2)) | has_immunity(X!4, T2!1)),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.14/0.45 tff(204,plain,
% 0.14/0.45 ($false),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[203, 197, 184, 183, 49, 182])).
% 0.14/0.45 tff(205,plain,(greater(hazard_of_mortality(X!4, T2!1), hazard_of_mortality(X!4, T1!2))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.45 tff(206,plain,
% 0.14/0.45 ((~(~((~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))))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(207,plain,
% 0.14/0.45 ((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)))))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(208,plain,
% 0.14/0.45 ((~(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))))))),
% 0.14/0.45 inference(monotonicity,[status(thm)],[207])).
% 0.14/0.45 tff(209,plain,
% 0.14/0.45 ((~(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))))),
% 0.14/0.45 inference(transitivity,[status(thm)],[208, 206])).
% 0.14/0.45 tff(210,plain,
% 0.14/0.45 (~(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)))),
% 0.14/0.45 inference(or_elim,[status(thm)],[36])).
% 0.14/0.45 tff(211,plain,
% 0.14/0.45 ((~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)))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.14/0.45 tff(212,plain,
% 0.14/0.45 (~(hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3))),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[211, 205])).
% 0.14/0.45 tff(213,plain,
% 0.14/0.45 (^[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))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(214,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[213])).
% 0.14/0.45 tff(215,plain,
% 0.14/0.45 (^[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)))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(216,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[215])).
% 0.14/0.45 tff(217,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(218,plain,
% 0.14/0.45 (^[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)))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(219,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[218])).
% 0.14/0.45 tff(220,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/sandbox2/benchmark/theBenchmark.p','assumption_2')).
% 0.14/0.45 tff(221,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.14/0.45 tff(222,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.14/0.45 tff(223,plain,(
% 0.14/0.45 ![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)))),
% 0.14/0.45 inference(skolemize,[status(sab)],[222])).
% 0.14/0.45 tff(224,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[223, 216])).
% 0.14/0.45 tff(225,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[224, 214])).
% 0.14/0.45 tff(226,plain,
% 0.14/0.45 (((~![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)))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(227,plain,
% 0.14/0.45 (((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)))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(228,plain,
% 0.14/0.46 (((~![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))))),
% 0.14/0.46 inference(monotonicity,[status(thm)],[227])).
% 0.14/0.46 tff(229,plain,
% 0.14/0.46 (((~![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)))),
% 0.14/0.46 inference(transitivity,[status(thm)],[228, 226])).
% 0.14/0.46 tff(230,plain,
% 0.14/0.46 ((~![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)))),
% 0.14/0.46 inference(quant_inst,[status(thm)],[])).
% 0.14/0.46 tff(231,plain,
% 0.14/0.46 ((~![X: $i, T0: $i, T: $i] : ((hazard_of_mortality(X, T0) = hazard_of_mortality(X, T)) | (~has_immunity(X, T)) | (~organization(X)) | (~has_immunity(X, T0)))) | (hazard_of_mortality(X!4, T1!2) = hazard_of_mortality(X!4, T0!3)) | (~organization(X!4)) | (~has_immunity(X!4, T0!3)) | (~has_immunity(X!4, T1!2))),
% 0.14/0.46 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.14/0.46 tff(232,plain,
% 0.14/0.46 ($false),
% 0.14/0.46 inference(unit_resolution,[status(thm)],[231, 225, 184, 212, 174, 49])).
% 0.14/0.46 % SZS output end Proof
% 0.14/0.46 % E exiting
%------------------------------------------------------------------------------