%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : AGT010+2 : TPTP v9.0.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 04:57:39 AM UTC 2025
% Result : Theorem 52.28s 52.44s
% Output : Proof 52.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : AGT010+2 : TPTP v9.0.0. Bugfixed v3.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 10:44:31 EDT 2025
% 0.12/0.34 % CPUTime :
% 52.28/52.44 % SZS status Theorem
% 52.28/52.44 % SZS output start Proof
% 52.28/52.44 tff(less_type, type, (
% 52.28/52.44 less: ( $i * $i ) > $o)).
% 52.28/52.44 tff(n65_type, type, (
% 52.28/52.44 n65: $i)).
% 52.28/52.44 tff(n0_type, type, (
% 52.28/52.44 n0: $i)).
% 52.28/52.44 tff(accept_population_type, type, (
% 52.28/52.44 accept_population: ( $i * $i * $i ) > $o)).
% 52.28/52.44 tff(muslim_type, type, (
% 52.28/52.44 muslim: $i)).
% 52.28/52.44 tff(countryamedicalorganization_type, type, (
% 52.28/52.44 countryamedicalorganization: $i)).
% 52.28/52.44 tff(n3_type, type, (
% 52.28/52.44 n3: $i)).
% 52.28/52.44 tff(christian_type, type, (
% 52.28/52.44 christian: $i)).
% 52.28/52.44 tff(n20_type, type, (
% 52.28/52.44 n20: $i)).
% 52.28/52.44 tff(rdn_positive_less_type, type, (
% 52.28/52.44 rdn_positive_less: ( $i * $i ) > $o)).
% 52.28/52.44 tff(rdn_type, type, (
% 52.28/52.44 rdn: ( $i * $i ) > $i)).
% 52.28/52.44 tff(rdnn_type, type, (
% 52.28/52.44 rdnn: $i > $i)).
% 52.28/52.44 tff(n2_type, type, (
% 52.28/52.44 n2: $i)).
% 52.28/52.44 tff(rdn_non_zero_type, type, (
% 52.28/52.44 rdn_non_zero: $i > $o)).
% 52.28/52.44 tff(rdn_non_zero_digit_type, type, (
% 52.28/52.44 rdn_non_zero_digit: $i > $o)).
% 52.28/52.44 tff(rdn_translate_type, type, (
% 52.28/52.44 rdn_translate: ( $i * $i ) > $o)).
% 52.28/52.44 tff(rdn_pos_type, type, (
% 52.28/52.44 rdn_pos: $i > $i)).
% 52.28/52.44 tff(n12_type, type, (
% 52.28/52.44 n12: $i)).
% 52.28/52.44 tff(atheist_type, type, (
% 52.28/52.44 atheist: $i)).
% 52.28/52.44 tff(n78_type, type, (
% 52.28/52.44 n78: $i)).
% 52.28/52.44 tff(n7_type, type, (
% 52.28/52.44 n7: $i)).
% 52.28/52.44 tff(n8_type, type, (
% 52.28/52.44 n8: $i)).
% 52.28/52.44 tff(n1_type, type, (
% 52.28/52.44 n1: $i)).
% 52.28/52.44 tff(n5_type, type, (
% 52.28/52.44 n5: $i)).
% 52.28/52.44 tff(n6_type, type, (
% 52.28/52.44 n6: $i)).
% 52.28/52.44 tff(n4_type, type, (
% 52.28/52.44 n4: $i)).
% 52.28/52.44 tff(other_type, type, (
% 52.28/52.44 other: $i)).
% 52.28/52.44 tff(n85_type, type, (
% 52.28/52.44 n85: $i)).
% 52.28/52.44 tff(native_type, type, (
% 52.28/52.44 native: $i)).
% 52.28/52.44 tff(accept_city_type, type, (
% 52.28/52.44 accept_city: ( $i * $i ) > $o)).
% 52.28/52.44 tff(coastvillage_type, type, (
% 52.28/52.44 coastvillage: $i)).
% 52.28/52.44 tff(1,plain,
% 52.28/52.44 (^[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)))))),
% 52.28/52.44 inference(bind,[status(th)],[])).
% 52.28/52.44 tff(2,plain,
% 52.28/52.44 (![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))))),
% 52.28/52.44 inference(quant_intro,[status(thm)],[1])).
% 52.28/52.44 tff(3,plain,
% 52.28/52.44 (![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))))),
% 52.28/52.44 inference(rewrite,[status(thm)],[])).
% 52.28/52.44 tff(4,plain,
% 52.28/52.44 (^[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)))))),
% 52.28/52.44 inference(bind,[status(th)],[])).
% 52.28/52.44 tff(5,plain,
% 52.28/52.44 (![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))))),
% 52.28/52.44 inference(quant_intro,[status(thm)],[4])).
% 52.28/52.44 tff(6,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')).
% 52.28/52.44 tff(7,plain,
% 52.28/52.44 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[6, 5])).
% 52.28/52.44 tff(8,plain,
% 52.28/52.44 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 52.28/52.44 tff(9,plain,(
% 52.28/52.44 ![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 52.28/52.44 inference(skolemize,[status(sab)],[8])).
% 52.28/52.44 tff(10,plain,
% 52.28/52.44 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[9, 2])).
% 52.28/52.44 tff(11,plain,
% 52.28/52.44 (rdn_non_zero_digit(rdnn(n2)) <=> rdn_non_zero_digit(rdnn(n2))),
% 52.28/52.44 inference(rewrite,[status(thm)],[])).
% 52.28/52.44 tff(12,axiom,(rdn_non_zero_digit(rdnn(n2))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_digit2')).
% 52.28/52.44 tff(13,plain,
% 52.28/52.44 (rdn_non_zero_digit(rdnn(n2))),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[12, 11])).
% 52.28/52.44 tff(14,plain,
% 52.28/52.44 (((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | (rdn_non_zero(rdnn(n2)) | (~rdn_non_zero_digit(rdnn(n2))))) <=> ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | rdn_non_zero(rdnn(n2)) | (~rdn_non_zero_digit(rdnn(n2))))),
% 52.28/52.44 inference(rewrite,[status(thm)],[])).
% 52.28/52.44 tff(15,plain,
% 52.28/52.44 ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | (rdn_non_zero(rdnn(n2)) | (~rdn_non_zero_digit(rdnn(n2))))),
% 52.28/52.44 inference(quant_inst,[status(thm)],[])).
% 52.28/52.44 tff(16,plain,
% 52.28/52.44 ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | rdn_non_zero(rdnn(n2)) | (~rdn_non_zero_digit(rdnn(n2)))),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[15, 14])).
% 52.28/52.44 tff(17,plain,
% 52.28/52.44 (rdn_non_zero(rdnn(n2))),
% 52.28/52.44 inference(unit_resolution,[status(thm)],[16, 13, 10])).
% 52.28/52.44 tff(18,plain,
% 52.28/52.44 (^[D: $i, Db: $i, Ob: $i] : refl(((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob))) <=> ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob))))),
% 52.28/52.44 inference(bind,[status(th)],[])).
% 52.28/52.44 tff(19,plain,
% 52.28/52.44 (![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob))) <=> ![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))),
% 52.28/52.44 inference(quant_intro,[status(thm)],[18])).
% 52.28/52.44 tff(20,plain,
% 52.28/52.44 (![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob))) <=> ![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))),
% 52.28/52.44 inference(rewrite,[status(thm)],[])).
% 52.28/52.44 tff(21,plain,
% 52.28/52.44 (^[D: $i, Db: $i, Ob: $i] : rewrite((rdn_non_zero(Ob) => rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob))) <=> ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob))))),
% 52.28/52.44 inference(bind,[status(th)],[])).
% 52.28/52.44 tff(22,plain,
% 52.28/52.44 (![D: $i, Db: $i, Ob: $i] : (rdn_non_zero(Ob) => rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob))) <=> ![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))),
% 52.28/52.44 inference(quant_intro,[status(thm)],[21])).
% 52.28/52.44 tff(23,axiom,(![D: $i, Db: $i, Ob: $i] : (rdn_non_zero(Ob) => rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_extra_digits_positive_less')).
% 52.28/52.44 tff(24,plain,
% 52.28/52.44 (![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 52.28/52.44 tff(25,plain,
% 52.28/52.44 (![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[24, 20])).
% 52.28/52.44 tff(26,plain,(
% 52.28/52.44 ![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))),
% 52.28/52.44 inference(skolemize,[status(sab)],[25])).
% 52.28/52.44 tff(27,plain,
% 52.28/52.44 (![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[26, 19])).
% 52.28/52.44 tff(28,plain,
% 52.28/52.44 (((~![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))) | ((~rdn_non_zero(rdnn(n2))) | rdn_positive_less(rdnn(n3), rdn(rdnn(n0), rdnn(n2))))) <=> ((~![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))) | (~rdn_non_zero(rdnn(n2))) | rdn_positive_less(rdnn(n3), rdn(rdnn(n0), rdnn(n2))))),
% 52.28/52.44 inference(rewrite,[status(thm)],[])).
