%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : AGT019+1 : TPTP v9.0.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 04:57:41 AM UTC 2025
% Result : Theorem 231.55s 231.81s
% Output : Proof 231.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : AGT019+1 : TPTP v9.0.0. Bugfixed v3.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 10:44:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 231.55/231.81 % SZS status Theorem
% 231.55/231.81 % SZS output start Proof
% 231.55/231.81 tff(less_type, type, (
% 231.55/231.81 less: ( $i * $i ) > $o)).
% 231.55/231.81 tff(n78_type, type, (
% 231.55/231.81 n78: $i)).
% 231.55/231.81 tff(n75_type, type, (
% 231.55/231.81 n75: $i)).
% 231.55/231.81 tff(accept_population_type, type, (
% 231.55/231.81 accept_population: ( $i * $i * $i ) > $o)).
% 231.55/231.81 tff(atheist_type, type, (
% 231.55/231.81 atheist: $i)).
% 231.55/231.81 tff(muslimcountrybhumanitarianorganization_type, type, (
% 231.55/231.81 muslimcountrybhumanitarianorganization: $i)).
% 231.55/231.81 tff(n1_type, type, (
% 231.55/231.81 n1: $i)).
% 231.55/231.81 tff(other_type, type, (
% 231.55/231.81 other: $i)).
% 231.55/231.81 tff(n0_type, type, (
% 231.55/231.81 n0: $i)).
% 231.55/231.81 tff(native_type, type, (
% 231.55/231.81 native: $i)).
% 231.55/231.81 tff(muslim_type, type, (
% 231.55/231.81 muslim: $i)).
% 231.55/231.81 tff(n20_type, type, (
% 231.55/231.81 n20: $i)).
% 231.55/231.81 tff(christian_type, type, (
% 231.55/231.81 christian: $i)).
% 231.55/231.81 tff(accept_city_type, type, (
% 231.55/231.81 accept_city: ( $i * $i ) > $o)).
% 231.55/231.81 tff(cityb_type, type, (
% 231.55/231.81 cityb: $i)).
% 231.55/231.81 tff(accept_number_type, type, (
% 231.55/231.81 accept_number: ( $i * $i ) > $o)).
% 231.55/231.81 tff(n4_type, type, (
% 231.55/231.81 n4: $i)).
% 231.55/231.81 tff(accept_leader_type, type, (
% 231.55/231.81 accept_leader: ( $i * $i ) > $o)).
% 231.55/231.81 tff(countrybhumanitarianorganization_type, type, (
% 231.55/231.81 countrybhumanitarianorganization: $i)).
% 231.55/231.81 tff(accept_team_type, type, (
% 231.55/231.81 accept_team: ( $i * $i * $i * $i ) > $o)).
% 231.55/231.81 tff(n24_type, type, (
% 231.55/231.81 n24: $i)).
% 231.55/231.81 tff(towna_type, type, (
% 231.55/231.81 towna: $i)).
% 231.55/231.81 tff(countryacivilorganization_type, type, (
% 231.55/231.81 countryacivilorganization: $i)).
% 231.55/231.81 tff(any_agent_in_all_proposed_teams_type, type, (
% 231.55/231.81 any_agent_in_all_proposed_teams: ( $i * $i * $i ) > $o)).
% 231.55/231.81 tff(the_agent_not_in_any_proposed_teams_type, type, (
% 231.55/231.81 the_agent_not_in_any_proposed_teams: ( $i * $i * $i ) > $o)).
% 231.55/231.81 tff(n85_type, type, (
% 231.55/231.81 n85: $i)).
% 231.55/231.81 tff(n3_type, type, (
% 231.55/231.81 n3: $i)).
% 231.55/231.81 tff(n12_type, type, (
% 231.55/231.81 n12: $i)).
% 231.55/231.81 tff(coastvillage_type, type, (
% 231.55/231.81 coastvillage: $i)).
% 231.55/231.81 tff(n5_type, type, (
% 231.55/231.81 n5: $i)).
% 231.55/231.81 tff(christiancountrychumanitarianorganization_type, type, (
% 231.55/231.81 christiancountrychumanitarianorganization: $i)).
% 231.55/231.81 tff(n65_type, type, (
% 231.55/231.81 n65: $i)).
% 231.55/231.81 tff(n30_type, type, (
% 231.55/231.81 n30: $i)).
% 231.55/231.81 tff(townc_type, type, (
% 231.55/231.81 townc: $i)).
% 231.55/231.81 tff(countryahumanitarianorganization_type, type, (
% 231.55/231.81 countryahumanitarianorganization: $i)).
% 231.55/231.81 tff(the_agent_in_all_proposed_teams_type, type, (
% 231.55/231.81 the_agent_in_all_proposed_teams: ( $i * $i * $i ) > $o)).
% 231.55/231.81 tff(rdn_positive_less_type, type, (
% 231.55/231.81 rdn_positive_less: ( $i * $i ) > $o)).
% 231.55/231.81 tff(rdn_type, type, (
% 231.55/231.81 rdn: ( $i * $i ) > $i)).
% 231.55/231.81 tff(rdnn_type, type, (
% 231.55/231.81 rdnn: $i > $i)).
% 231.55/231.81 tff(n7_type, type, (
% 231.55/231.81 n7: $i)).
% 231.55/231.81 tff(n8_type, type, (
% 231.55/231.81 n8: $i)).
% 231.55/231.81 tff(n6_type, type, (
% 231.55/231.81 n6: $i)).
% 231.55/231.81 tff(rdn_non_zero_type, type, (
% 231.55/231.81 rdn_non_zero: $i > $o)).
% 231.55/231.81 tff(rdn_non_zero_digit_type, type, (
% 231.55/231.81 rdn_non_zero_digit: $i > $o)).
% 231.55/231.81 tff(rdn_translate_type, type, (
% 231.55/231.81 rdn_translate: ( $i * $i ) > $o)).
% 231.55/231.81 tff(rdn_pos_type, type, (
% 231.55/231.81 rdn_pos: $i > $i)).
% 231.55/231.81 tff(1,plain,
% 231.55/231.81 (^[A: $i] : refl((~(((~accept_population(A, atheist, n78)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n1))) <=> accept_city(A, cityb))) <=> (~(((~accept_population(A, atheist, n78)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n1))) <=> accept_city(A, cityb))))),
% 231.55/231.81 inference(bind,[status(th)],[])).
% 231.55/231.81 tff(2,plain,
% 231.55/231.81 (![A: $i] : (~(((~accept_population(A, atheist, n78)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n1))) <=> accept_city(A, cityb))) <=> ![A: $i] : (~(((~accept_population(A, atheist, n78)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n1))) <=> accept_city(A, cityb)))),
% 231.55/231.81 inference(quant_intro,[status(thm)],[1])).
% 231.55/231.81 tff(3,plain,
% 231.55/231.81 (^[A: $i] : trans(trans(monotonicity(rewrite((accept_population(A, atheist, n78) & accept_population(A, christian, n20) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n1)) <=> (~((~accept_population(A, atheist, n78)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n1))))), (((accept_population(A, atheist, n78) & accept_population(A, christian, n20) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n1)) <=> accept_city(A, cityb)) <=> ((~((~accept_population(A, atheist, n78)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n1)))) <=> accept_city(A, cityb)))), rewrite(((~((~accept_population(A, atheist, n78)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n1)))) <=> accept_city(A, cityb)) <=> (~(((~accept_population(A, atheist, n78)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n1))) <=> accept_city(A, cityb)))), (((accept_population(A, atheist, n78) & accept_population(A, christian, n20) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n1)) <=> accept_city(A, cityb)) <=> (~(((~accept_population(A, atheist, n78)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n1))) <=> accept_city(A, cityb))))), rewrite((~(((~accept_population(A, atheist, n78)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n1))) <=> accept_city(A, cityb))) <=> (~(((~accept_population(A, atheist, n78)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n1))) <=> accept_city(A, cityb)))), (((accept_population(A, atheist, n78) & accept_population(A, christian, n20) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n1)) <=> accept_city(A, cityb)) <=> (~(((~accept_population(A, atheist, n78)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n1))) <=> accept_city(A, cityb)))))),
% 231.55/231.81 inference(bind,[status(th)],[])).
% 231.55/231.81 tff(4,plain,
% 231.55/231.81 (![A: $i] : ((accept_population(A, atheist, n78) & accept_population(A, christian, n20) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n1)) <=> accept_city(A, cityb)) <=> ![A: $i] : (~(((~accept_population(A, atheist, n78)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n1))) <=> accept_city(A, cityb)))),
% 231.55/231.81 inference(quant_intro,[status(thm)],[3])).
% 231.55/231.81 tff(5,plain,
% 231.55/231.81 (![A: $i] : ((accept_population(A, atheist, n78) & accept_population(A, christian, n20) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n1)) <=> accept_city(A, cityb)) <=> ![A: $i] : ((accept_population(A, atheist, n78) & accept_population(A, christian, n20) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n1)) <=> accept_city(A, cityb))),
% 231.55/231.81 inference(rewrite,[status(thm)],[])).
% 231.55/231.81 tff(6,plain,
% 231.55/231.81 (^[A: $i] : rewrite((((((accept_population(A, atheist, n78) & accept_population(A, christian, n20)) & accept_population(A, muslim, n1)) & accept_population(A, native, n0)) & accept_population(A, other, n1)) <=> accept_city(A, cityb)) <=> ((accept_population(A, atheist, n78) & accept_population(A, christian, n20) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n1)) <=> accept_city(A, cityb)))),
% 231.55/231.81 inference(bind,[status(th)],[])).
% 231.55/231.81 tff(7,plain,
% 231.55/231.81 (![A: $i] : (((((accept_population(A, atheist, n78) & accept_population(A, christian, n20)) & accept_population(A, muslim, n1)) & accept_population(A, native, n0)) & accept_population(A, other, n1)) <=> accept_city(A, cityb)) <=> ![A: $i] : ((accept_population(A, atheist, n78) & accept_population(A, christian, n20) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n1)) <=> accept_city(A, cityb))),
% 231.55/231.81 inference(quant_intro,[status(thm)],[6])).
% 231.55/231.81 tff(8,axiom,(![A: $i] : (((((accept_population(A, atheist, n78) & accept_population(A, christian, n20)) & accept_population(A, muslim, n1)) & accept_population(A, native, n0)) & accept_population(A, other, n1)) <=> accept_city(A, cityb))), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+0.ax','a2_12')).
% 231.55/231.81 tff(9,plain,
% 231.55/231.81 (![A: $i] : ((accept_population(A, atheist, n78) & accept_population(A, christian, n20) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n1)) <=> accept_city(A, cityb))),
% 231.55/231.81 inference(modus_ponens,[status(thm)],[8, 7])).
% 231.55/231.81 tff(10,plain,
% 231.55/231.81 (![A: $i] : ((accept_population(A, atheist, n78) & accept_population(A, christian, n20) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n1)) <=> accept_city(A, cityb))),
% 231.55/231.81 inference(modus_ponens,[status(thm)],[9, 5])).
% 231.55/231.81 tff(11,plain,(
% 231.55/231.81 ![A: $i] : ((accept_population(A, atheist, n78) & accept_population(A, christian, n20) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n1)) <=> accept_city(A, cityb))),
% 231.55/231.81 inference(skolemize,[status(sab)],[10])).
% 231.55/231.81 tff(12,plain,
% 231.55/231.81 (![A: $i] : (~(((~accept_population(A, atheist, n78)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n1))) <=> accept_city(A, cityb)))),
% 231.55/231.81 inference(modus_ponens,[status(thm)],[11, 4])).
% 231.55/231.81 tff(13,plain,
% 231.55/231.81 (![A: $i] : (~(((~accept_population(A, atheist, n78)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n1))) <=> accept_city(A, cityb)))),
% 231.55/231.81 inference(modus_ponens,[status(thm)],[12, 2])).
% 231.55/231.81 tff(14,plain,
% 231.55/231.81 ((~![A: $i] : (~(((~accept_population(A, atheist, n78)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n1))) <=> accept_city(A, cityb)))) | (~(((~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n20)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n1))) <=> accept_city(muslimcountrybhumanitarianorganization, cityb)))),
% 231.55/231.81 inference(quant_inst,[status(thm)],[])).
% 231.55/231.81 tff(15,plain,
% 231.55/231.81 (~(((~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n20)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n1))) <=> accept_city(muslimcountrybhumanitarianorganization, cityb))),
% 231.55/231.81 inference(unit_resolution,[status(thm)],[14, 13])).
% 231.55/231.81 tff(16,plain,
% 231.55/231.81 (^[A: $i, C: $i, N: $i, L: $i] : refl((~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N))) <=> (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N))))),
% 231.55/231.81 inference(bind,[status(th)],[])).
