%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : AGT012+2 : TPTP v9.0.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 04:57:40 AM UTC 2025
% Result : Theorem 3.94s 4.11s
% Output : Proof 3.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : AGT012+2 : TPTP v9.0.0. Bugfixed v3.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 10:43:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.94/4.11 % SZS status Theorem
% 3.94/4.11 % SZS output start Proof
% 3.94/4.11 tff(less_type, type, (
% 3.94/4.11 less: ( $i * $i ) > $o)).
% 3.94/4.11 tff(n78_type, type, (
% 3.94/4.11 n78: $i)).
% 3.94/4.11 tff(n75_type, type, (
% 3.94/4.11 n75: $i)).
% 3.94/4.11 tff(accept_population_type, type, (
% 3.94/4.11 accept_population: ( $i * $i * $i ) > $o)).
% 3.94/4.11 tff(atheist_type, type, (
% 3.94/4.11 atheist: $i)).
% 3.94/4.11 tff(muslimcountrybhumanitarianorganization_type, type, (
% 3.94/4.11 muslimcountrybhumanitarianorganization: $i)).
% 3.94/4.11 tff(n0_type, type, (
% 3.94/4.11 n0: $i)).
% 3.94/4.11 tff(other_type, type, (
% 3.94/4.11 other: $i)).
% 3.94/4.11 tff(native_type, type, (
% 3.94/4.11 native: $i)).
% 3.94/4.11 tff(n1_type, type, (
% 3.94/4.11 n1: $i)).
% 3.94/4.11 tff(muslim_type, type, (
% 3.94/4.11 muslim: $i)).
% 3.94/4.11 tff(n24_type, type, (
% 3.94/4.11 n24: $i)).
% 3.94/4.11 tff(christian_type, type, (
% 3.94/4.11 christian: $i)).
% 3.94/4.11 tff(accept_city_type, type, (
% 3.94/4.11 accept_city: ( $i * $i ) > $o)).
% 3.94/4.11 tff(towna_type, type, (
% 3.94/4.11 towna: $i)).
% 3.94/4.11 tff(rdn_positive_less_type, type, (
% 3.94/4.11 rdn_positive_less: ( $i * $i ) > $o)).
% 3.94/4.11 tff(rdn_type, type, (
% 3.94/4.11 rdn: ( $i * $i ) > $i)).
% 3.94/4.11 tff(rdnn_type, type, (
% 3.94/4.11 rdnn: $i > $i)).
% 3.94/4.11 tff(n7_type, type, (
% 3.94/4.11 n7: $i)).
% 3.94/4.11 tff(n8_type, type, (
% 3.94/4.11 n8: $i)).
% 3.94/4.11 tff(n5_type, type, (
% 3.94/4.11 n5: $i)).
% 3.94/4.11 tff(n6_type, type, (
% 3.94/4.11 n6: $i)).
% 3.94/4.11 tff(rdn_non_zero_type, type, (
% 3.94/4.11 rdn_non_zero: $i > $o)).
% 3.94/4.11 tff(rdn_non_zero_digit_type, type, (
% 3.94/4.11 rdn_non_zero_digit: $i > $o)).
% 3.94/4.11 tff(rdn_translate_type, type, (
% 3.94/4.11 rdn_translate: ( $i * $i ) > $o)).
% 3.94/4.11 tff(rdn_pos_type, type, (
% 3.94/4.11 rdn_pos: $i > $i)).
% 3.94/4.11 tff(1,plain,
% 3.94/4.11 (^[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))))),
% 3.94/4.11 inference(bind,[status(th)],[])).
% 3.94/4.11 tff(2,plain,
% 3.94/4.11 (![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)))),
% 3.94/4.11 inference(quant_intro,[status(thm)],[1])).
% 3.94/4.11 tff(3,plain,
% 3.94/4.11 (^[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)))))),
% 3.96/4.11 inference(bind,[status(th)],[])).