% 52.28/52.44 tff(29,plain,
% 52.28/52.44 ((~![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))) | ((~rdn_non_zero(rdnn(n2))) | rdn_positive_less(rdnn(n3), rdn(rdnn(n0), rdnn(n2))))),
% 52.28/52.44 inference(quant_inst,[status(thm)],[])).
% 52.28/52.44 tff(30,plain,
% 52.28/52.44 ((~![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))) | (~rdn_non_zero(rdnn(n2))) | rdn_positive_less(rdnn(n3), rdn(rdnn(n0), rdnn(n2)))),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[29, 28])).
% 52.28/52.44 tff(31,plain,
% 52.28/52.44 (rdn_positive_less(rdnn(n3), rdn(rdnn(n0), rdnn(n2)))),
% 52.28/52.44 inference(unit_resolution,[status(thm)],[30, 27, 17])).
% 52.28/52.44 tff(32,plain,
% 52.28/52.44 (^[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))))),
% 52.28/52.44 inference(bind,[status(th)],[])).
% 52.28/52.44 tff(33,plain,
% 52.28/52.44 (![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)))),
% 52.28/52.44 inference(quant_intro,[status(thm)],[32])).
% 52.28/52.44 tff(34,plain,
% 52.28/52.44 (^[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)))))),
% 52.28/52.44 inference(bind,[status(th)],[])).
% 52.28/52.44 tff(35,plain,
% 52.28/52.44 (![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)))),
% 52.28/52.44 inference(quant_intro,[status(thm)],[34])).
% 52.28/52.44 tff(36,plain,
% 52.28/52.44 (![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))),
% 52.28/52.44 inference(rewrite,[status(thm)],[])).
% 52.28/52.44 tff(37,plain,
% 52.28/52.44 (^[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))))),
% 52.28/52.44 inference(bind,[status(th)],[])).
% 52.28/52.44 tff(38,plain,
% 52.28/52.44 (![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))),
% 52.28/52.44 inference(quant_intro,[status(thm)],[37])).
% 52.28/52.44 tff(39,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')).
% 52.28/52.44 tff(40,plain,
% 52.28/52.44 (![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))),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[39, 38])).
% 52.28/52.44 tff(41,plain,
% 52.28/52.44 (![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))),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[40, 36])).
% 52.28/52.44 tff(42,plain,(
% 52.28/52.44 ![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))),
% 52.28/52.44 inference(skolemize,[status(sab)],[41])).
% 52.28/52.44 tff(43,plain,
% 52.28/52.44 (![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)))),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[42, 35])).
% 52.28/52.44 tff(44,plain,
% 52.28/52.44 (![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)))),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[43, 33])).
% 52.28/52.44 tff(45,plain,
% 52.28/52.44 (rdn_translate(n20, rdn_pos(rdn(rdnn(n0), rdnn(n2)))) <=> rdn_translate(n20, rdn_pos(rdn(rdnn(n0), rdnn(n2))))),
% 52.28/52.44 inference(rewrite,[status(thm)],[])).
% 52.28/52.44 tff(46,axiom,(rdn_translate(n20, rdn_pos(rdn(rdnn(n0), rdnn(n2))))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax','rdn20')).
% 52.28/52.44 tff(47,plain,
% 52.28/52.44 (rdn_translate(n20, rdn_pos(rdn(rdnn(n0), rdnn(n2))))),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[46, 45])).
% 52.28/52.44 tff(48,plain,
% 52.28/52.44 (rdn_translate(n3, rdn_pos(rdnn(n3))) <=> rdn_translate(n3, rdn_pos(rdnn(n3)))),
% 52.28/52.44 inference(rewrite,[status(thm)],[])).
% 52.28/52.44 tff(49,axiom,(rdn_translate(n3, rdn_pos(rdnn(n3)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax','rdn3')).
% 52.28/52.44 tff(50,plain,
% 52.28/52.44 (rdn_translate(n3, rdn_pos(rdnn(n3)))),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[49, 48])).
% 52.28/52.44 tff(51,plain,
% 52.28/52.44 (((~![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(rdnn(n3), rdn(rdnn(n0), rdnn(n2)))) | (~rdn_translate(n3, rdn_pos(rdnn(n3)))) | less(n3, n20) | (~rdn_translate(n20, rdn_pos(rdn(rdnn(n0), rdnn(n2))))))) <=> ((~![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(rdnn(n3), rdn(rdnn(n0), rdnn(n2)))) | (~rdn_translate(n3, rdn_pos(rdnn(n3)))) | less(n3, n20) | (~rdn_translate(n20, rdn_pos(rdn(rdnn(n0), rdnn(n2))))))),
% 52.28/52.44 inference(rewrite,[status(thm)],[])).
% 52.28/52.44 tff(52,plain,
% 52.28/52.44 ((less(n3, n20) | (~rdn_translate(n3, rdn_pos(rdnn(n3)))) | (~rdn_translate(n20, rdn_pos(rdn(rdnn(n0), rdnn(n2))))) | (~rdn_positive_less(rdnn(n3), rdn(rdnn(n0), rdnn(n2))))) <=> ((~rdn_positive_less(rdnn(n3), rdn(rdnn(n0), rdnn(n2)))) | (~rdn_translate(n3, rdn_pos(rdnn(n3)))) | less(n3, n20) | (~rdn_translate(n20, rdn_pos(rdn(rdnn(n0), rdnn(n2))))))),
% 52.28/52.44 inference(rewrite,[status(thm)],[])).
% 52.28/52.44 tff(53,plain,
% 52.28/52.44 (((~![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(n3, n20) | (~rdn_translate(n3, rdn_pos(rdnn(n3)))) | (~rdn_translate(n20, rdn_pos(rdn(rdnn(n0), rdnn(n2))))) | (~rdn_positive_less(rdnn(n3), rdn(rdnn(n0), rdnn(n2)))))) <=> ((~![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(rdnn(n3), rdn(rdnn(n0), rdnn(n2)))) | (~rdn_translate(n3, rdn_pos(rdnn(n3)))) | less(n3, n20) | (~rdn_translate(n20, rdn_pos(rdn(rdnn(n0), rdnn(n2)))))))),
% 52.28/52.44 inference(monotonicity,[status(thm)],[52])).
% 52.28/52.44 tff(54,plain,
% 52.28/52.44 (((~![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(n3, n20) | (~rdn_translate(n3, rdn_pos(rdnn(n3)))) | (~rdn_translate(n20, rdn_pos(rdn(rdnn(n0), rdnn(n2))))) | (~rdn_positive_less(rdnn(n3), rdn(rdnn(n0), rdnn(n2)))))) <=> ((~![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(rdnn(n3), rdn(rdnn(n0), rdnn(n2)))) | (~rdn_translate(n3, rdn_pos(rdnn(n3)))) | less(n3, n20) | (~rdn_translate(n20, rdn_pos(rdn(rdnn(n0), rdnn(n2))))))),
% 52.28/52.44 inference(transitivity,[status(thm)],[53, 51])).
% 52.28/52.44 tff(55,plain,
% 52.28/52.44 ((~![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(n3, n20) | (~rdn_translate(n3, rdn_pos(rdnn(n3)))) | (~rdn_translate(n20, rdn_pos(rdn(rdnn(n0), rdnn(n2))))) | (~rdn_positive_less(rdnn(n3), rdn(rdnn(n0), rdnn(n2)))))),
% 52.28/52.44 inference(quant_inst,[status(thm)],[])).
% 52.28/52.44 tff(56,plain,
% 52.28/52.44 ((~![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(rdnn(n3), rdn(rdnn(n0), rdnn(n2)))) | (~rdn_translate(n3, rdn_pos(rdnn(n3)))) | less(n3, n20) | (~rdn_translate(n20, rdn_pos(rdn(rdnn(n0), rdnn(n2)))))),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[55, 54])).
% 52.28/52.44 tff(57,plain,
% 52.28/52.44 (less(n3, n20)),
% 52.28/52.44 inference(unit_resolution,[status(thm)],[56, 50, 47, 44, 31])).
% 52.28/52.44 tff(58,assumption,(~accept_population(countryamedicalorganization, christian, n3)), introduced(assumption)).
% 52.28/52.44 tff(59,plain,
% 52.28/52.44 (accept_population(countryamedicalorganization, christian, n20) <=> accept_population(countryamedicalorganization, christian, n20)),
% 52.28/52.44 inference(rewrite,[status(thm)],[])).
% 52.28/52.44 tff(60,axiom,(accept_population(countryamedicalorganization, christian, n20)), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+2.ax','deduced_211')).
