%------------------------------------------------------------------------------
% 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 : n027.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 : Unsatisfiable 0.12s 0.42s
% Output : Proof 0.12s
% 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
% 0.08/0.35 % Computer : n027.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 7 13:32:17 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.42 % SZS status Unsatisfiable
% 0.12/0.42 % SZS output start Proof
% 0.12/0.42 tff(has_immunity_type, type, (
% 0.12/0.42 has_immunity: ( $i * $i ) > $o)).
% 0.12/0.42 tff(sk4_type, type, (
% 0.12/0.42 sk4: $i)).
% 0.12/0.42 tff(sk2_type, type, (
% 0.12/0.42 sk2: $i)).
% 0.12/0.42 tff(smaller_or_equal_type, type, (
% 0.12/0.42 smaller_or_equal: ( $i * $i ) > $o)).
% 0.12/0.42 tff(eta_type, type, (
% 0.12/0.42 eta: $i)).
% 0.12/0.42 tff(age_type, type, (
% 0.12/0.42 age: ( $i * $i ) > $i)).
% 0.12/0.42 tff(has_endowment_type, type, (
% 0.12/0.42 has_endowment: $i > $o)).
% 0.12/0.42 tff(sk3_type, type, (
% 0.12/0.42 sk3: $i)).
% 0.12/0.42 tff(greater_type, type, (
% 0.12/0.42 greater: ( $i * $i ) > $o)).
% 0.12/0.42 tff(zero_type, type, (
% 0.12/0.42 zero: $i)).
% 0.12/0.42 tff(smaller_type, type, (
% 0.12/0.42 smaller: ( $i * $i ) > $o)).
% 0.12/0.42 tff(sigma_type, type, (
% 0.12/0.42 sigma: $i)).
% 0.12/0.42 tff(greater_or_equal_type, type, (
% 0.12/0.42 greater_or_equal: ( $i * $i ) > $o)).
% 0.12/0.42 tff(hazard_of_mortality_type, type, (
% 0.12/0.42 hazard_of_mortality: ( $i * $i ) > $i)).
% 0.12/0.42 tff(sk5_type, type, (
% 0.12/0.42 sk5: $i)).
% 0.12/0.42 tff(organization_type, type, (
% 0.12/0.42 organization: $i > $o)).
% 0.12/0.42 tff(1,plain,
% 0.12/0.42 (smaller_or_equal(age(sk2, sk4), eta) <=> smaller_or_equal(age(sk2, sk4), eta)),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(2,axiom,(smaller_or_equal(age(sk2, sk4), eta)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma_9_43')).
% 0.12/0.42 tff(3,plain,
% 0.12/0.42 (smaller_or_equal(age(sk2, sk4), eta)),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.12/0.42 tff(4,plain,
% 0.12/0.42 (has_endowment(sk2) <=> has_endowment(sk2)),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(5,axiom,(has_endowment(sk2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma_9_41')).
% 0.12/0.42 tff(6,plain,
% 0.12/0.42 (has_endowment(sk2)),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.42 tff(7,plain,
% 0.12/0.42 (^[B: $i, A: $i] : refl(((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta))) <=> ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(8,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta))) <=> ![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[7])).
% 0.12/0.42 tff(9,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta))) <=> ![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(10,plain,
% 0.12/0.42 (^[B: $i, A: $i] : rewrite((((~has_endowment(A)) | (~smaller_or_equal(age(A, B), eta))) | has_immunity(A, B)) <=> ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(11,plain,
% 0.12/0.42 (![B: $i, A: $i] : (((~has_endowment(A)) | (~smaller_or_equal(age(A, B), eta))) | has_immunity(A, B)) <=> ![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.42 tff(12,axiom,(![B: $i, A: $i] : (((~has_endowment(A)) | (~smaller_or_equal(age(A, B), eta))) | has_immunity(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','definition_1_32')).
% 0.12/0.42 tff(13,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.12/0.42 tff(14,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.12/0.42 tff(15,plain,(
% 0.12/0.42 ![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))),
% 0.12/0.42 inference(skolemize,[status(sab)],[14])).
