%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : AGT006+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 04:57:38 AM UTC 2025
% Result : Theorem 262.45s 262.75s
% Output : Proof 262.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : AGT006+2 : TPTP v9.0.0. Bugfixed v3.1.0.
% 0.03/0.13 % 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 10:44:16 EDT 2025
% 0.12/0.34 % CPUTime :
% 262.45/262.75 % SZS status Theorem
% 262.45/262.75 % SZS output start Proof
% 262.45/262.75 tff(less_type, type, (
% 262.45/262.75 less: ( $i * $i ) > $o)).
% 262.45/262.75 tff(n5_type, type, (
% 262.45/262.75 n5: $i)).
% 262.45/262.75 tff(n4_type, type, (
% 262.45/262.75 n4: $i)).
% 262.45/262.75 tff(rdn_positive_less_type, type, (
% 262.45/262.75 rdn_positive_less: ( $i * $i ) > $o)).
% 262.45/262.75 tff(rdn_translate_type, type, (
% 262.45/262.75 rdn_translate: ( $i * $i ) > $o)).
% 262.45/262.75 tff(rdn_pos_type, type, (
% 262.45/262.75 rdn_pos: $i > $i)).
% 262.45/262.75 tff(rdnn_type, type, (
% 262.45/262.75 rdnn: $i > $i)).
% 262.45/262.75 tff(accept_population_type, type, (
% 262.45/262.75 accept_population: ( $i * $i * $i ) > $o)).
% 262.45/262.75 tff(other_type, type, (
% 262.45/262.75 other: $i)).
% 262.45/262.75 tff(countrybcivilorganization_type, type, (
% 262.45/262.75 countrybcivilorganization: $i)).
% 262.45/262.75 tff(n7_type, type, (
% 262.45/262.75 n7: $i)).
% 262.45/262.75 tff(muslim_type, type, (
% 262.45/262.75 muslim: $i)).
% 262.45/262.75 tff(n65_type, type, (
% 262.45/262.75 n65: $i)).
% 262.45/262.75 tff(rdn_type, type, (
% 262.45/262.75 rdn: ( $i * $i ) > $i)).
% 262.45/262.75 tff(n6_type, type, (
% 262.45/262.75 n6: $i)).
% 262.45/262.75 tff(rdn_non_zero_type, type, (
% 262.45/262.75 rdn_non_zero: $i > $o)).
% 262.45/262.75 tff(rdn_non_zero_digit_type, type, (
% 262.45/262.75 rdn_non_zero_digit: $i > $o)).
% 262.45/262.75 tff(atheist_type, type, (
% 262.45/262.75 atheist: $i)).
% 262.45/262.75 tff(n75_type, type, (
% 262.45/262.75 n75: $i)).
% 262.45/262.75 tff(native_type, type, (
% 262.45/262.75 native: $i)).
% 262.45/262.75 tff(n85_type, type, (
% 262.45/262.75 n85: $i)).
% 262.45/262.75 tff(n8_type, type, (
% 262.45/262.75 n8: $i)).
% 262.45/262.75 tff(n20_type, type, (
% 262.45/262.75 n20: $i)).
% 262.45/262.75 tff(christian_type, type, (
% 262.45/262.75 christian: $i)).
% 262.45/262.75 tff(accept_city_type, type, (
% 262.45/262.75 accept_city: ( $i * $i ) > $o)).
% 262.45/262.75 tff(suffertown_type, type, (
% 262.45/262.75 suffertown: $i)).
% 262.45/262.75 tff(accept_number_type, type, (
% 262.45/262.75 accept_number: ( $i * $i ) > $o)).
% 262.45/262.75 tff(accept_leader_type, type, (
% 262.45/262.75 accept_leader: ( $i * $i ) > $o)).
% 262.45/262.75 tff(countrybhumanitarianorganization_type, type, (
% 262.45/262.75 countrybhumanitarianorganization: $i)).
% 262.45/262.75 tff(accept_team_type, type, (
% 262.45/262.75 accept_team: ( $i * $i * $i * $i ) > $o)).
% 262.45/262.75 tff(1,assumption,(~less(n4, n5)), introduced(assumption)).
% 262.45/262.75 tff(2,plain,
% 262.45/262.75 (^[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))))),
% 262.45/262.75 inference(bind,[status(th)],[])).
% 262.45/262.75 tff(3,plain,
% 262.45/262.75 (![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)))),
% 262.45/262.75 inference(quant_intro,[status(thm)],[2])).
% 262.45/262.75 tff(4,plain,
% 262.45/262.75 (^[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)))))),
% 262.45/262.75 inference(bind,[status(th)],[])).
% 262.45/262.75 tff(5,plain,
% 262.45/262.75 (![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)))),
% 262.45/262.75 inference(quant_intro,[status(thm)],[4])).
% 262.45/262.75 tff(6,plain,
% 262.45/262.75 (![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))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(7,plain,
% 262.45/262.75 (^[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))))),
% 262.45/262.75 inference(bind,[status(th)],[])).
% 262.45/262.75 tff(8,plain,
% 262.45/262.75 (![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))),
% 262.45/262.75 inference(quant_intro,[status(thm)],[7])).
% 262.45/262.75 tff(9,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/sandbox2/benchmark/Axioms/NUM005+1.ax','less_entry_point_pos_pos')).
% 262.45/262.75 tff(10,plain,
% 262.45/262.75 (![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))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[9, 8])).
% 262.45/262.75 tff(11,plain,
% 262.45/262.75 (![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))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[10, 6])).
% 262.45/262.75 tff(12,plain,(
% 262.45/262.75 ![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))),
% 262.45/262.75 inference(skolemize,[status(sab)],[11])).
% 262.45/262.75 tff(13,plain,
% 262.45/262.75 (![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)))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[12, 5])).
% 262.45/262.75 tff(14,plain,
% 262.45/262.75 (![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)))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[13, 3])).
% 262.45/262.75 tff(15,plain,
% 262.45/262.75 (rdn_positive_less(rdnn(n4), rdnn(n5)) <=> rdn_positive_less(rdnn(n4), rdnn(n5))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(16,axiom,(rdn_positive_less(rdnn(n4), rdnn(n5))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax','rdn_positive_less45')).
% 262.45/262.75 tff(17,plain,
% 262.45/262.75 (rdn_positive_less(rdnn(n4), rdnn(n5))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[16, 15])).
% 262.45/262.75 tff(18,plain,
% 262.45/262.75 (rdn_translate(n5, rdn_pos(rdnn(n5))) <=> rdn_translate(n5, rdn_pos(rdnn(n5)))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(19,axiom,(rdn_translate(n5, rdn_pos(rdnn(n5)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax','rdn5')).
% 262.45/262.75 tff(20,plain,
% 262.45/262.75 (rdn_translate(n5, rdn_pos(rdnn(n5)))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[19, 18])).
% 262.45/262.75 tff(21,plain,
% 262.45/262.75 (rdn_translate(n4, rdn_pos(rdnn(n4))) <=> rdn_translate(n4, rdn_pos(rdnn(n4)))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(22,axiom,(rdn_translate(n4, rdn_pos(rdnn(n4)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax','rdn4')).
% 262.45/262.75 tff(23,plain,
% 262.45/262.75 (rdn_translate(n4, rdn_pos(rdnn(n4)))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[22, 21])).
% 262.45/262.75 tff(24,plain,
% 262.45/262.75 (((~![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(n4), rdnn(n5))) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | less(n4, n5) | (~rdn_translate(n5, rdn_pos(rdnn(n5)))))) <=> ((~![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(n4), rdnn(n5))) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | less(n4, n5) | (~rdn_translate(n5, rdn_pos(rdnn(n5)))))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(25,plain,
% 262.45/262.75 ((less(n4, n5) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | (~rdn_translate(n5, rdn_pos(rdnn(n5)))) | (~rdn_positive_less(rdnn(n4), rdnn(n5)))) <=> ((~rdn_positive_less(rdnn(n4), rdnn(n5))) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | less(n4, n5) | (~rdn_translate(n5, rdn_pos(rdnn(n5)))))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(26,plain,
% 262.45/262.75 (((~![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(n4, n5) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | (~rdn_translate(n5, rdn_pos(rdnn(n5)))) | (~rdn_positive_less(rdnn(n4), rdnn(n5))))) <=> ((~![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(n4), rdnn(n5))) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | less(n4, n5) | (~rdn_translate(n5, rdn_pos(rdnn(n5))))))),
% 262.45/262.75 inference(monotonicity,[status(thm)],[25])).
