%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : AGT013+2 : TPTP v9.0.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 04:57:40 AM UTC 2025
% Result : Theorem 166.48s 166.69s
% Output : Proof 166.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : AGT013+2 : TPTP v9.0.0. Bugfixed v3.1.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 10:43:21 EDT 2025
% 0.12/0.33 % CPUTime :
% 166.48/166.69 % SZS status Theorem
% 166.48/166.69 % SZS output start Proof
% 166.48/166.69 tff(less_type, type, (
% 166.48/166.69 less: ( $i * $i ) > $o)).
% 166.48/166.69 tff(n25_type, type, (
% 166.48/166.69 n25: $i)).
% 166.48/166.69 tff(n24_type, type, (
% 166.48/166.69 n24: $i)).
% 166.48/166.69 tff(accept_population_type, type, (
% 166.48/166.69 accept_population: ( $i * $i * $i ) > $o)).
% 166.48/166.69 tff(christian_type, type, (
% 166.48/166.69 christian: $i)).
% 166.48/166.69 tff(muslimcountrybhumanitarianorganization_type, type, (
% 166.48/166.69 muslimcountrybhumanitarianorganization: $i)).
% 166.48/166.69 tff(n75_type, type, (
% 166.48/166.69 n75: $i)).
% 166.48/166.69 tff(atheist_type, type, (
% 166.48/166.69 atheist: $i)).
% 166.48/166.69 tff(n78_type, type, (
% 166.48/166.69 n78: $i)).
% 166.48/166.69 tff(rdn_positive_less_type, type, (
% 166.48/166.69 rdn_positive_less: ( $i * $i ) > $o)).
% 166.48/166.69 tff(rdn_type, type, (
% 166.48/166.69 rdn: ( $i * $i ) > $i)).
% 166.48/166.69 tff(rdnn_type, type, (
% 166.48/166.69 rdnn: $i > $i)).
% 166.48/166.69 tff(n7_type, type, (
% 166.48/166.69 n7: $i)).
% 166.48/166.69 tff(n8_type, type, (
% 166.48/166.69 n8: $i)).
% 166.48/166.69 tff(n5_type, type, (
% 166.48/166.69 n5: $i)).
% 166.48/166.69 tff(n6_type, type, (
% 166.48/166.69 n6: $i)).
% 166.48/166.69 tff(rdn_non_zero_type, type, (
% 166.48/166.69 rdn_non_zero: $i > $o)).
% 166.48/166.69 tff(rdn_non_zero_digit_type, type, (
% 166.48/166.69 rdn_non_zero_digit: $i > $o)).
% 166.48/166.69 tff(rdn_translate_type, type, (
% 166.48/166.69 rdn_translate: ( $i * $i ) > $o)).
% 166.48/166.69 tff(rdn_pos_type, type, (
% 166.48/166.69 rdn_pos: $i > $i)).
% 166.48/166.69 tff(n0_type, type, (
% 166.48/166.69 n0: $i)).
% 166.48/166.69 tff(other_type, type, (
% 166.48/166.69 other: $i)).
% 166.48/166.69 tff(native_type, type, (
% 166.48/166.69 native: $i)).
% 166.48/166.69 tff(n1_type, type, (
% 166.48/166.69 n1: $i)).
% 166.48/166.69 tff(muslim_type, type, (
% 166.48/166.69 muslim: $i)).
% 166.48/166.69 tff(accept_city_type, type, (
% 166.48/166.69 accept_city: ( $i * $i ) > $o)).
% 166.48/166.69 tff(towna_type, type, (
% 166.48/166.69 towna: $i)).
% 166.48/166.69 tff(n2_type, type, (
% 166.48/166.69 n2: $i)).
% 166.48/166.69 tff(n4_type, type, (
% 166.48/166.69 n4: $i)).
% 166.48/166.69 tff(1,assumption,(~less(n75, n78)), introduced(assumption)).
% 166.48/166.69 tff(2,assumption,(~rdn_positive_less(rdnn(n5), rdnn(n8))), introduced(assumption)).
% 166.48/166.69 tff(3,assumption,(~rdn_positive_less(rdnn(n5), rdnn(n7))), introduced(assumption)).
% 166.48/166.69 tff(4,plain,
% 166.48/166.69 (^[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)))))),
% 166.48/166.69 inference(bind,[status(th)],[])).
% 166.48/166.69 tff(5,plain,
% 166.48/166.69 (![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))))),
% 166.48/166.69 inference(quant_intro,[status(thm)],[4])).
% 166.48/166.69 tff(6,plain,
% 166.48/166.69 (^[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))))))),
% 166.48/166.69 inference(bind,[status(th)],[])).
% 166.48/166.69 tff(7,plain,
% 166.48/166.69 (![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))))),
% 166.48/166.69 inference(quant_intro,[status(thm)],[6])).
% 166.48/166.69 tff(8,plain,
% 166.48/166.69 (![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)))),
% 166.48/166.69 inference(rewrite,[status(thm)],[])).
% 166.48/166.69 tff(9,plain,
% 166.48/166.69 (^[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))))),
% 166.48/166.69 inference(bind,[status(th)],[])).
% 166.48/166.69 tff(10,plain,
% 166.48/166.69 (![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)))),
% 166.48/166.69 inference(quant_intro,[status(thm)],[9])).
% 166.48/166.69 tff(11,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/sandbox2/benchmark/Axioms/NUM005+1.ax','rdn_positive_less_transitivity')).
% 166.48/166.69 tff(12,plain,
% 166.48/166.69 (![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)))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[11, 10])).
% 166.48/166.69 tff(13,plain,
% 166.48/166.69 (![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)))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[12, 8])).
% 166.48/166.69 tff(14,plain,(
% 166.48/166.69 ![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)))),
% 166.48/166.69 inference(skolemize,[status(sab)],[13])).
% 166.48/166.69 tff(15,plain,
% 166.48/166.69 (![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))))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[14, 7])).
% 166.48/166.69 tff(16,plain,
% 166.48/166.69 (![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))))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[15, 5])).
% 166.48/166.69 tff(17,plain,
% 166.48/166.69 (rdn_positive_less(rdnn(n6), rdnn(n7)) <=> rdn_positive_less(rdnn(n6), rdnn(n7))),
% 166.48/166.69 inference(rewrite,[status(thm)],[])).