% 0.12/0.42 tff(16,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.12/0.42 tff(17,plain,
% 0.12/0.42 (((~![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))) | ((~smaller_or_equal(age(sk2, sk4), eta)) | (~has_endowment(sk2)) | has_immunity(sk2, sk4))) <=> ((~![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))) | (~smaller_or_equal(age(sk2, sk4), eta)) | (~has_endowment(sk2)) | has_immunity(sk2, sk4))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(18,plain,
% 0.12/0.42 (((~has_endowment(sk2)) | has_immunity(sk2, sk4) | (~smaller_or_equal(age(sk2, sk4), eta))) <=> ((~smaller_or_equal(age(sk2, sk4), eta)) | (~has_endowment(sk2)) | has_immunity(sk2, sk4))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(19,plain,
% 0.12/0.42 (((~![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))) | ((~has_endowment(sk2)) | has_immunity(sk2, sk4) | (~smaller_or_equal(age(sk2, sk4), eta)))) <=> ((~![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))) | ((~smaller_or_equal(age(sk2, sk4), eta)) | (~has_endowment(sk2)) | has_immunity(sk2, sk4)))),
% 0.12/0.42 inference(monotonicity,[status(thm)],[18])).
% 0.12/0.42 tff(20,plain,
% 0.12/0.42 (((~![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))) | ((~has_endowment(sk2)) | has_immunity(sk2, sk4) | (~smaller_or_equal(age(sk2, sk4), eta)))) <=> ((~![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))) | (~smaller_or_equal(age(sk2, sk4), eta)) | (~has_endowment(sk2)) | has_immunity(sk2, sk4))),
% 0.12/0.42 inference(transitivity,[status(thm)],[19, 17])).
% 0.12/0.42 tff(21,plain,
% 0.12/0.42 ((~![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))) | ((~has_endowment(sk2)) | has_immunity(sk2, sk4) | (~smaller_or_equal(age(sk2, sk4), eta)))),
% 0.12/0.42 inference(quant_inst,[status(thm)],[])).
% 0.12/0.42 tff(22,plain,
% 0.12/0.42 ((~![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))) | (~smaller_or_equal(age(sk2, sk4), eta)) | (~has_endowment(sk2)) | has_immunity(sk2, sk4)),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.12/0.42 tff(23,plain,
% 0.12/0.42 (has_immunity(sk2, sk4)),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[22, 16, 6, 3])).
% 0.12/0.42 tff(24,plain,
% 0.12/0.42 ((age(sk2, sk3) = zero) <=> (age(sk2, sk3) = zero)),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(25,axiom,(age(sk2, sk3) = zero), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma_9_42')).
% 0.12/0.42 tff(26,plain,
% 0.12/0.42 (age(sk2, sk3) = zero),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.42 tff(27,plain,
% 0.12/0.42 (zero = age(sk2, sk3)),
% 0.12/0.42 inference(symmetry,[status(thm)],[26])).
% 0.12/0.42 tff(28,plain,
% 0.12/0.42 (smaller_or_equal(zero, eta) <=> smaller_or_equal(age(sk2, sk3), eta)),
% 0.12/0.42 inference(monotonicity,[status(thm)],[27])).
% 0.12/0.42 tff(29,plain,
% 0.12/0.42 (smaller_or_equal(age(sk2, sk3), eta) <=> smaller_or_equal(zero, eta)),
% 0.12/0.42 inference(symmetry,[status(thm)],[28])).
% 0.12/0.42 tff(30,plain,
% 0.12/0.42 ((~smaller_or_equal(age(sk2, sk3), eta)) <=> (~smaller_or_equal(zero, eta))),
% 0.12/0.42 inference(monotonicity,[status(thm)],[29])).
% 0.12/0.42 tff(31,assumption,(~smaller_or_equal(age(sk2, sk3), eta)), introduced(assumption)).
% 0.12/0.42 tff(32,plain,
% 0.12/0.42 (~smaller_or_equal(zero, eta)),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.42 tff(33,plain,
% 0.12/0.42 (^[B: $i, A: $i] : refl(((~smaller(A, B)) | smaller_or_equal(A, B)) <=> ((~smaller(A, B)) | smaller_or_equal(A, B)))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(34,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[33])).
% 0.12/0.42 tff(35,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(36,axiom,(![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT001-0.ax','definition_smaller_or_equal_2')).
% 0.12/0.42 tff(37,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.42 tff(38,plain,(
% 0.12/0.42 ![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))),
% 0.12/0.42 inference(skolemize,[status(sab)],[37])).