% 52.28/52.44 tff(61,plain,
% 52.28/52.44 (accept_population(countryamedicalorganization, christian, n20)),
% 52.28/52.44 inference(modus_ponens,[status(thm)],[60, 59])).
% 52.28/52.44 tff(62,plain,
% 52.28/52.44 (^[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))))),
% 52.28/52.44 inference(bind,[status(th)],[])).
% 52.28/52.44 tff(63,plain,
% 52.28/52.44 (![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)))),
% 52.28/52.44 inference(quant_intro,[status(thm)],[62])).
% 52.28/52.44 tff(64,plain,
% 52.28/52.44 (^[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)))))),
% 52.28/52.45 inference(bind,[status(th)],[])).
% 52.28/52.45 tff(65,plain,
% 52.28/52.45 (![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)))),
% 52.28/52.45 inference(quant_intro,[status(thm)],[64])).
% 52.28/52.45 tff(66,plain,
% 52.28/52.45 (![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))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(67,plain,
% 52.28/52.45 (^[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)))),
% 52.28/52.45 inference(bind,[status(th)],[])).
% 52.28/52.45 tff(68,plain,
% 52.28/52.45 (![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))),
% 52.28/52.45 inference(quant_intro,[status(thm)],[67])).
% 52.28/52.45 tff(69,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')).
% 52.28/52.45 tff(70,plain,
% 52.28/52.45 (![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[69, 68])).
% 52.28/52.45 tff(71,plain,
% 52.28/52.45 (![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[70, 66])).
% 52.28/52.45 tff(72,plain,(
% 52.28/52.45 ![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 52.28/52.45 inference(skolemize,[status(sab)],[71])).
% 52.28/52.45 tff(73,plain,
% 52.28/52.45 (![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[72, 65])).
% 52.28/52.45 tff(74,plain,
% 52.28/52.45 (![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[73, 63])).
% 52.28/52.45 tff(75,plain,
% 52.28/52.45 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | ((~accept_population(countryamedicalorganization, christian, n20)) | accept_population(countryamedicalorganization, christian, n3) | (~less(n3, n20)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (~accept_population(countryamedicalorganization, christian, n20)) | accept_population(countryamedicalorganization, christian, n3) | (~less(n3, n20)))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(76,plain,
% 52.28/52.45 ((accept_population(countryamedicalorganization, christian, n3) | (~accept_population(countryamedicalorganization, christian, n20)) | (~less(n3, n20))) <=> ((~accept_population(countryamedicalorganization, christian, n20)) | accept_population(countryamedicalorganization, christian, n3) | (~less(n3, n20)))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(77,plain,
% 52.28/52.45 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countryamedicalorganization, christian, n3) | (~accept_population(countryamedicalorganization, christian, n20)) | (~less(n3, n20)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | ((~accept_population(countryamedicalorganization, christian, n20)) | accept_population(countryamedicalorganization, christian, n3) | (~less(n3, n20))))),
% 52.28/52.45 inference(monotonicity,[status(thm)],[76])).
% 52.28/52.45 tff(78,plain,
% 52.28/52.45 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countryamedicalorganization, christian, n3) | (~accept_population(countryamedicalorganization, christian, n20)) | (~less(n3, n20)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (~accept_population(countryamedicalorganization, christian, n20)) | accept_population(countryamedicalorganization, christian, n3) | (~less(n3, n20)))),
% 52.28/52.45 inference(transitivity,[status(thm)],[77, 75])).
% 52.28/52.45 tff(79,plain,
% 52.28/52.45 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countryamedicalorganization, christian, n3) | (~accept_population(countryamedicalorganization, christian, n20)) | (~less(n3, n20)))),
% 52.28/52.45 inference(quant_inst,[status(thm)],[])).
% 52.28/52.45 tff(80,plain,
% 52.28/52.45 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (~accept_population(countryamedicalorganization, christian, n20)) | accept_population(countryamedicalorganization, christian, n3) | (~less(n3, n20))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[79, 78])).
% 52.28/52.45 tff(81,plain,
% 52.28/52.45 ($false),
% 52.28/52.45 inference(unit_resolution,[status(thm)],[80, 74, 61, 58, 57])).
% 52.28/52.45 tff(82,plain,(accept_population(countryamedicalorganization, christian, n3)), inference(lemma,lemma(discharge,[]))).
% 52.28/52.45 tff(83,assumption,(~less(n12, n78)), introduced(assumption)).
% 52.28/52.45 tff(84,assumption,(~rdn_positive_less(rdnn(n5), rdnn(n7))), introduced(assumption)).
% 52.28/52.45 tff(85,plain,
% 52.28/52.45 (^[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)))))),
% 52.28/52.45 inference(bind,[status(th)],[])).
% 52.28/52.45 tff(86,plain,
% 52.28/52.45 (![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))))),
% 52.28/52.45 inference(quant_intro,[status(thm)],[85])).
% 52.28/52.45 tff(87,plain,
% 52.28/52.45 (^[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))))))),
% 52.28/52.45 inference(bind,[status(th)],[])).
% 52.28/52.45 tff(88,plain,
% 52.28/52.45 (![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))))),
% 52.28/52.45 inference(quant_intro,[status(thm)],[87])).
% 52.28/52.45 tff(89,plain,
% 52.28/52.45 (![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)))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(90,plain,
% 52.28/52.45 (^[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))))),
% 52.28/52.45 inference(bind,[status(th)],[])).
% 52.28/52.45 tff(91,plain,
% 52.28/52.45 (![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)))),
% 52.28/52.45 inference(quant_intro,[status(thm)],[90])).
% 52.28/52.45 tff(92,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')).
% 52.28/52.45 tff(93,plain,
% 52.28/52.45 (![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)))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[92, 91])).
% 52.28/52.45 tff(94,plain,
% 52.28/52.45 (![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)))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[93, 89])).
% 52.28/52.45 tff(95,plain,(
% 52.28/52.45 ![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)))),
% 52.28/52.45 inference(skolemize,[status(sab)],[94])).
% 52.28/52.45 tff(96,plain,
% 52.28/52.45 (![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))))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[95, 88])).
% 52.28/52.45 tff(97,plain,
% 52.28/52.45 (![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))))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[96, 86])).
% 52.28/52.45 tff(98,plain,
% 52.28/52.45 (rdn_positive_less(rdnn(n6), rdnn(n7)) <=> rdn_positive_less(rdnn(n6), rdnn(n7))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(99,axiom,(rdn_positive_less(rdnn(n6), rdnn(n7))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less67')).
% 52.28/52.45 tff(100,plain,
% 52.28/52.45 (rdn_positive_less(rdnn(n6), rdnn(n7))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[99, 98])).
% 52.28/52.45 tff(101,plain,
% 52.28/52.45 (rdn_positive_less(rdnn(n5), rdnn(n6)) <=> rdn_positive_less(rdnn(n5), rdnn(n6))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(102,axiom,(rdn_positive_less(rdnn(n5), rdnn(n6))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less56')).
% 52.28/52.45 tff(103,plain,
% 52.28/52.45 (rdn_positive_less(rdnn(n5), rdnn(n6))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[102, 101])).
% 52.28/52.45 tff(104,plain,
% 52.28/52.45 (((~![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(n7)) | (~rdn_positive_less(rdnn(n6), rdnn(n7))))) <=> ((~![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(n7)) | (~rdn_positive_less(rdnn(n6), rdnn(n7))))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(105,plain,
% 52.28/52.45 ((rdn_positive_less(rdnn(n5), rdnn(n7)) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | (~rdn_positive_less(rdnn(n6), rdnn(n7)))) <=> ((~rdn_positive_less(rdnn(n5), rdnn(n6))) | rdn_positive_less(rdnn(n5), rdnn(n7)) | (~rdn_positive_less(rdnn(n6), rdnn(n7))))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(106,plain,
% 52.28/52.45 (((~![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(n7)) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | (~rdn_positive_less(rdnn(n6), rdnn(n7))))) <=> ((~![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(n7)) | (~rdn_positive_less(rdnn(n6), rdnn(n7)))))),
% 52.28/52.45 inference(monotonicity,[status(thm)],[105])).
% 52.28/52.45 tff(107,plain,
% 52.28/52.45 (((~![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(n7)) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | (~rdn_positive_less(rdnn(n6), rdnn(n7))))) <=> ((~![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(n7)) | (~rdn_positive_less(rdnn(n6), rdnn(n7))))),
% 52.28/52.45 inference(transitivity,[status(thm)],[106, 104])).
% 52.28/52.45 tff(108,plain,
% 52.28/52.45 ((~![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(n7)) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | (~rdn_positive_less(rdnn(n6), rdnn(n7))))),
% 52.28/52.45 inference(quant_inst,[status(thm)],[])).
% 52.28/52.45 tff(109,plain,
% 52.28/52.45 ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | rdn_positive_less(rdnn(n5), rdnn(n7)) | (~rdn_positive_less(rdnn(n6), rdnn(n7)))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[108, 107])).
