%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT045+1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n018.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 06:24:06 AM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT045+1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.35 % Computer : n018.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
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 7 13:10:39 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(position_type, type, (
% 0.14/0.41 position: ( $i * $i ) > $i)).
% 0.14/0.41 tff(tptp_fun_T0_1_type, type, (
% 0.14/0.41 tptp_fun_T0_1: $i)).
% 0.14/0.41 tff(tptp_fun_X_2_type, type, (
% 0.14/0.41 tptp_fun_X_2: $i)).
% 0.14/0.41 tff(tptp_fun_T_0_type, type, (
% 0.14/0.41 tptp_fun_T_0: $i)).
% 0.14/0.41 tff(external_ties_type, type, (
% 0.14/0.41 external_ties: ( $i * $i ) > $i)).
% 0.14/0.41 tff(greater_type, type, (
% 0.14/0.41 greater: ( $i * $i ) > $o)).
% 0.14/0.41 tff(age_type, type, (
% 0.14/0.41 age: ( $i * $i ) > $i)).
% 0.14/0.41 tff(organization_type, type, (
% 0.14/0.41 organization: $i > $o)).
% 0.14/0.41 tff(1,plain,
% 0.14/0.41 ((~![X: $i, T0: $i, T: $i] : ((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(position(X, T), position(X, T0)))) <=> (~![X: $i, T0: $i, T: $i] : ((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(position(X, T), position(X, T0))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 ((~![X: $i, T0: $i, T: $i] : ((organization(X) & greater(age(X, T), age(X, T0))) => greater(position(X, T), position(X, T0)))) <=> (~![X: $i, T0: $i, T: $i] : ((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(position(X, T), position(X, T0))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(3,axiom,(~![X: $i, T0: $i, T: $i] : ((organization(X) & greater(age(X, T), age(X, T0))) => greater(position(X, T), position(X, T0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_4')).
% 0.14/0.41 tff(4,plain,
% 0.14/0.41 (~![X: $i, T0: $i, T: $i] : ((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(position(X, T), position(X, T0)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.14/0.41 tff(5,plain,
% 0.14/0.41 (~![X: $i, T0: $i, T: $i] : ((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(position(X, T), position(X, T0)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.14/0.41 tff(6,plain,
% 0.14/0.41 (~![X: $i, T0: $i, T: $i] : ((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(position(X, T), position(X, T0)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (~![X: $i, T0: $i, T: $i] : ((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(position(X, T), position(X, T0)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.14/0.41 tff(8,plain,(
% 0.14/0.41 ~((~(organization(X!2) & greater(age(X!2, T!0), age(X!2, T0!1)))) | greater(position(X!2, T!0), position(X!2, T0!1)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[7])).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 (organization(X!2) & greater(age(X!2, T!0), age(X!2, T0!1))),
% 0.14/0.41 inference(or_elim,[status(thm)],[8])).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 (greater(age(X!2, T!0), age(X!2, T0!1))),
% 0.14/0.41 inference(and_elim,[status(thm)],[9])).
% 0.14/0.41 tff(11,plain,
% 0.14/0.41 (organization(X!2)),
% 0.14/0.41 inference(and_elim,[status(thm)],[9])).
% 0.14/0.41 tff(12,plain,
% 0.14/0.41 (^[X: $i, T0: $i, T: $i] : refl((greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0)))) <=> (greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(13,plain,
% 0.14/0.41 (![X: $i, T0: $i, T: $i] : (greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0)))) <=> ![X: $i, T0: $i, T: $i] : (greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.14/0.41 tff(14,plain,
% 0.14/0.41 (^[X: $i, T0: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((organization(X) & greater(age(X, T), age(X, T0))) <=> (~((~organization(X)) | (~greater(age(X, T), age(X, T0)))))), ((~(organization(X) & greater(age(X, T), age(X, T0)))) <=> (~(~((~organization(X)) | (~greater(age(X, T), age(X, T0)))))))), rewrite((~(~((~organization(X)) | (~greater(age(X, T), age(X, T0)))))) <=> ((~organization(X)) | (~greater(age(X, T), age(X, T0))))), ((~(organization(X) & greater(age(X, T), age(X, T0)))) <=> ((~organization(X)) | (~greater(age(X, T), age(X, T0)))))), (((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(external_ties(X, T), external_ties(X, T0))) <=> (((~organization(X)) | (~greater(age(X, T), age(X, T0)))) | greater(external_ties(X, T), external_ties(X, T0))))), rewrite((((~organization(X)) | (~greater(age(X, T), age(X, T0)))) | greater(external_ties(X, T), external_ties(X, T0))) <=> (greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0))))), (((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(external_ties(X, T), external_ties(X, T0))) <=> (greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(15,plain,
% 0.14/0.42 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(external_ties(X, T), external_ties(X, T0))) <=> ![X: $i, T0: $i, T: $i] : (greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[14])).