% 166.48/166.69 tff(18,axiom,(rdn_positive_less(rdnn(n6), rdnn(n7))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax','rdn_positive_less67')).
% 166.48/166.69 tff(19,plain,
% 166.48/166.69 (rdn_positive_less(rdnn(n6), rdnn(n7))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[18, 17])).
% 166.48/166.69 tff(20,plain,
% 166.48/166.69 (rdn_positive_less(rdnn(n5), rdnn(n6)) <=> rdn_positive_less(rdnn(n5), rdnn(n6))),
% 166.48/166.69 inference(rewrite,[status(thm)],[])).
% 166.48/166.69 tff(21,axiom,(rdn_positive_less(rdnn(n5), rdnn(n6))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax','rdn_positive_less56')).
% 166.48/166.69 tff(22,plain,
% 166.48/166.69 (rdn_positive_less(rdnn(n5), rdnn(n6))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[21, 20])).
% 166.48/166.69 tff(23,plain,
% 166.48/166.69 (((~![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))))),
% 166.48/166.69 inference(rewrite,[status(thm)],[])).
% 166.48/166.69 tff(24,plain,
% 166.48/166.69 ((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))))),
% 166.48/166.69 inference(rewrite,[status(thm)],[])).
% 166.48/166.69 tff(25,plain,
% 166.48/166.69 (((~![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)))))),
% 166.48/166.69 inference(monotonicity,[status(thm)],[24])).
% 166.48/166.69 tff(26,plain,
% 166.48/166.69 (((~![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))))),
% 166.48/166.69 inference(transitivity,[status(thm)],[25, 23])).
% 166.48/166.69 tff(27,plain,
% 166.48/166.69 ((~![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))))),
% 166.48/166.69 inference(quant_inst,[status(thm)],[])).
% 166.48/166.69 tff(28,plain,
% 166.48/166.69 ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | rdn_positive_less(rdnn(n5), rdnn(n7)) | (~rdn_positive_less(rdnn(n6), rdnn(n7)))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[27, 26])).
% 166.48/166.69 tff(29,plain,
% 166.48/166.69 ($false),
% 166.48/166.69 inference(unit_resolution,[status(thm)],[28, 22, 19, 16, 3])).
% 166.48/166.69 tff(30,plain,(rdn_positive_less(rdnn(n5), rdnn(n7))), inference(lemma,lemma(discharge,[]))).
% 166.48/166.69 tff(31,plain,
% 166.48/166.69 (rdn_positive_less(rdnn(n7), rdnn(n8)) <=> rdn_positive_less(rdnn(n7), rdnn(n8))),
% 166.48/166.69 inference(rewrite,[status(thm)],[])).
% 166.48/166.69 tff(32,axiom,(rdn_positive_less(rdnn(n7), rdnn(n8))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax','rdn_positive_less78')).
% 166.48/166.69 tff(33,plain,
% 166.48/166.69 (rdn_positive_less(rdnn(n7), rdnn(n8))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[32, 31])).
% 166.48/166.69 tff(34,plain,
% 166.48/166.69 (((~![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(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))) <=> ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n5), rdnn(n7))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))),
% 166.48/166.69 inference(rewrite,[status(thm)],[])).
% 166.48/166.69 tff(35,plain,
% 166.48/166.69 ((rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n5), rdnn(n7))) | (~rdn_positive_less(rdnn(n7), rdnn(n8)))) <=> ((~rdn_positive_less(rdnn(n5), rdnn(n7))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))),
% 166.48/166.69 inference(rewrite,[status(thm)],[])).
% 166.48/166.69 tff(36,plain,
% 166.48/166.69 (((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n5), rdnn(n7))) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))) <=> ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | ((~rdn_positive_less(rdnn(n5), rdnn(n7))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8)))))),
% 166.48/166.69 inference(monotonicity,[status(thm)],[35])).
% 166.48/166.69 tff(37,plain,
% 166.48/166.69 (((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n5), rdnn(n7))) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))) <=> ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n5), rdnn(n7))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))),
% 166.48/166.69 inference(transitivity,[status(thm)],[36, 34])).
% 166.48/166.69 tff(38,plain,
% 166.48/166.69 ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n5), rdnn(n7))) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))),
% 166.48/166.69 inference(quant_inst,[status(thm)],[])).
% 166.48/166.69 tff(39,plain,
% 166.48/166.69 ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n5), rdnn(n7))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8)))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[38, 37])).
% 166.48/166.69 tff(40,plain,
% 166.48/166.69 ($false),
% 166.48/166.69 inference(unit_resolution,[status(thm)],[39, 33, 16, 30, 2])).
% 166.48/166.69 tff(41,plain,(rdn_positive_less(rdnn(n5), rdnn(n8))), inference(lemma,lemma(discharge,[]))).
% 166.48/166.69 tff(42,plain,
% 166.48/166.69 (^[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)))))),
% 166.48/166.69 inference(bind,[status(th)],[])).
% 166.48/166.69 tff(43,plain,
% 166.48/166.69 (![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))))),
% 166.48/166.69 inference(quant_intro,[status(thm)],[42])).
% 166.48/166.69 tff(44,plain,
% 166.48/166.69 (![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))))),
% 166.48/166.69 inference(rewrite,[status(thm)],[])).
% 166.48/166.69 tff(45,plain,
% 166.48/166.69 (^[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)))))),
% 166.48/166.69 inference(bind,[status(th)],[])).
% 166.48/166.69 tff(46,plain,
% 166.48/166.69 (![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))))),
% 166.48/166.69 inference(quant_intro,[status(thm)],[45])).
% 166.48/166.69 tff(47,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')).
% 166.48/166.69 tff(48,plain,
% 166.48/166.69 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[47, 46])).
% 166.48/166.69 tff(49,plain,
% 166.48/166.69 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[48, 44])).
% 166.48/166.69 tff(50,plain,(
% 166.48/166.69 ![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 166.48/166.69 inference(skolemize,[status(sab)],[49])).
% 166.48/166.69 tff(51,plain,
% 166.48/166.69 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[50, 43])).