% 262.45/262.75 tff(27,plain,
% 262.45/262.75 (((~![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(n4, n5) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | (~rdn_translate(n5, rdn_pos(rdnn(n5)))) | (~rdn_positive_less(rdnn(n4), rdnn(n5))))) <=> ((~![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(n4), rdnn(n5))) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | less(n4, n5) | (~rdn_translate(n5, rdn_pos(rdnn(n5)))))),
% 262.45/262.75 inference(transitivity,[status(thm)],[26, 24])).
% 262.45/262.75 tff(28,plain,
% 262.45/262.75 ((~![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(n4, n5) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | (~rdn_translate(n5, rdn_pos(rdnn(n5)))) | (~rdn_positive_less(rdnn(n4), rdnn(n5))))),
% 262.45/262.75 inference(quant_inst,[status(thm)],[])).
% 262.45/262.75 tff(29,plain,
% 262.45/262.75 ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (~rdn_positive_less(rdnn(n4), rdnn(n5))) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | less(n4, n5) | (~rdn_translate(n5, rdn_pos(rdnn(n5))))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[28, 27])).
% 262.45/262.75 tff(30,plain,
% 262.45/262.75 ($false),
% 262.45/262.75 inference(unit_resolution,[status(thm)],[29, 23, 20, 17, 14, 1])).
% 262.45/262.75 tff(31,plain,(less(n4, n5)), inference(lemma,lemma(discharge,[]))).
% 262.45/262.75 tff(32,assumption,(~less(n7, n65)), introduced(assumption)).
% 262.45/262.75 tff(33,plain,
% 262.45/262.75 (^[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)))))),
% 262.45/262.75 inference(bind,[status(th)],[])).
% 262.45/262.75 tff(34,plain,
% 262.45/262.75 (![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))))),
% 262.45/262.75 inference(quant_intro,[status(thm)],[33])).
% 262.45/262.75 tff(35,plain,
% 262.45/262.75 (![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))))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(36,plain,
% 262.45/262.75 (^[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)))))),
% 262.45/262.75 inference(bind,[status(th)],[])).
% 262.45/262.75 tff(37,plain,
% 262.45/262.75 (![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))))),
% 262.45/262.75 inference(quant_intro,[status(thm)],[36])).
% 262.45/262.75 tff(38,axiom,(![X: $i] : (rdn_non_zero_digit(rdnn(X)) => rdn_non_zero(rdnn(X)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax','rdn_non_zero_by_digit')).
% 262.45/262.75 tff(39,plain,
% 262.45/262.75 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[38, 37])).
% 262.45/262.75 tff(40,plain,
% 262.45/262.75 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[39, 35])).
% 262.45/262.75 tff(41,plain,(
% 262.45/262.75 ![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 262.45/262.75 inference(skolemize,[status(sab)],[40])).
% 262.45/262.75 tff(42,plain,
% 262.45/262.75 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[41, 34])).
% 262.45/262.75 tff(43,plain,
% 262.45/262.75 (rdn_non_zero_digit(rdnn(n6)) <=> rdn_non_zero_digit(rdnn(n6))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(44,axiom,(rdn_non_zero_digit(rdnn(n6))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax','rdn_digit6')).
% 262.45/262.75 tff(45,plain,
% 262.45/262.75 (rdn_non_zero_digit(rdnn(n6))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[44, 43])).
% 262.45/262.75 tff(46,plain,
% 262.45/262.75 (((~![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))))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(47,plain,
% 262.45/262.75 ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | (rdn_non_zero(rdnn(n6)) | (~rdn_non_zero_digit(rdnn(n6))))),
% 262.45/262.75 inference(quant_inst,[status(thm)],[])).
% 262.45/262.75 tff(48,plain,
% 262.45/262.75 ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | rdn_non_zero(rdnn(n6)) | (~rdn_non_zero_digit(rdnn(n6)))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[47, 46])).
% 262.45/262.75 tff(49,plain,
% 262.45/262.75 (rdn_non_zero(rdnn(n6))),
% 262.45/262.75 inference(unit_resolution,[status(thm)],[48, 45, 42])).
% 262.45/262.75 tff(50,plain,
% 262.45/262.75 (^[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))))),
% 262.45/262.75 inference(bind,[status(th)],[])).
% 262.45/262.75 tff(51,plain,
% 262.45/262.75 (![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)))),
% 262.45/262.75 inference(quant_intro,[status(thm)],[50])).
% 262.45/262.75 tff(52,plain,
% 262.45/262.75 (![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)))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(53,plain,
% 262.45/262.75 (^[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))))),
% 262.45/262.75 inference(bind,[status(th)],[])).
% 262.45/262.75 tff(54,plain,
% 262.45/262.75 (![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)))),
% 262.45/262.75 inference(quant_intro,[status(thm)],[53])).
% 262.45/262.75 tff(55,axiom,(![D: $i, Db: $i, Ob: $i] : (rdn_non_zero(Ob) => rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax','rdn_extra_digits_positive_less')).
% 262.45/262.75 tff(56,plain,
% 262.45/262.75 (![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[55, 54])).
% 262.45/262.75 tff(57,plain,
% 262.45/262.75 (![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[56, 52])).
% 262.45/262.75 tff(58,plain,(
% 262.45/262.75 ![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))),
% 262.45/262.75 inference(skolemize,[status(sab)],[57])).
% 262.45/262.75 tff(59,plain,
% 262.45/262.75 (![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[58, 51])).
% 262.45/262.75 tff(60,plain,
% 262.45/262.75 (((~![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(n7), 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(n7), rdn(rdnn(n5), rdnn(n6))))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(61,plain,
% 262.45/262.75 ((~![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(n7), rdn(rdnn(n5), rdnn(n6))))),
% 262.45/262.75 inference(quant_inst,[status(thm)],[])).
% 262.45/262.75 tff(62,plain,
% 262.45/262.75 ((~![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(n7), rdn(rdnn(n5), rdnn(n6)))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[61, 60])).
% 262.45/262.75 tff(63,plain,
% 262.45/262.75 (rdn_positive_less(rdnn(n7), rdn(rdnn(n5), rdnn(n6)))),
% 262.45/262.75 inference(unit_resolution,[status(thm)],[62, 59, 49])).
% 262.45/262.75 tff(64,plain,
% 262.45/262.75 (rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6)))) <=> rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(65,axiom,(rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax','rdn65')).
% 262.45/262.75 tff(66,plain,
% 262.45/262.75 (rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[65, 64])).
% 262.45/262.75 tff(67,plain,
% 262.45/262.75 (rdn_translate(n7, rdn_pos(rdnn(n7))) <=> rdn_translate(n7, rdn_pos(rdnn(n7)))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(68,axiom,(rdn_translate(n7, rdn_pos(rdnn(n7)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax','rdn7')).
% 262.45/262.75 tff(69,plain,
% 262.45/262.75 (rdn_translate(n7, rdn_pos(rdnn(n7)))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[68, 67])).