% 3.96/4.11 tff(4,plain,
% 3.96/4.11 (![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)))),
% 3.96/4.11 inference(quant_intro,[status(thm)],[3])).
% 3.96/4.11 tff(5,plain,
% 3.96/4.11 (![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))),
% 3.96/4.11 inference(rewrite,[status(thm)],[])).
% 3.96/4.11 tff(6,plain,
% 3.96/4.11 (^[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)))),
% 3.96/4.11 inference(bind,[status(th)],[])).
% 3.96/4.11 tff(7,plain,
% 3.96/4.11 (![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))),
% 3.96/4.11 inference(quant_intro,[status(thm)],[6])).
% 3.96/4.11 tff(8,axiom,(![A: $i] : (((((accept_population(A, atheist, n75) & accept_population(A, christian, n24)) & accept_population(A, muslim, n1)) & accept_population(A, native, n0)) & accept_population(A, other, n0)) <=> accept_city(A, towna))), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+0.ax','a2_9')).
% 3.96/4.11 tff(9,plain,
% 3.96/4.11 (![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))),
% 3.96/4.11 inference(modus_ponens,[status(thm)],[8, 7])).
% 3.96/4.11 tff(10,plain,
% 3.96/4.11 (![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))),
% 3.96/4.11 inference(modus_ponens,[status(thm)],[9, 5])).
% 3.96/4.11 tff(11,plain,(
% 3.96/4.11 ![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))),
% 3.96/4.11 inference(skolemize,[status(sab)],[10])).
% 3.96/4.11 tff(12,plain,
% 3.96/4.11 (![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)))),
% 3.96/4.11 inference(modus_ponens,[status(thm)],[11, 4])).
% 3.96/4.11 tff(13,plain,
% 3.96/4.11 (![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)))),
% 3.96/4.11 inference(modus_ponens,[status(thm)],[12, 2])).
% 3.96/4.11 tff(14,plain,
% 3.96/4.11 ((~![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)))),
% 3.96/4.11 inference(quant_inst,[status(thm)],[])).
% 3.96/4.11 tff(15,plain,
% 3.96/4.11 (~(((~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))),
% 3.96/4.11 inference(unit_resolution,[status(thm)],[14, 13])).
% 3.96/4.11 tff(16,plain,
% 3.96/4.11 ((~accept_city(muslimcountrybhumanitarianorganization, towna)) <=> (~accept_city(muslimcountrybhumanitarianorganization, towna))),
% 3.96/4.11 inference(rewrite,[status(thm)],[])).
% 3.96/4.11 tff(17,axiom,(~accept_city(muslimcountrybhumanitarianorganization, towna)), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+2.ax','deduced_366')).
% 3.96/4.11 tff(18,plain,
% 3.96/4.11 (~accept_city(muslimcountrybhumanitarianorganization, towna)),
% 3.96/4.11 inference(modus_ponens,[status(thm)],[17, 16])).
% 3.96/4.11 tff(19,plain,
% 3.96/4.11 ((((~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)),
% 3.96/4.11 inference(tautology,[status(thm)],[])).
% 3.96/4.11 tff(20,plain,
% 3.96/4.11 ((((~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)))),
% 3.96/4.11 inference(unit_resolution,[status(thm)],[19, 18])).
% 3.96/4.11 tff(21,plain,
% 3.96/4.11 ((~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))),
% 3.96/4.11 inference(unit_resolution,[status(thm)],[20, 15])).
% 3.96/4.11 tff(22,plain,
% 3.96/4.11 (accept_population(muslimcountrybhumanitarianorganization, christian, n24) <=> accept_population(muslimcountrybhumanitarianorganization, christian, n24)),
% 3.96/4.11 inference(rewrite,[status(thm)],[])).