% 166.48/166.69 tff(52,plain,
% 166.48/166.69 (rdn_non_zero_digit(rdnn(n7)) <=> rdn_non_zero_digit(rdnn(n7))),
% 166.48/166.69 inference(rewrite,[status(thm)],[])).
% 166.48/166.69 tff(53,axiom,(rdn_non_zero_digit(rdnn(n7))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax','rdn_digit7')).
% 166.48/166.69 tff(54,plain,
% 166.48/166.69 (rdn_non_zero_digit(rdnn(n7))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[53, 52])).
% 166.48/166.69 tff(55,plain,
% 166.48/166.69 (((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | (rdn_non_zero(rdnn(n7)) | (~rdn_non_zero_digit(rdnn(n7))))) <=> ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | rdn_non_zero(rdnn(n7)) | (~rdn_non_zero_digit(rdnn(n7))))),
% 166.48/166.69 inference(rewrite,[status(thm)],[])).
% 166.48/166.69 tff(56,plain,
% 166.48/166.69 ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | (rdn_non_zero(rdnn(n7)) | (~rdn_non_zero_digit(rdnn(n7))))),
% 166.48/166.69 inference(quant_inst,[status(thm)],[])).
% 166.48/166.69 tff(57,plain,
% 166.48/166.69 ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | rdn_non_zero(rdnn(n7)) | (~rdn_non_zero_digit(rdnn(n7)))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[56, 55])).
% 166.48/166.69 tff(58,plain,
% 166.48/166.69 (rdn_non_zero(rdnn(n7))),
% 166.48/166.69 inference(unit_resolution,[status(thm)],[57, 54, 51])).
% 166.48/166.69 tff(59,plain,
% 166.48/166.69 (^[Ds: $i, O: $i, Db: $i] : refl((rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))) <=> (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))))),
% 166.48/166.69 inference(bind,[status(th)],[])).
% 166.48/166.69 tff(60,plain,
% 166.48/166.69 (![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))) <=> ![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))),
% 166.48/166.69 inference(quant_intro,[status(thm)],[59])).
% 166.48/166.69 tff(61,plain,
% 166.48/166.69 (^[Ds: $i, O: $i, Db: $i] : trans(monotonicity(trans(monotonicity(rewrite((rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O)) <=> (~((~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))))), ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) <=> (~(~((~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))))))), rewrite((~(~((~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))))) <=> ((~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))), ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) <=> ((~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))))), (((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))) <=> (((~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))))), rewrite((((~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))) <=> (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))), (((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))) <=> (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))))),
% 166.48/166.69 inference(bind,[status(th)],[])).
% 166.48/166.69 tff(62,plain,
% 166.48/166.69 (![Ds: $i, O: $i, Db: $i] : ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))) <=> ![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))),
% 166.48/166.69 inference(quant_intro,[status(thm)],[61])).
% 166.48/166.69 tff(63,plain,
% 166.48/166.69 (![Ds: $i, O: $i, Db: $i] : ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))) <=> ![Ds: $i, O: $i, Db: $i] : ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)))),
% 166.48/166.69 inference(rewrite,[status(thm)],[])).
% 166.48/166.69 tff(64,plain,
% 166.48/166.69 (^[Ds: $i, O: $i, Db: $i] : rewrite(((rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O)) => rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))) <=> ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))))),
% 166.48/166.69 inference(bind,[status(th)],[])).
% 166.48/166.69 tff(65,plain,
% 166.48/166.69 (![Ds: $i, O: $i, Db: $i] : ((rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O)) => rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O))) <=> ![Ds: $i, O: $i, Db: $i] : ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)))),
% 166.48/166.69 inference(quant_intro,[status(thm)],[64])).
% 166.48/166.69 tff(66,axiom,(![Ds: $i, O: $i, Db: $i] : ((rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O)) => rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax','rdn_positive_less_multi_digit_low')).
% 166.48/166.69 tff(67,plain,
% 166.48/166.69 (![Ds: $i, O: $i, Db: $i] : ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[66, 65])).
% 166.48/166.69 tff(68,plain,
% 166.48/166.69 (![Ds: $i, O: $i, Db: $i] : ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[67, 63])).
% 166.48/166.69 tff(69,plain,(
% 166.48/166.69 ![Ds: $i, O: $i, Db: $i] : ((~(rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O))) | rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)))),
% 166.48/166.69 inference(skolemize,[status(sab)],[68])).
% 166.48/166.69 tff(70,plain,
% 166.48/166.69 (![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[69, 62])).
% 166.48/166.69 tff(71,plain,
% 166.48/166.69 (![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))),
% 166.48/166.69 inference(modus_ponens,[status(thm)],[70, 60])).
% 166.48/166.69 tff(72,plain,
% 166.48/166.69 (((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | ((~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))))) <=> ((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))))),
% 166.48/166.69 inference(rewrite,[status(thm)],[])).
% 166.48/166.69 tff(73,plain,
% 166.48/166.69 ((rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))) | (~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7)))) <=> ((~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))))),
% 166.48/166.69 inference(rewrite,[status(thm)],[])).
% 166.48/166.69 tff(74,plain,
% 166.48/166.69 (((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))) | (~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))))) <=> ((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | ((~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))))),
% 166.48/166.69 inference(monotonicity,[status(thm)],[73])).
% 166.48/166.69 tff(75,plain,
% 166.48/166.69 (((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))) | (~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))))) <=> ((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))))),
% 166.48/166.69 inference(transitivity,[status(thm)],[74, 72])).
% 166.48/166.69 tff(76,plain,
% 166.48/166.69 ((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))) | (~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))))),
% 166.48/166.69 inference(quant_inst,[status(thm)],[])).
% 166.48/166.69 tff(77,plain,
% 166.48/166.70 ((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[76, 75])).
% 166.48/166.70 tff(78,plain,
% 166.48/166.70 ((~rdn_positive_less(rdnn(n5), rdnn(n8))) | (~rdn_non_zero(rdnn(n7))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))),
% 166.48/166.70 inference(unit_resolution,[status(thm)],[77, 71])).
% 166.48/166.70 tff(79,plain,
% 166.48/166.70 ((~rdn_positive_less(rdnn(n5), rdnn(n8))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))),
% 166.48/166.70 inference(unit_resolution,[status(thm)],[78, 58])).