% 0.12/0.42 tff(39,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.12/0.43 tff(40,plain,
% 0.12/0.43 (((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | ((~smaller(zero, eta)) | smaller_or_equal(zero, eta))) <=> ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | (~smaller(zero, eta)) | smaller_or_equal(zero, eta))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(41,plain,
% 0.12/0.43 ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | ((~smaller(zero, eta)) | smaller_or_equal(zero, eta))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(42,plain,
% 0.12/0.43 ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | (~smaller(zero, eta)) | smaller_or_equal(zero, eta)),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.12/0.43 tff(43,plain,
% 0.12/0.43 ((~smaller(zero, eta)) | smaller_or_equal(zero, eta)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[42, 39])).
% 0.12/0.43 tff(44,plain,
% 0.12/0.43 (~smaller(zero, eta)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[43, 32])).
% 0.12/0.43 tff(45,plain,
% 0.12/0.43 (^[B: $i, A: $i] : refl(((~greater(A, B)) | smaller(B, A)) <=> ((~greater(A, B)) | smaller(B, A)))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(46,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A)) <=> ![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[45])).
% 0.12/0.43 tff(47,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A)) <=> ![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(48,axiom,(![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT001-0.ax','definition_smaller_8')).
% 0.12/0.43 tff(49,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.12/0.43 tff(50,plain,(
% 0.12/0.43 ![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))),
% 0.12/0.43 inference(skolemize,[status(sab)],[49])).
% 0.12/0.43 tff(51,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.12/0.43 tff(52,plain,
% 0.12/0.43 (((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | ((~greater(eta, zero)) | smaller(zero, eta))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | (~greater(eta, zero)) | smaller(zero, eta))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(53,plain,
% 0.12/0.43 ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | ((~greater(eta, zero)) | smaller(zero, eta))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(54,plain,
% 0.12/0.43 ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | (~greater(eta, zero)) | smaller(zero, eta)),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.12/0.43 tff(55,plain,
% 0.12/0.43 (~greater(eta, zero)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[54, 51, 44])).
% 0.12/0.43 tff(56,assumption,(eta = sigma), introduced(assumption)).
% 0.12/0.43 tff(57,plain,
% 0.12/0.43 (sigma = eta),
% 0.12/0.43 inference(symmetry,[status(thm)],[56])).
% 0.12/0.43 tff(58,plain,
% 0.12/0.43 (smaller_or_equal(zero, sigma) <=> smaller_or_equal(age(sk2, sk3), eta)),
% 0.12/0.43 inference(monotonicity,[status(thm)],[27, 57])).
% 0.12/0.43 tff(59,plain,
% 0.12/0.43 (smaller_or_equal(age(sk2, sk3), eta) <=> smaller_or_equal(zero, sigma)),
% 0.12/0.43 inference(symmetry,[status(thm)],[58])).
% 0.12/0.43 tff(60,plain,
% 0.12/0.43 ((~smaller_or_equal(age(sk2, sk3), eta)) <=> (~smaller_or_equal(zero, sigma))),
% 0.12/0.43 inference(monotonicity,[status(thm)],[59])).
% 0.12/0.43 tff(61,plain,
% 0.12/0.43 (~smaller_or_equal(zero, sigma)),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[31, 60])).
% 0.12/0.43 tff(62,plain,
% 0.12/0.43 (greater(sigma, zero) <=> greater(sigma, zero)),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(63,axiom,(greater(sigma, zero)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma_9_46')).
% 0.12/0.43 tff(64,plain,
% 0.12/0.43 (greater(sigma, zero)),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.12/0.43 tff(65,plain,
% 0.12/0.43 (((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | ((~greater(sigma, zero)) | smaller(zero, sigma))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | (~greater(sigma, zero)) | smaller(zero, sigma))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(66,plain,
% 0.12/0.43 ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | ((~greater(sigma, zero)) | smaller(zero, sigma))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(67,plain,
% 0.12/0.43 ((~![B: $i, A: $i] : ((~greater(A, B)) | smaller(B, A))) | (~greater(sigma, zero)) | smaller(zero, sigma)),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.12/0.43 tff(68,plain,
% 0.12/0.43 (smaller(zero, sigma)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[67, 51, 64])).