% 3.96/4.11 tff(23,plain,
% 3.96/4.11 ((~(~accept_population(muslimcountrybhumanitarianorganization, christian, n24))) <=> accept_population(muslimcountrybhumanitarianorganization, christian, n24)),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(24,axiom,(~(~accept_population(muslimcountrybhumanitarianorganization, christian, n24))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','query_12')).
% 3.96/4.12 tff(25,plain,
% 3.96/4.12 (accept_population(muslimcountrybhumanitarianorganization, christian, n24)),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[24, 23])).
% 3.96/4.12 tff(26,plain,
% 3.96/4.12 (accept_population(muslimcountrybhumanitarianorganization, christian, n24)),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[25, 22])).
% 3.96/4.12 tff(27,plain,
% 3.96/4.12 (accept_population(muslimcountrybhumanitarianorganization, muslim, n1) <=> accept_population(muslimcountrybhumanitarianorganization, muslim, n1)),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(28,axiom,(accept_population(muslimcountrybhumanitarianorganization, muslim, n1)), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+2.ax','deduced_204')).
% 3.96/4.12 tff(29,plain,
% 3.96/4.12 (accept_population(muslimcountrybhumanitarianorganization, muslim, n1)),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[28, 27])).
% 3.96/4.12 tff(30,plain,
% 3.96/4.12 (accept_population(muslimcountrybhumanitarianorganization, native, n0) <=> accept_population(muslimcountrybhumanitarianorganization, native, n0)),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(31,axiom,(accept_population(muslimcountrybhumanitarianorganization, native, n0)), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+2.ax','deduced_203')).
% 3.96/4.12 tff(32,plain,
% 3.96/4.12 (accept_population(muslimcountrybhumanitarianorganization, native, n0)),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[31, 30])).
% 3.96/4.12 tff(33,plain,
% 3.96/4.12 (accept_population(muslimcountrybhumanitarianorganization, other, n0) <=> accept_population(muslimcountrybhumanitarianorganization, other, n0)),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(34,axiom,(accept_population(muslimcountrybhumanitarianorganization, other, n0)), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+2.ax','deduced_93')).
% 3.96/4.12 tff(35,plain,
% 3.96/4.12 (accept_population(muslimcountrybhumanitarianorganization, other, n0)),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[34, 33])).
% 3.96/4.12 tff(36,plain,
% 3.96/4.12 ((~((~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))),
% 3.96/4.12 inference(tautology,[status(thm)],[])).
% 3.96/4.12 tff(37,plain,
% 3.96/4.12 ((~((~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))),
% 3.96/4.12 inference(unit_resolution,[status(thm)],[36, 35, 32, 29, 26])).
% 3.96/4.12 tff(38,plain,
% 3.96/4.12 (~accept_population(muslimcountrybhumanitarianorganization, atheist, n75)),
% 3.96/4.12 inference(unit_resolution,[status(thm)],[37, 21])).
% 3.96/4.12 tff(39,plain,
% 3.96/4.12 (accept_population(muslimcountrybhumanitarianorganization, atheist, n78) <=> accept_population(muslimcountrybhumanitarianorganization, atheist, n78)),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(40,axiom,(accept_population(muslimcountrybhumanitarianorganization, atheist, n78)), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+2.ax','deduced_206')).
% 3.96/4.12 tff(41,plain,
% 3.96/4.12 (accept_population(muslimcountrybhumanitarianorganization, atheist, n78)),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[40, 39])).
% 3.96/4.12 tff(42,plain,
% 3.96/4.12 (^[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))))),
% 3.96/4.12 inference(bind,[status(th)],[])).
% 3.96/4.12 tff(43,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(quant_intro,[status(thm)],[42])).
% 3.96/4.12 tff(44,plain,
% 3.96/4.12 (^[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)))))),
% 3.96/4.12 inference(bind,[status(th)],[])).
% 3.96/4.12 tff(45,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(quant_intro,[status(thm)],[44])).
