0.04/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s 0.14/0.35 % Computer : n014.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1440 0.14/0.35 % WCLimit : 180 0.14/0.35 % DateTime : Thu Jul 4 08:52:54 EDT 2024 0.14/0.35 % CPUTime : 0.14/0.36 0.14/0.36 No.of.Axioms: 10 0.14/0.36 0.14/0.36 Length.of.Defs: 0 0.14/0.36 0.14/0.36 Contains.Choice.Funs: true 0.14/0.37 (rf:0,axioms:10,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:12,loop_count:0,foatp_calls:0,translation:fof_full)...eprover: CPU time limit exceeded, terminating 25.27/25.47 .eprover: CPU time limit exceeded, terminating 50.45/50.71 . 50.58/50.82 50.58/50.82 Prim_subst applied to clause 50.58/50.82 50.58/50.82 85:[ 0:-w(1)-i() 1:-w(1)-i() 2:-w(1)-i() ]-mln(3)-w(3)-i(rename 55)-o(AXIOM)-fv([ SV37 ]) 50.75/51.00 .eprover: CPU time limit exceeded, terminating 76.52/76.82 .. 77.33/77.63 77.33/77.63 Prim_subst applied to clause 77.33/77.63 77.33/77.63 194:[ 0:-w(1)-i() 1:-w(1)-i() 2:-w(1)-i() ]-mln(3)-w(3)-i(rename 64)-o(AXIOM)-fv([ SV85 ]) 77.76/78.08 ....eprover: CPU time limit exceeded, terminating 105.64/105.97 .... 106.99/107.31 106.99/107.31 Prim_subst applied to clause 106.99/107.31 106.99/107.31 464:[ 0:-w(1)-i() 1:-w(1)-i() 2:-w(1)-i() 3:-w(1)-i() ]-mln(4)-w(4)-i(rename 114)-o(AXIOM)-fv([ SV165 SV166 ]) 107.99/108.28 107.99/108.28 Prim_subst applied to clause 107.99/108.28 107.99/108.28 464:[ 0:-w(1)-i() 1:-w(1)-i() 2:-w(1)-i() 3:-w(1)-i() ]-mln(4)-w(4)-i(rename 114)-o(AXIOM)-fv([ SV165 SV166 ]) 109.33/109.61 ........ 159.86/160.20 159.86/160.20 ******************************** 159.86/160.20 * All subproblems solved! * 159.86/160.20 ******************************** 159.86/160.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:867,loop_count:30,foatp_calls:5,translation:fof_full) 160.12/160.41 160.12/160.41 %**** Beginning of derivation protocol **** 160.12/160.41 % SZS output start CNFRefutation 160.12/160.41 thf(tp_frac,type,(frac: $tType)). 160.12/160.41 thf(tp_nat,type,(nat: $tType)). 160.12/160.41 thf(tp_amone,type,(amone: ((nat>$o)>$o))). 160.12/160.41 thf(tp_den,type,(den: (frac>nat))). 160.12/160.41 thf(tp_eq,type,(eq: (frac>(frac>$o)))). 160.12/160.41 thf(tp_fr,type,(fr: (nat>(nat>frac)))). 160.12/160.41 thf(tp_ind,type,(ind: ((nat>$o)>nat))). 160.12/160.41 thf(tp_num,type,(num: (frac>nat))). 160.12/160.41 thf(tp_pf,type,(pf: (frac>(frac>frac)))). 160.12/160.41 thf(tp_pl,type,(pl: (nat>(nat>nat)))). 160.12/160.41 thf(tp_sK10_E,type,(sK10_E: nat)). 160.12/160.41 thf(tp_sK11_E,type,(sK11_E: nat)). 160.12/160.41 thf(tp_sK12_E,type,(sK12_E: nat)). 160.12/160.41 thf(tp_sK13_E,type,(sK13_E: nat)). 160.12/160.41 thf(tp_sK14_E,type,(sK14_E: (nat>(nat>nat)))). 160.12/160.41 thf(tp_sK15_E,type,(sK15_E: nat)). 160.12/160.41 thf(tp_sK16_E,type,(sK16_E: nat)). 160.12/160.41 thf(tp_sK17_E,type,(sK17_E: (nat>(nat>nat)))). 160.12/160.41 thf(tp_sK18_E,type,(sK18_E: nat)). 160.12/160.41 thf(tp_sK19_E,type,(sK19_E: nat)). 160.12/160.41 thf(tp_sK1_E,type,(sK1_E: nat)). 160.12/160.41 thf(tp_sK20_E,type,(sK20_E: nat)). 160.12/160.41 thf(tp_sK21_E,type,(sK21_E: nat)). 160.12/160.41 thf(tp_sK22_E,type,(sK22_E: nat)). 160.12/160.41 thf(tp_sK23_E,type,(sK23_E: nat)). 160.12/160.41 thf(tp_sK24_E,type,(sK24_E: nat)). 160.12/160.41 thf(tp_sK25_E,type,(sK25_E: ((nat>$o)>((nat>$o)>nat)))). 160.12/160.41 thf(tp_sK26_E,type,(sK26_E: (nat>(nat>((nat>$o)>((nat>$o)>nat)))))). 160.12/160.41 thf(tp_sK2_E,type,(sK2_E: ((nat>$o)>nat))). 160.12/160.41 thf(tp_sK3_E,type,(sK3_E: (nat>(nat>((nat>$o)>nat))))). 160.12/160.41 thf(tp_sK4_E,type,(sK4_E: nat)). 160.12/160.41 thf(tp_sK5_E,type,(sK5_E: nat)). 160.12/160.41 thf(tp_sK6_E,type,(sK6_E: nat)). 160.12/160.41 thf(tp_sK7_E,type,(sK7_E: (nat>(nat>nat)))). 160.12/160.41 thf(tp_sK8_E,type,(sK8_E: nat)). 160.12/160.41 thf(tp_sK9_E,type,(sK9_E: nat)). 160.12/160.41 thf(tp_some,type,(some: ((nat>$o)>$o))). 160.12/160.41 thf(tp_ts,type,(ts: (nat>(nat>nat)))). 160.12/160.41 thf(tp_x,type,(x: frac)). 160.12/160.41 thf(tp_y,type,(y: frac)). 160.12/160.41 thf(1,axiom,(![Xp:(nat>$o)]: ((Xp@(ind@Xp)) <= (~ ((~ (some@Xp)) <= (amone@Xp))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',oneax)). 160.12/160.41 thf(2,axiom,(![Xx:frac]: ((eq@Xx)@Xx)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz37)). 160.12/160.41 thf(3,axiom,(![Xx:frac,Xn:nat]: ((eq@((fr@((ts@(num@Xx))@Xn))@((ts@(den@Xx))@Xn)))@Xx)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz40a)). 160.12/160.41 thf(4,axiom,(![Xx:frac,Xy:frac,Xz:frac,Xu:frac]: (((eq@Xx)@Xy) => (((eq@Xz)@Xu) => ((eq@((pf@Xx)@Xz))@((pf@Xy)@Xu))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz56)). 160.12/160.41 thf(5,axiom,(![Xx1:nat,Xx2:nat,Xn:nat]: ((eq@((pf@((fr@Xx1)@Xn))@((fr@Xx2)@Xn)))@((fr@((pl@Xx1)@Xx2))@Xn))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz57)). 160.12/160.41 thf(6,axiom,(some@(^[Xu:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xu)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',m)). 160.12/160.41 thf(7,axiom,(![Xx:frac,Xn:nat]: ((eq@Xx)@((fr@((ts@(num@Xx))@Xn))@((ts@(den@Xx))@Xn)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz40)). 160.12/160.41 thf(8,axiom,(![Xx:nat,Xy:nat]: (((ts@Xx)@Xy) = ((ts@Xy)@Xx))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz29)). 160.12/160.41 thf(9,axiom,(![Xx:nat,Xy:nat]: (amone@(^[Xz:nat]: (Xx = ((pl@Xy)@Xz))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz8b)). 160.12/160.41 thf(10,axiom,(![Xx:frac,Xy:frac,Xz:frac]: ((((eq@Xy)@Xz) => ((eq@Xx)@Xz)) <= ((eq@Xx)@Xy))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz39)). 160.12/160.41 thf(11,conjecture,((eq@((pf@y)@((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y)))))@x),file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz67c)). 160.12/160.41 thf(12,negated_conjecture,((((eq@((pf@y)@((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y)))))@x)=$false)),inference(negate_conjecture,[status(cth)],[11])). 160.12/160.41 thf(13,plain,(((~ ((eq@((pf@y)@((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y)))))@x))=$true)),inference(polarity_switch,[status(thm)],[12])). 160.12/160.41 thf(14,plain,(((![Xp:(nat>$o)]: (((~ (amone@Xp)) | (~ (some@Xp))) | (Xp@(ind@Xp))))=$true)),inference(extcnf_combined,[status(esa)],[1])). 160.12/160.41 thf(15,plain,(((![Xx:frac,Xy:frac]: ((~ ((eq@Xx)@Xy)) | (![Xz:frac,Xu:frac]: ((~ ((eq@Xz)@Xu)) | ((eq@((pf@Xx)@Xz))@((pf@Xy)@Xu))))))=$true)),inference(extcnf_combined,[status(esa)],[4])). 160.12/160.41 thf(16,plain,(((![Xx:frac,Xy:frac]: ((~ ((eq@Xx)@Xy)) | (![Xz:frac]: ((~ ((eq@Xy)@Xz)) | ((eq@Xx)@Xz)))))=$true)),inference(extcnf_combined,[status(esa)],[10])). 160.12/160.41 thf(17,plain,(((![Xx:frac,Xy:frac]: ((~ ((eq@Xx)@Xy)) | (![Xz:frac]: ((~ ((eq@Xy)@Xz)) | ((eq@Xx)@Xz)))))=$true)),inference(copy,[status(thm)],[16])). 160.12/160.41 thf(18,plain,(((![Xx:nat,Xy:nat]: (amone@(^[Xz:nat]: (Xx = ((pl@Xy)@Xz)))))=$true)),inference(copy,[status(thm)],[9])). 160.12/160.41 thf(19,plain,(((![Xx:nat,Xy:nat]: (((ts@Xx)@Xy) = ((ts@Xy)@Xx)))=$true)),inference(copy,[status(thm)],[8])). 160.12/160.41 thf(20,plain,(((![Xx:frac,Xn:nat]: ((eq@Xx)@((fr@((ts@(num@Xx))@Xn))@((ts@(den@Xx))@Xn))))=$true)),inference(copy,[status(thm)],[7])). 160.12/160.41 thf(21,plain,(((some@(^[Xu:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xu))))=$true)),inference(copy,[status(thm)],[6])). 160.12/160.41 thf(22,plain,(((![Xx1:nat,Xx2:nat,Xn:nat]: ((eq@((pf@((fr@Xx1)@Xn))@((fr@Xx2)@Xn)))@((fr@((pl@Xx1)@Xx2))@Xn)))=$true)),inference(copy,[status(thm)],[5])). 160.12/160.41 thf(23,plain,(((![Xx:frac,Xy:frac]: ((~ ((eq@Xx)@Xy)) | (![Xz:frac,Xu:frac]: ((~ ((eq@Xz)@Xu)) | ((eq@((pf@Xx)@Xz))@((pf@Xy)@Xu))))))=$true)),inference(copy,[status(thm)],[15])). 160.12/160.41 thf(24,plain,(((![Xx:frac,Xn:nat]: ((eq@((fr@((ts@(num@Xx))@Xn))@((ts@(den@Xx))@Xn)))@Xx))=$true)),inference(copy,[status(thm)],[3])). 160.12/160.41 thf(25,plain,(((![Xx:frac]: ((eq@Xx)@Xx))=$true)),inference(copy,[status(thm)],[2])). 160.12/160.41 thf(26,plain,(((![Xp:(nat>$o)]: (((~ (amone@Xp)) | (~ (some@Xp))) | (Xp@(ind@Xp))))=$true)),inference(copy,[status(thm)],[14])). 160.12/160.41 thf(27,plain,(((~ ((eq@((pf@y)@((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y)))))@x))=$true)),inference(copy,[status(thm)],[13])). 160.12/160.41 thf(28,plain,(![SV1:frac]: (((![SY0:frac]: ((~ ((eq@SV1)@SY0)) | (![SY1:frac]: ((~ ((eq@SY0)@SY1)) | ((eq@SV1)@SY1)))))=$true))),inference(extcnf_forall_pos,[status(thm)],[17])). 160.12/160.41 thf(29,plain,(![SV2:nat]: (((![SY2:nat]: (amone@(^[SY3:nat]: (SV2 = ((pl@SY2)@SY3)))))=$true))),inference(extcnf_forall_pos,[status(thm)],[18])). 160.12/160.41 thf(30,plain,(![SV3:nat]: (((![SY4:nat]: (((ts@SV3)@SY4) = ((ts@SY4)@SV3)))=$true))),inference(extcnf_forall_pos,[status(thm)],[19])). 160.12/160.41 thf(31,plain,(![SV4:frac]: (((![SY5:nat]: ((eq@SV4)@((fr@((ts@(num@SV4))@SY5))@((ts@(den@SV4))@SY5))))=$true))),inference(extcnf_forall_pos,[status(thm)],[20])). 160.12/160.41 thf(32,plain,(![SV5:nat]: (((![SY6:nat,SY7:nat]: ((eq@((pf@((fr@SV5)@SY7))@((fr@SY6)@SY7)))@((fr@((pl@SV5)@SY6))@SY7)))=$true))),inference(extcnf_forall_pos,[status(thm)],[22])). 160.12/160.41 thf(33,plain,(![SV6:frac]: (((![SY8:frac]: ((~ ((eq@SV6)@SY8)) | (![SY9:frac,SY10:frac]: ((~ ((eq@SY9)@SY10)) | ((eq@((pf@SV6)@SY9))@((pf@SY8)@SY10))))))=$true))),inference(extcnf_forall_pos,[status(thm)],[23])). 160.12/160.41 thf(34,plain,(![SV7:frac]: (((![SY11:nat]: ((eq@((fr@((ts@(num@SV7))@SY11))@((ts@(den@SV7))@SY11)))@SV7))=$true))),inference(extcnf_forall_pos,[status(thm)],[24])). 160.12/160.41 thf(35,plain,(![SV8:frac]: ((((eq@SV8)@SV8)=$true))),inference(extcnf_forall_pos,[status(thm)],[25])). 160.12/160.41 thf(36,plain,(![SV9:(nat>$o)]: (((((~ (amone@SV9)) | (~ (some@SV9))) | (SV9@(ind@SV9)))=$true))),inference(extcnf_forall_pos,[status(thm)],[26])). 160.12/160.41 thf(37,plain,((((eq@((pf@y)@((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y)))))@x)=$false)),inference(extcnf_not_pos,[status(thm)],[27])). 160.12/160.41 thf(38,plain,(![SV10:frac,SV1:frac]: ((((~ ((eq@SV1)@SV10)) | (![SY12:frac]: ((~ ((eq@SV10)@SY12)) | ((eq@SV1)@SY12))))=$true))),inference(extcnf_forall_pos,[status(thm)],[28])). 160.12/160.41 thf(39,plain,(![SV11:nat,SV2:nat]: (((amone@(^[SY13:nat]: (SV2 = ((pl@SV11)@SY13))))=$true))),inference(extcnf_forall_pos,[status(thm)],[29])). 160.12/160.41 thf(40,plain,(![SV12:nat,SV3:nat]: (((((ts@SV3)@SV12) = ((ts@SV12)@SV3))=$true))),inference(extcnf_forall_pos,[status(thm)],[30])). 160.12/160.41 thf(41,plain,(![SV13:nat,SV4:frac]: ((((eq@SV4)@((fr@((ts@(num@SV4))@SV13))@((ts@(den@SV4))@SV13)))=$true))),inference(extcnf_forall_pos,[status(thm)],[31])). 160.12/160.41 thf(42,plain,(![SV14:nat,SV5:nat]: (((![SY14:nat]: ((eq@((pf@((fr@SV5)@SY14))@((fr@SV14)@SY14)))@((fr@((pl@SV5)@SV14))@SY14)))=$true))),inference(extcnf_forall_pos,[status(thm)],[32])). 160.12/160.41 thf(43,plain,(![SV15:frac,SV6:frac]: ((((~ ((eq@SV6)@SV15)) | (![SY15:frac,SY16:frac]: ((~ ((eq@SY15)@SY16)) | ((eq@((pf@SV6)@SY15))@((pf@SV15)@SY16)))))=$true))),inference(extcnf_forall_pos,[status(thm)],[33])). 160.12/160.41 thf(44,plain,(![SV16:nat,SV7:frac]: ((((eq@((fr@((ts@(num@SV7))@SV16))@((ts@(den@SV7))@SV16)))@SV7)=$true))),inference(extcnf_forall_pos,[status(thm)],[34])). 160.12/160.41 thf(45,plain,(![SV9:(nat>$o)]: ((((~ (amone@SV9)) | (~ (some@SV9)))=$true) | ((SV9@(ind@SV9))=$true))),inference(extcnf_or_pos,[status(thm)],[36])). 160.12/160.41 thf(46,plain,(![SV10:frac,SV1:frac]: (((~ ((eq@SV1)@SV10))=$true) | ((![SY12:frac]: ((~ ((eq@SV10)@SY12)) | ((eq@SV1)@SY12)))=$true))),inference(extcnf_or_pos,[status(thm)],[38])). 160.12/160.41 thf(47,plain,(![SV14:nat,SV17:nat,SV5:nat]: ((((eq@((pf@((fr@SV5)@SV17))@((fr@SV14)@SV17)))@((fr@((pl@SV5)@SV14))@SV17))=$true))),inference(extcnf_forall_pos,[status(thm)],[42])). 160.12/160.41 thf(48,plain,(![SV15:frac,SV6:frac]: (((~ ((eq@SV6)@SV15))=$true) | ((![SY15:frac,SY16:frac]: ((~ ((eq@SY15)@SY16)) | ((eq@((pf@SV6)@SY15))@((pf@SV15)@SY16))))=$true))),inference(extcnf_or_pos,[status(thm)],[43])). 160.12/160.41 thf(49,plain,(![SV9:(nat>$o)]: (((~ (amone@SV9))=$true) | ((~ (some@SV9))=$true) | ((SV9@(ind@SV9))=$true))),inference(extcnf_or_pos,[status(thm)],[45])). 160.12/160.41 thf(50,plain,(![SV10:frac,SV1:frac]: ((((eq@SV1)@SV10)=$false) | ((![SY12:frac]: ((~ ((eq@SV10)@SY12)) | ((eq@SV1)@SY12)))=$true))),inference(extcnf_not_pos,[status(thm)],[46])). 160.12/160.41 thf(51,plain,(![SV15:frac,SV6:frac]: ((((eq@SV6)@SV15)=$false) | ((![SY15:frac,SY16:frac]: ((~ ((eq@SY15)@SY16)) | ((eq@((pf@SV6)@SY15))@((pf@SV15)@SY16))))=$true))),inference(extcnf_not_pos,[status(thm)],[48])). 160.12/160.41 thf(52,plain,(![SV9:(nat>$o)]: (((amone@SV9)=$false) | ((~ (some@SV9))=$true) | ((SV9@(ind@SV9))=$true))),inference(extcnf_not_pos,[status(thm)],[49])). 160.12/160.41 thf(53,plain,(![SV1:frac,SV18:frac,SV10:frac]: ((((~ ((eq@SV10)@SV18)) | ((eq@SV1)@SV18))=$true) | (((eq@SV1)@SV10)=$false))),inference(extcnf_forall_pos,[status(thm)],[50])). 160.12/160.41 thf(54,plain,(![SV15:frac,SV6:frac,SV19:frac]: (((![SY17:frac]: ((~ ((eq@SV19)@SY17)) | ((eq@((pf@SV6)@SV19))@((pf@SV15)@SY17))))=$true) | (((eq@SV6)@SV15)=$false))),inference(extcnf_forall_pos,[status(thm)],[51])). 160.12/160.41 thf(55,plain,(![SV9:(nat>$o)]: (((some@SV9)=$false) | ((amone@SV9)=$false) | ((SV9@(ind@SV9))=$true))),inference(extcnf_not_pos,[status(thm)],[52])). 160.12/160.41 thf(56,plain,(![SV1:frac,SV18:frac,SV10:frac]: (((~ ((eq@SV10)@SV18))=$true) | (((eq@SV1)@SV18)=$true) | (((eq@SV1)@SV10)=$false))),inference(extcnf_or_pos,[status(thm)],[53])). 160.12/160.41 thf(57,plain,(![SV15:frac,SV6:frac,SV20:frac,SV19:frac]: ((((~ ((eq@SV19)@SV20)) | ((eq@((pf@SV6)@SV19))@((pf@SV15)@SV20)))=$true) | (((eq@SV6)@SV15)=$false))),inference(extcnf_forall_pos,[status(thm)],[54])). 160.12/160.41 thf(58,plain,(![SV1:frac,SV18:frac,SV10:frac]: ((((eq@SV10)@SV18)=$false) | (((eq@SV1)@SV18)=$true) | (((eq@SV1)@SV10)=$false))),inference(extcnf_not_pos,[status(thm)],[56])). 160.12/160.41 thf(59,plain,(![SV15:frac,SV6:frac,SV20:frac,SV19:frac]: (((~ ((eq@SV19)@SV20))=$true) | (((eq@((pf@SV6)@SV19))@((pf@SV15)@SV20))=$true) | (((eq@SV6)@SV15)=$false))),inference(extcnf_or_pos,[status(thm)],[57])). 160.12/160.41 thf(60,plain,(![SV15:frac,SV6:frac,SV20:frac,SV19:frac]: ((((eq@SV19)@SV20)=$false) | (((eq@((pf@SV6)@SV19))@((pf@SV15)@SV20))=$true) | (((eq@SV6)@SV15)=$false))),inference(extcnf_not_pos,[status(thm)],[59])). 160.12/160.41 thf(62,plain,(((some@(^[SX0:nat]: $false))=$false) | ((amone@(^[SX0:nat]: $false))=$false) | (($false)=$true)),inference(prim_subst,[status(thm)],[55:[bind(SV9,$thf(^[SV23:nat]: $false))]])). 160.12/160.41 thf(63,plain,(![SV22:(nat>$o)]: (((some@(^[SX0:nat]: (~ (SV22@SX0))))=$false) | ((amone@(^[SX0:nat]: (~ (SV22@SX0))))=$false) | ((~ (SV22@(ind@(^[SX0:nat]: (~ (SV22@SX0))))))=$true))),inference(prim_subst,[status(thm)],[55:[bind(SV9,$thf(^[SV21:nat]: (~ (SV22@SV21))))]])). 