% 231.55/231.81 tff(17,plain,
% 231.55/231.81 (![A: $i, C: $i, N: $i, L: $i] : (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N))) <=> ![A: $i, C: $i, N: $i, L: $i] : (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))),
% 231.55/231.81 inference(quant_intro,[status(thm)],[16])).
% 231.55/231.81 tff(18,plain,
% 231.55/231.81 (^[A: $i, C: $i, N: $i, L: $i] : trans(trans(monotonicity(rewrite((accept_city(A, C) & accept_leader(A, L) & accept_number(A, N)) <=> (~((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))))), ((accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N))) <=> (accept_team(A, L, C, N) <=> (~((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))))))), rewrite((accept_team(A, L, C, N) <=> (~((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))))) <=> (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))), ((accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N))) <=> (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N))))), rewrite((~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N))) <=> (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))), ((accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N))) <=> (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))))),
% 231.55/231.81 inference(bind,[status(th)],[])).
% 231.55/231.81 tff(19,plain,
% 231.55/231.81 (![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N))) <=> ![A: $i, C: $i, N: $i, L: $i] : (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))),
% 231.55/231.81 inference(quant_intro,[status(thm)],[18])).
% 231.55/231.81 tff(20,plain,
% 231.55/231.81 (![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N))) <=> ![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N)))),
% 231.55/231.81 inference(rewrite,[status(thm)],[])).
% 231.55/231.81 tff(21,plain,
% 231.55/231.81 (^[A: $i, C: $i, N: $i, L: $i] : rewrite((accept_team(A, L, C, N) <=> ((accept_city(A, C) & accept_leader(A, L)) & accept_number(A, N))) <=> (accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N))))),
% 231.55/231.81 inference(bind,[status(th)],[])).
% 231.55/231.81 tff(22,plain,
% 231.55/231.81 (![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> ((accept_city(A, C) & accept_leader(A, L)) & accept_number(A, N))) <=> ![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N)))),
% 231.55/231.81 inference(quant_intro,[status(thm)],[21])).
% 231.55/231.81 tff(23,axiom,(![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> ((accept_city(A, C) & accept_leader(A, L)) & accept_number(A, N)))), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+0.ax','a1_1')).
% 231.55/231.81 tff(24,plain,
% 231.55/231.81 (![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N)))),
% 231.55/231.81 inference(modus_ponens,[status(thm)],[23, 22])).
% 231.55/231.81 tff(25,plain,
% 231.55/231.81 (![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N)))),
% 231.55/231.81 inference(modus_ponens,[status(thm)],[24, 20])).
% 231.55/231.81 tff(26,plain,(
% 231.55/231.81 ![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N)))),
% 231.55/231.81 inference(skolemize,[status(sab)],[25])).
% 231.55/231.81 tff(27,plain,
% 231.55/231.81 (![A: $i, C: $i, N: $i, L: $i] : (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))),
% 231.55/231.81 inference(modus_ponens,[status(thm)],[26, 19])).
% 231.55/231.81 tff(28,plain,
% 231.55/231.81 (![A: $i, C: $i, N: $i, L: $i] : (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))),
% 231.55/231.81 inference(modus_ponens,[status(thm)],[27, 17])).
% 231.55/231.81 tff(29,plain,
% 231.55/231.81 ((~![A: $i, C: $i, N: $i, L: $i] : (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))) | (~(((~accept_city(muslimcountrybhumanitarianorganization, cityb)) | (~accept_leader(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization)) | (~accept_number(muslimcountrybhumanitarianorganization, n4))) <=> accept_team(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization, cityb, n4)))),
% 231.55/231.81 inference(quant_inst,[status(thm)],[])).
% 231.55/231.81 tff(30,plain,
% 231.55/231.81 (~(((~accept_city(muslimcountrybhumanitarianorganization, cityb)) | (~accept_leader(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization)) | (~accept_number(muslimcountrybhumanitarianorganization, n4))) <=> accept_team(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization, cityb, n4))),
% 231.55/231.81 inference(unit_resolution,[status(thm)],[29, 28])).
% 231.55/231.81 tff(31,plain,
% 231.55/231.81 (accept_team(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization, cityb, n4) <=> accept_team(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization, cityb, n4)),
% 231.55/231.81 inference(rewrite,[status(thm)],[])).
% 231.55/231.81 tff(32,axiom,(accept_team(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization, cityb, n4)), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+1.ax','event_8')).
% 231.55/231.81 tff(33,plain,
% 231.55/231.81 (accept_team(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization, cityb, n4)),
% 231.55/231.81 inference(modus_ponens,[status(thm)],[32, 31])).
% 231.55/231.81 tff(34,plain,
% 231.55/231.81 ((((~accept_city(muslimcountrybhumanitarianorganization, cityb)) | (~accept_leader(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization)) | (~accept_number(muslimcountrybhumanitarianorganization, n4))) <=> accept_team(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization, cityb, n4)) | (~((~accept_city(muslimcountrybhumanitarianorganization, cityb)) | (~accept_leader(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization)) | (~accept_number(muslimcountrybhumanitarianorganization, n4)))) | (~accept_team(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization, cityb, n4))),
% 231.55/231.81 inference(tautology,[status(thm)],[])).
% 231.55/231.81 tff(35,plain,
% 231.55/231.81 ((((~accept_city(muslimcountrybhumanitarianorganization, cityb)) | (~accept_leader(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization)) | (~accept_number(muslimcountrybhumanitarianorganization, n4))) <=> accept_team(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization, cityb, n4)) | (~((~accept_city(muslimcountrybhumanitarianorganization, cityb)) | (~accept_leader(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization)) | (~accept_number(muslimcountrybhumanitarianorganization, n4))))),
% 231.55/231.81 inference(unit_resolution,[status(thm)],[34, 33])).
% 231.55/231.81 tff(36,plain,
% 231.55/231.81 (~((~accept_city(muslimcountrybhumanitarianorganization, cityb)) | (~accept_leader(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization)) | (~accept_number(muslimcountrybhumanitarianorganization, n4)))),
% 231.55/231.81 inference(unit_resolution,[status(thm)],[35, 30])).
% 231.55/231.81 tff(37,plain,
% 231.55/231.81 (((~accept_city(muslimcountrybhumanitarianorganization, cityb)) | (~accept_leader(muslimcountrybhumanitarianorganization, countrybhumanitarianorganization)) | (~accept_number(muslimcountrybhumanitarianorganization, n4))) | accept_city(muslimcountrybhumanitarianorganization, cityb)),
% 231.55/231.81 inference(tautology,[status(thm)],[])).
% 231.55/231.81 tff(38,plain,
% 231.55/231.81 (accept_city(muslimcountrybhumanitarianorganization, cityb)),
% 231.55/231.81 inference(unit_resolution,[status(thm)],[37, 36])).
% 231.55/231.81 tff(39,plain,
% 231.55/231.81 ((((~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n20)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n1))) <=> accept_city(muslimcountrybhumanitarianorganization, cityb)) | (~((~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n20)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n1)))) | (~accept_city(muslimcountrybhumanitarianorganization, cityb))),
% 231.55/231.82 inference(tautology,[status(thm)],[])).
% 231.55/231.82 tff(40,plain,
% 231.55/231.82 ((((~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n20)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n1))) <=> accept_city(muslimcountrybhumanitarianorganization, cityb)) | (~((~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n20)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n1))))),
% 231.55/231.82 inference(unit_resolution,[status(thm)],[39, 38])).
% 231.55/231.82 tff(41,plain,
% 231.55/231.82 (~((~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n20)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n1)))),
% 231.55/231.82 inference(unit_resolution,[status(thm)],[40, 15])).
% 231.55/231.82 tff(42,plain,
% 231.55/231.82 (((~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n20)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n1))) | accept_population(muslimcountrybhumanitarianorganization, atheist, n78)),
% 231.55/231.82 inference(tautology,[status(thm)],[])).
% 231.55/231.82 tff(43,plain,
% 231.55/231.82 (accept_population(muslimcountrybhumanitarianorganization, atheist, n78)),
% 231.55/231.82 inference(unit_resolution,[status(thm)],[42, 41])).
% 231.55/231.82 tff(44,assumption,(~accept_population(muslimcountrybhumanitarianorganization, christian, n24)), introduced(assumption)).
% 231.55/231.82 tff(45,plain,
% 231.55/231.82 (^[X: $i, Y: $i] : refl(accept_population(X, Y, n24) <=> accept_population(X, Y, n24))),
% 231.55/231.82 inference(bind,[status(th)],[])).
% 231.55/231.82 tff(46,plain,
% 231.55/231.82 (![X: $i, Y: $i] : accept_population(X, Y, n24) <=> ![X: $i, Y: $i] : accept_population(X, Y, n24)),
% 231.55/231.82 inference(quant_intro,[status(thm)],[45])).
% 231.55/231.82 tff(47,plain,
% 231.55/231.82 ((~?[X: $i, Y: $i] : (~accept_population(X, Y, n24))) <=> (~?[X: $i, Y: $i] : (~accept_population(X, Y, n24)))),
% 231.55/231.82 inference(rewrite,[status(thm)],[])).
% 231.55/231.82 tff(48,axiom,(~?[X: $i, Y: $i] : (~accept_population(X, Y, n24))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','query_19')).
% 231.55/231.82 tff(49,plain,
% 231.55/231.82 (~?[X: $i, Y: $i] : (~accept_population(X, Y, n24))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[48, 47])).
% 231.55/231.82 tff(50,plain,
% 231.55/231.82 (~?[X: $i, Y: $i] : (~accept_population(X, Y, n24))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[49, 47])).
% 231.55/231.82 tff(51,plain,
% 231.55/231.82 (~?[X: $i, Y: $i] : (~accept_population(X, Y, n24))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[50, 47])).
% 231.55/231.82 tff(52,plain,
% 231.55/231.82 (~?[X: $i, Y: $i] : (~accept_population(X, Y, n24))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[51, 47])).
% 231.55/231.82 tff(53,plain,
% 231.55/231.82 (^[X: $i, Y: $i] : refl($oeq(accept_population(X, Y, n24), accept_population(X, Y, n24)))),
% 231.55/231.82 inference(bind,[status(th)],[])).
% 231.55/231.82 tff(54,plain,(
% 231.55/231.82 ![X: $i, Y: $i] : accept_population(X, Y, n24)),
% 231.55/231.82 inference(nnf-neg,[status(sab)],[52, 53])).
% 231.55/231.82 tff(55,plain,
% 231.55/231.82 (![X: $i, Y: $i] : accept_population(X, Y, n24)),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[54, 46])).
% 231.55/231.82 tff(56,plain,
% 231.55/231.82 ((~![X: $i, Y: $i] : accept_population(X, Y, n24)) | accept_population(muslimcountrybhumanitarianorganization, christian, n24)),
% 231.55/231.82 inference(quant_inst,[status(thm)],[])).
% 231.55/231.82 tff(57,plain,
% 231.55/231.82 ($false),
% 231.55/231.82 inference(unit_resolution,[status(thm)],[56, 55, 44])).
% 231.55/231.82 tff(58,plain,(accept_population(muslimcountrybhumanitarianorganization, christian, n24)), inference(lemma,lemma(discharge,[]))).
% 231.55/231.82 tff(59,plain,
% 231.55/231.82 (^[A: $i] : refl((~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna))) <=> (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna))))),
% 231.55/231.82 inference(bind,[status(th)],[])).
% 231.55/231.82 tff(60,plain,
% 231.55/231.82 (![A: $i] : (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna))) <=> ![A: $i] : (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna)))),
% 231.55/231.82 inference(quant_intro,[status(thm)],[59])).
% 231.55/231.82 tff(61,plain,
% 231.55/231.82 (^[A: $i] : trans(trans(monotonicity(rewrite((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> (~((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))))), (((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna)) <=> ((~((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0)))) <=> accept_city(A, towna)))), rewrite(((~((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0)))) <=> accept_city(A, towna)) <=> (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna)))), (((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna)) <=> (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna))))), rewrite((~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna))) <=> (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna)))), (((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna)) <=> (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna)))))),
% 231.55/231.82 inference(bind,[status(th)],[])).
% 231.55/231.82 tff(62,plain,
% 231.55/231.82 (![A: $i] : ((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna)) <=> ![A: $i] : (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna)))),
% 231.55/231.82 inference(quant_intro,[status(thm)],[61])).
% 231.55/231.82 tff(63,plain,
% 231.55/231.82 (![A: $i] : ((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna)) <=> ![A: $i] : ((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna))),
% 231.55/231.82 inference(rewrite,[status(thm)],[])).
% 231.55/231.82 tff(64,plain,
% 231.55/231.82 (^[A: $i] : rewrite((((((accept_population(A, atheist, n75) & accept_population(A, christian, n24)) & accept_population(A, muslim, n1)) & accept_population(A, native, n0)) & accept_population(A, other, n0)) <=> accept_city(A, towna)) <=> ((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna)))),
% 231.55/231.82 inference(bind,[status(th)],[])).