% 3.96/4.12 tff(46,plain,
% 3.96/4.12 (![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))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(47,plain,
% 3.96/4.12 (^[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)))),
% 3.96/4.12 inference(bind,[status(th)],[])).
% 3.96/4.12 tff(48,plain,
% 3.96/4.12 (![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))),
% 3.96/4.12 inference(quant_intro,[status(thm)],[47])).
% 3.96/4.12 tff(49,axiom,(![A: $i, N: $i, M: $i, P: $i] : ((accept_population(A, P, N) & less(M, N)) => accept_population(A, P, M))), file('/export/starexec/sandbox/benchmark/Axioms/AGT001+0.ax','a1_3')).
% 3.96/4.12 tff(50,plain,
% 3.96/4.12 (![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[49, 48])).
% 3.96/4.12 tff(51,plain,
% 3.96/4.12 (![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[50, 46])).
% 3.96/4.12 tff(52,plain,(
% 3.96/4.12 ![A: $i, N: $i, M: $i, P: $i] : ((~(accept_population(A, P, N) & less(M, N))) | accept_population(A, P, M))),
% 3.96/4.12 inference(skolemize,[status(sab)],[51])).
% 3.96/4.12 tff(53,plain,
% 3.96/4.12 (![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[52, 45])).
% 3.96/4.12 tff(54,plain,
% 3.96/4.12 (![A: $i, N: $i, M: $i, P: $i] : (accept_population(A, P, M) | (~accept_population(A, P, N)) | (~less(M, N)))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[53, 43])).
% 3.96/4.12 tff(55,plain,
% 3.96/4.12 (((~![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)))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(56,plain,
% 3.96/4.12 ((~![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)))),
% 3.96/4.12 inference(quant_inst,[status(thm)],[])).
% 3.96/4.12 tff(57,plain,
% 3.96/4.12 ((~![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))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[56, 55])).
% 3.96/4.12 tff(58,plain,
% 3.96/4.12 (~less(n75, n78)),
% 3.96/4.12 inference(unit_resolution,[status(thm)],[57, 54, 41, 38])).
% 3.96/4.12 tff(59,assumption,(~rdn_positive_less(rdnn(n6), rdnn(n8))), introduced(assumption)).
% 3.96/4.12 tff(60,plain,
% 3.96/4.12 (^[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)))))),
% 3.96/4.12 inference(bind,[status(th)],[])).
% 3.96/4.12 tff(61,plain,
% 3.96/4.12 (![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))))),
% 3.96/4.12 inference(quant_intro,[status(thm)],[60])).
% 3.96/4.12 tff(62,plain,
% 3.96/4.12 (^[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))))))),
% 3.96/4.12 inference(bind,[status(th)],[])).
% 3.96/4.12 tff(63,plain,
% 3.96/4.12 (![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))))),
% 3.96/4.12 inference(quant_intro,[status(thm)],[62])).
% 3.96/4.12 tff(64,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(65,plain,
% 3.96/4.12 (^[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))))),
% 3.96/4.12 inference(bind,[status(th)],[])).
% 3.96/4.12 tff(66,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(quant_intro,[status(thm)],[65])).
% 3.96/4.12 tff(67,axiom,(![X: $i, Y: $i, Z: $i] : ((rdn_positive_less(rdnn(X), rdnn(Y)) & rdn_positive_less(rdnn(Y), rdnn(Z))) => rdn_positive_less(rdnn(X), rdnn(Z)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less_transitivity')).
% 3.96/4.12 tff(68,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[67, 66])).
% 3.96/4.12 tff(69,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[68, 64])).
% 3.96/4.12 tff(70,plain,(
% 3.96/4.12 ![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)))),
% 3.96/4.12 inference(skolemize,[status(sab)],[69])).
% 3.96/4.12 tff(71,plain,
% 3.96/4.12 (![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))))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[70, 63])).
% 3.96/4.12 tff(72,plain,
% 3.96/4.12 (![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))))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[71, 61])).