% 262.45/262.75 tff(70,plain,
% 262.45/262.75 (((~![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(n7), rdn(rdnn(n5), rdnn(n6)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | less(n7, n65) | (~rdn_translate(n7, rdn_pos(rdnn(n7)))))) <=> ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (~rdn_positive_less(rdnn(n7), rdn(rdnn(n5), rdnn(n6)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | less(n7, n65) | (~rdn_translate(n7, rdn_pos(rdnn(n7)))))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(71,plain,
% 262.45/262.75 ((less(n7, n65) | (~rdn_translate(n7, rdn_pos(rdnn(n7)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | (~rdn_positive_less(rdnn(n7), rdn(rdnn(n5), rdnn(n6))))) <=> ((~rdn_positive_less(rdnn(n7), rdn(rdnn(n5), rdnn(n6)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | less(n7, n65) | (~rdn_translate(n7, rdn_pos(rdnn(n7)))))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(72,plain,
% 262.45/262.75 (((~![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(n7, n65) | (~rdn_translate(n7, rdn_pos(rdnn(n7)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | (~rdn_positive_less(rdnn(n7), 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(n7), rdn(rdnn(n5), rdnn(n6)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | less(n7, n65) | (~rdn_translate(n7, rdn_pos(rdnn(n7))))))),
% 262.45/262.75 inference(monotonicity,[status(thm)],[71])).
% 262.45/262.75 tff(73,plain,
% 262.45/262.75 (((~![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(n7, n65) | (~rdn_translate(n7, rdn_pos(rdnn(n7)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | (~rdn_positive_less(rdnn(n7), 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(n7), rdn(rdnn(n5), rdnn(n6)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | less(n7, n65) | (~rdn_translate(n7, rdn_pos(rdnn(n7)))))),
% 262.45/262.75 inference(transitivity,[status(thm)],[72, 70])).
% 262.45/262.75 tff(74,plain,
% 262.45/262.75 ((~![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(n7, n65) | (~rdn_translate(n7, rdn_pos(rdnn(n7)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | (~rdn_positive_less(rdnn(n7), rdn(rdnn(n5), rdnn(n6)))))),
% 262.45/262.75 inference(quant_inst,[status(thm)],[])).
% 262.45/262.75 tff(75,plain,
% 262.45/262.75 ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (~rdn_positive_less(rdnn(n7), rdn(rdnn(n5), rdnn(n6)))) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | less(n7, n65) | (~rdn_translate(n7, rdn_pos(rdnn(n7))))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[74, 73])).
% 262.45/262.75 tff(76,plain,
% 262.45/262.75 ($false),
% 262.45/262.75 inference(unit_resolution,[status(thm)],[75, 69, 66, 14, 63, 32])).
% 262.45/262.75 tff(77,plain,(less(n7, n65)), inference(lemma,lemma(discharge,[]))).
% 262.45/262.75 tff(78,assumption,(~accept_population(countrybcivilorganization, muslim, n7)), introduced(assumption)).
% 262.45/262.75 tff(79,plain,
% 262.45/262.75 (accept_population(countrybcivilorganization, muslim, n65) <=> accept_population(countrybcivilorganization, muslim, n65)),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(80,axiom,(accept_population(countrybcivilorganization, muslim, n65)), file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+2.ax','deduced_45')).
% 262.45/262.75 tff(81,plain,
% 262.45/262.75 (accept_population(countrybcivilorganization, muslim, n65)),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[80, 79])).
% 262.45/262.75 tff(82,plain,
% 262.45/262.75 (^[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))))),
% 262.45/262.75 inference(bind,[status(th)],[])).
% 262.45/262.75 tff(83,plain,
% 262.45/262.75 (![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)))),
% 262.45/262.75 inference(quant_intro,[status(thm)],[82])).
% 262.45/262.75 tff(84,plain,
% 262.45/262.75 (^[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)))))),
% 262.45/262.75 inference(bind,[status(th)],[])).
% 262.45/262.75 tff(85,plain,
% 262.45/262.75 (![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)))),
% 262.45/262.75 inference(quant_intro,[status(thm)],[84])).
% 262.45/262.75 tff(86,plain,
% 262.45/262.75 (![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))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(87,plain,
% 262.45/262.75 (^[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)))),
% 262.45/262.75 inference(bind,[status(th)],[])).
% 262.45/262.75 tff(88,plain,
% 262.45/262.75 (![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))),
% 262.45/262.75 inference(quant_intro,[status(thm)],[87])).
% 262.45/262.75 tff(89,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/sandbox2/benchmark/Axioms/AGT001+0.ax','a1_3')).
% 262.45/262.75 tff(90,plain,
% 262.45/262.75 (![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[89, 88])).
% 262.45/262.75 tff(91,plain,
% 262.45/262.75 (![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[90, 86])).
% 262.45/262.75 tff(92,plain,(
% 262.45/262.75 ![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 262.45/262.75 inference(skolemize,[status(sab)],[91])).
% 262.45/262.75 tff(93,plain,
% 262.45/262.75 (![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[92, 85])).
% 262.45/262.75 tff(94,plain,
% 262.45/262.75 (![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[93, 83])).
% 262.45/262.75 tff(95,plain,
% 262.45/262.75 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countrybcivilorganization, muslim, n7) | (~less(n7, n65)) | (~accept_population(countrybcivilorganization, muslim, n65)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | accept_population(countrybcivilorganization, muslim, n7) | (~less(n7, n65)) | (~accept_population(countrybcivilorganization, muslim, n65)))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(96,plain,
% 262.45/262.75 ((accept_population(countrybcivilorganization, muslim, n7) | (~accept_population(countrybcivilorganization, muslim, n65)) | (~less(n7, n65))) <=> (accept_population(countrybcivilorganization, muslim, n7) | (~less(n7, n65)) | (~accept_population(countrybcivilorganization, muslim, n65)))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(97,plain,
% 262.45/262.75 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countrybcivilorganization, muslim, n7) | (~accept_population(countrybcivilorganization, muslim, n65)) | (~less(n7, n65)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countrybcivilorganization, muslim, n7) | (~less(n7, n65)) | (~accept_population(countrybcivilorganization, muslim, n65))))),
% 262.45/262.75 inference(monotonicity,[status(thm)],[96])).
% 262.45/262.75 tff(98,plain,
% 262.45/262.75 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countrybcivilorganization, muslim, n7) | (~accept_population(countrybcivilorganization, muslim, n65)) | (~less(n7, n65)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | accept_population(countrybcivilorganization, muslim, n7) | (~less(n7, n65)) | (~accept_population(countrybcivilorganization, muslim, n65)))),
% 262.45/262.75 inference(transitivity,[status(thm)],[97, 95])).
% 262.45/262.75 tff(99,plain,
% 262.45/262.75 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countrybcivilorganization, muslim, n7) | (~accept_population(countrybcivilorganization, muslim, n65)) | (~less(n7, n65)))),
% 262.45/262.75 inference(quant_inst,[status(thm)],[])).
% 262.45/262.75 tff(100,plain,
% 262.45/262.75 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | accept_population(countrybcivilorganization, muslim, n7) | (~less(n7, n65)) | (~accept_population(countrybcivilorganization, muslim, n65))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[99, 98])).
% 262.45/262.75 tff(101,plain,
% 262.45/262.75 ($false),
% 262.45/262.75 inference(unit_resolution,[status(thm)],[100, 94, 81, 78, 77])).
% 262.45/262.75 tff(102,plain,(accept_population(countrybcivilorganization, muslim, n7)), inference(lemma,lemma(discharge,[]))).
% 262.45/262.75 tff(103,assumption,(~less(n65, n75)), introduced(assumption)).
% 262.45/262.75 tff(104,plain,
% 262.45/262.75 (^[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))))),
% 262.45/262.75 inference(bind,[status(th)],[])).
% 262.45/262.75 tff(105,plain,
% 262.45/262.75 (![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)))),
% 262.45/262.75 inference(quant_intro,[status(thm)],[104])).
% 262.45/262.75 tff(106,plain,
% 262.45/262.75 (![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)))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(107,plain,
% 262.45/262.75 (^[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))))),
% 262.45/262.75 inference(bind,[status(th)],[])).
% 262.45/262.75 tff(108,plain,
% 262.45/262.75 (![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)))),
% 262.45/262.75 inference(quant_intro,[status(thm)],[107])).
% 262.45/262.75 tff(109,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/sandbox2/benchmark/Axioms/NUM005+1.ax','rdn_positive_less_multi_digit_high')).