160.12/160.41 thf(64,plain,(![SV22:(nat>$o)]: (((SV22@(ind@(^[SX0:nat]: (~ (SV22@SX0)))))=$false) | ((amone@(^[SX0:nat]: (~ (SV22@SX0))))=$false) | ((some@(^[SX0:nat]: (~ (SV22@SX0))))=$false))),inference(extcnf_not_pos,[status(thm)],[63])). 160.12/160.41 thf(65,plain,(((some@(^[SX0:nat]: $false))=$false) | ((amone@(^[SX0:nat]: $false))=$false)),inference(sim,[status(thm)],[62])). 160.12/160.41 thf(66,plain,(![SV25:frac]: ((((eq@SV25)@SV25)=$true))),inference(rename,[status(thm)],[35])). 160.12/160.41 thf(67,plain,(![SV25:frac]: (((((eq@((pf@y)@((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y)))))@x) = ((eq@SV25)@SV25))=$false))),inference(res,[status(thm)],[37,66])). 160.12/160.41 thf(69,plain,(((x = ((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))=$false)),inference(extuni,[status(esa)],[67:[bind(SV25,$thf((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))]])). 160.12/160.41 thf(70,plain,(![SV26:nat,SV27:nat]: (((amone@(^[SX0:nat]: (SV27 = ((pl@SV26)@SX0))))=$true))),inference(rename,[status(thm)],[39])). 160.12/160.41 thf(72,plain,(![SV28:nat,SV29:nat]: (((((ts@SV29)@SV28) = ((ts@SV28)@SV29))=$true))),inference(rename,[status(thm)],[40])). 160.12/160.41 thf(74,plain,(![SV30:nat,SV31:frac]: ((((eq@SV31)@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30)))=$true))),inference(rename,[status(thm)],[41])). 160.12/160.41 thf(75,plain,(![SV30:nat,SV31:frac]: (((((eq@SV31)@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))) = ((eq@((pf@y)@((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y)))))@x))=$false))),inference(res,[status(thm)],[74,37])). 160.12/160.41 thf(76,plain,(![SV30:nat]: (((((fr@((ts@(num@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))))@SV30))@((ts@(den@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))))@SV30)) = x)=$false))),inference(extuni,[status(esa)],[75:[bind(SV31,$thf((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))]])). 160.12/160.41 thf(77,plain,(![SV32:nat,SV33:frac]: ((((eq@((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))@SV33)=$true))),inference(rename,[status(thm)],[44])). 160.12/160.41 thf(78,plain,(![SV32:nat,SV33:frac]: (((((eq@((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))@SV33) = ((eq@((pf@y)@((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y)))))@x))=$false))),inference(res,[status(thm)],[77,37])). 160.12/160.41 thf(79,plain,(![SV32:nat]: (((((fr@((ts@(num@x))@SV32))@((ts@(den@x))@SV32)) = ((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))=$false))),inference(extuni,[status(esa)],[78:[bind(SV33,$thf(x))]])). 160.12/160.41 thf(80,plain,(![SV34:nat,SV35:nat,SV36:nat]: ((((eq@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))@((fr@((pl@SV36)@SV34))@SV35))=$true))),inference(rename,[status(thm)],[47])). 160.12/160.41 thf(81,plain,(![SV34:nat,SV35:nat,SV36:nat]: (((((eq@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))@((fr@((pl@SV36)@SV34))@SV35)) = ((eq@((pf@y)@((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y)))))@x))=$false))),inference(res,[status(thm)],[80,37])). 160.12/160.41 thf(82,plain,(![SV36:nat]: (((((fr@((pl@SV36)@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))))@((ts@(den@x))@(den@y))) = x)=$false) | ((((fr@SV36)@((ts@(den@x))@(den@y))) = y)=$false))),inference(extuni,[status(esa)],[81:[bind(SV35,$thf((ts@(den@x))@(den@y))),bind(SV34,$thf(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))]])). 160.12/160.41 thf(83,plain,(![SV35:nat,SV34:nat,SV36:nat]: (((((fr@((pl@SV36)@SV34))@SV35) = x)=$false) | ((((fr@SV34)@SV35) = ((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y))))=$false) | ((((fr@SV36)@SV35) = y)=$false))),inference(extuni,[status(esa)],[81])). 160.12/160.41 thf(84,plain,(![SV35:nat,SV34:nat,SV36:nat]: (((((fr@((pl@SV36)@SV34))@SV35) = x)=$false) | ((((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)) = ((pf@y)@((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y)))))=$false))),inference(extuni,[status(esa)],[81])). 160.12/160.41 thf(85,plain,(![SV37:(nat>$o)]: (((some@SV37)=$false) | ((amone@SV37)=$false) | ((SV37@(ind@SV37))=$true))),inference(rename,[status(thm)],[55])). 160.12/160.41 thf(98,plain,(![SV37:(nat>$o),SV26:nat,SV27:nat]: ((((amone@SV37) = (amone@(^[SX0:nat]: (SV27 = ((pl@SV26)@SX0)))))=$false) | ((some@SV37)=$false) | ((SV37@(ind@SV37))=$true))),inference(res,[status(thm)],[85,70])). 160.12/160.41 thf(104,plain,(![SV37:(nat>$o)]: ((((some@SV37) = (some@(^[Xu:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xu)))))=$false) | ((amone@SV37)=$false) | ((SV37@(ind@SV37))=$true))),inference(res,[status(thm)],[85,21])). 160.12/160.41 thf(109,plain,(![SV48:(nat>$o),SV47:(nat>$o)]: (((some@(^[SX0:nat]: ((SV47@SX0) | (SV48@SX0))))=$false) | ((amone@(^[SX0:nat]: ((SV47@SX0) | (SV48@SX0))))=$false) | (((SV47@(ind@(^[SX0:nat]: ((SV47@SX0) | (SV48@SX0))))) | (SV48@(ind@(^[SX0:nat]: ((SV47@SX0) | (SV48@SX0))))))=$true))),inference(prim_subst,[status(thm)],[85:[bind(SV37, $thf(^[SV46:nat]: ((SV47@SV46) | (SV48@SV46))))]])). 160.12/160.41 thf(111,plain,(((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))))=$true) | ((amone@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))=$false)),inference(extuni,[status(esa)],[104:[bind(SV37,$thf(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))]])). 160.12/160.41 thf(112,plain,(![SV26:nat,SV27:nat]: (((SV27 = ((pl@SV26)@(ind@(^[SX0:nat]: (SV27 = ((pl@SV26)@SX0))))))=$true) | ((some@(^[SX0:nat]: (SV27 = ((pl@SV26)@SX0))))=$false))),inference(extuni,[status(esa)],[98:[bind(SV37,$thf(^[SX0:nat]: (SV27 = ((pl@SV26)@SX0))))]])). 160.12/160.41 thf(114,plain,(![SV48:(nat>$o),SV47:(nat>$o)]: (((SV47@(ind@(^[SX0:nat]: ((SV47@SX0) | (SV48@SX0)))))=$true) | ((SV48@(ind@(^[SX0:nat]: ((SV47@SX0) | (SV48@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SV47@SX0) | (SV48@SX0))))=$false) | ((some@(^[SX0:nat]: ((SV47@SX0) | (SV48@SX0))))=$false))),inference(extcnf_or_pos,[status(thm)],[109])). 160.12/160.41 thf(115,plain,(![SV78:frac,SV79:frac,SV80:frac]: ((((eq@SV80)@SV79)=$false) | (((eq@SV78)@SV79)=$true) | (((eq@SV78)@SV80)=$false))),inference(rename,[status(thm)],[58])). 160.12/160.41 thf(124,plain,(![SV78:frac,SV79:frac,SV80:frac,SV34:nat,SV35:nat,SV36:nat]: (((((eq@SV78)@SV80) = ((eq@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))@((fr@((pl@SV36)@SV34))@SV35)))=$false) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@SV79)=$true))),inference(res,[status(thm)],[115,80])). 160.12/160.41 thf(125,plain,(![SV78:frac,SV79:frac,SV80:frac,SV34:nat,SV35:nat,SV36:nat]: (((((eq@SV80)@SV79) = ((eq@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))@((fr@((pl@SV36)@SV34))@SV35)))=$false) | (((eq@SV78)@SV79)=$true) | (((eq@SV78)@SV80)=$false))),inference(res,[status(thm)],[115,80])). 160.12/160.41 thf(126,plain,(![SV78:frac,SV79:frac,SV80:frac,SV32:nat,SV33:frac]: (((((eq@SV78)@SV80) = ((eq@((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))@SV33))=$false) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@SV79)=$true))),inference(res,[status(thm)],[115,77])). 160.12/160.41 thf(127,plain,(![SV78:frac,SV79:frac,SV80:frac,SV32:nat,SV33:frac]: (((((eq@SV80)@SV79) = ((eq@((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))@SV33))=$false) | (((eq@SV78)@SV79)=$true) | (((eq@SV78)@SV80)=$false))),inference(res,[status(thm)],[115,77])). 160.12/160.41 thf(128,plain,(![SV78:frac,SV79:frac,SV80:frac,SV30:nat,SV31:frac]: (((((eq@SV78)@SV80) = ((eq@SV31)@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))))=$false) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@SV79)=$true))),inference(res,[status(thm)],[115,74])). 160.12/160.41 thf(129,plain,(![SV78:frac,SV79:frac,SV80:frac,SV30:nat,SV31:frac]: (((((eq@SV80)@SV79) = ((eq@SV31)@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))))=$false) | (((eq@SV78)@SV79)=$true) | (((eq@SV78)@SV80)=$false))),inference(res,[status(thm)],[115,74])). 160.12/160.41 thf(136,plain,(![SV78:frac,SV79:frac,SV80:frac]: (((((eq@SV78)@SV79) = ((eq@((pf@y)@((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y)))))@x))=$false) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@SV80)=$false))),inference(res,[status(thm)],[115,37])). 160.12/160.41 thf(139,plain,(![SV80:frac]: ((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV80)=$false) | (((eq@SV80)@x)=$false))),inference(extuni,[status(esa)],[136:[bind(SV79,$thf(x)),bind(SV78,$thf((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))]])). 160.12/160.41 thf(142,plain,(![SV30:nat,SV31:frac,SV78:frac]: ((((eq@SV78)@SV31)=$false) | (((eq@SV78)@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30)))=$true))),inference(extuni,[status(esa)],[129:[bind(SV79,$thf((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))),bind(SV80,$thf(SV31))]])). 160.12/160.41 thf(143,plain,(![SV30:nat,SV79:frac,SV31:frac]: ((((eq@SV31)@SV79)=$true) | (((eq@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30)))@SV79)=$false))),inference(extuni,[status(esa)],[128:[bind(SV80,$thf((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))),bind(SV78,$thf(SV31))]])). 160.12/160.41 thf(144,plain,(![SV32:nat,SV33:frac,SV78:frac]: ((((eq@SV78)@((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))=$false) | (((eq@SV78)@SV33)=$true))),inference(extuni,[status(esa)],[127:[bind(SV79,$thf(SV33)),bind(SV80,$thf((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))]])). 160.12/160.41 thf(145,plain,(![SV79:frac,SV32:nat,SV33:frac]: ((((eq@((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))@SV79)=$true) | (((eq@SV33)@SV79)=$false))),inference(extuni,[status(esa)],[126:[bind(SV80,$thf(SV33)),bind(SV78,$thf((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))]])). 160.12/160.41 thf(146,plain,(![SV34:nat,SV35:nat,SV36:nat,SV78:frac]: ((((eq@SV78)@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))=$false) | (((eq@SV78)@((fr@((pl@SV36)@SV34))@SV35))=$true))),inference(extuni,[status(esa)],[125:[bind(SV79,$thf((fr@((pl@SV36)@SV34))@SV35)),bind(SV80,$thf((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))]])). 160.12/160.41 thf(147,plain,(![SV79:frac,SV34:nat,SV35:nat,SV36:nat]: ((((eq@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))@SV79)=$true) | (((eq@((fr@((pl@SV36)@SV34))@SV35))@SV79)=$false))),inference(extuni,[status(esa)],[124:[bind(SV80,$thf((fr@((pl@SV36)@SV34))@SV35)),bind(SV78,$thf((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))]])). 160.12/160.41 thf(152,plain,(![SV81:frac,SV82:frac,SV83:frac,SV84:frac]: ((((eq@SV84)@SV83)=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true) | (((eq@SV82)@SV81)=$false))),inference(rename,[status(thm)],[60])). 160.12/160.41 thf(157,plain,(![SV81:frac,SV82:frac,SV83:frac,SV84:frac,SV78:frac,SV79:frac,SV80:frac]: (((((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83)) = ((eq@SV78)@SV80))=$false) | (((eq@SV84)@SV83)=$false) | (((eq@SV82)@SV81)=$false) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@SV79)=$true))),inference(res,[status(thm)],[152,115])). 160.12/160.41 thf(158,plain,(![SV81:frac,SV82:frac,SV83:frac,SV84:frac,SV78:frac,SV79:frac,SV80:frac]: (((((eq@SV82)@SV81) = ((eq@SV78)@SV79))=$false) | (((eq@SV84)@SV83)=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@SV80)=$false))),inference(res,[status(thm)],[152,115])). 160.12/160.41 thf(159,plain,(![SV81:frac,SV82:frac,SV83:frac,SV84:frac,SV78:frac,SV79:frac,SV80:frac]: (((((eq@SV84)@SV83) = ((eq@SV78)@SV79))=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true) | (((eq@SV82)@SV81)=$false) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@SV80)=$false))),inference(res,[status(thm)],[152,115])). 160.12/160.41 thf(160,plain,(![SV81:frac,SV82:frac,SV83:frac,SV84:frac,SV78:frac,SV79:frac,SV80:frac]: (((((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83)) = ((eq@SV80)@SV79))=$false) | (((eq@SV84)@SV83)=$false) | (((eq@SV82)@SV81)=$false) | (((eq@SV78)@SV79)=$true) | (((eq@SV78)@SV80)=$false))),inference(res,[status(thm)],[152,115])). 160.12/160.41 thf(165,plain,(![SV81:frac,SV82:frac,SV83:frac,SV84:frac,SV34:nat,SV35:nat,SV36:nat]: (((((eq@SV82)@SV81) = ((eq@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))@((fr@((pl@SV36)@SV34))@SV35)))=$false) | (((eq@SV84)@SV83)=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true))),inference(res,[status(thm)],[152,80])). 160.12/160.41 thf(166,plain,(![SV81:frac,SV82:frac,SV83:frac,SV84:frac,SV34:nat,SV35:nat,SV36:nat]: (((((eq@SV84)@SV83) = ((eq@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))@((fr@((pl@SV36)@SV34))@SV35)))=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true) | (((eq@SV82)@SV81)=$false))),inference(res,[status(thm)],[152,80])). 160.12/160.41 thf(167,plain,(![SV81:frac,SV82:frac,SV83:frac,SV84:frac,SV32:nat,SV33:frac]: (((((eq@SV82)@SV81) = ((eq@((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))@SV33))=$false) | (((eq@SV84)@SV83)=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true))),inference(res,[status(thm)],[152,77])). 160.12/160.41 thf(168,plain,(![SV81:frac,SV82:frac,SV83:frac,SV84:frac,SV32:nat,SV33:frac]: (((((eq@SV84)@SV83) = ((eq@((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))@SV33))=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true) | (((eq@SV82)@SV81)=$false))),inference(res,[status(thm)],[152,77])). 160.12/160.41 thf(169,plain,(![SV81:frac,SV82:frac,SV83:frac,SV84:frac,SV30:nat,SV31:frac]: (((((eq@SV82)@SV81) = ((eq@SV31)@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))))=$false) | (((eq@SV84)@SV83)=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true))),inference(res,[status(thm)],[152,74])). 160.12/160.41 thf(170,plain,(![SV81:frac,SV82:frac,SV83:frac,SV84:frac,SV30:nat,SV31:frac]: (((((eq@SV84)@SV83) = ((eq@SV31)@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))))=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true) | (((eq@SV82)@SV81)=$false))),inference(res,[status(thm)],[152,74])). 160.12/160.41 thf(175,plain,(![SV81:frac,SV82:frac,SV83:frac,SV84:frac,SV25:frac]: (((((eq@SV82)@SV81) = ((eq@SV25)@SV25))=$false) | (((eq@SV84)@SV83)=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true))),inference(res,[status(thm)],[152,66])). 160.12/160.41 thf(176,plain,(![SV81:frac,SV82:frac,SV83:frac,SV84:frac,SV25:frac]: (((((eq@SV84)@SV83) = ((eq@SV25)@SV25))=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true) | (((eq@SV82)@SV81)=$false))),inference(res,[status(thm)],[152,66])). 160.12/160.41 thf(177,plain,(![SV81:frac,SV82:frac,SV83:frac,SV84:frac]: (((((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83)) = ((eq@((pf@y)@((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y)))))@x))=$false) | (((eq@SV84)@SV83)=$false) | (((eq@SV82)@SV81)=$false))),inference(res,[status(thm)],[152,37])). 160.12/160.41 thf(180,plain,(![SV83:frac,SV81:frac]: ((((eq@y)@SV81)=$false) | (((eq@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))@SV83)=$false) | ((((pf@SV81)@SV83) = x)=$false))),inference(extuni,[status(esa)],[177:[bind(SV84,$thf((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))),bind(SV82,$thf(y))]])). 