% 3.96/4.12 tff(73,plain,
% 3.96/4.12 (rdn_positive_less(rdnn(n7), rdnn(n8)) <=> rdn_positive_less(rdnn(n7), rdnn(n8))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(74,axiom,(rdn_positive_less(rdnn(n7), rdnn(n8))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less78')).
% 3.96/4.12 tff(75,plain,
% 3.96/4.12 (rdn_positive_less(rdnn(n7), rdnn(n8))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[74, 73])).
% 3.96/4.12 tff(76,plain,
% 3.96/4.12 (rdn_positive_less(rdnn(n6), rdnn(n7)) <=> rdn_positive_less(rdnn(n6), rdnn(n7))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(77,axiom,(rdn_positive_less(rdnn(n6), rdnn(n7))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less67')).
% 3.96/4.12 tff(78,plain,
% 3.96/4.12 (rdn_positive_less(rdnn(n6), rdnn(n7))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[77, 76])).
% 3.96/4.12 tff(79,plain,
% 3.96/4.12 (((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | ((~rdn_positive_less(rdnn(n6), rdnn(n7))) | rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))) <=> ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n6), rdnn(n7))) | rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(80,plain,
% 3.96/4.12 ((rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n7))) | (~rdn_positive_less(rdnn(n7), rdnn(n8)))) <=> ((~rdn_positive_less(rdnn(n6), rdnn(n7))) | rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(81,plain,
% 3.96/4.12 (((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n7))) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))) <=> ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | ((~rdn_positive_less(rdnn(n6), rdnn(n7))) | rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8)))))),
% 3.96/4.12 inference(monotonicity,[status(thm)],[80])).
% 3.96/4.12 tff(82,plain,
% 3.96/4.12 (((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n7))) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))) <=> ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n6), rdnn(n7))) | rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))),
% 3.96/4.12 inference(transitivity,[status(thm)],[81, 79])).
% 3.96/4.12 tff(83,plain,
% 3.96/4.12 ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n7))) | (~rdn_positive_less(rdnn(n7), rdnn(n8))))),
% 3.96/4.12 inference(quant_inst,[status(thm)],[])).
% 3.96/4.12 tff(84,plain,
% 3.96/4.12 ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n6), rdnn(n7))) | rdn_positive_less(rdnn(n6), rdnn(n8)) | (~rdn_positive_less(rdnn(n7), rdnn(n8)))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[83, 82])).
% 3.96/4.12 tff(85,plain,
% 3.96/4.12 ($false),
% 3.96/4.12 inference(unit_resolution,[status(thm)],[84, 78, 75, 72, 59])).
% 3.96/4.12 tff(86,plain,(rdn_positive_less(rdnn(n6), rdnn(n8))), inference(lemma,lemma(discharge,[]))).
% 3.96/4.12 tff(87,assumption,(~rdn_positive_less(rdnn(n5), rdnn(n8))), introduced(assumption)).
% 3.96/4.12 tff(88,plain,
% 3.96/4.12 (rdn_positive_less(rdnn(n5), rdnn(n6)) <=> rdn_positive_less(rdnn(n5), rdnn(n6))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(89,axiom,(rdn_positive_less(rdnn(n5), rdnn(n6))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less56')).
% 3.96/4.12 tff(90,plain,
% 3.96/4.12 (rdn_positive_less(rdnn(n5), rdnn(n6))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[89, 88])).
% 3.96/4.12 tff(91,plain,
% 3.96/4.12 (((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | ((~rdn_positive_less(rdnn(n5), rdnn(n6))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n8))))) <=> ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n8))))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(92,plain,
% 3.96/4.12 ((rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | (~rdn_positive_less(rdnn(n6), rdnn(n8)))) <=> ((~rdn_positive_less(rdnn(n5), rdnn(n6))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n8))))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(93,plain,
% 3.96/4.12 (((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | (~rdn_positive_less(rdnn(n6), rdnn(n8))))) <=> ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | ((~rdn_positive_less(rdnn(n5), rdnn(n6))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n8)))))),
% 3.96/4.12 inference(monotonicity,[status(thm)],[92])).