% 262.45/262.75 tff(110,plain,
% 262.45/262.75 (![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob)))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[109, 108])).
% 262.45/262.75 tff(111,plain,
% 262.45/262.75 (![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob)))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[110, 106])).
% 262.45/262.75 tff(112,plain,(
% 262.45/262.75 ![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob)))),
% 262.45/262.75 inference(skolemize,[status(sab)],[111])).
% 262.45/262.75 tff(113,plain,
% 262.45/262.75 (![Ds: $i, Os: $i, Db: $i, Ob: $i] : ((~rdn_positive_less(Os, Ob)) | rdn_positive_less(rdn(rdnn(Ds), Os), rdn(rdnn(Db), Ob)))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[112, 105])).
% 262.45/262.75 tff(114,plain,
% 262.45/262.75 (rdn_positive_less(rdnn(n6), rdnn(n7)) <=> rdn_positive_less(rdnn(n6), rdnn(n7))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(115,axiom,(rdn_positive_less(rdnn(n6), rdnn(n7))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax','rdn_positive_less67')).
% 262.45/262.75 tff(116,plain,
% 262.45/262.75 (rdn_positive_less(rdnn(n6), rdnn(n7))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[115, 114])).
% 262.45/262.75 tff(117,plain,
% 262.45/262.75 (((~![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(n6), rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n6)), rdn(rdnn(n5), 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(n6), rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n6)), rdn(rdnn(n5), rdnn(n7))))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(118,plain,
% 262.45/262.75 ((~![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(n6), rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n6)), rdn(rdnn(n5), rdnn(n7))))),
% 262.45/262.75 inference(quant_inst,[status(thm)],[])).
% 262.45/262.75 tff(119,plain,
% 262.45/262.75 ((~![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(n6), rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n6)), rdn(rdnn(n5), rdnn(n7)))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[118, 117])).
% 262.45/262.75 tff(120,plain,
% 262.45/262.75 (rdn_positive_less(rdn(rdnn(n5), rdnn(n6)), rdn(rdnn(n5), rdnn(n7)))),
% 262.45/262.75 inference(unit_resolution,[status(thm)],[119, 116, 113])).
% 262.45/262.75 tff(121,plain,
% 262.45/262.75 (rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7)))) <=> rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(122,axiom,(rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax','rdn75')).
% 262.45/262.75 tff(123,plain,
% 262.45/262.75 (rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))),
% 262.45/262.75 inference(modus_ponens,[status(thm)],[122, 121])).
% 262.45/262.75 tff(124,plain,
% 262.45/262.75 (((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | ((~rdn_positive_less(rdn(rdnn(n5), rdnn(n6)), rdn(rdnn(n5), rdnn(n7)))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n65, n75) | (~rdn_translate(n65, rdn_pos(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(rdn(rdnn(n5), rdnn(n6)), rdn(rdnn(n5), rdnn(n7)))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n65, n75) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(125,plain,
% 262.45/262.75 ((less(n65, n75) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n6)), rdn(rdnn(n5), rdnn(n7))))) <=> ((~rdn_positive_less(rdn(rdnn(n5), rdnn(n6)), rdn(rdnn(n5), rdnn(n7)))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n65, n75) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))))),
% 262.45/262.75 inference(rewrite,[status(thm)],[])).
% 262.45/262.75 tff(126,plain,
% 262.45/262.75 (((~![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(n65, n75) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n6)), rdn(rdnn(n5), rdnn(n7)))))) <=> ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | ((~rdn_positive_less(rdn(rdnn(n5), rdnn(n6)), rdn(rdnn(n5), rdnn(n7)))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n65, n75) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6)))))))),
% 262.45/262.76 inference(monotonicity,[status(thm)],[125])).
% 262.45/262.76 tff(127,plain,
% 262.45/262.76 (((~![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(n65, n75) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n6)), rdn(rdnn(n5), rdnn(n7)))))) <=> ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n6)), rdn(rdnn(n5), rdnn(n7)))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n65, n75) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))))),
% 262.45/262.76 inference(transitivity,[status(thm)],[126, 124])).
% 262.45/262.76 tff(128,plain,
% 262.45/262.76 ((~![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(n65, n75) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6))))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n6)), rdn(rdnn(n5), rdnn(n7)))))),
% 262.45/262.76 inference(quant_inst,[status(thm)],[])).
% 262.45/262.76 tff(129,plain,
% 262.45/262.76 ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n6)), rdn(rdnn(n5), rdnn(n7)))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n65, n75) | (~rdn_translate(n65, rdn_pos(rdn(rdnn(n5), rdnn(n6)))))),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[128, 127])).
% 262.45/262.76 tff(130,plain,
% 262.45/262.76 ($false),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[129, 66, 123, 14, 120, 103])).
% 262.45/262.76 tff(131,plain,(less(n65, n75)), inference(lemma,lemma(discharge,[]))).
% 262.45/262.76 tff(132,assumption,(~accept_population(countrybcivilorganization, atheist, n65)), introduced(assumption)).
% 262.45/262.76 tff(133,plain,
% 262.45/262.76 (accept_population(countrybcivilorganization, atheist, n75) <=> accept_population(countrybcivilorganization, atheist, n75)),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(134,axiom,(accept_population(countrybcivilorganization, atheist, n75)), file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+2.ax','deduced_299')).
% 262.45/262.76 tff(135,plain,
% 262.45/262.76 (accept_population(countrybcivilorganization, atheist, n75)),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[134, 133])).
% 262.45/262.76 tff(136,plain,
% 262.45/262.76 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | ((~accept_population(countrybcivilorganization, atheist, n75)) | accept_population(countrybcivilorganization, atheist, n65) | (~less(n65, n75)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (~accept_population(countrybcivilorganization, atheist, n75)) | accept_population(countrybcivilorganization, atheist, n65) | (~less(n65, n75)))),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(137,plain,
% 262.45/262.76 ((accept_population(countrybcivilorganization, atheist, n65) | (~accept_population(countrybcivilorganization, atheist, n75)) | (~less(n65, n75))) <=> ((~accept_population(countrybcivilorganization, atheist, n75)) | accept_population(countrybcivilorganization, atheist, n65) | (~less(n65, n75)))),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(138,plain,
% 262.45/262.76 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countrybcivilorganization, atheist, n65) | (~accept_population(countrybcivilorganization, atheist, n75)) | (~less(n65, n75)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | ((~accept_population(countrybcivilorganization, atheist, n75)) | accept_population(countrybcivilorganization, atheist, n65) | (~less(n65, n75))))),
% 262.45/262.76 inference(monotonicity,[status(thm)],[137])).
% 262.45/262.76 tff(139,plain,
% 262.45/262.76 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countrybcivilorganization, atheist, n65) | (~accept_population(countrybcivilorganization, atheist, n75)) | (~less(n65, n75)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (~accept_population(countrybcivilorganization, atheist, n75)) | accept_population(countrybcivilorganization, atheist, n65) | (~less(n65, n75)))),
% 262.45/262.76 inference(transitivity,[status(thm)],[138, 136])).
% 262.45/262.76 tff(140,plain,
% 262.45/262.76 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countrybcivilorganization, atheist, n65) | (~accept_population(countrybcivilorganization, atheist, n75)) | (~less(n65, n75)))),
% 262.45/262.76 inference(quant_inst,[status(thm)],[])).
% 262.45/262.76 tff(141,plain,
% 262.45/262.76 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (~accept_population(countrybcivilorganization, atheist, n75)) | accept_population(countrybcivilorganization, atheist, n65) | (~less(n65, n75))),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[140, 139])).
% 262.45/262.76 tff(142,plain,
% 262.45/262.76 ($false),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[141, 94, 135, 132, 131])).
% 262.45/262.76 tff(143,plain,(accept_population(countrybcivilorganization, atheist, n65)), inference(lemma,lemma(discharge,[]))).
% 262.45/262.76 tff(144,assumption,(~less(n4, n85)), introduced(assumption)).