% 0.14/0.42 tff(16,plain,
% 0.14/0.42 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(external_ties(X, T), external_ties(X, T0))) <=> ![X: $i, T0: $i, T: $i] : ((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(external_ties(X, T), external_ties(X, T0)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(17,plain,
% 0.14/0.42 (^[X: $i, T0: $i, T: $i] : rewrite(((organization(X) & greater(age(X, T), age(X, T0))) => greater(external_ties(X, T), external_ties(X, T0))) <=> ((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(external_ties(X, T), external_ties(X, T0))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(18,plain,
% 0.14/0.42 (![X: $i, T0: $i, T: $i] : ((organization(X) & greater(age(X, T), age(X, T0))) => greater(external_ties(X, T), external_ties(X, T0))) <=> ![X: $i, T0: $i, T: $i] : ((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(external_ties(X, T), external_ties(X, T0)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[17])).
% 0.14/0.42 tff(19,axiom,(![X: $i, T0: $i, T: $i] : ((organization(X) & greater(age(X, T), age(X, T0))) => greater(external_ties(X, T), external_ties(X, T0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','assumption_8')).
% 0.14/0.42 tff(20,plain,
% 0.14/0.42 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(external_ties(X, T), external_ties(X, T0)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.14/0.42 tff(21,plain,
% 0.14/0.42 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(external_ties(X, T), external_ties(X, T0)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.14/0.42 tff(22,plain,(
% 0.14/0.42 ![X: $i, T0: $i, T: $i] : ((~(organization(X) & greater(age(X, T), age(X, T0)))) | greater(external_ties(X, T), external_ties(X, T0)))),
% 0.14/0.42 inference(skolemize,[status(sab)],[21])).
% 0.14/0.42 tff(23,plain,
% 0.14/0.42 (![X: $i, T0: $i, T: $i] : (greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.14/0.42 tff(24,plain,
% 0.14/0.42 (![X: $i, T0: $i, T: $i] : (greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.14/0.42 tff(25,plain,
% 0.14/0.42 (((~![X: $i, T0: $i, T: $i] : (greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0))))) | ((~greater(age(X!2, T!0), age(X!2, T0!1))) | (~organization(X!2)) | greater(external_ties(X!2, T!0), external_ties(X!2, T0!1)))) <=> ((~![X: $i, T0: $i, T: $i] : (greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0))))) | (~greater(age(X!2, T!0), age(X!2, T0!1))) | (~organization(X!2)) | greater(external_ties(X!2, T!0), external_ties(X!2, T0!1)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(26,plain,
% 0.14/0.42 ((greater(external_ties(X!2, T!0), external_ties(X!2, T0!1)) | (~organization(X!2)) | (~greater(age(X!2, T!0), age(X!2, T0!1)))) <=> ((~greater(age(X!2, T!0), age(X!2, T0!1))) | (~organization(X!2)) | greater(external_ties(X!2, T!0), external_ties(X!2, T0!1)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(27,plain,
% 0.14/0.42 (((~![X: $i, T0: $i, T: $i] : (greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0))))) | (greater(external_ties(X!2, T!0), external_ties(X!2, T0!1)) | (~organization(X!2)) | (~greater(age(X!2, T!0), age(X!2, T0!1))))) <=> ((~![X: $i, T0: $i, T: $i] : (greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0))))) | ((~greater(age(X!2, T!0), age(X!2, T0!1))) | (~organization(X!2)) | greater(external_ties(X!2, T!0), external_ties(X!2, T0!1))))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[26])).
% 0.14/0.42 tff(28,plain,
% 0.14/0.42 (((~![X: $i, T0: $i, T: $i] : (greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0))))) | (greater(external_ties(X!2, T!0), external_ties(X!2, T0!1)) | (~organization(X!2)) | (~greater(age(X!2, T!0), age(X!2, T0!1))))) <=> ((~![X: $i, T0: $i, T: $i] : (greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0))))) | (~greater(age(X!2, T!0), age(X!2, T0!1))) | (~organization(X!2)) | greater(external_ties(X!2, T!0), external_ties(X!2, T0!1)))),
% 0.14/0.42 inference(transitivity,[status(thm)],[27, 25])).
% 0.14/0.42 tff(29,plain,
% 0.14/0.42 ((~![X: $i, T0: $i, T: $i] : (greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0))))) | (greater(external_ties(X!2, T!0), external_ties(X!2, T0!1)) | (~organization(X!2)) | (~greater(age(X!2, T!0), age(X!2, T0!1))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(30,plain,
% 0.14/0.42 ((~![X: $i, T0: $i, T: $i] : (greater(external_ties(X, T), external_ties(X, T0)) | (~organization(X)) | (~greater(age(X, T), age(X, T0))))) | (~greater(age(X!2, T!0), age(X!2, T0!1))) | (~organization(X!2)) | greater(external_ties(X!2, T!0), external_ties(X!2, T0!1))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.14/0.42 tff(31,plain,
% 0.14/0.42 (greater(external_ties(X!2, T!0), external_ties(X!2, T0!1))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[30, 24, 11, 10])).