% 3.96/4.12 tff(94,plain,
% 3.96/4.12 (((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | (~rdn_positive_less(rdnn(n6), rdnn(n8))))) <=> ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n8))))),
% 3.96/4.12 inference(transitivity,[status(thm)],[93, 91])).
% 3.96/4.12 tff(95,plain,
% 3.96/4.12 ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | (~rdn_positive_less(rdnn(n6), rdnn(n8))))),
% 3.96/4.12 inference(quant_inst,[status(thm)],[])).
% 3.96/4.12 tff(96,plain,
% 3.96/4.12 ((~![X: $i, Y: $i, Z: $i] : (rdn_positive_less(rdnn(X), rdnn(Z)) | (~rdn_positive_less(rdnn(X), rdnn(Y))) | (~rdn_positive_less(rdnn(Y), rdnn(Z))))) | (~rdn_positive_less(rdnn(n5), rdnn(n6))) | rdn_positive_less(rdnn(n5), rdnn(n8)) | (~rdn_positive_less(rdnn(n6), rdnn(n8)))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[95, 94])).
% 3.96/4.12 tff(97,plain,
% 3.96/4.12 ($false),
% 3.96/4.12 inference(unit_resolution,[status(thm)],[96, 90, 72, 87, 86])).
% 3.96/4.12 tff(98,plain,(rdn_positive_less(rdnn(n5), rdnn(n8))), inference(lemma,lemma(discharge,[]))).
% 3.96/4.12 tff(99,plain,
% 3.96/4.12 (^[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)))))),
% 3.96/4.12 inference(bind,[status(th)],[])).
% 3.96/4.12 tff(100,plain,
% 3.96/4.12 (![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))))),
% 3.96/4.12 inference(quant_intro,[status(thm)],[99])).
% 3.96/4.12 tff(101,plain,
% 3.96/4.12 (![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))))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(102,plain,
% 3.96/4.12 (^[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)))))),
% 3.96/4.12 inference(bind,[status(th)],[])).
% 3.96/4.12 tff(103,plain,
% 3.96/4.12 (![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))))),
% 3.96/4.12 inference(quant_intro,[status(thm)],[102])).
% 3.96/4.12 tff(104,axiom,(![X: $i] : (rdn_non_zero_digit(rdnn(X)) => rdn_non_zero(rdnn(X)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_non_zero_by_digit')).
% 3.96/4.12 tff(105,plain,
% 3.96/4.12 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[104, 103])).
% 3.96/4.12 tff(106,plain,
% 3.96/4.12 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[105, 101])).
% 3.96/4.12 tff(107,plain,(
% 3.96/4.12 ![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 3.96/4.12 inference(skolemize,[status(sab)],[106])).
% 3.96/4.12 tff(108,plain,
% 3.96/4.12 (![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[107, 100])).
% 3.96/4.12 tff(109,plain,
% 3.96/4.12 (rdn_non_zero_digit(rdnn(n7)) <=> rdn_non_zero_digit(rdnn(n7))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(110,axiom,(rdn_non_zero_digit(rdnn(n7))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_digit7')).
% 3.96/4.12 tff(111,plain,
% 3.96/4.12 (rdn_non_zero_digit(rdnn(n7))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[110, 109])).
% 3.96/4.12 tff(112,plain,
% 3.96/4.12 (((~![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))))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(113,plain,
% 3.96/4.12 ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | (rdn_non_zero(rdnn(n7)) | (~rdn_non_zero_digit(rdnn(n7))))),
% 3.96/4.12 inference(quant_inst,[status(thm)],[])).