160.12/160.41 thf(181,plain,(![SV83:frac,SV84:frac,SV81:frac,SV82:frac]: ((((eq@SV82)@SV81)=$false) | (((eq@SV84)@SV83)=$false) | ((((pf@SV81)@SV83) = x)=$false) | ((((pf@SV82)@SV84) = ((pf@y)@((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y)))))=$false))),inference(extuni,[status(esa)],[177])). 160.12/160.41 thf(182,plain,(![SV25:frac,SV81:frac,SV82:frac]: ((((eq@SV82)@SV81)=$false) | (((eq@((pf@SV82)@SV25))@((pf@SV81)@SV25))=$true))),inference(extuni,[status(esa)],[176:[bind(SV83,$thf(SV25)),bind(SV84,$thf(SV25))]])). 160.12/160.41 thf(183,plain,(![SV83:frac,SV84:frac,SV25:frac]: ((((eq@((pf@SV25)@SV84))@((pf@SV25)@SV83))=$true) | (((eq@SV84)@SV83)=$false))),inference(extuni,[status(esa)],[175:[bind(SV81,$thf(SV25)),bind(SV82,$thf(SV25))]])). 160.12/160.41 thf(184,plain,(![SV30:nat,SV31:frac,SV81:frac,SV82:frac]: ((((eq@SV82)@SV81)=$false) | (((eq@((pf@SV82)@SV31))@((pf@SV81)@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))))=$true))),inference(extuni,[status(esa)],[170:[bind(SV83,$thf((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))),bind(SV84,$thf(SV31))]])). 160.12/160.41 thf(185,plain,(![SV83:frac,SV30:nat,SV84:frac,SV31:frac]: ((((eq@((pf@SV31)@SV84))@((pf@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30)))@SV83))=$true) | (((eq@SV84)@SV83)=$false))),inference(extuni,[status(esa)],[169:[bind(SV81,$thf((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))),bind(SV82,$thf(SV31))]])). 160.12/160.41 thf(186,plain,(![SV32:nat,SV33:frac,SV81:frac,SV82:frac]: ((((eq@SV82)@SV81)=$false) | (((eq@((pf@SV82)@((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32))))@((pf@SV81)@SV33))=$true))),inference(extuni,[status(esa)],[168:[bind(SV83,$thf(SV33)),bind(SV84,$thf((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))]])). 160.12/160.41 thf(187,plain,(![SV83:frac,SV84:frac,SV32:nat,SV33:frac]: ((((eq@((pf@((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))@SV84))@((pf@SV33)@SV83))=$true) | (((eq@SV84)@SV83)=$false))),inference(extuni,[status(esa)],[167:[bind(SV81,$thf(SV33)),bind(SV82,$thf((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))]])). 160.12/160.41 thf(188,plain,(![SV34:nat,SV35:nat,SV36:nat,SV81:frac,SV82:frac]: ((((eq@SV82)@SV81)=$false) | (((eq@((pf@SV82)@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35))))@((pf@SV81)@((fr@((pl@SV36)@SV34))@SV35)))=$true))),inference(extuni,[status(esa)],[166:[bind(SV83,$thf((fr@((pl@SV36)@SV34))@SV35)),bind(SV84,$thf((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))]])). 160.12/160.41 thf(189,plain,(![SV83:frac,SV84:frac,SV34:nat,SV35:nat,SV36:nat]: ((((eq@((pf@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))@SV84))@((pf@((fr@((pl@SV36)@SV34))@SV35))@SV83))=$true) | (((eq@SV84)@SV83)=$false))),inference(extuni,[status(esa)],[165:[bind(SV81,$thf((fr@((pl@SV36)@SV34))@SV35)),bind(SV82,$thf((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))]])). 160.12/160.41 thf(190,plain,(![SV83:frac,SV81:frac,SV84:frac,SV82:frac,SV78:frac]: ((((eq@SV78)@((pf@SV82)@SV84))=$false) | (((eq@SV78)@((pf@SV81)@SV83))=$true) | (((eq@SV82)@SV81)=$false) | (((eq@SV84)@SV83)=$false))),inference(extuni,[status(esa)],[160:[bind(SV79,$thf((pf@SV81)@SV83)),bind(SV80,$thf((pf@SV82)@SV84))]])). 160.12/160.41 thf(191,plain,(![SV81:frac,SV82:frac,SV79:frac,SV80:frac,SV78:frac]: ((((eq@SV78)@SV80)=$false) | (((eq@SV80)@SV79)=$false) | (((eq@SV82)@SV81)=$false) | (((eq@((pf@SV82)@SV78))@((pf@SV81)@SV79))=$true))),inference(extuni,[status(esa)],[159:[bind(SV83,$thf(SV79)),bind(SV84,$thf(SV78))]])). 160.12/160.41 thf(192,plain,(![SV83:frac,SV84:frac,SV79:frac,SV80:frac,SV78:frac]: ((((eq@SV78)@SV80)=$false) | (((eq@SV80)@SV79)=$false) | (((eq@((pf@SV78)@SV84))@((pf@SV79)@SV83))=$true) | (((eq@SV84)@SV83)=$false))),inference(extuni,[status(esa)],[158:[bind(SV81,$thf(SV79)),bind(SV82,$thf(SV78))]])). 160.12/160.41 thf(193,plain,(![SV83:frac,SV81:frac,SV79:frac,SV84:frac,SV82:frac]: ((((eq@((pf@SV82)@SV84))@SV79)=$true) | (((eq@((pf@SV81)@SV83))@SV79)=$false) | (((eq@SV82)@SV81)=$false) | (((eq@SV84)@SV83)=$false))),inference(extuni,[status(esa)],[157:[bind(SV80,$thf((pf@SV81)@SV83)),bind(SV78,$thf((pf@SV82)@SV84))]])). 160.12/160.41 thf(194,plain,(![SV85:(nat>$o)]: (((SV85@(ind@(^[SX0:nat]: (~ (SV85@SX0)))))=$false) | ((amone@(^[SX0:nat]: (~ (SV85@SX0))))=$false) | ((some@(^[SX0:nat]: (~ (SV85@SX0))))=$false))),inference(rename,[status(thm)],[64])). 160.12/160.41 thf(217,plain,(![SV85:(nat>$o),SV26:nat,SV27:nat]: ((((amone@(^[SX0:nat]: (~ (SV85@SX0)))) = (amone@(^[SX0:nat]: (SV27 = ((pl@SV26)@SX0)))))=$false) | ((SV85@(ind@(^[SX0:nat]: (~ (SV85@SX0)))))=$false) | ((some@(^[SX0:nat]: (~ (SV85@SX0))))=$false))),inference(res,[status(thm)],[194,70])). 160.12/160.41 thf(222,plain,(![SV85:(nat>$o)]: ((((some@(^[SX0:nat]: (~ (SV85@SX0)))) = (some@(^[Xu:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xu)))))=$false) | ((SV85@(ind@(^[SX0:nat]: (~ (SV85@SX0)))))=$false) | ((amone@(^[SX0:nat]: (~ (SV85@SX0))))=$false))),inference(res,[status(thm)],[194,21])). 160.12/160.41 thf(225,plain,((($true)=$false) | ((amone@(^[SX0:nat]: (~ ($true))))=$false) | ((some@(^[SX0:nat]: (~ ($true))))=$false)),inference(prim_subst,[status(thm)],[194:[bind(SV85, $thf(^[SV89:nat]: $true))]])). 160.12/160.41 thf(226,plain,(((amone@(^[SX0:nat]: (~ ($true))))=$false) | ((some@(^[SX0:nat]: (~ ($true))))=$false)),inference(sim,[status(thm)],[225])). 160.12/160.41 thf(228,plain,(![SV87:(nat>$o)]: (((~ (SV87@(ind@(^[SX0:nat]: (~ (~ (SV87@SX0)))))))=$false) | ((amone@(^[SX0:nat]: (~ (~ (SV87@SX0)))))=$false) | ((some@(^[SX0:nat]: (~ (~ (SV87@SX0)))))=$false))),inference(prim_subst,[status(thm)],[194:[bind(SV85, $thf(^[SV86:nat]: (~ (SV87@SV86))))]])). 160.12/160.41 thf(230,plain,(![SV97:(nat>$o),SV96:(nat>$o)]: ((((SV96@(ind@(^[SX0:nat]: (~ ((SV96@SX0) | (SV97@SX0)))))) | (SV97@(ind@(^[SX0:nat]: (~ ((SV96@SX0) | (SV97@SX0)))))))=$false) | ((amone@(^[SX0:nat]: (~ ((SV96@SX0) | (SV97@SX0)))))=$false) | ((some@(^[SX0:nat]: (~ ((SV96@SX0) | (SV97@SX0)))))=$false))),inference(prim_subst,[status(thm)],[194:[bind(SV85, $thf(^[SV95:nat]: ((SV96@SV95) | (SV97@SV95))))]])). 160.12/160.41 thf(232,plain,(![SV85:(nat>$o)]: (((amone@(^[SX0:nat]: (~ (SV85@SX0))))=$false) | ((SV85@(ind@(^[SX0:nat]: (~ (SV85@SX0)))))=$false) | ((~ (SV85@(sK2_E@SV85)))=$true) | ((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@(sK2_E@SV85)))=$true))),inference(extuni,[status(esa)],[222])). 160.12/160.41 thf(233,plain,(![SV85:(nat>$o)]: (((amone@(^[SX0:nat]: (~ (SV85@SX0))))=$false) | ((SV85@(ind@(^[SX0:nat]: (~ (SV85@SX0)))))=$false) | ((~ (SV85@(sK2_E@SV85)))=$false) | ((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@(sK2_E@SV85)))=$false))),inference(extuni,[status(esa)],[222])). 160.12/160.41 thf(234,plain,(![SV27:nat,SV26:nat,SV85:(nat>$o)]: (((some@(^[SX0:nat]: (~ (SV85@SX0))))=$false) | ((SV85@(ind@(^[SX0:nat]: (~ (SV85@SX0)))))=$false) | ((~ (SV85@(((sK3_E@SV26)@SV27)@SV85)))=$true) | ((SV27 = ((pl@SV26)@(((sK3_E@SV26)@SV27)@SV85)))=$true))),inference(extuni,[status(esa)],[217])). 160.12/160.41 thf(235,plain,(![SV27:nat,SV26:nat,SV85:(nat>$o)]: (((some@(^[SX0:nat]: (~ (SV85@SX0))))=$false) | ((SV85@(ind@(^[SX0:nat]: (~ (SV85@SX0)))))=$false) | ((~ (SV85@(((sK3_E@SV26)@SV27)@SV85)))=$false) | ((SV27 = ((pl@SV26)@(((sK3_E@SV26)@SV27)@SV85)))=$false))),inference(extuni,[status(esa)],[217])). 160.12/160.41 thf(236,plain,(![SV85:(nat>$o)]: (((SV85@(sK2_E@SV85))=$true) | ((SV85@(ind@(^[SX0:nat]: (~ (SV85@SX0)))))=$false) | ((amone@(^[SX0:nat]: (~ (SV85@SX0))))=$false) | ((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@(sK2_E@SV85)))=$false))),inference(extcnf_not_neg,[status(thm)],[233])). 160.12/160.41 thf(237,plain,(![SV85:(nat>$o)]: (((SV85@(sK2_E@SV85))=$false) | ((SV85@(ind@(^[SX0:nat]: (~ (SV85@SX0)))))=$false) | ((amone@(^[SX0:nat]: (~ (SV85@SX0))))=$false) | ((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@(sK2_E@SV85)))=$true))),inference(extcnf_not_pos,[status(thm)],[232])). 160.12/160.41 thf(238,plain,(![SV27:nat,SV26:nat,SV85:(nat>$o)]: (((SV85@(((sK3_E@SV26)@SV27)@SV85))=$true) | ((SV85@(ind@(^[SX0:nat]: (~ (SV85@SX0)))))=$false) | ((some@(^[SX0:nat]: (~ (SV85@SX0))))=$false) | ((SV27 = ((pl@SV26)@(((sK3_E@SV26)@SV27)@SV85)))=$false))),inference(extcnf_not_neg,[status(thm)],[235])). 160.12/160.41 thf(239,plain,(![SV27:nat,SV26:nat,SV85:(nat>$o)]: (((SV85@(((sK3_E@SV26)@SV27)@SV85))=$false) | ((SV85@(ind@(^[SX0:nat]: (~ (SV85@SX0)))))=$false) | ((some@(^[SX0:nat]: (~ (SV85@SX0))))=$false) | ((SV27 = ((pl@SV26)@(((sK3_E@SV26)@SV27)@SV85)))=$true))),inference(extcnf_not_pos,[status(thm)],[234])). 160.12/160.41 thf(240,plain,(![SV87:(nat>$o)]: (((SV87@(ind@(^[SX0:nat]: (~ (~ (SV87@SX0))))))=$true) | ((amone@(^[SX0:nat]: (~ (~ (SV87@SX0)))))=$false) | ((some@(^[SX0:nat]: (~ (~ (SV87@SX0)))))=$false))),inference(extcnf_not_neg,[status(thm)],[228])). 160.12/160.41 thf(241,plain,(![SV97:(nat>$o),SV96:(nat>$o)]: (((SV96@(ind@(^[SX0:nat]: (~ ((SV96@SX0) | (SV97@SX0))))))=$false) | ((amone@(^[SX0:nat]: (~ ((SV96@SX0) | (SV97@SX0)))))=$false) | ((some@(^[SX0:nat]: (~ ((SV96@SX0) | (SV97@SX0)))))=$false))),inference(extcnf_or_neg,[status(thm)],[230])). 160.12/160.41 thf(242,plain,(![SV96:(nat>$o),SV97:(nat>$o)]: (((SV97@(ind@(^[SX0:nat]: (~ ((SV96@SX0) | (SV97@SX0))))))=$false) | ((amone@(^[SX0:nat]: (~ ((SV96@SX0) | (SV97@SX0)))))=$false) | ((some@(^[SX0:nat]: (~ ((SV96@SX0) | (SV97@SX0)))))=$false))),inference(extcnf_or_neg,[status(thm)],[230])). 160.12/160.41 thf(257,plain,(![SV26:nat,SV27:nat]: ((((amone@(^[SX0:nat]: $false)) = (amone@(^[SX0:nat]: (SV27 = ((pl@SV26)@SX0)))))=$false) | ((some@(^[SX0:nat]: $false))=$false))),inference(res,[status(thm)],[65,70])). 160.12/160.41 thf(262,plain,((((some@(^[SX0:nat]: $false)) = (some@(^[Xu:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xu)))))=$false) | ((amone@(^[SX0:nat]: $false))=$false)),inference(res,[status(thm)],[65,21])). 160.12/160.41 thf(264,plain,(((amone@(^[SX0:nat]: $false))=$false) | (($false)=$true) | ((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@sK6_E))=$true)),inference(extuni,[status(esa)],[262])). 160.12/160.41 thf(266,plain,(![SV26:nat,SV27:nat]: (((some@(^[SX0:nat]: $false))=$false) | (($false)=$true) | ((SV27 = ((pl@SV26)@((sK7_E@SV26)@SV27)))=$true))),inference(extuni,[status(esa)],[257])). 160.12/160.41 thf(268,plain,(((amone@(^[SX0:nat]: $false))=$false) | ((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@sK6_E))=$true)),inference(sim,[status(thm)],[264])). 160.12/160.41 thf(269,plain,(![SV26:nat,SV27:nat]: (((some@(^[SX0:nat]: $false))=$false) | ((SV27 = ((pl@SV26)@((sK7_E@SV26)@SV27)))=$true))),inference(sim,[status(thm)],[266])). 160.12/160.41 thf(280,plain,(![SV151:nat]: (((((fr@((ts@(num@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))))@SV151))@((ts@(den@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))))@SV151)) = x)=$false))),inference(rename,[status(thm)],[76])). 160.12/160.41 thf(291,plain,(![SV152:nat]: (((((fr@((ts@(num@x))@SV152))@((ts@(den@x))@SV152)) = ((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))=$false))),inference(rename,[status(thm)],[79])). 160.12/160.41 thf(302,plain,(![SV153:nat]: (((((fr@((pl@SV153)@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))))@((ts@(den@x))@(den@y))) = x)=$false) | ((((fr@SV153)@((ts@(den@x))@(den@y))) = y)=$false))),inference(rename,[status(thm)],[82])). 160.12/160.41 thf(324,plain,(![SV154:nat,SV155:nat,SV156:nat]: (((((fr@((pl@SV156)@SV155))@SV154) = x)=$false) | ((((fr@SV155)@SV154) = ((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))=$false) | ((((fr@SV156)@SV154) = y)=$false))),inference(rename,[status(thm)],[83])). 160.12/160.41 thf(355,plain,(![SV157:nat,SV158:nat,SV159:nat]: (((((fr@((pl@SV159)@SV158))@SV157) = x)=$false) | ((((pf@((fr@SV159)@SV157))@((fr@SV158)@SV157)) = ((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))=$false))),inference(rename,[status(thm)],[84])). 160.12/160.41 thf(376,plain,(![SV157:nat,SV158:nat,SV159:nat]: (((((pf@((fr@SV159)@SV157))@((fr@SV158)@SV157)) = ((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))=$false) | (((((fr@((pl@SV159)@SV158))@SV157) = x) = (((pf@((fr@SV159)@SV157))@((fr@SV158)@SV157)) = ((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))))=$false))),inference(fac_restr,[status(thm)],[355])). 160.12/160.41 thf(377,plain,(![SV159:nat]: (((((fr@((pl@SV159)@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))))@((ts@(den@x))@(den@y))) = ((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))=$false) | ((x = ((pf@((fr@SV159)@((ts@(den@x))@(den@y))))@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))=$false) | ((((fr@SV159)@((ts@(den@x))@(den@y))) = y)=$false))),inference(extuni,[status(esa)],[376:[bind(SV157,$thf((ts@(den@x))@(den@y))),bind(SV158,$thf(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))]])). 160.12/160.41 thf(378,plain,(![SV159:nat]: (((x = ((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))=$false) | ((((fr@((pl@SV159)@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))))@((ts@(den@x))@(den@y))) = ((pf@((fr@SV159)@((ts@(den@x))@(den@y))))@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))=$false) | ((((fr@SV159)@((ts@(den@x))@(den@y))) = y)=$false))),inference(extuni,[status(esa)],[376:[bind(SV157,$thf((ts@(den@x))@(den@y))),bind(SV158,$thf(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))]])). 160.12/160.41 thf(379,plain,(![SV159:nat]: (((((fr@((pl@SV159)@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))))@((ts@(den@x))@(den@y))) = x)=$true) | ((((pf@((fr@SV159)@((ts@(den@x))@(den@y))))@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))) = ((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))=$true) | ((((fr@SV159)@((ts@(den@x))@(den@y))) = y)=$false))),inference(extuni,[status(esa)],[376:[bind(SV157,$thf((ts@(den@x))@(den@y))),bind(SV158,$thf(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))]])). 160.12/160.41 thf(380,plain,(![SV159:nat]: (((((fr@((pl@SV159)@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))))@((ts@(den@x))@(den@y))) = x)=$false) | ((((pf@((fr@SV159)@((ts@(den@x))@(den@y))))@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))) = ((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))=$false) | ((((fr@SV159)@((ts@(den@x))@(den@y))) = y)=$false))),inference(extuni,[status(esa)],[376:[bind(SV157,$thf((ts@(den@x))@(den@y))),bind(SV158,$thf(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))]])). 160.12/160.41 thf(381,plain,(![SV157:nat,SV158:nat,SV159:nat]: (((((fr@((pl@SV159)@SV158))@SV157) = ((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))=$false) | ((x = ((pf@((fr@SV159)@SV157))@((fr@SV158)@SV157)))=$false) | ((((fr@SV158)@SV157) = ((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))=$false) | ((((fr@SV159)@SV157) = y)=$false))),inference(extuni,[status(esa)],[376])). 