% 231.55/231.82 tff(65,plain,
% 231.55/231.82 (![A: $i] : (((((accept_population(A, atheist, n75) & accept_population(A, christian, n24)) & accept_population(A, muslim, n1)) & accept_population(A, native, n0)) & accept_population(A, other, n0)) <=> accept_city(A, towna)) <=> ![A: $i] : ((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna))),
% 231.55/231.82 inference(quant_intro,[status(thm)],[64])).
% 231.55/231.82 tff(66,axiom,(![A: $i] : (((((accept_population(A, atheist, n75) & accept_population(A, christian, n24)) & accept_population(A, muslim, n1)) & accept_population(A, native, n0)) & accept_population(A, other, n0)) <=> accept_city(A, towna))), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+0.ax','a2_9')).
% 231.55/231.82 tff(67,plain,
% 231.55/231.82 (![A: $i] : ((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[66, 65])).
% 231.55/231.82 tff(68,plain,
% 231.55/231.82 (![A: $i] : ((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[67, 63])).
% 231.55/231.82 tff(69,plain,(
% 231.55/231.82 ![A: $i] : ((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna))),
% 231.55/231.82 inference(skolemize,[status(sab)],[68])).
% 231.55/231.82 tff(70,plain,
% 231.55/231.82 (![A: $i] : (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna)))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[69, 62])).
% 231.55/231.82 tff(71,plain,
% 231.55/231.82 (![A: $i] : (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna)))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[70, 60])).
% 231.55/231.82 tff(72,plain,
% 231.55/231.82 ((~![A: $i] : (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna)))) | (~(((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))) <=> accept_city(muslimcountrybhumanitarianorganization, towna)))),
% 231.55/231.82 inference(quant_inst,[status(thm)],[])).
% 231.55/231.82 tff(73,plain,
% 231.55/231.82 (~(((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))) <=> accept_city(muslimcountrybhumanitarianorganization, towna))),
% 231.55/231.82 inference(unit_resolution,[status(thm)],[72, 71])).
% 231.55/231.82 tff(74,plain,
% 231.55/231.82 (any_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna) <=> any_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)),
% 231.55/231.82 inference(rewrite,[status(thm)],[])).
% 231.55/231.82 tff(75,axiom,(any_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+1.ax','event_12')).
% 231.55/231.82 tff(76,plain,
% 231.55/231.82 (any_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[75, 74])).
% 231.55/231.82 tff(77,plain,
% 231.55/231.82 (^[A: $i, L: $i, C: $i] : refl(((~any_agent_in_all_proposed_teams(A, L, C)) | accept_leader(A, L)) <=> ((~any_agent_in_all_proposed_teams(A, L, C)) | accept_leader(A, L)))),
% 231.55/231.82 inference(bind,[status(th)],[])).
% 231.55/231.82 tff(78,plain,
% 231.55/231.82 (![A: $i, L: $i, C: $i] : ((~any_agent_in_all_proposed_teams(A, L, C)) | accept_leader(A, L)) <=> ![A: $i, L: $i, C: $i] : ((~any_agent_in_all_proposed_teams(A, L, C)) | accept_leader(A, L))),
% 231.55/231.82 inference(quant_intro,[status(thm)],[77])).
% 231.55/231.82 tff(79,plain,
% 231.55/231.82 (![A: $i, L: $i, C: $i] : ((~any_agent_in_all_proposed_teams(A, L, C)) | accept_leader(A, L)) <=> ![A: $i, L: $i, C: $i] : ((~any_agent_in_all_proposed_teams(A, L, C)) | accept_leader(A, L))),
% 231.55/231.82 inference(rewrite,[status(thm)],[])).
% 231.55/231.82 tff(80,plain,
% 231.55/231.82 (^[A: $i, L: $i, C: $i] : rewrite((any_agent_in_all_proposed_teams(A, L, C) => accept_leader(A, L)) <=> ((~any_agent_in_all_proposed_teams(A, L, C)) | accept_leader(A, L)))),
% 231.55/231.82 inference(bind,[status(th)],[])).
% 231.55/231.82 tff(81,plain,
% 231.55/231.82 (![A: $i, L: $i, C: $i] : (any_agent_in_all_proposed_teams(A, L, C) => accept_leader(A, L)) <=> ![A: $i, L: $i, C: $i] : ((~any_agent_in_all_proposed_teams(A, L, C)) | accept_leader(A, L))),
% 231.55/231.82 inference(quant_intro,[status(thm)],[80])).
% 231.55/231.82 tff(82,axiom,(![A: $i, L: $i, C: $i] : (any_agent_in_all_proposed_teams(A, L, C) => accept_leader(A, L))), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+0.ax','a1_5')).
% 231.55/231.82 tff(83,plain,
% 231.55/231.82 (![A: $i, L: $i, C: $i] : ((~any_agent_in_all_proposed_teams(A, L, C)) | accept_leader(A, L))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[82, 81])).
% 231.55/231.82 tff(84,plain,
% 231.55/231.82 (![A: $i, L: $i, C: $i] : ((~any_agent_in_all_proposed_teams(A, L, C)) | accept_leader(A, L))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[83, 79])).
% 231.55/231.82 tff(85,plain,(
% 231.55/231.82 ![A: $i, L: $i, C: $i] : ((~any_agent_in_all_proposed_teams(A, L, C)) | accept_leader(A, L))),
% 231.55/231.82 inference(skolemize,[status(sab)],[84])).
% 231.55/231.82 tff(86,plain,
% 231.55/231.82 (![A: $i, L: $i, C: $i] : ((~any_agent_in_all_proposed_teams(A, L, C)) | accept_leader(A, L))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[85, 78])).
% 231.55/231.82 tff(87,plain,
% 231.55/231.82 (((~![A: $i, L: $i, C: $i] : ((~any_agent_in_all_proposed_teams(A, L, C)) | accept_leader(A, L))) | ((~any_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)) | accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization))) <=> ((~![A: $i, L: $i, C: $i] : ((~any_agent_in_all_proposed_teams(A, L, C)) | accept_leader(A, L))) | (~any_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)) | accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization))),
% 231.55/231.82 inference(rewrite,[status(thm)],[])).
% 231.55/231.82 tff(88,plain,
% 231.55/231.82 ((~![A: $i, L: $i, C: $i] : ((~any_agent_in_all_proposed_teams(A, L, C)) | accept_leader(A, L))) | ((~any_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)) | accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization))),
% 231.55/231.82 inference(quant_inst,[status(thm)],[])).
% 231.55/231.82 tff(89,plain,
% 231.55/231.82 ((~![A: $i, L: $i, C: $i] : ((~any_agent_in_all_proposed_teams(A, L, C)) | accept_leader(A, L))) | (~any_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)) | accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization)),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[88, 87])).
% 231.55/231.82 tff(90,plain,
% 231.55/231.82 (accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization)),
% 231.55/231.82 inference(unit_resolution,[status(thm)],[89, 86, 76])).
% 231.55/231.82 tff(91,plain,
% 231.55/231.82 (the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna) <=> the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)),
% 231.55/231.82 inference(rewrite,[status(thm)],[])).
% 231.55/231.82 tff(92,axiom,(the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+1.ax','event_11')).
% 231.55/231.82 tff(93,plain,
% 231.55/231.82 (the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[92, 91])).
% 231.55/231.82 tff(94,plain,
% 231.55/231.82 (^[A: $i, L: $i, C: $i] : refl(((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C))) <=> ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C))))),
% 231.55/231.82 inference(bind,[status(th)],[])).
% 231.55/231.82 tff(95,plain,
% 231.55/231.82 (![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C))) <=> ![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C)))),
% 231.55/231.82 inference(quant_intro,[status(thm)],[94])).
% 231.55/231.82 tff(96,plain,
% 231.55/231.82 (^[A: $i, L: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((accept_city(A, C) & accept_leader(A, L)) <=> (~((~accept_city(A, C)) | (~accept_leader(A, L))))), ((~(accept_city(A, C) & accept_leader(A, L))) <=> (~(~((~accept_city(A, C)) | (~accept_leader(A, L))))))), rewrite((~(~((~accept_city(A, C)) | (~accept_leader(A, L))))) <=> ((~accept_city(A, C)) | (~accept_leader(A, L)))), ((~(accept_city(A, C) & accept_leader(A, L))) <=> ((~accept_city(A, C)) | (~accept_leader(A, L))))), (((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~(accept_city(A, C) & accept_leader(A, L)))) <=> ((~the_agent_not_in_any_proposed_teams(A, L, C)) | ((~accept_city(A, C)) | (~accept_leader(A, L)))))), rewrite(((~the_agent_not_in_any_proposed_teams(A, L, C)) | ((~accept_city(A, C)) | (~accept_leader(A, L)))) <=> ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C)))), (((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~(accept_city(A, C) & accept_leader(A, L)))) <=> ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C)))))),
% 231.55/231.82 inference(bind,[status(th)],[])).
% 231.55/231.82 tff(97,plain,
% 231.55/231.82 (![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~(accept_city(A, C) & accept_leader(A, L)))) <=> ![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C)))),
% 231.55/231.82 inference(quant_intro,[status(thm)],[96])).
% 231.55/231.82 tff(98,plain,
% 231.55/231.82 (![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~(accept_city(A, C) & accept_leader(A, L)))) <=> ![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~(accept_city(A, C) & accept_leader(A, L))))),
% 231.55/231.82 inference(rewrite,[status(thm)],[])).
% 231.55/231.82 tff(99,plain,
% 231.55/231.82 (^[A: $i, L: $i, C: $i] : rewrite((the_agent_not_in_any_proposed_teams(A, L, C) => (~(accept_city(A, C) & accept_leader(A, L)))) <=> ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~(accept_city(A, C) & accept_leader(A, L)))))),
% 231.55/231.82 inference(bind,[status(th)],[])).
% 231.55/231.82 tff(100,plain,
% 231.55/231.82 (![A: $i, L: $i, C: $i] : (the_agent_not_in_any_proposed_teams(A, L, C) => (~(accept_city(A, C) & accept_leader(A, L)))) <=> ![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~(accept_city(A, C) & accept_leader(A, L))))),
% 231.55/231.82 inference(quant_intro,[status(thm)],[99])).
% 231.55/231.82 tff(101,axiom,(![A: $i, L: $i, C: $i] : (the_agent_not_in_any_proposed_teams(A, L, C) => (~(accept_city(A, C) & accept_leader(A, L))))), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+0.ax','a1_6')).
% 231.55/231.82 tff(102,plain,
% 231.55/231.82 (![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~(accept_city(A, C) & accept_leader(A, L))))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[101, 100])).
% 231.55/231.82 tff(103,plain,
% 231.55/231.82 (![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~(accept_city(A, C) & accept_leader(A, L))))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[102, 98])).
% 231.55/231.82 tff(104,plain,(
% 231.55/231.82 ![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~(accept_city(A, C) & accept_leader(A, L))))),
% 231.55/231.82 inference(skolemize,[status(sab)],[103])).
% 231.55/231.82 tff(105,plain,
% 231.55/231.82 (![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C)))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[104, 97])).
% 231.55/231.82 tff(106,plain,
% 231.55/231.82 (![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C)))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[105, 95])).
% 231.55/231.82 tff(107,plain,
% 231.55/231.82 (((~![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C)))) | ((~accept_city(muslimcountrybhumanitarianorganization, towna)) | (~the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization)))) <=> ((~![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C)))) | (~accept_city(muslimcountrybhumanitarianorganization, towna)) | (~the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization)))),
% 231.55/231.82 inference(rewrite,[status(thm)],[])).
% 231.55/231.82 tff(108,plain,
% 231.55/231.82 (((~the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization)) | (~accept_city(muslimcountrybhumanitarianorganization, towna))) <=> ((~accept_city(muslimcountrybhumanitarianorganization, towna)) | (~the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization)))),
% 231.55/231.82 inference(rewrite,[status(thm)],[])).
% 231.55/231.82 tff(109,plain,
% 231.55/231.82 (((~![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C)))) | ((~the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization)) | (~accept_city(muslimcountrybhumanitarianorganization, towna)))) <=> ((~![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C)))) | ((~accept_city(muslimcountrybhumanitarianorganization, towna)) | (~the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization))))),
% 231.55/231.82 inference(monotonicity,[status(thm)],[108])).
% 231.55/231.82 tff(110,plain,
% 231.55/231.82 (((~![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C)))) | ((~the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization)) | (~accept_city(muslimcountrybhumanitarianorganization, towna)))) <=> ((~![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C)))) | (~accept_city(muslimcountrybhumanitarianorganization, towna)) | (~the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization)))),
% 231.55/231.82 inference(transitivity,[status(thm)],[109, 107])).