% 3.96/4.12 tff(114,plain,
% 3.96/4.12 ((~![X: $i] : (rdn_non_zero(rdnn(X)) | (~rdn_non_zero_digit(rdnn(X))))) | rdn_non_zero(rdnn(n7)) | (~rdn_non_zero_digit(rdnn(n7)))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[113, 112])).
% 3.96/4.12 tff(115,plain,
% 3.96/4.12 (rdn_non_zero(rdnn(n7))),
% 3.96/4.12 inference(unit_resolution,[status(thm)],[114, 111, 108])).
% 3.96/4.12 tff(116,plain,
% 3.96/4.12 (^[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))))),
% 3.96/4.12 inference(bind,[status(th)],[])).
% 3.96/4.12 tff(117,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(quant_intro,[status(thm)],[116])).
% 3.96/4.12 tff(118,plain,
% 3.96/4.12 (^[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)))))),
% 3.96/4.12 inference(bind,[status(th)],[])).
% 3.96/4.12 tff(119,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(quant_intro,[status(thm)],[118])).
% 3.96/4.12 tff(120,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(121,plain,
% 3.96/4.12 (^[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))))),
% 3.96/4.12 inference(bind,[status(th)],[])).
% 3.96/4.12 tff(122,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(quant_intro,[status(thm)],[121])).
% 3.96/4.12 tff(123,axiom,(![Ds: $i, O: $i, Db: $i] : ((rdn_positive_less(rdnn(Ds), rdnn(Db)) & rdn_non_zero(O)) => rdn_positive_less(rdn(rdnn(Ds), O), rdn(rdnn(Db), O)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','rdn_positive_less_multi_digit_low')).
% 3.96/4.12 tff(124,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[123, 122])).
% 3.96/4.12 tff(125,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[124, 120])).
% 3.96/4.12 tff(126,plain,(
% 3.96/4.12 ![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)))),
% 3.96/4.12 inference(skolemize,[status(sab)],[125])).
% 3.96/4.12 tff(127,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[126, 119])).
% 3.96/4.12 tff(128,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[127, 117])).
% 3.96/4.12 tff(129,plain,
% 3.96/4.12 (((~![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))))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(130,plain,
% 3.96/4.12 ((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))))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(131,plain,
% 3.96/4.12 (((~![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)))))),
% 3.96/4.12 inference(monotonicity,[status(thm)],[130])).
% 3.96/4.12 tff(132,plain,
% 3.96/4.12 (((~![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))))),
% 3.96/4.12 inference(transitivity,[status(thm)],[131, 129])).
% 3.96/4.12 tff(133,plain,
% 3.96/4.12 ((~![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))))),
% 3.96/4.12 inference(quant_inst,[status(thm)],[])).
% 3.96/4.12 tff(134,plain,
% 3.96/4.12 ((~![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)))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[133, 132])).
% 3.96/4.12 tff(135,plain,
% 3.96/4.12 ((~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)))),
% 3.96/4.12 inference(unit_resolution,[status(thm)],[134, 128])).
% 3.96/4.12 tff(136,plain,
% 3.96/4.12 ((~rdn_positive_less(rdnn(n5), rdnn(n8))) | rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))),
% 3.96/4.12 inference(unit_resolution,[status(thm)],[135, 115])).
% 3.96/4.12 tff(137,plain,
% 3.96/4.12 (rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7)))),
% 3.96/4.12 inference(unit_resolution,[status(thm)],[136, 98])).
% 3.96/4.12 tff(138,plain,
% 3.96/4.12 (^[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))))),
% 3.96/4.12 inference(bind,[status(th)],[])).
% 3.96/4.12 tff(139,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(quant_intro,[status(thm)],[138])).
% 3.96/4.12 tff(140,plain,
% 3.96/4.12 (^[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)))))),
% 3.96/4.12 inference(bind,[status(th)],[])).
% 3.96/4.12 tff(141,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(quant_intro,[status(thm)],[140])).