160.12/160.41 thf(382,plain,(![SV157:nat,SV158:nat,SV159:nat]: (((x = ((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))=$false) | ((((fr@((pl@SV159)@SV158))@SV157) = ((pf@((fr@SV159)@SV157))@((fr@SV158)@SV157)))=$false) | ((((fr@SV158)@SV157) = ((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))=$false) | ((((fr@SV159)@SV157) = y)=$false))),inference(extuni,[status(esa)],[376])). 160.12/160.41 thf(411,plain,(![SV26:nat,SV27:nat]: ((((amone@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))) = (amone@(^[SX0:nat]: (SV27 = ((pl@SV26)@SX0)))))=$false) | ((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))))=$true))),inference(res,[status(thm)],[111,70])). 160.12/160.41 thf(418,plain,(((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))))=$true)),inference(extuni,[status(esa)],[411:[bind(SV26,$thf((ts@(num@y))@(den@x))),bind(SV27,$thf((ts@(num@x))@(den@y)))]])). 160.12/160.41 thf(419,plain,(![SV26:nat]: (((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))))=$true) | ((((pl@((ts@(num@y))@(den@x)))@((sK14_E@SV26)@((ts@(num@x))@(den@y)))) = ((pl@SV26)@((sK14_E@SV26)@((ts@(num@x))@(den@y)))))=$false))),inference(extuni,[status(esa)],[411:[bind(SV27,$thf((ts@(num@x))@(den@y)))]])). 160.12/160.41 thf(420,plain,(![SV27:nat,SV26:nat]: (((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))))=$true) | ((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@((sK14_E@SV26)@SV27)))=$true) | ((SV27 = ((pl@SV26)@((sK14_E@SV26)@SV27)))=$true))),inference(extuni,[status(esa)],[411])). 160.12/160.41 thf(421,plain,(![SV27:nat,SV26:nat]: (((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))))=$true) | ((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@((sK14_E@SV26)@SV27)))=$false) | ((SV27 = ((pl@SV26)@((sK14_E@SV26)@SV27)))=$false))),inference(extuni,[status(esa)],[411])). 160.12/160.41 thf(422,plain,(![SV162:nat,SV163:nat]: (((SV163 = ((pl@SV162)@(ind@(^[SX0:nat]: (SV163 = ((pl@SV162)@SX0))))))=$true) | ((some@(^[SX0:nat]: (SV163 = ((pl@SV162)@SX0))))=$false))),inference(rename,[status(thm)],[112])). 160.12/160.41 thf(458,plain,(![SV162:nat,SV163:nat]: ((((some@(^[SX0:nat]: (SV163 = ((pl@SV162)@SX0)))) = (some@(^[Xu:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xu)))))=$false) | ((SV163 = ((pl@SV162)@(ind@(^[SX0:nat]: (SV163 = ((pl@SV162)@SX0))))))=$true))),inference(res,[status(thm)],[422,21])). 160.12/160.41 thf(459,plain,(((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))))=$true)),inference(extuni,[status(esa)],[458:[bind(SV162,$thf((ts@(num@y))@(den@x))),bind(SV163,$thf((ts@(num@x))@(den@y)))]])). 160.12/160.41 thf(460,plain,(![SV162:nat]: (((((ts@(num@x))@(den@y)) = ((pl@SV162)@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@SV162)@SX0))))))=$true) | ((((pl@SV162)@((sK17_E@SV162)@((ts@(num@x))@(den@y)))) = ((pl@((ts@(num@y))@(den@x)))@((sK17_E@SV162)@((ts@(num@x))@(den@y)))))=$false))),inference(extuni,[status(esa)],[458:[bind(SV163,$thf((ts@(num@x))@(den@y)))]])). 160.12/160.41 thf(461,plain,(![SV162:nat,SV163:nat]: (((SV163 = ((pl@SV162)@(ind@(^[SX0:nat]: (SV163 = ((pl@SV162)@SX0))))))=$true) | ((SV163 = ((pl@SV162)@((sK17_E@SV162)@SV163)))=$true) | ((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@((sK17_E@SV162)@SV163)))=$true))),inference(extuni,[status(esa)],[458])). 160.12/160.41 thf(462,plain,(![SV162:nat,SV163:nat]: (((SV163 = ((pl@SV162)@(ind@(^[SX0:nat]: (SV163 = ((pl@SV162)@SX0))))))=$true) | ((SV163 = ((pl@SV162)@((sK17_E@SV162)@SV163)))=$false) | ((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@((sK17_E@SV162)@SV163)))=$false))),inference(extuni,[status(esa)],[458])). 160.12/160.41 thf(464,plain,(![SV165:(nat>$o),SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((SV165@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0))))=$false))),inference(rename,[status(thm)],[114])). 160.12/160.41 thf(532,plain,(![SV165:(nat>$o),SV166:(nat>$o),SV26:nat,SV27:nat]: ((((amone@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))) = (amone@(^[SX0:nat]: (SV27 = ((pl@SV26)@SX0)))))=$false) | ((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((SV165@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0))))=$false))),inference(res,[status(thm)],[464,70])). 160.12/160.41 thf(543,plain,(![SV165:(nat>$o),SV166:(nat>$o)]: ((((some@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))) = (some@(^[Xu:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xu)))))=$false) | ((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((SV165@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0))))=$false))),inference(res,[status(thm)],[464,21])). 160.12/160.41 thf(546,plain,(![SV165:(nat>$o)]: ((($false)=$true) | ((SV165@(ind@(^[SX0:nat]: ($false | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ($false | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ($false | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV169:nat]: $false))]])). 160.12/160.41 thf(547,plain,(![SV165:(nat>$o)]: (((SV165@(ind@(^[SX0:nat]: ($false | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ($false | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ($false | (SV165@SX0))))=$false))),inference(sim,[status(thm)],[546])). 160.12/160.41 thf(548,plain,(![SV165:(nat>$o),SV168:(nat>$o)]: (((~ (SV168@(ind@(^[SX0:nat]: ((~ (SV168@SX0)) | (SV165@SX0))))))=$true) | ((SV165@(ind@(^[SX0:nat]: ((~ (SV168@SX0)) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((~ (SV168@SX0)) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((~ (SV168@SX0)) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV167:nat]: (~ (SV168@SV167))))]])). 160.12/160.41 thf(549,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK6_E) | (SV165@SX0)))) = sK6_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK6_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK6_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK6_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV171:nat]: (SV171 = sK6_E)))]])). 160.12/160.41 thf(550,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK12_E) | (SV165@SX0)))) = sK12_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK12_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK12_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK12_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV172:nat]: (SV172 = sK12_E)))]])). 160.12/160.41 thf(551,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK19_E) | (SV165@SX0)))) = sK19_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK19_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK19_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK19_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV173:nat]: (SV173 = sK19_E)))]])). 160.12/160.41 thf(552,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK23_E) | (SV165@SX0)))) = sK23_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK23_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK23_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK23_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV174:nat]: (SV174 = sK23_E)))]])). 160.12/160.41 thf(553,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK22_E) | (SV165@SX0)))) = sK22_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK22_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK22_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK22_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV175:nat]: (SV175 = sK22_E)))]])). 160.12/160.41 thf(554,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK18_E) | (SV165@SX0)))) = sK18_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK18_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK18_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK18_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV176:nat]: (SV176 = sK18_E)))]])). 160.12/160.41 thf(555,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK9_E) | (SV165@SX0)))) = sK9_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK9_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK9_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK9_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV177:nat]: (SV177 = sK9_E)))]])). 160.12/160.41 thf(556,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK10_E) | (SV165@SX0)))) = sK10_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK10_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK10_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK10_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV178:nat]: (SV178 = sK10_E)))]])). 160.12/160.41 thf(557,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK20_E) | (SV165@SX0)))) = sK20_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK20_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK20_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK20_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV179:nat]: (SV179 = sK20_E)))]])). 160.12/160.41 thf(558,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK24_E) | (SV165@SX0)))) = sK24_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK24_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK24_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK24_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV180:nat]: (SV180 = sK24_E)))]])). 160.12/160.41 thf(559,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK5_E) | (SV165@SX0)))) = sK5_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK5_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK5_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK5_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV181:nat]: (SV181 = sK5_E)))]])). 160.12/160.41 thf(560,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK21_E) | (SV165@SX0)))) = sK21_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK21_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK21_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK21_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV182:nat]: (SV182 = sK21_E)))]])). 160.12/160.41 thf(561,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK13_E) | (SV165@SX0)))) = sK13_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK13_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK13_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK13_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV183:nat]: (SV183 = sK13_E)))]])). 160.12/160.41 thf(562,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK4_E) | (SV165@SX0)))) = sK4_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK4_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK4_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK4_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV184:nat]: (SV184 = sK4_E)))]])). 160.12/160.41 thf(563,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK16_E) | (SV165@SX0)))) = sK16_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK16_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK16_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK16_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV185:nat]: (SV185 = sK16_E)))]])). 160.12/160.41 thf(564,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK11_E) | (SV165@SX0)))) = sK11_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK11_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK11_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK11_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV186:nat]: (SV186 = sK11_E)))]])). 160.12/160.41 thf(565,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK15_E) | (SV165@SX0)))) = sK15_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK15_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK15_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK15_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV187:nat]: (SV187 = sK15_E)))]])). 160.12/160.41 thf(566,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK1_E) | (SV165@SX0)))) = sK1_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK1_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK1_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK1_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV188:nat]: (SV188 = sK1_E)))]])). 160.12/160.41 thf(567,plain,(![SV165:(nat>$o)]: ((((ind@(^[SX0:nat]: ((SX0 = sK8_E) | (SV165@SX0)))) = sK8_E)=$true) | ((SV165@(ind@(^[SX0:nat]: ((SX0 = sK8_E) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SX0 = sK8_E) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((SX0 = sK8_E) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV189:nat]: (SV189 = sK8_E)))]])). 160.12/160.41 thf(568,plain,(![SV165:(nat>$o),SV196:(nat>$o),SV195:(nat>$o)]: ((((SV195@(ind@(^[SX0:nat]: (((SV195@SX0) | (SV196@SX0)) | (SV165@SX0))))) | (SV196@(ind@(^[SX0:nat]: (((SV195@SX0) | (SV196@SX0)) | (SV165@SX0))))))=$true) | ((SV165@(ind@(^[SX0:nat]: (((SV195@SX0) | (SV196@SX0)) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: (((SV195@SX0) | (SV196@SX0)) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: (((SV195@SX0) | (SV196@SX0)) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV194:nat]: ((SV195@SV194) | (SV196@SV194))))]])). 160.12/160.41 thf(569,plain,(![SV165:(nat>$o),SV193:(nat>$i),SV192:(nat>$i)]: ((((SV192@(ind@(^[SX0:nat]: (((SV192@SX0) = (SV193@SX0)) | (SV165@SX0))))) = (SV193@(ind@(^[SX0:nat]: (((SV192@SX0) = (SV193@SX0)) | (SV165@SX0))))))=$true) | ((SV165@(ind@(^[SX0:nat]: (((SV192@SX0) = (SV193@SX0)) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: (((SV192@SX0) = (SV193@SX0)) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: (((SV192@SX0) = (SV193@SX0)) | (SV165@SX0))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV166, $thf(^[SV191:nat]: ((SV192@SV191) = (SV193@SV191))))]])). 160.12/160.41 thf(571,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | $false))))=$true) | (($false)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | $false)))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | $false)))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV218:nat]: $false))]])). 160.12/160.41 thf(572,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | $false))))=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | $false)))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | $false)))=$false))),inference(sim,[status(thm)],[571])). 160.12/160.41 thf(573,plain,(![SV217:(nat>$o),SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (~ (SV217@SX0))))))=$true) | ((~ (SV217@(ind@(^[SX0:nat]: ((SV166@SX0) | (~ (SV217@SX0)))))))=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (~ (SV217@SX0)))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (~ (SV217@SX0)))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV216:nat]: (~ (SV217@SV216))))]])). 160.12/160.41 thf(574,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK6_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK6_E)))) = sK6_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK6_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK6_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV220:nat]: (SV220 = sK6_E)))]])). 