% 0.12/0.43 tff(69,plain,
% 0.12/0.43 (((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | ((~smaller(zero, sigma)) | smaller_or_equal(zero, sigma))) <=> ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | (~smaller(zero, sigma)) | smaller_or_equal(zero, sigma))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(70,plain,
% 0.12/0.43 ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | ((~smaller(zero, sigma)) | smaller_or_equal(zero, sigma))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(71,plain,
% 0.12/0.43 ((~![B: $i, A: $i] : ((~smaller(A, B)) | smaller_or_equal(A, B))) | (~smaller(zero, sigma)) | smaller_or_equal(zero, sigma)),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.12/0.43 tff(72,plain,
% 0.12/0.43 (smaller_or_equal(zero, sigma)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[71, 39, 68])).
% 0.12/0.43 tff(73,plain,
% 0.12/0.43 ($false),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[72, 61])).
% 0.12/0.43 tff(74,plain,((~(eta = sigma)) | smaller_or_equal(age(sk2, sk3), eta)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.43 tff(75,plain,
% 0.12/0.43 (~(eta = sigma)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[74, 31])).
% 0.12/0.43 tff(76,plain,
% 0.12/0.43 (greater_or_equal(eta, sigma) <=> greater_or_equal(eta, sigma)),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(77,axiom,(greater_or_equal(eta, sigma)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma_9_45')).
% 0.12/0.43 tff(78,plain,
% 0.12/0.43 (greater_or_equal(eta, sigma)),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.12/0.43 tff(79,plain,
% 0.12/0.43 (^[B: $i, A: $i] : refl(((A = B) | greater(A, B) | (~greater_or_equal(A, B))) <=> ((A = B) | greater(A, B) | (~greater_or_equal(A, B))))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(80,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B))) <=> ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[79])).
% 0.12/0.43 tff(81,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B))) <=> ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(82,plain,
% 0.12/0.43 (^[B: $i, A: $i] : rewrite((((~greater_or_equal(A, B)) | greater(A, B)) | (A = B)) <=> ((A = B) | greater(A, B) | (~greater_or_equal(A, B))))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(83,plain,
% 0.12/0.43 (![B: $i, A: $i] : (((~greater_or_equal(A, B)) | greater(A, B)) | (A = B)) <=> ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[82])).
% 0.12/0.43 tff(84,axiom,(![B: $i, A: $i] : (((~greater_or_equal(A, B)) | greater(A, B)) | (A = B))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT001-0.ax','definition_greater_or_equal_4')).
% 0.12/0.43 tff(85,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.12/0.43 tff(86,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.12/0.43 tff(87,plain,(
% 0.12/0.43 ![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.12/0.43 inference(skolemize,[status(sab)],[86])).
% 0.12/0.43 tff(88,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.12/0.43 tff(89,plain,
% 0.12/0.43 (((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((eta = sigma) | greater(eta, sigma) | (~greater_or_equal(eta, sigma)))) <=> ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (eta = sigma) | greater(eta, sigma) | (~greater_or_equal(eta, sigma)))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(90,plain,
% 0.12/0.43 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | ((eta = sigma) | greater(eta, sigma) | (~greater_or_equal(eta, sigma)))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(91,plain,
% 0.12/0.43 ((~![B: $i, A: $i] : ((A = B) | greater(A, B) | (~greater_or_equal(A, B)))) | (eta = sigma) | greater(eta, sigma) | (~greater_or_equal(eta, sigma))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.12/0.43 tff(92,plain,
% 0.12/0.43 ((eta = sigma) | greater(eta, sigma)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[91, 88, 78])).
% 0.12/0.43 tff(93,plain,
% 0.12/0.43 (greater(eta, sigma)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[92, 75])).
% 0.12/0.43 tff(94,plain,
% 0.12/0.43 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B))) <=> ![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(95,plain,
% 0.12/0.43 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B))) <=> ![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(96,plain,
% 0.12/0.43 (^[B: $i, A: $i, C: $i] : rewrite((((~greater(A, B)) | (~greater(B, C))) | greater(A, C)) <=> (greater(A, C) | (~greater(B, C)) | (~greater(A, B))))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(97,plain,
% 0.12/0.43 (![B: $i, A: $i, C: $i] : (((~greater(A, B)) | (~greater(B, C))) | greater(A, C)) <=> ![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[96])).
% 0.12/0.43 tff(98,axiom,(![B: $i, A: $i, C: $i] : (((~greater(A, B)) | (~greater(B, C))) | greater(A, C))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT001-0.ax','meaning_postulate_greater_transitive_10')).