% 166.48/166.70 tff(80,plain,
% 166.48/166.70 (rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))),
% 166.48/166.70 inference(unit_resolution,[status(thm)],[79, 41])).
% 166.48/166.70 tff(81,plain,
% 166.48/166.70 (^[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))))),
% 166.48/166.70 inference(bind,[status(th)],[])).
% 166.48/166.70 tff(82,plain,
% 166.48/166.70 (![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)))),
% 166.48/166.70 inference(quant_intro,[status(thm)],[81])).
% 166.48/166.70 tff(83,plain,
% 166.48/166.70 (^[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)))))),
% 166.48/166.70 inference(bind,[status(th)],[])).
% 166.48/166.70 tff(84,plain,
% 166.48/166.70 (![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)))),
% 166.48/166.70 inference(quant_intro,[status(thm)],[83])).
% 166.48/166.70 tff(85,plain,
% 166.48/166.70 (![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))),
% 166.48/166.70 inference(rewrite,[status(thm)],[])).
% 166.48/166.70 tff(86,plain,
% 166.48/166.70 (^[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))))),
% 166.48/166.70 inference(bind,[status(th)],[])).
% 166.48/166.70 tff(87,plain,
% 166.48/166.70 (![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))),
% 166.48/166.70 inference(quant_intro,[status(thm)],[86])).
% 166.48/166.70 tff(88,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')).
% 166.48/166.70 tff(89,plain,
% 166.48/166.70 (![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))),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[88, 87])).
% 166.48/166.70 tff(90,plain,
% 166.48/166.70 (![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))),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[89, 85])).
% 166.48/166.70 tff(91,plain,(
% 166.48/166.70 ![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))),
% 166.48/166.70 inference(skolemize,[status(sab)],[90])).
% 166.48/166.70 tff(92,plain,
% 166.48/166.70 (![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)))),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[91, 84])).
% 166.48/166.70 tff(93,plain,
% 166.48/166.70 (![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)))),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[92, 82])).
% 166.48/166.70 tff(94,plain,
% 166.48/166.70 (rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7)))) <=> rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))),
% 166.48/166.70 inference(rewrite,[status(thm)],[])).
% 166.48/166.70 tff(95,axiom,(rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax','rdn78')).
% 166.48/166.70 tff(96,plain,
% 166.48/166.70 (rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[95, 94])).
% 166.48/166.70 tff(97,plain,
% 166.48/166.70 (rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7)))) <=> rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))),
% 166.48/166.70 inference(rewrite,[status(thm)],[])).
% 166.48/166.70 tff(98,axiom,(rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax','rdn75')).
% 166.48/166.70 tff(99,plain,
% 166.48/166.70 (rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[98, 97])).
% 166.48/166.70 tff(100,plain,
% 166.48/166.70 (((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | ((~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n75, n78))) <=> ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n75, n78))),
% 166.48/166.70 inference(rewrite,[status(thm)],[])).
% 166.48/166.70 tff(101,plain,
% 166.48/166.70 ((less(n75, n78) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))))) <=> ((~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n75, n78))),
% 166.48/166.70 inference(rewrite,[status(thm)],[])).
% 166.48/166.70 tff(102,plain,
% 166.48/166.70 (((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (less(n75, n78) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))))) <=> ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | ((~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n75, n78)))),
% 166.48/166.70 inference(monotonicity,[status(thm)],[101])).
% 166.48/166.70 tff(103,plain,
% 166.48/166.70 (((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (less(n75, n78) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))))) <=> ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n75, n78))),
% 166.48/166.70 inference(transitivity,[status(thm)],[102, 100])).
% 166.48/166.70 tff(104,plain,
% 166.48/166.70 ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (less(n75, n78) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))))),
% 166.48/166.70 inference(quant_inst,[status(thm)],[])).
% 166.48/166.70 tff(105,plain,
% 166.48/166.70 ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | less(n75, n78)),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[104, 103])).
% 166.48/166.70 tff(106,plain,
% 166.48/166.70 ($false),
% 166.48/166.70 inference(unit_resolution,[status(thm)],[105, 99, 96, 93, 80, 1])).
% 166.48/166.70 tff(107,plain,(less(n75, n78)), inference(lemma,lemma(discharge,[]))).
% 166.48/166.70 tff(108,assumption,(~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)), introduced(assumption)).
% 166.48/166.70 tff(109,plain,
% 166.48/166.70 (accept_population(muslimcountrybhumanitarianorganization, atheist, n78) <=> accept_population(muslimcountrybhumanitarianorganization, atheist, n78)),
% 166.48/166.70 inference(rewrite,[status(thm)],[])).
% 166.48/166.70 tff(110,axiom,(accept_population(muslimcountrybhumanitarianorganization, atheist, n78)), file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+2.ax','deduced_206')).
% 166.48/166.70 tff(111,plain,
% 166.48/166.70 (accept_population(muslimcountrybhumanitarianorganization, atheist, n78)),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[110, 109])).
% 166.48/166.70 tff(112,plain,
% 166.48/166.70 (^[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))))),
% 166.48/166.70 inference(bind,[status(th)],[])).
% 166.48/166.70 tff(113,plain,
% 166.48/166.70 (![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)))),
% 166.48/166.70 inference(quant_intro,[status(thm)],[112])).
% 166.48/166.70 tff(114,plain,
% 166.48/166.70 (^[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)))))),
% 166.48/166.70 inference(bind,[status(th)],[])).
% 166.48/166.70 tff(115,plain,
% 166.48/166.70 (![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)))),
% 166.48/166.70 inference(quant_intro,[status(thm)],[114])).
% 166.48/166.70 tff(116,plain,
% 166.48/166.70 (![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))),
% 166.48/166.70 inference(rewrite,[status(thm)],[])).
% 166.48/166.70 tff(117,plain,
% 166.48/166.70 (^[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)))),
% 166.48/166.70 inference(bind,[status(th)],[])).
% 166.48/166.70 tff(118,plain,
% 166.48/166.70 (![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))),
% 166.48/166.70 inference(quant_intro,[status(thm)],[117])).
% 166.48/166.70 tff(119,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')).
% 166.48/166.70 tff(120,plain,
% 166.48/166.70 (![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[119, 118])).
% 166.48/166.70 tff(121,plain,
% 166.48/166.70 (![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[120, 116])).
