%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n032.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 04:11:55 EDT 2023 % Result : Theorem 45.89s 6.79s % Output : Proof 117.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.32 % Computer : n032.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Sun Aug 27 14:35:44 EDT 2023 % 0.12/0.32 % CPUTime : % 0.17/0.53 ________ _____ % 0.17/0.53 ___ __ \_________(_)________________________________ % 0.17/0.53 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.53 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.53 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.53 % 0.17/0.53 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.53 (2023-06-19) % 0.17/0.53 % 0.17/0.53 (c) Philipp Rümmer, 2009-2023 % 0.17/0.53 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.53 Amanda Stjerna. % 0.17/0.53 Free software under BSD-3-Clause. % 0.17/0.53 % 0.17/0.53 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.53 % 0.17/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.17/0.54 Running up to 7 provers in parallel. % 0.17/0.56 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.56 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.79/0.93 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.79/0.93 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 1.79/0.93 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 1.79/0.93 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.79/0.93 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 2.31/0.94 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 2.31/0.95 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 15.38/2.73 Prover 1: Preprocessing ... % 15.38/2.73 Prover 6: Preprocessing ... % 15.38/2.73 Prover 2: Preprocessing ... % 15.38/2.73 Prover 4: Preprocessing ... % 15.38/2.78 Prover 0: Preprocessing ... % 16.03/2.80 Prover 5: Preprocessing ... % 16.03/2.81 Prover 3: Preprocessing ... % 36.80/5.55 Prover 1: Warning: ignoring some quantifiers % 37.58/5.76 Prover 1: Constructing countermodel ... % 37.58/5.80 Prover 3: Warning: ignoring some quantifiers % 38.52/5.85 Prover 3: Constructing countermodel ... % 39.74/5.92 Prover 6: Proving ... % 43.28/6.53 Prover 4: Warning: ignoring some quantifiers % 45.89/6.79 Prover 3: proved (6233ms) % 45.89/6.79 % 45.89/6.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 45.89/6.79 % 46.46/6.80 Prover 4: Constructing countermodel ... % 46.46/6.80 Prover 6: stopped % 46.46/6.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 46.46/6.80 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 46.46/6.82 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 46.46/6.82 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 48.18/7.14 Prover 0: Proving ... % 48.18/7.14 Prover 0: stopped % 48.18/7.15 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 48.18/7.16 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 53.27/7.77 Prover 7: Preprocessing ... % 54.18/7.82 Prover 8: Preprocessing ... % 54.18/7.88 Prover 5: Proving ... % 54.18/7.88 Prover 5: stopped % 54.18/7.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 54.18/7.90 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 54.46/8.03 Prover 10: Preprocessing ... % 56.04/8.06 Prover 2: Proving ... % 56.04/8.06 Prover 2: stopped % 56.04/8.06 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 56.04/8.08 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 63.24/9.03 Prover 11: Preprocessing ... % 64.13/9.14 Prover 13: Preprocessing ... % 64.51/9.21 Prover 8: Warning: ignoring some quantifiers % 65.61/9.34 Prover 8: Constructing countermodel ... % 65.61/9.49 Prover 10: Warning: ignoring some quantifiers % 67.81/9.63 Prover 10: Constructing countermodel ... % 69.10/9.82 Prover 7: Warning: ignoring some quantifiers % 70.87/10.06 Prover 7: Constructing countermodel ... % 79.62/11.19 Prover 13: Warning: ignoring some quantifiers % 81.23/11.32 Prover 11: Warning: ignoring some quantifiers % 81.23/11.38 Prover 13: Constructing countermodel ... % 81.23/11.54 Prover 11: Constructing countermodel ... % 90.86/12.61 Prover 13: stopped % 90.86/12.63 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 90.86/12.65 Prover 16: Warning: Problem contains reals, using incomplete axiomatisation % 96.42/13.36 Prover 16: Preprocessing ... % 104.54/14.41 Prover 16: Warning: ignoring some quantifiers % 104.86/14.52 Prover 16: Constructing countermodel ... % 114.55/15.69 Prover 1: Found proof (size 685) % 114.55/15.69 Prover 1: proved (15132ms) % 114.55/15.69 Prover 7: stopped % 114.55/15.69 Prover 11: stopped % 114.55/15.69 Prover 8: stopped % 114.55/15.70 Prover 4: stopped % 114.55/15.70 Prover 16: stopped % 114.55/15.70 Prover 10: stopped % 114.55/15.70 % 114.55/15.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 114.55/15.70 % 115.81/15.97 % SZS output start Proof for theBenchmark % 116.13/15.99 Assumptions after simplification: % 116.13/15.99 --------------------------------- % 116.13/15.99 % 116.13/15.99 (axiom101) % 116.26/16.01 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.26/16.01 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.26/16.01 % 116.26/16.01 (axiom127) % 116.26/16.01 Nat$(zero$) & ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: Nat$] : ! % 116.26/16.01 [v2: Nat_nat_fun$] : (v1 = zero$ | ~ (power$(v1) = v2) | ~ Nat$(v1) | ? % 116.26/16.01 [v3: Nat$] : ( ~ (v3 = zero$) & fun_app$b(v2, v0) = v3 & Nat$(v3))) & ! % 116.26/16.01 [v1: Nat_nat_fun$] : ( ~ (power$(zero$) = v1) | fun_app$b(v1, v0) = zero$)) % 116.26/16.01 % 116.26/16.01 (axiom128) % 116.26/16.01 ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: int] : ! [v2: % 116.26/16.01 Nat_int_fun$] : (v1 = 0 | ~ (power$a(v1) = v2) | ? [v3: int] : ( ~ (v3 = % 116.26/16.01 0) & fun_app$a(v2, v0) = v3)) & ! [v1: Nat_int_fun$] : ( ~ % 116.26/16.01 (power$a(0) = v1) | fun_app$a(v1, v0) = 0)) % 116.26/16.01 % 116.26/16.01 (axiom129) % 116.26/16.01 ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: $real] : ! [v2: % 116.26/16.01 Nat_real_fun$] : (v1 = real_0 | ~ (power$c(v1) = v2) | ? [v3: $real] : ( % 116.26/16.01 ~ (v3 = real_0) & fun_app$m(v2, v0) = v3)) & ! [v1: Nat_real_fun$] : ( % 116.26/16.01 ~ (power$c(real_0) = v1) | fun_app$m(v1, v0) = real_0)) % 116.26/16.01 % 116.26/16.01 (axiom146) % 116.26/16.01 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.26/16.01 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.26/16.01 % 116.26/16.01 (axiom176) % 116.26/16.02 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.26/16.02 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.26/16.02 % 116.26/16.02 (axiom177) % 116.26/16.02 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.26/16.02 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.26/16.02 % 116.26/16.02 (axiom178) % 116.26/16.02 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.26/16.02 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.26/16.02 % 116.26/16.02 (axiom179) % 116.26/16.02 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.26/16.02 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.26/16.02 % 116.26/16.02 (axiom2) % 116.26/16.02 Nat_int_fun$(of_nat$) & Nat$(n$) & A_ltln_list$(ys$) & ? [v0: int] : ? [v1: % 116.26/16.02 Nat$] : ? [v2: int] : ($lesseq(v2, v0) & size$(ys$) = v1 & % 116.26/16.02 fun_app$a(of_nat$, v1) = v2 & fun_app$a(of_nat$, n$) = v0 & Nat$(v1)) % 116.26/16.02 % 116.26/16.02 (axiom3) % 116.26/16.02 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_nat_fun$] % 116.26/16.02 : ! [v3: Nat$] : ( ~ (power$(v0) = v2) | ~ (fun_app$b(v2, v1) = v3) | ~ % 116.26/16.02 Nat$(v1) | ~ Nat$(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : % 116.26/16.02 (fun_app$a(of_nat$, v3) = v5 & fun_app$a(of_nat$, v1) = v6 & % 116.26/16.02 fun_app$a(of_nat$, v0) = v4 & ( ~ ($lesseq(1, $difference(v6, v5))) | ~ % 116.26/16.02 ($lesseq(2, v4))))) % 116.26/16.02 % 116.26/16.02 (axiom323) % 116.26/16.02 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_nat_fun$] % 116.26/16.02 : ! [v3: Nat$] : ( ~ (power$(v0) = v2) | ~ (fun_app$b(v2, v1) = v3) | ~ % 116.26/16.02 Nat$(v1) | ~ Nat$(v0) | ? [v4: int] : ? [v5: int] : (fun_app$a(of_nat$, % 116.26/16.02 v3) = v5 & fun_app$a(of_nat$, v0) = v4 & ( ~ ($lesseq(v5, 0) | ~ % 116.26/16.02 ($lesseq(1, v4))))) % 116.26/16.02 % 116.26/16.02 (axiom324) % 116.26/16.02 Enat$(zero$a) & ? [v0: Nat_enat_fun$] : ? [v1: Nat$] : (power$b(zero$a) = v0 % 116.26/16.02 & fun_app$l(v0, v1) = zero$a & nat$(2) = v1 & Nat$(v1) & Nat_enat_fun$(v0)) % 116.26/16.02 % 116.26/16.02 (axiom325) % 116.26/16.02 Nat$(zero$) & ? [v0: Nat_nat_fun$] : ? [v1: Nat$] : (nat$(2) = v1 & % 116.26/16.02 power$(zero$) = v0 & fun_app$b(v0, v1) = zero$ & Nat$(v1) & % 116.26/16.02 Nat_nat_fun$(v0)) % 116.26/16.02 % 116.26/16.02 (axiom326) % 116.26/16.03 ? [v0: Nat_int_fun$] : ? [v1: Nat$] : (power$a(0) = v0 & nat$(2) = v1 & % 116.26/16.03 fun_app$a(v0, v1) = 0 & Nat_int_fun$(v0) & Nat$(v1)) % 116.26/16.03 % 116.26/16.03 (axiom327) % 116.35/16.03 ? [v0: Nat_real_fun$] : ? [v1: Nat$] : (power$c(real_0) = v0 & fun_app$m(v0, % 116.35/16.03 v1) = real_0 & nat$(2) = v1 & Nat_real_fun$(v0) & Nat$(v1)) % 116.35/16.03 % 116.35/16.03 (axiom329) % 116.35/16.03 ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: int] : ! [v2: % 116.35/16.03 Nat_int_fun$] : ( ~ (power$a(v1) = v2) | ? [v3: int] : ($lesseq(0, v3) & % 116.35/16.03 fun_app$a(v2, v0) = v3))) % 116.35/16.03 % 116.35/16.03 (axiom330) % 116.35/16.03 ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: $real] : ! [v2: % 116.35/16.03 Nat_real_fun$] : ( ~ (power$c(v1) = v2) | ? [v3: $real] : (fun_app$m(v2, % 116.35/16.03 v0) = v3 & real_$lesseq(real_0, v3) = 0))) % 116.35/16.03 % 116.35/16.03 (axiom331) % 116.35/16.03 Nat$(zero$) & Nat_nat_bool_fun_fun$(less_eq$b) & ? [v0: Nat$] : ? [v1: % 116.35/16.03 Nat_bool_fun$] : (fun_app$o(less_eq$b, zero$) = v1 & nat$(2) = v0 & % 116.35/16.03 Nat_bool_fun$(v1) & Nat$(v0) & ! [v2: Nat$] : ! [v3: Nat$] : (v3 = v2 | ~ % 116.35/16.03 (fun_app$n(v1, v3) = 0) | ~ (fun_app$n(v1, v2) = 0) | ~ Nat$(v3) | ~ % 116.35/16.03 Nat$(v2) | ? [v4: Nat_nat_fun$] : ? [v5: Nat$] : ? [v6: Nat_nat_fun$] : % 116.35/16.03 ? [v7: Nat$] : ( ~ (v7 = v5) & power$(v3) = v6 & power$(v2) = v4 & % 116.35/16.03 fun_app$b(v6, v0) = v7 & fun_app$b(v4, v0) = v5 & Nat$(v7) & Nat$(v5) & % 116.35/16.03 Nat_nat_fun$(v6) & Nat_nat_fun$(v4)))) % 116.35/16.03 % 116.35/16.03 (axiom332) % 116.35/16.03 ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: int] : ! [v2: int] : ! % 116.35/16.03 [v3: Nat_int_fun$] : ! [v4: Nat_int_fun$] : (v2 = v1 | ~ ($lesseq(0, v2)) % 116.35/16.03 | ~ ($lesseq(0, v1)) | ~ (power$a(v2) = v4) | ~ (power$a(v1) = v3) | ? % 116.35/16.03 [v5: int] : ? [v6: int] : ( ~ (v6 = v5) & fun_app$a(v4, v0) = v6 & % 116.35/16.03 fun_app$a(v3, v0) = v5))) % 116.35/16.03 % 116.35/16.03 (axiom333) % 116.35/16.03 ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: $real] : ! [v2: $real] : % 116.35/16.03 (v2 = v1 | ~ (real_$lesseq(real_0, v2) = 0) | ~ (real_$lesseq(real_0, v1) % 116.35/16.03 = 0) | ? [v3: Nat_real_fun$] : ? [v4: $real] : ? [v5: Nat_real_fun$] % 116.35/16.03 : ? [v6: $real] : ( ~ (v6 = v4) & power$c(v2) = v5 & power$c(v1) = v3 & % 116.35/16.03 fun_app$m(v5, v0) = v6 & fun_app$m(v3, v0) = v4 & Nat_real_fun$(v5) & % 116.35/16.03 Nat_real_fun$(v3)))) % 116.35/16.03 % 116.35/16.03 (axiom334) % 116.35/16.04 Nat$(zero$) & Nat_nat_bool_fun_fun$(less_eq$b) & ? [v0: Nat$] : ? [v1: % 116.35/16.04 Nat_bool_fun$] : (fun_app$o(less_eq$b, zero$) = v1 & nat$(2) = v0 & % 116.35/16.04 Nat_bool_fun$(v1) & Nat$(v0) & ! [v2: Nat$] : ! [v3: Nat$] : ! [v4: % 116.35/16.04 Nat_nat_fun$] : ! [v5: Nat$] : ! [v6: Nat_bool_fun$] : ! [v7: % 116.35/16.04 Nat_nat_fun$] : ! [v8: Nat$] : ( ~ (fun_app$o(less_eq$b, v5) = v6) | ~ % 116.35/16.04 (fun_app$n(v6, v8) = 0) | ~ (power$(v3) = v7) | ~ (power$(v2) = v4) | ~ % 116.35/16.04 (fun_app$b(v7, v0) = v8) | ~ (fun_app$b(v4, v0) = v5) | ~ Nat$(v3) | ~ % 116.35/16.04 Nat$(v2) | ? [v9: any] : ? [v10: Nat_bool_fun$] : ? [v11: any] : % 116.35/16.04 (fun_app$o(less_eq$b, v2) = v10 & fun_app$n(v10, v3) = v11 & fun_app$n(v1, % 116.35/16.04 v3) = v9 & Nat_bool_fun$(v10) & ( ~ (v9 = 0) | v11 = 0)))) % 116.35/16.04 % 116.35/16.04 (axiom335) % 116.35/16.04 ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: int] : ! [v2: int] : ! % 116.35/16.04 [v3: Nat_int_fun$] : ! [v4: Nat_int_fun$] : ( ~ ($lesseq(1, $difference(v1, % 116.35/16.04 v2))) | ~ ($lesseq(0, v2)) | ~ (power$a(v2) = v3) | ~ % 116.35/16.04 (power$a(v1) = v4) | ? [v5: int] : ? [v6: int] : ($lesseq(1, % 116.35/16.04 $difference(v6, v5)) & fun_app$a(v4, v0) = v6 & fun_app$a(v3, v0) = % 116.35/16.04 v5))) % 116.35/16.04 % 116.35/16.04 (axiom336) % 116.35/16.04 ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: $real] : ! [v2: $real] : % 116.35/16.04 ! [v3: Nat_real_fun$] : ! [v4: $real] : ! [v5: Nat_real_fun$] : ! [v6: % 116.35/16.04 $real] : ( ~ (power$c(v2) = v5) | ~ (power$c(v1) = v3) | ~ % 116.35/16.04 (fun_app$m(v5, v0) = v6) | ~ (fun_app$m(v3, v0) = v4) | ~ % 116.35/16.04 (real_$lesseq(v4, v6) = 0) | ? [v7: any] : ? [v8: any] : % 116.35/16.04 (real_$lesseq(v1, v2) = v8 & real_$lesseq(real_0, v2) = v7 & ( ~ (v7 = 0) % 116.35/16.04 | v8 = 0)))) % 116.35/16.04 % 116.35/16.04 (axiom345) % 116.35/16.04 ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: int] : ! [v2: % 116.35/16.04 Nat_int_fun$] : (v1 = 0 | ~ (power$a(v1) = v2) | ? [v3: int] : % 116.35/16.04 ($lesseq(1, v3) & fun_app$a(v2, v0) = v3)) & ! [v1: Nat_int_fun$] : ( ~ % 116.35/16.04 (power$a(0) = v1) | ? [v2: int] : ($lesseq(v2, 0)fun_app$a(v1, v0) = % 116.35/16.04 v2))) % 116.35/16.04 % 116.35/16.04 (axiom346) % 116.35/16.04 ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: $real] : ! [v2: % 116.35/16.04 Nat_real_fun$] : (v1 = real_0 | ~ (power$c(v1) = v2) | ? [v3: $real] : % 116.35/16.04 (real_$less(real_0, v3) = 0 & fun_app$m(v2, v0) = v3)) & ! [v1: % 116.35/16.04 Nat_real_fun$] : ( ~ (power$c(real_0) = v1) | ? [v2: $real] : ? [v3: % 116.35/16.04 int] : ( ~ (v3 = 0) & real_$less(real_0, v2) = v3 & fun_app$m(v1, v0) = % 116.35/16.04 v2))) % 116.35/16.04 % 116.35/16.04 (axiom351) % 116.35/16.04 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.35/16.04 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.35/16.04 % 116.35/16.04 (axiom352) % 116.35/16.04 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.35/16.04 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.35/16.04 % 116.35/16.04 (axiom353) % 116.35/16.04 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.35/16.04 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.35/16.04 % 116.35/16.04 (axiom374) % 116.35/16.04 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.35/16.04 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.35/16.04 % 116.35/16.04 (axiom375) % 116.35/16.04 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.35/16.04 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.35/16.04 % 116.35/16.04 (axiom383) % 116.35/16.05 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_nat_fun$] % 116.35/16.05 : ! [v3: Nat$] : ( ~ (power$(v0) = v2) | ~ (fun_app$b(v2, v1) = v3) | ~ % 116.35/16.05 Nat$(v1) | ~ Nat$(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : % 116.35/16.05 (fun_app$a(of_nat$, v3) = v6 & fun_app$a(of_nat$, v1) = v5 & % 116.35/16.05 fun_app$a(of_nat$, v0) = v4 & ( ~ ($lesseq(v6, 0) | ( ~ (v5 = 0) & % 116.35/16.05 $lesseq(v4, 0))))) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: % 116.35/16.05 Nat_nat_fun$] : ! [v3: Nat$] : ( ~ (power$(v0) = v2) | ~ (fun_app$b(v2, % 116.35/16.05 v1) = v3) | ~ Nat$(v1) | ~ Nat$(v0) | ? [v4: int] : ? [v5: int] : % 116.35/16.05 ? [v6: int] : (fun_app$a(of_nat$, v3) = v4 & fun_app$a(of_nat$, v1) = v6 & % 116.35/16.05 fun_app$a(of_nat$, v0) = v5 & (v6 = 0 | ~ ($lesseq(v5, 0) | ~ % 116.35/16.05 ($lesseq(1, v4))))) % 116.35/16.05 % 116.35/16.05 (axiom4) % 116.35/16.05 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: % 116.35/16.05 Nat$] : ! [v2: Nat$] : ! [v3: int] : ! [v4: int] : ( ~ ($lesseq(v4, % 116.35/16.05 v3)) | ~ (fun_app$a(of_nat$, v2) = v3) | ~ (fun_app$a(of_nat$, v1) = % 116.35/16.05 v4) | ~ Nat$(v2) | ~ Nat$(v1) | ? [v5: Nat_nat_fun$] : ? [v6: Nat$] % 116.35/16.05 : ? [v7: int] : ? [v8: Nat_nat_fun$] : ? [v9: Nat$] : ? [v10: int] : % 116.35/16.05 ($lesseq(v10, v7) & power$(v2) = v5 & power$(v1) = v8 & fun_app$b(v8, v0) % 116.35/16.05 = v9 & fun_app$b(v5, v0) = v6 & fun_app$a(of_nat$, v9) = v10 & % 116.35/16.05 fun_app$a(of_nat$, v6) = v7 & Nat$(v9) & Nat$(v6) & Nat_nat_fun$(v8) & % 116.35/16.05 Nat_nat_fun$(v5))) & ! [v1: Nat$] : ! [v2: Nat$] : ! [v3: int] : ! % 116.35/16.05 [v4: int] : ( ~ ($lesseq(1, $difference(v4, v3))) | ~ (fun_app$a(of_nat$, % 116.35/16.05 v2) = v3) | ~ (fun_app$a(of_nat$, v1) = v4) | ~ Nat$(v2) | ~ % 116.35/16.05 Nat$(v1) | ? [v5: Nat_nat_fun$] : ? [v6: Nat$] : ? [v7: int] : ? [v8: % 116.35/16.05 Nat_nat_fun$] : ? [v9: Nat$] : ? [v10: int] : ($lesseq(1, % 116.35/16.05 $difference(v10, v7)) & power$(v2) = v5 & power$(v1) = v8 & % 116.35/16.05 fun_app$b(v8, v0) = v9 & fun_app$b(v5, v0) = v6 & fun_app$a(of_nat$, v9) % 116.35/16.05 = v10 & fun_app$a(of_nat$, v6) = v7 & Nat$(v9) & Nat$(v6) & % 116.35/16.05 Nat_nat_fun$(v8) & Nat_nat_fun$(v5)))) % 116.35/16.05 % 116.35/16.05 (axiom423) % 116.35/16.05 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.35/16.05 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.35/16.05 % 116.35/16.05 (axiom430) % 116.35/16.05 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.35/16.05 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.35/16.05 % 116.35/16.05 (axiom431) % 116.35/16.05 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.35/16.05 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.35/16.05 % 116.35/16.05 (axiom432) % 116.35/16.05 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.35/16.05 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.35/16.05 % 116.35/16.05 (axiom433) % 116.35/16.05 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.35/16.05 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.35/16.05 % 116.35/16.05 (axiom5) % 116.35/16.05 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: % 116.35/16.05 Nat$] : ! [v2: Nat$] : ! [v3: int] : ! [v4: int] : ( ~ ($lesseq(1, % 116.35/16.05 $difference(v4, v3))) | ~ (fun_app$a(of_nat$, v2) = v3) | ~ % 116.35/16.05 (fun_app$a(of_nat$, v1) = v4) | ~ Nat$(v2) | ~ Nat$(v1) | ? [v5: % 116.35/16.05 Nat_nat_fun$] : ? [v6: Nat$] : ? [v7: int] : ($lesseq(1, % 116.35/16.05 $difference(v7, v3)) & power$(v1) = v5 & fun_app$b(v5, v0) = v6 & % 116.35/16.05 fun_app$a(of_nat$, v6) = v7 & Nat$(v6) & Nat_nat_fun$(v5)))) % 116.35/16.05 % 116.35/16.05 (axiom585) % 116.35/16.06 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat$] : ! % 116.35/16.06 [v3: Nat_nat_fun$] : ! [v4: Nat$] : ! [v5: Nat$] : ( ~ (power$(v0) = v3) | % 116.35/16.06 ~ (fun_app$b(v3, v2) = v4) | ~ (fun_app$b(v3, v1) = v5) | ~ Nat$(v2) | ~ % 116.35/16.06 Nat$(v1) | ~ Nat$(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 116.35/16.06 [v9: int] : ? [v10: int] : (fun_app$a(of_nat$, v5) = v8 & % 116.35/16.06 fun_app$a(of_nat$, v4) = v7 & fun_app$a(of_nat$, v2) = v9 & % 116.35/16.06 fun_app$a(of_nat$, v1) = v10 & fun_app$a(of_nat$, v0) = v6 & ( ~ % 116.35/16.06 ($lesseq(v9, v10)) | ~ ($lesseq(1, $difference(v7, v8))) | ~ % 116.35/16.06 ($lesseq(1, v6))))) % 116.35/16.06 % 116.35/16.06 (axiom598) % 116.35/16.06 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_nat_fun$] % 116.35/16.06 : ! [v3: Nat$] : ( ~ (power$(v0) = v2) | ~ (fun_app$b(v2, v1) = v3) | ~ % 116.35/16.06 Nat$(v1) | ~ Nat$(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : % 116.35/16.06 (fun_app$a(of_nat$, v3) = v5 & fun_app$a(of_nat$, v1) = v6 & % 116.35/16.06 fun_app$a(of_nat$, v0) = v4 & ( ~ ($lesseq(v5, v6)) | ~ ($lesseq(2, % 116.35/16.06 v4))))) % 116.35/16.06 % 116.35/16.06 (axiom599) % 116.35/16.06 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat$] : ! % 116.35/16.06 [v3: Nat_nat_fun$] : ! [v4: Nat$] : ! [v5: Nat$] : ( ~ (power$(v2) = v3) | % 116.35/16.06 ~ (fun_app$b(v3, v1) = v4) | ~ (fun_app$b(v3, v0) = v5) | ~ Nat$(v2) | ~ % 116.35/16.06 Nat$(v1) | ~ Nat$(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 116.35/16.06 [v9: int] : (fun_app$a(of_nat$, v5) = v9 & fun_app$a(of_nat$, v4) = v8 & % 116.35/16.06 fun_app$a(of_nat$, v1) = v7 & fun_app$a(of_nat$, v0) = v6 & ( ~ % 116.35/16.06 ($lesseq(1, $difference(v9, v8))) | ~ ($lesseq(v6, v7)) | ~ % 116.35/16.06 ($lesseq(1, v6))))) % 116.35/16.06 % 116.35/16.06 (axiom602) % 116.35/16.06 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.35/16.06 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.35/16.06 % 116.35/16.06 (axiom603) % 116.35/16.06 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.35/16.06 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.35/16.06 % 116.35/16.06 (axiom604) % 116.35/16.06 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : ? [v1: Nat_nat_fun$] : (nat$(2) = v0 % 116.35/16.06 & power$(v0) = v1 & Nat$(v0) & Nat_nat_fun$(v1) & ! [v2: Nat$] : ! [v3: % 116.35/16.06 Nat$] : ( ~ (fun_app$b(v1, v2) = v3) | ~ Nat$(v2) | ? [v4: int] : ? % 116.35/16.06 [v5: int] : ($lesseq(1, $difference(v4, v5)) & fun_app$a(of_nat$, v3) = v4 % 116.35/16.06 & fun_app$a(of_nat$, v2) = v5))) % 116.35/16.06 % 116.35/16.06 (axiom630) % 116.35/16.06 ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: $real] : ! [v2: $real] : ( % 116.35/16.06 ~ (real_$product(real_2, v1) = v2) | ? [v3: Nat_real_fun$] : ? [v4: % 116.35/16.06 $real] : ? [v5: $real] : ? [v6: Nat_real_fun$] : % 116.35/16.06 (real_$product(real_4, v4) = v5 & power$c(v2) = v6 & power$c(v1) = v3 & % 116.35/16.06 fun_app$m(v6, v0) = v5 & fun_app$m(v3, v0) = v4 & Nat_real_fun$(v6) & % 116.35/16.06 Nat_real_fun$(v3)))) % 116.35/16.06 % 116.35/16.06 (axiom635) % 116.35/16.06 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.35/16.06 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.35/16.06 % 116.35/16.06 (axiom637) % 116.35/16.06 Nat_int_fun$(of_nat$) & ! [v0: int] : ! [v1: Nat$] : ( ~ ($lesseq(v0, -1)) | % 116.35/16.06 ~ (nat$(v0) = v1) | fun_app$a(of_nat$, v1) = 0) & ! [v0: int] : ! [v1: % 116.35/16.06 Nat$] : ( ~ ($lesseq(0, v0)) | ~ (nat$(v0) = v1) | fun_app$a(of_nat$, v1) = % 116.35/16.06 v0) % 116.35/16.06 % 116.35/16.06 (axiom74) % 116.35/16.07 Nat$(zero$) & Nat_nat_bool_fun_fun$(less_eq$b) & ? [v0: Nat_bool_fun$] : ? % 116.35/16.07 [v1: Nat$] : (fun_app$o(less_eq$b, zero$) = v0 & nat$(2) = v1 & % 116.35/16.07 Nat_bool_fun$(v0) & Nat$(v1) & ! [v2: Nat$] : ! [v3: Nat$] : ( ~ % 116.35/16.07 (fun_app$n(v0, v3) = 0) | ~ (fun_app$n(v0, v2) = 0) | ~ Nat$(v3) | ~ % 116.35/16.07 Nat$(v2) | ? [v4: Nat_nat_fun$] : ? [v5: Nat$] : ? [v6: Nat_nat_fun$] : % 116.35/16.07 ? [v7: Nat$] : (power$(v3) = v6 & power$(v2) = v4 & fun_app$b(v6, v1) = % 116.35/16.07 v7 & fun_app$b(v4, v1) = v5 & Nat$(v7) & Nat$(v5) & Nat_nat_fun$(v6) & % 116.35/16.07 Nat_nat_fun$(v4) & ( ~ (v7 = v5) | v3 = v2) & ( ~ (v3 = v2) | v7 = % 116.35/16.07 v5)))) % 116.35/16.07 % 116.35/16.07 (axiom75) % 116.35/16.07 ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: int] : ! [v2: int] : ! % 116.35/16.07 [v3: Nat_int_fun$] : ! [v4: Nat_int_fun$] : ( ~ ($lesseq(0, v2)) | ~ % 116.35/16.07 ($lesseq(0, v1)) | ~ (power$a(v2) = v4) | ~ (power$a(v1) = v3) | ? [v5: % 116.35/16.07 int] : ? [v6: int] : (fun_app$a(v4, v0) = v6 & fun_app$a(v3, v0) = v5 & % 116.35/16.07 ( ~ (v6 = v5) | v2 = v1) & ( ~ (v2 = v1) | v6 = v5)))) % 116.35/16.07 % 116.35/16.07 (axiom76) % 116.35/16.07 ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: $real] : ! [v2: $real] : ( % 116.35/16.07 ~ (real_$lesseq(real_0, v2) = 0) | ~ (real_$lesseq(real_0, v1) = 0) | ? % 116.35/16.07 [v3: Nat_real_fun$] : ? [v4: $real] : ? [v5: Nat_real_fun$] : ? [v6: % 116.35/16.07 $real] : (power$c(v2) = v5 & power$c(v1) = v3 & fun_app$m(v5, v0) = v6 & % 116.35/16.07 fun_app$m(v3, v0) = v4 & Nat_real_fun$(v5) & Nat_real_fun$(v3) & ( ~ (v6 % 116.35/16.07 = v4) | v2 = v1) & ( ~ (v2 = v1) | v6 = v4)))) % 116.35/16.07 % 116.35/16.07 (axiom77) % 116.35/16.07 ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: int] : ! [v2: % 116.35/16.07 Nat_int_fun$] : (v1 = 0 | ~ (power$a(v1) = v2) | ? [v3: int] : % 116.35/16.07 ($lesseq(1, v3) & fun_app$a(v2, v0) = v3)) & ! [v1: Nat_int_fun$] : ( ~ % 116.35/16.07 (power$a(0) = v1) | ? [v2: int] : ($lesseq(v2, 0)fun_app$a(v1, v0) = % 116.35/16.07 v2))) % 116.35/16.07 % 116.35/16.07 (axiom78) % 116.35/16.07 ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: $real] : ! [v2: % 116.35/16.07 Nat_real_fun$] : (v1 = real_0 | ~ (power$c(v1) = v2) | ? [v3: $real] : % 116.35/16.07 ? [v4: int] : ( ~ (v4 = 0) & fun_app$m(v2, v0) = v3 & real_$lesseq(v3, % 116.35/16.07 real_0) = v4)) & ! [v1: Nat_real_fun$] : ( ~ (power$c(real_0) = v1) | % 116.35/16.07 ? [v2: $real] : (fun_app$m(v1, v0) = v2 & real_$lesseq(v2, real_0) = 0))) % 116.35/16.07 % 116.35/16.07 (axiom81) % 116.35/16.07 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.35/16.07 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.35/16.07 % 116.35/16.07 (axiom82) % 116.35/16.07 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 116.35/16.07 ~ (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.35/16.07 % 116.35/16.07 (axiom98) % 116.35/16.08 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_nat_fun$] % 116.35/16.08 : ! [v3: Nat$] : ( ~ (power$(v0) = v2) | ~ (fun_app$b(v2, v1) = v3) | ~ % 116.35/16.08 Nat$(v1) | ~ Nat$(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : % 116.35/16.08 (fun_app$a(of_nat$, v3) = v6 & fun_app$a(of_nat$, v1) = v4 & % 116.35/16.08 fun_app$a(of_nat$, v0) = v5 & (v6 = 1 | ( ~ (v5 = 1) & ~ (v4 = 0))))) & % 116.35/16.08 ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_nat_fun$] : ! [v3: Nat$] : ( ~ % 116.35/16.08 (power$(v0) = v2) | ~ (fun_app$b(v2, v1) = v3) | ~ Nat$(v1) | ~ Nat$(v0) % 116.35/16.08 | ? [v4: int] : ? [v5: int] : ? [v6: int] : (fun_app$a(of_nat$, v3) = v4 % 116.35/16.08 & fun_app$a(of_nat$, v1) = v5 & fun_app$a(of_nat$, v0) = v6 & ( ~ (v4 = 1) % 116.35/16.08 | v6 = 1 | v5 = 0))) % 116.35/16.08 % 116.35/16.08 (conjecture1) % 116.35/16.08 Nat_int_fun$(of_nat$) & Nat$(n$) & A_ltln_list$(ys$) & ? [v0: Nat$] : ? [v1: % 116.35/16.08 Nat_nat_fun$] : ? [v2: int] : ? [v3: Nat$] : ? [v4: Nat$] : ? [v5: Nat$] % 116.35/16.08 : ? [v6: Nat_nat_fun$] : ? [v7: Nat$] : ? [v8: int] : ? [v9: Nat$] : ? % 116.35/16.08 [v10: Nat$] : ? [v11: int] : ($lesseq(1, $difference(v11, v8)) & % 116.35/16.08 nat$($sum(v2, 1)) = v3 & nat$(2) = v0 & power$(v5) = v6 & power$(v0) = v1 & % 116.35/16.08 fun_app$b(v6, v9) = v10 & fun_app$b(v6, n$) = v7 & fun_app$b(v1, v4) = v5 & % 116.35/16.08 fun_app$b(v1, v3) = v4 & size$(ys$) = v9 & fun_app$a(of_nat$, v10) = v11 & % 116.35/16.08 fun_app$a(of_nat$, v7) = v8 & fun_app$a(of_nat$, n$) = v2 & Nat$(v10) & % 116.35/16.08 Nat$(v9) & Nat$(v7) & Nat$(v5) & Nat$(v4) & Nat$(v3) & Nat$(v0) & % 116.35/16.08 Nat_nat_fun$(v6) & Nat_nat_fun$(v1)) % 116.35/16.08 % 116.35/16.08 (function-axioms) % 116.35/16.10 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 116.35/16.10 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 116.35/16.10 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 116.35/16.10 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & ! % 116.35/16.10 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 116.35/16.10 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: % 116.35/16.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 116.35/16.10 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~ % 116.35/16.10 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 116.35/16.10 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 116.35/16.10 (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, v2) = v0)) & ! [v0: % 116.35/16.10 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 116.35/16.10 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0: % 116.35/16.10 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 116.35/16.10 (times$d(v3, v2) = v1) | ~ (times$d(v3, v2) = v0)) & ! [v0: Enat$] : ! % 116.35/16.10 [v1: Enat$] : ! [v2: Enat$] : ! [v3: Enat$] : (v1 = v0 | ~ (times$c(v3, v2) % 116.35/16.10 = v1) | ~ (times$c(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 116.35/16.10 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 116.35/16.10 (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) = v0)) & ! [v0: $real] : % 116.35/16.10 ! [v1: $real] : ! [v2: int] : ! [v3: Int_real_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$z(v3, v2) = v1) | ~ (fun_app$z(v3, v2) = v0)) & ! [v0: Enat$] : % 116.35/16.10 ! [v1: Enat$] : ! [v2: int] : ! [v3: Int_enat_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$y(v3, v2) = v1) | ~ (fun_app$y(v3, v2) = v0)) & ! [v0: Num$] : ! % 116.35/16.10 [v1: Num$] : ! [v2: $real] : ! [v3: Real_num_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$x(v3, v2) = v1) | ~ (fun_app$x(v3, v2) = v0)) & ! [v0: Num$] : ! % 116.35/16.10 [v1: Num$] : ! [v2: Enat$] : ! [v3: Enat_num_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$w(v3, v2) = v1) | ~ (fun_app$w(v3, v2) = v0)) & ! [v0: Num$] : ! % 116.35/16.10 [v1: Num$] : ! [v2: int] : ! [v3: Int_num_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$v(v3, v2) = v1) | ~ (fun_app$v(v3, v2) = v0)) & ! [v0: int] : ! % 116.35/16.10 [v1: int] : ! [v2: $real] : ! [v3: Real_int_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$u(v3, v2) = v1) | ~ (fun_app$u(v3, v2) = v0)) & ! [v0: int] : ! % 116.35/16.10 [v1: int] : ! [v2: Enat$] : ! [v3: Enat_int_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$t(v3, v2) = v1) | ~ (fun_app$t(v3, v2) = v0)) & ! [v0: % 116.35/16.10 Real_bool_fun$] : ! [v1: Real_bool_fun$] : ! [v2: $real] : ! [v3: % 116.35/16.10 Real_real_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$s(v3, v2) = v1) | ~ % 116.35/16.10 (fun_app$s(v3, v2) = v0)) & ! [v0: Int_bool_fun$] : ! [v1: Int_bool_fun$] % 116.35/16.10 : ! [v2: int] : ! [v3: Int_int_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$r(v3, % 116.35/16.10 v2) = v1) | ~ (fun_app$r(v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 116.35/16.10 ! [v1: MultipleValueBool] : ! [v2: int] : ! [v3: Int_bool_fun$] : (v1 = v0 | % 116.35/16.10 ~ (fun_app$q(v3, v2) = v1) | ~ (fun_app$q(v3, v2) = v0)) & ! [v0: int] : % 116.35/16.10 ! [v1: int] : ! [v2: int] : ! [v3: Int_int_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$p(v3, v2) = v1) | ~ (fun_app$p(v3, v2) = v0)) & ! [v0: % 116.35/16.10 Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: Nat$] : ! [v3: % 116.35/16.10 Nat_nat_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$o(v3, v2) = v1) | ~ % 116.35/16.10 (fun_app$o(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 116.35/16.10 MultipleValueBool] : ! [v2: Nat$] : ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$n(v3, v2) = v1) | ~ (fun_app$n(v3, v2) = v0)) & ! [v0: $real] : % 116.35/16.10 ! [v1: $real] : ! [v2: Nat$] : ! [v3: Nat_real_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$m(v3, v2) = v1) | ~ (fun_app$m(v3, v2) = v0)) & ! [v0: Enat$] : % 116.35/16.10 ! [v1: Enat$] : ! [v2: Nat$] : ! [v3: Nat_enat_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$l(v3, v2) = v1) | ~ (fun_app$l(v3, v2) = v0)) & ! [v0: Num$] : ! % 116.35/16.10 [v1: Num$] : ! [v2: Nat$] : ! [v3: Nat_num_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$k(v3, v2) = v1) | ~ (fun_app$k(v3, v2) = v0)) & ! [v0: $real] : % 116.35/16.10 ! [v1: $real] : ! [v2: Num$] : ! [v3: Num_real_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$j(v3, v2) = v1) | ~ (fun_app$j(v3, v2) = v0)) & ! [v0: % 116.35/16.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 116.35/16.10 $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, % 116.35/16.10 v2) = v0)) & ! [v0: Enat_bool_fun$] : ! [v1: Enat_bool_fun$] : ! [v2: % 116.35/16.10 Enat$] : ! [v3: Enat_enat_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$h(v3, v2) % 116.35/16.10 = v1) | ~ (fun_app$h(v3, v2) = v0)) & ! [v0: Enat$] : ! [v1: Enat$] : % 116.35/16.10 ! [v2: Num$] : ! [v3: Num_enat_fun$] : (v1 = v0 | ~ (fun_app$i(v3, v2) = v1) % 116.35/16.10 | ~ (fun_app$i(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 116.35/16.10 MultipleValueBool] : ! [v2: Enat$] : ! [v3: Enat_bool_fun$] : (v1 = v0 | % 116.35/16.10 ~ (fun_app$g(v3, v2) = v1) | ~ (fun_app$g(v3, v2) = v0)) & ! [v0: % 116.35/16.10 Num_bool_fun$] : ! [v1: Num_bool_fun$] : ! [v2: Num$] : ! [v3: % 116.35/16.10 Num_num_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$f(v3, v2) = v1) | ~ % 116.35/16.10 (fun_app$f(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 116.35/16.10 MultipleValueBool] : ! [v2: Num$] : ! [v3: Num_bool_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$e(v3, v2) = v1) | ~ (fun_app$e(v3, v2) = v0)) & ! [v0: int] : ! % 116.35/16.10 [v1: int] : ! [v2: Num$] : ! [v3: Num_int_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$d(v3, v2) = v1) | ~ (fun_app$d(v3, v2) = v0)) & ! [v0: Num$] : ! % 116.35/16.10 [v1: Num$] : ! [v2: Num$] : ! [v3: Num_num_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$c(v3, v2) = v1) | ~ (fun_app$c(v3, v2) = v0)) & ! [v0: Nat$] : ! % 116.35/16.10 [v1: Nat$] : ! [v2: Nat$] : ! [v3: Nat_nat_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$b(v3, v2) = v1) | ~ (fun_app$b(v3, v2) = v0)) & ! [v0: int] : ! % 116.35/16.10 [v1: int] : ! [v2: Nat$] : ! [v3: Nat_int_fun$] : (v1 = v0 | ~ % 116.35/16.10 (fun_app$a(v3, v2) = v1) | ~ (fun_app$a(v3, v2) = v0)) & ! [v0: % 116.35/16.