% 262.45/262.76 tff(145,plain,
% 262.45/262.76 (rdn_non_zero_digit(rdnn(n8)) <=> rdn_non_zero_digit(rdnn(n8))),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(146,axiom,(rdn_non_zero_digit(rdnn(n8))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax','rdn_digit8')).
% 262.45/262.76 tff(147,plain,
% 262.45/262.76 (rdn_non_zero_digit(rdnn(n8))),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[146, 145])).
% 262.45/262.76 tff(148,plain,
% 262.45/262.76 (((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | (rdn_non_zero(rdnn(n8)) | (~rdn_non_zero_digit(rdnn(n8))))) <=> ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | rdn_non_zero(rdnn(n8)) | (~rdn_non_zero_digit(rdnn(n8))))),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(149,plain,
% 262.45/262.76 ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | (rdn_non_zero(rdnn(n8)) | (~rdn_non_zero_digit(rdnn(n8))))),
% 262.45/262.76 inference(quant_inst,[status(thm)],[])).
% 262.45/262.76 tff(150,plain,
% 262.45/262.76 ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | rdn_non_zero(rdnn(n8)) | (~rdn_non_zero_digit(rdnn(n8)))),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[149, 148])).
% 262.45/262.76 tff(151,plain,
% 262.45/262.76 (rdn_non_zero(rdnn(n8))),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[150, 147, 42])).
% 262.45/262.76 tff(152,plain,
% 262.45/262.76 (((~![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))) | ((~rdn_non_zero(rdnn(n8))) | rdn_positive_less(rdnn(n4), rdn(rdnn(n5), rdnn(n8))))) <=> ((~![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))) | (~rdn_non_zero(rdnn(n8))) | rdn_positive_less(rdnn(n4), rdn(rdnn(n5), rdnn(n8))))),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(153,plain,
% 262.45/262.76 ((~![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))) | ((~rdn_non_zero(rdnn(n8))) | rdn_positive_less(rdnn(n4), rdn(rdnn(n5), rdnn(n8))))),
% 262.45/262.76 inference(quant_inst,[status(thm)],[])).
% 262.45/262.76 tff(154,plain,
% 262.45/262.76 ((~![D: $i, Db: $i, Ob: $i] : ((~rdn_non_zero(Ob)) | rdn_positive_less(rdnn(D), rdn(rdnn(Db), Ob)))) | (~rdn_non_zero(rdnn(n8))) | rdn_positive_less(rdnn(n4), rdn(rdnn(n5), rdnn(n8)))),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[153, 152])).
% 262.45/262.76 tff(155,plain,
% 262.45/262.76 ((~rdn_non_zero(rdnn(n8))) | rdn_positive_less(rdnn(n4), rdn(rdnn(n5), rdnn(n8)))),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[154, 59])).
% 262.45/262.76 tff(156,plain,
% 262.45/262.76 (rdn_positive_less(rdnn(n4), rdn(rdnn(n5), rdnn(n8)))),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[155, 151])).
% 262.45/262.76 tff(157,plain,
% 262.45/262.76 (rdn_translate(n85, rdn_pos(rdn(rdnn(n5), rdnn(n8)))) <=> rdn_translate(n85, rdn_pos(rdn(rdnn(n5), rdnn(n8))))),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(158,axiom,(rdn_translate(n85, rdn_pos(rdn(rdnn(n5), rdnn(n8))))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax','rdn85')).
% 262.45/262.76 tff(159,plain,
% 262.45/262.76 (rdn_translate(n85, rdn_pos(rdn(rdnn(n5), rdnn(n8))))),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[158, 157])).
% 262.45/262.76 tff(160,plain,
% 262.45/262.76 (((~![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(n4), rdn(rdnn(n5), rdnn(n8)))) | (~rdn_translate(n85, rdn_pos(rdn(rdnn(n5), rdnn(n8))))) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | less(n4, n85))) <=> ((~![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(n4), rdn(rdnn(n5), rdnn(n8)))) | (~rdn_translate(n85, rdn_pos(rdn(rdnn(n5), rdnn(n8))))) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | less(n4, n85))),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(161,plain,
% 262.45/262.76 ((less(n4, n85) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | (~rdn_translate(n85, rdn_pos(rdn(rdnn(n5), rdnn(n8))))) | (~rdn_positive_less(rdnn(n4), rdn(rdnn(n5), rdnn(n8))))) <=> ((~rdn_positive_less(rdnn(n4), rdn(rdnn(n5), rdnn(n8)))) | (~rdn_translate(n85, rdn_pos(rdn(rdnn(n5), rdnn(n8))))) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | less(n4, n85))),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(162,plain,
% 262.45/262.76 (((~![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(n4, n85) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | (~rdn_translate(n85, rdn_pos(rdn(rdnn(n5), rdnn(n8))))) | (~rdn_positive_less(rdnn(n4), rdn(rdnn(n5), rdnn(n8)))))) <=> ((~![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(n4), rdn(rdnn(n5), rdnn(n8)))) | (~rdn_translate(n85, rdn_pos(rdn(rdnn(n5), rdnn(n8))))) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | less(n4, n85)))),
% 262.45/262.76 inference(monotonicity,[status(thm)],[161])).
% 262.45/262.76 tff(163,plain,
% 262.45/262.76 (((~![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(n4, n85) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | (~rdn_translate(n85, rdn_pos(rdn(rdnn(n5), rdnn(n8))))) | (~rdn_positive_less(rdnn(n4), rdn(rdnn(n5), rdnn(n8)))))) <=> ((~![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(n4), rdn(rdnn(n5), rdnn(n8)))) | (~rdn_translate(n85, rdn_pos(rdn(rdnn(n5), rdnn(n8))))) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | less(n4, n85))),
% 262.45/262.76 inference(transitivity,[status(thm)],[162, 160])).
% 262.45/262.76 tff(164,plain,
% 262.45/262.76 ((~![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(n4, n85) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | (~rdn_translate(n85, rdn_pos(rdn(rdnn(n5), rdnn(n8))))) | (~rdn_positive_less(rdnn(n4), rdn(rdnn(n5), rdnn(n8)))))),
% 262.45/262.76 inference(quant_inst,[status(thm)],[])).
% 262.45/262.76 tff(165,plain,
% 262.45/262.76 ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (~rdn_positive_less(rdnn(n4), rdn(rdnn(n5), rdnn(n8)))) | (~rdn_translate(n85, rdn_pos(rdn(rdnn(n5), rdnn(n8))))) | (~rdn_translate(n4, rdn_pos(rdnn(n4)))) | less(n4, n85)),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[164, 163])).
% 262.45/262.76 tff(166,plain,
% 262.45/262.76 ($false),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[165, 23, 159, 14, 156, 144])).
% 262.45/262.76 tff(167,plain,(less(n4, n85)), inference(lemma,lemma(discharge,[]))).
% 262.45/262.76 tff(168,assumption,(~accept_population(countrybcivilorganization, native, n4)), introduced(assumption)).
% 262.45/262.76 tff(169,plain,
% 262.45/262.76 (accept_population(countrybcivilorganization, native, n85) <=> accept_population(countrybcivilorganization, native, n85)),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(170,axiom,(accept_population(countrybcivilorganization, native, n85)), file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+2.ax','deduced_38')).
% 262.45/262.76 tff(171,plain,
% 262.45/262.76 (accept_population(countrybcivilorganization, native, n85)),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[170, 169])).
% 262.45/262.76 tff(172,plain,
% 262.45/262.76 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countrybcivilorganization, native, n4) | (~accept_population(countrybcivilorganization, native, n85)) | (~less(n4, n85)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | accept_population(countrybcivilorganization, native, n4) | (~accept_population(countrybcivilorganization, native, n85)) | (~less(n4, n85)))),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(173,plain,
% 262.45/262.76 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countrybcivilorganization, native, n4) | (~accept_population(countrybcivilorganization, native, n85)) | (~less(n4, n85)))),
% 262.45/262.76 inference(quant_inst,[status(thm)],[])).