% 0.12/0.43 tff(99,plain,
% 0.12/0.43 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.12/0.43 tff(100,plain,
% 0.12/0.43 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.12/0.43 tff(101,plain,(
% 0.12/0.43 ![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.12/0.43 inference(skolemize,[status(sab)],[100])).
% 0.12/0.43 tff(102,plain,
% 0.12/0.43 (![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.12/0.43 tff(103,plain,
% 0.12/0.43 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | ((~greater(sigma, zero)) | greater(eta, zero) | (~greater(eta, sigma)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (~greater(sigma, zero)) | greater(eta, zero) | (~greater(eta, sigma)))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(104,plain,
% 0.12/0.43 ((greater(eta, zero) | (~greater(sigma, zero)) | (~greater(eta, sigma))) <=> ((~greater(sigma, zero)) | greater(eta, zero) | (~greater(eta, sigma)))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(105,plain,
% 0.12/0.43 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(eta, zero) | (~greater(sigma, zero)) | (~greater(eta, sigma)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | ((~greater(sigma, zero)) | greater(eta, zero) | (~greater(eta, sigma))))),
% 0.12/0.43 inference(monotonicity,[status(thm)],[104])).
% 0.12/0.43 tff(106,plain,
% 0.12/0.43 (((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(eta, zero) | (~greater(sigma, zero)) | (~greater(eta, sigma)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (~greater(sigma, zero)) | greater(eta, zero) | (~greater(eta, sigma)))),
% 0.12/0.43 inference(transitivity,[status(thm)],[105, 103])).
% 0.12/0.43 tff(107,plain,
% 0.12/0.43 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (greater(eta, zero) | (~greater(sigma, zero)) | (~greater(eta, sigma)))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(108,plain,
% 0.12/0.43 ((~![B: $i, A: $i, C: $i] : (greater(A, C) | (~greater(B, C)) | (~greater(A, B)))) | (~greater(sigma, zero)) | greater(eta, zero) | (~greater(eta, sigma))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.12/0.43 tff(109,plain,
% 0.12/0.43 ($false),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[108, 102, 64, 93, 55])).
% 0.12/0.43 tff(110,plain,(smaller_or_equal(age(sk2, sk3), eta)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.43 tff(111,plain,
% 0.12/0.43 (((~![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))) | ((~has_endowment(sk2)) | has_immunity(sk2, sk3) | (~smaller_or_equal(age(sk2, sk3), eta)))) <=> ((~![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))) | (~has_endowment(sk2)) | has_immunity(sk2, sk3) | (~smaller_or_equal(age(sk2, sk3), eta)))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(112,plain,
% 0.12/0.43 ((~![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))) | ((~has_endowment(sk2)) | has_immunity(sk2, sk3) | (~smaller_or_equal(age(sk2, sk3), eta)))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(113,plain,
% 0.12/0.43 ((~![B: $i, A: $i] : ((~has_endowment(A)) | has_immunity(A, B) | (~smaller_or_equal(age(A, B), eta)))) | (~has_endowment(sk2)) | has_immunity(sk2, sk3) | (~smaller_or_equal(age(sk2, sk3), eta))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.12/0.43 tff(114,plain,
% 0.12/0.43 (has_immunity(sk2, sk3) | (~smaller_or_equal(age(sk2, sk3), eta))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[113, 16, 6])).
% 0.12/0.43 tff(115,plain,
% 0.12/0.43 (has_immunity(sk2, sk3)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[114, 110])).
% 0.12/0.43 tff(116,plain,
% 0.12/0.43 (greater(age(sk2, sk5), eta) <=> greater(age(sk2, sk5), eta)),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(117,axiom,(greater(age(sk2, sk5), eta)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma_9_44')).
% 0.12/0.43 tff(118,plain,
% 0.12/0.43 (greater(age(sk2, sk5), eta)),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.12/0.43 tff(119,plain,
% 0.12/0.43 (^[B: $i, A: $i] : refl(((~has_endowment(A)) | (~has_immunity(A, B)) | (~greater(age(A, B), eta))) <=> ((~has_endowment(A)) | (~has_immunity(A, B)) | (~greater(age(A, B), eta))))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(120,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((~has_endowment(A)) | (~has_immunity(A, B)) | (~greater(age(A, B), eta))) <=> ![B: $i, A: $i] : ((~has_endowment(A)) | (~has_immunity(A, B)) | (~greater(age(A, B), eta)))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[119])).