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 116.35/16.10 Real_bool_fun$] : (v1 = v0 | ~ (fun_app$(v3, v2) = v1) | ~ (fun_app$(v3, % 116.35/16.10 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 116.35/16.10 ! [v2: Real_set$] : ! [v3: $real] : (v1 = v0 | ~ (member$(v3, v2) = v1) | ~ % 116.35/16.10 (member$(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 116.35/16.10 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1) % 116.35/16.10 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 116.35/16.10 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1) % 116.35/16.10 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 116.35/16.10 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) & % 116.35/16.10 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 116.35/16.10 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] : % 116.35/16.10 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ % 116.35/16.10 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 116.35/16.10 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) & % 116.35/16.10 ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2) % 116.35/16.10 = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 116.35/16.10 [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = % 116.35/16.10 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 116.35/16.10 (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] : % 116.35/16.10 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ % 116.35/16.10 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 116.35/16.10 : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) & ! % 116.35/16.10 [v0: Int_int_fun$] : ! [v1: Int_int_fun$] : ! [v2: int] : (v1 = v0 | ~ % 116.35/16.10 (times$b(v2) = v1) | ~ (times$b(v2) = v0)) & ! [v0: Nat_nat_fun$] : ! % 116.35/16.10 [v1: Nat_nat_fun$] : ! [v2: Nat$] : (v1 = v0 | ~ (times$(v2) = v1) | ~ % 116.35/16.10 (times$(v2) = v0)) & ! [v0: Num_num_fun$] : ! [v1: Num_num_fun$] : ! [v2: % 116.35/16.10 Num$] : (v1 = v0 | ~ (times$a(v2) = v1) | ~ (times$a(v2) = v0)) & ! [v0: % 116.35/16.10 $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (dbl$a(v2) = v1) | % 116.35/16.10 ~ (dbl$a(v2) = v0)) & ! [v0: Real_set$] : ! [v1: Real_set$] : ! [v2: % 116.35/16.10 Real_bool_fun$] : (v1 = v0 | ~ (collect$(v2) = v1) | ~ (collect$(v2) = % 116.35/16.10 v0)) & ! [v0: Nat_real_fun$] : ! [v1: Nat_real_fun$] : ! [v2: $real] : % 116.35/16.10 (v1 = v0 | ~ (power$c(v2) = v1) | ~ (power$c(v2) = v0)) & ! [v0: % 116.35/16.10 Nat_enat_fun$] : ! [v1: Nat_enat_fun$] : ! [v2: Enat$] : (v1 = v0 | ~ % 116.35/16.10 (power$b(v2) = v1) | ~ (power$b(v2) = v0)) & ! [v0: Nat_int_fun$] : ! % 116.35/16.10 [v1: Nat_int_fun$] : ! [v2: int] : (v1 = v0 | ~ (power$a(v2) = v1) | ~ % 116.35/16.10 (power$a(v2) = v0)) & ! [v0: Num_num_fun$] : ! [v1: Num_num_fun$] : ! % 116.35/16.10 [v2: Num$] : (v1 = v0 | ~ (pow$(v2) = v1) | ~ (pow$(v2) = v0)) & ! [v0: % 116.35/16.10 Nat$] : ! [v1: Nat$] : ! [v2: Num$] : (v1 = v0 | ~ (numeral$c(v2) = v1) | % 116.35/16.10 ~ (numeral$c(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Num$] : % 116.35/16.10 (v1 = v0 | ~ (size$a(v2) = v1) | ~ (size$a(v2) = v0)) & ! [v0: Nat$] : ! % 116.35/16.10 [v1: Nat$] : ! [v2: int] : (v1 = v0 | ~ (nat$(v2) = v1) | ~ (nat$(v2) = % 116.35/16.10 v0)) & ! [v0: Nat_nat_fun$] : ! [v1: Nat_nat_fun$] : ! [v2: Nat$] : (v1 % 116.35/16.10 = v0 | ~ (power$(v2) = v1) | ~ (power$(v2) = v0)) & ! [v0: Nat$] : ! % 116.35/16.10 [v1: Nat$] : ! [v2: A_ltln_list$] : (v1 = v0 | ~ (size$(v2) = v1) | ~ % 116.35/16.10 (size$(v2) = v0)) & ! [v0: Real_bool_fun$] : ! [v1: Real_bool_fun$] : ! % 116.35/16.10 [v2: Real_set$] : (v1 = v0 | ~ (uu$(v2) = v1) | ~ (uu$(v2) = v0)) % 116.35/16.10 % 116.35/16.10 Further assumptions not needed in the proof: % 116.35/16.10 -------------------------------------------- % 116.35/16.10 axiom0, axiom10, axiom100, axiom102, axiom103, axiom104, axiom105, axiom106, % 116.35/16.10 axiom107, axiom108, axiom109, axiom11, axiom110, axiom111, axiom112, axiom113, % 116.35/16.10 axiom114, axiom115, axiom116, axiom117, axiom118, axiom119, axiom12, axiom120, % 116.35/16.10 axiom121, axiom122, axiom123, axiom124, axiom125, axiom126, axiom13, axiom130, % 116.35/16.10 axiom131, axiom132, axiom133, axiom134, axiom135, axiom136, axiom137, axiom138, % 116.35/16.10 axiom139, axiom14, axiom140, axiom141, axiom142, axiom143, axiom144, axiom145, % 116.35/16.10 axiom147, axiom148, axiom149, axiom15, axiom150, axiom151, axiom152, axiom153, % 116.35/16.10 axiom154, axiom155, axiom156, axiom157, axiom158, axiom159, axiom16, axiom160, % 116.35/16.10 axiom161, axiom162, axiom163, axiom164, axiom165, axiom166, axiom167, axiom168, % 116.35/16.10 axiom169, axiom17, axiom170, axiom171, axiom172, axiom173, axiom174, axiom175, % 116.35/16.10 axiom18, axiom180, axiom181, axiom182, axiom183, axiom184, axiom185, axiom186, % 116.35/16.10 axiom187, axiom188, axiom189, axiom19, axiom190, axiom191, axiom192, axiom193, % 116.35/16.10 axiom194, axiom195, axiom196, axiom197, axiom198, axiom199, axiom20, axiom200, % 116.35/16.10 axiom201, axiom202, axiom203, axiom204, axiom205, axiom206, axiom207, axiom208, % 116.35/16.10 axiom209, axiom21, axiom210, axiom211, axiom212, axiom213, axiom214, axiom215, % 116.35/16.10 axiom216, axiom217, axiom218, axiom219, axiom22, axiom220, axiom221, axiom222, % 116.35/16.10 axiom223, axiom224, axiom225, axiom226, axiom227, axiom228, axiom229, axiom23, % 116.35/16.10 axiom230, axiom231, axiom232, axiom233, axiom234, axiom235, axiom236, axiom237, % 116.35/16.10 axiom238, axiom239, axiom24, axiom240, axiom241, axiom242, axiom243, axiom244, % 116.35/16.10 axiom245, axiom246, axiom247, axiom248, axiom249, axiom25, axiom250, axiom251, % 116.35/16.10 axiom252, axiom253, axiom254, axiom255, axiom256, axiom257, axiom258, axiom259, % 116.35/16.10 axiom26, axiom260, axiom261, axiom262, axiom263, axiom264, axiom265, axiom266, % 116.35/16.10 axiom267, axiom268, axiom269, axiom27, axiom270, axiom271, axiom272, axiom273, % 116.35/16.10 axiom274, axiom275, axiom276, axiom277, axiom278, axiom279, axiom28, axiom280, % 116.35/16.10 axiom281, axiom282, axiom283, axiom284, axiom285, axiom286, axiom287, axiom288, % 116.35/16.10 axiom289, axiom29, axiom290, axiom291, axiom292, axiom293, axiom294, axiom295, % 116.35/16.10 axiom296, axiom297, axiom298, axiom299, axiom30, axiom300, axiom301, axiom302, % 116.35/16.10 axiom303, axiom304, axiom305, axiom306, axiom307, axiom308, axiom309, axiom31, % 116.35/16.10 axiom310, axiom311, axiom312, axiom313, axiom314, axiom315, axiom316, axiom317, % 116.35/16.10 axiom318, axiom319, axiom32, axiom320, axiom321, axiom322, axiom328, axiom33, % 116.35/16.10 axiom337, axiom338, axiom339, axiom34, axiom340, axiom341, axiom342, axiom343, % 116.35/16.10 axiom344, axiom347, axiom348, axiom349, axiom35, axiom350, axiom354, axiom355, % 116.35/16.10 axiom356, axiom357, axiom358, axiom359, axiom36, axiom360, axiom361, axiom362, % 116.35/16.10 axiom363, axiom364, axiom365, axiom366, axiom367, axiom368, axiom369, axiom37, % 116.35/16.10 axiom370, axiom371, axiom372, axiom373, axiom376, axiom377, axiom378, axiom379, % 116.35/16.10 axiom38, axiom380, axiom381, axiom382, axiom384, axiom385, axiom386, axiom387, % 116.35/16.10 axiom388, axiom389, axiom39, axiom390, axiom391, axiom392, axiom393, axiom394, % 116.35/16.10 axiom395, axiom396, axiom397, axiom398, axiom399, axiom40, axiom400, axiom401, % 116.35/16.10 axiom402, axiom403, axiom404, axiom405, axiom406, axiom407, axiom408, axiom409, % 116.35/16.10 axiom41, axiom410, axiom411, axiom412, axiom413, axiom414, axiom415, axiom416, % 116.35/16.10 axiom417, axiom418, axiom419, axiom42, axiom420, axiom421, axiom422, axiom424, % 116.35/16.10 axiom425, axiom426, axiom427, axiom428, axiom429, axiom43, axiom434, axiom435, % 116.35/16.10 axiom436, axiom437, axiom438, axiom439, axiom44, axiom440, axiom441, axiom442, % 116.35/16.10 axiom443, axiom444, axiom445, axiom446, axiom447, axiom448, axiom449, axiom45, % 116.35/16.10 axiom450, axiom451, axiom452, axiom453, axiom454, axiom455, axiom456, axiom457, % 116.35/16.10 axiom458, axiom459, axiom46, axiom460, axiom461, axiom462, axiom463, axiom464, % 116.35/16.10 axiom465, axiom466, axiom467, axiom468, axiom469, axiom47, axiom470, axiom471, % 116.35/16.10 axiom472, axiom473, axiom474, axiom475, axiom476, axiom477, axiom478, axiom479, % 116.35/16.10 axiom48, axiom480, axiom481, axiom482, axiom483, axiom484, axiom485, axiom486, % 116.35/16.10 axiom487, axiom488, axiom489, axiom49, axiom490, axiom491, axiom492, axiom493, % 116.35/16.10 axiom494, axiom495, axiom496, axiom497, axiom498, axiom499, axiom50, axiom500, % 116.35/16.10 axiom501, axiom502, axiom503, axiom504, axiom505, axiom506, axiom507, axiom508, % 116.35/16.10 axiom509, axiom51, axiom510, axiom511, axiom512, axiom513, axiom514, axiom515, % 116.35/16.10 axiom516, axiom517, axiom518, axiom519, axiom52, axiom520, axiom521, axiom522, % 116.35/16.10 axiom523, axiom524, axiom525, axiom526, axiom527, axiom528, axiom529, axiom53, % 116.35/16.10 axiom530, axiom531, axiom532, axiom533, axiom534, axiom535, axiom536, axiom537, % 116.35/16.10 axiom538, axiom539, axiom54, axiom540, axiom541, axiom542, axiom543, axiom544, % 116.35/16.10 axiom545, axiom546, axiom547, axiom548, axiom549, axiom55, axiom550, axiom551, % 116.35/16.10 axiom552, axiom553, axiom554, axiom555, axiom556, axiom557, axiom558, axiom559, % 116.35/16.10 axiom56, axiom560, axiom561, axiom562, axiom563, axiom564, axiom565, axiom566, % 116.35/16.10 axiom567, axiom568, axiom569, axiom57, axiom570, axiom571, axiom572, axiom573, % 116.35/16.10 axiom574, axiom575, axiom576, axiom577, axiom578, axiom579, axiom58, axiom580, % 116.35/16.10 axiom581, axiom582, axiom583, axiom584, axiom586, axiom587, axiom588, axiom589, % 116.35/16.10 axiom59, axiom590, axiom591, axiom592, axiom593, axiom594, axiom595, axiom596, % 116.35/16.10 axiom597, axiom6, axiom60, axiom600, axiom601, axiom605, axiom606, axiom607, % 116.35/16.10 axiom608, axiom609, axiom61, axiom610, axiom611, axiom612, axiom613, axiom614, % 116.35/16.10 axiom615, axiom616, axiom617, axiom618, axiom619, axiom62, axiom620, axiom621, % 116.35/16.10 axiom622, axiom623, axiom624, axiom625, axiom626, axiom627, axiom628, axiom629, % 116.35/16.10 axiom63, axiom631, axiom632, axiom633, axiom634, axiom636, axiom64, axiom65, % 116.35/16.10 axiom66, axiom67, axiom68, axiom69, axiom7, axiom70, axiom71, axiom72, axiom73, % 116.35/16.10 axiom79, axiom8, axiom80, axiom83, axiom84, axiom85, axiom86, axiom87, axiom88, % 116.35/16.10 axiom89, axiom9, axiom90, axiom91, axiom92, axiom93, axiom94, axiom95, axiom96, % 116.35/16.10 axiom97, axiom99, formula_639, formula_640 % 116.35/16.10 % 116.35/16.10 Those formulas are unsatisfiable: % 116.35/16.10 --------------------------------- % 116.35/16.10 % 116.35/16.10 Begin of proof % 116.35/16.10 | % 116.35/16.10 | ALPHA: (axiom2) implies: % 116.35/16.11 | (1) ? [v0: int] : ? [v1: Nat$] : ? [v2: int] : ($lesseq(v2, v0) & % 116.35/16.11 | size$(ys$) = v1 & fun_app$a(of_nat$, v1) = v2 & fun_app$a(of_nat$, % 116.35/16.11 | n$) = v0 & Nat$(v1)) % 116.35/16.11 | % 116.35/16.11 | ALPHA: (axiom3) implies: % 116.35/16.11 | (2) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_nat_fun$] : ! [v3: Nat$] : % 116.35/16.11 | ( ~ (power$(v0) = v2) | ~ (fun_app$b(v2, v1) = v3) | ~ Nat$(v1) | ~ % 116.35/16.11 | Nat$(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : % 116.35/16.11 | (fun_app$a(of_nat$, v3) = v5 & fun_app$a(of_nat$, v1) = v6 & % 116.35/16.11 | fun_app$a(of_nat$, v0) = v4 & ( ~ ($lesseq(1, $difference(v6, v5))) % 116.35/16.11 | | ~ ($lesseq(2, v4))))) % 116.35/16.11 | % 116.35/16.11 | ALPHA: (axiom4) implies: % 116.35/16.11 | (3) ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: Nat$] : ! [v2: % 116.35/16.11 | Nat$] : ! [v3: int] : ! [v4: int] : ( ~ ($lesseq(v4, v3)) | ~ % 116.35/16.11 | (fun_app$a(of_nat$, v2) = v3) | ~ (fun_app$a(of_nat$, v1) = v4) | % 116.35/16.11 | ~ Nat$(v2) | ~ Nat$(v1) | ? [v5: Nat_nat_fun$] : ? [v6: Nat$] : % 116.35/16.11 | ? [v7: int] : ? [v8: Nat_nat_fun$] : ? [v9: Nat$] : ? [v10: int] % 116.35/16.11 | : ($lesseq(v10, v7) & power$(v2) = v5 & power$(v1) = v8 & % 116.35/16.11 | fun_app$b(v8, v0) = v9 & fun_app$b(v5, v0) = v6 & % 116.35/16.11 | fun_app$a(of_nat$, v9) = v10 & fun_app$a(of_nat$, v6) = v7 & % 116.35/16.11 | Nat$(v9) & Nat$(v6) & Nat_nat_fun$(v8) & Nat_nat_fun$(v5))) & ! % 116.35/16.11 | [v1: Nat$] : ! [v2: Nat$] : ! [v3: int] : ! [v4: int] : ( ~ % 116.35/16.11 | ($lesseq(1, $difference(v4, v3))) | ~ (fun_app$a(of_nat$, v2) = % 116.35/16.11 | v3) | ~ (fun_app$a(of_nat$, v1) = v4) | ~ Nat$(v2) | ~ % 116.35/16.11 | Nat$(v1) | ? [v5: Nat_nat_fun$] : ? [v6: Nat$] : ? [v7: int] : % 116.35/16.11 | ? [v8: Nat_nat_fun$] : ? [v9: Nat$] : ? [v10: int] : ($lesseq(1, % 116.35/16.11 | $difference(v10, v7)) & power$(v2) = v5 & power$(v1) = v8 & % 116.35/16.11 | fun_app$b(v8, v0) = v9 & fun_app$b(v5, v0) = v6 & % 116.35/16.11 | fun_app$a(of_nat$, v9) = v10 & fun_app$a(of_nat$, v6) = v7 & % 116.35/16.11 | Nat$(v9) & Nat$(v6) & Nat_nat_fun$(v8) & Nat_nat_fun$(v5)))) % 116.35/16.11 | % 116.35/16.11 | ALPHA: (axiom5) implies: % 116.35/16.11 | (4) ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: Nat$] : ! [v2: % 116.35/16.11 | Nat$] : ! [v3: int] : ! [v4: int] : ( ~ ($lesseq(1, % 116.35/16.11 | $difference(v4, v3))) | ~ (fun_app$a(of_nat$, v2) = v3) | ~ % 116.35/16.11 | (fun_app$a(of_nat$, v1) = v4) | ~ Nat$(v2) | ~ Nat$(v1) | ? [v5: % 116.35/16.11 | Nat_nat_fun$] : ? [v6: Nat$] : ? [v7: int] : ($lesseq(1, % 116.35/16.11 | $difference(v7, v3)) & power$(v1) = v5 & fun_app$b(v5, v0) = v6 % 116.35/16.11 | & fun_app$a(of_nat$, v6) = v7 & Nat$(v6) & Nat_nat_fun$(v5)))) % 116.35/16.11 | % 116.35/16.11 | ALPHA: (axiom74) implies: % 116.35/16.11 | (5) ? [v0: Nat_bool_fun$] : ? [v1: Nat$] : (fun_app$o(less_eq$b, zero$) = % 116.35/16.11 | v0 & nat$(2) = v1 & Nat_bool_fun$(v0) & Nat$(v1) & ! [v2: Nat$] : ! % 116.35/16.11 | [v3: Nat$] : ( ~ (fun_app$n(v0, v3) = 0) | ~ (fun_app$n(v0, v2) = 0) % 116.35/16.11 | | ~ Nat$(v3) | ~ Nat$(v2) | ? [v4: Nat_nat_fun$] : ? [v5: Nat$] % 116.35/16.11 | : ? [v6: Nat_nat_fun$] : ? [v7: Nat$] : (power$(v3) = v6 & % 116.35/16.11 | power$(v2) = v4 & fun_app$b(v6, v1) = v7 & fun_app$b(v4, v1) = v5 % 116.35/16.11 | & Nat$(v7) & Nat$(v5) & Nat_nat_fun$(v6) & Nat_nat_fun$(v4) & ( ~ % 116.35/16.11 | (v7 = v5) | v3 = v2) & ( ~ (v3 = v2) | v7 = v5)))) % 116.35/16.11 | % 116.35/16.11 | ALPHA: (axiom98) implies: % 116.35/16.11 | (6) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_nat_fun$] : ! [v3: Nat$] : % 116.35/16.11 | ( ~ (power$(v0) = v2) | ~ (fun_app$b(v2, v1) = v3) | ~ Nat$(v1) | ~ % 116.35/16.11 | Nat$(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : % 116.35/16.12 | (fun_app$a(of_nat$, v3) = v4 & fun_app$a(of_nat$, v1) = v5 & % 116.35/16.12 | fun_app$a(of_nat$, v0) = v6 & ( ~ (v4 = 1) | v6 = 1 | v5 = 0))) % 116.35/16.12 | (7) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_nat_fun$] : ! [v3: Nat$] : % 116.35/16.12 | ( ~ (power$(v0) = v2) | ~ (fun_app$b(v2, v1) = v3) | ~ Nat$(v1) | ~ % 116.35/16.12 | Nat$(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : % 116.35/16.12 | (fun_app$a(of_nat$, v3) = v6 & fun_app$a(of_nat$, v1) = v4 & % 116.35/16.12 | fun_app$a(of_nat$, v0) = v5 & (v6 = 1 | ( ~ (v5 = 1) & ~ (v4 = % 116.35/16.12 | 0))))) % 116.35/16.12 | % 116.35/16.12 | ALPHA: (axiom127) implies: % 116.35/16.12 | (8) ? [v0: Nat$] : (nat$(2) = v0 & Nat$(v0) & ! [v1: Nat$] : ! [v2: % 116.35/16.12 | Nat_nat_fun$] : (v1 = zero$ | ~ (power$(v1) = v2) | ~ Nat$(v1) | % 116.35/16.12 | ? [v3: Nat$] : ( ~ (v3 = zero$) & fun_app$b(v2, v0) = v3 & % 116.35/16.12 | Nat$(v3))) & ! [v1: Nat_nat_fun$] : ( ~ (power$(zero$) = v1) | % 116.35/16.12 | fun_app$b(v1, v0) = zero$)) % 116.35/16.12 | % 116.35/16.12 | ALPHA: (axiom323) implies: % 116.35/16.12 | (9) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_nat_fun$] : ! [v3: Nat$] : % 116.35/16.12 | ( ~ (power$(v0) = v2) | ~ (fun_app$b(v2, v1) = v3) | ~ Nat$(v1) | ~ % 116.35/16.12 | Nat$(v0) | ? [v4: int] : ? [v5: int] : (fun_app$a(of_nat$, v3) = v5 % 116.35/16.12 | & fun_app$a(of_nat$, v0) = v4 & ( ~ ($lesseq(v5, 0) | ~ % 116.35/16.12 | ($lesseq(1, v4))))) % 116.35/16.12 | % 116.35/16.12 | ALPHA: (axiom324) implies: % 116.35/16.12 | (10) ? [v0: Nat_enat_fun$] : ? [v1: Nat$] : (power$b(zero$a) = v0 & % 116.35/16.12 | fun_app$l(v0, v1) = zero$a & nat$(2) = v1 & Nat$(v1) & % 116.35/16.12 | Nat_enat_fun$(v0)) % 116.35/16.12 | % 116.35/16.12 | ALPHA: (axiom325) implies: % 116.77/16.12 | (11) ? [v0: Nat_nat_fun$] : ? [v1: Nat$] : (nat$(2) = v1 & power$(zero$) % 116.77/16.12 | = v0 & fun_app$b(v0, v1) = zero$ & Nat$(v1) & Nat_nat_fun$(v0)) % 116.77/16.12 | % 116.77/16.12 | ALPHA: (axiom331) implies: % 116.77/16.12 | (12) ? [v0: Nat$] : ? [v1: Nat_bool_fun$] : (fun_app$o(less_eq$b, zero$) % 116.77/16.12 | = v1 & nat$(2) = v0 & Nat_bool_fun$(v1) & Nat$(v0) & ! [v2: Nat$] : % 116.77/16.12 | ! [v3: Nat$] : (v3 = v2 | ~ (fun_app$n(v1, v3) = 0) | ~ % 116.77/16.12 | (fun_app$n(v1, v2) = 0) | ~ Nat$(v3) | ~ Nat$(v2) | ? [v4: % 116.77/16.12 | Nat_nat_fun$] : ? [v5: Nat$] : ? [v6: Nat_nat_fun$] : ? [v7: % 116.77/16.12 | Nat$] : ( ~ (v7 = v5) & power$(v3) = v6 & power$(v2) = v4 & % 116.77/16.12 | fun_app$b(v6, v0) = v7 & fun_app$b(v4, v0) = v5 & Nat$(v7) & % 116.77/16.12 | Nat$(v5) & Nat_nat_fun$(v6) & Nat_nat_fun$(v4)))) % 116.77/16.12 | % 116.77/16.12 | ALPHA: (axiom334) implies: % 116.77/16.12 | (13) ? [v0: Nat$] : ? [v1: Nat_bool_fun$] : (fun_app$o(less_eq$b, zero$) % 116.77/16.12 | = v1 & nat$(2) = v0 & Nat_bool_fun$(v1) & Nat$(v0) & ! [v2: Nat$] : % 116.77/16.12 | ! [v3: Nat$] : ! [v4: Nat_nat_fun$] : ! [v5: Nat$] : ! [v6: % 116.77/16.12 | Nat_bool_fun$] : ! [v7: Nat_nat_fun$] : ! [v8: Nat$] : ( ~ % 116.77/16.12 | (fun_app$o(less_eq$b, v5) = v6) | ~ (fun_app$n(v6, v8) = 0) | ~ % 116.77/16.12 | (power$(v3) = v7) | ~ (power$(v2) = v4) | ~ (fun_app$b(v7, v0) = % 116.77/16.12 | v8) | ~ (fun_app$b(v4, v0) = v5) | ~ Nat$(v3) | ~ Nat$(v2) | % 116.77/16.12 | ? [v9: any] : ? [v10: Nat_bool_fun$] : ? [v11: any] : % 116.77/16.12 | (fun_app$o(less_eq$b, v2) = v10 & fun_app$n(v10, v3) = v11 & % 116.77/16.12 | fun_app$n(v1, v3) = v9 & Nat_bool_fun$(v10) & ( ~ (v9 = 0) | v11 % 116.77/16.12 | = 0)))) % 116.77/16.12 | % 116.77/16.12 | ALPHA: (axiom383) implies: % 116.77/16.12 | (14) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_nat_fun$] : ! [v3: Nat$] % 116.77/16.12 | : ( ~ (power$(v0) = v2) | ~ (fun_app$b(v2, v1) = v3) | ~ Nat$(v1) | % 116.77/16.12 | ~ Nat$(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : % 116.77/16.12 | (fun_app$a(of_nat$, v3) = v4 & fun_app$a(of_nat$, v1) = v6 & % 116.77/16.12 | fun_app$a(of_nat$, v0) = v5 & (v6 = 0 | ~ ($lesseq(v5, 0) | ~ % 116.77/16.12 | ($lesseq(1, v4))))) % 116.77/16.12 | (15) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_nat_fun$] : ! [v3: Nat$] % 116.77/16.12 | : ( ~ (power$(v0) = v2) | ~ (fun_app$b(v2, v1) = v3) | ~ Nat$(v1) | % 116.77/16.12 | ~ Nat$(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : % 116.77/16.12 | (fun_app$a(of_nat$, v3) = v6 & fun_app$a(of_nat$, v1) = v5 & % 116.77/16.12 | fun_app$a(of_nat$, v0) = v4 & ( ~ ($lesseq(v6, 0) | ( ~ (v5 = 0) & % 116.77/16.12 | $lesseq(v4, 0))))) % 116.77/16.12 | % 116.77/16.12 | ALPHA: (axiom585) implies: % 116.77/16.13 | (16) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat$] : ! [v3: Nat_nat_fun$] % 116.77/16.13 | : ! [v4: Nat$] : ! [v5: Nat$] : ( ~ (power$(v0) = v3) | ~ % 116.77/16.13 | (fun_app$b(v3, v2) = v4) | ~ (fun_app$b(v3, v1) = v5) | ~ Nat$(v2) % 116.77/16.13 | | ~ Nat$(v1) | ~ Nat$(v0) | ? [v6: int] : ? [v7: int] : ? [v8: % 116.77/16.13 | int] : ? [v9: int] : ? [v10: int] : (fun_app$a(of_nat$, v5) = v8 % 116.77/16.13 | & fun_app$a(of_nat$, v4) = v7 & fun_app$a(of_nat$, v2) = v9 & % 116.77/16.13 | fun_app$a(of_nat$, v1) = v10 & fun_app$a(of_nat$, v0) = v6 & ( ~ % 116.77/16.13 | ($lesseq(v9, v10)) | ~ ($lesseq(1, $difference(v7, v8))) | ~ % 116.77/16.13 | ($lesseq(1, v6))))) % 116.77/16.13 | % 116.77/16.13 | ALPHA: (axiom598) implies: % 116.77/16.13 | (17) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_nat_fun$] : ! [v3: Nat$] % 116.77/16.13 | : ( ~ (power$(v0) = v2) | ~ (fun_app$b(v2, v1) = v3) | ~ Nat$(v1) | % 116.77/16.13 | ~ Nat$(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : % 116.77/16.13 | (fun_app$a(of_nat$, v3) = v5 & fun_app$a(of_nat$, v1) = v6 & % 116.77/16.13 | fun_app$a(of_nat$, v0) = v4 & ( ~ ($lesseq(v5, v6)) | ~ % 116.77/16.13 | ($lesseq(2, v4))))) % 116.77/16.13 | % 116.77/16.13 | ALPHA: (axiom599) implies: % 116.77/16.13 | (18) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat$] : ! [v3: Nat_nat_fun$] % 116.77/16.13 | : ! [v4: Nat$] : ! [v5: Nat$] : ( ~ (power$(v2) = v3) | ~ % 116.77/16.13 | (fun_app$b(v3, v1) = v4) | ~ (fun_app$b(v3, v0) = v5) | ~ Nat$(v2) % 116.77/16.13 | | ~ Nat$(v1) | ~ Nat$(v0) | ? [v6: int] : ? [v7: int] : ? [v8: % 116.77/16.13 | int] : ? [v9: int] : (fun_app$a(of_nat$, v5) = v9 & % 116.77/16.13 | fun_app$a(of_nat$, v4) = v8 & fun_app$a(of_nat$, v1) = v7 & % 116.77/16.13 | fun_app$a(of_nat$, v0) = v6 & ( ~ ($lesseq(1, $difference(v9, % 116.77/16.13 | v8))) | ~ ($lesseq(v6, v7)) | ~ ($lesseq(1, v6))))) % 116.77/16.13 | % 116.77/16.13 | ALPHA: (axiom604) implies: % 116.77/16.13 | (19) ? [v0: Nat$] : ? [v1: Nat_nat_fun$] : (nat$(2) = v0 & power$(v0) = % 116.77/16.13 | v1 & Nat$(v0) & Nat_nat_fun$(v1) & ! [v2: Nat$] : ! [v3: Nat$] : ( % 116.77/16.13 | ~ (fun_app$b(v1, v2) = v3) | ~ Nat$(v2) | ? [v4: int] : ? [v5: % 116.77/16.13 | int] : ($lesseq(1, $difference(v4, v5)) & fun_app$a(of_nat$, v3) % 116.77/16.13 | = v4 & fun_app$a(of_nat$, v2) = v5))) % 116.77/16.13 | % 116.77/16.13 | ALPHA: (axiom82) implies: % 116.77/16.13 | (20) ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | ~ % 116.77/16.13 | (fun_app$a(of_nat$, v0) = v1) | ~ Nat$(v0)) % 116.77/16.13 | % 116.77/16.13 | ALPHA: (axiom637) implies: % 116.77/16.13 | (21) ! [v0: int] : ! [v1: Nat$] : ( ~ ($lesseq(0, v0)) | ~ (nat$(v0) = % 116.77/16.13 | v1) | fun_app$a(of_nat$, v1) = v0) % 116.77/16.13 | % 116.77/16.13 | ALPHA: (conjecture1) implies: % 116.77/16.13 | (22) Nat$(n$) % 116.77/16.13 | (23) ? [v0: Nat$] : ? [v1: Nat_nat_fun$] : ? [v2: int] : ? [v3: Nat$] : % 116.77/16.13 | ? [v4: Nat$] : ? [v5: Nat$] : ? [v6: Nat_nat_fun$] : ? [v7: Nat$] % 116.77/16.13 | : ? [v8: int] : ? [v9: Nat$] : ? [v10: Nat$] : ? [v11: int] : % 116.77/16.13 | ($lesseq(1, $difference(v11, v8)) & nat$($sum(v2, 1)) = v3 & nat$(2) = % 116.77/16.13 | v0 & power$(v5) = v6 & power$(v0) = v1 & fun_app$b(v6, v9) = v10 & % 116.77/16.13 | fun_app$b(v6, n$) = v7 & fun_app$b(v1, v4) = v5 & fun_app$b(v1, v3) % 116.77/16.13 | = v4 & size$(ys$) = v9 & fun_app$a(of_nat$, v10) = v11 & % 116.77/16.13 | fun_app$a(of_nat$, v7) = v8 & fun_app$a(of_nat$, n$) = v2 & % 116.77/16.13 | Nat$(v10) & Nat$(v9) & Nat$(v7) & Nat$(v5) & Nat$(v4) & Nat$(v3) & % 116.77/16.13 | Nat$(v0) & Nat_nat_fun$(v6) & Nat_nat_fun$(v1)) % 116.77/16.13 | % 116.77/16.13 | ALPHA: (function-axioms) implies: % 116.77/16.13 | (24) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: A_ltln_list$] : (v1 = v0 | ~ % 116.77/16.13 | (size$(v2) = v1) | ~ (size$(v2) = v0)) % 116.77/16.13 | (25) ! [v0: Nat_nat_fun$] : ! [v1: Nat_nat_fun$] : ! [v2: Nat$] : (v1 = % 116.77/16.13 | v0 | ~ (power$(v2) = v1) | ~ (power$(v2) = v0)) % 116.77/16.13 | (26) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: int] : (v1 = v0 | ~ (nat$(v2) % 116.77/16.13 | = v1) | ~ (nat$(v2) = v0)) % 116.77/16.13 | (27) ! [v0: int] : ! [v1: int] : ! [v2: Nat$] : ! [v3: Nat_int_fun$] : % 116.77/16.13 | (v1 = v0 | ~ (fun_app$a(v3, v2) = v1) | ~ (fun_app$a(v3, v2) = v0)) % 116.77/16.13 | % 116.77/16.14 | DELTA: instantiating (11) with fresh symbols all_520_0, all_520_1 gives: % 116.77/16.14 | (28) nat$(2) = all_520_0 & power$(zero$) = all_520_1 & fun_app$b(all_520_1, % 116.77/16.14 | all_520_0) = zero$ & Nat$(all_520_0) & Nat_nat_fun$(all_520_1) % 116.77/16.14 | % 116.77/16.14 | ALPHA: (28) implies: % 116.77/16.14 | (29) nat$(2) = all_520_0 % 116.77/16.14 | % 116.77/16.14 | DELTA: instantiating (10) with fresh symbols all_531_0, all_531_1 gives: % 116.77/16.14 | (30) power$b(zero$a) = all_531_1 & fun_app$l(all_531_1, all_531_0) = zero$a % 116.77/16.14 | & nat$(2) = all_531_0 & Nat$(all_531_0) & Nat_enat_fun$(all_531_1) % 116.77/16.14 | % 116.77/16.14 | ALPHA: (30) implies: % 116.77/16.14 | (31) Nat$(all_531_0) % 116.77/16.14 | (32) nat$(2) = all_531_0 % 116.77/16.14 | % 116.77/16.14 | DELTA: instantiating (1) with fresh symbols all_539_0, all_539_1, all_539_2 % 116.77/16.14 | gives: % 116.77/16.14 | (33) $lesseq(all_539_0, all_539_2) & size$(ys$) = all_539_1 & % 116.77/16.14 | fun_app$a(of_nat$, all_539_1) = all_539_0 & fun_app$a(of_nat$, n$) = % 116.77/16.14 | all_539_2 & Nat$(all_539_1) % 116.77/16.14 | % 116.77/16.14 | ALPHA: (33) implies: % 116.77/16.14 | (34) $lesseq(all_539_0, all_539_2) % 116.77/16.14 | (35) fun_app$a(of_nat$, n$) = all_539_2 % 116.77/16.14 | (36) fun_app$a(of_nat$, all_539_1) = all_539_0 % 116.77/16.14 | (37) size$(ys$) = all_539_1 % 116.77/16.14 | % 116.77/16.14 | DELTA: instantiating (axiom326) with fresh symbols all_547_0, all_547_1 gives: % 116.77/16.14 | (38) power$a(0) = all_547_1 & nat$(2) = all_547_0 & fun_app$a(all_547_1, % 116.77/16.14 | all_547_0) = 0 & Nat_int_fun$(all_547_1) & Nat$(all_547_0) % 116.77/16.14 | % 116.77/16.14 | ALPHA: (38) implies: % 116.77/16.14 | (39) nat$(2) = all_547_0 % 116.77/16.14 | % 116.77/16.14 | DELTA: instantiating (axiom327) with fresh symbols all_549_0, all_549_1 gives: % 116.77/16.14 | (40) power$c(real_0) = all_549_1 & fun_app$m(all_549_1, all_549_0) = real_0 % 116.77/16.14 | & nat$(2) = all_549_0 & Nat_real_fun$(all_549_1) & Nat$(all_549_0) % 116.77/16.14 | % 116.77/16.14 | ALPHA: (40) implies: % 116.77/16.14 | (41) nat$(2) = all_549_0 % 116.77/16.14 | % 116.77/16.14 | DELTA: instantiating (axiom329) with fresh symbol all_560_0 gives: % 116.77/16.14 | (42) nat$(2) = all_560_0 & Nat$(all_560_0) & ! [v0: int] : ! [v1: % 116.77/16.14 | Nat_int_fun$] : ( ~ (power$a(v0) = v1) | ? [v2: int] : ($lesseq(0, % 116.77/16.14 | v2) & fun_app$a(v1, all_560_0) = v2)) % 116.77/16.14 | % 116.77/16.14 | ALPHA: (42) implies: % 116.77/16.14 | (43) nat$(2) = all_560_0 % 116.77/16.14 | % 116.77/16.14 | DELTA: instantiating (axiom330) with fresh symbol all_563_0 gives: % 116.77/16.14 | (44) nat$(2) = all_563_0 & Nat$(all_563_0) & ! [v0: $real] : ! [v1: % 116.77/16.14 | Nat_real_fun$] : ( ~ (power$c(v0) = v1) | ? [v2: $real] : % 116.77/16.14 | (fun_app$m(v1, all_563_0) = v2 & real_$lesseq(real_0, v2) = 0)) % 116.77/16.14 | % 116.77/16.14 | ALPHA: (44) implies: % 116.77/16.14 | (45) nat$(2) = all_563_0 % 116.77/16.14 | % 116.77/16.14 | DELTA: instantiating (axiom128) with fresh symbol all_602_0 gives: % 116.77/16.14 | (46) nat$(2) = all_602_0 & Nat$(all_602_0) & ! [v0: int] : ! [v1: % 116.77/16.14 | Nat_int_fun$] : (v0 = 0 | ~ (power$a(v0) = v1) | ? [v2: int] : ( ~ % 116.77/16.14 | (v2 = 0) & fun_app$a(v1, all_602_0) = v2)) & ! [v0: Nat_int_fun$] % 116.77/16.14 | : ( ~ (power$a(0) = v0) | fun_app$a(v0, all_602_0) = 0) % 116.77/16.14 | % 116.77/16.14 | ALPHA: (46) implies: % 116.77/16.14 | (47) nat$(2) = all_602_0 % 116.77/16.14 | % 116.77/16.14 | DELTA: instantiating (axiom129) with fresh symbol all_605_0 gives: % 116.77/16.14 | (48) nat$(2) = all_605_0 & Nat$(all_605_0) & ! [v0: $real] : ! [v1: % 116.77/16.14 | Nat_real_fun$] : (v0 = real_0 | ~ (power$c(v0) = v1) | ? [v2: % 116.77/16.14 | $real] : ( ~ (v2 = real_0) & fun_app$m(v1, all_605_0) = v2)) & ! % 116.77/16.14 | [v0: Nat_real_fun$] : ( ~ (power$c(real_0) = v0) | fun_app$m(v0, % 116.77/16.14 | all_605_0) = real_0) % 116.77/16.14 | % 116.77/16.14 | ALPHA: (48) implies: % 116.77/16.14 | (49) nat$(2) = all_605_0 % 116.77/16.14 | % 116.77/16.14 | DELTA: instantiating (axiom77) with fresh symbol all_608_0 gives: % 116.77/16.14 | (50) nat$(2) = all_608_0 & Nat$(all_608_0) & ! [v0: int] : ! [v1: % 116.77/16.14 | Nat_int_fun$] : (v0 = 0 | ~ (power$a(v0) = v1) | ? [v2: int] : % 116.77/16.14 | ($lesseq(1, v2) & fun_app$a(v1, all_608_0) = v2)) & ! [v0: % 116.77/16.14 | Nat_int_fun$] : ( ~ (power$a(0) = v0) | ? [v1: int] : ($lesseq(v1, % 116.77/16.14 | 0)fun_app$a(v0, all_608_0) = v1)) % 116.77/16.14 | % 116.77/16.14 | ALPHA: (50) implies: % 116.77/16.14 | (51) nat$(2) = all_608_0 % 116.77/16.14 | % 116.77/16.14 | DELTA: instantiating (19) with fresh symbols all_611_0, all_611_1 gives: % 116.77/16.14 | (52) nat$(2) = all_611_1 & power$(all_611_1) = all_611_0 & Nat$(all_611_1) % 116.77/16.14 | & Nat_nat_fun$(all_611_0) & ! [v0: Nat$] : ! [v1: Nat$] : ( ~ % 116.77/16.14 | (fun_app$b(all_611_0, v0) = v1) | ~ Nat$(v0) | ? [v2: int] : ? % 116.77/16.14 | [v3: int] : ($lesseq(1, $difference(v2, v3)) & fun_app$a(of_nat$, % 116.77/16.14 | v1) = v2 & fun_app$a(of_nat$, v0) = v3)) % 116.77/16.14 | % 116.77/16.14 | ALPHA: (52) implies: % 116.77/16.14 | (53) power$(all_611_1) = all_611_0 % 116.77/16.14 | (54) nat$(2) = all_611_1 % 116.77/16.14 | (55) ! [v0: Nat$] : ! [v1: Nat$] : ( ~ (fun_app$b(all_611_0, v0) = v1) | % 116.77/16.14 | ~ Nat$(v0) | ? [v2: int] : ? [v3: int] : ($lesseq(1, % 116.77/16.14 | $difference(v2, v3)) & fun_app$a(of_nat$, v1) = v2 & % 116.77/16.14 | fun_app$a(of_nat$, v0) = v3)) % 116.77/16.14 | % 116.77/16.14 | DELTA: instantiating (axiom335) with fresh symbol all_614_0 gives: % 116.77/16.15 | (56) nat$(2) = all_614_0 & Nat$(all_614_0) & ! [v0: int] : ! [v1: int] : % 116.77/16.15 | ! [v2: Nat_int_fun$] : ! [v3: Nat_int_fun$] : ( ~ ($lesseq(1, % 116.77/16.15 | $difference(v0, v1))) | ~ ($lesseq(0, v1)) | ~ (power$a(v1) = % 116.77/16.15 | v2) | ~ (power$a(v0) = v3) | ? [v4: int] : ? [v5: int] : % 116.77/16.15 | ($lesseq(1, $difference(v5, v4)) & fun_app$a(v3, all_614_0) = v5 & % 116.77/16.15 | fun_app$a(v2, all_614_0) = v4)) % 116.77/16.15 | % 116.77/16.15 | ALPHA: (56) implies: % 116.77/16.15 | (57) nat$(2) = all_614_0 % 116.77/16.15 | % 116.77/16.15 | DELTA: instantiating (axiom77) with fresh symbol all_617_0 gives: % 116.77/16.15 | (58) nat$(2) = all_617_0 & Nat$(all_617_0) & ! [v0: int] : ! [v1: % 116.77/16.15 | Nat_int_fun$] : (v0 = 0 | ~ (power$a(v0) = v1) | ? [v2: int] : % 116.77/16.15 | ($lesseq(1, v2) & fun_app$a(v1, all_617_0) = v2)) & ! [v0: % 116.77/16.15 | Nat_int_fun$] : ( ~ (power$a(0) = v0) | ? [v1: int] : ($lesseq(v1, % 116.77/16.15 | 0)fun_app$a(v0, all_617_0) = v1)) % 116.77/16.15 | % 116.77/16.15 | ALPHA: (58) implies: % 116.77/16.15 | (59) nat$(2) = all_617_0 % 116.77/16.15 | % 116.77/16.15 | DELTA: instantiating (axiom78) with fresh symbol all_622_0 gives: % 116.77/16.15 | (60) nat$(2) = all_622_0 & Nat$(all_622_0) & ! [v0: $real] : ! [v1: % 116.77/16.15 | Nat_real_fun$] : (v0 = real_0 | ~ (power$c(v0) = v1) | ? [v2: % 116.77/16.15 | $real] : ? [v3: int] : ( ~ (v3 = 0) & fun_app$m(v1, all_622_0) = % 116.77/16.15 | v2 & real_$lesseq(v2, real_0) = v3)) & ! [v0: Nat_real_fun$] : ( % 116.77/16.15 | ~ (power$c(real_0) = v0) | ? [v1: $real] : (fun_app$m(v0, % 116.77/16.15 | all_622_0) = v1 & real_$lesseq(v1, real_0) = 0)) % 116.77/16.15 | % 116.77/16.15 | ALPHA: (60) implies: % 116.77/16.15 | (61) nat$(2) = all_622_0 % 116.77/16.15 | % 116.77/16.15 | DELTA: instantiating (axiom630) with fresh symbol all_625_0 gives: % 116.77/16.15 | (62) nat$(2) = all_625_0 & Nat$(all_625_0) & ! [v0: $real] : ! [v1: % 116.77/16.15 | $real] : ( ~ (real_$product(real_2, v0) = v1) | ? [v2: % 116.77/16.15 | Nat_real_fun$] : ? [v3: $real] : ? [v4: $real] : ? [v5: % 116.77/16.15 | Nat_real_fun$] : (real_$product(real_4, v3) = v4 & power$c(v1) = % 116.77/16.15 | v5 & power$c(v0) = v2 & fun_app$m(v5, all_625_0) = v4 & % 116.77/16.15 | fun_app$m(v2, all_625_0) = v3 & Nat_real_fun$(v5) & % 116.77/16.15 | Nat_real_fun$(v2))) % 116.77/16.15 | % 116.77/16.15 | ALPHA: (62) implies: % 116.77/16.15 | (63) nat$(2) = all_625_0 % 116.77/16.15 | % 116.77/16.15 | DELTA: instantiating (8) with fresh symbol all_628_0 gives: % 116.77/16.15 | (64) nat$(2) = all_628_0 & Nat$(all_628_0) & ! [v0: Nat$] : ! [v1: % 116.77/16.15 | Nat_nat_fun$] : (v0 = zero$ | ~ (power$(v0) = v1) | ~ Nat$(v0) | % 116.77/16.15 | ? [v2: Nat$] : ( ~ (v2 = zero$) & fun_app$b(v1, all_628_0) = v2 & % 116.77/16.15 | Nat$(v2))) & ! [v0: Nat_nat_fun$] : ( ~ (power$(zero$) = v0) | % 116.77/16.15 | fun_app$b(v0, all_628_0) = zero$) % 116.77/16.15 | % 116.77/16.15 | ALPHA: (64) implies: % 116.77/16.15 | (65) nat$(2) = all_628_0 % 116.77/16.15 | % 116.77/16.15 | DELTA: instantiating (axiom332) with fresh symbol all_631_0 gives: % 116.77/16.15 | (66) nat$(2) = all_631_0 & Nat$(all_631_0) & ! [v0: int] : ! [v1: int] : % 116.77/16.15 | ! [v2: Nat_int_fun$] : ! [v3: Nat_int_fun$] : (v1 = v0 | ~ % 116.77/16.15 | ($lesseq(0, v1)) | ~ ($lesseq(0, v0)) | ~ (power$a(v1) = v3) | ~ % 116.77/16.15 | (power$a(v0) = v2) | ? [v4: int] : ? [v5: int] : ( ~ (v5 = v4) & % 116.77/16.15 | fun_app$a(v3, all_631_0) = v5 & fun_app$a(v2, all_631_0) = v4)) % 116.77/16.15 | % 116.77/16.15 | ALPHA: (66) implies: % 116.77/16.15 | (67) nat$(2) = all_631_0 % 116.77/16.15 | % 116.77/16.15 | DELTA: instantiating (axiom346) with fresh symbol