% 0.14/0.42 tff(32,assumption,(~((~((~greater(external_ties(X!2, T!0), external_ties(X!2, T0!1))) | greater(position(X!2, T!0), position(X!2, T0!1)))) | (~((~(external_ties(X!2, T!0) = external_ties(X!2, T0!1))) | (position(X!2, T!0) = position(X!2, T0!1)))))), introduced(assumption)).
% 0.14/0.42 tff(33,plain,
% 0.14/0.42 (((~((~greater(external_ties(X!2, T!0), external_ties(X!2, T0!1))) | greater(position(X!2, T!0), position(X!2, T0!1)))) | (~((~(external_ties(X!2, T!0) = external_ties(X!2, T0!1))) | (position(X!2, T!0) = position(X!2, T0!1))))) | ((~greater(external_ties(X!2, T!0), external_ties(X!2, T0!1))) | greater(position(X!2, T!0), position(X!2, T0!1)))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(34,plain,
% 0.14/0.42 ((~greater(external_ties(X!2, T!0), external_ties(X!2, T0!1))) | greater(position(X!2, T!0), position(X!2, T0!1))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.14/0.42 tff(35,plain,
% 0.14/0.42 (~greater(position(X!2, T!0), position(X!2, T0!1))),
% 0.14/0.42 inference(or_elim,[status(thm)],[8])).
% 0.14/0.42 tff(36,plain,
% 0.14/0.42 ((~((~greater(external_ties(X!2, T!0), external_ties(X!2, T0!1))) | greater(position(X!2, T!0), position(X!2, T0!1)))) | (~greater(external_ties(X!2, T!0), external_ties(X!2, T0!1))) | greater(position(X!2, T!0), position(X!2, T0!1))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(37,plain,
% 0.14/0.42 ((~((~greater(external_ties(X!2, T!0), external_ties(X!2, T0!1))) | greater(position(X!2, T!0), position(X!2, T0!1)))) | (~greater(external_ties(X!2, T!0), external_ties(X!2, T0!1)))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.14/0.42 tff(38,plain,
% 0.14/0.42 ($false),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[37, 34, 31])).
% 0.14/0.42 tff(39,plain,((~((~greater(external_ties(X!2, T!0), external_ties(X!2, T0!1))) | greater(position(X!2, T!0), position(X!2, T0!1)))) | (~((~(external_ties(X!2, T!0) = external_ties(X!2, T0!1))) | (position(X!2, T!0) = position(X!2, T0!1))))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.42 tff(40,plain,
% 0.14/0.42 (^[X: $i, T0: $i, T: $i] : refl(((~organization(X)) | (~((~((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0)))) | (~((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0))))))) <=> ((~organization(X)) | (~((~((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0)))) | (~((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(41,plain,
% 0.14/0.42 (![X: $i, T0: $i, T: $i] : ((~organization(X)) | (~((~((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0)))) | (~((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0))))))) <=> ![X: $i, T0: $i, T: $i] : ((~organization(X)) | (~((~((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0)))) | (~((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0)))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[40])).
% 0.14/0.42 tff(42,plain,
% 0.14/0.42 (^[X: $i, T0: $i, T: $i] : rewrite(((~organization(X)) | (((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0))) & ((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0))))) <=> ((~organization(X)) | (~((~((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0)))) | (~((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(43,plain,
% 0.14/0.42 (![X: $i, T0: $i, T: $i] : ((~organization(X)) | (((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0))) & ((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0))))) <=> ![X: $i, T0: $i, T: $i] : ((~organization(X)) | (~((~((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0)))) | (~((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0)))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[42])).