% 0.12/0.43 tff(121,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((~has_endowment(A)) | (~has_immunity(A, B)) | (~greater(age(A, B), eta))) <=> ![B: $i, A: $i] : ((~has_endowment(A)) | (~has_immunity(A, B)) | (~greater(age(A, B), eta)))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(122,plain,
% 0.12/0.43 (^[B: $i, A: $i] : rewrite((((~has_endowment(A)) | (~greater(age(A, B), eta))) | (~has_immunity(A, B))) <=> ((~has_endowment(A)) | (~has_immunity(A, B)) | (~greater(age(A, B), eta))))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(123,plain,
% 0.12/0.43 (![B: $i, A: $i] : (((~has_endowment(A)) | (~greater(age(A, B), eta))) | (~has_immunity(A, B))) <=> ![B: $i, A: $i] : ((~has_endowment(A)) | (~has_immunity(A, B)) | (~greater(age(A, B), eta)))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[122])).
% 0.12/0.43 tff(124,axiom,(![B: $i, A: $i] : (((~has_endowment(A)) | (~greater(age(A, B), eta))) | (~has_immunity(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','definition_1_33')).
% 0.12/0.43 tff(125,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((~has_endowment(A)) | (~has_immunity(A, B)) | (~greater(age(A, B), eta)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.12/0.43 tff(126,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((~has_endowment(A)) | (~has_immunity(A, B)) | (~greater(age(A, B), eta)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.12/0.43 tff(127,plain,(
% 0.12/0.43 ![B: $i, A: $i] : ((~has_endowment(A)) | (~has_immunity(A, B)) | (~greater(age(A, B), eta)))),
% 0.12/0.43 inference(skolemize,[status(sab)],[126])).
% 0.12/0.43 tff(128,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((~has_endowment(A)) | (~has_immunity(A, B)) | (~greater(age(A, B), eta)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.12/0.43 tff(129,plain,
% 0.12/0.43 (((~![B: $i, A: $i] : ((~has_endowment(A)) | (~has_immunity(A, B)) | (~greater(age(A, B), eta)))) | ((~has_endowment(sk2)) | (~has_immunity(sk2, sk5)) | (~greater(age(sk2, sk5), eta)))) <=> ((~![B: $i, A: $i] : ((~has_endowment(A)) | (~has_immunity(A, B)) | (~greater(age(A, B), eta)))) | (~has_endowment(sk2)) | (~has_immunity(sk2, sk5)) | (~greater(age(sk2, sk5), eta)))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(130,plain,
% 0.12/0.43 ((~![B: $i, A: $i] : ((~has_endowment(A)) | (~has_immunity(A, B)) | (~greater(age(A, B), eta)))) | ((~has_endowment(sk2)) | (~has_immunity(sk2, sk5)) | (~greater(age(sk2, sk5), eta)))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(131,plain,
% 0.12/0.43 ((~![B: $i, A: $i] : ((~has_endowment(A)) | (~has_immunity(A, B)) | (~greater(age(A, B), eta)))) | (~has_endowment(sk2)) | (~has_immunity(sk2, sk5)) | (~greater(age(sk2, sk5), eta))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.12/0.43 tff(132,plain,
% 0.12/0.43 (~has_immunity(sk2, sk5)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[131, 128, 6, 118])).
% 0.12/0.43 tff(133,assumption,(~greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4))), introduced(assumption)).
% 0.12/0.43 tff(134,plain,
% 0.12/0.43 (organization(sk2) <=> organization(sk2)),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(135,axiom,(organization(sk2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma_9_40')).
% 0.12/0.43 tff(136,plain,
% 0.12/0.43 (organization(sk2)),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.12/0.43 tff(137,plain,
% 0.12/0.43 (^[B: $i, A: $i, C: $i] : refl((greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A))) <=> (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A))))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(138,plain,
% 0.12/0.43 (![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A))) <=> ![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[137])).
% 0.12/0.43 tff(139,plain,
% 0.12/0.43 (![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A))) <=> ![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(140,plain,
% 0.12/0.43 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite((((~organization(A)) | (~has_immunity(A, B))) | has_immunity(A, C)) <=> (has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))), (((((~organization(A)) | (~has_immunity(A, B))) | has_immunity(A, C)) | greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B))) <=> ((has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A))) | greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B))))), rewrite(((has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A))) | greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B))) <=> (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))), (((((~organization(A)) | (~has_immunity(A, B))) | has_immunity(A, C)) | greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B))) <=> (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(141,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : ((((~organization(A)) | (~has_immunity(A, B))) | has_immunity(A, C)) | greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B))) <=> ![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[140])).