% 52.28/52.45 tff(110,plain,
% 52.28/52.45 ($false),
% 52.28/52.45 inference(unit_resolution,[status(thm)],[109, 103, 100, 97, 84])).
% 52.28/52.45 tff(111,plain,(rdn_positive_less(rdnn(n5), rdnn(n7))), inference(lemma,lemma(discharge,[]))).
% 52.28/52.45 tff(112,assumption,(~rdn_positive_less(rdnn(n2), rdnn(n7))), introduced(assumption)).
% 52.28/52.45 tff(113,assumption,(~rdn_positive_less(rdnn(n3), rdnn(n5))), introduced(assumption)).
% 52.28/52.45 tff(114,plain,
% 52.28/52.45 (rdn_positive_less(rdnn(n4), rdnn(n5)) <=> rdn_positive_less(rdnn(n4), rdnn(n5))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(115,axiom,(rdn_positive_less(rdnn(n4), rdnn(n5))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less45')).
% 52.28/52.45 tff(116,plain,
% 52.28/52.45 (rdn_positive_less(rdnn(n4), rdnn(n5))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[115, 114])).
% 52.28/52.45 tff(117,plain,
% 52.28/52.45 (rdn_positive_less(rdnn(n3), rdnn(n4)) <=> rdn_positive_less(rdnn(n3), rdnn(n4))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(118,axiom,(rdn_positive_less(rdnn(n3), rdnn(n4))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less34')).
% 52.28/52.45 tff(119,plain,
% 52.28/52.45 (rdn_positive_less(rdnn(n3), rdnn(n4))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[118, 117])).
% 52.28/52.45 tff(120,plain,
% 52.28/52.45 (((~![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(n3), rdnn(n4))) | rdn_positive_less(rdnn(n3), rdnn(n5)) | (~rdn_positive_less(rdnn(n4), rdnn(n5))))) <=> ((~![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(n3), rdnn(n4))) | rdn_positive_less(rdnn(n3), rdnn(n5)) | (~rdn_positive_less(rdnn(n4), rdnn(n5))))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(121,plain,
% 52.28/52.45 ((rdn_positive_less(rdnn(n3), rdnn(n5)) | (~rdn_positive_less(rdnn(n3), rdnn(n4))) | (~rdn_positive_less(rdnn(n4), rdnn(n5)))) <=> ((~rdn_positive_less(rdnn(n3), rdnn(n4))) | rdn_positive_less(rdnn(n3), rdnn(n5)) | (~rdn_positive_less(rdnn(n4), rdnn(n5))))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(122,plain,
% 52.28/52.45 (((~![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(n3), rdnn(n5)) | (~rdn_positive_less(rdnn(n3), rdnn(n4))) | (~rdn_positive_less(rdnn(n4), rdnn(n5))))) <=> ((~![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(n3), rdnn(n4))) | rdn_positive_less(rdnn(n3), rdnn(n5)) | (~rdn_positive_less(rdnn(n4), rdnn(n5)))))),
% 52.28/52.45 inference(monotonicity,[status(thm)],[121])).
% 52.28/52.45 tff(123,plain,
% 52.28/52.45 (((~![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(n3), rdnn(n5)) | (~rdn_positive_less(rdnn(n3), rdnn(n4))) | (~rdn_positive_less(rdnn(n4), rdnn(n5))))) <=> ((~![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(n3), rdnn(n4))) | rdn_positive_less(rdnn(n3), rdnn(n5)) | (~rdn_positive_less(rdnn(n4), rdnn(n5))))),
% 52.28/52.45 inference(transitivity,[status(thm)],[122, 120])).
% 52.28/52.45 tff(124,plain,
% 52.28/52.45 ((~![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(n3), rdnn(n5)) | (~rdn_positive_less(rdnn(n3), rdnn(n4))) | (~rdn_positive_less(rdnn(n4), rdnn(n5))))),
% 52.28/52.45 inference(quant_inst,[status(thm)],[])).
% 52.28/52.45 tff(125,plain,
% 52.28/52.45 ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n3), rdnn(n4))) | rdn_positive_less(rdnn(n3), rdnn(n5)) | (~rdn_positive_less(rdnn(n4), rdnn(n5)))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[124, 123])).
% 52.28/52.45 tff(126,plain,
% 52.28/52.45 ($false),
% 52.28/52.45 inference(unit_resolution,[status(thm)],[125, 119, 116, 97, 113])).
% 52.28/52.45 tff(127,plain,(rdn_positive_less(rdnn(n3), rdnn(n5))), inference(lemma,lemma(discharge,[]))).
% 52.28/52.45 tff(128,assumption,(~rdn_positive_less(rdnn(n2), rdnn(n5))), introduced(assumption)).
% 52.28/52.45 tff(129,plain,
% 52.28/52.45 (rdn_positive_less(rdnn(n2), rdnn(n3)) <=> rdn_positive_less(rdnn(n2), rdnn(n3))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(130,axiom,(rdn_positive_less(rdnn(n2), rdnn(n3))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less23')).
% 52.28/52.45 tff(131,plain,
% 52.28/52.45 (rdn_positive_less(rdnn(n2), rdnn(n3))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[130, 129])).
% 52.28/52.45 tff(132,plain,
% 52.28/52.45 (((~![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(n2), rdnn(n3))) | rdn_positive_less(rdnn(n2), rdnn(n5)) | (~rdn_positive_less(rdnn(n3), rdnn(n5))))) <=> ((~![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(n2), rdnn(n3))) | rdn_positive_less(rdnn(n2), rdnn(n5)) | (~rdn_positive_less(rdnn(n3), rdnn(n5))))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(133,plain,
% 52.28/52.45 ((rdn_positive_less(rdnn(n2), rdnn(n5)) | (~rdn_positive_less(rdnn(n2), rdnn(n3))) | (~rdn_positive_less(rdnn(n3), rdnn(n5)))) <=> ((~rdn_positive_less(rdnn(n2), rdnn(n3))) | rdn_positive_less(rdnn(n2), rdnn(n5)) | (~rdn_positive_less(rdnn(n3), rdnn(n5))))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(134,plain,
% 52.28/52.45 (((~![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(n2), rdnn(n5)) | (~rdn_positive_less(rdnn(n2), rdnn(n3))) | (~rdn_positive_less(rdnn(n3), rdnn(n5))))) <=> ((~![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(n2), rdnn(n3))) | rdn_positive_less(rdnn(n2), rdnn(n5)) | (~rdn_positive_less(rdnn(n3), rdnn(n5)))))),
% 52.28/52.45 inference(monotonicity,[status(thm)],[133])).
% 52.28/52.45 tff(135,plain,
% 52.28/52.45 (((~![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(n2), rdnn(n5)) | (~rdn_positive_less(rdnn(n2), rdnn(n3))) | (~rdn_positive_less(rdnn(n3), rdnn(n5))))) <=> ((~![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(n2), rdnn(n3))) | rdn_positive_less(rdnn(n2), rdnn(n5)) | (~rdn_positive_less(rdnn(n3), rdnn(n5))))),
% 52.28/52.45 inference(transitivity,[status(thm)],[134, 132])).
% 52.28/52.45 tff(136,plain,
% 52.28/52.45 ((~![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(n2), rdnn(n5)) | (~rdn_positive_less(rdnn(n2), rdnn(n3))) | (~rdn_positive_less(rdnn(n3), rdnn(n5))))),
% 52.28/52.45 inference(quant_inst,[status(thm)],[])).
% 52.28/52.45 tff(137,plain,
% 52.28/52.45 ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n2), rdnn(n3))) | rdn_positive_less(rdnn(n2), rdnn(n5)) | (~rdn_positive_less(rdnn(n3), rdnn(n5)))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[136, 135])).
% 52.28/52.45 tff(138,plain,
% 52.28/52.45 ($false),
% 52.28/52.45 inference(unit_resolution,[status(thm)],[137, 131, 97, 128, 127])).
% 52.28/52.45 tff(139,plain,(rdn_positive_less(rdnn(n2), rdnn(n5))), inference(lemma,lemma(discharge,[]))).