% 231.55/231.82 tff(111,plain,
% 231.55/231.82 ((~![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C)))) | ((~the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization)) | (~accept_city(muslimcountrybhumanitarianorganization, towna)))),
% 231.55/231.82 inference(quant_inst,[status(thm)],[])).
% 231.55/231.82 tff(112,plain,
% 231.55/231.82 ((~![A: $i, L: $i, C: $i] : ((~the_agent_not_in_any_proposed_teams(A, L, C)) | (~accept_leader(A, L)) | (~accept_city(A, C)))) | (~accept_city(muslimcountrybhumanitarianorganization, towna)) | (~the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[111, 110])).
% 231.55/231.82 tff(113,plain,
% 231.55/231.82 (~accept_city(muslimcountrybhumanitarianorganization, towna)),
% 231.55/231.82 inference(unit_resolution,[status(thm)],[112, 106, 93, 90])).
% 231.55/231.82 tff(114,plain,
% 231.55/231.82 ((((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))) <=> accept_city(muslimcountrybhumanitarianorganization, towna)) | ((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))) | accept_city(muslimcountrybhumanitarianorganization, towna)),
% 231.55/231.82 inference(tautology,[status(thm)],[])).
% 231.55/231.82 tff(115,plain,
% 231.55/231.82 ((((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))) <=> accept_city(muslimcountrybhumanitarianorganization, towna)) | ((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0)))),
% 231.55/231.82 inference(unit_resolution,[status(thm)],[114, 113])).
% 231.55/231.82 tff(116,plain,
% 231.55/231.82 ((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))),
% 231.55/231.82 inference(unit_resolution,[status(thm)],[115, 73])).
% 231.55/231.82 tff(117,plain,
% 231.55/231.82 (^[A: $i] : refl((~(((~accept_population(A, atheist, n12)) | (~accept_population(A, christian, n3)) | (~accept_population(A, muslim, n0)) | (~accept_population(A, native, n85)) | (~accept_population(A, other, n0))) <=> accept_city(A, coastvillage))) <=> (~(((~accept_population(A, atheist, n12)) | (~accept_population(A, christian, n3)) | (~accept_population(A, muslim, n0)) | (~accept_population(A, native, n85)) | (~accept_population(A, other, n0))) <=> accept_city(A, coastvillage))))),
% 231.55/231.82 inference(bind,[status(th)],[])).
% 231.55/231.82 tff(118,plain,
% 231.55/231.82 (![A: $i] : (~(((~accept_population(A, atheist, n12)) | (~accept_population(A, christian, n3)) | (~accept_population(A, muslim, n0)) | (~accept_population(A, native, n85)) | (~accept_population(A, other, n0))) <=> accept_city(A, coastvillage))) <=> ![A: $i] : (~(((~accept_population(A, atheist, n12)) | (~accept_population(A, christian, n3)) | (~accept_population(A, muslim, n0)) | (~accept_population(A, native, n85)) | (~accept_population(A, other, n0))) <=> accept_city(A, coastvillage)))),
% 231.55/231.82 inference(quant_intro,[status(thm)],[117])).
% 231.55/231.82 tff(119,plain,
% 231.55/231.82 (^[A: $i] : trans(trans(monotonicity(rewrite((accept_population(A, atheist, n12) & accept_population(A, christian, n3) & accept_population(A, muslim, n0) & accept_population(A, native, n85) & accept_population(A, other, n0)) <=> (~((~accept_population(A, atheist, n12)) | (~accept_population(A, christian, n3)) | (~accept_population(A, muslim, n0)) | (~accept_population(A, native, n85)) | (~accept_population(A, other, n0))))), (((accept_population(A, atheist, n12) & accept_population(A, christian, n3) & accept_population(A, muslim, n0) & accept_population(A, native, n85) & accept_population(A, other, n0)) <=> accept_city(A, coastvillage)) <=> ((~((~accept_population(A, atheist, n12)) | (~accept_population(A, christian, n3)) | (~accept_population(A, muslim, n0)) | (~accept_population(A, native, n85)) | (~accept_population(A, other, n0)))) <=> accept_city(A, coastvillage)))), rewrite(((~((~accept_population(A, atheist, n12)) | (~accept_population(A, christian, n3)) | (~accept_population(A, muslim, n0)) | (~accept_population(A, native, n85)) | (~accept_population(A, other, n0)))) <=> accept_city(A, coastvillage)) <=> (~(((~accept_population(A, atheist, n12)) | (~accept_population(A, christian, n3)) | (~accept_population(A, muslim, n0)) | (~accept_population(A, native, n85)) | (~accept_population(A, other, n0))) <=> accept_city(A, coastvillage)))), (((accept_population(A, atheist, n12) & accept_population(A, christian, n3) & accept_population(A, muslim, n0) & accept_population(A, native, n85) & accept_population(A, other, n0)) <=> accept_city(A, coastvillage)) <=> (~(((~accept_population(A, atheist, n12)) | (~accept_population(A, christian, n3)) | (~accept_population(A, muslim, n0)) | (~accept_population(A, native, n85)) | (~accept_population(A, other, n0))) <=> accept_city(A, coastvillage))))), rewrite((~(((~accept_population(A, atheist, n12)) | (~accept_population(A, christian, n3)) | (~accept_population(A, muslim, n0)) | (~accept_population(A, native, n85)) | (~accept_population(A, other, n0))) <=> accept_city(A, coastvillage))) <=> (~(((~accept_population(A, atheist, n12)) | (~accept_population(A, christian, n3)) | (~accept_population(A, muslim, n0)) | (~accept_population(A, native, n85)) | (~accept_population(A, other, n0))) <=> accept_city(A, coastvillage)))), (((accept_population(A, atheist, n12) & accept_population(A, christian, n3) & accept_population(A, muslim, n0) & accept_population(A, native, n85) & accept_population(A, other, n0)) <=> accept_city(A, coastvillage)) <=> (~(((~accept_population(A, atheist, n12)) | (~accept_population(A, christian, n3)) | (~accept_population(A, muslim, n0)) | (~accept_population(A, native, n85)) | (~accept_population(A, other, n0))) <=> accept_city(A, coastvillage)))))),
% 231.55/231.82 inference(bind,[status(th)],[])).
% 231.55/231.82 tff(120,plain,
% 231.55/231.82 (![A: $i] : ((accept_population(A, atheist, n12) & accept_population(A, christian, n3) & accept_population(A, muslim, n0) & accept_population(A, native, n85) & accept_population(A, other, n0)) <=> accept_city(A, coastvillage)) <=> ![A: $i] : (~(((~accept_population(A, atheist, n12)) | (~accept_population(A, christian, n3)) | (~accept_population(A, muslim, n0)) | (~accept_population(A, native, n85)) | (~accept_population(A, other, n0))) <=> accept_city(A, coastvillage)))),
% 231.55/231.82 inference(quant_intro,[status(thm)],[119])).
% 231.55/231.82 tff(121,plain,
% 231.55/231.82 (![A: $i] : ((accept_population(A, atheist, n12) & accept_population(A, christian, n3) & accept_population(A, muslim, n0) & accept_population(A, native, n85) & accept_population(A, other, n0)) <=> accept_city(A, coastvillage)) <=> ![A: $i] : ((accept_population(A, atheist, n12) & accept_population(A, christian, n3) & accept_population(A, muslim, n0) & accept_population(A, native, n85) & accept_population(A, other, n0)) <=> accept_city(A, coastvillage))),
% 231.55/231.82 inference(rewrite,[status(thm)],[])).
% 231.55/231.82 tff(122,plain,
% 231.55/231.82 (^[A: $i] : rewrite((((((accept_population(A, atheist, n12) & accept_population(A, christian, n3)) & accept_population(A, muslim, n0)) & accept_population(A, native, n85)) & accept_population(A, other, n0)) <=> accept_city(A, coastvillage)) <=> ((accept_population(A, atheist, n12) & accept_population(A, christian, n3) & accept_population(A, muslim, n0) & accept_population(A, native, n85) & accept_population(A, other, n0)) <=> accept_city(A, coastvillage)))),
% 231.55/231.82 inference(bind,[status(th)],[])).
% 231.55/231.82 tff(123,plain,
% 231.55/231.82 (![A: $i] : (((((accept_population(A, atheist, n12) & accept_population(A, christian, n3)) & accept_population(A, muslim, n0)) & accept_population(A, native, n85)) & accept_population(A, other, n0)) <=> accept_city(A, coastvillage)) <=> ![A: $i] : ((accept_population(A, atheist, n12) & accept_population(A, christian, n3) & accept_population(A, muslim, n0) & accept_population(A, native, n85) & accept_population(A, other, n0)) <=> accept_city(A, coastvillage))),
% 231.55/231.82 inference(quant_intro,[status(thm)],[122])).
% 231.55/231.82 tff(124,axiom,(![A: $i] : (((((accept_population(A, atheist, n12) & accept_population(A, christian, n3)) & accept_population(A, muslim, n0)) & accept_population(A, native, n85)) & accept_population(A, other, n0)) <=> accept_city(A, coastvillage))), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+0.ax','a2_7')).
% 231.55/231.82 tff(125,plain,
% 231.55/231.82 (![A: $i] : ((accept_population(A, atheist, n12) & accept_population(A, christian, n3) & accept_population(A, muslim, n0) & accept_population(A, native, n85) & accept_population(A, other, n0)) <=> accept_city(A, coastvillage))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[124, 123])).
% 231.55/231.82 tff(126,plain,
% 231.55/231.82 (![A: $i] : ((accept_population(A, atheist, n12) & accept_population(A, christian, n3) & accept_population(A, muslim, n0) & accept_population(A, native, n85) & accept_population(A, other, n0)) <=> accept_city(A, coastvillage))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[125, 121])).
% 231.55/231.82 tff(127,plain,(
% 231.55/231.82 ![A: $i] : ((accept_population(A, atheist, n12) & accept_population(A, christian, n3) & accept_population(A, muslim, n0) & accept_population(A, native, n85) & accept_population(A, other, n0)) <=> accept_city(A, coastvillage))),
% 231.55/231.82 inference(skolemize,[status(sab)],[126])).
% 231.55/231.82 tff(128,plain,
% 231.55/231.82 (![A: $i] : (~(((~accept_population(A, atheist, n12)) | (~accept_population(A, christian, n3)) | (~accept_population(A, muslim, n0)) | (~accept_population(A, native, n85)) | (~accept_population(A, other, n0))) <=> accept_city(A, coastvillage)))),
% 231.55/231.82 inference(modus_ponens,[status(thm)],[127, 120])).
% 231.55/231.82 tff(129,plain,
% 231.55/231.82 (![A: $i] : (~(((~accept_population(A, atheist, n12)) | (~accept_population(A, christian, n3)) | (~accept_population(A, muslim, n0)) | (~accept_population(A, native, n85)) | (~accept_population(A, other, n0))) <=> accept_city(A, coastvillage)))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[128, 118])).
% 231.55/231.83 tff(130,plain,
% 231.55/231.83 ((~![A: $i] : (~(((~accept_population(A, atheist, n12)) | (~accept_population(A, christian, n3)) | (~accept_population(A, muslim, n0)) | (~accept_population(A, native, n85)) | (~accept_population(A, other, n0))) <=> accept_city(A, coastvillage)))) | (~(((~accept_population(muslimcountrybhumanitarianorganization, atheist, n12)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n3)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n85)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))) <=> accept_city(muslimcountrybhumanitarianorganization, coastvillage)))),
% 231.55/231.83 inference(quant_inst,[status(thm)],[])).
% 231.55/231.83 tff(131,plain,
% 231.55/231.83 (~(((~accept_population(muslimcountrybhumanitarianorganization, atheist, n12)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n3)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n85)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))) <=> accept_city(muslimcountrybhumanitarianorganization, coastvillage))),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[130, 129])).
% 231.55/231.83 tff(132,plain,
% 231.55/231.83 ((~![A: $i, C: $i, N: $i, L: $i] : (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))) | (~(((~accept_city(muslimcountrybhumanitarianorganization, coastvillage)) | (~accept_leader(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization)) | (~accept_number(muslimcountrybhumanitarianorganization, n5))) <=> accept_team(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization, coastvillage, n5)))),
% 231.55/231.83 inference(quant_inst,[status(thm)],[])).
% 231.55/231.83 tff(133,plain,
% 231.55/231.83 (~(((~accept_city(muslimcountrybhumanitarianorganization, coastvillage)) | (~accept_leader(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization)) | (~accept_number(muslimcountrybhumanitarianorganization, n5))) <=> accept_team(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization, coastvillage, n5))),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[132, 28])).