% 262.45/262.76 tff(174,plain,
% 262.45/262.76 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | accept_population(countrybcivilorganization, native, n4) | (~accept_population(countrybcivilorganization, native, n85)) | (~less(n4, n85))),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[173, 172])).
% 262.45/262.76 tff(175,plain,
% 262.45/262.76 ($false),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[174, 94, 171, 168, 167])).
% 262.45/262.76 tff(176,plain,(accept_population(countrybcivilorganization, native, n4)), inference(lemma,lemma(discharge,[]))).
% 262.45/262.76 tff(177,plain,
% 262.45/262.76 (^[A: $i] : refl((~(((~accept_population(A, atheist, n65)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n7)) | (~accept_population(A, native, n4)) | (~accept_population(A, other, n4))) <=> accept_city(A, suffertown))) <=> (~(((~accept_population(A, atheist, n65)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n7)) | (~accept_population(A, native, n4)) | (~accept_population(A, other, n4))) <=> accept_city(A, suffertown))))),
% 262.45/262.76 inference(bind,[status(th)],[])).
% 262.45/262.76 tff(178,plain,
% 262.45/262.76 (![A: $i] : (~(((~accept_population(A, atheist, n65)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n7)) | (~accept_population(A, native, n4)) | (~accept_population(A, other, n4))) <=> accept_city(A, suffertown))) <=> ![A: $i] : (~(((~accept_population(A, atheist, n65)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n7)) | (~accept_population(A, native, n4)) | (~accept_population(A, other, n4))) <=> accept_city(A, suffertown)))),
% 262.45/262.76 inference(quant_intro,[status(thm)],[177])).
% 262.45/262.76 tff(179,plain,
% 262.45/262.76 (^[A: $i] : trans(trans(monotonicity(rewrite((accept_population(A, atheist, n65) & accept_population(A, christian, n20) & accept_population(A, muslim, n7) & accept_population(A, native, n4) & accept_population(A, other, n4)) <=> (~((~accept_population(A, atheist, n65)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n7)) | (~accept_population(A, native, n4)) | (~accept_population(A, other, n4))))), (((accept_population(A, atheist, n65) & accept_population(A, christian, n20) & accept_population(A, muslim, n7) & accept_population(A, native, n4) & accept_population(A, other, n4)) <=> accept_city(A, suffertown)) <=> ((~((~accept_population(A, atheist, n65)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n7)) | (~accept_population(A, native, n4)) | (~accept_population(A, other, n4)))) <=> accept_city(A, suffertown)))), rewrite(((~((~accept_population(A, atheist, n65)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n7)) | (~accept_population(A, native, n4)) | (~accept_population(A, other, n4)))) <=> accept_city(A, suffertown)) <=> (~(((~accept_population(A, atheist, n65)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n7)) | (~accept_population(A, native, n4)) | (~accept_population(A, other, n4))) <=> accept_city(A, suffertown)))), (((accept_population(A, atheist, n65) & accept_population(A, christian, n20) & accept_population(A, muslim, n7) & accept_population(A, native, n4) & accept_population(A, other, n4)) <=> accept_city(A, suffertown)) <=> (~(((~accept_population(A, atheist, n65)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n7)) | (~accept_population(A, native, n4)) | (~accept_population(A, other, n4))) <=> accept_city(A, suffertown))))), rewrite((~(((~accept_population(A, atheist, n65)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n7)) | (~accept_population(A, native, n4)) | (~accept_population(A, other, n4))) <=> accept_city(A, suffertown))) <=> (~(((~accept_population(A, atheist, n65)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n7)) | (~accept_population(A, native, n4)) | (~accept_population(A, other, n4))) <=> accept_city(A, suffertown)))), (((accept_population(A, atheist, n65) & accept_population(A, christian, n20) & accept_population(A, muslim, n7) & accept_population(A, native, n4) & accept_population(A, other, n4)) <=> accept_city(A, suffertown)) <=> (~(((~accept_population(A, atheist, n65)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n7)) | (~accept_population(A, native, n4)) | (~accept_population(A, other, n4))) <=> accept_city(A, suffertown)))))),
% 262.45/262.76 inference(bind,[status(th)],[])).
% 262.45/262.76 tff(180,plain,
% 262.45/262.76 (![A: $i] : ((accept_population(A, atheist, n65) & accept_population(A, christian, n20) & accept_population(A, muslim, n7) & accept_population(A, native, n4) & accept_population(A, other, n4)) <=> accept_city(A, suffertown)) <=> ![A: $i] : (~(((~accept_population(A, atheist, n65)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n7)) | (~accept_population(A, native, n4)) | (~accept_population(A, other, n4))) <=> accept_city(A, suffertown)))),
% 262.45/262.76 inference(quant_intro,[status(thm)],[179])).
% 262.45/262.76 tff(181,plain,
% 262.45/262.76 (![A: $i] : ((accept_population(A, atheist, n65) & accept_population(A, christian, n20) & accept_population(A, muslim, n7) & accept_population(A, native, n4) & accept_population(A, other, n4)) <=> accept_city(A, suffertown)) <=> ![A: $i] : ((accept_population(A, atheist, n65) & accept_population(A, christian, n20) & accept_population(A, muslim, n7) & accept_population(A, native, n4) & accept_population(A, other, n4)) <=> accept_city(A, suffertown))),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(182,plain,
% 262.45/262.76 (^[A: $i] : rewrite((((((accept_population(A, atheist, n65) & accept_population(A, christian, n20)) & accept_population(A, muslim, n7)) & accept_population(A, native, n4)) & accept_population(A, other, n4)) <=> accept_city(A, suffertown)) <=> ((accept_population(A, atheist, n65) & accept_population(A, christian, n20) & accept_population(A, muslim, n7) & accept_population(A, native, n4) & accept_population(A, other, n4)) <=> accept_city(A, suffertown)))),
% 262.45/262.76 inference(bind,[status(th)],[])).
% 262.45/262.76 tff(183,plain,
% 262.45/262.76 (![A: $i] : (((((accept_population(A, atheist, n65) & accept_population(A, christian, n20)) & accept_population(A, muslim, n7)) & accept_population(A, native, n4)) & accept_population(A, other, n4)) <=> accept_city(A, suffertown)) <=> ![A: $i] : ((accept_population(A, atheist, n65) & accept_population(A, christian, n20) & accept_population(A, muslim, n7) & accept_population(A, native, n4) & accept_population(A, other, n4)) <=> accept_city(A, suffertown))),
% 262.45/262.76 inference(quant_intro,[status(thm)],[182])).
% 262.45/262.76 tff(184,axiom,(![A: $i] : (((((accept_population(A, atheist, n65) & accept_population(A, christian, n20)) & accept_population(A, muslim, n7)) & accept_population(A, native, n4)) & accept_population(A, other, n4)) <=> accept_city(A, suffertown))), file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+0.ax','a2_1')).
% 262.45/262.76 tff(185,plain,
% 262.45/262.76 (![A: $i] : ((accept_population(A, atheist, n65) & accept_population(A, christian, n20) & accept_population(A, muslim, n7) & accept_population(A, native, n4) & accept_population(A, other, n4)) <=> accept_city(A, suffertown))),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[184, 183])).
% 262.45/262.76 tff(186,plain,
% 262.45/262.76 (![A: $i] : ((accept_population(A, atheist, n65) & accept_population(A, christian, n20) & accept_population(A, muslim, n7) & accept_population(A, native, n4) & accept_population(A, other, n4)) <=> accept_city(A, suffertown))),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[185, 181])).
% 262.45/262.76 tff(187,plain,(
% 262.45/262.76 ![A: $i] : ((accept_population(A, atheist, n65) & accept_population(A, christian, n20) & accept_population(A, muslim, n7) & accept_population(A, native, n4) & accept_population(A, other, n4)) <=> accept_city(A, suffertown))),
% 262.45/262.76 inference(skolemize,[status(sab)],[186])).
% 262.45/262.76 tff(188,plain,
% 262.45/262.76 (![A: $i] : (~(((~accept_population(A, atheist, n65)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n7)) | (~accept_population(A, native, n4)) | (~accept_population(A, other, n4))) <=> accept_city(A, suffertown)))),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[187, 180])).