% 0.12/0.44 tff(142,axiom,(![B: $i, A: $i, C: $i] : ((((~organization(A)) | (~has_immunity(A, B))) | has_immunity(A, C)) | greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','assumption_3_39')).
% 0.12/0.44 tff(143,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.12/0.44 tff(144,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.12/0.44 tff(145,plain,(
% 0.12/0.44 ![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))),
% 0.12/0.44 inference(skolemize,[status(sab)],[144])).
% 0.12/0.44 tff(146,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.12/0.44 tff(147,plain,
% 0.12/0.44 (((~![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))) | (greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4)) | (~has_immunity(sk2, sk4)) | has_immunity(sk2, sk5) | (~organization(sk2)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))) | greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4)) | (~has_immunity(sk2, sk4)) | has_immunity(sk2, sk5) | (~organization(sk2)))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(148,plain,
% 0.12/0.44 ((greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4)) | has_immunity(sk2, sk5) | (~has_immunity(sk2, sk4)) | (~organization(sk2))) <=> (greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4)) | (~has_immunity(sk2, sk4)) | has_immunity(sk2, sk5) | (~organization(sk2)))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(149,plain,
% 0.12/0.44 (((~![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))) | (greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4)) | has_immunity(sk2, sk5) | (~has_immunity(sk2, sk4)) | (~organization(sk2)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))) | (greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4)) | (~has_immunity(sk2, sk4)) | has_immunity(sk2, sk5) | (~organization(sk2))))),
% 0.12/0.44 inference(monotonicity,[status(thm)],[148])).
% 0.12/0.44 tff(150,plain,
% 0.12/0.44 (((~![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))) | (greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4)) | has_immunity(sk2, sk5) | (~has_immunity(sk2, sk4)) | (~organization(sk2)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))) | greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4)) | (~has_immunity(sk2, sk4)) | has_immunity(sk2, sk5) | (~organization(sk2)))),
% 0.12/0.44 inference(transitivity,[status(thm)],[149, 147])).
% 0.12/0.44 tff(151,plain,
% 0.12/0.44 ((~![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))) | (greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4)) | has_immunity(sk2, sk5) | (~has_immunity(sk2, sk4)) | (~organization(sk2)))),
% 0.12/0.44 inference(quant_inst,[status(thm)],[])).
% 0.12/0.44 tff(152,plain,
% 0.12/0.44 ((~![B: $i, A: $i, C: $i] : (greater(hazard_of_mortality(A, C), hazard_of_mortality(A, B)) | has_immunity(A, C) | (~has_immunity(A, B)) | (~organization(A)))) | greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4)) | (~has_immunity(sk2, sk4)) | has_immunity(sk2, sk5) | (~organization(sk2))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.12/0.44 tff(153,plain,
% 0.12/0.44 ($false),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[152, 146, 136, 133, 23, 132])).
% 0.12/0.44 tff(154,plain,(greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.44 tff(155,plain,
% 0.12/0.44 (((~greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4))) | (~(hazard_of_mortality(sk2, sk4) = hazard_of_mortality(sk2, sk3)))) <=> ((~greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4))) | (~(hazard_of_mortality(sk2, sk4) = hazard_of_mortality(sk2, sk3))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(156,axiom,((~greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4))) | (~(hazard_of_mortality(sk2, sk4) = hazard_of_mortality(sk2, sk3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma_9_47')).
% 0.12/0.44 tff(157,plain,
% 0.12/0.44 ((~greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4))) | (~(hazard_of_mortality(sk2, sk4) = hazard_of_mortality(sk2, sk3)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.12/0.44 tff(158,plain,
% 0.12/0.44 ((~greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4))) | (~(hazard_of_mortality(sk2, sk4) = hazard_of_mortality(sk2, sk3)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[157, 155])).
% 0.12/0.44 tff(159,plain,
% 0.12/0.44 ((~greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4))) | (~(hazard_of_mortality(sk2, sk4) = hazard_of_mortality(sk2, sk3)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[158, 155])).