% 0.14/0.42 tff(44,plain,
% 0.14/0.42 (![X: $i, T0: $i, T: $i] : ((~organization(X)) | (((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0))) & ((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0))))) <=> ![X: $i, T0: $i, T: $i] : ((~organization(X)) | (((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0))) & ((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0)))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(45,plain,
% 0.14/0.42 (^[X: $i, T0: $i, T: $i] : trans(monotonicity(rewrite(((greater(external_ties(X, T), external_ties(X, T0)) => greater(position(X, T), position(X, T0))) & ((external_ties(X, T) = external_ties(X, T0)) => (position(X, T) = position(X, T0)))) <=> (((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0))) & ((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0))))), ((organization(X) => ((greater(external_ties(X, T), external_ties(X, T0)) => greater(position(X, T), position(X, T0))) & ((external_ties(X, T) = external_ties(X, T0)) => (position(X, T) = position(X, T0))))) <=> (organization(X) => (((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0))) & ((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0))))))), rewrite((organization(X) => (((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0))) & ((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0))))) <=> ((~organization(X)) | (((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0))) & ((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0)))))), ((organization(X) => ((greater(external_ties(X, T), external_ties(X, T0)) => greater(position(X, T), position(X, T0))) & ((external_ties(X, T) = external_ties(X, T0)) => (position(X, T) = position(X, T0))))) <=> ((~organization(X)) | (((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0))) & ((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0)))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(46,plain,
% 0.14/0.42 (![X: $i, T0: $i, T: $i] : (organization(X) => ((greater(external_ties(X, T), external_ties(X, T0)) => greater(position(X, T), position(X, T0))) & ((external_ties(X, T) = external_ties(X, T0)) => (position(X, T) = position(X, T0))))) <=> ![X: $i, T0: $i, T: $i] : ((~organization(X)) | (((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0))) & ((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0)))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.14/0.42 tff(47,axiom,(![X: $i, T0: $i, T: $i] : (organization(X) => ((greater(external_ties(X, T), external_ties(X, T0)) => greater(position(X, T), position(X, T0))) & ((external_ties(X, T) = external_ties(X, T0)) => (position(X, T) = position(X, T0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','assumption_6')).
% 0.14/0.42 tff(48,plain,
% 0.14/0.42 (![X: $i, T0: $i, T: $i] : ((~organization(X)) | (((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0))) & ((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.14/0.42 tff(49,plain,
% 0.14/0.42 (![X: $i, T0: $i, T: $i] : ((~organization(X)) | (((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0))) & ((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.14/0.42 tff(50,plain,(
% 0.14/0.42 ![X: $i, T0: $i, T: $i] : ((~organization(X)) | (((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0))) & ((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0)))))),
% 0.14/0.42 inference(skolemize,[status(sab)],[49])).
% 0.14/0.42 tff(51,plain,
% 0.14/0.42 (![X: $i, T0: $i, T: $i] : ((~organization(X)) | (~((~((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0)))) | (~((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0)))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.14/0.42 tff(52,plain,
% 0.14/0.42 (![X: $i, T0: $i, T: $i] : ((~organization(X)) | (~((~((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0)))) | (~((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0)))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[51, 41])).
% 0.14/0.42 tff(53,plain,
% 0.14/0.42 (((~![X: $i, T0: $i, T: $i] : ((~organization(X)) | (~((~((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0)))) | (~((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0)))))))) | ((~organization(X!2)) | (~((~((~greater(external_ties(X!2, T!0), external_ties(X!2, T0!1))) | greater(position(X!2, T!0), position(X!2, T0!1)))) | (~((~(external_ties(X!2, T!0) = external_ties(X!2, T0!1))) | (position(X!2, T!0) = position(X!2, T0!1)))))))) <=> ((~![X: $i, T0: $i, T: $i] : ((~organization(X)) | (~((~((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0)))) | (~((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0)))))))) | (~organization(X!2)) | (~((~((~greater(external_ties(X!2, T!0), external_ties(X!2, T0!1))) | greater(position(X!2, T!0), position(X!2, T0!1)))) | (~((~(external_ties(X!2, T!0) = external_ties(X!2, T0!1))) | (position(X!2, T!0) = position(X!2, T0!1)))))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(54,plain,
% 0.14/0.42 ((~![X: $i, T0: $i, T: $i] : ((~organization(X)) | (~((~((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0)))) | (~((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0)))))))) | ((~organization(X!2)) | (~((~((~greater(external_ties(X!2, T!0), external_ties(X!2, T0!1))) | greater(position(X!2, T!0), position(X!2, T0!1)))) | (~((~(external_ties(X!2, T!0) = external_ties(X!2, T0!1))) | (position(X!2, T!0) = position(X!2, T0!1)))))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(55,plain,
% 0.14/0.42 ((~![X: $i, T0: $i, T: $i] : ((~organization(X)) | (~((~((~greater(external_ties(X, T), external_ties(X, T0))) | greater(position(X, T), position(X, T0)))) | (~((~(external_ties(X, T) = external_ties(X, T0))) | (position(X, T) = position(X, T0)))))))) | (~organization(X!2)) | (~((~((~greater(external_ties(X!2, T!0), external_ties(X!2, T0!1))) | greater(position(X!2, T!0), position(X!2, T0!1)))) | (~((~(external_ties(X!2, T!0) = external_ties(X!2, T0!1))) | (position(X!2, T!0) = position(X!2, T0!1))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.14/0.42 tff(56,plain,
% 0.14/0.42 ($false),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[55, 52, 11, 39])).
% 0.14/0.42 % SZS output end Proof
% 0.14/0.43 % E exiting
%------------------------------------------------------------------------------