% 231.55/231.83 tff(134,plain,
% 231.55/231.83 (accept_team(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization, coastvillage, n5) <=> accept_team(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization, coastvillage, n5)),
% 231.55/231.83 inference(rewrite,[status(thm)],[])).
% 231.55/231.83 tff(135,axiom,(accept_team(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization, coastvillage, n5)), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+1.ax','event_13')).
% 231.55/231.83 tff(136,plain,
% 231.55/231.83 (accept_team(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization, coastvillage, n5)),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[135, 134])).
% 231.55/231.83 tff(137,plain,
% 231.55/231.83 ((((~accept_city(muslimcountrybhumanitarianorganization, coastvillage)) | (~accept_leader(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization)) | (~accept_number(muslimcountrybhumanitarianorganization, n5))) <=> accept_team(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization, coastvillage, n5)) | (~((~accept_city(muslimcountrybhumanitarianorganization, coastvillage)) | (~accept_leader(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization)) | (~accept_number(muslimcountrybhumanitarianorganization, n5)))) | (~accept_team(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization, coastvillage, n5))),
% 231.55/231.83 inference(tautology,[status(thm)],[])).
% 231.55/231.83 tff(138,plain,
% 231.55/231.83 ((((~accept_city(muslimcountrybhumanitarianorganization, coastvillage)) | (~accept_leader(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization)) | (~accept_number(muslimcountrybhumanitarianorganization, n5))) <=> accept_team(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization, coastvillage, n5)) | (~((~accept_city(muslimcountrybhumanitarianorganization, coastvillage)) | (~accept_leader(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization)) | (~accept_number(muslimcountrybhumanitarianorganization, n5))))),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[137, 136])).
% 231.55/231.83 tff(139,plain,
% 231.55/231.83 (~((~accept_city(muslimcountrybhumanitarianorganization, coastvillage)) | (~accept_leader(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization)) | (~accept_number(muslimcountrybhumanitarianorganization, n5)))),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[138, 133])).
% 231.55/231.83 tff(140,plain,
% 231.55/231.83 (((~accept_city(muslimcountrybhumanitarianorganization, coastvillage)) | (~accept_leader(muslimcountrybhumanitarianorganization, christiancountrychumanitarianorganization)) | (~accept_number(muslimcountrybhumanitarianorganization, n5))) | accept_city(muslimcountrybhumanitarianorganization, coastvillage)),
% 231.55/231.83 inference(tautology,[status(thm)],[])).
% 231.55/231.83 tff(141,plain,
% 231.55/231.83 (accept_city(muslimcountrybhumanitarianorganization, coastvillage)),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[140, 139])).
% 231.55/231.83 tff(142,plain,
% 231.55/231.83 ((((~accept_population(muslimcountrybhumanitarianorganization, atheist, n12)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n3)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n85)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))) <=> accept_city(muslimcountrybhumanitarianorganization, coastvillage)) | (~((~accept_population(muslimcountrybhumanitarianorganization, atheist, n12)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n3)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n85)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0)))) | (~accept_city(muslimcountrybhumanitarianorganization, coastvillage))),
% 231.55/231.83 inference(tautology,[status(thm)],[])).
% 231.55/231.83 tff(143,plain,
% 231.55/231.83 ((((~accept_population(muslimcountrybhumanitarianorganization, atheist, n12)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n3)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n85)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))) <=> accept_city(muslimcountrybhumanitarianorganization, coastvillage)) | (~((~accept_population(muslimcountrybhumanitarianorganization, atheist, n12)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n3)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n85)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))))),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[142, 141])).
% 231.55/231.83 tff(144,plain,
% 231.55/231.83 (~((~accept_population(muslimcountrybhumanitarianorganization, atheist, n12)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n3)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n85)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0)))),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[143, 131])).
% 231.55/231.83 tff(145,plain,
% 231.55/231.83 (((~accept_population(muslimcountrybhumanitarianorganization, atheist, n12)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n3)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n85)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))) | accept_population(muslimcountrybhumanitarianorganization, other, n0)),
% 231.55/231.83 inference(tautology,[status(thm)],[])).
% 231.55/231.83 tff(146,plain,
% 231.55/231.83 (accept_population(muslimcountrybhumanitarianorganization, other, n0)),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[145, 144])).
% 231.55/231.83 tff(147,plain,
% 231.55/231.83 (((~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n20)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n1))) | accept_population(muslimcountrybhumanitarianorganization, muslim, n1)),
% 231.55/231.83 inference(tautology,[status(thm)],[])).
% 231.55/231.83 tff(148,plain,
% 231.55/231.83 (accept_population(muslimcountrybhumanitarianorganization, muslim, n1)),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[147, 41])).
% 231.55/231.83 tff(149,plain,
% 231.55/231.83 (^[A: $i] : refl((~(((~accept_population(A, atheist, n30)) | (~accept_population(A, christian, n0)) | (~accept_population(A, muslim, n65)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n5))) <=> accept_city(A, townc))) <=> (~(((~accept_population(A, atheist, n30)) | (~accept_population(A, christian, n0)) | (~accept_population(A, muslim, n65)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n5))) <=> accept_city(A, townc))))),
% 231.55/231.83 inference(bind,[status(th)],[])).
% 231.55/231.83 tff(150,plain,
% 231.55/231.83 (![A: $i] : (~(((~accept_population(A, atheist, n30)) | (~accept_population(A, christian, n0)) | (~accept_population(A, muslim, n65)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n5))) <=> accept_city(A, townc))) <=> ![A: $i] : (~(((~accept_population(A, atheist, n30)) | (~accept_population(A, christian, n0)) | (~accept_population(A, muslim, n65)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n5))) <=> accept_city(A, townc)))),
% 231.55/231.83 inference(quant_intro,[status(thm)],[149])).
% 231.55/231.83 tff(151,plain,
% 231.55/231.83 (^[A: $i] : trans(trans(monotonicity(rewrite((accept_population(A, atheist, n30) & accept_population(A, christian, n0) & accept_population(A, muslim, n65) & accept_population(A, native, n0) & accept_population(A, other, n5)) <=> (~((~accept_population(A, atheist, n30)) | (~accept_population(A, christian, n0)) | (~accept_population(A, muslim, n65)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n5))))), (((accept_population(A, atheist, n30) & accept_population(A, christian, n0) & accept_population(A, muslim, n65) & accept_population(A, native, n0) & accept_population(A, other, n5)) <=> accept_city(A, townc)) <=> ((~((~accept_population(A, atheist, n30)) | (~accept_population(A, christian, n0)) | (~accept_population(A, muslim, n65)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n5)))) <=> accept_city(A, townc)))), rewrite(((~((~accept_population(A, atheist, n30)) | (~accept_population(A, christian, n0)) | (~accept_population(A, muslim, n65)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n5)))) <=> accept_city(A, townc)) <=> (~(((~accept_population(A, atheist, n30)) | (~accept_population(A, christian, n0)) | (~accept_population(A, muslim, n65)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n5))) <=> accept_city(A, townc)))), (((accept_population(A, atheist, n30) & accept_population(A, christian, n0) & accept_population(A, muslim, n65) & accept_population(A, native, n0) & accept_population(A, other, n5)) <=> accept_city(A, townc)) <=> (~(((~accept_population(A, atheist, n30)) | (~accept_population(A, christian, n0)) | (~accept_population(A, muslim, n65)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n5))) <=> accept_city(A, townc))))), rewrite((~(((~accept_population(A, atheist, n30)) | (~accept_population(A, christian, n0)) | (~accept_population(A, muslim, n65)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n5))) <=> accept_city(A, townc))) <=> (~(((~accept_population(A, atheist, n30)) | (~accept_population(A, christian, n0)) | (~accept_population(A, muslim, n65)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n5))) <=> accept_city(A, townc)))), (((accept_population(A, atheist, n30) & accept_population(A, christian, n0) & accept_population(A, muslim, n65) & accept_population(A, native, n0) & accept_population(A, other, n5)) <=> accept_city(A, townc)) <=> (~(((~accept_population(A, atheist, n30)) | (~accept_population(A, christian, n0)) | (~accept_population(A, muslim, n65)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n5))) <=> accept_city(A, townc)))))),
% 231.55/231.83 inference(bind,[status(th)],[])).
% 231.55/231.83 tff(152,plain,
% 231.55/231.83 (![A: $i] : ((accept_population(A, atheist, n30) & accept_population(A, christian, n0) & accept_population(A, muslim, n65) & accept_population(A, native, n0) & accept_population(A, other, n5)) <=> accept_city(A, townc)) <=> ![A: $i] : (~(((~accept_population(A, atheist, n30)) | (~accept_population(A, christian, n0)) | (~accept_population(A, muslim, n65)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n5))) <=> accept_city(A, townc)))),
% 231.55/231.83 inference(quant_intro,[status(thm)],[151])).
% 231.55/231.83 tff(153,plain,
% 231.55/231.83 (![A: $i] : ((accept_population(A, atheist, n30) & accept_population(A, christian, n0) & accept_population(A, muslim, n65) & accept_population(A, native, n0) & accept_population(A, other, n5)) <=> accept_city(A, townc)) <=> ![A: $i] : ((accept_population(A, atheist, n30) & accept_population(A, christian, n0) & accept_population(A, muslim, n65) & accept_population(A, native, n0) & accept_population(A, other, n5)) <=> accept_city(A, townc))),
% 231.55/231.83 inference(rewrite,[status(thm)],[])).
% 231.55/231.83 tff(154,plain,
% 231.55/231.83 (^[A: $i] : rewrite((((((accept_population(A, atheist, n30) & accept_population(A, christian, n0)) & accept_population(A, muslim, n65)) & accept_population(A, native, n0)) & accept_population(A, other, n5)) <=> accept_city(A, townc)) <=> ((accept_population(A, atheist, n30) & accept_population(A, christian, n0) & accept_population(A, muslim, n65) & accept_population(A, native, n0) & accept_population(A, other, n5)) <=> accept_city(A, townc)))),
% 231.55/231.83 inference(bind,[status(th)],[])).
% 231.55/231.83 tff(155,plain,
% 231.55/231.83 (![A: $i] : (((((accept_population(A, atheist, n30) & accept_population(A, christian, n0)) & accept_population(A, muslim, n65)) & accept_population(A, native, n0)) & accept_population(A, other, n5)) <=> accept_city(A, townc)) <=> ![A: $i] : ((accept_population(A, atheist, n30) & accept_population(A, christian, n0) & accept_population(A, muslim, n65) & accept_population(A, native, n0) & accept_population(A, other, n5)) <=> accept_city(A, townc))),
% 231.55/231.83 inference(quant_intro,[status(thm)],[154])).
% 231.55/231.83 tff(156,axiom,(![A: $i] : (((((accept_population(A, atheist, n30) & accept_population(A, christian, n0)) & accept_population(A, muslim, n65)) & accept_population(A, native, n0)) & accept_population(A, other, n5)) <=> accept_city(A, townc))), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+0.ax','a2_13')).
% 231.55/231.83 tff(157,plain,
% 231.55/231.83 (![A: $i] : ((accept_population(A, atheist, n30) & accept_population(A, christian, n0) & accept_population(A, muslim, n65) & accept_population(A, native, n0) & accept_population(A, other, n5)) <=> accept_city(A, townc))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[156, 155])).
% 231.55/231.83 tff(158,plain,
% 231.55/231.83 (![A: $i] : ((accept_population(A, atheist, n30) & accept_population(A, christian, n0) & accept_population(A, muslim, n65) & accept_population(A, native, n0) & accept_population(A, other, n5)) <=> accept_city(A, townc))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[157, 153])).
% 231.55/231.83 tff(159,plain,(
% 231.55/231.83 ![A: $i] : ((accept_population(A, atheist, n30) & accept_population(A, christian, n0) & accept_population(A, muslim, n65) & accept_population(A, native, n0) & accept_population(A, other, n5)) <=> accept_city(A, townc))),
% 231.55/231.83 inference(skolemize,[status(sab)],[158])).
% 231.55/231.83 tff(160,plain,
% 231.55/231.83 (![A: $i] : (~(((~accept_population(A, atheist, n30)) | (~accept_population(A, christian, n0)) | (~accept_population(A, muslim, n65)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n5))) <=> accept_city(A, townc)))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[159, 152])).
% 231.55/231.83 tff(161,plain,
% 231.55/231.83 (![A: $i] : (~(((~accept_population(A, atheist, n30)) | (~accept_population(A, christian, n0)) | (~accept_population(A, muslim, n65)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n5))) <=> accept_city(A, townc)))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[160, 150])).
% 231.55/231.83 tff(162,plain,
% 231.55/231.83 ((~![A: $i] : (~(((~accept_population(A, atheist, n30)) | (~accept_population(A, christian, n0)) | (~accept_population(A, muslim, n65)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n5))) <=> accept_city(A, townc)))) | (~(((~accept_population(muslimcountrybhumanitarianorganization, atheist, n30)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n65)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n5))) <=> accept_city(muslimcountrybhumanitarianorganization, townc)))),
% 231.55/231.83 inference(quant_inst,[status(thm)],[])).