% 262.45/262.76 tff(189,plain,
% 262.45/262.76 (![A: $i] : (~(((~accept_population(A, atheist, n65)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n7)) | (~accept_population(A, native, n4)) | (~accept_population(A, other, n4))) <=> accept_city(A, suffertown)))),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[188, 178])).
% 262.45/262.76 tff(190,plain,
% 262.45/262.76 ((~![A: $i] : (~(((~accept_population(A, atheist, n65)) | (~accept_population(A, christian, n20)) | (~accept_population(A, muslim, n7)) | (~accept_population(A, native, n4)) | (~accept_population(A, other, n4))) <=> accept_city(A, suffertown)))) | (~(((~accept_population(countrybcivilorganization, atheist, n65)) | (~accept_population(countrybcivilorganization, christian, n20)) | (~accept_population(countrybcivilorganization, muslim, n7)) | (~accept_population(countrybcivilorganization, native, n4)) | (~accept_population(countrybcivilorganization, other, n4))) <=> accept_city(countrybcivilorganization, suffertown)))),
% 262.45/262.76 inference(quant_inst,[status(thm)],[])).
% 262.45/262.76 tff(191,plain,
% 262.45/262.76 (~(((~accept_population(countrybcivilorganization, atheist, n65)) | (~accept_population(countrybcivilorganization, christian, n20)) | (~accept_population(countrybcivilorganization, muslim, n7)) | (~accept_population(countrybcivilorganization, native, n4)) | (~accept_population(countrybcivilorganization, other, n4))) <=> accept_city(countrybcivilorganization, suffertown))),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[190, 189])).
% 262.45/262.76 tff(192,plain,
% 262.45/262.76 (^[A: $i, C: $i, N: $i, L: $i] : refl((~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N))) <=> (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N))))),
% 262.45/262.76 inference(bind,[status(th)],[])).
% 262.45/262.76 tff(193,plain,
% 262.45/262.76 (![A: $i, C: $i, N: $i, L: $i] : (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N))) <=> ![A: $i, C: $i, N: $i, L: $i] : (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))),
% 262.45/262.76 inference(quant_intro,[status(thm)],[192])).
% 262.45/262.76 tff(194,plain,
% 262.45/262.76 (^[A: $i, C: $i, N: $i, L: $i] : trans(trans(monotonicity(rewrite((accept_city(A, C) & accept_leader(A, L) & accept_number(A, N)) <=> (~((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))))), ((accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N))) <=> (accept_team(A, L, C, N) <=> (~((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))))))), rewrite((accept_team(A, L, C, N) <=> (~((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))))) <=> (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))), ((accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N))) <=> (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N))))), rewrite((~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N))) <=> (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))), ((accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N))) <=> (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))))),
% 262.45/262.76 inference(bind,[status(th)],[])).
% 262.45/262.76 tff(195,plain,
% 262.45/262.76 (![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N))) <=> ![A: $i, C: $i, N: $i, L: $i] : (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))),
% 262.45/262.76 inference(quant_intro,[status(thm)],[194])).
% 262.45/262.76 tff(196,plain,
% 262.45/262.76 (![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N))) <=> ![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N)))),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(197,plain,
% 262.45/262.76 (^[A: $i, C: $i, N: $i, L: $i] : rewrite((accept_team(A, L, C, N) <=> ((accept_city(A, C) & accept_leader(A, L)) & accept_number(A, N))) <=> (accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N))))),
% 262.45/262.76 inference(bind,[status(th)],[])).
% 262.45/262.76 tff(198,plain,
% 262.45/262.76 (![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> ((accept_city(A, C) & accept_leader(A, L)) & accept_number(A, N))) <=> ![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N)))),
% 262.45/262.76 inference(quant_intro,[status(thm)],[197])).
% 262.45/262.76 tff(199,axiom,(![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> ((accept_city(A, C) & accept_leader(A, L)) & accept_number(A, N)))), file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+0.ax','a1_1')).
% 262.45/262.76 tff(200,plain,
% 262.45/262.76 (![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N)))),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[199, 198])).
% 262.45/262.76 tff(201,plain,
% 262.45/262.76 (![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N)))),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[200, 196])).
% 262.45/262.76 tff(202,plain,(
% 262.45/262.76 ![A: $i, C: $i, N: $i, L: $i] : (accept_team(A, L, C, N) <=> (accept_city(A, C) & accept_leader(A, L) & accept_number(A, N)))),
% 262.45/262.76 inference(skolemize,[status(sab)],[201])).
% 262.45/262.76 tff(203,plain,
% 262.45/262.76 (![A: $i, C: $i, N: $i, L: $i] : (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[202, 195])).
% 262.45/262.76 tff(204,plain,
% 262.45/262.76 (![A: $i, C: $i, N: $i, L: $i] : (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[203, 193])).
% 262.45/262.76 tff(205,plain,
% 262.45/262.76 ((~![A: $i, C: $i, N: $i, L: $i] : (~(((~accept_city(A, C)) | (~accept_leader(A, L)) | (~accept_number(A, N))) <=> accept_team(A, L, C, N)))) | (~(((~accept_city(countrybcivilorganization, suffertown)) | (~accept_leader(countrybcivilorganization, countrybhumanitarianorganization)) | (~accept_number(countrybcivilorganization, n4))) <=> accept_team(countrybcivilorganization, countrybhumanitarianorganization, suffertown, n4)))),
% 262.45/262.76 inference(quant_inst,[status(thm)],[])).
% 262.45/262.76 tff(206,plain,
% 262.45/262.76 (~(((~accept_city(countrybcivilorganization, suffertown)) | (~accept_leader(countrybcivilorganization, countrybhumanitarianorganization)) | (~accept_number(countrybcivilorganization, n4))) <=> accept_team(countrybcivilorganization, countrybhumanitarianorganization, suffertown, n4))),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[205, 204])).
% 262.45/262.76 tff(207,plain,
% 262.45/262.76 ((~accept_team(countrybcivilorganization, countrybhumanitarianorganization, suffertown, n4)) <=> (~accept_team(countrybcivilorganization, countrybhumanitarianorganization, suffertown, n4))),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(208,axiom,(~accept_team(countrybcivilorganization, countrybhumanitarianorganization, suffertown, n4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','query_6')).
% 262.45/262.76 tff(209,plain,
% 262.45/262.76 (~accept_team(countrybcivilorganization, countrybhumanitarianorganization, suffertown, n4)),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[208, 207])).
% 262.45/262.76 tff(210,plain,
% 262.45/262.76 ((((~accept_city(countrybcivilorganization, suffertown)) | (~accept_leader(countrybcivilorganization, countrybhumanitarianorganization)) | (~accept_number(countrybcivilorganization, n4))) <=> accept_team(countrybcivilorganization, countrybhumanitarianorganization, suffertown, n4)) | ((~accept_city(countrybcivilorganization, suffertown)) | (~accept_leader(countrybcivilorganization, countrybhumanitarianorganization)) | (~accept_number(countrybcivilorganization, n4))) | accept_team(countrybcivilorganization, countrybhumanitarianorganization, suffertown, n4)),
% 262.45/262.76 inference(tautology,[status(thm)],[])).
% 262.45/262.76 tff(211,plain,
% 262.45/262.76 ((((~accept_city(countrybcivilorganization, suffertown)) | (~accept_leader(countrybcivilorganization, countrybhumanitarianorganization)) | (~accept_number(countrybcivilorganization, n4))) <=> accept_team(countrybcivilorganization, countrybhumanitarianorganization, suffertown, n4)) | ((~accept_city(countrybcivilorganization, suffertown)) | (~accept_leader(countrybcivilorganization, countrybhumanitarianorganization)) | (~accept_number(countrybcivilorganization, n4)))),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[210, 209])).
% 262.45/262.76 tff(212,plain,
% 262.45/262.76 ((~accept_city(countrybcivilorganization, suffertown)) | (~accept_leader(countrybcivilorganization, countrybhumanitarianorganization)) | (~accept_number(countrybcivilorganization, n4))),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[211, 206])).