% 52.28/52.45 tff(140,plain,
% 52.28/52.45 (((~![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(n2), rdnn(n5))) | rdn_positive_less(rdnn(n2), rdnn(n7)) | (~rdn_positive_less(rdnn(n5), rdnn(n7))))) <=> ((~![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(n2), rdnn(n5))) | rdn_positive_less(rdnn(n2), rdnn(n7)) | (~rdn_positive_less(rdnn(n5), rdnn(n7))))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(141,plain,
% 52.28/52.45 ((rdn_positive_less(rdnn(n2), rdnn(n7)) | (~rdn_positive_less(rdnn(n2), rdnn(n5))) | (~rdn_positive_less(rdnn(n5), rdnn(n7)))) <=> ((~rdn_positive_less(rdnn(n2), rdnn(n5))) | rdn_positive_less(rdnn(n2), rdnn(n7)) | (~rdn_positive_less(rdnn(n5), rdnn(n7))))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(142,plain,
% 52.28/52.45 (((~![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(n2), rdnn(n7)) | (~rdn_positive_less(rdnn(n2), rdnn(n5))) | (~rdn_positive_less(rdnn(n5), rdnn(n7))))) <=> ((~![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(n2), rdnn(n5))) | rdn_positive_less(rdnn(n2), rdnn(n7)) | (~rdn_positive_less(rdnn(n5), rdnn(n7)))))),
% 52.28/52.45 inference(monotonicity,[status(thm)],[141])).
% 52.28/52.45 tff(143,plain,
% 52.28/52.45 (((~![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(n2), rdnn(n7)) | (~rdn_positive_less(rdnn(n2), rdnn(n5))) | (~rdn_positive_less(rdnn(n5), rdnn(n7))))) <=> ((~![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(n2), rdnn(n5))) | rdn_positive_less(rdnn(n2), rdnn(n7)) | (~rdn_positive_less(rdnn(n5), rdnn(n7))))),
% 52.28/52.45 inference(transitivity,[status(thm)],[142, 140])).
% 52.28/52.45 tff(144,plain,
% 52.28/52.45 ((~![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(n2), rdnn(n7)) | (~rdn_positive_less(rdnn(n2), rdnn(n5))) | (~rdn_positive_less(rdnn(n5), rdnn(n7))))),
% 52.28/52.45 inference(quant_inst,[status(thm)],[])).
% 52.28/52.45 tff(145,plain,
% 52.28/52.45 ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n2), rdnn(n5))) | rdn_positive_less(rdnn(n2), rdnn(n7)) | (~rdn_positive_less(rdnn(n5), rdnn(n7)))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[144, 143])).
% 52.28/52.45 tff(146,plain,
% 52.28/52.45 ($false),
% 52.28/52.45 inference(unit_resolution,[status(thm)],[145, 97, 139, 112, 111])).
% 52.28/52.45 tff(147,plain,(rdn_positive_less(rdnn(n2), rdnn(n7))), inference(lemma,lemma(discharge,[]))).
% 52.28/52.45 tff(148,assumption,(~rdn_positive_less(rdnn(n1), rdnn(n7))), introduced(assumption)).
% 52.28/52.45 tff(149,plain,
% 52.28/52.45 (rdn_positive_less(rdnn(n1), rdnn(n2)) <=> rdn_positive_less(rdnn(n1), rdnn(n2))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(150,axiom,(rdn_positive_less(rdnn(n1), rdnn(n2))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less12')).
% 52.28/52.45 tff(151,plain,
% 52.28/52.45 (rdn_positive_less(rdnn(n1), rdnn(n2))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[150, 149])).
% 52.28/52.45 tff(152,plain,
% 52.28/52.45 (((~![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(n1), rdnn(n2))) | rdn_positive_less(rdnn(n1), rdnn(n7)) | (~rdn_positive_less(rdnn(n2), rdnn(n7))))) <=> ((~![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(n1), rdnn(n2))) | rdn_positive_less(rdnn(n1), rdnn(n7)) | (~rdn_positive_less(rdnn(n2), rdnn(n7))))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(153,plain,
% 52.28/52.45 ((rdn_positive_less(rdnn(n1), rdnn(n7)) | (~rdn_positive_less(rdnn(n1), rdnn(n2))) | (~rdn_positive_less(rdnn(n2), rdnn(n7)))) <=> ((~rdn_positive_less(rdnn(n1), rdnn(n2))) | rdn_positive_less(rdnn(n1), rdnn(n7)) | (~rdn_positive_less(rdnn(n2), rdnn(n7))))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(154,plain,
% 52.28/52.45 (((~![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(n1), rdnn(n7)) | (~rdn_positive_less(rdnn(n1), rdnn(n2))) | (~rdn_positive_less(rdnn(n2), rdnn(n7))))) <=> ((~![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(n1), rdnn(n2))) | rdn_positive_less(rdnn(n1), rdnn(n7)) | (~rdn_positive_less(rdnn(n2), rdnn(n7)))))),
% 52.28/52.45 inference(monotonicity,[status(thm)],[153])).
% 52.28/52.45 tff(155,plain,
% 52.28/52.45 (((~![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(n1), rdnn(n7)) | (~rdn_positive_less(rdnn(n1), rdnn(n2))) | (~rdn_positive_less(rdnn(n2), rdnn(n7))))) <=> ((~![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(n1), rdnn(n2))) | rdn_positive_less(rdnn(n1), rdnn(n7)) | (~rdn_positive_less(rdnn(n2), rdnn(n7))))),
% 52.28/52.45 inference(transitivity,[status(thm)],[154, 152])).
% 52.28/52.45 tff(156,plain,
% 52.28/52.45 ((~![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(n1), rdnn(n7)) | (~rdn_positive_less(rdnn(n1), rdnn(n2))) | (~rdn_positive_less(rdnn(n2), rdnn(n7))))),
% 52.28/52.45 inference(quant_inst,[status(thm)],[])).
% 52.28/52.45 tff(157,plain,
% 52.28/52.45 ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n1), rdnn(n2))) | rdn_positive_less(rdnn(n1), rdnn(n7)) | (~rdn_positive_less(rdnn(n2), rdnn(n7)))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[156, 155])).
% 52.28/52.45 tff(158,plain,
% 52.28/52.45 ($false),
% 52.28/52.45 inference(unit_resolution,[status(thm)],[157, 151, 97, 148, 147])).
% 52.28/52.45 tff(159,plain,(rdn_positive_less(rdnn(n1), rdnn(n7))), inference(lemma,lemma(discharge,[]))).
% 52.28/52.45 tff(160,plain,
% 52.28/52.45 (^[Ds: $i, Os: $i, Db: $i, Ob: $i] : refl(((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob))) <=> ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob))))),
% 52.28/52.45 inference(bind,[status(th)],[])).
% 52.28/52.45 tff(161,plain,
% 52.28/52.45 (![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob))) <=> ![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob)))),
% 52.28/52.45 inference(quant_intro,[status(thm)],[160])).
% 52.28/52.45 tff(162,plain,
% 52.28/52.45 (![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob))) <=> ![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob)))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(163,plain,
% 52.28/52.45 (^[Ds: $i, Os: $i, Db: $i, Ob: $i] : rewrite((rdn_positive_less(Os, Ob) => rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob))) <=> ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob))))),
% 52.28/52.45 inference(bind,[status(th)],[])).
% 52.28/52.45 tff(164,plain,
% 52.28/52.45 (![Ds: $i, Os: $i, Db: $i, Ob: $i] : (rdn_positive_less(Os, Ob) => rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob))) <=> ![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob)))),
% 52.28/52.45 inference(quant_intro,[status(thm)],[163])).
% 52.28/52.45 tff(165,axiom,(![Ds: $i, Os: $i, Db: $i, Ob: $i] : (rdn_positive_less(Os, Ob) => rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less_multi_digit_high')).
% 52.28/52.45 tff(166,plain,
% 52.28/52.45 (![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob)))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[165, 164])).
% 52.28/52.45 tff(167,plain,
% 52.28/52.45 (![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob)))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[166, 162])).
% 52.28/52.45 tff(168,plain,(
% 52.28/52.45 ![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob)))),
% 52.28/52.45 inference(skolemize,[status(sab)],[167])).
% 52.28/52.45 tff(169,plain,
% 52.28/52.45 (![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob)))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[168, 161])).
% 52.28/52.45 tff(170,plain,
% 52.28/52.45 (((~![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob)))) | ((~rdn_positive_less(rdnn(n1), rdnn(n7))) | rdn_positive_less(rdn(rdnn(n2), rdnn(n1)), rdn(rdnn(n8), rdnn(n7))))) <=> ((~![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob)))) | (~rdn_positive_less(rdnn(n1), rdnn(n7))) | rdn_positive_less(rdn(rdnn(n2), rdnn(n1)), rdn(rdnn(n8), rdnn(n7))))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(171,plain,
% 52.28/52.45 ((~![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob)))) | ((~rdn_positive_less(rdnn(n1), rdnn(n7))) | rdn_positive_less(rdn(rdnn(n2), rdnn(n1)), rdn(rdnn(n8), rdnn(n7))))),
% 52.28/52.45 inference(quant_inst,[status(thm)],[])).
% 52.28/52.45 tff(172,plain,
% 52.28/52.45 ((~![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob)))) | (~rdn_positive_less(rdnn(n1), rdnn(n7))) | rdn_positive_less(rdn(rdnn(n2), rdnn(n1)), rdn(rdnn(n8), rdnn(n7)))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[171, 170])).