% 231.55/231.83 tff(163,plain,
% 231.55/231.83 (~(((~accept_population(muslimcountrybhumanitarianorganization, atheist, n30)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n65)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n5))) <=> accept_city(muslimcountrybhumanitarianorganization, townc))),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[162, 161])).
% 231.55/231.83 tff(164,plain,
% 231.55/231.83 (the_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryahumanitarianorganization, townc) <=> the_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryahumanitarianorganization, townc)),
% 231.55/231.83 inference(rewrite,[status(thm)],[])).
% 231.55/231.83 tff(165,axiom,(the_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryahumanitarianorganization, townc)), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+1.ax','event_104')).
% 231.55/231.83 tff(166,plain,
% 231.55/231.83 (the_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryahumanitarianorganization, townc)),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[165, 164])).
% 231.55/231.83 tff(167,plain,
% 231.55/231.83 (^[A: $i, L: $i, C: $i] : refl(((~the_agent_in_all_proposed_teams(A, L, C)) | (~((~accept_leader(A, L)) | (~accept_city(A, C))))) <=> ((~the_agent_in_all_proposed_teams(A, L, C)) | (~((~accept_leader(A, L)) | (~accept_city(A, C))))))),
% 231.55/231.83 inference(bind,[status(th)],[])).
% 231.55/231.83 tff(168,plain,
% 231.55/231.83 (![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (~((~accept_leader(A, L)) | (~accept_city(A, C))))) <=> ![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (~((~accept_leader(A, L)) | (~accept_city(A, C)))))),
% 231.55/231.83 inference(quant_intro,[status(thm)],[167])).
% 231.55/231.83 tff(169,plain,
% 231.55/231.83 (^[A: $i, L: $i, C: $i] : rewrite(((~the_agent_in_all_proposed_teams(A, L, C)) | (accept_leader(A, L) & accept_city(A, C))) <=> ((~the_agent_in_all_proposed_teams(A, L, C)) | (~((~accept_leader(A, L)) | (~accept_city(A, C))))))),
% 231.55/231.83 inference(bind,[status(th)],[])).
% 231.55/231.83 tff(170,plain,
% 231.55/231.83 (![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (accept_leader(A, L) & accept_city(A, C))) <=> ![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (~((~accept_leader(A, L)) | (~accept_city(A, C)))))),
% 231.55/231.83 inference(quant_intro,[status(thm)],[169])).
% 231.55/231.83 tff(171,plain,
% 231.55/231.83 (![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (accept_leader(A, L) & accept_city(A, C))) <=> ![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (accept_leader(A, L) & accept_city(A, C)))),
% 231.55/231.83 inference(rewrite,[status(thm)],[])).
% 231.55/231.83 tff(172,plain,
% 231.55/231.83 (^[A: $i, L: $i, C: $i] : rewrite((the_agent_in_all_proposed_teams(A, L, C) => (accept_leader(A, L) & accept_city(A, C))) <=> ((~the_agent_in_all_proposed_teams(A, L, C)) | (accept_leader(A, L) & accept_city(A, C))))),
% 231.55/231.83 inference(bind,[status(th)],[])).
% 231.55/231.83 tff(173,plain,
% 231.55/231.83 (![A: $i, L: $i, C: $i] : (the_agent_in_all_proposed_teams(A, L, C) => (accept_leader(A, L) & accept_city(A, C))) <=> ![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (accept_leader(A, L) & accept_city(A, C)))),
% 231.55/231.83 inference(quant_intro,[status(thm)],[172])).
% 231.55/231.83 tff(174,axiom,(![A: $i, L: $i, C: $i] : (the_agent_in_all_proposed_teams(A, L, C) => (accept_leader(A, L) & accept_city(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+0.ax','a1_4')).
% 231.55/231.83 tff(175,plain,
% 231.55/231.83 (![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (accept_leader(A, L) & accept_city(A, C)))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[174, 173])).
% 231.55/231.83 tff(176,plain,
% 231.55/231.83 (![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (accept_leader(A, L) & accept_city(A, C)))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[175, 171])).
% 231.55/231.83 tff(177,plain,(
% 231.55/231.83 ![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (accept_leader(A, L) & accept_city(A, C)))),
% 231.55/231.83 inference(skolemize,[status(sab)],[176])).
% 231.55/231.83 tff(178,plain,
% 231.55/231.83 (![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (~((~accept_leader(A, L)) | (~accept_city(A, C)))))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[177, 170])).
% 231.55/231.83 tff(179,plain,
% 231.55/231.83 (![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (~((~accept_leader(A, L)) | (~accept_city(A, C)))))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[178, 168])).
% 231.55/231.83 tff(180,plain,
% 231.55/231.83 (((~![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (~((~accept_leader(A, L)) | (~accept_city(A, C)))))) | ((~the_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryahumanitarianorganization, townc)) | (~((~accept_city(muslimcountrybhumanitarianorganization, townc)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryahumanitarianorganization)))))) <=> ((~![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (~((~accept_leader(A, L)) | (~accept_city(A, C)))))) | (~the_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryahumanitarianorganization, townc)) | (~((~accept_city(muslimcountrybhumanitarianorganization, townc)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryahumanitarianorganization)))))),
% 231.55/231.83 inference(rewrite,[status(thm)],[])).
% 231.55/231.83 tff(181,plain,
% 231.55/231.83 (((~the_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryahumanitarianorganization, townc)) | (~((~accept_leader(muslimcountrybhumanitarianorganization, countryahumanitarianorganization)) | (~accept_city(muslimcountrybhumanitarianorganization, townc))))) <=> ((~the_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryahumanitarianorganization, townc)) | (~((~accept_city(muslimcountrybhumanitarianorganization, townc)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryahumanitarianorganization)))))),
% 231.55/231.83 inference(rewrite,[status(thm)],[])).
% 231.55/231.83 tff(182,plain,
% 231.55/231.83 (((~![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (~((~accept_leader(A, L)) | (~accept_city(A, C)))))) | ((~the_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryahumanitarianorganization, townc)) | (~((~accept_leader(muslimcountrybhumanitarianorganization, countryahumanitarianorganization)) | (~accept_city(muslimcountrybhumanitarianorganization, townc)))))) <=> ((~![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (~((~accept_leader(A, L)) | (~accept_city(A, C)))))) | ((~the_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryahumanitarianorganization, townc)) | (~((~accept_city(muslimcountrybhumanitarianorganization, townc)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryahumanitarianorganization))))))),
% 231.55/231.83 inference(monotonicity,[status(thm)],[181])).
% 231.55/231.83 tff(183,plain,
% 231.55/231.83 (((~![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (~((~accept_leader(A, L)) | (~accept_city(A, C)))))) | ((~the_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryahumanitarianorganization, townc)) | (~((~accept_leader(muslimcountrybhumanitarianorganization, countryahumanitarianorganization)) | (~accept_city(muslimcountrybhumanitarianorganization, townc)))))) <=> ((~![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (~((~accept_leader(A, L)) | (~accept_city(A, C)))))) | (~the_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryahumanitarianorganization, townc)) | (~((~accept_city(muslimcountrybhumanitarianorganization, townc)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryahumanitarianorganization)))))),
% 231.55/231.83 inference(transitivity,[status(thm)],[182, 180])).
% 231.55/231.83 tff(184,plain,
% 231.55/231.83 ((~![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (~((~accept_leader(A, L)) | (~accept_city(A, C)))))) | ((~the_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryahumanitarianorganization, townc)) | (~((~accept_leader(muslimcountrybhumanitarianorganization, countryahumanitarianorganization)) | (~accept_city(muslimcountrybhumanitarianorganization, townc)))))),
% 231.55/231.83 inference(quant_inst,[status(thm)],[])).
% 231.55/231.83 tff(185,plain,
% 231.55/231.83 ((~![A: $i, L: $i, C: $i] : ((~the_agent_in_all_proposed_teams(A, L, C)) | (~((~accept_leader(A, L)) | (~accept_city(A, C)))))) | (~the_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryahumanitarianorganization, townc)) | (~((~accept_city(muslimcountrybhumanitarianorganization, townc)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryahumanitarianorganization))))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[184, 183])).
% 231.55/231.83 tff(186,plain,
% 231.55/231.83 (~((~accept_city(muslimcountrybhumanitarianorganization, townc)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryahumanitarianorganization)))),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[185, 179, 166])).
% 231.55/231.83 tff(187,plain,
% 231.55/231.83 (((~accept_city(muslimcountrybhumanitarianorganization, townc)) | (~accept_leader(muslimcountrybhumanitarianorganization, countryahumanitarianorganization))) | accept_city(muslimcountrybhumanitarianorganization, townc)),
% 231.55/231.83 inference(tautology,[status(thm)],[])).
% 231.55/231.83 tff(188,plain,
% 231.55/231.83 (accept_city(muslimcountrybhumanitarianorganization, townc)),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[187, 186])).
% 231.55/231.83 tff(189,plain,
% 231.55/231.83 ((((~accept_population(muslimcountrybhumanitarianorganization, atheist, n30)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n65)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n5))) <=> accept_city(muslimcountrybhumanitarianorganization, townc)) | (~((~accept_population(muslimcountrybhumanitarianorganization, atheist, n30)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n65)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n5)))) | (~accept_city(muslimcountrybhumanitarianorganization, townc))),
% 231.55/231.83 inference(tautology,[status(thm)],[])).
% 231.55/231.83 tff(190,plain,
% 231.55/231.83 ((((~accept_population(muslimcountrybhumanitarianorganization, atheist, n30)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n65)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n5))) <=> accept_city(muslimcountrybhumanitarianorganization, townc)) | (~((~accept_population(muslimcountrybhumanitarianorganization, atheist, n30)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n65)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n5))))),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[189, 188])).
% 231.55/231.83 tff(191,plain,
% 231.55/231.83 (~((~accept_population(muslimcountrybhumanitarianorganization, atheist, n30)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n65)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n5)))),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[190, 163])).
% 231.55/231.83 tff(192,plain,
% 231.55/231.83 (((~accept_population(muslimcountrybhumanitarianorganization, atheist, n30)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n65)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n5))) | accept_population(muslimcountrybhumanitarianorganization, native, n0)),
% 231.55/231.83 inference(tautology,[status(thm)],[])).
% 231.55/231.83 tff(193,plain,
% 231.55/231.83 (accept_population(muslimcountrybhumanitarianorganization, native, n0)),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[192, 191])).
% 231.55/231.83 tff(194,plain,
% 231.55/231.83 ((~((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0)))) | (~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))),
% 231.55/231.83 inference(tautology,[status(thm)],[])).
% 231.55/231.83 tff(195,plain,
% 231.55/231.83 ((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24))),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[194, 193, 148, 146, 116])).
% 231.55/231.83 tff(196,plain,
% 231.55/231.83 (~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[195, 58])).
% 231.55/231.83 tff(197,plain,
% 231.55/231.83 (^[A: $i, N: $i, M: $i, P: $i] : refl((accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N))) <=> (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N))))),
% 231.55/231.83 inference(bind,[status(th)],[])).
% 231.55/231.83 tff(198,plain,
% 231.55/231.83 (![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N))) <=> ![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))),
% 231.55/231.83 inference(quant_intro,[status(thm)],[197])).
% 231.55/231.83 tff(199,plain,
% 231.55/231.83 (^[A: $i, N: $i, M: $i, P: $i] : trans(monotonicity(trans(monotonicity(rewrite((accept_population(A, P, N) & less(M, N)) <=> (~((~accept_population(A, P, N)) | (~less(M, N))))), ((~(accept_population(A, P, N) & less(M, N))) <=> (~(~((~accept_population(A, P, N)) | (~less(M, N))))))), rewrite((~(~((~accept_population(A, P, N)) | (~less(M, N))))) <=> ((~accept_population(A, P, N)) | (~less(M, N)))), ((~(accept_population(A, P, N) & less(M, N))) <=> ((~accept_population(A, P, N)) | (~less(M, N))))), (((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M)) <=> (((~accept_population(A, P, N)) | (~less(M, N))) | accept_population(A, P, M)))), rewrite((((~accept_population(A, P, N)) | (~less(M, N))) | accept_population(A, P, M)) <=> (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))), (((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M)) <=> (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))))),
% 231.55/231.83 inference(bind,[status(th)],[])).
% 231.55/231.83 tff(200,plain,
% 231.55/231.83 (![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M)) <=> ![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))),
% 231.55/231.83 inference(quant_intro,[status(thm)],[199])).