% 262.45/262.76 tff(213,plain,
% 262.45/262.76 (accept_number(countrybcivilorganization, n4) <=> accept_number(countrybcivilorganization, n4)),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(214,axiom,(accept_number(countrybcivilorganization, n4)), file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+2.ax','deduced_327')).
% 262.45/262.76 tff(215,plain,
% 262.45/262.76 (accept_number(countrybcivilorganization, n4)),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[214, 213])).
% 262.45/262.76 tff(216,plain,
% 262.45/262.76 (accept_leader(countrybcivilorganization, countrybhumanitarianorganization) <=> accept_leader(countrybcivilorganization, countrybhumanitarianorganization)),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(217,axiom,(accept_leader(countrybcivilorganization, countrybhumanitarianorganization)), file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+2.ax','deduced_292')).
% 262.45/262.76 tff(218,plain,
% 262.45/262.76 (accept_leader(countrybcivilorganization, countrybhumanitarianorganization)),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[217, 216])).
% 262.45/262.76 tff(219,plain,
% 262.45/262.76 ((~((~accept_city(countrybcivilorganization, suffertown)) | (~accept_leader(countrybcivilorganization, countrybhumanitarianorganization)) | (~accept_number(countrybcivilorganization, n4)))) | (~accept_city(countrybcivilorganization, suffertown)) | (~accept_leader(countrybcivilorganization, countrybhumanitarianorganization)) | (~accept_number(countrybcivilorganization, n4))),
% 262.45/262.76 inference(tautology,[status(thm)],[])).
% 262.45/262.76 tff(220,plain,
% 262.45/262.76 ((~((~accept_city(countrybcivilorganization, suffertown)) | (~accept_leader(countrybcivilorganization, countrybhumanitarianorganization)) | (~accept_number(countrybcivilorganization, n4)))) | (~accept_city(countrybcivilorganization, suffertown))),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[219, 218, 215])).
% 262.45/262.76 tff(221,plain,
% 262.45/262.76 (~accept_city(countrybcivilorganization, suffertown)),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[220, 212])).
% 262.45/262.76 tff(222,plain,
% 262.45/262.76 ((((~accept_population(countrybcivilorganization, atheist, n65)) | (~accept_population(countrybcivilorganization, christian, n20)) | (~accept_population(countrybcivilorganization, muslim, n7)) | (~accept_population(countrybcivilorganization, native, n4)) | (~accept_population(countrybcivilorganization, other, n4))) <=> accept_city(countrybcivilorganization, suffertown)) | ((~accept_population(countrybcivilorganization, atheist, n65)) | (~accept_population(countrybcivilorganization, christian, n20)) | (~accept_population(countrybcivilorganization, muslim, n7)) | (~accept_population(countrybcivilorganization, native, n4)) | (~accept_population(countrybcivilorganization, other, n4))) | accept_city(countrybcivilorganization, suffertown)),
% 262.45/262.76 inference(tautology,[status(thm)],[])).
% 262.45/262.76 tff(223,plain,
% 262.45/262.76 ((~accept_population(countrybcivilorganization, atheist, n65)) | (~accept_population(countrybcivilorganization, christian, n20)) | (~accept_population(countrybcivilorganization, muslim, n7)) | (~accept_population(countrybcivilorganization, native, n4)) | (~accept_population(countrybcivilorganization, other, n4))),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[222, 221, 191])).
% 262.45/262.76 tff(224,plain,
% 262.45/262.76 (accept_population(countrybcivilorganization, christian, n20) <=> accept_population(countrybcivilorganization, christian, n20)),
% 262.45/262.76 inference(rewrite,[status(thm)],[])).
% 262.45/262.76 tff(225,axiom,(accept_population(countrybcivilorganization, christian, n20)), file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+2.ax','deduced_51')).
% 262.45/262.76 tff(226,plain,
% 262.45/262.76 (accept_population(countrybcivilorganization, christian, n20)),
% 262.45/262.76 inference(modus_ponens,[status(thm)],[225, 224])).
% 262.45/262.76 tff(227,plain,
% 262.45/262.76 ((~((~accept_population(countrybcivilorganization, atheist, n65)) | (~accept_population(countrybcivilorganization, christian, n20)) | (~accept_population(countrybcivilorganization, muslim, n7)) | (~accept_population(countrybcivilorganization, native, n4)) | (~accept_population(countrybcivilorganization, other, n4)))) | (~accept_population(countrybcivilorganization, atheist, n65)) | (~accept_population(countrybcivilorganization, christian, n20)) | (~accept_population(countrybcivilorganization, muslim, n7)) | (~accept_population(countrybcivilorganization, native, n4)) | (~accept_population(countrybcivilorganization, other, n4))),
% 262.45/262.76 inference(tautology,[status(thm)],[])).
% 262.45/262.76 tff(228,plain,
% 262.45/262.76 ((~((~accept_population(countrybcivilorganization, atheist, n65)) | (~accept_population(countrybcivilorganization, christian, n20)) | (~accept_population(countrybcivilorganization, muslim, n7)) | (~accept_population(countrybcivilorganization, native, n4)) | (~accept_population(countrybcivilorganization, other, n4)))) | (~accept_population(countrybcivilorganization, atheist, n65)) | (~accept_population(countrybcivilorganization, muslim, n7)) | (~accept_population(countrybcivilorganization, native, n4)) | (~accept_population(countrybcivilorganization, other, n4))),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[227, 226])).
% 262.45/262.76 tff(229,plain,
% 262.45/262.76 ((~accept_population(countrybcivilorganization, atheist, n65)) | (~accept_population(countrybcivilorganization, muslim, n7)) | (~accept_population(countrybcivilorganization, native, n4)) | (~accept_population(countrybcivilorganization, other, n4))),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[228, 223])).
% 262.45/262.76 tff(230,plain,
% 262.45/262.76 (~accept_population(countrybcivilorganization, other, n4)),
% 262.45/262.76 inference(unit_resolution,[status(thm)],[229, 176, 143, 102])).
% 262.45/262.76 tff(231,plain,
% 262.45/262.76 (accept_population(countrybcivilorganization, other, n5) <=> accept_population(countrybcivilorganization, other, n5)),
% 262.51/262.84 inference(rewrite,[status(thm)],[])).
% 262.51/262.84 tff(232,axiom,(accept_population(countrybcivilorganization, other, n5)), file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+2.ax','deduced_44')).
% 262.51/262.84 tff(233,plain,
% 262.51/262.84 (accept_population(countrybcivilorganization, other, n5)),
% 262.51/262.84 inference(modus_ponens,[status(thm)],[232, 231])).
% 262.51/262.84 tff(234,plain,
% 262.51/262.84 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countrybcivilorganization, other, n4) | (~accept_population(countrybcivilorganization, other, n5)) | (~less(n4, n5)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | accept_population(countrybcivilorganization, other, n4) | (~accept_population(countrybcivilorganization, other, n5)) | (~less(n4, n5)))),
% 262.51/262.84 inference(rewrite,[status(thm)],[])).
% 262.51/262.84 tff(235,plain,
% 262.51/262.84 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(countrybcivilorganization, other, n4) | (~accept_population(countrybcivilorganization, other, n5)) | (~less(n4, n5)))),
% 262.51/262.84 inference(quant_inst,[status(thm)],[])).
% 262.51/262.84 tff(236,plain,
% 262.51/262.84 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | accept_population(countrybcivilorganization, other, n4) | (~accept_population(countrybcivilorganization, other, n5)) | (~less(n4, n5))),
% 262.51/262.84 inference(modus_ponens,[status(thm)],[235, 234])).
% 262.51/262.84 tff(237,plain,
% 262.51/262.84 ($false),
% 262.51/262.84 inference(unit_resolution,[status(thm)],[236, 94, 233, 230, 31])).
% 262.51/262.84 % SZS output end Proof
% 262.51/262.84 % E exiting
%------------------------------------------------------------------------------