% 0.12/0.44 tff(160,plain,
% 0.12/0.44 ((~greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4))) | (~(hazard_of_mortality(sk2, sk4) = hazard_of_mortality(sk2, sk3)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.12/0.44 tff(161,plain,
% 0.12/0.44 ((~greater(hazard_of_mortality(sk2, sk5), hazard_of_mortality(sk2, sk4))) | (~(hazard_of_mortality(sk2, sk4) = hazard_of_mortality(sk2, sk3)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[160, 155])).
% 0.12/0.44 tff(162,plain,
% 0.12/0.44 (~(hazard_of_mortality(sk2, sk4) = hazard_of_mortality(sk2, sk3))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[161, 154])).
% 0.12/0.44 tff(163,plain,
% 0.12/0.44 (^[B: $i, A: $i, C: $i] : refl(((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A))) <=> ((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(164,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : ((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A))) <=> ![B: $i, A: $i, C: $i] : ((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A)))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[163])).
% 0.12/0.44 tff(165,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : ((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A))) <=> ![B: $i, A: $i, C: $i] : ((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A)))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(166,plain,
% 0.12/0.44 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite((((~organization(A)) | (~has_immunity(A, B))) | (~has_immunity(A, C))) <=> ((~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A)))), (((((~organization(A)) | (~has_immunity(A, B))) | (~has_immunity(A, C))) | (hazard_of_mortality(A, B) = hazard_of_mortality(A, C))) <=> (((~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A))) | (hazard_of_mortality(A, B) = hazard_of_mortality(A, C))))), rewrite((((~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A))) | (hazard_of_mortality(A, B) = hazard_of_mortality(A, C))) <=> ((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A)))), (((((~organization(A)) | (~has_immunity(A, B))) | (~has_immunity(A, C))) | (hazard_of_mortality(A, B) = hazard_of_mortality(A, C))) <=> ((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A)))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(167,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : ((((~organization(A)) | (~has_immunity(A, B))) | (~has_immunity(A, C))) | (hazard_of_mortality(A, B) = hazard_of_mortality(A, C))) <=> ![B: $i, A: $i, C: $i] : ((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A)))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[166])).
% 0.12/0.44 tff(168,axiom,(![B: $i, A: $i, C: $i] : ((((~organization(A)) | (~has_immunity(A, B))) | (~has_immunity(A, C))) | (hazard_of_mortality(A, B) = hazard_of_mortality(A, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','assumption_2_38')).
% 0.12/0.44 tff(169,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : ((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.12/0.44 tff(170,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : ((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.12/0.44 tff(171,plain,(
% 0.12/0.44 ![B: $i, A: $i, C: $i] : ((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A)))),
% 0.12/0.44 inference(skolemize,[status(sab)],[170])).
% 0.12/0.44 tff(172,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : ((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.12/0.44 tff(173,plain,
% 0.12/0.44 (((~![B: $i, A: $i, C: $i] : ((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A)))) | ((hazard_of_mortality(sk2, sk4) = hazard_of_mortality(sk2, sk3)) | (~has_immunity(sk2, sk3)) | (~has_immunity(sk2, sk4)) | (~organization(sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A)))) | (hazard_of_mortality(sk2, sk4) = hazard_of_mortality(sk2, sk3)) | (~has_immunity(sk2, sk3)) | (~has_immunity(sk2, sk4)) | (~organization(sk2)))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(174,plain,
% 0.12/0.44 ((~![B: $i, A: $i, C: $i] : ((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A)))) | ((hazard_of_mortality(sk2, sk4) = hazard_of_mortality(sk2, sk3)) | (~has_immunity(sk2, sk3)) | (~has_immunity(sk2, sk4)) | (~organization(sk2)))),
% 0.12/0.44 inference(quant_inst,[status(thm)],[])).
% 0.12/0.44 tff(175,plain,
% 0.12/0.44 ((~![B: $i, A: $i, C: $i] : ((hazard_of_mortality(A, B) = hazard_of_mortality(A, C)) | (~has_immunity(A, C)) | (~has_immunity(A, B)) | (~organization(A)))) | (hazard_of_mortality(sk2, sk4) = hazard_of_mortality(sk2, sk3)) | (~has_immunity(sk2, sk3)) | (~has_immunity(sk2, sk4)) | (~organization(sk2))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.12/0.44 tff(176,plain,
% 0.12/0.44 ($false),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[175, 172, 136, 162, 115, 23])).
% 0.12/0.44 % SZS output end Proof
% 0.12/0.45 % E exiting
%------------------------------------------------------------------------------