% 231.55/231.83 tff(201,plain,
% 231.55/231.83 (![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M)) <=> ![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 231.55/231.83 inference(rewrite,[status(thm)],[])).
% 231.55/231.83 tff(202,plain,
% 231.55/231.83 (^[A: $i, N: $i, M: $i, P: $i] : rewrite(((accept_population(A, P, N) & less(M, N)) => accept_population(A, P, M)) <=> ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M)))),
% 231.55/231.83 inference(bind,[status(th)],[])).
% 231.55/231.83 tff(203,plain,
% 231.55/231.83 (![A: $i, N: $i, M: $i, P: $i] : ((accept_population(A, P, N) & less(M, N)) => accept_population(A, P, M)) <=> ![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 231.55/231.83 inference(quant_intro,[status(thm)],[202])).
% 231.55/231.83 tff(204,axiom,(![A: $i, N: $i, M: $i, P: $i] : ((accept_population(A, P, N) & less(M, N)) => accept_population(A, P, M))), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+0.ax','a1_3')).
% 231.55/231.83 tff(205,plain,
% 231.55/231.83 (![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[204, 203])).
% 231.55/231.83 tff(206,plain,
% 231.55/231.83 (![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[205, 201])).
% 231.55/231.83 tff(207,plain,(
% 231.55/231.83 ![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 231.55/231.83 inference(skolemize,[status(sab)],[206])).
% 231.55/231.83 tff(208,plain,
% 231.55/231.83 (![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[207, 200])).
% 231.55/231.83 tff(209,plain,
% 231.55/231.83 (![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[208, 198])).
% 231.55/231.83 tff(210,plain,
% 231.55/231.83 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(muslimcountrybhumanitarianorganization, atheist, n75) | (~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~less(n75, n78)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | accept_population(muslimcountrybhumanitarianorganization, atheist, n75) | (~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~less(n75, n78)))),
% 231.55/231.83 inference(rewrite,[status(thm)],[])).
% 231.55/231.83 tff(211,plain,
% 231.55/231.83 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(muslimcountrybhumanitarianorganization, atheist, n75) | (~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~less(n75, n78)))),
% 231.55/231.83 inference(quant_inst,[status(thm)],[])).
% 231.55/231.83 tff(212,plain,
% 231.55/231.83 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | accept_population(muslimcountrybhumanitarianorganization, atheist, n75) | (~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~less(n75, n78))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[211, 210])).
% 231.55/231.83 tff(213,plain,
% 231.55/231.83 (~less(n75, n78)),
% 231.55/231.83 inference(unit_resolution,[status(thm)],[212, 209, 196, 43])).
% 231.55/231.83 tff(214,assumption,(~rdn_positive_less(rdnn(n6), rdnn(n8))), introduced(assumption)).
% 231.55/231.83 tff(215,plain,
% 231.55/231.83 (^[X: $i, Y: $i, Z: $i] : refl((rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z)))) <=> (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z)))))),
% 231.55/231.83 inference(bind,[status(th)],[])).
% 231.55/231.83 tff(216,plain,
% 231.55/231.83 (![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z)))) <=> ![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))),
% 231.55/231.83 inference(quant_intro,[status(thm)],[215])).
% 231.55/231.83 tff(217,plain,
% 231.55/231.83 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z))) <=> (~((~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z)))))), ((~(rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z)))) <=> (~(~((~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z)))))))), rewrite((~(~((~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z)))))) <=> ((~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))), ((~(rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z)))) <=> ((~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z)))))), (((~(rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z)))) | rdn_positive_less(rdnn(X), rdnn(Z))) <=> (((~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z)))) | rdn_positive_less(rdnn(X), rdnn(Z))))), rewrite((((~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z)))) | rdn_positive_less(rdnn(X), rdnn(Z))) <=> (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))), (((~(rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z)))) | rdn_positive_less(rdnn(X), rdnn(Z))) <=> (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))))),
% 231.55/231.83 inference(bind,[status(th)],[])).
% 231.55/231.83 tff(218,plain,
% 231.55/231.83 (![X: $i, Y: $i, Z: $i] : ((~(rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z)))) | rdn_positive_less(rdnn(X), rdnn(Z))) <=> ![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))),
% 231.55/231.83 inference(quant_intro,[status(thm)],[217])).
% 231.55/231.83 tff(219,plain,
% 231.55/231.83 (![X: $i, Y: $i, Z: $i] : ((~(rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z)))) | rdn_positive_less(rdnn(X), rdnn(Z))) <=> ![X: $i, Y: $i, Z: $i] : ((~(rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z)))) | rdn_positive_less(rdnn(X), rdnn(Z)))),
% 231.55/231.83 inference(rewrite,[status(thm)],[])).
% 231.55/231.83 tff(220,plain,
% 231.55/231.83 (^[X: $i, Y: $i, Z: $i] : rewrite(((rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z))) => rdn_positive_less(rdnn(X), rdnn(Z))) <=> ((~(rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z)))) | rdn_positive_less(rdnn(X), rdnn(Z))))),
% 231.55/231.83 inference(bind,[status(th)],[])).
% 231.55/231.83 tff(221,plain,
% 231.55/231.83 (![X: $i, Y: $i, Z: $i] : ((rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z))) => rdn_positive_less(rdnn(X), rdnn(Z))) <=> ![X: $i, Y: $i, Z: $i] : ((~(rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z)))) | rdn_positive_less(rdnn(X), rdnn(Z)))),
% 231.55/231.83 inference(quant_intro,[status(thm)],[220])).
% 231.55/231.83 tff(222,axiom,(![X: $i, Y: $i, Z: $i] : ((rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z))) => rdn_positive_less(rdnn(X), rdnn(Z)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less_transitivity')).
% 231.55/231.83 tff(223,plain,
% 231.55/231.83 (![X: $i, Y: $i, Z: $i] : ((~(rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z)))) | rdn_positive_less(rdnn(X), rdnn(Z)))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[222, 221])).
% 231.55/231.83 tff(224,plain,
% 231.55/231.83 (![X: $i, Y: $i, Z: $i] : ((~(rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z)))) | rdn_positive_less(rdnn(X), rdnn(Z)))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[223, 219])).
% 231.55/231.83 tff(225,plain,(
% 231.55/231.83 ![X: $i, Y: $i, Z: $i] : ((~(rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z)))) | rdn_positive_less(rdnn(X), rdnn(Z)))),
% 231.55/231.83 inference(skolemize,[status(sab)],[224])).
% 231.55/231.83 tff(226,plain,
% 231.55/231.83 (![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[225, 218])).
% 231.55/231.83 tff(227,plain,
% 231.55/231.83 (![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[226, 216])).
% 231.55/231.83 tff(228,plain,
% 231.55/231.83 (rdn_positive_less(rdnn(n7), rdnn(n8)) <=> rdn_positive_less(rdnn(n7), rdnn(n8))),
% 231.55/231.83 inference(rewrite,[status(thm)],[])).
% 231.55/231.83 tff(229,axiom,(rdn_positive_less(rdnn(n7), rdnn(n8))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less78')).
% 231.55/231.83 tff(230,plain,
% 231.55/231.83 (rdn_positive_less(rdnn(n7), rdnn(n8))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[229, 228])).
% 231.55/231.83 tff(231,plain,
% 231.55/231.83 (rdn_positive_less(rdnn(n6), rdnn(n7)) <=> rdn_positive_less(rdnn(n6), rdnn(n7))),
% 231.55/231.83 inference(rewrite,[status(thm)],[])).
% 231.55/231.83 tff(232,axiom,(rdn_positive_less(rdnn(n6), rdnn(n7))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less67')).
% 231.55/231.83 tff(233,plain,
% 231.55/231.83 (rdn_positive_less(rdnn(n6), rdnn(n7))),
% 231.55/231.83 inference(modus_ponens,[status(thm)],[232, 231])).
% 231.55/231.83 tff(234,plain,
% 231.55/231.83 (((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | ((~rdn_positive_less(rdnn(n6), rdnn(n7))) | rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))) <=> ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n6), rdnn(n7))) | rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))),
% 231.55/231.83 inference(rewrite,[status(thm)],[])).
% 231.55/231.83 tff(235,plain,
% 231.55/231.83 ((rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n7))) | (~rdn_positive_less(rdnn(n7), rdnn(n8)))) <=> ((~rdn_positive_less(rdnn(n6), rdnn(n7))) | rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))),
% 231.55/231.83 inference(rewrite,[status(thm)],[])).
% 231.55/231.83 tff(236,plain,
% 231.55/231.83 (((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n7))) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))) <=> ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | ((~rdn_positive_less(rdnn(n6), rdnn(n7))) | rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8)))))),
% 231.55/231.83 inference(monotonicity,[status(thm)],[235])).
% 231.55/231.83 tff(237,plain,
% 231.55/231.83 (((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n7))) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))) <=> ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n6), rdnn(n7))) | rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))),
% 231.55/231.84 inference(transitivity,[status(thm)],[236, 234])).
% 231.55/231.84 tff(238,plain,
% 231.55/231.84 ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n7))) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))),
% 231.55/231.84 inference(quant_inst,[status(thm)],[])).
% 231.55/231.84 tff(239,plain,
% 231.55/231.84 ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n6), rdnn(n7))) | rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8)))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[238, 237])).
% 231.55/231.84 tff(240,plain,
% 231.55/231.84 ($false),
% 231.55/231.84 inference(unit_resolution,[status(thm)],[239, 233, 230, 227, 214])).
% 231.55/231.84 tff(241,plain,(rdn_positive_less(rdnn(n6), rdnn(n8))), inference(lemma,lemma(discharge,[]))).
% 231.55/231.84 tff(242,assumption,(~rdn_positive_less(rdnn(n5), rdnn(n8))), introduced(assumption)).
% 231.55/231.84 tff(243,plain,
% 231.55/231.84 (rdn_positive_less(rdnn(n5), rdnn(n6)) <=> rdn_positive_less(rdnn(n5), rdnn(n6))),
% 231.55/231.84 inference(rewrite,[status(thm)],[])).
% 231.55/231.84 tff(244,axiom,(rdn_positive_less(rdnn(n5), rdnn(n6))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less56')).
% 231.55/231.84 tff(245,plain,
% 231.55/231.84 (rdn_positive_less(rdnn(n5), rdnn(n6))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[244, 243])).
% 231.55/231.84 tff(246,plain,
% 231.55/231.84 (((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | ((~rdn_positive_less(rdnn(n5), rdnn(n6))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n8))))) <=> ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n8))))),
% 231.55/231.84 inference(rewrite,[status(thm)],[])).
% 231.55/231.84 tff(247,plain,
% 231.55/231.84 ((rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | (~rdn_positive_less(rdnn(n6), rdnn(n8)))) <=> ((~rdn_positive_less(rdnn(n5), rdnn(n6))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n8))))),
% 231.55/231.84 inference(rewrite,[status(thm)],[])).
% 231.55/231.84 tff(248,plain,
% 231.55/231.84 (((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | (~rdn_positive_less(rdnn(n6), rdnn(n8))))) <=> ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | ((~rdn_positive_less(rdnn(n5), rdnn(n6))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n8)))))),
% 231.55/231.84 inference(monotonicity,[status(thm)],[247])).
% 231.55/231.84 tff(249,plain,
% 231.55/231.84 (((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | (~rdn_positive_less(rdnn(n6), rdnn(n8))))) <=> ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n8))))),
% 231.55/231.84 inference(transitivity,[status(thm)],[248, 246])).
% 231.55/231.84 tff(250,plain,
% 231.55/231.84 ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | (~rdn_positive_less(rdnn(n6), rdnn(n8))))),
% 231.55/231.84 inference(quant_inst,[status(thm)],[])).
% 231.55/231.84 tff(251,plain,
% 231.55/231.84 ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n8)))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[250, 249])).
% 231.55/231.84 tff(252,plain,
% 231.55/231.84 ($false),
% 231.55/231.84 inference(unit_resolution,[status(thm)],[251, 245, 227, 242, 241])).
% 231.55/231.84 tff(253,plain,(rdn_positive_less(rdnn(n5), rdnn(n8))), inference(lemma,lemma(discharge,[]))).
% 231.55/231.84 tff(254,plain,
% 231.55/231.84 (^[X: $i] : refl((rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X)))) <=> (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X)))))),
% 231.55/231.84 inference(bind,[status(th)],[])).
% 231.55/231.84 tff(255,plain,
% 231.55/231.84 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X)))) <=> ![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 231.55/231.84 inference(quant_intro,[status(thm)],[254])).
% 231.55/231.84 tff(256,plain,
% 231.55/231.84 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X)))) <=> ![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 231.55/231.84 inference(rewrite,[status(thm)],[])).
% 231.55/231.84 tff(257,plain,
% 231.55/231.84 (^[X: $i] : rewrite((rdn_non_zero_digit(rdnn(X)) => rdn_non_zero(rdnn(X))) <=> (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X)))))),
% 231.55/231.84 inference(bind,[status(th)],[])).