160.12/160.41 thf(575,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK12_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK12_E)))) = sK12_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK12_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK12_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV221:nat]: (SV221 = sK12_E)))]])). 160.12/160.41 thf(576,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK19_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK19_E)))) = sK19_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK19_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK19_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV222:nat]: (SV222 = sK19_E)))]])). 160.12/160.41 thf(577,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK23_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK23_E)))) = sK23_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK23_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK23_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV223:nat]: (SV223 = sK23_E)))]])). 160.12/160.41 thf(578,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK22_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK22_E)))) = sK22_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK22_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK22_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV224:nat]: (SV224 = sK22_E)))]])). 160.12/160.41 thf(579,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK18_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK18_E)))) = sK18_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK18_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK18_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV225:nat]: (SV225 = sK18_E)))]])). 160.12/160.41 thf(580,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK9_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK9_E)))) = sK9_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK9_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK9_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV226:nat]: (SV226 = sK9_E)))]])). 160.12/160.41 thf(581,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK10_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK10_E)))) = sK10_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK10_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK10_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV227:nat]: (SV227 = sK10_E)))]])). 160.12/160.41 thf(582,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK20_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK20_E)))) = sK20_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK20_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK20_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV228:nat]: (SV228 = sK20_E)))]])). 160.12/160.41 thf(583,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK24_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK24_E)))) = sK24_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK24_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK24_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV229:nat]: (SV229 = sK24_E)))]])). 160.12/160.41 thf(584,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK5_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK5_E)))) = sK5_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK5_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK5_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV230:nat]: (SV230 = sK5_E)))]])). 160.12/160.41 thf(585,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK21_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK21_E)))) = sK21_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK21_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK21_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV231:nat]: (SV231 = sK21_E)))]])). 160.12/160.41 thf(586,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK13_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK13_E)))) = sK13_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK13_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK13_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV232:nat]: (SV232 = sK13_E)))]])). 160.12/160.41 thf(587,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK4_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK4_E)))) = sK4_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK4_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK4_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV233:nat]: (SV233 = sK4_E)))]])). 160.12/160.41 thf(588,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK16_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK16_E)))) = sK16_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK16_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK16_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV234:nat]: (SV234 = sK16_E)))]])). 160.12/160.41 thf(589,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK11_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK11_E)))) = sK11_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK11_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK11_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV235:nat]: (SV235 = sK11_E)))]])). 160.12/160.41 thf(590,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK15_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK15_E)))) = sK15_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK15_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK15_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV236:nat]: (SV236 = sK15_E)))]])). 160.12/160.41 thf(591,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK1_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK1_E)))) = sK1_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK1_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK1_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV237:nat]: (SV237 = sK1_E)))]])). 160.12/160.41 thf(592,plain,(![SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK8_E)))))=$true) | (((ind@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK8_E)))) = sK8_E)=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK8_E))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SX0 = sK8_E))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV238:nat]: (SV238 = sK8_E)))]])). 160.12/160.41 thf(593,plain,(![SV245:(nat>$o),SV244:(nat>$o),SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | ((SV244@SX0) | (SV245@SX0))))))=$true) | (((SV244@(ind@(^[SX0:nat]: ((SV166@SX0) | ((SV244@SX0) | (SV245@SX0)))))) | (SV245@(ind@(^[SX0:nat]: ((SV166@SX0) | ((SV244@SX0) | (SV245@SX0)))))))=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | ((SV244@SX0) | (SV245@SX0)))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | ((SV244@SX0) | (SV245@SX0)))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV243:nat]: ((SV244@SV243) | (SV245@SV243))))]])). 160.12/160.41 thf(594,plain,(![SV242:(nat>$i),SV241:(nat>$i),SV166:(nat>$o)]: (((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | ((SV241@SX0) = (SV242@SX0))))))=$true) | (((SV241@(ind@(^[SX0:nat]: ((SV166@SX0) | ((SV241@SX0) = (SV242@SX0)))))) = (SV242@(ind@(^[SX0:nat]: ((SV166@SX0) | ((SV241@SX0) = (SV242@SX0)))))))=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | ((SV241@SX0) = (SV242@SX0)))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | ((SV241@SX0) = (SV242@SX0)))))=$false))),inference(prim_subst,[status(thm)],[464:[bind(SV165, $thf(^[SV240:nat]: ((SV241@SV240) = (SV242@SV240))))]])). 160.12/160.41 thf(595,plain,(![SV165:(nat>$o),SV166:(nat>$o)]: (((amone@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0))))=$false) | ((SV165@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | (((SV166@((sK25_E@SV165)@SV166)) | (SV165@((sK25_E@SV165)@SV166)))=$true) | ((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@((sK25_E@SV165)@SV166)))=$true))),inference(extuni,[status(esa)],[543])). 160.12/160.41 thf(596,plain,(![SV165:(nat>$o),SV166:(nat>$o)]: (((amone@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0))))=$false) | ((SV165@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | (((SV166@((sK25_E@SV165)@SV166)) | (SV165@((sK25_E@SV165)@SV166)))=$false) | ((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@((sK25_E@SV165)@SV166)))=$false))),inference(extuni,[status(esa)],[543])). 160.12/160.41 thf(597,plain,(![SV27:nat,SV26:nat,SV165:(nat>$o),SV166:(nat>$o)]: (((some@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0))))=$false) | ((SV165@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | (((SV166@((((sK26_E@SV26)@SV27)@SV165)@SV166)) | (SV165@((((sK26_E@SV26)@SV27)@SV165)@SV166)))=$true) | ((SV27 = ((pl@SV26)@((((sK26_E@SV26)@SV27)@SV165)@SV166)))=$true))),inference(extuni,[status(esa)],[532])). 160.12/160.41 thf(598,plain,(![SV27:nat,SV26:nat,SV165:(nat>$o),SV166:(nat>$o)]: (((some@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0))))=$false) | ((SV165@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | (((SV166@((((sK26_E@SV26)@SV27)@SV165)@SV166)) | (SV165@((((sK26_E@SV26)@SV27)@SV165)@SV166)))=$false) | ((SV27 = ((pl@SV26)@((((sK26_E@SV26)@SV27)@SV165)@SV166)))=$false))),inference(extuni,[status(esa)],[532])). 160.12/160.41 thf(599,plain,(![SV165:(nat>$o),SV166:(nat>$o)]: (((SV166@((sK25_E@SV165)@SV166))=$false) | ((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((SV165@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0))))=$false) | ((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@((sK25_E@SV165)@SV166)))=$false))),inference(extcnf_or_neg,[status(thm)],[596])). 160.12/160.41 thf(600,plain,(![SV166:(nat>$o),SV165:(nat>$o)]: (((SV165@((sK25_E@SV165)@SV166))=$false) | ((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((SV165@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0))))=$false) | ((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@((sK25_E@SV165)@SV166)))=$false))),inference(extcnf_or_neg,[status(thm)],[596])). 160.12/160.41 thf(601,plain,(![SV165:(nat>$o),SV166:(nat>$o)]: (((SV166@((sK25_E@SV165)@SV166))=$true) | ((SV165@((sK25_E@SV165)@SV166))=$true) | ((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((SV165@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0))))=$false) | ((((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@((sK25_E@SV165)@SV166)))=$true))),inference(extcnf_or_pos,[status(thm)],[595])). 160.12/160.41 thf(602,plain,(![SV165:(nat>$o),SV27:nat,SV26:nat,SV166:(nat>$o)]: (((SV166@((((sK26_E@SV26)@SV27)@SV165)@SV166))=$false) | ((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((SV165@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0))))=$false) | ((SV27 = ((pl@SV26)@((((sK26_E@SV26)@SV27)@SV165)@SV166)))=$false))),inference(extcnf_or_neg,[status(thm)],[598])). 160.12/160.41 thf(603,plain,(![SV166:(nat>$o),SV27:nat,SV26:nat,SV165:(nat>$o)]: (((SV165@((((sK26_E@SV26)@SV27)@SV165)@SV166))=$false) | ((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((SV165@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0))))=$false) | ((SV27 = ((pl@SV26)@((((sK26_E@SV26)@SV27)@SV165)@SV166)))=$false))),inference(extcnf_or_neg,[status(thm)],[598])). 160.12/160.41 thf(604,plain,(![SV165:(nat>$o),SV27:nat,SV26:nat,SV166:(nat>$o)]: (((SV166@((((sK26_E@SV26)@SV27)@SV165)@SV166))=$true) | ((SV165@((((sK26_E@SV26)@SV27)@SV165)@SV166))=$true) | ((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((SV165@(ind@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0)))))=$true) | ((some@(^[SX0:nat]: ((SV166@SX0) | (SV165@SX0))))=$false) | ((SV27 = ((pl@SV26)@((((sK26_E@SV26)@SV27)@SV165)@SV166)))=$true))),inference(extcnf_or_pos,[status(thm)],[597])). 160.12/160.41 thf(605,plain,(![SV165:(nat>$o),SV168:(nat>$o)]: (((SV168@(ind@(^[SX0:nat]: ((~ (SV168@SX0)) | (SV165@SX0)))))=$false) | ((SV165@(ind@(^[SX0:nat]: ((~ (SV168@SX0)) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: ((~ (SV168@SX0)) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: ((~ (SV168@SX0)) | (SV165@SX0))))=$false))),inference(extcnf_not_pos,[status(thm)],[548])). 160.12/160.41 thf(606,plain,(![SV165:(nat>$o),SV196:(nat>$o),SV195:(nat>$o)]: (((SV195@(ind@(^[SX0:nat]: (((SV195@SX0) | (SV196@SX0)) | (SV165@SX0)))))=$true) | ((SV196@(ind@(^[SX0:nat]: (((SV195@SX0) | (SV196@SX0)) | (SV165@SX0)))))=$true) | ((SV165@(ind@(^[SX0:nat]: (((SV195@SX0) | (SV196@SX0)) | (SV165@SX0)))))=$true) | ((amone@(^[SX0:nat]: (((SV195@SX0) | (SV196@SX0)) | (SV165@SX0))))=$false) | ((some@(^[SX0:nat]: (((SV195@SX0) | (SV196@SX0)) | (SV165@SX0))))=$false))),inference(extcnf_or_pos,[status(thm)],[568])). 160.12/160.41 thf(607,plain,(![SV166:(nat>$o),SV217:(nat>$o)]: (((SV217@(ind@(^[SX0:nat]: ((SV166@SX0) | (~ (SV217@SX0))))))=$false) | ((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | (~ (SV217@SX0))))))=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | (~ (SV217@SX0)))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | (~ (SV217@SX0)))))=$false))),inference(extcnf_not_pos,[status(thm)],[573])). 160.12/160.41 thf(608,plain,(![SV245:(nat>$o),SV166:(nat>$o),SV244:(nat>$o)]: (((SV244@(ind@(^[SX0:nat]: ((SV166@SX0) | ((SV244@SX0) | (SV245@SX0))))))=$true) | ((SV245@(ind@(^[SX0:nat]: ((SV166@SX0) | ((SV244@SX0) | (SV245@SX0))))))=$true) | ((SV166@(ind@(^[SX0:nat]: ((SV166@SX0) | ((SV244@SX0) | (SV245@SX0))))))=$true) | ((amone@(^[SX0:nat]: ((SV166@SX0) | ((SV244@SX0) | (SV245@SX0)))))=$false) | ((some@(^[SX0:nat]: ((SV166@SX0) | ((SV244@SX0) | (SV245@SX0)))))=$false))),inference(extcnf_or_pos,[status(thm)],[593])). 160.12/160.41 thf(609,plain,(![SV445:frac]: ((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445)=$false) | (((eq@SV445)@x)=$false))),inference(rename,[status(thm)],[139])). 160.12/160.41 thf(616,plain,(![SV445:frac,SV81:frac,SV82:frac,SV83:frac,SV84:frac]: (((((eq@SV445)@x) = ((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83)))=$false) | (((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445)=$false) | (((eq@SV84)@SV83)=$false) | (((eq@SV82)@SV81)=$false))),inference(res,[status(thm)],[609,152])). 160.12/160.41 thf(617,plain,(![SV445:frac,SV81:frac,SV82:frac,SV83:frac,SV84:frac]: (((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445) = ((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83)))=$false) | (((eq@SV445)@x)=$false) | (((eq@SV84)@SV83)=$false) | (((eq@SV82)@SV81)=$false))),inference(res,[status(thm)],[609,152])). 160.12/160.41 thf(618,plain,(![SV445:frac,SV78:frac,SV79:frac,SV80:frac]: (((((eq@SV445)@x) = ((eq@SV78)@SV79))=$false) | (((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445)=$false) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@SV80)=$false))),inference(res,[status(thm)],[609,115])). 160.12/160.41 thf(619,plain,(![SV445:frac,SV78:frac,SV79:frac,SV80:frac]: (((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445) = ((eq@SV78)@SV79))=$false) | (((eq@SV445)@x)=$false) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@SV80)=$false))),inference(res,[status(thm)],[609,115])). 