% 166.48/166.70 tff(122,plain,(
% 166.48/166.70 ![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 166.48/166.70 inference(skolemize,[status(sab)],[121])).
% 166.48/166.70 tff(123,plain,
% 166.48/166.70 (![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[122, 115])).
% 166.48/166.70 tff(124,plain,
% 166.48/166.70 (![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[123, 113])).
% 166.48/166.70 tff(125,plain,
% 166.48/166.70 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(muslimcountrybhumanitarianorganization, atheist, n75) | (~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~less(n75, n78)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | accept_population(muslimcountrybhumanitarianorganization, atheist, n75) | (~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~less(n75, n78)))),
% 166.48/166.70 inference(rewrite,[status(thm)],[])).
% 166.48/166.70 tff(126,plain,
% 166.48/166.70 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(muslimcountrybhumanitarianorganization, atheist, n75) | (~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~less(n75, n78)))),
% 166.48/166.70 inference(quant_inst,[status(thm)],[])).
% 166.48/166.70 tff(127,plain,
% 166.48/166.70 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | accept_population(muslimcountrybhumanitarianorganization, atheist, n75) | (~accept_population(muslimcountrybhumanitarianorganization, atheist, n78)) | (~less(n75, n78))),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[126, 125])).
% 166.48/166.70 tff(128,plain,
% 166.48/166.70 ($false),
% 166.48/166.70 inference(unit_resolution,[status(thm)],[127, 124, 111, 108, 107])).
% 166.48/166.70 tff(129,plain,(accept_population(muslimcountrybhumanitarianorganization, atheist, n75)), inference(lemma,lemma(discharge,[]))).
% 166.48/166.70 tff(130,plain,
% 166.48/166.70 (^[A: $i] : refl((~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna))) <=> (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna))))),
% 166.48/166.70 inference(bind,[status(th)],[])).
% 166.48/166.70 tff(131,plain,
% 166.48/166.70 (![A: $i] : (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna))) <=> ![A: $i] : (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna)))),
% 166.48/166.70 inference(quant_intro,[status(thm)],[130])).
% 166.48/166.70 tff(132,plain,
% 166.48/166.70 (^[A: $i] : trans(trans(monotonicity(rewrite((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> (~((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))))), (((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna)) <=> ((~((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0)))) <=> accept_city(A, towna)))), rewrite(((~((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0)))) <=> accept_city(A, towna)) <=> (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna)))), (((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna)) <=> (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna))))), rewrite((~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna))) <=> (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna)))), (((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna)) <=> (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna)))))),
% 166.48/166.70 inference(bind,[status(th)],[])).
% 166.48/166.70 tff(133,plain,
% 166.48/166.70 (![A: $i] : ((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna)) <=> ![A: $i] : (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna)))),
% 166.48/166.70 inference(quant_intro,[status(thm)],[132])).
% 166.48/166.70 tff(134,plain,
% 166.48/166.70 (![A: $i] : ((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna)) <=> ![A: $i] : ((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna))),
% 166.48/166.70 inference(rewrite,[status(thm)],[])).
% 166.48/166.70 tff(135,plain,
% 166.48/166.70 (^[A: $i] : rewrite((((((accept_population(A, atheist, n75) & accept_population(A, christian, n24)) & accept_population(A, muslim, n1)) & accept_population(A, native, n0)) & accept_population(A, other, n0)) <=> accept_city(A, towna)) <=> ((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna)))),
% 166.48/166.70 inference(bind,[status(th)],[])).
% 166.48/166.70 tff(136,plain,
% 166.48/166.70 (![A: $i] : (((((accept_population(A, atheist, n75) & accept_population(A, christian, n24)) & accept_population(A, muslim, n1)) & accept_population(A, native, n0)) & accept_population(A, other, n0)) <=> accept_city(A, towna)) <=> ![A: $i] : ((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna))),
% 166.48/166.70 inference(quant_intro,[status(thm)],[135])).
% 166.48/166.70 tff(137,axiom,(![A: $i] : (((((accept_population(A, atheist, n75) & accept_population(A, christian, n24)) & accept_population(A, muslim, n1)) & accept_population(A, native, n0)) & accept_population(A, other, n0)) <=> accept_city(A, towna))), file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+0.ax','a2_9')).
% 166.48/166.70 tff(138,plain,
% 166.48/166.70 (![A: $i] : ((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna))),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[137, 136])).
% 166.48/166.70 tff(139,plain,
% 166.48/166.70 (![A: $i] : ((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna))),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[138, 134])).
% 166.48/166.70 tff(140,plain,(
% 166.48/166.70 ![A: $i] : ((accept_population(A, atheist, n75) & accept_population(A, christian, n24) & accept_population(A, muslim, n1) & accept_population(A, native, n0) & accept_population(A, other, n0)) <=> accept_city(A, towna))),
% 166.48/166.70 inference(skolemize,[status(sab)],[139])).
% 166.48/166.70 tff(141,plain,
% 166.48/166.70 (![A: $i] : (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna)))),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[140, 133])).
% 166.48/166.70 tff(142,plain,
% 166.48/166.70 (![A: $i] : (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna)))),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[141, 131])).
% 166.48/166.70 tff(143,plain,
% 166.48/166.70 ((~![A: $i] : (~(((~accept_population(A, atheist, n75)) | (~accept_population(A, christian, n24)) | (~accept_population(A, muslim, n1)) | (~accept_population(A, native, n0)) | (~accept_population(A, other, n0))) <=> accept_city(A, towna)))) | (~(((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))) <=> accept_city(muslimcountrybhumanitarianorganization, towna)))),
% 166.48/166.70 inference(quant_inst,[status(thm)],[])).
% 166.48/166.70 tff(144,plain,
% 166.48/166.70 (~(((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))) <=> accept_city(muslimcountrybhumanitarianorganization, towna))),
% 166.48/166.70 inference(unit_resolution,[status(thm)],[143, 142])).
% 166.48/166.70 tff(145,plain,
% 166.48/166.70 ((~accept_city(muslimcountrybhumanitarianorganization, towna)) <=> (~accept_city(muslimcountrybhumanitarianorganization, towna))),
% 166.48/166.70 inference(rewrite,[status(thm)],[])).