% 231.55/231.84 tff(258,plain,
% 231.55/231.84 (![X: $i] : (rdn_non_zero_digit(rdnn(X)) => rdn_non_zero(rdnn(X))) <=> ![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 231.55/231.84 inference(quant_intro,[status(thm)],[257])).
% 231.55/231.84 tff(259,axiom,(![X: $i] : (rdn_non_zero_digit(rdnn(X)) => rdn_non_zero(rdnn(X)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_non_zero_by_digit')).
% 231.55/231.84 tff(260,plain,
% 231.55/231.84 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[259, 258])).
% 231.55/231.84 tff(261,plain,
% 231.55/231.84 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[260, 256])).
% 231.55/231.84 tff(262,plain,(
% 231.55/231.84 ![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 231.55/231.84 inference(skolemize,[status(sab)],[261])).
% 231.55/231.84 tff(263,plain,
% 231.55/231.84 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[262, 255])).
% 231.55/231.84 tff(264,plain,
% 231.55/231.84 (rdn_non_zero_digit(rdnn(n7)) <=> rdn_non_zero_digit(rdnn(n7))),
% 231.55/231.84 inference(rewrite,[status(thm)],[])).
% 231.55/231.84 tff(265,axiom,(rdn_non_zero_digit(rdnn(n7))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_digit7')).
% 231.55/231.84 tff(266,plain,
% 231.55/231.84 (rdn_non_zero_digit(rdnn(n7))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[265, 264])).
% 231.55/231.84 tff(267,plain,
% 231.55/231.84 (((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | (rdn_non_zero(rdnn(n7)) | (~rdn_non_zero_digit(rdnn(n7))))) <=> ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | rdn_non_zero(rdnn(n7)) | (~rdn_non_zero_digit(rdnn(n7))))),
% 231.55/231.84 inference(rewrite,[status(thm)],[])).
% 231.55/231.84 tff(268,plain,
% 231.55/231.84 ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | (rdn_non_zero(rdnn(n7)) | (~rdn_non_zero_digit(rdnn(n7))))),
% 231.55/231.84 inference(quant_inst,[status(thm)],[])).
% 231.55/231.84 tff(269,plain,
% 231.55/231.84 ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | rdn_non_zero(rdnn(n7)) | (~rdn_non_zero_digit(rdnn(n7)))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[268, 267])).
% 231.55/231.84 tff(270,plain,
% 231.55/231.84 (rdn_non_zero(rdnn(n7))),
% 231.55/231.84 inference(unit_resolution,[status(thm)],[269, 266, 263])).
% 231.55/231.84 tff(271,plain,
% 231.55/231.84 (^[Ds: $i, O: $i, Db: $i] : refl((rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))) <=> (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))))),
% 231.55/231.84 inference(bind,[status(th)],[])).
% 231.55/231.84 tff(272,plain,
% 231.55/231.84 (![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))) <=> ![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))),
% 231.55/231.84 inference(quant_intro,[status(thm)],[271])).
% 231.55/231.84 tff(273,plain,
% 231.55/231.84 (^[Ds: $i, O: $i, Db: $i] : trans(monotonicity(trans(monotonicity(rewrite((rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O)) <=> (~((~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))))), ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) <=> (~(~((~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))))))), rewrite((~(~((~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))))) <=> ((~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))), ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) <=> ((~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))))), (((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))) <=> (((~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))))), rewrite((((~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))) <=> (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))), (((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))) <=> (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))))),
% 231.55/231.84 inference(bind,[status(th)],[])).
% 231.55/231.84 tff(274,plain,
% 231.55/231.84 (![Ds: $i, O: $i, Db: $i] : ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))) <=> ![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))),
% 231.55/231.84 inference(quant_intro,[status(thm)],[273])).
% 231.55/231.84 tff(275,plain,
% 231.55/231.84 (![Ds: $i, O: $i, Db: $i] : ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))) <=> ![Ds: $i, O: $i, Db: $i] : ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)))),
% 231.55/231.84 inference(rewrite,[status(thm)],[])).
% 231.55/231.84 tff(276,plain,
% 231.55/231.84 (^[Ds: $i, O: $i, Db: $i] : rewrite(((rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O)) => rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))) <=> ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))))),
% 231.55/231.84 inference(bind,[status(th)],[])).
% 231.55/231.84 tff(277,plain,
% 231.55/231.84 (![Ds: $i, O: $i, Db: $i] : ((rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O)) => rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))) <=> ![Ds: $i, O: $i, Db: $i] : ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)))),
% 231.55/231.84 inference(quant_intro,[status(thm)],[276])).
% 231.55/231.84 tff(278,axiom,(![Ds: $i, O: $i, Db: $i] : ((rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O)) => rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less_multi_digit_low')).
% 231.55/231.84 tff(279,plain,
% 231.55/231.84 (![Ds: $i, O: $i, Db: $i] : ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[278, 277])).
% 231.55/231.84 tff(280,plain,
% 231.55/231.84 (![Ds: $i, O: $i, Db: $i] : ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[279, 275])).
% 231.55/231.84 tff(281,plain,(
% 231.55/231.84 ![Ds: $i, O: $i, Db: $i] : ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)))),
% 231.55/231.84 inference(skolemize,[status(sab)],[280])).
% 231.55/231.84 tff(282,plain,
% 231.55/231.84 (![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[281, 274])).
% 231.55/231.84 tff(283,plain,
% 231.55/231.84 (![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[282, 272])).
% 231.55/231.84 tff(284,plain,
% 231.55/231.84 (((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | ((~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))))) <=> ((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))))),
% 231.55/231.84 inference(rewrite,[status(thm)],[])).
% 231.55/231.84 tff(285,plain,
% 231.55/231.84 ((rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))) | (~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7)))) <=> ((~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))))),
% 231.55/231.84 inference(rewrite,[status(thm)],[])).
% 231.55/231.84 tff(286,plain,
% 231.55/231.84 (((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))) | (~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))))) <=> ((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | ((~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))))),
% 231.55/231.84 inference(monotonicity,[status(thm)],[285])).
% 231.55/231.84 tff(287,plain,
% 231.55/231.84 (((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))) | (~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))))) <=> ((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))))),
% 231.55/231.84 inference(transitivity,[status(thm)],[286, 284])).
% 231.55/231.84 tff(288,plain,
% 231.55/231.84 ((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))) | (~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))))),
% 231.55/231.84 inference(quant_inst,[status(thm)],[])).
% 231.55/231.84 tff(289,plain,
% 231.55/231.84 ((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[288, 287])).
% 231.55/231.84 tff(290,plain,
% 231.55/231.84 ((~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))),
% 231.55/231.84 inference(unit_resolution,[status(thm)],[289, 283])).
% 231.55/231.84 tff(291,plain,
% 231.55/231.84 ((~rdn_positive_less(rdnn(n5), rdnn(n8))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))),
% 231.55/231.84 inference(unit_resolution,[status(thm)],[290, 270])).
% 231.55/231.84 tff(292,plain,
% 231.55/231.84 (rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))),
% 231.55/231.84 inference(unit_resolution,[status(thm)],[291, 253])).
% 231.55/231.84 tff(293,plain,
% 231.55/231.84 (^[X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : refl((less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y))) <=> (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y))))),
% 231.55/231.84 inference(bind,[status(th)],[])).
% 231.55/231.84 tff(294,plain,
% 231.55/231.84 (![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y))) <=> ![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))),
% 231.55/231.84 inference(quant_intro,[status(thm)],[293])).
% 231.55/231.84 tff(295,plain,
% 231.55/231.84 (^[X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y)) <=> (~((~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y))))), ((~(rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y))) <=> (~(~((~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y))))))), rewrite((~(~((~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y))))) <=> ((~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))), ((~(rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y))) <=> ((~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y))))), (((~(rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y))) | less(X, Y)) <=> (((~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y))) | less(X, Y)))), rewrite((((~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y))) | less(X, Y)) <=> (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))), (((~(rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y))) | less(X, Y)) <=> (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))))),
% 231.55/231.84 inference(bind,[status(th)],[])).
% 231.55/231.84 tff(296,plain,
% 231.55/231.84 (![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : ((~(rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y))) | less(X, Y)) <=> ![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))),
% 231.55/231.84 inference(quant_intro,[status(thm)],[295])).
% 231.55/231.84 tff(297,plain,
% 231.55/231.84 (![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : ((~(rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y))) | less(X, Y)) <=> ![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : ((~(rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y))) | less(X, Y))),
% 231.55/231.84 inference(rewrite,[status(thm)],[])).
% 231.55/231.84 tff(298,plain,
% 231.55/231.84 (^[X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : trans(monotonicity(rewrite(((rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y))) & rdn_positive_less(RDN_X, RDN_Y)) <=> (rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y))), ((((rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y))) & rdn_positive_less(RDN_X, RDN_Y)) => less(X, Y)) <=> ((rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y)) => less(X, Y)))), rewrite(((rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y)) => less(X, Y)) <=> ((~(rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y))) | less(X, Y))), ((((rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y))) & rdn_positive_less(RDN_X, RDN_Y)) => less(X, Y)) <=> ((~(rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y))) | less(X, Y))))),
% 231.55/231.84 inference(bind,[status(th)],[])).
% 231.55/231.84 tff(299,plain,
% 231.55/231.84 (![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (((rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y))) & rdn_positive_less(RDN_X, RDN_Y)) => less(X, Y)) <=> ![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : ((~(rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y))) | less(X, Y))),
% 231.55/231.84 inference(quant_intro,[status(thm)],[298])).
% 231.55/231.84 tff(300,axiom,(![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (((rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y))) & rdn_positive_less(RDN_X, RDN_Y)) => less(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','less_entry_point_pos_pos')).
% 231.55/231.84 tff(301,plain,
% 231.55/231.84 (![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : ((~(rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y))) | less(X, Y))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[300, 299])).
% 231.55/231.84 tff(302,plain,
% 231.55/231.84 (![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : ((~(rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y))) | less(X, Y))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[301, 297])).
% 231.55/231.84 tff(303,plain,(
% 231.55/231.84 ![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : ((~(rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X, RDN_Y))) | less(X, Y))),
% 231.55/231.84 inference(skolemize,[status(sab)],[302])).
% 231.55/231.84 tff(304,plain,
% 231.55/231.84 (![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[303, 296])).
% 231.55/231.84 tff(305,plain,
% 231.55/231.84 (![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[304, 294])).
% 231.55/231.84 tff(306,plain,
% 231.55/231.84 (rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7)))) <=> rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))),
% 231.55/231.84 inference(rewrite,[status(thm)],[])).
% 231.55/231.84 tff(307,axiom,(rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax','rdn78')).
% 231.55/231.84 tff(308,plain,
% 231.55/231.84 (rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[307, 306])).
% 231.55/231.84 tff(309,plain,
% 231.55/231.84 (rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7)))) <=> rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))),
% 231.55/231.84 inference(rewrite,[status(thm)],[])).
% 231.55/231.84 tff(310,axiom,(rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax','rdn75')).
% 231.55/231.84 tff(311,plain,
% 231.55/231.84 (rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))),
% 231.55/231.84 inference(modus_ponens,[status(thm)],[310, 309])).
% 231.55/231.84 tff(312,plain,
% 231.55/231.84 (((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | ((~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n75, n78))) <=> ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n75, n78))),
% 231.55/231.84 inference(rewrite,[status(thm)],[])).
% 231.55/231.84 tff(313,plain,
% 231.55/231.84 ((less(n75, n78) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))))) <=> ((~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n75, n78))),
% 231.55/231.84 inference(rewrite,[status(thm)],[])).
% 231.55/231.84 tff(314,plain,
% 231.55/231.84 (((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (less(n75, n78) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))))) <=> ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | ((~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n75, n78)))),
% 231.67/231.93 inference(monotonicity,[status(thm)],[313])).
% 231.67/231.93 tff(315,plain,
% 231.67/231.93 (((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (less(n75, n78) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))))) <=> ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n75, n78))),
% 231.67/231.93 inference(transitivity,[status(thm)],[314, 312])).
% 231.67/231.93 tff(316,plain,
% 231.67/231.93 ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (less(n75, n78) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))))),
% 231.67/231.93 inference(quant_inst,[status(thm)],[])).
% 231.67/231.93 tff(317,plain,
% 231.67/231.93 ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n75, n78)),
% 231.67/231.93 inference(modus_ponens,[status(thm)],[316, 315])).
% 231.67/231.93 tff(318,plain,
% 231.67/231.93 ($false),
% 231.67/231.93 inference(unit_resolution,[status(thm)],[317, 311, 308, 305, 292, 213])).
% 231.67/231.93 % SZS output end Proof
% 231.67/231.93 % E exiting
%------------------------------------------------------------------------------