160.12/160.41 thf(624,plain,(![SV445:frac,SV34:nat,SV35:nat,SV36:nat]: (((((eq@SV445)@x) = ((eq@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))@((fr@((pl@SV36)@SV34))@SV35)))=$false) | (((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445)=$false))),inference(res,[status(thm)],[609,80])). 160.12/160.41 thf(625,plain,(![SV445:frac,SV34:nat,SV35:nat,SV36:nat]: (((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445) = ((eq@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))@((fr@((pl@SV36)@SV34))@SV35)))=$false) | (((eq@SV445)@x)=$false))),inference(res,[status(thm)],[609,80])). 160.12/160.41 thf(626,plain,(![SV445:frac,SV32:nat,SV33:frac]: (((((eq@SV445)@x) = ((eq@((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))@SV33))=$false) | (((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445)=$false))),inference(res,[status(thm)],[609,77])). 160.12/160.41 thf(627,plain,(![SV445:frac,SV32:nat,SV33:frac]: (((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445) = ((eq@((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))@SV33))=$false) | (((eq@SV445)@x)=$false))),inference(res,[status(thm)],[609,77])). 160.12/160.41 thf(628,plain,(![SV445:frac,SV30:nat,SV31:frac]: (((((eq@SV445)@x) = ((eq@SV31)@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))))=$false) | (((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445)=$false))),inference(res,[status(thm)],[609,74])). 160.12/160.41 thf(629,plain,(![SV445:frac,SV30:nat,SV31:frac]: (((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445) = ((eq@SV31)@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))))=$false) | (((eq@SV445)@x)=$false))),inference(res,[status(thm)],[609,74])). 160.12/160.41 thf(634,plain,(![SV445:frac,SV25:frac]: (((((eq@SV445)@x) = ((eq@SV25)@SV25))=$false) | (((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445)=$false))),inference(res,[status(thm)],[609,66])). 160.12/160.41 thf(635,plain,(![SV445:frac,SV25:frac]: (((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445) = ((eq@SV25)@SV25))=$false) | (((eq@SV445)@x)=$false))),inference(res,[status(thm)],[609,66])). 160.12/160.41 thf(638,plain,(![SV445:frac]: ((((eq@SV445)@x)=$false) | ((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445) = ((eq@SV445)@x))=$false))),inference(fac_restr,[status(thm)],[609])). 160.12/160.41 thf(639,plain,((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@x)=$false)),inference(extuni,[status(esa)],[635:[bind(SV445,$thf((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))),bind(SV25,$thf((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))]])). 160.12/160.41 thf(640,plain,((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@x)=$false)),inference(extuni,[status(esa)],[634:[bind(SV25,$thf(x)),bind(SV445,$thf(x))]])). 160.12/160.41 thf(641,plain,(![SV30:nat]: ((((eq@((fr@((ts@(num@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))))@SV30))@((ts@(den@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))))@SV30)))@x)=$false))),inference(extuni,[status(esa)],[629:[bind(SV445,$thf((fr@((ts@(num@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))))@SV30))@((ts@(den@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))))@SV30))),bind(SV31,$thf((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))]])). 160.12/160.41 thf(642,plain,(![SV30:nat,SV31:frac]: ((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV31)=$false) | ((x = ((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30)))=$false))),inference(extuni,[status(esa)],[628:[bind(SV445,$thf(SV31))]])). 160.12/160.41 thf(643,plain,(![SV32:nat,SV33:frac]: ((((eq@SV33)@x)=$false) | ((((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))) = ((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))=$false))),inference(extuni,[status(esa)],[627:[bind(SV445,$thf(SV33))]])). 160.12/160.41 thf(644,plain,(![SV32:nat]: ((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@((fr@((ts@(num@x))@SV32))@((ts@(den@x))@SV32)))=$false))),inference(extuni,[status(esa)],[626:[bind(SV33,$thf(x)),bind(SV445,$thf((fr@((ts@(num@x))@SV32))@((ts@(den@x))@SV32)))]])). 160.12/160.41 thf(645,plain,(![SV36:nat]: ((((eq@((fr@((pl@SV36)@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))))@((ts@(den@x))@(den@y))))@x)=$false) | ((y = ((fr@SV36)@((ts@(den@x))@(den@y))))=$false))),inference(extuni,[status(esa)],[625:[bind(SV445,$thf((fr@((pl@SV36)@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0))))))@((ts@(den@x))@(den@y)))),bind(SV35,$thf((ts@(den@x))@(den@y))),bind(SV34,$thf(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))]])). 160.12/160.41 thf(646,plain,(![SV35:nat,SV34:nat,SV36:nat]: ((((eq@((fr@((pl@SV36)@SV34))@SV35))@x)=$false) | ((((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))) = ((fr@SV34)@SV35))=$false) | ((y = ((fr@SV36)@SV35))=$false))),inference(extuni,[status(esa)],[625:[bind(SV445,$thf((fr@((pl@SV36)@SV34))@SV35))]])). 160.12/160.41 thf(647,plain,(![SV35:nat,SV34:nat,SV36:nat]: ((((eq@((fr@((pl@SV36)@SV34))@SV35))@x)=$false) | ((((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))) = ((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))=$false))),inference(extuni,[status(esa)],[625:[bind(SV445,$thf((fr@((pl@SV36)@SV34))@SV35))]])). 160.12/160.41 thf(648,plain,(![SV34:nat,SV35:nat,SV36:nat]: ((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))=$false) | ((x = ((fr@((pl@SV36)@SV34))@SV35))=$false))),inference(extuni,[status(esa)],[624:[bind(SV445,$thf((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))]])). 160.12/160.41 thf(649,plain,(![SV79:frac,SV80:frac]: ((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV80)=$false) | (((eq@SV80)@SV79)=$false) | (((eq@SV79)@x)=$false))),inference(extuni,[status(esa)],[619:[bind(SV445,$thf(SV79)),bind(SV78,$thf((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))]])). 160.12/160.41 thf(650,plain,(![SV80:frac,SV78:frac]: ((((eq@SV78)@SV80)=$false) | (((eq@SV80)@x)=$false) | (((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV78)=$false))),inference(extuni,[status(esa)],[618:[bind(SV79,$thf(x)),bind(SV445,$thf(SV78))]])). 160.12/160.41 thf(651,plain,(![SV83:frac,SV81:frac]: ((((eq@y)@SV81)=$false) | (((eq@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))@SV83)=$false) | (((eq@((pf@SV81)@SV83))@x)=$false))),inference(extuni,[status(esa)],[617:[bind(SV445,$thf((pf@SV81)@SV83)),bind(SV84,$thf((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))),bind(SV82,$thf(y))]])). 160.12/160.41 thf(652,plain,(![SV83:frac,SV84:frac,SV81:frac,SV82:frac]: ((((eq@SV82)@SV81)=$false) | (((eq@SV84)@SV83)=$false) | (((eq@((pf@SV81)@SV83))@x)=$false) | ((((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))) = ((pf@SV82)@SV84))=$false))),inference(extuni,[status(esa)],[617:[bind(SV445,$thf((pf@SV81)@SV83))]])). 160.12/160.41 thf(653,plain,(![SV83:frac,SV84:frac,SV81:frac,SV82:frac]: ((((eq@SV82)@SV81)=$false) | (((eq@SV84)@SV83)=$false) | (((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@((pf@SV82)@SV84))=$false) | ((x = ((pf@SV81)@SV83))=$false))),inference(extuni,[status(esa)],[616:[bind(SV445,$thf((pf@SV82)@SV84))]])). 160.12/160.41 thf(654,plain,(((((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))) = x)=$false) | (((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@x)=$false)),inference(extuni,[status(esa)],[638:[bind(SV445,$thf((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))]])). 160.12/160.41 thf(655,plain,(![SV446:nat,SV447:frac,SV448:frac]: ((((eq@SV448)@SV447)=$false) | (((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))=$true))),inference(rename,[status(thm)],[142])). 160.12/160.41 thf(658,plain,(![SV446:nat,SV447:frac,SV448:frac,SV445:frac]: (((((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446))) = ((eq@SV445)@x))=$false) | (((eq@SV448)@SV447)=$false) | (((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445)=$false))),inference(res,[status(thm)],[655,609])). 160.12/160.41 thf(659,plain,(![SV446:nat,SV447:frac,SV448:frac,SV445:frac]: (((((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446))) = ((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445))=$false) | (((eq@SV448)@SV447)=$false) | (((eq@SV445)@x)=$false))),inference(res,[status(thm)],[655,609])). 160.12/160.41 thf(678,plain,(![SV446:nat,SV447:frac,SV448:frac,SV81:frac,SV82:frac,SV83:frac,SV84:frac]: (((((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446))) = ((eq@SV82)@SV81))=$false) | (((eq@SV448)@SV447)=$false) | (((eq@SV84)@SV83)=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true))),inference(res,[status(thm)],[655,152])). 160.12/160.41 thf(679,plain,(![SV446:nat,SV447:frac,SV448:frac,SV81:frac,SV82:frac,SV83:frac,SV84:frac]: (((((eq@SV448)@SV447) = ((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83)))=$false) | (((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))=$true) | (((eq@SV84)@SV83)=$false) | (((eq@SV82)@SV81)=$false))),inference(res,[status(thm)],[655,152])). 160.12/160.41 thf(680,plain,(![SV446:nat,SV447:frac,SV448:frac,SV81:frac,SV82:frac,SV83:frac,SV84:frac]: (((((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446))) = ((eq@SV84)@SV83))=$false) | (((eq@SV448)@SV447)=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true) | (((eq@SV82)@SV81)=$false))),inference(res,[status(thm)],[655,152])). 160.12/160.41 thf(681,plain,(![SV446:nat,SV447:frac,SV448:frac,SV78:frac,SV79:frac,SV80:frac]: (((((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446))) = ((eq@SV78)@SV80))=$false) | (((eq@SV448)@SV447)=$false) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@SV79)=$true))),inference(res,[status(thm)],[655,115])). 160.12/160.41 thf(682,plain,(![SV446:nat,SV447:frac,SV448:frac,SV78:frac,SV79:frac,SV80:frac]: (((((eq@SV448)@SV447) = ((eq@SV78)@SV79))=$false) | (((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))=$true) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@SV80)=$false))),inference(res,[status(thm)],[655,115])). 160.12/160.41 thf(683,plain,(![SV446:nat,SV447:frac,SV448:frac,SV78:frac,SV79:frac,SV80:frac]: (((((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446))) = ((eq@SV80)@SV79))=$false) | (((eq@SV448)@SV447)=$false) | (((eq@SV78)@SV79)=$true) | (((eq@SV78)@SV80)=$false))),inference(res,[status(thm)],[655,115])). 160.12/160.41 thf(689,plain,(![SV446:nat,SV447:frac,SV448:frac,SV34:nat,SV35:nat,SV36:nat]: (((((eq@SV448)@SV447) = ((eq@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))@((fr@((pl@SV36)@SV34))@SV35)))=$false) | (((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))=$true))),inference(res,[status(thm)],[655,80])). 160.12/160.41 thf(690,plain,(![SV446:nat,SV447:frac,SV448:frac,SV32:nat,SV33:frac]: (((((eq@SV448)@SV447) = ((eq@((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))@SV33))=$false) | (((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))=$true))),inference(res,[status(thm)],[655,77])). 160.12/160.41 thf(691,plain,(![SV446:nat,SV447:frac,SV448:frac,SV30:nat,SV31:frac]: (((((eq@SV448)@SV447) = ((eq@SV31)@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))))=$false) | (((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))=$true))),inference(res,[status(thm)],[655,74])). 160.12/160.41 thf(695,plain,(![SV446:nat,SV447:frac,SV448:frac,SV25:frac]: (((((eq@SV448)@SV447) = ((eq@SV25)@SV25))=$false) | (((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))=$true))),inference(res,[status(thm)],[655,66])). 160.12/160.41 thf(698,plain,(![SV446:nat,SV447:frac,SV448:frac]: (((((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446))) = ((eq@((pf@y)@((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y)))))@x))=$false) | (((eq@SV448)@SV447)=$false))),inference(res,[status(thm)],[655,37])). 160.12/160.41 thf(700,plain,(![SV446:nat,SV447:frac]: ((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV447)=$false) | ((((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)) = x)=$false))),inference(extuni,[status(esa)],[698:[bind(SV448,$thf((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))]])). 160.12/160.41 thf(701,plain,(![SV446:nat,SV25:frac]: ((((eq@SV25)@((fr@((ts@(num@SV25))@SV446))@((ts@(den@SV25))@SV446)))=$true))),inference(extuni,[status(esa)],[695:[bind(SV447,$thf(SV25)),bind(SV448,$thf(SV25))]])). 160.12/160.41 thf(702,plain,(![SV446:nat,SV30:nat,SV31:frac]: ((((eq@SV31)@((fr@((ts@(num@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))))@SV446))@((ts@(den@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))))@SV446)))=$true))),inference(extuni,[status(esa)],[691:[bind(SV447,$thf((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))),bind(SV448,$thf(SV31))]])). 160.12/160.41 thf(703,plain,(![SV446:nat,SV32:nat,SV33:frac]: ((((eq@((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))@((fr@((ts@(num@SV33))@SV446))@((ts@(den@SV33))@SV446)))=$true))),inference(extuni,[status(esa)],[690:[bind(SV447,$thf(SV33)),bind(SV448,$thf((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))]])). 160.12/160.41 thf(704,plain,(![SV446:nat,SV34:nat,SV35:nat,SV36:nat]: ((((eq@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))@((fr@((ts@(num@((fr@((pl@SV36)@SV34))@SV35)))@SV446))@((ts@(den@((fr@((pl@SV36)@SV34))@SV35)))@SV446)))=$true))),inference(extuni,[status(esa)],[689:[bind(SV447,$thf((fr@((pl@SV36)@SV34))@SV35)),bind(SV448,$thf((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))]])). 160.12/160.41 thf(705,plain,(![SV446:nat,SV447:frac,SV80:frac,SV78:frac]: ((((eq@SV78)@SV80)=$false) | (((eq@SV78)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))=$true) | (((eq@SV80)@SV447)=$false))),inference(extuni,[status(esa)],[683:[bind(SV79,$thf((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446))),bind(SV448,$thf(SV80))]])). 160.12/160.41 thf(706,plain,(![SV446:nat,SV79:frac,SV80:frac,SV78:frac]: ((((eq@SV78)@SV80)=$false) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@((fr@((ts@(num@SV79))@SV446))@((ts@(den@SV79))@SV446)))=$true))),inference(extuni,[status(esa)],[682:[bind(SV447,$thf(SV79)),bind(SV448,$thf(SV78))]])). 160.12/160.41 thf(707,plain,(![SV446:nat,SV447:frac,SV79:frac,SV78:frac]: ((((eq@SV78)@SV79)=$true) | (((eq@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))@SV79)=$false) | (((eq@SV78)@SV447)=$false))),inference(extuni,[status(esa)],[681:[bind(SV80,$thf((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446))),bind(SV448,$thf(SV78))]])). 160.12/160.41 thf(708,plain,(![SV446:nat,SV447:frac,SV84:frac,SV81:frac,SV82:frac]: ((((eq@SV82)@SV81)=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446))))=$true) | (((eq@SV84)@SV447)=$false))),inference(extuni,[status(esa)],[680:[bind(SV83,$thf((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446))),bind(SV448,$thf(SV84))]])). 160.12/160.41 thf(709,plain,(![SV446:nat,SV83:frac,SV84:frac,SV81:frac,SV82:frac]: ((((eq@SV82)@SV81)=$false) | (((eq@SV84)@SV83)=$false) | (((eq@((pf@SV82)@SV84))@((fr@((ts@(num@((pf@SV81)@SV83)))@SV446))@((ts@(den@((pf@SV81)@SV83)))@SV446)))=$true))),inference(extuni,[status(esa)],[679:[bind(SV447,$thf((pf@SV81)@SV83)),bind(SV448,$thf((pf@SV82)@SV84))]])). 