% 166.48/166.70 tff(146,axiom,(~accept_city(muslimcountrybhumanitarianorganization, towna)), file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+2.ax','deduced_366')).
% 166.48/166.70 tff(147,plain,
% 166.48/166.70 (~accept_city(muslimcountrybhumanitarianorganization, towna)),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[146, 145])).
% 166.48/166.70 tff(148,plain,
% 166.48/166.70 ((((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))) <=> accept_city(muslimcountrybhumanitarianorganization, towna)) | ((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))) | accept_city(muslimcountrybhumanitarianorganization, towna)),
% 166.48/166.70 inference(tautology,[status(thm)],[])).
% 166.48/166.70 tff(149,plain,
% 166.48/166.70 ((((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))) <=> accept_city(muslimcountrybhumanitarianorganization, towna)) | ((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0)))),
% 166.48/166.70 inference(unit_resolution,[status(thm)],[148, 147])).
% 166.48/166.70 tff(150,plain,
% 166.48/166.70 ((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))),
% 166.48/166.70 inference(unit_resolution,[status(thm)],[149, 144])).
% 166.48/166.70 tff(151,plain,
% 166.48/166.70 (accept_population(muslimcountrybhumanitarianorganization, muslim, n1) <=> accept_population(muslimcountrybhumanitarianorganization, muslim, n1)),
% 166.48/166.70 inference(rewrite,[status(thm)],[])).
% 166.48/166.70 tff(152,axiom,(accept_population(muslimcountrybhumanitarianorganization, muslim, n1)), file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+2.ax','deduced_204')).
% 166.48/166.70 tff(153,plain,
% 166.48/166.70 (accept_population(muslimcountrybhumanitarianorganization, muslim, n1)),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[152, 151])).
% 166.48/166.70 tff(154,plain,
% 166.48/166.70 (accept_population(muslimcountrybhumanitarianorganization, native, n0) <=> accept_population(muslimcountrybhumanitarianorganization, native, n0)),
% 166.48/166.70 inference(rewrite,[status(thm)],[])).
% 166.48/166.70 tff(155,axiom,(accept_population(muslimcountrybhumanitarianorganization, native, n0)), file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+2.ax','deduced_203')).
% 166.48/166.70 tff(156,plain,
% 166.48/166.70 (accept_population(muslimcountrybhumanitarianorganization, native, n0)),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[155, 154])).
% 166.48/166.70 tff(157,plain,
% 166.48/166.70 (accept_population(muslimcountrybhumanitarianorganization, other, n0) <=> accept_population(muslimcountrybhumanitarianorganization, other, n0)),
% 166.48/166.70 inference(rewrite,[status(thm)],[])).
% 166.48/166.70 tff(158,axiom,(accept_population(muslimcountrybhumanitarianorganization, other, n0)), file('/export/starexec/sandbox2/benchmark/Axioms/AGT001+2.ax','deduced_93')).
% 166.48/166.70 tff(159,plain,
% 166.48/166.70 (accept_population(muslimcountrybhumanitarianorganization, other, n0)),
% 166.48/166.70 inference(modus_ponens,[status(thm)],[158, 157])).
% 166.48/166.70 tff(160,plain,
% 166.48/166.70 ((~((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0)))) | (~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0))),
% 166.48/166.70 inference(tautology,[status(thm)],[])).
% 166.48/166.70 tff(161,plain,
% 166.48/166.70 ((~((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)) | (~accept_population(muslimcountrybhumanitarianorganization, muslim, n1)) | (~accept_population(muslimcountrybhumanitarianorganization, native, n0)) | (~accept_population(muslimcountrybhumanitarianorganization, other, n0)))) | (~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24))),
% 166.48/166.71 inference(unit_resolution,[status(thm)],[160, 159, 156, 153])).
% 166.48/166.71 tff(162,plain,
% 166.48/166.71 ((~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n24))),
% 166.48/166.71 inference(unit_resolution,[status(thm)],[161, 150])).
% 166.48/166.71 tff(163,plain,
% 166.48/166.71 (~accept_population(muslimcountrybhumanitarianorganization, christian, n24)),
% 166.48/166.71 inference(unit_resolution,[status(thm)],[162, 129])).
% 166.48/166.71 tff(164,plain,
% 166.48/166.71 (accept_population(muslimcountrybhumanitarianorganization, christian, n25) <=> accept_population(muslimcountrybhumanitarianorganization, christian, n25)),
% 166.48/166.71 inference(rewrite,[status(thm)],[])).
% 166.48/166.71 tff(165,plain,
% 166.48/166.71 ((~(~accept_population(muslimcountrybhumanitarianorganization, christian, n25))) <=> accept_population(muslimcountrybhumanitarianorganization, christian, n25)),
% 166.48/166.71 inference(rewrite,[status(thm)],[])).
% 166.48/166.71 tff(166,axiom,(~(~accept_population(muslimcountrybhumanitarianorganization, christian, n25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','query_13')).
% 166.48/166.71 tff(167,plain,
% 166.48/166.71 (accept_population(muslimcountrybhumanitarianorganization, christian, n25)),
% 166.48/166.71 inference(modus_ponens,[status(thm)],[166, 165])).
% 166.48/166.71 tff(168,plain,
% 166.48/166.71 (accept_population(muslimcountrybhumanitarianorganization, christian, n25)),
% 166.48/166.71 inference(modus_ponens,[status(thm)],[167, 164])).
% 166.48/166.71 tff(169,plain,
% 166.48/166.71 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | ((~accept_population(muslimcountrybhumanitarianorganization, christian, n25)) | accept_population(muslimcountrybhumanitarianorganization, christian, n24) | (~less(n24, n25)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n25)) | accept_population(muslimcountrybhumanitarianorganization, christian, n24) | (~less(n24, n25)))),
% 166.48/166.71 inference(rewrite,[status(thm)],[])).
% 166.48/166.71 tff(170,plain,
% 166.48/166.71 ((accept_population(muslimcountrybhumanitarianorganization, christian, n24) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n25)) | (~less(n24, n25))) <=> ((~accept_population(muslimcountrybhumanitarianorganization, christian, n25)) | accept_population(muslimcountrybhumanitarianorganization, christian, n24) | (~less(n24, n25)))),
% 166.48/166.71 inference(rewrite,[status(thm)],[])).