% 3.96/4.12 tff(142,plain,
% 3.96/4.12 (![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))),
% 3.96/4.12 inference(rewrite,[status(thm)],[])).
% 3.96/4.12 tff(143,plain,
% 3.96/4.12 (^[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))))),
% 3.96/4.12 inference(bind,[status(th)],[])).
% 3.96/4.12 tff(144,plain,
% 3.96/4.12 (![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))),
% 3.96/4.12 inference(quant_intro,[status(thm)],[143])).
% 3.96/4.12 tff(145,axiom,(![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (((rdn_translate(X, rdn_pos(RDN_X)) & rdn_translate(Y, rdn_pos(RDN_Y))) & rdn_positive_less(RDN_X, RDN_Y)) => less(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax','less_entry_point_pos_pos')).
% 3.96/4.12 tff(146,plain,
% 3.96/4.12 (![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))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[145, 144])).
% 3.96/4.12 tff(147,plain,
% 3.96/4.12 (![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))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[146, 142])).
% 3.96/4.12 tff(148,plain,(
% 3.96/4.12 ![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))),
% 3.96/4.12 inference(skolemize,[status(sab)],[147])).
% 3.96/4.12 tff(149,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[148, 141])).
% 3.96/4.12 tff(150,plain,
% 3.96/4.12 (![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)))),
% 3.96/4.12 inference(modus_ponens,[status(thm)],[149, 139])).
% 3.98/4.16 tff(151,plain,
% 3.98/4.16 (rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7)))) <=> rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))),
% 3.98/4.16 inference(rewrite,[status(thm)],[])).
% 3.98/4.16 tff(152,axiom,(rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax','rdn78')).
% 3.98/4.16 tff(153,plain,
% 3.98/4.16 (rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))),
% 3.98/4.16 inference(modus_ponens,[status(thm)],[152, 151])).
% 3.98/4.16 tff(154,plain,
% 3.98/4.16 (rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7)))) <=> rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))),
% 3.98/4.16 inference(rewrite,[status(thm)],[])).
% 3.98/4.16 tff(155,axiom,(rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))), file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax','rdn75')).
% 3.98/4.16 tff(156,plain,
% 3.98/4.16 (rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))),
% 3.98/4.16 inference(modus_ponens,[status(thm)],[155, 154])).
% 3.98/4.16 tff(157,plain,
% 3.98/4.16 (((~![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)))) | 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)))))),
% 3.98/4.16 inference(rewrite,[status(thm)],[])).
% 3.98/4.16 tff(158,plain,
% 3.98/4.16 ((~![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)))))),
% 3.98/4.16 inference(quant_inst,[status(thm)],[])).
% 3.98/4.16 tff(159,plain,
% 3.98/4.16 ((~![X: $i, Y: $i, RDN_X: $i, RDN_Y: $i] : (less(X, Y) | (~rdn_translate(X, rdn_pos(RDN_X))) | (~rdn_translate(Y, rdn_pos(RDN_Y))) | (~rdn_positive_less(RDN_X, RDN_Y)))) | less(n75, n78) | (~rdn_translate(n75, rdn_pos(rdn(rdnn(n5), rdnn(n7))))) | (~rdn_translate(n78, rdn_pos(rdn(rdnn(n8), rdnn(n7))))) | (~rdn_positive_less(rdn(rdnn(n5), rdnn(n7)), rdn(rdnn(n8), rdnn(n7))))),
% 3.98/4.16 inference(modus_ponens,[status(thm)],[158, 157])).
% 3.98/4.16 tff(160,plain,
% 3.98/4.16 ($false),
% 3.98/4.16 inference(unit_resolution,[status(thm)],[159, 156, 153, 150, 137, 58])).
% 3.98/4.16 % SZS output end Proof
% 3.98/4.16 % E exiting
%------------------------------------------------------------------------------