160.12/160.41 thf(710,plain,(![SV83:frac,SV446:nat,SV447:frac,SV84:frac,SV82:frac]: ((((eq@((pf@SV82)@SV84))@((pf@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))@SV83))=$true) | (((eq@SV84)@SV83)=$false) | (((eq@SV82)@SV447)=$false))),inference(extuni,[status(esa)],[678:[bind(SV81,$thf((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446))),bind(SV448,$thf(SV82))]])). 160.12/160.41 thf(711,plain,(![SV446:nat,SV447:frac]: ((((eq@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))@x)=$false) | (((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV447)=$false))),inference(extuni,[status(esa)],[659:[bind(SV445,$thf((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446))),bind(SV448,$thf((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))]])). 160.12/160.41 thf(712,plain,(![SV446:nat,SV447:frac,SV445:frac]: ((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445)=$false) | (((eq@SV445)@SV447)=$false) | ((((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)) = x)=$false))),inference(extuni,[status(esa)],[658:[bind(SV448,$thf(SV445))]])). 160.12/160.41 thf(713,plain,(![SV449:nat,SV450:frac,SV451:frac]: ((((eq@SV451)@SV450)=$true) | (((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450)=$false))),inference(rename,[status(thm)],[143])). 160.12/160.41 thf(716,plain,(![SV449:nat,SV450:frac,SV451:frac,SV446:nat,SV447:frac,SV448:frac]: (((((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450) = ((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446))))=$false) | (((eq@SV451)@SV450)=$true) | (((eq@SV448)@SV447)=$false))),inference(res,[status(thm)],[713,655])). 160.12/160.41 thf(717,plain,(![SV449:nat,SV450:frac,SV451:frac,SV446:nat,SV447:frac,SV448:frac]: (((((eq@SV451)@SV450) = ((eq@SV448)@SV447))=$false) | (((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450)=$false) | (((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))=$true))),inference(res,[status(thm)],[713,655])). 160.12/160.41 thf(718,plain,(![SV449:nat,SV450:frac,SV451:frac,SV445:frac]: (((((eq@SV451)@SV450) = ((eq@SV445)@x))=$false) | (((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450)=$false) | (((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445)=$false))),inference(res,[status(thm)],[713,609])). 160.12/160.41 thf(719,plain,(![SV449:nat,SV450:frac,SV451:frac,SV445:frac]: (((((eq@SV451)@SV450) = ((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445))=$false) | (((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450)=$false) | (((eq@SV445)@x)=$false))),inference(res,[status(thm)],[713,609])). 160.12/160.41 thf(738,plain,(![SV449:nat,SV450:frac,SV451:frac,SV81:frac,SV82:frac,SV83:frac,SV84:frac]: (((((eq@SV451)@SV450) = ((eq@SV82)@SV81))=$false) | (((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450)=$false) | (((eq@SV84)@SV83)=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true))),inference(res,[status(thm)],[713,152])). 160.12/160.41 thf(739,plain,(![SV449:nat,SV450:frac,SV451:frac,SV81:frac,SV82:frac,SV83:frac,SV84:frac]: (((((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450) = ((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83)))=$false) | (((eq@SV451)@SV450)=$true) | (((eq@SV84)@SV83)=$false) | (((eq@SV82)@SV81)=$false))),inference(res,[status(thm)],[713,152])). 160.12/160.41 thf(740,plain,(![SV449:nat,SV450:frac,SV451:frac,SV81:frac,SV82:frac,SV83:frac,SV84:frac]: (((((eq@SV451)@SV450) = ((eq@SV84)@SV83))=$false) | (((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450)=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true) | (((eq@SV82)@SV81)=$false))),inference(res,[status(thm)],[713,152])). 160.12/160.41 thf(741,plain,(![SV449:nat,SV450:frac,SV451:frac,SV78:frac,SV79:frac,SV80:frac]: (((((eq@SV451)@SV450) = ((eq@SV78)@SV80))=$false) | (((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450)=$false) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@SV79)=$true))),inference(res,[status(thm)],[713,115])). 160.12/160.41 thf(742,plain,(![SV449:nat,SV450:frac,SV451:frac,SV78:frac,SV79:frac,SV80:frac]: (((((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450) = ((eq@SV78)@SV79))=$false) | (((eq@SV451)@SV450)=$true) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@SV80)=$false))),inference(res,[status(thm)],[713,115])). 160.12/160.41 thf(743,plain,(![SV449:nat,SV450:frac,SV451:frac,SV78:frac,SV79:frac,SV80:frac]: (((((eq@SV451)@SV450) = ((eq@SV80)@SV79))=$false) | (((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450)=$false) | (((eq@SV78)@SV79)=$true) | (((eq@SV78)@SV80)=$false))),inference(res,[status(thm)],[713,115])). 160.12/160.41 thf(749,plain,(![SV449:nat,SV450:frac,SV451:frac,SV34:nat,SV35:nat,SV36:nat]: (((((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450) = ((eq@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))@((fr@((pl@SV36)@SV34))@SV35)))=$false) | (((eq@SV451)@SV450)=$true))),inference(res,[status(thm)],[713,80])). 160.12/160.41 thf(750,plain,(![SV449:nat,SV450:frac,SV451:frac,SV32:nat,SV33:frac]: (((((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450) = ((eq@((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))@SV33))=$false) | (((eq@SV451)@SV450)=$true))),inference(res,[status(thm)],[713,77])). 160.12/160.41 thf(751,plain,(![SV449:nat,SV450:frac,SV451:frac,SV30:nat,SV31:frac]: (((((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450) = ((eq@SV31)@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))))=$false) | (((eq@SV451)@SV450)=$true))),inference(res,[status(thm)],[713,74])). 160.12/160.41 thf(755,plain,(![SV449:nat,SV450:frac,SV451:frac,SV25:frac]: (((((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450) = ((eq@SV25)@SV25))=$false) | (((eq@SV451)@SV450)=$true))),inference(res,[status(thm)],[713,66])). 160.12/160.41 thf(758,plain,(![SV449:nat,SV450:frac,SV451:frac]: (((((eq@SV451)@SV450) = ((eq@((pf@y)@((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y)))))@x))=$false) | (((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450)=$false))),inference(res,[status(thm)],[713,37])). 160.12/160.41 thf(760,plain,(![SV449:nat]: ((((eq@((fr@((ts@(num@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))))@SV449))@((ts@(den@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))))@SV449)))@x)=$false))),inference(extuni,[status(esa)],[758:[bind(SV450,$thf(x)),bind(SV451,$thf((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))]])). 160.12/160.41 thf(761,plain,(![SV449:nat,SV451:frac]: ((((eq@SV451)@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))=$true))),inference(extuni,[status(esa)],[755:[bind(SV450,$thf((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449))),bind(SV25,$thf((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))]])). 160.12/160.41 thf(762,plain,(![SV30:nat,SV449:nat,SV451:frac]: ((((eq@SV451)@((fr@((ts@(num@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449))))@SV30))@((ts@(den@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449))))@SV30)))=$true))),inference(extuni,[status(esa)],[751:[bind(SV450,$thf((fr@((ts@(num@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449))))@SV30))@((ts@(den@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449))))@SV30))),bind(SV31,$thf((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))]])). 160.12/160.41 thf(763,plain,(![SV33:frac]: ((((eq@SV33)@SV33)=$true))),inference(extuni,[status(esa)],[750:[bind(SV450,$thf(SV33)),bind(SV449,$thf(SV32)),bind(SV451,$thf(SV33))]])). 160.12/160.41 thf(764,plain,(![SV33:frac]: ((((eq@SV33)@SV33)=$true) | (((num@SV33) = (num@SV33))=$false))),inference(extuni,[status(esa)],[750:[bind(SV450,$thf(SV33)),bind(SV451,$thf(SV33)),bind(SV449,$thf(SV32))]])). 160.12/160.41 thf(765,plain,(![SV33:frac,SV451:frac]: ((((eq@SV451)@SV33)=$true) | (((den@SV451) = (den@SV33))=$false) | (((num@SV451) = (num@SV33))=$false))),inference(extuni,[status(esa)],[750:[bind(SV450,$thf(SV33)),bind(SV449,$thf(SV32))]])). 160.12/160.41 thf(766,plain,(![SV32:nat,SV33:frac,SV451:frac]: ((((eq@SV451)@SV33)=$true) | ((((ts@(den@SV451))@SV32) = ((ts@(den@SV33))@SV32))=$false) | (((num@SV451) = (num@SV33))=$false))),inference(extuni,[status(esa)],[750:[bind(SV450,$thf(SV33)),bind(SV449,$thf(SV32))]])). 160.12/160.41 thf(767,plain,(![SV32:nat,SV33:frac]: ((((eq@SV33)@SV33)=$true) | ((((ts@(num@SV33))@SV32) = ((ts@(num@SV33))@SV32))=$false))),inference(extuni,[status(esa)],[750:[bind(SV450,$thf(SV33)),bind(SV449,$thf(SV32)),bind(SV451,$thf(SV33))]])). 160.12/160.41 thf(768,plain,(![SV32:nat,SV33:frac,SV451:frac]: ((((eq@SV451)@SV33)=$true) | (((den@SV451) = (den@SV33))=$false) | ((((ts@(num@SV451))@SV32) = ((ts@(num@SV33))@SV32))=$false))),inference(extuni,[status(esa)],[750:[bind(SV450,$thf(SV33)),bind(SV449,$thf(SV32))]])). 160.12/160.41 thf(769,plain,(![SV32:nat,SV449:nat,SV33:frac,SV451:frac]: ((((eq@SV451)@SV33)=$true) | ((((ts@(den@SV451))@SV449) = ((ts@(den@SV33))@SV32))=$false) | ((((ts@(num@SV451))@SV449) = ((ts@(num@SV33))@SV32))=$false))),inference(extuni,[status(esa)],[750:[bind(SV450,$thf(SV33))]])). 160.12/160.41 thf(770,plain,(![SV32:nat,SV449:nat,SV33:frac,SV451:frac]: ((((eq@SV451)@SV33)=$true) | ((((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)) = ((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))=$false))),inference(extuni,[status(esa)],[750:[bind(SV450,$thf(SV33))]])). 160.12/160.41 thf(771,plain,(![SV449:nat,SV35:nat,SV34:nat,SV36:nat,SV451:frac]: ((((eq@SV451)@((fr@((pl@SV36)@SV34))@SV35))=$true) | ((((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)) = ((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))=$false))),inference(extuni,[status(esa)],[749:[bind(SV450,$thf((fr@((pl@SV36)@SV34))@SV35))]])). 160.12/160.41 thf(772,plain,(![SV449:nat,SV79:frac,SV80:frac,SV78:frac]: ((((eq@SV78)@SV80)=$false) | (((eq@SV78)@SV79)=$true) | (((eq@((fr@((ts@(num@SV80))@SV449))@((ts@(den@SV80))@SV449)))@SV79)=$false))),inference(extuni,[status(esa)],[743:[bind(SV450,$thf(SV79)),bind(SV451,$thf(SV80))]])). 160.12/160.41 thf(773,plain,(![SV79:frac,SV80:frac,SV449:nat,SV451:frac]: ((((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV80)=$false) | (((eq@SV80)@SV79)=$false) | (((eq@SV451)@SV79)=$true))),inference(extuni,[status(esa)],[742:[bind(SV450,$thf(SV79)),bind(SV78,$thf((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))]])). 160.12/160.41 thf(774,plain,(![SV449:nat,SV80:frac,SV79:frac,SV78:frac]: ((((eq@SV78)@SV79)=$true) | (((eq@SV80)@SV79)=$false) | (((eq@((fr@((ts@(num@SV78))@SV449))@((ts@(den@SV78))@SV449)))@SV80)=$false))),inference(extuni,[status(esa)],[741:[bind(SV450,$thf(SV80)),bind(SV451,$thf(SV78))]])). 160.12/160.41 thf(775,plain,(![SV449:nat,SV83:frac,SV84:frac,SV81:frac,SV82:frac]: ((((eq@SV82)@SV81)=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true) | (((eq@((fr@((ts@(num@SV84))@SV449))@((ts@(den@SV84))@SV449)))@SV83)=$false))),inference(extuni,[status(esa)],[740:[bind(SV450,$thf(SV83)),bind(SV451,$thf(SV84))]])). 160.12/160.41 thf(776,plain,(![SV449:nat,SV451:frac,SV83:frac,SV84:frac,SV81:frac,SV82:frac]: ((((eq@SV82)@SV81)=$false) | (((eq@SV84)@SV83)=$false) | (((eq@SV451)@((pf@SV81)@SV83))=$true) | ((((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)) = ((pf@SV82)@SV84))=$false))),inference(extuni,[status(esa)],[739:[bind(SV450,$thf((pf@SV81)@SV83))]])). 160.12/160.41 thf(777,plain,(![SV449:nat,SV83:frac,SV81:frac,SV84:frac,SV82:frac]: ((((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true) | (((eq@SV84)@SV83)=$false) | (((eq@((fr@((ts@(num@SV82))@SV449))@((ts@(den@SV82))@SV449)))@SV81)=$false))),inference(extuni,[status(esa)],[738:[bind(SV450,$thf(SV81)),bind(SV451,$thf(SV82))]])). 160.12/160.41 thf(778,plain,(![SV449:nat,SV445:frac]: ((((eq@SV445)@x)=$false) | (((eq@((fr@((ts@(num@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))))@SV449))@((ts@(den@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y))))))@SV449)))@SV445)=$false))),inference(extuni,[status(esa)],[719:[bind(SV450,$thf(SV445)),bind(SV451,$thf((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))]])). 160.12/160.41 thf(779,plain,(![SV449:nat,SV445:frac]: ((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445)=$false) | (((eq@((fr@((ts@(num@SV445))@SV449))@((ts@(den@SV445))@SV449)))@x)=$false))),inference(extuni,[status(esa)],[718:[bind(SV450,$thf(x)),bind(SV451,$thf(SV445))]])). 160.12/160.41 thf(780,plain,(![SV449:nat,SV446:nat,SV447:frac,SV448:frac]: ((((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))=$true) | (((eq@((fr@((ts@(num@SV448))@SV449))@((ts@(den@SV448))@SV449)))@SV447)=$false))),inference(extuni,[status(esa)],[717:[bind(SV450,$thf(SV447)),bind(SV451,$thf(SV448))]])). 160.12/160.41 thf(781,plain,(![SV446:nat,SV447:frac,SV449:nat,SV451:frac]: ((((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV447)=$false) | (((eq@SV451)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))=$true))),inference(extuni,[status(esa)],[716:[bind(SV450,$thf((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446))),bind(SV448,$thf((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))]])). 160.12/160.41 thf(782,plain,(![SV32:nat,SV33:frac]: ((((eq@SV33)@SV33)=$true))),inference(sim,[status(thm)],[767])). 160.12/160.41 thf(783,plain,(![SV33:frac]: ((((eq@SV33)@SV33)=$true))),inference(sim,[status(thm)],[764])). 160.12/160.41 thf(784,plain,(![SV452:nat,SV453:frac,SV454:frac]: ((((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)))=$false) | (((eq@SV454)@SV453)=$true))),inference(rename,[status(thm)],[144])). 160.12/160.41 thf(787,plain,(![SV452:nat,SV453:frac,SV454:frac,SV449:nat,SV450:frac,SV451:frac]: (((((eq@SV454)@SV453) = ((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450))=$false) | (((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)))=$false) | (((eq@SV451)@SV450)=$true))),inference(res,[status(thm)],[784,713])). 160.12/160.41 thf(788,plain,(![SV452:nat,SV453:frac,SV454:frac,SV449:nat,SV450:frac,SV451:frac]: (((((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452))) = ((eq@SV451)@SV450))=$false) | (((eq@SV454)@SV453)=$true) | (((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@SV450)=$false))),inference(res,[status(thm)],[784,713])). 160.12/160.41 thf(789,plain,(![SV452:nat,SV453:frac,SV454:frac,SV446:nat,SV447:frac,SV448:frac]: (((((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452))) = ((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446))))=$false) | (((eq@SV454)@SV453)=$true) | (((eq@SV448)@SV447)=$false))),inference(res,[status(thm)],[784,655])). 160.12/160.41 thf(790,plain,(![SV452:nat,SV453:frac,SV454:frac,SV446:nat,SV447:frac,SV448:frac]: (((((eq@SV454)@SV453) = ((eq@SV448)@SV447))=$false) | (((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)))=$false) | (((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))=$true))),inference(res,[status(thm)],[784,655])). 