% 166.48/166.71 tff(171,plain,
% 166.48/166.71 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(muslimcountrybhumanitarianorganization, christian, n24) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n25)) | (~less(n24, n25)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | ((~accept_population(muslimcountrybhumanitarianorganization, christian, n25)) | accept_population(muslimcountrybhumanitarianorganization, christian, n24) | (~less(n24, n25))))),
% 166.48/166.71 inference(monotonicity,[status(thm)],[170])).
% 166.48/166.71 tff(172,plain,
% 166.48/166.71 (((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(muslimcountrybhumanitarianorganization, christian, n24) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n25)) | (~less(n24, n25)))) <=> ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n25)) | accept_population(muslimcountrybhumanitarianorganization, christian, n24) | (~less(n24, n25)))),
% 166.48/166.71 inference(transitivity,[status(thm)],[171, 169])).
% 166.48/166.71 tff(173,plain,
% 166.48/166.71 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (accept_population(muslimcountrybhumanitarianorganization, christian, n24) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n25)) | (~less(n24, n25)))),
% 166.48/166.71 inference(quant_inst,[status(thm)],[])).
% 166.48/166.71 tff(174,plain,
% 166.48/166.71 ((~![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))) | (~accept_population(muslimcountrybhumanitarianorganization, christian, n25)) | accept_population(muslimcountrybhumanitarianorganization, christian, n24) | (~less(n24, n25))),
% 166.48/166.71 inference(modus_ponens,[status(thm)],[173, 172])).
% 166.48/166.71 tff(175,plain,
% 166.48/166.71 (~less(n24, n25)),
% 166.48/166.71 inference(unit_resolution,[status(thm)],[174, 124, 168, 163])).
% 166.48/166.71 tff(176,plain,
% 166.48/166.71 (rdn_non_zero_digit(rdnn(n2)) <=> rdn_non_zero_digit(rdnn(n2))),
% 166.48/166.71 inference(rewrite,[status(thm)],[])).
% 166.48/166.71 tff(177,axiom,(rdn_non_zero_digit(rdnn(n2))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax','rdn_digit2')).
% 166.48/166.71 tff(178,plain,
% 166.48/166.71 (rdn_non_zero_digit(rdnn(n2))),
% 166.48/166.71 inference(modus_ponens,[status(thm)],[177, 176])).
% 166.48/166.71 tff(179,plain,
% 166.48/166.71 (((~![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))))),
% 166.48/166.71 inference(rewrite,[status(thm)],[])).
% 166.48/166.71 tff(180,plain,
% 166.48/166.71 ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | (rdn_non_zero(rdnn(n2)) | (~rdn_non_zero_digit(rdnn(n2))))),
% 166.48/166.71 inference(quant_inst,[status(thm)],[])).
% 166.48/166.71 tff(181,plain,
% 166.48/166.71 ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | rdn_non_zero(rdnn(n2)) | (~rdn_non_zero_digit(rdnn(n2)))),
% 166.48/166.71 inference(modus_ponens,[status(thm)],[180, 179])).
% 166.48/166.71 tff(182,plain,
% 166.48/166.71 (rdn_non_zero(rdnn(n2))),
% 166.48/166.71 inference(unit_resolution,[status(thm)],[181, 178, 51])).
% 166.48/166.71 tff(183,plain,
% 166.48/166.71 (rdn_positive_less(rdnn(n4), rdnn(n5)) <=> rdn_positive_less(rdnn(n4), rdnn(n5))),
% 166.48/166.71 inference(rewrite,[status(thm)],[])).
% 166.48/166.71 tff(184,axiom,(rdn_positive_less(rdnn(n4), rdnn(n5))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax','rdn_positive_less45')).
% 166.48/166.71 tff(185,plain,
% 166.48/166.71 (rdn_positive_less(rdnn(n4), rdnn(n5))),
% 166.48/166.71 inference(modus_ponens,[status(thm)],[184, 183])).
% 166.48/166.71 tff(186,plain,
% 166.48/166.71 (((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | ((~rdn_positive_less(rdnn(n4), rdnn(n5))) | (~rdn_non_zero(rdnn(n2))) | rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2))))) <=> ((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (~rdn_positive_less(rdnn(n4), rdnn(n5))) | (~rdn_non_zero(rdnn(n2))) | rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2))))),
% 166.48/166.71 inference(rewrite,[status(thm)],[])).
% 166.48/166.71 tff(187,plain,
% 166.48/166.71 ((rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2))) | (~rdn_positive_less(rdnn(n4), rdnn(n5))) | (~rdn_non_zero(rdnn(n2)))) <=> ((~rdn_positive_less(rdnn(n4), rdnn(n5))) | (~rdn_non_zero(rdnn(n2))) | rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2))))),
% 166.48/166.71 inference(rewrite,[status(thm)],[])).
% 166.48/166.71 tff(188,plain,
% 166.48/166.71 (((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2))) | (~rdn_positive_less(rdnn(n4), rdnn(n5))) | (~rdn_non_zero(rdnn(n2))))) <=> ((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | ((~rdn_positive_less(rdnn(n4), rdnn(n5))) | (~rdn_non_zero(rdnn(n2))) | rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2)))))),
% 166.48/166.71 inference(monotonicity,[status(thm)],[187])).
% 166.48/166.71 tff(189,plain,
% 166.48/166.71 (((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2))) | (~rdn_positive_less(rdnn(n4), rdnn(n5))) | (~rdn_non_zero(rdnn(n2))))) <=> ((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (~rdn_positive_less(rdnn(n4), rdnn(n5))) | (~rdn_non_zero(rdnn(n2))) | rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2))))),
% 166.48/166.71 inference(transitivity,[status(thm)],[188, 186])).
% 166.48/166.71 tff(190,plain,
% 166.48/166.71 ((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2))) | (~rdn_positive_less(rdnn(n4), rdnn(n5))) | (~rdn_non_zero(rdnn(n2))))),
% 166.48/166.71 inference(quant_inst,[status(thm)],[])).