% 52.28/52.45 tff(173,plain,
% 52.28/52.45 ((~rdn_positive_less(rdnn(n1), rdnn(n7))) | rdn_positive_less(rdn(rdnn(n2), rdnn(n1)), rdn(rdnn(n8), rdnn(n7)))),
% 52.28/52.45 inference(unit_resolution,[status(thm)],[172, 169])).
% 52.28/52.45 tff(174,plain,
% 52.28/52.45 (rdn_positive_less(rdn(rdnn(n2), rdnn(n1)), rdn(rdnn(n8), rdnn(n7)))),
% 52.28/52.45 inference(unit_resolution,[status(thm)],[173, 159])).
% 52.28/52.45 tff(175,plain,
% 52.28/52.45 (rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7)))) <=> rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(176,axiom,(rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax','rdn78')).
% 52.28/52.45 tff(177,plain,
% 52.28/52.45 (rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[176, 175])).
% 52.28/52.45 tff(178,plain,
% 52.28/52.45 (rdn_translate(n12, rdn_pos(rdn(rdnn(n2), rdnn(n1)))) <=> rdn_translate(n12, rdn_pos(rdn(rdnn(n2), rdnn(n1))))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(179,axiom,(rdn_translate(n12, rdn_pos(rdn(rdnn(n2), rdnn(n1))))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax','rdn12')).
% 52.28/52.45 tff(180,plain,
% 52.28/52.45 (rdn_translate(n12, rdn_pos(rdn(rdnn(n2), rdnn(n1))))),
% 52.28/52.45 inference(modus_ponens,[status(thm)],[179, 178])).
% 52.28/52.45 tff(181,plain,
% 52.28/52.45 (((~![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_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n2), rdnn(n1)), rdn(rdnn(n8), rdnn(n7)))) | less(n12, n78) | (~rdn_translate(n12, rdn_pos(rdn(rdnn(n2), rdnn(n1))))))) <=> ((~![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_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n2), rdnn(n1)), rdn(rdnn(n8), rdnn(n7)))) | less(n12, n78) | (~rdn_translate(n12, rdn_pos(rdn(rdnn(n2), rdnn(n1))))))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(182,plain,
% 52.28/52.45 ((less(n12, n78) | (~rdn_translate(n12, rdn_pos(rdn(rdnn(n2), rdnn(n1))))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n2), rdnn(n1)), rdn(rdnn(n8), rdnn(n7))))) <=> ((~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n2), rdnn(n1)), rdn(rdnn(n8), rdnn(n7)))) | less(n12, n78) | (~rdn_translate(n12, rdn_pos(rdn(rdnn(n2), rdnn(n1))))))),
% 52.28/52.45 inference(rewrite,[status(thm)],[])).
% 52.28/52.45 tff(183,plain,
% 52.28/52.45 (((~![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(n12, n78) | (~rdn_translate(n12, rdn_pos(rdn(rdnn(n2), rdnn(n1))))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n2), rdnn(n1)), 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_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n2), rdnn(n1)), rdn(rdnn(n8), rdnn(n7)))) | less(n12, n78) | (~rdn_translate(n12, rdn_pos(rdn(rdnn(n2), rdnn(n1)))))))),
% 52.28/52.45 inference(monotonicity,[status(thm)],[182])).
% 52.28/52.45 tff(184,plain,
% 52.28/52.45 (((~![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(n12, n78) | (~rdn_translate(n12, rdn_pos(rdn(rdnn(n2), rdnn(n1))))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n2), rdnn(n1)), 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_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n2), rdnn(n1)), rdn(rdnn(n8), rdnn(n7)))) | less(n12, n78) | (~rdn_translate(n12, rdn_pos(rdn(rdnn(n2), rdnn(n1))))))),
% 52.28/52.45 inference(transitivity,[status(thm)],[183, 181])).
% 52.28/52.45 tff(185,plain,
% 52.28/52.45 ((~![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(n12, n78) | (~rdn_translate(n12, rdn_pos(rdn(rdnn(n2), rdnn(n1))))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n2), rdnn(n1)), rdn(rdnn(n8), rdnn(n7)))))),
% 52.28/52.46 inference(quant_inst,[status(thm)],[])).
% 52.28/52.46 tff(186,plain,
% 52.28/52.46 ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n2), rdnn(n1)), rdn(rdnn(n8), rdnn(n7)))) | less(n12, n78) | (~rdn_translate(n12, rdn_pos(rdn(rdnn(n2), rdnn(n1)))))),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[185, 184])).
% 52.28/52.46 tff(187,plain,
% 52.28/52.46 ($false),
% 52.28/52.46 inference(unit_resolution,[status(thm)],[186, 180, 177, 44, 174, 83])).
% 52.28/52.46 tff(188,plain,(less(n12, n78)), inference(lemma,lemma(discharge,[]))).
% 52.28/52.46 tff(189,assumption,(~accept_population(countryamedicalorganization, atheist, n12)), introduced(assumption)).
% 52.28/52.46 tff(190,plain,
% 52.28/52.46 (accept_population(countryamedicalorganization, atheist, n78) <=> accept_population(countryamedicalorganization, atheist, n78)),
% 52.28/52.46 inference(rewrite,[status(thm)],[])).
% 52.28/52.46 tff(191,axiom,(accept_population(countryamedicalorganization, atheist, n78)), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+2.ax','deduced_212')).
% 52.28/52.46 tff(192,plain,
% 52.28/52.46 (accept_population(countryamedicalorganization, atheist, n78)),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[191, 190])).
% 52.28/52.46 tff(193,plain,
% 52.28/52.46 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countryamedicalorganization, atheist, n12) | (~less(n12, n78)) | (~accept_population(countryamedicalorganization, atheist, n78)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | accept_population(countryamedicalorganization, atheist, n12) | (~less(n12, n78)) | (~accept_population(countryamedicalorganization, atheist, n78)))),
% 52.28/52.46 inference(rewrite,[status(thm)],[])).
% 52.28/52.46 tff(194,plain,
% 52.28/52.46 ((accept_population(countryamedicalorganization, atheist, n12) | (~accept_population(countryamedicalorganization, atheist, n78)) | (~less(n12, n78))) <=> (accept_population(countryamedicalorganization, atheist, n12) | (~less(n12, n78)) | (~accept_population(countryamedicalorganization, atheist, n78)))),
% 52.28/52.46 inference(rewrite,[status(thm)],[])).
% 52.28/52.46 tff(195,plain,
% 52.28/52.46 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countryamedicalorganization, atheist, n12) | (~accept_population(countryamedicalorganization, atheist, n78)) | (~less(n12, n78)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countryamedicalorganization, atheist, n12) | (~less(n12, n78)) | (~accept_population(countryamedicalorganization, atheist, n78))))),
% 52.28/52.46 inference(monotonicity,[status(thm)],[194])).
% 52.28/52.46 tff(196,plain,
% 52.28/52.46 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countryamedicalorganization, atheist, n12) | (~accept_population(countryamedicalorganization, atheist, n78)) | (~less(n12, n78)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | accept_population(countryamedicalorganization, atheist, n12) | (~less(n12, n78)) | (~accept_population(countryamedicalorganization, atheist, n78)))),
% 52.28/52.46 inference(transitivity,[status(thm)],[195, 193])).
% 52.28/52.46 tff(197,plain,
% 52.28/52.46 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countryamedicalorganization, atheist, n12) | (~accept_population(countryamedicalorganization, atheist, n78)) | (~less(n12, n78)))),
% 52.28/52.46 inference(quant_inst,[status(thm)],[])).
% 52.28/52.46 tff(198,plain,
% 52.28/52.46 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | accept_population(countryamedicalorganization, atheist, n12) | (~less(n12, n78)) | (~accept_population(countryamedicalorganization, atheist, n78))),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[197, 196])).
% 52.28/52.46 tff(199,plain,
% 52.28/52.46 ($false),
% 52.28/52.46 inference(unit_resolution,[status(thm)],[198, 74, 192, 189, 188])).
% 52.28/52.46 tff(200,plain,(accept_population(countryamedicalorganization, atheist, n12)), inference(lemma,lemma(discharge,[]))).
% 52.28/52.46 tff(201,plain,
% 52.28/52.46 (^[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))))),
% 52.28/52.46 inference(bind,[status(th)],[])).
% 52.28/52.46 tff(202,plain,
% 52.28/52.46 (![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)))),
% 52.28/52.46 inference(quant_intro,[status(thm)],[201])).
% 52.28/52.46 tff(203,plain,
% 52.28/52.46 (^[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)))))),
% 52.28/52.46 inference(bind,[status(th)],[])).
% 52.28/52.46 tff(204,plain,
% 52.28/52.46 (![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)))),
% 52.28/52.46 inference(quant_intro,[status(thm)],[203])).