160.12/160.41 thf(791,plain,(![SV452:nat,SV453:frac,SV454:frac,SV445:frac]: (((((eq@SV454)@SV453) = ((eq@SV445)@x))=$false) | (((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)))=$false) | (((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445)=$false))),inference(res,[status(thm)],[784,609])). 160.12/160.41 thf(792,plain,(![SV452:nat,SV453:frac,SV454:frac,SV445:frac]: (((((eq@SV454)@SV453) = ((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445))=$false) | (((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)))=$false) | (((eq@SV445)@x)=$false))),inference(res,[status(thm)],[784,609])). 160.12/160.41 thf(811,plain,(![SV452:nat,SV453:frac,SV454:frac,SV81:frac,SV82:frac,SV83:frac,SV84:frac]: (((((eq@SV454)@SV453) = ((eq@SV82)@SV81))=$false) | (((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)))=$false) | (((eq@SV84)@SV83)=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true))),inference(res,[status(thm)],[784,152])). 160.12/160.41 thf(812,plain,(![SV452:nat,SV453:frac,SV454:frac,SV81:frac,SV82:frac,SV83:frac,SV84:frac]: (((((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452))) = ((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83)))=$false) | (((eq@SV454)@SV453)=$true) | (((eq@SV84)@SV83)=$false) | (((eq@SV82)@SV81)=$false))),inference(res,[status(thm)],[784,152])). 160.12/160.41 thf(813,plain,(![SV452:nat,SV453:frac,SV454:frac,SV81:frac,SV82:frac,SV83:frac,SV84:frac]: (((((eq@SV454)@SV453) = ((eq@SV84)@SV83))=$false) | (((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)))=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true) | (((eq@SV82)@SV81)=$false))),inference(res,[status(thm)],[784,152])). 160.12/160.41 thf(814,plain,(![SV452:nat,SV453:frac,SV454:frac,SV78:frac,SV79:frac,SV80:frac]: (((((eq@SV454)@SV453) = ((eq@SV78)@SV80))=$false) | (((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)))=$false) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@SV79)=$true))),inference(res,[status(thm)],[784,115])). 160.12/160.41 thf(815,plain,(![SV452:nat,SV453:frac,SV454:frac,SV78:frac,SV79:frac,SV80:frac]: (((((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452))) = ((eq@SV78)@SV79))=$false) | (((eq@SV454)@SV453)=$true) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@SV80)=$false))),inference(res,[status(thm)],[784,115])). 160.12/160.41 thf(816,plain,(![SV452:nat,SV453:frac,SV454:frac,SV78:frac,SV79:frac,SV80:frac]: (((((eq@SV454)@SV453) = ((eq@SV80)@SV79))=$false) | (((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)))=$false) | (((eq@SV78)@SV79)=$true) | (((eq@SV78)@SV80)=$false))),inference(res,[status(thm)],[784,115])). 160.12/160.41 thf(822,plain,(![SV452:nat,SV453:frac,SV454:frac,SV34:nat,SV35:nat,SV36:nat]: (((((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452))) = ((eq@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))@((fr@((pl@SV36)@SV34))@SV35)))=$false) | (((eq@SV454)@SV453)=$true))),inference(res,[status(thm)],[784,80])). 160.12/160.41 thf(823,plain,(![SV452:nat,SV453:frac,SV454:frac,SV32:nat,SV33:frac]: (((((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452))) = ((eq@((fr@((ts@(num@SV33))@SV32))@((ts@(den@SV33))@SV32)))@SV33))=$false) | (((eq@SV454)@SV453)=$true))),inference(res,[status(thm)],[784,77])). 160.12/160.41 thf(824,plain,(![SV452:nat,SV453:frac,SV454:frac,SV30:nat,SV31:frac]: (((((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452))) = ((eq@SV31)@((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30))))=$false) | (((eq@SV454)@SV453)=$true))),inference(res,[status(thm)],[784,74])). 160.12/160.41 thf(828,plain,(![SV452:nat,SV453:frac,SV454:frac,SV25:frac]: (((((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452))) = ((eq@SV25)@SV25))=$false) | (((eq@SV454)@SV453)=$true))),inference(res,[status(thm)],[784,66])). 160.12/160.41 thf(831,plain,(![SV452:nat,SV453:frac,SV454:frac]: (((((eq@SV454)@SV453) = ((eq@((pf@y)@((fr@(ind@(^[Xt:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@Xt)))))@((ts@(den@x))@(den@y)))))@x))=$false) | (((eq@SV454)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)))=$false))),inference(res,[status(thm)],[784,37])). 160.12/160.41 thf(833,plain,(![SV452:nat]: ((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@((fr@((ts@(num@x))@SV452))@((ts@(den@x))@SV452)))=$false))),inference(extuni,[status(esa)],[831:[bind(SV453,$thf(x)),bind(SV454,$thf((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))]])). 160.12/160.41 thf(834,plain,(![SV452:nat,SV453:frac]: ((((eq@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)))@SV453)=$true))),inference(extuni,[status(esa)],[828:[bind(SV25,$thf((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452))),bind(SV454,$thf((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)))]])). 160.12/160.41 thf(835,plain,(![SV31:frac]: ((((eq@SV31)@SV31)=$true))),inference(extuni,[status(esa)],[824:[bind(SV452,$thf(SV30)),bind(SV453,$thf(SV31)),bind(SV454,$thf(SV31))]])). 160.12/160.41 thf(836,plain,(![SV31:frac]: ((((eq@SV31)@SV31)=$true) | (((num@SV31) = (num@SV31))=$false))),inference(extuni,[status(esa)],[824:[bind(SV453,$thf(SV31)),bind(SV452,$thf(SV30)),bind(SV454,$thf(SV31))]])). 160.12/160.41 thf(837,plain,(![SV453:frac,SV31:frac]: ((((eq@SV31)@SV453)=$true) | (((den@SV453) = (den@SV31))=$false) | (((num@SV453) = (num@SV31))=$false))),inference(extuni,[status(esa)],[824:[bind(SV452,$thf(SV30)),bind(SV454,$thf(SV31))]])). 160.12/160.41 thf(838,plain,(![SV30:nat,SV453:frac,SV31:frac]: ((((eq@SV31)@SV453)=$true) | ((((ts@(den@SV453))@SV30) = ((ts@(den@SV31))@SV30))=$false) | (((num@SV453) = (num@SV31))=$false))),inference(extuni,[status(esa)],[824:[bind(SV452,$thf(SV30)),bind(SV454,$thf(SV31))]])). 160.12/160.41 thf(839,plain,(![SV30:nat,SV31:frac]: ((((eq@SV31)@SV31)=$true) | ((((ts@(num@SV31))@SV30) = ((ts@(num@SV31))@SV30))=$false))),inference(extuni,[status(esa)],[824:[bind(SV452,$thf(SV30)),bind(SV453,$thf(SV31)),bind(SV454,$thf(SV31))]])). 160.12/160.41 thf(840,plain,(![SV30:nat,SV453:frac,SV31:frac]: ((((eq@SV31)@SV453)=$true) | (((den@SV453) = (den@SV31))=$false) | ((((ts@(num@SV453))@SV30) = ((ts@(num@SV31))@SV30))=$false))),inference(extuni,[status(esa)],[824:[bind(SV452,$thf(SV30)),bind(SV454,$thf(SV31))]])). 160.12/160.41 thf(841,plain,(![SV30:nat,SV452:nat,SV453:frac,SV31:frac]: ((((eq@SV31)@SV453)=$true) | ((((ts@(den@SV453))@SV452) = ((ts@(den@SV31))@SV30))=$false) | ((((ts@(num@SV453))@SV452) = ((ts@(num@SV31))@SV30))=$false))),inference(extuni,[status(esa)],[824:[bind(SV454,$thf(SV31))]])). 160.12/160.41 thf(842,plain,(![SV30:nat,SV452:nat,SV453:frac,SV31:frac]: ((((eq@SV31)@SV453)=$true) | ((((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)) = ((fr@((ts@(num@SV31))@SV30))@((ts@(den@SV31))@SV30)))=$false))),inference(extuni,[status(esa)],[824:[bind(SV454,$thf(SV31))]])). 160.12/160.41 thf(843,plain,(![SV32:nat,SV452:nat,SV453:frac]: ((((eq@((fr@((ts@(num@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452))))@SV32))@((ts@(den@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452))))@SV32)))@SV453)=$true))),inference(extuni,[status(esa)],[823:[bind(SV33,$thf((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452))),bind(SV454,$thf((fr@((ts@(num@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452))))@SV32))@((ts@(den@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452))))@SV32)))]])). 160.12/160.41 thf(844,plain,(![SV34:nat,SV452:nat,SV453:frac,SV36:nat]: ((((eq@((pf@((fr@SV36)@((ts@(den@SV453))@SV452)))@((fr@SV34)@((ts@(den@SV453))@SV452))))@SV453)=$true) | ((((ts@(num@SV453))@SV452) = ((pl@SV36)@SV34))=$false))),inference(extuni,[status(esa)],[822:[bind(SV35,$thf((ts@(den@SV453))@SV452)),bind(SV454,$thf((pf@((fr@SV36)@((ts@(den@SV453))@SV452)))@((fr@SV34)@((ts@(den@SV453))@SV452))))]])). 160.12/160.41 thf(845,plain,(![SV452:nat,SV453:frac,SV34:nat,SV35:nat,SV36:nat]: ((((eq@((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))@SV453)=$true) | ((((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)) = ((fr@((pl@SV36)@SV34))@SV35))=$false))),inference(extuni,[status(esa)],[822:[bind(SV454,$thf((pf@((fr@SV36)@SV35))@((fr@SV34)@SV35)))]])). 160.12/160.41 thf(846,plain,(![SV452:nat,SV79:frac,SV80:frac,SV78:frac]: ((((eq@SV78)@SV80)=$false) | (((eq@SV78)@SV79)=$true) | (((eq@SV80)@((fr@((ts@(num@SV79))@SV452))@((ts@(den@SV79))@SV452)))=$false))),inference(extuni,[status(esa)],[816:[bind(SV453,$thf(SV79)),bind(SV454,$thf(SV80))]])). 160.12/160.41 thf(847,plain,(![SV452:nat,SV453:frac,SV80:frac,SV78:frac]: ((((eq@SV78)@SV80)=$false) | (((eq@SV80)@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)))=$false) | (((eq@SV78)@SV453)=$true))),inference(extuni,[status(esa)],[815:[bind(SV79,$thf((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452))),bind(SV454,$thf(SV78))]])). 160.12/160.41 thf(848,plain,(![SV452:nat,SV80:frac,SV79:frac,SV78:frac]: ((((eq@SV78)@SV79)=$true) | (((eq@SV80)@SV79)=$false) | (((eq@SV78)@((fr@((ts@(num@SV80))@SV452))@((ts@(den@SV80))@SV452)))=$false))),inference(extuni,[status(esa)],[814:[bind(SV453,$thf(SV80)),bind(SV454,$thf(SV78))]])). 160.12/160.41 thf(849,plain,(![SV452:nat,SV83:frac,SV84:frac,SV81:frac,SV82:frac]: ((((eq@SV82)@SV81)=$false) | (((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true) | (((eq@SV84)@((fr@((ts@(num@SV83))@SV452))@((ts@(den@SV83))@SV452)))=$false))),inference(extuni,[status(esa)],[813:[bind(SV453,$thf(SV83)),bind(SV454,$thf(SV84))]])). 160.12/160.41 thf(850,plain,(![SV452:nat,SV453:frac,SV83:frac,SV84:frac,SV81:frac,SV82:frac]: ((((eq@SV82)@SV81)=$false) | (((eq@SV84)@SV83)=$false) | (((eq@((pf@SV82)@SV84))@SV453)=$true) | ((((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)) = ((pf@SV81)@SV83))=$false))),inference(extuni,[status(esa)],[812:[bind(SV454,$thf((pf@SV82)@SV84))]])). 160.12/160.41 thf(851,plain,(![SV452:nat,SV83:frac,SV81:frac,SV84:frac,SV82:frac]: ((((eq@((pf@SV82)@SV84))@((pf@SV81)@SV83))=$true) | (((eq@SV84)@SV83)=$false) | (((eq@SV82)@((fr@((ts@(num@SV81))@SV452))@((ts@(den@SV81))@SV452)))=$false))),inference(extuni,[status(esa)],[811:[bind(SV453,$thf(SV81)),bind(SV454,$thf(SV82))]])). 160.12/160.41 thf(852,plain,(![SV452:nat,SV445:frac]: ((((eq@SV445)@x)=$false) | (((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@((fr@((ts@(num@SV445))@SV452))@((ts@(den@SV445))@SV452)))=$false))),inference(extuni,[status(esa)],[792:[bind(SV453,$thf(SV445)),bind(SV454,$thf((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))]])). 160.12/160.41 thf(853,plain,(![SV452:nat,SV445:frac]: ((((eq@((pf@y)@((fr@(ind@(^[SX0:nat]: (((ts@(num@x))@(den@y)) = ((pl@((ts@(num@y))@(den@x)))@SX0)))))@((ts@(den@x))@(den@y)))))@SV445)=$false) | (((eq@SV445)@((fr@((ts@(num@x))@SV452))@((ts@(den@x))@SV452)))=$false))),inference(extuni,[status(esa)],[791:[bind(SV453,$thf(x)),bind(SV454,$thf(SV445))]])). 160.12/160.41 thf(854,plain,(![SV452:nat,SV446:nat,SV447:frac,SV448:frac]: ((((eq@SV448)@((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))=$true) | (((eq@SV448)@((fr@((ts@(num@SV447))@SV452))@((ts@(den@SV447))@SV452)))=$false))),inference(extuni,[status(esa)],[790:[bind(SV453,$thf(SV447)),bind(SV454,$thf(SV448))]])). 160.12/160.41 thf(857,plain,(![SV453:frac,SV447:frac,SV448:frac]: ((((eq@SV448)@SV447)=$false) | (((eq@SV448)@SV453)=$true) | (((den@SV453) = (den@SV447))=$false) | (((num@SV453) = (num@SV447))=$false))),inference(extuni,[status(esa)],[789:[bind(SV452,$thf(SV446)),bind(SV454,$thf(SV448))]])). 160.12/160.41 thf(858,plain,(![SV446:nat,SV453:frac,SV447:frac,SV448:frac]: ((((eq@SV448)@SV447)=$false) | (((eq@SV448)@SV453)=$true) | ((((ts@(den@SV453))@SV446) = ((ts@(den@SV447))@SV446))=$false) | (((num@SV453) = (num@SV447))=$false))),inference(extuni,[status(esa)],[789:[bind(SV452,$thf(SV446)),bind(SV454,$thf(SV448))]])). 160.12/160.41 thf(860,plain,(![SV446:nat,SV453:frac,SV447:frac,SV448:frac]: ((((eq@SV448)@SV447)=$false) | (((eq@SV448)@SV453)=$true) | (((den@SV453) = (den@SV447))=$false) | ((((ts@(num@SV453))@SV446) = ((ts@(num@SV447))@SV446))=$false))),inference(extuni,[status(esa)],[789:[bind(SV452,$thf(SV446)),bind(SV454,$thf(SV448))]])). 160.12/160.41 thf(861,plain,(![SV446:nat,SV452:nat,SV453:frac,SV447:frac,SV448:frac]: ((((eq@SV448)@SV447)=$false) | (((eq@SV448)@SV453)=$true) | ((((ts@(den@SV453))@SV452) = ((ts@(den@SV447))@SV446))=$false) | ((((ts@(num@SV453))@SV452) = ((ts@(num@SV447))@SV446))=$false))),inference(extuni,[status(esa)],[789:[bind(SV454,$thf(SV448))]])). 160.12/160.41 thf(862,plain,(![SV446:nat,SV452:nat,SV453:frac,SV447:frac,SV448:frac]: ((((eq@SV448)@SV447)=$false) | (((eq@SV448)@SV453)=$true) | ((((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)) = ((fr@((ts@(num@SV447))@SV446))@((ts@(den@SV447))@SV446)))=$false))),inference(extuni,[status(esa)],[789:[bind(SV454,$thf(SV448))]])). 160.12/160.41 thf(863,plain,(![SV452:nat,SV453:frac,SV449:nat,SV451:frac]: ((((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452)))=$false) | (((eq@SV451)@SV453)=$true))),inference(extuni,[status(esa)],[788:[bind(SV450,$thf((fr@((ts@(num@SV453))@SV452))@((ts@(den@SV453))@SV452))),bind(SV454,$thf(SV451))]])). 160.12/160.41 thf(864,plain,(![SV452:nat,SV449:nat,SV450:frac,SV451:frac]: ((((eq@SV451)@SV450)=$true) | (((eq@((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))@((fr@((ts@(num@SV450))@SV452))@((ts@(den@SV450))@SV452)))=$false))),inference(extuni,[status(esa)],[787:[bind(SV453,$thf(SV450)),bind(SV454,$thf((fr@((ts@(num@SV451))@SV449))@((ts@(den@SV451))@SV449)))]])). 160.12/160.41 thf(865,plain,(![SV30:nat,SV31:frac]: ((((eq@SV31)@SV31)=$true))),inference(sim,[status(thm)],[839])). 160.12/160.41 thf(866,plain,(![SV31:frac]: ((((eq@SV31)@SV31)=$true))),inference(sim,[status(thm)],[836])). 160.12/160.41 thf(867,plain,((($false)=$true)),inference(fo_atp_e,[status(thm)],[21,866,865,864,863,862,861,860,858,857,854,853,852,851,850,849,848,847,846,845,844,843,842,841,840,838,837,835,834,833,784,783,782,781,780,779,778,777,776,775,774,773,772,771,770,769,768,766,765,763,762,761,760,713,712,711,710,709,708,707,706,705,704,703,702,701,700,655,654,653,652,651,650,649,648,647,646,645,644,643,642,641,640,639,609,608,607,606,605,604,603,602,601,600,599,594,592,591,590,589,588,587,586,585,584,583,582,581,580,579,578,577,576,575,574,572,569,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,547,464,462,461,460,459,422,421,420,419,418,382,381,380,379,378,377,355,324,302,291,280,269,268,242,241,240,239,238,237,236,226,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,152,147,146,145,115,111,85,80,77,74,72,70,69,66,65,37])). 160.12/160.41 thf(868,plain,($false),inference(solved_all_splits,[solved_all_splits(join,[])],[867])). 160.12/160.41 % SZS output end CNFRefutation 160.12/160.41 160.12/160.41 %**** End of derivation protocol **** 160.12/160.41 %**** no. of clauses in derivation: 390 **** 160.12/160.41 %**** clause counter: 867 **** 160.12/160.41 160.12/160.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:867,loop_count:30,foatp_calls:5,translation:fof_full) 160.12/160.42 EOF