% 166.48/166.71 tff(191,plain,
% 166.48/166.71 ((~![Ds: $i, O: $i, Db: $i] : (rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)) | (~rdn_positive_less(rdnn(Ds), rdnn(Db))) | (~rdn_non_zero(O)))) | (~rdn_positive_less(rdnn(n4), rdnn(n5))) | (~rdn_non_zero(rdnn(n2))) | rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2)))),
% 166.48/166.71 inference(modus_ponens,[status(thm)],[190, 189])).
% 166.48/166.71 tff(192,plain,
% 166.48/166.71 ((~rdn_non_zero(rdnn(n2))) | rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2)))),
% 166.48/166.71 inference(unit_resolution,[status(thm)],[191, 185, 71])).
% 166.48/166.71 tff(193,plain,
% 166.48/166.71 (rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2)))),
% 166.48/166.71 inference(unit_resolution,[status(thm)],[192, 182])).
% 166.48/166.71 tff(194,plain,
% 166.48/166.71 (rdn_translate(n25, rdn_pos(rdn(rdnn(n5), rdnn(n2)))) <=> rdn_translate(n25, rdn_pos(rdn(rdnn(n5), rdnn(n2))))),
% 166.48/166.71 inference(rewrite,[status(thm)],[])).
% 166.48/166.71 tff(195,axiom,(rdn_translate(n25, rdn_pos(rdn(rdnn(n5), rdnn(n2))))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax','rdn25')).
% 166.48/166.71 tff(196,plain,
% 166.48/166.71 (rdn_translate(n25, rdn_pos(rdn(rdnn(n5), rdnn(n2))))),
% 166.48/166.71 inference(modus_ponens,[status(thm)],[195, 194])).
% 166.48/166.71 tff(197,plain,
% 166.48/166.71 (rdn_translate(n24, rdn_pos(rdn(rdnn(n4), rdnn(n2)))) <=> rdn_translate(n24, rdn_pos(rdn(rdnn(n4), rdnn(n2))))),
% 166.48/166.71 inference(rewrite,[status(thm)],[])).
% 166.48/166.71 tff(198,axiom,(rdn_translate(n24, rdn_pos(rdn(rdnn(n4), rdnn(n2))))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax','rdn24')).
% 166.48/166.71 tff(199,plain,
% 166.48/166.71 (rdn_translate(n24, rdn_pos(rdn(rdnn(n4), rdnn(n2))))),
% 166.48/166.71 inference(modus_ponens,[status(thm)],[198, 197])).
% 166.48/166.71 tff(200,plain,
% 166.48/166.71 (((~![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(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2)))) | (~rdn_translate(n25, rdn_pos(rdn(rdnn(n5), rdnn(n2))))) | less(n24, n25) | (~rdn_translate(n24, rdn_pos(rdn(rdnn(n4), 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(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2)))) | (~rdn_translate(n25, rdn_pos(rdn(rdnn(n5), rdnn(n2))))) | less(n24, n25) | (~rdn_translate(n24, rdn_pos(rdn(rdnn(n4), rdnn(n2))))))),
% 166.48/166.71 inference(rewrite,[status(thm)],[])).
% 166.48/166.71 tff(201,plain,
% 166.48/166.71 ((less(n24, n25) | (~rdn_translate(n24, rdn_pos(rdn(rdnn(n4), rdnn(n2))))) | (~rdn_translate(n25, rdn_pos(rdn(rdnn(n5), rdnn(n2))))) | (~rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2))))) <=> ((~rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2)))) | (~rdn_translate(n25, rdn_pos(rdn(rdnn(n5), rdnn(n2))))) | less(n24, n25) | (~rdn_translate(n24, rdn_pos(rdn(rdnn(n4), rdnn(n2))))))),
% 166.48/166.71 inference(rewrite,[status(thm)],[])).
% 166.48/166.71 tff(202,plain,
% 166.48/166.71 (((~![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(n24, n25) | (~rdn_translate(n24, rdn_pos(rdn(rdnn(n4), rdnn(n2))))) | (~rdn_translate(n25, rdn_pos(rdn(rdnn(n5), rdnn(n2))))) | (~rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), 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(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2)))) | (~rdn_translate(n25, rdn_pos(rdn(rdnn(n5), rdnn(n2))))) | less(n24, n25) | (~rdn_translate(n24, rdn_pos(rdn(rdnn(n4), rdnn(n2)))))))),
% 166.58/166.78 inference(monotonicity,[status(thm)],[201])).
% 166.58/166.78 tff(203,plain,
% 166.58/166.78 (((~![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(n24, n25) | (~rdn_translate(n24, rdn_pos(rdn(rdnn(n4), rdnn(n2))))) | (~rdn_translate(n25, rdn_pos(rdn(rdnn(n5), rdnn(n2))))) | (~rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), 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(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2)))) | (~rdn_translate(n25, rdn_pos(rdn(rdnn(n5), rdnn(n2))))) | less(n24, n25) | (~rdn_translate(n24, rdn_pos(rdn(rdnn(n4), rdnn(n2))))))),
% 166.58/166.78 inference(transitivity,[status(thm)],[202, 200])).
% 166.58/166.78 tff(204,plain,
% 166.58/166.78 ((~![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(n24, n25) | (~rdn_translate(n24, rdn_pos(rdn(rdnn(n4), rdnn(n2))))) | (~rdn_translate(n25, rdn_pos(rdn(rdnn(n5), rdnn(n2))))) | (~rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2)))))),
% 166.58/166.78 inference(quant_inst,[status(thm)],[])).
% 166.58/166.78 tff(205,plain,
% 166.58/166.78 ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | (~rdn_positive_less(rdn(rdnn(n4), rdnn(n2)), rdn(rdnn(n5), rdnn(n2)))) | (~rdn_translate(n25, rdn_pos(rdn(rdnn(n5), rdnn(n2))))) | less(n24, n25) | (~rdn_translate(n24, rdn_pos(rdn(rdnn(n4), rdnn(n2)))))),
% 166.58/166.78 inference(modus_ponens,[status(thm)],[204, 203])).
% 166.58/166.78 tff(206,plain,
% 166.58/166.78 ($false),
% 166.58/166.78 inference(unit_resolution,[status(thm)],[205, 199, 196, 93, 193, 175])).
% 166.58/166.78 % SZS output end Proof
% 166.58/166.78 % E exiting
%------------------------------------------------------------------------------