% 52.28/52.46 tff(205,plain,
% 52.28/52.46 (![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))),
% 52.28/52.46 inference(rewrite,[status(thm)],[])).
% 52.28/52.46 tff(206,plain,
% 52.28/52.46 (^[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)))),
% 52.28/52.46 inference(bind,[status(th)],[])).
% 52.28/52.46 tff(207,plain,
% 52.28/52.46 (![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))),
% 52.28/52.46 inference(quant_intro,[status(thm)],[206])).
% 52.28/52.46 tff(208,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')).
% 52.28/52.46 tff(209,plain,
% 52.28/52.46 (![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))),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[208, 207])).
% 52.28/52.46 tff(210,plain,
% 52.28/52.46 (![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))),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[209, 205])).
% 52.28/52.46 tff(211,plain,(
% 52.28/52.46 ![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))),
% 52.28/52.46 inference(skolemize,[status(sab)],[210])).
% 52.28/52.46 tff(212,plain,
% 52.28/52.46 (![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)))),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[211, 204])).
% 52.28/52.46 tff(213,plain,
% 52.28/52.46 (![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)))),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[212, 202])).
% 52.28/52.46 tff(214,plain,
% 52.28/52.46 ((~![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(countryamedicalorganization, atheist, n12)) | (~accept_population(countryamedicalorganization, christian, n3)) | (~accept_population(countryamedicalorganization, muslim, n0)) | (~accept_population(countryamedicalorganization, native, n85)) | (~accept_population(countryamedicalorganization, other, n0))) <=> accept_city(countryamedicalorganization, coastvillage)))),
% 52.28/52.46 inference(quant_inst,[status(thm)],[])).
% 52.28/52.46 tff(215,plain,
% 52.28/52.46 (~(((~accept_population(countryamedicalorganization, atheist, n12)) | (~accept_population(countryamedicalorganization, christian, n3)) | (~accept_population(countryamedicalorganization, muslim, n0)) | (~accept_population(countryamedicalorganization, native, n85)) | (~accept_population(countryamedicalorganization, other, n0))) <=> accept_city(countryamedicalorganization, coastvillage))),
% 52.28/52.46 inference(unit_resolution,[status(thm)],[214, 213])).
% 52.28/52.46 tff(216,plain,
% 52.28/52.46 ((~accept_city(countryamedicalorganization, coastvillage)) <=> (~accept_city(countryamedicalorganization, coastvillage))),
% 52.28/52.46 inference(rewrite,[status(thm)],[])).
% 52.28/52.46 tff(217,axiom,(~accept_city(countryamedicalorganization, coastvillage)), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+2.ax','deduced_13')).
% 52.28/52.46 tff(218,plain,
% 52.28/52.46 (~accept_city(countryamedicalorganization, coastvillage)),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[217, 216])).
% 52.28/52.46 tff(219,plain,
% 52.28/52.46 ((((~accept_population(countryamedicalorganization, atheist, n12)) | (~accept_population(countryamedicalorganization, christian, n3)) | (~accept_population(countryamedicalorganization, muslim, n0)) | (~accept_population(countryamedicalorganization, native, n85)) | (~accept_population(countryamedicalorganization, other, n0))) <=> accept_city(countryamedicalorganization, coastvillage)) | ((~accept_population(countryamedicalorganization, atheist, n12)) | (~accept_population(countryamedicalorganization, christian, n3)) | (~accept_population(countryamedicalorganization, muslim, n0)) | (~accept_population(countryamedicalorganization, native, n85)) | (~accept_population(countryamedicalorganization, other, n0))) | accept_city(countryamedicalorganization, coastvillage)),
% 52.28/52.46 inference(tautology,[status(thm)],[])).
% 52.28/52.46 tff(220,plain,
% 52.28/52.46 ((((~accept_population(countryamedicalorganization, atheist, n12)) | (~accept_population(countryamedicalorganization, christian, n3)) | (~accept_population(countryamedicalorganization, muslim, n0)) | (~accept_population(countryamedicalorganization, native, n85)) | (~accept_population(countryamedicalorganization, other, n0))) <=> accept_city(countryamedicalorganization, coastvillage)) | ((~accept_population(countryamedicalorganization, atheist, n12)) | (~accept_population(countryamedicalorganization, christian, n3)) | (~accept_population(countryamedicalorganization, muslim, n0)) | (~accept_population(countryamedicalorganization, native, n85)) | (~accept_population(countryamedicalorganization, other, n0)))),
% 52.28/52.46 inference(unit_resolution,[status(thm)],[219, 218])).
% 52.28/52.46 tff(221,plain,
% 52.28/52.46 ((~accept_population(countryamedicalorganization, atheist, n12)) | (~accept_population(countryamedicalorganization, christian, n3)) | (~accept_population(countryamedicalorganization, muslim, n0)) | (~accept_population(countryamedicalorganization, native, n85)) | (~accept_population(countryamedicalorganization, other, n0))),
% 52.28/52.46 inference(unit_resolution,[status(thm)],[220, 215])).
% 52.28/52.46 tff(222,plain,
% 52.28/52.46 (accept_population(countryamedicalorganization, native, n85) <=> accept_population(countryamedicalorganization, native, n85)),
% 52.28/52.46 inference(rewrite,[status(thm)],[])).
% 52.28/52.46 tff(223,plain,
% 52.28/52.46 ((~(~accept_population(countryamedicalorganization, native, n85))) <=> accept_population(countryamedicalorganization, native, n85)),
% 52.28/52.46 inference(rewrite,[status(thm)],[])).
% 52.28/52.46 tff(224,axiom,(~(~accept_population(countryamedicalorganization, native, n85))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','query_10')).
% 52.28/52.46 tff(225,plain,
% 52.28/52.46 (accept_population(countryamedicalorganization, native, n85)),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[224, 223])).
% 52.28/52.46 tff(226,plain,
% 52.28/52.46 (accept_population(countryamedicalorganization, native, n85)),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[225, 222])).
% 52.28/52.46 tff(227,plain,
% 52.28/52.46 (accept_population(countryamedicalorganization, other, n0) <=> accept_population(countryamedicalorganization, other, n0)),
% 52.28/52.46 inference(rewrite,[status(thm)],[])).
% 52.28/52.46 tff(228,axiom,(accept_population(countryamedicalorganization, other, n0)), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+2.ax','deduced_220')).
% 52.28/52.46 tff(229,plain,
% 52.28/52.46 (accept_population(countryamedicalorganization, other, n0)),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[228, 227])).
% 52.28/52.46 tff(230,plain,
% 52.28/52.46 ((~((~accept_population(countryamedicalorganization, atheist, n12)) | (~accept_population(countryamedicalorganization, christian, n3)) | (~accept_population(countryamedicalorganization, muslim, n0)) | (~accept_population(countryamedicalorganization, native, n85)) | (~accept_population(countryamedicalorganization, other, n0)))) | (~accept_population(countryamedicalorganization, atheist, n12)) | (~accept_population(countryamedicalorganization, christian, n3)) | (~accept_population(countryamedicalorganization, muslim, n0)) | (~accept_population(countryamedicalorganization, native, n85)) | (~accept_population(countryamedicalorganization, other, n0))),
% 52.28/52.46 inference(tautology,[status(thm)],[])).
% 52.28/52.46 tff(231,plain,
% 52.28/52.46 ((~((~accept_population(countryamedicalorganization, atheist, n12)) | (~accept_population(countryamedicalorganization, christian, n3)) | (~accept_population(countryamedicalorganization, muslim, n0)) | (~accept_population(countryamedicalorganization, native, n85)) | (~accept_population(countryamedicalorganization, other, n0)))) | (~accept_population(countryamedicalorganization, atheist, n12)) | (~accept_population(countryamedicalorganization, christian, n3)) | (~accept_population(countryamedicalorganization, muslim, n0))),
% 52.28/52.46 inference(unit_resolution,[status(thm)],[230, 229, 226])).
% 52.28/52.46 tff(232,plain,
% 52.28/52.46 ((~accept_population(countryamedicalorganization, atheist, n12)) | (~accept_population(countryamedicalorganization, christian, n3)) | (~accept_population(countryamedicalorganization, muslim, n0))),
% 52.28/52.46 inference(unit_resolution,[status(thm)],[231, 221])).
% 52.28/52.46 tff(233,plain,
% 52.28/52.46 (~accept_population(countryamedicalorganization, muslim, n0)),
% 52.28/52.46 inference(unit_resolution,[status(thm)],[232, 200, 82])).
% 52.28/52.46 tff(234,plain,
% 52.28/52.46 (accept_population(countryamedicalorganization, muslim, n65) <=> accept_population(countryamedicalorganization, muslim, n65)),
% 52.28/52.46 inference(rewrite,[status(thm)],[])).
% 52.28/52.46 tff(235,axiom,(accept_population(countryamedicalorganization, muslim, n65)), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+2.ax','deduced_16')).
% 52.28/52.46 tff(236,plain,
% 52.28/52.46 (accept_population(countryamedicalorganization, muslim, n65)),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[235, 234])).
% 52.28/52.46 tff(237,plain,
% 52.28/52.46 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countryamedicalorganization, muslim, n0) | (~accept_population(countryamedicalorganization, muslim, n65)) | (~less(n0, n65)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | accept_population(countryamedicalorganization, muslim, n0) | (~accept_population(countryamedicalorganization, muslim, n65)) | (~less(n0, n65)))),
% 52.28/52.46 inference(rewrite,[status(thm)],[])).
% 52.28/52.46 tff(238,plain,
% 52.28/52.46 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countryamedicalorganization, muslim, n0) | (~accept_population(countryamedicalorganization, muslim, n65)) | (~less(n0, n65)))),
% 52.28/52.46 inference(quant_inst,[status(thm)],[])).
% 52.28/52.46 tff(239,plain,
% 52.28/52.46 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | accept_population(countryamedicalorganization, muslim, n0) | (~accept_population(countryamedicalorganization, muslim, n65)) | (~less(n0, n65))),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[238, 237])).
% 52.28/52.46 tff(240,plain,
% 52.28/52.46 (~less(n0, n65)),
% 52.28/52.46 inference(unit_resolution,[status(thm)],[239, 74, 236, 233])).
% 52.28/52.46 tff(241,plain,
% 52.28/52.46 (rdn_non_zero_digit(rdnn(n6)) <=> rdn_non_zero_digit(rdnn(n6))),
% 52.28/52.46 inference(rewrite,[status(thm)],[])).
% 52.28/52.46 tff(242,axiom,(rdn_non_zero_digit(rdnn(n6))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_digit6')).
% 52.28/52.46 tff(243,plain,
% 52.28/52.46 (rdn_non_zero_digit(rdnn(n6))),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[242, 241])).
% 52.28/52.46 tff(244,plain,
% 52.28/52.46 (((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | (rdn_non_zero(rdnn(n6)) | (~rdn_non_zero_digit(rdnn(n6))))) <=> ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | rdn_non_zero(rdnn(n6)) | (~rdn_non_zero_digit(rdnn(n6))))),
% 52.28/52.46 inference(rewrite,[status(thm)],[])).
% 52.28/52.46 tff(245,plain,
% 52.28/52.46 ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | (rdn_non_zero(rdnn(n6)) | (~rdn_non_zero_digit(rdnn(n6))))),
% 52.28/52.46 inference(quant_inst,[status(thm)],[])).
% 52.28/52.46 tff(246,plain,
% 52.28/52.46 ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | rdn_non_zero(rdnn(n6)) | (~rdn_non_zero_digit(rdnn(n6)))),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[245, 244])).
% 52.28/52.46 tff(247,plain,
% 52.28/52.46 (rdn_non_zero(rdnn(n6))),
% 52.28/52.46 inference(unit_resolution,[status(thm)],[246, 243, 10])).
% 52.28/52.46 tff(248,plain,
% 52.28/52.46 (((~![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))) | ((~rdn_non_zero(rdnn(n6))) | rdn_positive_less(rdnn(n0), rdn(rdnn(n5), rdnn(n6))))) <=> ((~![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))) | (~rdn_non_zero(rdnn(n6))) | rdn_positive_less(rdnn(n0), rdn(rdnn(n5), rdnn(n6))))),
% 52.28/52.46 inference(rewrite,[status(thm)],[])).
% 52.28/52.46 tff(249,plain,
% 52.28/52.46 ((~![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))) | ((~rdn_non_zero(rdnn(n6))) | rdn_positive_less(rdnn(n0), rdn(rdnn(n5), rdnn(n6))))),
% 52.28/52.46 inference(quant_inst,[status(thm)],[])).
% 52.28/52.46 tff(250,plain,
% 52.28/52.46 ((~![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))) | (~rdn_non_zero(rdnn(n6))) | rdn_positive_less(rdnn(n0), rdn(rdnn(n5), rdnn(n6)))),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[249, 248])).
% 52.28/52.46 tff(251,plain,
% 52.28/52.46 ((~rdn_non_zero(rdnn(n6))) | rdn_positive_less(rdnn(n0), rdn(rdnn(n5), rdnn(n6)))),
% 52.28/52.46 inference(unit_resolution,[status(thm)],[250, 27])).
% 52.28/52.46 tff(252,plain,
% 52.28/52.46 (rdn_positive_less(rdnn(n0), rdn(rdnn(n5), rdnn(n6)))),
% 52.28/52.46 inference(unit_resolution,[status(thm)],[251, 247])).
% 52.28/52.46 tff(253,plain,
% 52.28/52.46 (rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6)))) <=> rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))),
% 52.28/52.46 inference(rewrite,[status(thm)],[])).
% 52.28/52.46 tff(254,axiom,(rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax','rdn65')).
% 52.28/52.46 tff(255,plain,
% 52.28/52.46 (rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[254, 253])).
% 52.28/52.46 tff(256,plain,
% 52.28/52.46 (rdn_translate(n0, rdn_pos(rdnn(n0))) <=> rdn_translate(n0, rdn_pos(rdnn(n0)))),
% 52.28/52.46 inference(rewrite,[status(thm)],[])).
% 52.28/52.46 tff(257,axiom,(rdn_translate(n0, rdn_pos(rdnn(n0)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax','rdn0')).
% 52.28/52.46 tff(258,plain,
% 52.28/52.46 (rdn_translate(n0, rdn_pos(rdnn(n0)))),
% 52.28/52.46 inference(modus_ponens,[status(thm)],[257, 256])).
% 52.28/52.46 tff(259,plain,
% 52.28/52.46 (((~![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(rdnn(n0), rdn(rdnn(n5), rdnn(n6)))) | (~rdn_translate(n0, rdn_pos(rdnn(n0)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | less(n0, n65))) <=> ((~![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(rdnn(n0), rdn(rdnn(n5), rdnn(n6)))) | (~rdn_translate(n0, rdn_pos(rdnn(n0)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | less(n0, n65))),
% 52.35/52.52 inference(rewrite,[status(thm)],[])).
% 52.35/52.52 tff(260,plain,
% 52.35/52.52 ((less(n0, n65) | (~rdn_translate(n0, rdn_pos(rdnn(n0)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | (~rdn_positive_less(rdnn(n0), rdn(rdnn(n5), rdnn(n6))))) <=> ((~rdn_positive_less(rdnn(n0), rdn(rdnn(n5), rdnn(n6)))) | (~rdn_translate(n0, rdn_pos(rdnn(n0)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | less(n0, n65))),
% 52.35/52.52 inference(rewrite,[status(thm)],[])).
% 52.35/52.52 tff(261,plain,
% 52.35/52.52 (((~![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(n0, n65) | (~rdn_translate(n0, rdn_pos(rdnn(n0)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | (~rdn_positive_less(rdnn(n0), rdn(rdnn(n5), rdnn(n6)))))) <=> ((~![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(rdnn(n0), rdn(rdnn(n5), rdnn(n6)))) | (~rdn_translate(n0, rdn_pos(rdnn(n0)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | less(n0, n65)))),
% 52.35/52.52 inference(monotonicity,[status(thm)],[260])).
% 52.35/52.52 tff(262,plain,
% 52.35/52.52 (((~![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(n0, n65) | (~rdn_translate(n0, rdn_pos(rdnn(n0)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | (~rdn_positive_less(rdnn(n0), rdn(rdnn(n5), rdnn(n6)))))) <=> ((~![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(rdnn(n0), rdn(rdnn(n5), rdnn(n6)))) | (~rdn_translate(n0, rdn_pos(rdnn(n0)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | less(n0, n65))),
% 52.35/52.52 inference(transitivity,[status(thm)],[261, 259])).
% 52.35/52.52 tff(263,plain,
% 52.35/52.52 ((~![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(n0, n65) | (~rdn_translate(n0, rdn_pos(rdnn(n0)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | (~rdn_positive_less(rdnn(n0), rdn(rdnn(n5), rdnn(n6)))))),
% 52.35/52.52 inference(quant_inst,[status(thm)],[])).
% 52.35/52.52 tff(264,plain,
% 52.35/52.52 ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (~rdn_positive_less(rdnn(n0), rdn(rdnn(n5), rdnn(n6)))) | (~rdn_translate(n0, rdn_pos(rdnn(n0)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | less(n0, n65)),
% 52.35/52.52 inference(modus_ponens,[status(thm)],[263, 262])).
% 52.35/52.52 tff(265,plain,
% 52.35/52.52 ($false),
% 52.35/52.52 inference(unit_resolution,[status(thm)],[264, 258, 255, 44, 252, 240])).
% 52.35/52.52 % SZS output end Proof
% 52.35/52.53 % E exiting
%------------------------------------------------------------------------------