all_637_0 gives: % 116.77/16.15 | (68) nat$(2) = all_637_0 & Nat$(all_637_0) & ! [v0: $real] : ! [v1: % 116.77/16.15 | Nat_real_fun$] : (v0 = real_0 | ~ (power$c(v0) = v1) | ? [v2: % 116.77/16.15 | $real] : (real_$less(real_0, v2) = 0 & fun_app$m(v1, all_637_0) = % 116.77/16.15 | v2)) & ! [v0: Nat_real_fun$] : ( ~ (power$c(real_0) = v0) | ? % 116.77/16.15 | [v1: $real] : ? [v2: int] : ( ~ (v2 = 0) & real_$less(real_0, v1) = % 116.77/16.15 | v2 & fun_app$m(v0, all_637_0) = v1)) % 116.77/16.15 | % 116.77/16.15 | ALPHA: (68) implies: % 116.77/16.15 | (69) nat$(2) = all_637_0 % 116.77/16.15 | % 116.77/16.15 | DELTA: instantiating (axiom336) with fresh symbol all_642_0 gives: % 116.77/16.15 | (70) nat$(2) = all_642_0 & Nat$(all_642_0) & ! [v0: $real] : ! [v1: % 116.77/16.15 | $real] : ! [v2: Nat_real_fun$] : ! [v3: $real] : ! [v4: % 116.77/16.15 | Nat_real_fun$] : ! [v5: $real] : ( ~ (power$c(v1) = v4) | ~ % 116.77/16.15 | (power$c(v0) = v2) | ~ (fun_app$m(v4, all_642_0) = v5) | ~ % 116.77/16.15 | (fun_app$m(v2, all_642_0) = v3) | ~ (real_$lesseq(v3, v5) = 0) | ? % 116.77/16.15 | [v6: any] : ? [v7: any] : (real_$lesseq(v0, v1) = v7 & % 116.77/16.15 | real_$lesseq(real_0, v1) = v6 & ( ~ (v6 = 0) | v7 = 0))) % 116.77/16.15 | % 116.77/16.15 | ALPHA: (70) implies: % 116.77/16.15 | (71) nat$(2) = all_642_0 % 116.77/16.15 | % 116.77/16.15 | DELTA: instantiating (axiom75) with fresh symbol all_645_0 gives: % 116.77/16.15 | (72) nat$(2) = all_645_0 & Nat$(all_645_0) & ! [v0: int] : ! [v1: int] : % 116.77/16.15 | ! [v2: Nat_int_fun$] : ! [v3: Nat_int_fun$] : ( ~ ($lesseq(0, v1)) | % 116.77/16.15 | ~ ($lesseq(0, v0)) | ~ (power$a(v1) = v3) | ~ (power$a(v0) = v2) | % 116.77/16.15 | ? [v4: int] : ? [v5: int] : (fun_app$a(v3, all_645_0) = v5 & % 116.77/16.15 | fun_app$a(v2, all_645_0) = v4 & ( ~ (v5 = v4) | v1 = v0) & ( ~ (v1 % 116.77/16.15 | = v0) | v5 = v4))) % 116.77/16.15 | % 116.77/16.15 | ALPHA: (72) implies: % 116.77/16.15 | (73) nat$(2) = all_645_0 % 116.77/16.15 | % 116.77/16.15 | DELTA: instantiating (axiom333) with fresh symbol all_649_0 gives: % 116.77/16.15 | (74) nat$(2) = all_649_0 & Nat$(all_649_0) & ! [v0: $real] : ! [v1: % 116.77/16.15 | $real] : (v1 = v0 | ~ (real_$lesseq(real_0, v1) = 0) | ~ % 116.77/16.15 | (real_$lesseq(real_0, v0) = 0) | ? [v2: Nat_real_fun$] : ? [v3: % 116.77/16.15 | $real] : ? [v4: Nat_real_fun$] : ? [v5: $real] : ( ~ (v5 = v3) & % 116.77/16.15 | power$c(v1) = v4 & power$c(v0) = v2 & fun_app$m(v4, all_649_0) = % 116.77/16.15 | v5 & fun_app$m(v2, all_649_0) = v3 & Nat_real_fun$(v4) & % 116.77/16.15 | Nat_real_fun$(v2))) % 116.77/16.15 | % 116.77/16.15 | ALPHA: (74) implies: % 116.77/16.15 | (75) nat$(2) = all_649_0 % 116.77/16.15 | % 116.77/16.15 | DELTA: instantiating (4) with fresh symbol all_655_0 gives: % 116.77/16.16 | (76) nat$(2) = all_655_0 & Nat$(all_655_0) & ! [v0: Nat$] : ! [v1: Nat$] % 116.77/16.16 | : ! [v2: int] : ! [v3: int] : ( ~ ($lesseq(1, $difference(v3, v2))) % 116.77/16.16 | | ~ (fun_app$a(of_nat$, v1) = v2) | ~ (fun_app$a(of_nat$, v0) = % 116.77/16.16 | v3) | ~ Nat$(v1) | ~ Nat$(v0) | ? [v4: Nat_nat_fun$] : ? [v5: % 116.77/16.16 | Nat$] : ? [v6: int] : ($lesseq(1, $difference(v6, v2)) & % 116.77/16.16 | power$(v0) = v4 & fun_app$b(v4, all_655_0) = v5 & % 116.77/16.16 | fun_app$a(of_nat$, v5) = v6 & Nat$(v5) & Nat_nat_fun$(v4))) % 116.77/16.16 | % 116.77/16.16 | ALPHA: (76) implies: % 116.77/16.16 | (77) nat$(2) = all_655_0 % 116.77/16.16 | % 116.77/16.16 | DELTA: instantiating (axiom76) with fresh symbol all_658_0 gives: % 116.77/16.16 | (78) nat$(2) = all_658_0 & Nat$(all_658_0) & ! [v0: $real] : ! [v1: % 116.77/16.16 | $real] : ( ~ (real_$lesseq(real_0, v1) = 0) | ~ % 116.77/16.16 | (real_$lesseq(real_0, v0) = 0) | ? [v2: Nat_real_fun$] : ? [v3: % 116.77/16.16 | $real] : ? [v4: Nat_real_fun$] : ? [v5: $real] : (power$c(v1) = % 116.77/16.16 | v4 & power$c(v0) = v2 & fun_app$m(v4, all_658_0) = v5 & % 116.77/16.16 | fun_app$m(v2, all_658_0) = v3 & Nat_real_fun$(v4) & % 116.77/16.16 | Nat_real_fun$(v2) & ( ~ (v5 = v3) | v1 = v0) & ( ~ (v1 = v0) | v5 % 116.77/16.16 | = v3))) % 116.77/16.16 | % 116.77/16.16 | ALPHA: (78) implies: % 116.77/16.16 | (79) nat$(2) = all_658_0 % 116.77/16.16 | % 116.77/16.16 | DELTA: instantiating (12) with fresh symbols all_703_0, all_703_1 gives: % 116.77/16.16 | (80) fun_app$o(less_eq$b, zero$) = all_703_0 & nat$(2) = all_703_1 & % 116.77/16.16 | Nat_bool_fun$(all_703_0) & Nat$(all_703_1) & ! [v0: Nat$] : ! [v1: % 116.77/16.16 | Nat$] : (v1 = v0 | ~ (fun_app$n(all_703_0, v1) = 0) | ~ % 116.77/16.16 | (fun_app$n(all_703_0, v0) = 0) | ~ Nat$(v1) | ~ Nat$(v0) | ? [v2: % 116.77/16.16 | Nat_nat_fun$] : ? [v3: Nat$] : ? [v4: Nat_nat_fun$] : ? [v5: % 116.77/16.16 | Nat$] : ( ~ (v5 = v3) & power$(v1) = v4 & power$(v0) = v2 & % 116.77/16.16 | fun_app$b(v4, all_703_1) = v5 & fun_app$b(v2, all_703_1) = v3 & % 116.77/16.16 | Nat$(v5) & Nat$(v3) & Nat_nat_fun$(v4) & Nat_nat_fun$(v2))) % 116.77/16.16 | % 116.77/16.16 | ALPHA: (80) implies: % 116.77/16.16 | (81) nat$(2) = all_703_1 % 116.77/16.16 | % 116.77/16.16 | DELTA: instantiating (13) with fresh symbols all_709_0, all_709_1 gives: % 116.77/16.16 | (82) fun_app$o(less_eq$b, zero$) = all_709_0 & nat$(2) = all_709_1 & % 116.77/16.16 | Nat_bool_fun$(all_709_0) & Nat$(all_709_1) & ! [v0: Nat$] : ! [v1: % 116.77/16.16 | Nat$] : ! [v2: Nat_nat_fun$] : ! [v3: Nat$] : ! [v4: % 116.77/16.16 | Nat_bool_fun$] : ! [v5: Nat_nat_fun$] : ! [v6: Nat$] : ( ~ % 116.77/16.16 | (fun_app$o(less_eq$b, v3) = v4) | ~ (fun_app$n(v4, v6) = 0) | ~ % 116.77/16.16 | (power$(v1) = v5) | ~ (power$(v0) = v2) | ~ (fun_app$b(v5, % 116.77/16.16 | all_709_1) = v6) | ~ (fun_app$b(v2, all_709_1) = v3) | ~ % 116.77/16.16 | Nat$(v1) | ~ Nat$(v0) | ? [v7: any] : ? [v8: Nat_bool_fun$] : ? % 116.77/16.16 | [v9: any] : (fun_app$o(less_eq$b, v0) = v8 & fun_app$n(v8, v1) = v9 % 116.77/16.16 | & fun_app$n(all_709_0, v1) = v7 & Nat_bool_fun$(v8) & ( ~ (v7 = 0) % 116.77/16.16 | | v9 = 0))) % 116.77/16.16 | % 116.77/16.16 | ALPHA: (82) implies: % 116.77/16.16 | (83) nat$(2) = all_709_1 % 116.77/16.16 | % 116.77/16.16 | DELTA: instantiating (5) with fresh symbols all_718_0, all_718_1 gives: % 116.77/16.16 | (84) fun_app$o(less_eq$b, zero$) = all_718_1 & nat$(2) = all_718_0 & % 116.77/16.16 | Nat_bool_fun$(all_718_1) & Nat$(all_718_0) & ! [v0: Nat$] : ! [v1: % 116.77/16.16 | Nat$] : ( ~ (fun_app$n(all_718_1, v1) = 0) | ~ % 116.77/16.16 | (fun_app$n(all_718_1, v0) = 0) | ~ Nat$(v1) | ~ Nat$(v0) | ? [v2: % 116.77/16.16 | Nat_nat_fun$] : ? [v3: Nat$] : ? [v4: Nat_nat_fun$] : ? [v5: % 116.77/16.16 | Nat$] : (power$(v1) = v4 & power$(v0) = v2 & fun_app$b(v4, % 116.77/16.16 | all_718_0) = v5 & fun_app$b(v2, all_718_0) = v3 & Nat$(v5) & % 116.77/16.16 | Nat$(v3) & Nat_nat_fun$(v4) & Nat_nat_fun$(v2) & ( ~ (v5 = v3) | % 116.77/16.16 | v1 = v0) & ( ~ (v1 = v0) | v5 = v3))) % 116.77/16.16 | % 116.77/16.16 | ALPHA: (84) implies: % 116.77/16.16 | (85) nat$(2) = all_718_0 % 116.77/16.16 | % 116.77/16.16 | DELTA: instantiating (23) with fresh symbols all_724_0, all_724_1, all_724_2, % 116.77/16.16 | all_724_3, all_724_4, all_724_5, all_724_6, all_724_7, all_724_8, % 116.77/16.16 | all_724_9, all_724_10, all_724_11 gives: % 116.77/16.16 | (86) $lesseq(1, $difference(all_724_0, all_724_3)) & nat$($sum(all_724_9, % 116.77/16.16 | 1)) = all_724_8 & nat$(2) = all_724_11 & power$(all_724_6) = % 116.77/16.16 | all_724_5 & power$(all_724_11) = all_724_10 & fun_app$b(all_724_5, % 116.77/16.16 | all_724_2) = all_724_1 & fun_app$b(all_724_5, n$) = all_724_4 & % 116.77/16.16 | fun_app$b(all_724_10, all_724_7) = all_724_6 & fun_app$b(all_724_10, % 116.77/16.16 | all_724_8) = all_724_7 & size$(ys$) = all_724_2 & fun_app$a(of_nat$, % 116.77/16.16 | all_724_1) = all_724_0 & fun_app$a(of_nat$, all_724_4) = all_724_3 & % 116.77/16.16 | fun_app$a(of_nat$, n$) = all_724_9 & Nat$(all_724_1) & Nat$(all_724_2) % 116.77/16.16 | & Nat$(all_724_4) & Nat$(all_724_6) & Nat$(all_724_7) & % 116.77/16.16 | Nat$(all_724_8) & Nat$(all_724_11) & Nat_nat_fun$(all_724_5) & % 116.77/16.16 | Nat_nat_fun$(all_724_10) % 116.77/16.16 | % 116.77/16.16 | ALPHA: (86) implies: % 116.77/16.16 | (87) $lesseq(1, $difference(all_724_0, all_724_3)) % 116.77/16.16 | (88) Nat$(all_724_8) % 116.77/16.16 | (89) Nat$(all_724_7) % 116.77/16.16 | (90) Nat$(all_724_6) % 116.77/16.16 | (91) Nat$(all_724_2) % 116.77/16.16 | (92) fun_app$a(of_nat$, n$) = all_724_9 % 116.77/16.16 | (93) fun_app$a(of_nat$, all_724_4) = all_724_3 % 116.77/16.16 | (94) fun_app$a(of_nat$, all_724_1) = all_724_0 % 116.77/16.16 | (95) size$(ys$) = all_724_2 % 116.77/16.16 | (96) fun_app$b(all_724_10, all_724_8) = all_724_7 % 116.77/16.16 | (97) fun_app$b(all_724_10, all_724_7) = all_724_6 % 116.77/16.16 | (98) fun_app$b(all_724_5, n$) = all_724_4 % 116.77/16.16 | (99) fun_app$b(all_724_5, all_724_2) = all_724_1 % 116.77/16.16 | (100) power$(all_724_11) = all_724_10 % 116.77/16.16 | (101) power$(all_724_6) = all_724_5 % 116.77/16.16 | (102) nat$(2) = all_724_11 % 116.77/16.16 | (103) nat$($sum(all_724_9, 1)) = all_724_8 % 116.77/16.16 | % 116.77/16.16 | DELTA: instantiating (3) with fresh symbol all_742_0 gives: % 116.77/16.16 | (104) nat$(2) = all_742_0 & Nat$(all_742_0) & ! [v0: Nat$] : ! [v1: Nat$] % 116.77/16.16 | : ! [v2: int] : ! [v3: int] : ( ~ ($lesseq(v3, v2)) | ~ % 116.77/16.16 | (fun_app$a(of_nat$, v1) = v2) | ~ (fun_app$a(of_nat$, v0) = v3) | % 116.77/16.16 | ~ Nat$(v1) | ~ Nat$(v0) | ? [v4: Nat_nat_fun$] : ? [v5: Nat$] : % 116.77/16.16 | ? [v6: int] : ? [v7: Nat_nat_fun$] : ? [v8: Nat$] : ? [v9: int] % 116.77/16.16 | : ($lesseq(v9, v6) & power$(v1) = v4 & power$(v0) = v7 & % 116.77/16.16 | fun_app$b(v7, all_742_0) = v8 & fun_app$b(v4, all_742_0) = v5 & % 116.77/16.16 | fun_app$a(of_nat$, v8) = v9 & fun_app$a(of_nat$, v5) = v6 & % 116.77/16.16 | Nat$(v8) & Nat$(v5) & Nat_nat_fun$(v7) & Nat_nat_fun$(v4))) & ! % 116.77/16.17 | [v0: Nat$] : ! [v1: Nat$] : ! [v2: int] : ! [v3: int] : ( ~ % 116.77/16.17 | ($lesseq(1, $difference(v3, v2))) | ~ (fun_app$a(of_nat$, v1) = % 116.77/16.17 | v2) | ~ (fun_app$a(of_nat$, v0) = v3) | ~ Nat$(v1) | ~ % 116.77/16.17 | Nat$(v0) | ? [v4: Nat_nat_fun$] : ? [v5: Nat$] : ? [v6: int] : % 116.77/16.17 | ? [v7: Nat_nat_fun$] : ? [v8: Nat$] : ? [v9: int] : ($lesseq(1, % 116.77/16.17 | $difference(v9, v6)) & power$(v1) = v4 & power$(v0) = v7 & % 116.77/16.17 | fun_app$b(v7, all_742_0) = v8 & fun_app$b(v4, all_742_0) = v5 & % 116.77/16.17 | fun_app$a(of_nat$, v8) = v9 & fun_app$a(of_nat$, v5) = v6 & % 116.77/16.17 | Nat$(v8) & Nat$(v5) & Nat_nat_fun$(v7) & Nat_nat_fun$(v4))) % 116.77/16.17 | % 116.77/16.17 | ALPHA: (104) implies: % 116.77/16.17 | (105) nat$(2) = all_742_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (27) with all_539_2, all_724_9, n$, of_nat$, % 116.77/16.17 | simplifying with (35), (92) gives: % 116.77/16.17 | (106) all_724_9 = all_539_2 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (24) with all_539_1, all_724_2, ys$, simplifying % 116.77/16.17 | with (37), (95) gives: % 116.77/16.17 | (107) all_724_2 = all_539_1 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_560_0, all_563_0, 2, simplifying with % 116.77/16.17 | (43), (45) gives: % 116.77/16.17 | (108) all_563_0 = all_560_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_531_0, all_563_0, 2, simplifying with % 116.77/16.17 | (32), (45) gives: % 116.77/16.17 | (109) all_563_0 = all_531_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_563_0, all_605_0, 2, simplifying with % 116.77/16.17 | (45), (49) gives: % 116.77/16.17 | (110) all_605_0 = all_563_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_549_0, all_605_0, 2, simplifying with % 116.77/16.17 | (41), (49) gives: % 116.77/16.17 | (111) all_605_0 = all_549_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_560_0, all_608_0, 2, simplifying with % 116.77/16.17 | (43), (51) gives: % 116.77/16.17 | (112) all_608_0 = all_560_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_563_0, all_611_1, 2, simplifying with % 116.77/16.17 | (45), (54) gives: % 116.77/16.17 | (113) all_611_1 = all_563_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_611_1, all_614_0, 2, simplifying with % 116.77/16.17 | (54), (57) gives: % 116.77/16.17 | (114) all_614_0 = all_611_1 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_625_0, all_637_0, 2, simplifying with % 116.77/16.17 | (63), (69) gives: % 116.77/16.17 | (115) all_637_0 = all_625_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_622_0, all_637_0, 2, simplifying with % 116.77/16.17 | (61), (69) gives: % 116.77/16.17 | (116) all_637_0 = all_622_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_617_0, all_637_0, 2, simplifying with % 116.77/16.17 | (59), (69) gives: % 116.77/16.17 | (117) all_637_0 = all_617_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_611_1, all_637_0, 2, simplifying with % 116.77/16.17 | (54), (69) gives: % 116.77/16.17 | (118) all_637_0 = all_611_1 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_547_0, all_637_0, 2, simplifying with % 116.77/16.17 | (39), (69) gives: % 116.77/16.17 | (119) all_637_0 = all_547_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_608_0, all_642_0, 2, simplifying with % 116.77/16.17 | (51), (71) gives: % 116.77/16.17 | (120) all_642_0 = all_608_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_631_0, all_645_0, 2, simplifying with % 116.77/16.17 | (67), (73) gives: % 116.77/16.17 | (121) all_645_0 = all_631_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_614_0, all_645_0, 2, simplifying with % 116.77/16.17 | (57), (73) gives: % 116.77/16.17 | (122) all_645_0 = all_614_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_642_0, all_649_0, 2, simplifying with % 116.77/16.17 | (71), (75) gives: % 116.77/16.17 | (123) all_649_0 = all_642_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_631_0, all_655_0, 2, simplifying with % 116.77/16.17 | (67), (77) gives: % 116.77/16.17 | (124) all_655_0 = all_631_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_655_0, all_703_1, 2, simplifying with % 116.77/16.17 | (77), (81) gives: % 116.77/16.17 | (125) all_703_1 = all_655_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_602_0, all_703_1, 2, simplifying with % 116.77/16.17 | (47), (81) gives: % 116.77/16.17 | (126) all_703_1 = all_602_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_649_0, all_718_0, 2, simplifying with % 116.77/16.17 | (75), (85) gives: % 116.77/16.17 | (127) all_718_0 = all_649_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_520_0, all_718_0, 2, simplifying with % 116.77/16.17 | (29), (85) gives: % 116.77/16.17 | (128) all_718_0 = all_520_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_658_0, all_724_11, 2, simplifying % 116.77/16.17 | with (79), (102) gives: % 116.77/16.17 | (129) all_724_11 = all_658_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_645_0, all_724_11, 2, simplifying % 116.77/16.17 | with (73), (102) gives: % 116.77/16.17 | (130) all_724_11 = all_645_0 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_724_11, all_742_0, 2, simplifying % 116.77/16.17 | with (102), (105) gives: % 116.77/16.17 | (131) all_742_0 = all_724_11 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_709_1, all_742_0, 2, simplifying with % 116.77/16.17 | (83), (105) gives: % 116.77/16.17 | (132) all_742_0 = all_709_1 % 116.77/16.17 | % 116.77/16.17 | GROUND_INST: instantiating (26) with all_628_0, all_742_0, 2, simplifying with % 116.77/16.17 | (65), (105) gives: % 116.77/16.17 | (133) all_742_0 = all_628_0 % 116.77/16.17 | % 116.77/16.17 | COMBINE_EQS: (132), (133) imply: % 116.77/16.17 | (134) all_709_1 = all_628_0 % 116.77/16.17 | % 116.77/16.17 | COMBINE_EQS: (131), (132) imply: % 116.77/16.17 | (135) all_724_11 = all_709_1 % 116.77/16.17 | % 116.77/16.17 | SIMP: (135) implies: % 116.77/16.17 | (136) all_724_11 = all_709_1 % 116.77/16.17 | % 116.77/16.17 | COMBINE_EQS: (129), (130) imply: % 116.77/16.17 | (137) all_658_0 = all_645_0 % 116.77/16.17 | % 116.77/16.17 | COMBINE_EQS: (129), (136) imply: % 116.77/16.17 | (138) all_709_1 = all_658_0 % 116.77/16.17 | % 116.77/16.17 | SIMP: (138) implies: % 116.77/16.17 | (139) all_709_1 = all_658_0 % 116.77/16.17 | % 116.77/16.17 | COMBINE_EQS: (127), (128) imply: % 116.77/16.17 | (140) all_649_0 = all_520_0 % 116.77/16.17 | % 116.77/16.17 | SIMP: (140) implies: % 116.77/16.17 | (141) all_649_0 = all_520_0 % 116.77/16.17 | % 116.77/16.17 | COMBINE_EQS: (134), (139) imply: % 116.77/16.17 | (142) all_658_0 = all_628_0 % 116.77/16.17 | % 116.77/16.17 | SIMP: (142) implies: % 116.77/16.17 | (143) all_658_0 = all_628_0 % 116.77/16.17 | % 116.77/16.17 | COMBINE_EQS: (125), (126) imply: % 116.77/16.17 | (144) all_655_0 = all_602_0 % 116.77/16.17 | % 116.77/16.17 | SIMP: (144) implies: % 116.77/16.17 | (145) all_655_0 = all_602_0 % 116.77/16.17 | % 116.77/16.17 | COMBINE_EQS: (137), (143) imply: % 116.77/16.17 | (146) all_645_0 = all_628_0 % 116.77/16.17 | % 116.77/16.17 | SIMP: (146) implies: % 116.77/16.17 | (147) all_645_0 = all_628_0 % 116.77/16.17 | % 116.77/16.17 | COMBINE_EQS: (124), (145) imply: % 116.77/16.17 | (148) all_631_0 = all_602_0 % 116.77/16.17 | % 116.77/16.17 | SIMP: (148) implies: % 116.77/16.17 | (149) all_631_0 = all_602_0 % 116.77/16.17 | % 116.77/16.17 | COMBINE_EQS: (123), (141) imply: % 116.77/16.17 | (150) all_642_0 = all_520_0 % 116.77/16.17 | % 116.77/16.17 | SIMP: (150) implies: % 116.77/16.17 | (151) all_642_0 = all_520_0 % 116.77/16.17 | % 116.77/16.17 | COMBINE_EQS: (122), (147) imply: % 116.77/16.17 | (152) all_628_0 = all_614_0 % 116.77/16.17 | % 116.77/16.17 | COMBINE_EQS: (121), (147) imply: % 116.77/16.17 | (153) all_631_0 = all_628_0 % 116.77/16.17 | % 116.77/16.17 | SIMP: (153) implies: % 116.77/16.17 | (154) all_631_0 = all_628_0 % 116.77/16.17 | % 116.77/16.17 | COMBINE_EQS: (120), (151) imply: % 116.77/16.18 | (155) all_608_0 = all_520_0 % 116.77/16.18 | % 116.77/16.18 | SIMP: (155) implies: % 116.77/16.18 | (156) all_608_0 = all_520_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (115), (118) imply: % 116.77/16.18 | (157) all_625_0 = all_611_1 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (115), (116) imply: % 116.77/16.18 | (158) all_625_0 = all_622_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (115), (119) imply: % 116.77/16.18 | (159) all_625_0 = all_547_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (115), (117) imply: % 116.77/16.18 | (160) all_625_0 = all_617_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (149), (154) imply: % 116.77/16.18 | (161) all_628_0 = all_602_0 % 116.77/16.18 | % 116.77/16.18 | SIMP: (161) implies: % 116.77/16.18 | (162) all_628_0 = all_602_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (152), (162) imply: % 116.77/16.18 | (163) all_614_0 = all_602_0 % 116.77/16.18 | % 116.77/16.18 | SIMP: (163) implies: % 116.77/16.18 | (164) all_614_0 = all_602_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (158), (159) imply: % 116.77/16.18 | (165) all_622_0 = all_547_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (158), (160) imply: % 116.77/16.18 | (166) all_622_0 = all_617_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (157), (158) imply: % 116.77/16.18 | (167) all_622_0 = all_611_1 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (166), (167) imply: % 116.77/16.18 | (168) all_617_0 = all_611_1 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (165), (166) imply: % 116.77/16.18 | (169) all_617_0 = all_547_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (168), (169) imply: % 116.77/16.18 | (170) all_611_1 = all_547_0 % 116.77/16.18 | % 116.77/16.18 | SIMP: (170) implies: % 116.77/16.18 | (171) all_611_1 = all_547_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (114), (164) imply: % 116.77/16.18 | (172) all_611_1 = all_602_0 % 116.77/16.18 | % 116.77/16.18 | SIMP: (172) implies: % 116.77/16.18 | (173) all_611_1 = all_602_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (113), (173) imply: % 116.77/16.18 | (174) all_602_0 = all_563_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (171), (173) imply: % 116.77/16.18 | (175) all_602_0 = all_547_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (112), (156) imply: % 116.77/16.18 | (176) all_560_0 = all_520_0 % 116.77/16.18 | % 116.77/16.18 | SIMP: (176) implies: % 116.77/16.18 | (177) all_560_0 = all_520_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (110), (111) imply: % 116.77/16.18 | (178) all_563_0 = all_549_0 % 116.77/16.18 | % 116.77/16.18 | SIMP: (178) implies: % 116.77/16.18 | (179) all_563_0 = all_549_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (174), (175) imply: % 116.77/16.18 | (180) all_563_0 = all_547_0 % 116.77/16.18 | % 116.77/16.18 | SIMP: (180) implies: % 116.77/16.18 | (181) all_563_0 = all_547_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (108), (179) imply: % 116.77/16.18 | (182) all_560_0 = all_549_0 % 116.77/16.18 | % 116.77/16.18 | SIMP: (182) implies: % 116.77/16.18 | (183) all_560_0 = all_549_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (109), (179) imply: % 116.77/16.18 | (184) all_549_0 = all_531_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (179), (181) imply: % 116.77/16.18 | (185) all_549_0 = all_547_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (177), (183) imply: % 116.77/16.18 | (186) all_549_0 = all_520_0 % 116.77/16.18 | % 116.77/16.18 | SIMP: (186) implies: % 116.77/16.18 | (187) all_549_0 = all_520_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (184), (185) imply: % 116.77/16.18 | (188) all_547_0 = all_531_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (185), (187) imply: % 116.77/16.18 | (189) all_547_0 = all_520_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (188), (189) imply: % 116.77/16.18 | (190) all_531_0 = all_520_0 % 116.77/16.18 | % 116.77/16.18 | SIMP: (190) implies: % 116.77/16.18 | (191) all_531_0 = all_520_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (175), (189) imply: % 116.77/16.18 | (192) all_602_0 = all_520_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (173), (192) imply: % 116.77/16.18 | (193) all_611_1 = all_520_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (162), (192) imply: % 116.77/16.18 | (194) all_628_0 = all_520_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (143), (194) imply: % 116.77/16.18 | (195) all_658_0 = all_520_0 % 116.77/16.18 | % 116.77/16.18 | COMBINE_EQS: (129), (195) imply: % 116.77/16.18 | (196) all_724_11 = all_520_0 % 116.77/16.18 | % 116.77/16.18 | REDUCE: (103), (106) imply: % 116.77/16.18 | (197) nat$($sum(all_539_2, 1)) = all_724_8 % 116.77/16.18 | % 116.77/16.18 | REDUCE: (100), (196) imply: % 116.77/16.18 | (198) power$(all_520_0) = all_724_10 % 116.77/16.18 | % 116.77/16.18 | REDUCE: (53), (193) imply: % 116.77/16.18 | (199) power$(all_520_0) = all_611_0 % 116.77/16.18 | % 116.77/16.18 | REDUCE: (99), (107) imply: % 116.77/16.18 | (200) fun_app$b(all_724_5, all_539_1) = all_724_1 % 116.77/16.18 | % 116.77/16.18 | REDUCE: (91), (107) imply: % 116.77/16.18 | (201) Nat$(all_539_1) % 116.77/16.18 | % 116.77/16.18 | REDUCE: (31), (191) imply: % 116.77/16.18 | (202) Nat$(all_520_0) % 116.77/16.18 | % 116.77/16.18 | GROUND_INST: instantiating (25) with all_611_0, all_724_10, all_520_0, % 116.77/16.18 | simplifying with (198), (199) gives: % 116.77/16.18 | (203) all_724_10 = all_611_0 % 116.77/16.18 | % 116.77/16.18 | REDUCE: (97), (203) imply: % 116.77/16.18 | (204) fun_app$b(all_611_0, all_724_7) = all_724_6 % 116.77/16.18 | % 116.77/16.18 | REDUCE: (96), (203) imply: % 116.77/16.18 | (205) fun_app$b(all_611_0, all_724_8) = all_724_7 % 116.77/16.18 | % 116.77/16.18 | GROUND_INST: instantiating (20) with all_539_1, all_539_0, simplifying with % 116.77/16.18 | (36), (201) gives: % 116.77/16.18 | (206) $lesseq(0, all_539_0) % 116.77/16.18 | % 116.77/16.18 | GROUND_INST: instantiating (55) with all_724_8, all_724_7, simplifying with % 116.77/16.18 | (88), (205) gives: % 116.77/16.18 | (207) ? [v0: int] : ? [v1: int] : ($lesseq(1, $difference(v0, v1)) & % 116.77/16.18 | fun_app$a(of_nat$, all_724_7) = v0 & fun_app$a(of_nat$, all_724_8) % 116.77/16.18 | = v1) % 116.77/16.18 | % 116.77/16.18 | GROUND_INST: instantiating (55) with all_724_7, all_724_6, simplifying with % 116.77/16.18 | (89), (204) gives: % 116.77/16.18 | (208) ? [v0: int] : ? [v1: int] : ($lesseq(1, $difference(v0, v1)) & % 116.77/16.18 | fun_app$a(of_nat$, all_724_6) = v0 & fun_app$a(of_nat$, all_724_7) % 116.77/16.18 | = v1) % 116.77/16.18 | % 116.77/16.18 | GROUND_INST: instantiating (18) with all_724_7, all_724_7, all_520_0, % 116.77/16.18 | all_611_0, all_724_6, all_724_6, simplifying with (89), (199), % 116.77/16.18 | (202), (204) gives: % 116.77/16.18 | (209) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 116.77/16.18 | (fun_app$a(of_nat$, all_724_6) = v3 & fun_app$a(of_nat$, all_724_6) = % 116.77/16.18 | v2 & fun_app$a(of_nat$, all_724_7) = v1 & fun_app$a(of_nat$, % 116.77/16.18 | all_724_7) = v0 & ( ~ ($lesseq(1, $difference(v3, v2))) | ~ % 116.77/16.18 | ($lesseq(v0, v1)) | ~ ($lesseq(1, v0)))) % 116.77/16.18 | % 116.77/16.18 | GROUND_INST: instantiating (16) with all_520_0, all_724_7, all_724_7, % 116.77/16.18 | all_611_0, all_724_6, all_724_6, simplifying with (89), (199), % 116.77/16.18 | (202), (204) gives: % 116.77/16.18 | (210) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: % 116.77/16.18 | int] : (fun_app$a(of_nat$, all_724_6) = v2 & fun_app$a(of_nat$, % 116.77/16.18 | all_724_6) = v1 & fun_app$a(of_nat$, all_724_7) = v4 & % 116.77/16.18 | fun_app$a(of_nat$, all_724_7) = v3 & fun_app$a(of_nat$, all_520_0) % 116.77/16.18 | = v0 & ( ~ ($lesseq(v3, v4)) | ~ ($lesseq(1, $difference(v1, v2))) % 116.77/16.18 | | ~ ($lesseq(1, v0)))) % 116.77/16.18 | % 116.77/16.18 | GROUND_INST: instantiating (18) with all_724_8, all_724_7, all_520_0, % 116.77/16.18 | all_611_0, all_724_6, all_724_7, simplifying with (88), (89), % 116.77/16.18 | (199), (202), (204), (205) gives: % 116.77/16.19 | (211) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 116.77/16.19 | (fun_app$a(of_nat$, all_724_6) = v2 & fun_app$a(of_nat$, all_724_7) = % 116.77/16.19 | v3 & fun_app$a(of_nat$, all_724_7) = v1 & fun_app$a(of_nat$, % 116.77/16.19 | all_724_8) = v0 & ( ~ ($lesseq(1, $difference(v3, v2))) | ~ % 116.77/16.19 | ($lesseq(v0, v1)) | ~ ($lesseq(1, v0)))) % 116.77/16.19 | % 116.77/16.19 | GROUND_INST: instantiating (16) with all_520_0, all_724_8, all_724_7, % 116.77/16.19 | all_611_0, all_724_6, all_724_7, simplifying with (88), (89), % 116.77/16.19 | (199), (202), (204), (205) gives: % 116.77/16.19 | (212) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: % 116.77/16.19 | int] : (fun_app$a(of_nat$, all_724_6) = v1 & fun_app$a(of_nat$, % 116.77/16.19 | all_724_7) = v3 & fun_app$a(of_nat$, all_724_7) = v2 & % 116.77/16.19 | fun_app$a(of_nat$, all_724_8) = v4 & fun_app$a(of_nat$, all_520_0) % 116.77/16.19 | = v0 & ( ~ ($lesseq(v3, v4)) | ~ ($lesseq(1, $difference(v1, v2))) % 116.77/16.19 | | ~ ($lesseq(1, v0)))) % 116.77/16.19 | % 116.77/16.19 | GROUND_INST: instantiating (15) with all_520_0, all_724_7, all_611_0, % 116.77/16.19 | all_724_6, simplifying with (89), (199), (202), (204) gives: % 116.77/16.19 | (213) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 116.77/16.19 | all_724_6) = v2 & fun_app$a(of_nat$, all_724_7) = v1 & % 116.77/16.19 | fun_app$a(of_nat$, all_520_0) = v0 & ( ~ ($lesseq(v2, 0) | ( ~ (v1 % 116.77/16.19 | = 0) & $lesseq(v0, 0)))) % 116.77/16.19 | % 116.77/16.19 | GROUND_INST: instantiating (7) with all_520_0, all_724_7, all_611_0, % 116.77/16.19 | all_724_6, simplifying with (89), (199), (202), (204) gives: % 116.77/16.19 | (214) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 116.77/16.19 | all_724_6) = v2 & fun_app$a(of_nat$, all_724_7) = v0 & % 116.77/16.19 | fun_app$a(of_nat$, all_520_0) = v1 & (v2 = 1 | ( ~ (v1 = 1) & ~ % 116.77/16.19 | (v0 = 0)))) % 116.77/16.19 | % 116.77/16.19 | GROUND_INST: instantiating (2) with all_520_0, all_724_7, all_611_0, % 116.77/16.19 | all_724_6, simplifying with (89), (199), (202), (204) gives: % 116.77/16.19 | (215) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 116.77/16.19 | all_724_6) = v1 & fun_app$a(of_nat$, all_724_7) = v2 & % 116.77/16.19 | fun_app$a(of_nat$, all_520_0) = v0 & ( ~ ($lesseq(1, % 116.77/16.19 | $difference(v2, v1))) | ~ ($lesseq(2, v0)))) % 116.77/16.19 | % 116.77/16.19 | GROUND_INST: instantiating (17) with all_520_0, all_724_7, all_611_0, % 116.77/16.19 | all_724_6, simplifying with (89), (199), (202), (204) gives: % 116.77/16.19 | (216) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 116.77/16.19 | all_724_6) = v1 & fun_app$a(of_nat$, all_724_7) = v2 & % 116.77/16.19 | fun_app$a(of_nat$, all_520_0) = v0 & ( ~ ($lesseq(v1, v2)) | ~ % 116.77/16.19 | ($lesseq(2, v0)))) % 116.77/16.19 | % 116.77/16.19 | GROUND_INST: instantiating (14) with all_520_0, all_724_7, all_611_0, % 116.77/16.19 | all_724_6, simplifying with (89), (199), (202), (204) gives: % 117.10/16.19 | (217) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.19 | all_724_6) = v0 & fun_app$a(of_nat$, all_724_7) = v2 & % 117.10/16.19 | fun_app$a(of_nat$, all_520_0) = v1 & (v2 = 0 | ~ ($lesseq(v1, 0) | % 117.10/16.19 | ~ ($lesseq(1, v0)))) % 117.10/16.19 | % 117.10/16.19 | GROUND_INST: instantiating (6) with all_520_0, all_724_7, all_611_0, % 117.10/16.19 | all_724_6, simplifying with (89), (199), (202), (204) gives: % 117.10/16.19 | (218) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.19 | all_724_6) = v0 & fun_app$a(of_nat$, all_724_7) = v1 & % 117.10/16.19 | fun_app$a(of_nat$, all_520_0) = v2 & ( ~ (v0 = 1) | v2 = 1 | v1 = % 117.10/16.19 | 0)) % 117.10/16.19 | % 117.10/16.19 | GROUND_INST: instantiating (9) with all_520_0, all_724_7, all_611_0, % 117.10/16.19 | all_724_6, simplifying with (89), (199), (202), (204) gives: % 117.10/16.19 | (219) ? [v0: int] : ? [v1: int] : (fun_app$a(of_nat$, all_724_6) = v1 & % 117.10/16.19 | fun_app$a(of_nat$, all_520_0) = v0 & ( ~ ($lesseq(v1, 0) | ~ % 117.10/16.19 | ($lesseq(1, v0)))) % 117.10/16.19 | % 117.10/16.19 | GROUND_INST: instantiating (18) with all_724_7, all_724_8, all_520_0, % 117.10/16.19 | all_611_0, all_724_7, all_724_6, simplifying with (88), (89), % 117.10/16.19 | (199), (202), (204), (205) gives: % 117.10/16.19 | (220) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 117.10/16.19 | (fun_app$a(of_nat$, all_724_6) = v3 & fun_app$a(of_nat$, all_724_7) = % 117.10/16.19 | v2 & fun_app$a(of_nat$, all_724_7) = v0 & fun_app$a(of_nat$, % 117.10/16.19 | all_724_8) = v1 & ( ~ ($lesseq(1, $difference(v3, v2))) | ~ % 117.10/16.19 | ($lesseq(v0, v1)) | ~ ($lesseq(1, v0)))) % 117.10/16.19 | % 117.10/16.19 | GROUND_INST: instantiating (16) with all_520_0, all_724_7, all_724_8, % 117.10/16.19 | all_611_0, all_724_7, all_724_6, simplifying with (88), (89), % 117.10/16.19 | (199), (202), (204), (205) gives: % 117.10/16.19 | (221) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: % 117.10/16.19 | int] : (fun_app$a(of_nat$, all_724_6) = v2 & fun_app$a(of_nat$, % 117.10/16.19 | all_724_7) = v4 & fun_app$a(of_nat$, all_724_7) = v1 & % 117.10/16.19 | fun_app$a(of_nat$, all_724_8) = v3 & fun_app$a(of_nat$, all_520_0) % 117.10/16.19 | = v0 & ( ~ ($lesseq(v3, v4)) | ~ ($lesseq(1, $difference(v1, v2))) % 117.10/16.19 | | ~ ($lesseq(1, v0)))) % 117.10/16.19 | % 117.10/16.19 | GROUND_INST: instantiating (18) with all_724_8, all_724_8, all_520_0, % 117.10/16.19 | all_611_0, all_724_7, all_724_7, simplifying with (88), (199), % 117.10/16.19 | (202), (205) gives: % 117.10/16.19 | (222) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 117.10/16.19 | (fun_app$a(of_nat$, all_724_7) = v3 & fun_app$a(of_nat$, all_724_7) = % 117.10/16.19 | v2 & fun_app$a(of_nat$, all_724_8) = v1 & fun_app$a(of_nat$, % 117.10/16.19 | all_724_8) = v0 & ( ~ ($lesseq(1, $difference(v3, v2))) | ~ % 117.10/16.19 | ($lesseq(v0, v1)) | ~ ($lesseq(1, v0)))) % 117.10/16.19 | % 117.10/16.19 | GROUND_INST: instantiating (16) with all_520_0, all_724_8, all_724_8, % 117.10/16.19 | all_611_0, all_724_7, all_724_7, simplifying with (88), (199), % 117.10/16.19 | (202), (205) gives: % 117.10/16.19 | (223) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: % 117.10/16.19 | int] : (fun_app$a(of_nat$, all_724_7) = v2 & fun_app$a(of_nat$, % 117.10/16.19 | all_724_7) = v1 & fun_app$a(of_nat$, all_724_8) = v4 & % 117.10/16.19 | fun_app$a(of_nat$, all_724_8) = v3 & fun_app$a(of_nat$, all_520_0) % 117.10/16.19 | = v0 & ( ~ ($lesseq(v3, v4)) | ~ ($lesseq(1, $difference(v1, v2))) % 117.10/16.19 | | ~ ($lesseq(1, v0)))) % 117.10/16.19 | % 117.10/16.19 | GROUND_INST: instantiating (15) with all_520_0, all_724_8, all_611_0, % 117.10/16.19 | all_724_7, simplifying with (88), (199), (202), (205) gives: % 117.10/16.19 | (224) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.19 | all_724_7) = v2 & fun_app$a(of_nat$, all_724_8) = v1 & % 117.10/16.19 | fun_app$a(of_nat$, all_520_0) = v0 & ( ~ ($lesseq(v2, 0) | ( ~ (v1 % 117.10/16.19 | = 0) & $lesseq(v0, 0)))) % 117.10/16.19 | % 117.10/16.19 | GROUND_INST: instantiating (7) with all_520_0, all_724_8, all_611_0, % 117.10/16.19 | all_724_7, simplifying with (88), (199), (202), (205) gives: % 117.10/16.19 | (225) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.19 | all_724_7) = v2 & fun_app$a(of_nat$, all_724_8) = v0 & % 117.10/16.19 | fun_app$a(of_nat$, all_520_0) = v1 & (v2 = 1 | ( ~ (v1 = 1) & ~ % 117.10/16.19 | (v0 = 0)))) % 117.10/16.19 | % 117.10/16.20 | GROUND_INST: instantiating (2) with all_520_0, all_724_8, all_611_0, % 117.10/16.20 | all_724_7, simplifying with (88), (199), (202), (205) gives: % 117.10/16.20 | (226) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.20 | all_724_7) = v1 & fun_app$a(of_nat$, all_724_8) = v2 & % 117.10/16.20 | fun_app$a(of_nat$, all_520_0) = v0 & ( ~ ($lesseq(1, % 117.10/16.20 | $difference(v2, v1))) | ~ ($lesseq(2, v0)))) % 117.10/16.20 | % 117.10/16.20 | GROUND_INST: instantiating (17) with all_520_0, all_724_8, all_611_0, % 117.10/16.20 | all_724_7, simplifying with (88), (199), (202), (205) gives: % 117.10/16.20 | (227) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.20 | all_724_7) = v1 & fun_app$a(of_nat$, all_724_8) = v2 & % 117.10/16.20 | fun_app$a(of_nat$, all_520_0) = v0 & ( ~ ($lesseq(v1, v2)) | ~ % 117.10/16.20 | ($lesseq(2, v0)))) % 117.10/16.20 | % 117.10/16.20 | GROUND_INST: instantiating (14) with all_520_0, all_724_8, all_611_0, % 117.10/16.20 | all_724_7, simplifying with (88), (199), (202), (205) gives: % 117.10/16.20 | (228) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.20 | all_724_7) = v0 & fun_app$a(of_nat$, all_724_8) = v2 & % 117.10/16.20 | fun_app$a(of_nat$, all_520_0) = v1 & (v2 = 0 | ~ ($lesseq(v1, 0) | % 117.10/16.20 | ~ ($lesseq(1, v0)))) % 117.10/16.20 | % 117.10/16.20 | GROUND_INST: instantiating (6) with all_520_0, all_724_8, all_611_0, % 117.10/16.20 | all_724_7, simplifying with (88), (199), (202), (205) gives: % 117.10/16.20 | (229) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.20 | all_724_7) = v0 & fun_app$a(of_nat$, all_724_8) = v1 & % 117.10/16.20 | fun_app$a(of_nat$, all_520_0) = v2 & ( ~ (v0 = 1) | v2 = 1 | v1 = % 117.10/16.20 | 0)) % 117.10/16.20 | % 117.10/16.20 | GROUND_INST: instantiating (9) with all_520_0, all_724_8, all_611_0, % 117.10/16.20 | all_724_7, simplifying with (88), (199), (202), (205) gives: % 117.10/16.20 | (230) ? [v0: int] : ? [v1: int] : (fun_app$a(of_nat$, all_724_7) = v1 & % 117.10/16.20 | fun_app$a(of_nat$, all_520_0) = v0 & ( ~ ($lesseq(v1, 0) | ~ % 117.10/16.20 | ($lesseq(1, v0)))) % 117.10/16.20 | % 117.10/16.20 | GROUND_INST: instantiating (16) with all_724_6, all_539_1, all_539_1, % 117.10/16.20 | all_724_5, all_724_1, all_724_1, simplifying with (90), (101), % 117.10/16.20 | (200), (201) gives: % 117.10/16.20 | (231) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: % 117.10/16.20 | int] : (fun_app$a(of_nat$, all_724_1) = v2 & fun_app$a(of_nat$, % 117.10/16.20 | all_724_1) = v1 & fun_app$a(of_nat$, all_724_6) = v0 & % 117.10/16.20 | fun_app$a(of_nat$, all_539_1) = v4 & fun_app$a(of_nat$, all_539_1) % 117.10/16.20 | = v3 & ( ~ ($lesseq(v3, v4)) | ~ ($lesseq(1, $difference(v1, v2))) % 117.10/16.20 | | ~ ($lesseq(1, v0)))) % 117.10/16.20 | % 117.10/16.20 | GROUND_INST: instantiating (16) with all_724_6, n$, all_539_1, all_724_5, % 117.10/16.20 | all_724_1, all_724_4, simplifying with (22), (90), (98), (101), % 117.10/16.20 | (200), (201) gives: % 117.10/16.20 | (232) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: % 117.10/16.20 | int] : (fun_app$a(of_nat$, all_724_1) = v1 & fun_app$a(of_nat$, % 117.10/16.20 | all_724_4) = v2 & fun_app$a(of_nat$, all_724_6) = v0 & % 117.10/16.20 | fun_app$a(of_nat$, all_539_1) = v3 & fun_app$a(of_nat$, n$) = v4 & % 117.10/16.20 | ( ~ ($lesseq(v3, v4)) | ~ ($lesseq(1, $difference(v1, v2))) | ~ % 117.10/16.20 | ($lesseq(1, v0)))) % 117.10/16.20 | % 117.10/16.20 | GROUND_INST: instantiating (15) with all_724_6, all_539_1, all_724_5, % 117.10/16.20 | all_724_1, simplifying with (90), (101), (200), (201) gives: % 117.10/16.20 | (233) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.20 | all_724_1) = v2 & fun_app$a(of_nat$, all_724_6) = v0 & % 117.10/16.20 | fun_app$a(of_nat$, all_539_1) = v1 & ( ~ ($lesseq(v2, 0) | ( ~ (v1 % 117.10/16.20 | = 0) & $lesseq(v0, 0)))) % 117.10/16.20 | % 117.10/16.20 | GROUND_INST: instantiating (7) with all_724_6, all_539_1, all_724_5, % 117.10/16.20 | all_724_1, simplifying with (90), (101), (200), (201) gives: % 117.10/16.20 | (234) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.20 | all_724_1) = v2 & fun_app$a(of_nat$, all_724_6) = v1 & % 117.10/16.20 | fun_app$a(of_nat$, all_539_1) = v0 & (v2 = 1 | ( ~ (v1 = 1) & ~ % 117.10/16.20 | (v0 = 0)))) % 117.10/16.20 | % 117.10/16.20 | GROUND_INST: instantiating (2) with all_724_6, all_539_1, all_724_5, % 117.10/16.20 | all_724_1, simplifying with (90), (101), (200), (201) gives: % 117.10/16.20 | (235) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.20 | all_724_1) = v1 & fun_app$a(of_nat$, all_724_6) = v0 & % 117.10/16.20 | fun_app$a(of_nat$, all_539_1) = v2 & ( ~ ($lesseq(1, % 117.10/16.20 | $difference(v2, v1))) | ~ ($lesseq(2, v0)))) % 117.10/16.20 | % 117.10/16.20 | GROUND_INST: instantiating (17) with all_724_6, all_539_1, all_724_5, % 117.10/16.20 | all_724_1, simplifying with (90), (101), (200), (201) gives: % 117.10/16.20 | (236) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.20 | all_724_1) = v1 & fun_app$a(of_nat$, all_724_6) = v0 & % 117.10/16.20 | fun_app$a(of_nat$, all_539_1) = v2 & ( ~ ($lesseq(v1, v2)) | ~ % 117.10/16.20 | ($lesseq(2, v0)))) % 117.10/16.20 | % 117.10/16.20 | GROUND_INST: instantiating (14) with all_724_6, all_539_1, all_724_5, % 117.10/16.20 | all_724_1, simplifying with (90), (101), (200), (201) gives: % 117.10/16.20 | (237) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.20 | all_724_1) = v0 & fun_app$a(of_nat$, all_724_6) = v1 & % 117.10/16.20 | fun_app$a(of_nat$, all_539_1) = v2 & (v2 = 0 | ~ ($lesseq(v1, 0) | % 117.10/16.20 | ~ ($lesseq(1, v0)))) % 117.10/16.20 | % 117.10/16.20 | GROUND_INST: instantiating (6) with all_724_6, all_539_1, all_724_5, % 117.10/16.20 | all_724_1, simplifying with (90), (101), (200), (201) gives: % 117.10/16.20 | (238) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.20 | all_724_1) = v0 & fun_app$a(of_nat$, all_724_6) = v2 & % 117.10/16.20 | fun_app$a(of_nat$, all_539_1) = v1 & ( ~ (v0 = 1) | v2 = 1 | v1 = % 117.10/16.20 | 0)) % 117.10/16.20 | % 117.10/16.20 | GROUND_INST: instantiating (18) with all_539_1, n$, all_724_6, all_724_5, % 117.10/16.20 | all_724_4, all_724_1, simplifying with (22), (90), (98), (101), % 117.10/16.20 | (200), (201) gives: % 117.10/16.20 | (239) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 117.10/16.20 | (fun_app$a(of_nat$, all_724_1) = v3 & fun_app$a(of_nat$, all_724_4) = % 117.10/16.20 | v2 & fun_app$a(of_nat$, all_539_1) = v0 & fun_app$a(of_nat$, n$) = % 117.10/16.20 | v1 & ( ~ ($lesseq(1, $difference(v3, v2))) | ~ ($lesseq(v0, v1)) | % 117.10/16.20 | ~ ($lesseq(1, v0)))) % 117.10/16.20 | % 117.10/16.20 | GROUND_INST: instantiating (16) with all_724_6, all_539_1, n$, all_724_5, % 117.10/16.20 | all_724_4, all_724_1, simplifying with (22), (90), (98), (101), % 117.10/16.20 | (200), (201) gives: % 117.10/16.21 | (240) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: % 117.10/16.21 | int] : (fun_app$a(of_nat$, all_724_1) = v2 & fun_app$a(of_nat$, % 117.10/16.21 | all_724_4) = v1 & fun_app$a(of_nat$, all_724_6) = v0 & % 117.10/16.21 | fun_app$a(of_nat$, all_539_1) = v4 & fun_app$a(of_nat$, n$) = v3 & % 117.10/16.21 | ( ~ ($lesseq(v3, v4)) | ~ ($lesseq(1, $difference(v1, v2))) | ~ % 117.10/16.21 | ($lesseq(1, v0)))) % 117.10/16.21 | % 117.10/16.21 | GROUND_INST: instantiating (16) with all_724_6, n$, n$, all_724_5, all_724_4, % 117.10/16.21 | all_724_4, simplifying with (22), (90), (98), (101) gives: % 117.10/16.21 | (241) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: % 117.10/16.21 | int] : (fun_app$a(of_nat$, all_724_4) = v2 & fun_app$a(of_nat$, % 117.10/16.21 | all_724_4) = v1 & fun_app$a(of_nat$, all_724_6) = v0 & % 117.10/16.21 | fun_app$a(of_nat$, n$) = v4 & fun_app$a(of_nat$, n$) = v3 & ( ~ % 117.10/16.21 | ($lesseq(v3, v4)) | ~ ($lesseq(1, $difference(v1, v2))) | ~ % 117.10/16.21 | ($lesseq(1, v0)))) % 117.10/16.21 | % 117.10/16.21 | GROUND_INST: instantiating (15) with all_724_6, n$, all_724_5, all_724_4, % 117.10/16.21 | simplifying with (22), (90), (98), (101) gives: % 117.10/16.21 | (242) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.21 | all_724_4) = v2 & fun_app$a(of_nat$, all_724_6) = v0 & % 117.10/16.21 | fun_app$a(of_nat$, n$) = v1 & ( ~ ($lesseq(v2, 0) | ( ~ (v1 = 0) & % 117.10/16.21 | $lesseq(v0, 0)))) % 117.10/16.21 | % 117.10/16.21 | GROUND_INST: instantiating (7) with all_724_6, n$, all_724_5, all_724_4, % 117.10/16.21 | simplifying with (22), (90), (98), (101) gives: % 117.10/16.21 | (243) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.21 | all_724_4) = v2 & fun_app$a(of_nat$, all_724_6) = v1 & % 117.10/16.21 | fun_app$a(of_nat$, n$) = v0 & (v2 = 1 | ( ~ (v1 = 1) & ~ (v0 = % 117.10/16.21 | 0)))) % 117.10/16.21 | % 117.10/16.21 | GROUND_INST: instantiating (2) with all_724_6, n$, all_724_5, all_724_4, % 117.10/16.21 | simplifying with (22), (90), (98), (101) gives: % 117.10/16.21 | (244) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.21 | all_724_4) = v1 & fun_app$a(of_nat$, all_724_6) = v0 & % 117.10/16.21 | fun_app$a(of_nat$, n$) = v2 & ( ~ ($lesseq(1, $difference(v2, v1))) % 117.10/16.21 | | ~ ($lesseq(2, v0)))) % 117.10/16.21 | % 117.10/16.21 | GROUND_INST: instantiating (17) with all_724_6, n$, all_724_5, all_724_4, % 117.10/16.21 | simplifying with (22), (90), (98), (101) gives: % 117.10/16.21 | (245) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.21 | all_724_4) = v1 & fun_app$a(of_nat$, all_724_6) = v0 & % 117.10/16.21 | fun_app$a(of_nat$, n$) = v2 & ( ~ ($lesseq(v1, v2)) | ~ % 117.10/16.21 | ($lesseq(2, v0)))) % 117.10/16.21 | % 117.10/16.21 | GROUND_INST: instantiating (14) with all_724_6, n$, all_724_5, all_724_4, % 117.10/16.21 | simplifying with (22), (90), (98), (101) gives: % 117.10/16.21 | (246) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.21 | all_724_4) = v0 & fun_app$a(of_nat$, all_724_6) = v1 & % 117.10/16.21 | fun_app$a(of_nat$, n$) = v2 & (v2 = 0 | ~ ($lesseq(v1, 0) | ~ % 117.10/16.21 | ($lesseq(1, v0)))) % 117.10/16.21 | % 117.10/16.21 | GROUND_INST: instantiating (6) with all_724_6, n$, all_724_5, all_724_4, % 117.10/16.21 | simplifying with (22), (90), (98), (101) gives: % 117.10/16.21 | (247) ? [v0: int] : ? [v1: int] : ? [v2: int] : (fun_app$a(of_nat$, % 117.10/16.21 | all_724_4) = v0 & fun_app$a(of_nat$, all_724_6) = v2 & % 117.10/16.21 | fun_app$a(of_nat$, n$) = v1 & ( ~ (v0 = 1) | v2 = 1 | v1 = 0)) % 117.10/16.21 | % 117.10/16.21 | GROUND_INST: instantiating (21) with $sum(all_539_2, 1), all_724_8, % 117.10/16.21 | simplifying with (197) gives: % 117.10/16.21 | (248) ~ ($lesseq(-1, all_539_2)) | fun_app$a(of_nat$, all_724_8) = % 117.10/16.21 | $sum(all_539_2, 1) % 117.10/16.21 | % 117.10/16.21 | DELTA: instantiating (207) with fresh symbols all_819_0, all_819_1 gives: % 117.10/16.21 | (249) $lesseq(1, $difference(all_819_1, all_819_0)) & fun_app$a(of_nat$, % 117.10/16.21 | all_724_7) = all_819_1 & fun_app$a(of_nat$, all_724_8) = all_819_0 % 117.10/16.21 | % 117.10/16.21 | ALPHA: (249) implies: % 117.10/16.21 | (250) $lesseq(1, $difference(all_819_1, all_819_0)) % 117.10/16.21 | (251) fun_app$a(of_nat$, all_724_8) = all_819_0 % 117.10/16.21 | (252) fun_app$a(of_nat$, all_724_7) = all_819_1 % 117.10/16.21 | % 117.10/16.21 | DELTA: instantiating (208) with fresh symbols all_828_0, all_828_1 gives: % 117.10/16.21 | (253) $lesseq(1, $difference(all_828_1, all_828_0)) & fun_app$a(of_nat$, % 117.10/16.21 | all_724_6) = all_828_1 & fun_app$a(of_nat$, all_724_7) = all_828_0 % 117.10/16.21 | % 117.10/16.21 | ALPHA: (253) implies: % 117.10/16.21 | (254) $lesseq(1, $difference(all_828_1, all_828_0)) % 117.10/16.21 | (255) fun_app$a(of_nat$, all_724_7) = all_828_0 % 117.10/16.21 | (256) fun_app$a(of_nat$, all_724_6) = all_828_1 % 117.10/16.21 | % 117.10/16.21 | DELTA: instantiating (230) with fresh symbols all_910_0, all_910_1 gives: % 117.10/16.21 | (257) fun_app$a(of_nat$, all_724_7) = all_910_0 & fun_app$a(of_nat$, % 117.10/16.21 | all_520_0) = all_910_1 & ( ~ ($lesseq(all_910_0, 0) | ~ % 117.10/16.21 | ($lesseq(1, all_910_1))) % 117.10/16.21 | % 117.10/16.21 | ALPHA: (257) implies: % 117.10/16.21 | (258) fun_app$a(of_nat$, all_724_7) = all_910_0 % 117.10/16.21 | % 117.10/16.21 | DELTA: instantiating (219) with fresh symbols all_916_0, all_916_1 gives: % 117.10/16.21 | (259) fun_app$a(of_nat$, all_724_6) = all_916_0 & fun_app$a(of_nat$, % 117.10/16.21 | all_520_0) = all_916_1 & ( ~ ($lesseq(all_916_0, 0) | ~ % 117.10/16.21 | ($lesseq(1, all_916_1))) % 117.10/16.21 | % 117.10/16.21 | ALPHA: (259) implies: % 117.10/16.21 | (260) fun_app$a(of_nat$, all_724_6) = all_916_0 % 117.10/16.21 | % 117.10/16.21 | DELTA: instantiating (216) with fresh symbols all_938_0, all_938_1, all_938_2 % 117.10/16.21 | gives: % 117.10/16.21 | (261) fun_app$a(of_nat$, all_724_6) = all_938_1 & fun_app$a(of_nat$, % 117.10/16.21 | all_724_7) = all_938_0 & fun_app$a(of_nat$, all_520_0) = all_938_2 % 117.10/16.21 | & ( ~ ($lesseq(all_938_1, all_938_0)) | ~ ($lesseq(2, all_938_2))) % 117.10/16.21 | % 117.10/16.21 | ALPHA: (261) implies: % 117.10/16.21 | (262) fun_app$a(of_nat$, all_724_7) = all_938_0 % 117.10/16.21 | (263) fun_app$a(of_nat$, all_724_6) = all_938_1 % 117.10/16.21 | % 117.10/16.21 | DELTA: instantiating (215) with fresh symbols all_940_0, all_940_1, all_940_2 % 117.10/16.21 | gives: % 117.10/16.21 | (264) fun_app$a(of_nat$, all_724_6) = all_940_1 & fun_app$a(of_nat$, % 117.10/16.21 | all_724_7) = all_940_0 & fun_app$a(of_nat$, all_520_0) = all_940_2 % 117.10/16.21 | & ( ~ ($lesseq(1, $difference(all_940_0, all_940_1))) | ~ % 117.10/16.21 | ($lesseq(2, all_940_2))) % 117.10/16.21 | % 117.10/16.21 | ALPHA: (264) implies: % 117.10/16.21 | (265) fun_app$a(of_nat$, all_724_7) = all_940_0 % 117.10/16.21 | (266) fun_app$a(of_nat$, all_724_6) = all_940_1 % 117.10/16.21 | % 117.10/16.21 | DELTA: instantiating (245) with fresh symbols all_944_0, all_944_1, all_944_2 % 117.10/16.21 | gives: % 117.10/16.21 | (267) fun_app$a(of_nat$, all_724_4) = all_944_1 & fun_app$a(of_nat$, % 117.10/16.21 | all_724_6) = all_944_2 & fun_app$a(of_nat$, n$) = all_944_0 & ( ~ % 117.10/16.21 | ($lesseq(all_944_1, all_944_0)) | ~ ($lesseq(2, all_944_2))) % 117.10/16.21 | % 117.10/16.21 | ALPHA: (267) implies: % 117.10/16.21 | (268) fun_app$a(of_nat$, all_724_6) = all_944_2 % 117.10/16.21 | % 117.10/16.21 | DELTA: instantiating (244) with fresh symbols all_946_0, all_946_1, all_946_2 % 117.10/16.21 | gives: % 117.10/16.21 | (269) fun_app$a(of_nat$, all_724_4) = all_946_1 & fun_app$a(of_nat$, % 117.10/16.21 | all_724_6) = all_946_2 & fun_app$a(of_nat$, n$) = all_946_0 & ( ~ % 117.10/16.21 | ($lesseq(1, $difference(all_946_0, all_946_1))) | ~ ($lesseq(2, % 117.10/16.21 | all_946_2))) % 117.10/16.21 | % 117.10/16.21 | ALPHA: (269) implies: % 117.10/16.21 | (270) fun_app$a(of_nat$, n$) = all_946_0 % 117.10/16.21 | (271) fun_app$a(of_nat$, all_724_6) = all_946_2 % 117.10/16.21 | % 117.10/16.21 | DELTA: instantiating (236) with fresh symbols all_952_0, all_952_1, all_952_2 % 117.10/16.21 | gives: % 117.10/16.21 | (272) fun_app$a(of_nat$, all_724_1) = all_952_1 & fun_app$a(of_nat$, % 117.10/16.21 | all_724_6) = all_952_2 & fun_app$a(of_nat$, all_539_1) = all_952_0 % 117.10/16.21 | & ( ~ ($lesseq(all_952_1, all_952_0)) | ~ ($lesseq(2, all_952_2))) % 117.10/16.21 | % 117.10/16.21 | ALPHA: (272) implies: % 117.10/16.21 | (273) fun_app$a(of_nat$, all_539_1) = all_952_0 % 117.10/16.21 | (274) fun_app$a(of_nat$, all_724_6) = all_952_2 % 117.10/16.21 | (275) fun_app$a(of_nat$, all_724_1) = all_952_1 % 117.10/16.21 | % 117.10/16.22 | DELTA: instantiating (235) with fresh symbols all_954_0, all_954_1, all_954_2 % 117.10/16.22 | gives: % 117.10/16.22 | (276) fun_app$a(of_nat$, all_724_1) = all_954_1 & fun_app$a(of_nat$, % 117.10/16.22 | all_724_6) = all_954_2 & fun_app$a(of_nat$, all_539_1) = all_954_0 % 117.10/16.22 | & ( ~ ($lesseq(1, $difference(all_954_0, all_954_1))) | ~ % 117.10/16.22 | ($lesseq(2, all_954_2))) % 117.10/16.22 | % 117.10/16.22 | ALPHA: (276) implies: % 117.10/16.22 | (277) fun_app$a(of_nat$, all_539_1) = all_954_0 % 117.10/16.22 | (278) fun_app$a(of_nat$, all_724_6) = all_954_2 % 117.10/16.22 | (279) fun_app$a(of_nat$, all_724_1) = all_954_1 % 117.10/16.22 | (280) ~ ($lesseq(1, $difference(all_954_0, all_954_1))) | ~ ($lesseq(2, % 117.10/16.22 | all_954_2)) % 117.10/16.22 | % 117.10/16.22 | DELTA: instantiating (227) with fresh symbols all_962_0, all_962_1, all_962_2 % 117.10/16.22 | gives: % 117.10/16.22 | (281) fun_app$a(of_nat$, all_724_7) = all_962_1 & fun_app$a(of_nat$, % 117.10/16.22 | all_724_8) = all_962_0 & fun_app$a(of_nat$, all_520_0) = all_962_2 % 117.10/16.22 | & ( ~ ($lesseq(all_962_1, all_962_0)) | ~ ($lesseq(2, all_962_2))) % 117.10/16.22 | % 117.10/16.22 | ALPHA: (281) implies: % 117.10/16.22 | (282) fun_app$a(of_nat$, all_724_8) = all_962_0 % 117.10/16.22 | (283) fun_app$a(of_nat$, all_724_7) = all_962_1 % 117.10/16.22 | % 117.10/16.22 | DELTA: instantiating (226) with fresh symbols all_964_0, all_964_1, all_964_2 % 117.10/16.22 | gives: % 117.10/16.22 | (284) fun_app$a(of_nat$, all_724_7) = all_964_1 & fun_app$a(of_nat$, % 117.10/16.22 | all_724_8) = all_964_0 & fun_app$a(of_nat$, all_520_0) = all_964_2 % 117.10/16.22 | & ( ~ ($lesseq(1, $difference(all_964_0, all_964_1))) | ~ % 117.10/16.22 | ($lesseq(2, all_964_2))) % 117.10/16.22 | % 117.10/16.22 | ALPHA: (284) implies: % 117.10/16.22 | (285) fun_app$a(of_nat$, all_724_8) = all_964_0 % 117.10/16.22 | (286) fun_app$a(of_nat$, all_724_7) = all_964_1 % 117.10/16.22 | % 117.10/16.22 | DELTA: instantiating (243) with fresh symbols all_976_0, all_976_1, all_976_2 % 117.10/16.22 | gives: % 117.10/16.22 | (287) fun_app$a(of_nat$, all_724_4) = all_976_0 & fun_app$a(of_nat$, % 117.10/16.22 | all_724_6) = all_976_1 & fun_app$a(of_nat$, n$) = all_976_2 & % 117.10/16.22 | (all_976_0 = 1 | ( ~ (all_976_1 = 1) & ~ (all_976_2 = 0))) % 117.10/16.22 | % 117.10/16.22 | ALPHA: (287) implies: % 117.10/16.22 | (288) fun_app$a(of_nat$, n$) = all_976_2 % 117.10/16.22 | (289) fun_app$a(of_nat$, all_724_6) = all_976_1 % 117.10/16.22 | % 117.10/16.22 | DELTA: instantiating (234) with fresh symbols all_978_0, all_978_1, all_978_2 % 117.10/16.22 | gives: % 117.10/16.22 | (290) fun_app$a(of_nat$, all_724_1) = all_978_0 & fun_app$a(of_nat$, % 117.10/16.22 | all_724_6) = all_978_1 & fun_app$a(of_nat$, all_539_1) = all_978_2 % 117.10/16.22 | & (all_978_0 = 1 | ( ~ (all_978_1 = 1) & ~ (all_978_2 = 0))) % 117.10/16.22 | % 117.10/16.22 | ALPHA: (290) implies: % 117.10/16.22 | (291) fun_app$a(of_nat$, all_539_1) = all_978_2 % 117.10/16.22 | (292) fun_app$a(of_nat$, all_724_6) = all_978_1 % 117.10/16.22 | (293) fun_app$a(of_nat$, all_724_1) = all_978_0 % 117.10/16.22 | % 117.10/16.22 | DELTA: instantiating (233) with fresh symbols all_990_0, all_990_1, all_990_2 % 117.10/16.22 | gives: % 117.10/16.22 | (294) fun_app$a(of_nat$, all_724_1) = all_990_0 & fun_app$a(of_nat$, % 117.10/16.22 | all_724_6) = all_990_2 & fun_app$a(of_nat$, all_539_1) = all_990_1 % 117.10/16.22 | & ( ~ ($lesseq(all_990_0, 0) | ( ~ (all_990_1 = 0) & % 117.10/16.22 | $lesseq(all_990_2, 0))) % 117.10/16.22 | % 117.10/16.22 | ALPHA: (294) implies: % 117.10/16.22 | (295) fun_app$a(of_nat$, all_539_1) = all_990_1 % 117.10/16.22 | (296) fun_app$a(of_nat$, all_724_6) = all_990_2 % 117.10/16.22 | (297) fun_app$a(of_nat$, all_724_1) = all_990_0 % 117.10/16.22 | % 117.10/16.22 | DELTA: instantiating (242) with fresh symbols all_994_0, all_994_1, all_994_2 % 117.10/16.22 | gives: % 117.10/16.22 | (298) fun_app$a(of_nat$, all_724_4) = all_994_0 & fun_app$a(of_nat$, % 117.10/16.22 | all_724_6) = all_994_2 & fun_app$a(of_nat$, n$) = all_994_1 & ( ~ % 117.10/16.22 | ($lesseq(all_994_0, 0) | ( ~ (all_994_1 = 0) & $lesseq(all_994_2, % 117.10/16.22 | 0))) % 117.10/16.22 | % 117.10/16.22 | ALPHA: (298) implies: % 117.10/16.22 | (299) fun_app$a(of_nat$, n$) = all_994_1 % 117.10/16.22 | (300) fun_app$a(of_nat$, all_724_6) = all_994_2 % 117.10/16.22 | % 117.10/16.22 | DELTA: instantiating (214) with fresh symbols all_1000_0, all_1000_1, % 117.10/16.22 | all_1000_2 gives: % 117.10/16.22 | (301) fun_app$a(of_nat$, all_724_6) = all_1000_0 & fun_app$a(of_nat$, % 117.10/16.22 | all_724_7) = all_1000_2 & fun_app$a(of_nat$, all_520_0) = % 117.10/16.22 | all_1000_1 & (all_1000_0 = 1 | ( ~ (all_1000_1 = 1) & ~ (all_1000_2 % 117.10/16.22 | = 0))) % 117.10/16.22 | % 117.10/16.22 | ALPHA: (301) implies: % 117.10/16.22 | (302) fun_app$a(of_nat$, all_724_7) = all_1000_2 % 117.10/16.22 | (303) fun_app$a(of_nat$, all_724_6) = all_1000_0 % 117.10/16.22 | % 117.10/16.22 | DELTA: instantiating (213) with fresh symbols all_1002_0, all_1002_1, % 117.10/16.22 | all_1002_2 gives: % 117.10/16.22 | (304) fun_app$a(of_nat$, all_724_6) = all_1002_0 & fun_app$a(of_nat$, % 117.10/16.22 | all_724_7) = all_1002_1 & fun_app$a(of_nat$, all_520_0) = % 117.10/16.22 | all_1002_2 & ( ~ ($lesseq(all_1002_0, 0) | ( ~ (all_1002_1 = 0) & % 117.10/16.22 | $lesseq(all_1002_2, 0))) % 117.10/16.22 | % 117.10/16.22 | ALPHA: (304) implies: % 117.10/16.22 | (305) fun_app$a(of_nat$, all_724_7) = all_1002_1 % 117.10/16.22 | (306) fun_app$a(of_nat$, all_724_6) = all_1002_0 % 117.10/16.22 | % 117.10/16.22 | DELTA: instantiating (246) with fresh symbols all_1008_0, all_1008_1, % 117.10/16.22 | all_1008_2 gives: % 117.10/16.22 | (307) fun_app$a(of_nat$, all_724_4) = all_1008_2 & fun_app$a(of_nat$, % 117.10/16.22 | all_724_6) = all_1008_1 & fun_app$a(of_nat$, n$) = all_1008_0 & % 117.10/16.22 | (all_1008_0 = 0 | ~ ($lesseq(all_1008_1, 0) | ~ ($lesseq(1, % 117.10/16.22 | all_1008_2))) % 117.10/16.22 | % 117.10/16.22 | ALPHA: (307) implies: % 117.10/16.22 | (308) fun_app$a(of_nat$, n$) = all_1008_0 % 117.10/16.22 | (309) fun_app$a(of_nat$, all_724_6) = all_1008_1 % 117.10/16.22 | (310) fun_app$a(of_nat$, all_724_4) = all_1008_2 % 117.10/16.22 | % 117.10/16.22 | DELTA: instantiating (247) with fresh symbols all_1012_0, all_1012_1, % 117.10/16.22 | all_1012_2 gives: % 117.10/16.22 | (311) fun_app$a(of_nat$, all_724_4) = all_1012_2 & fun_app$a(of_nat$, % 117.10/16.22 | all_724_6) = all_1012_0 & fun_app$a(of_nat$, n$) = all_1012_1 & ( ~ % 117.10/16.22 | (all_1012_2 = 1) | all_1012_0 = 1 | all_1012_1 = 0) % 117.10/16.22 | % 117.10/16.22 | ALPHA: (311) implies: % 117.10/16.22 | (312) fun_app$a(of_nat$, n$) = all_1012_1 % 117.10/16.22 | (313) fun_app$a(of_nat$, all_724_6) = all_1012_0 % 117.10/16.22 | (314) fun_app$a(of_nat$, all_724_4) = all_1012_2 % 117.10/16.22 | % 117.10/16.22 | DELTA: instantiating (238) with fresh symbols all_1018_0, all_1018_1, % 117.10/16.22 | all_1018_2 gives: % 117.10/16.22 | (315) fun_app$a(of_nat$, all_724_1) = all_1018_2 & fun_app$a(of_nat$, % 117.10/16.22 | all_724_6) = all_1018_0 & fun_app$a(of_nat$, all_539_1) = % 117.10/16.22 | all_1018_1 & ( ~ (all_1018_2 = 1) | all_1018_0 = 1 | all_1018_1 = 0) % 117.10/16.22 | % 117.10/16.22 | ALPHA: (315) implies: % 117.10/16.22 | (316) fun_app$a(of_nat$, all_539_1) = all_1018_1 % 117.10/16.22 | (317) fun_app$a(of_nat$, all_724_6) = all_1018_0 % 117.10/16.22 | (318) fun_app$a(of_nat$, all_724_1) = all_1018_2 % 117.10/16.22 | % 117.10/16.22 | DELTA: instantiating (237) with fresh symbols all_1032_0, all_1032_1, % 117.10/16.22 | all_1032_2 gives: % 117.10/16.22 | (319) fun_app$a(of_nat$, all_724_1) = all_1032_2 & fun_app$a(of_nat$, % 117.10/16.22 | all_724_6) = all_1032_1 & fun_app$a(of_nat$, all_539_1) = % 117.10/16.22 | all_1032_0 & (all_1032_0 = 0 | ~ ($lesseq(all_1032_1, 0) | ~ % 117.10/16.22 | ($lesseq(1, all_1032_2))) % 117.10/16.22 | % 117.10/16.22 | ALPHA: (319) implies: % 117.10/16.22 | (320) fun_app$a(of_nat$, all_539_1) = all_1032_0 % 117.10/16.22 | (321) fun_app$a(of_nat$, all_724_6) = all_1032_1 % 117.10/16.22 | (322) fun_app$a(of_nat$, all_724_1) = all_1032_2 % 117.10/16.22 | % 117.10/16.22 | DELTA: instantiating (225) with fresh symbols all_1036_0, all_1036_1, % 117.10/16.22 | all_1036_2 gives: % 117.10/16.22 | (323) fun_app$a(of_nat$, all_724_7) = all_1036_0 & fun_app$a(of_nat$, % 117.10/16.22 | all_724_8) = all_1036_2 & fun_app$a(of_nat$, all_520_0) = % 117.10/16.22 | all_1036_1 & (all_1036_0 = 1 | ( ~ (all_1036_1 = 1) & ~ (all_1036_2 % 117.10/16.22 | = 0))) % 117.10/16.22 | % 117.10/16.22 | ALPHA: (323) implies: % 117.10/16.22 | (324) fun_app$a(of_nat$, all_724_8) = all_1036_2 % 117.10/16.22 | (325) fun_app$a(of_nat$, all_724_7) = all_1036_0 % 117.10/16.22 | % 117.10/16.22 | DELTA: instantiating (224) with fresh symbols all_1038_0, all_1038_1, % 117.10/16.22 | all_1038_2 gives: % 117.10/16.22 | (326) fun_app$a(of_nat$, all_724_7) = all_1038_0 & fun_app$a(of_nat$, % 117.10/16.22 | all_724_8) = all_1038_1 & fun_app$a(of_nat$, all_520_0) = % 117.10/16.22 | all_1038_2 & ( ~ ($lesseq(all_1038_0, 0) | ( ~ (all_1038_1 = 0) & % 117.10/16.22 | $lesseq(all_1038_2, 0))) % 117.10/16.22 | % 117.10/16.22 | ALPHA: (326) implies: % 117.10/16.22 | (327) fun_app$a(of_nat$, all_724_8) = all_1038_1 % 117.10/16.22 | (328) fun_app$a(of_nat$, all_724_7) = all_1038_0 % 117.10/16.22 | % 117.10/16.22 | DELTA: instantiating (229) with fresh symbols all_1042_0, all_1042_1, % 117.10/16.22 | all_1042_2 gives: % 117.10/16.23 | (329) fun_app$a(of_nat$, all_724_7) = all_1042_2 & fun_app$a(of_nat$, % 117.10/16.23 | all_724_8) = all_1042_1 & fun_app$a(of_nat$, all_520_0) = % 117.10/16.23 | all_1042_0 & ( ~ (all_1042_2 = 1) | all_1042_0 = 1 | all_1042_1 = 0) % 117.10/16.23 | % 117.10/16.23 | ALPHA: (329) implies: % 117.10/16.23 | (330) fun_app$a(of_nat$, all_724_8) = all_1042_1 % 117.10/16.23 | (331) fun_app$a(of_nat$, all_724_7) = all_1042_2 % 117.10/16.23 | % 117.10/16.23 | DELTA: instantiating (228) with fresh symbols all_1044_0, all_1044_1, % 117.10/16.23 | all_1044_2 gives: % 117.10/16.23 | (332) fun_app$a(of_nat$, all_724_7) = all_1044_2 & fun_app$a(of_nat$, % 117.10/16.23 | all_724_8) = all_1044_0 & fun_app$a(of_nat$, all_520_0) = % 117.10/16.23 | all_1044_1 & (all_1044_0 = 0 | ~ ($lesseq(all_1044_1, 0) | ~ % 117.10/16.23 | ($lesseq(1, all_1044_2))) % 117.10/16.23 | % 117.10/16.23 | ALPHA: (332) implies: % 117.10/16.23 | (333) fun_app$a(of_nat$, all_724_8) = all_1044_0 % 117.10/16.23 | (334) fun_app$a(of_nat$, all_724_7) = all_1044_2 % 117.10/16.23 | % 117.10/16.23 | DELTA: instantiating (218) with fresh symbols all_1048_0, all_1048_1, % 117.10/16.23 | all_1048_2 gives: % 117.10/16.23 | (335) fun_app$a(of_nat$, all_724_6) = all_1048_2 & fun_app$a(of_nat$, % 117.10/16.23 | all_724_7) = all_1048_1 & fun_app$a(of_nat$, all_520_0) = % 117.10/16.23 | all_1048_0 & ( ~ (all_1048_2 = 1) | all_1048_0 = 1 | all_1048_1 = 0) % 117.10/16.23 | % 117.10/16.23 | ALPHA: (335) implies: % 117.10/16.23 | (336) fun_app$a(of_nat$, all_724_7) = all_1048_1 % 117.10/16.23 | (337) fun_app$a(of_nat$, all_724_6) = all_1048_2 % 117.10/16.23 | % 117.10/16.23 | DELTA: instantiating (217) with fresh symbols all_1050_0, all_1050_1, % 117.10/16.23 | all_1050_2 gives: % 117.10/16.23 | (338) fun_app$a(of_nat$, all_724_6) = all_1050_2 & fun_app$a(of_nat$, % 117.10/16.23 | all_724_7) = all_1050_0 & fun_app$a(of_nat$, all_520_0) = % 117.10/16.23 | all_1050_1 & (all_1050_0 = 0 | ~ ($lesseq(all_1050_1, 0) | ~ % 117.10/16.23 | ($lesseq(1, all_1050_2))) % 117.10/16.23 | % 117.10/16.23 | ALPHA: (338) implies: % 117.10/16.23 | (339) fun_app$a(of_nat$, all_724_7) = all_1050_0 % 117.10/16.23 | (340) fun_app$a(of_nat$, all_724_6) = all_1050_2 % 117.10/16.23 | % 117.10/16.23 | DELTA: instantiating (222) with fresh symbols all_1070_0, all_1070_1, % 117.10/16.23 | all_1070_2, all_1070_3 gives: % 117.10/16.23 | (341) fun_app$a(of_nat$, all_724_7) = all_1070_0 & fun_app$a(of_nat$, % 117.10/16.23 | all_724_7) = all_1070_1 & fun_app$a(of_nat$, all_724_8) = % 117.10/16.23 | all_1070_2 & fun_app$a(of_nat$, all_724_8) = all_1070_3 & ( ~ % 117.10/16.23 | ($lesseq(1, $difference(all_1070_0, all_1070_1))) | ~ % 117.10/16.23 | ($lesseq(all_1070_3, all_1070_2)) | ~ ($lesseq(1, all_1070_3))) % 117.10/16.23 | % 117.10/16.23 | ALPHA: (341) implies: % 117.10/16.23 | (342) fun_app$a(of_nat$, all_724_8) = all_1070_3 % 117.10/16.23 | (343) fun_app$a(of_nat$, all_724_8) = all_1070_2 % 117.10/16.23 | (344) fun_app$a(of_nat$, all_724_7) = all_1070_1 % 117.10/16.23 | (345) fun_app$a(of_nat$, all_724_7) = all_1070_0 % 117.10/16.23 | % 117.10/16.23 | DELTA: instantiating (220) with fresh symbols all_1072_0, all_1072_1, % 117.10/16.23 | all_1072_2, all_1072_3 gives: % 117.10/16.23 | (346) fun_app$a(of_nat$, all_724_6) = all_1072_0 & fun_app$a(of_nat$, % 117.10/16.23 | all_724_7) = all_1072_1 & fun_app$a(of_nat$, all_724_7) = % 117.10/16.23 | all_1072_3 & fun_app$a(of_nat$, all_724_8) = all_1072_2 & ( ~ % 117.10/16.23 | ($lesseq(1, $difference(all_1072_0, all_1072_1))) | ~ % 117.10/16.23 | ($lesseq(all_1072_3, all_1072_2)) | ~ ($lesseq(1, all_1072_3))) % 117.10/16.23 | % 117.10/16.23 | ALPHA: (346) implies: % 117.10/16.23 | (347) fun_app$a(of_nat$, all_724_8) = all_1072_2 % 117.10/16.23 | (348) fun_app$a(of_nat$, all_724_7) = all_1072_3 % 117.10/16.23 | (349) fun_app$a(of_nat$, all_724_7) = all_1072_1 % 117.10/16.23 | (350) fun_app$a(of_nat$, all_724_6) = all_1072_0 % 117.10/16.23 | % 117.10/16.23 | DELTA: instantiating (211) with fresh symbols all_1083_0, all_1083_1, % 117.10/16.23 | all_1083_2, all_1083_3 gives: % 117.10/16.23 | (351) fun_app$a(of_nat$, all_724_6) = all_1083_1 & fun_app$a(of_nat$, % 117.10/16.23 | all_724_7) = all_1083_0 & fun_app$a(of_nat$, all_724_7) = % 117.10/16.23 | all_1083_2 & fun_app$a(of_nat$, all_724_8) = all_1083_3 & ( ~ % 117.10/16.23 | ($lesseq(1, $difference(all_1083_0, all_1083_1))) | ~ % 117.10/16.23 | ($lesseq(all_1083_3, all_1083_2)) | ~ ($lesseq(1, all_1083_3))) % 117.10/16.23 | % 117.10/16.23 | ALPHA: (351) implies: % 117.10/16.23 | (352) fun_app$a(of_nat$, all_724_8) = all_1083_3 % 117.10/16.23 | (353) fun_app$a(of_nat$, all_724_7) = all_1083_2 % 117.10/16.23 | (354) fun_app$a(of_nat$, all_724_7) = all_1083_0 % 117.10/16.23 | (355) fun_app$a(of_nat$, all_724_6) = all_1083_1 % 117.10/16.23 | % 117.10/16.23 | DELTA: instantiating (209) with fresh symbols all_1085_0, all_1085_1, % 117.10/16.23 | all_1085_2, all_1085_3 gives: % 117.10/16.23 | (356) fun_app$a(of_nat$, all_724_6) = all_1085_0 & fun_app$a(of_nat$, % 117.10/16.23 | all_724_6) = all_1085_1 & fun_app$a(of_nat$, all_724_7) = % 117.10/16.23 | all_1085_2 & fun_app$a(of_nat$, all_724_7) = all_1085_3 & ( ~ % 117.10/16.23 | ($lesseq(1, $difference(all_1085_0, all_1085_1))) | ~ % 117.10/16.23 | ($lesseq(all_1085_3, all_1085_2)) | ~ ($lesseq(1, all_1085_3))) % 117.10/16.23 | % 117.10/16.23 | ALPHA: (356) implies: % 117.10/16.23 | (357) fun_app$a(of_nat$, all_724_7) = all_1085_3 % 117.10/16.23 | (358) fun_app$a(of_nat$, all_724_7) = all_1085_2 % 117.10/16.23 | (359) fun_app$a(of_nat$, all_724_6) = all_1085_1 % 117.10/16.23 | (360) fun_app$a(of_nat$, all_724_6) = all_1085_0 % 117.10/16.23 | % 117.10/16.23 | DELTA: instantiating (239) with fresh symbols all_1094_0, all_1094_1, % 117.10/16.23 | all_1094_2, all_1094_3 gives: % 117.10/16.23 | (361) fun_app$a(of_nat$, all_724_1) = all_1094_0 & fun_app$a(of_nat$, % 117.10/16.23 | all_724_4) = all_1094_1 & fun_app$a(of_nat$, all_539_1) = % 117.10/16.23 | all_1094_3 & fun_app$a(of_nat$, n$) = all_1094_2 & ( ~ ($lesseq(1, % 117.10/16.23 | $difference(all_1094_0, all_1094_1))) | ~ ($lesseq(all_1094_3, % 117.10/16.23 | all_1094_2)) | ~ ($lesseq(1, all_1094_3))) % 117.10/16.23 | % 117.10/16.23 | ALPHA: (361) implies: % 117.10/16.23 | (362) fun_app$a(of_nat$, n$) = all_1094_2 % 117.10/16.23 | (363) fun_app$a(of_nat$, all_539_1) = all_1094_3 % 117.10/16.23 | (364) fun_app$a(of_nat$, all_724_4) = all_1094_1 % 117.10/16.23 | (365) fun_app$a(of_nat$, all_724_1) = all_1094_0 % 117.10/16.23 | % 117.10/16.23 | DELTA: instantiating (240) with fresh symbols all_1096_0, all_1096_1, % 117.10/16.23 | all_1096_2, all_1096_3, all_1096_4 gives: % 117.10/16.23 | (366) fun_app$a(of_nat$, all_724_1) = all_1096_2 & fun_app$a(of_nat$, % 117.10/16.23 | all_724_4) = all_1096_3 & fun_app$a(of_nat$, all_724_6) = % 117.10/16.23 | all_1096_4 & fun_app$a(of_nat$, all_539_1) = all_1096_0 & % 117.10/16.23 | fun_app$a(of_nat$, n$) = all_1096_1 & ( ~ ($lesseq(all_1096_1, % 117.10/16.23 | all_1096_0)) | ~ ($lesseq(1, $difference(all_1096_3, % 117.10/16.23 | all_1096_2))) | ~ ($lesseq(1, all_1096_4))) % 117.10/16.23 | % 117.10/16.23 | ALPHA: (366) implies: % 117.10/16.23 | (367) fun_app$a(of_nat$, n$) = all_1096_1 % 117.10/16.23 | (368) fun_app$a(of_nat$, all_539_1) = all_1096_0 % 117.10/16.23 | (369) fun_app$a(of_nat$, all_724_6) = all_1096_4 % 117.10/16.23 | (370) fun_app$a(of_nat$, all_724_1) = all_1096_2 % 117.10/16.23 | % 117.10/16.23 | DELTA: instantiating (221) with fresh symbols all_1100_0, all_1100_1, % 117.10/16.23 | all_1100_2, all_1100_3, all_1100_4 gives: % 117.10/16.23 | (371) fun_app$a(of_nat$, all_724_6) = all_1100_2 & fun_app$a(of_nat$, % 117.10/16.23 | all_724_7) = all_1100_0 & fun_app$a(of_nat$, all_724_7) = % 117.10/16.23 | all_1100_3 & fun_app$a(of_nat$, all_724_8) = all_1100_1 & % 117.10/16.23 | fun_app$a(of_nat$, all_520_0) = all_1100_4 & ( ~ ($lesseq(all_1100_1, % 117.10/16.23 | all_1100_0)) | ~ ($lesseq(1, $difference(all_1100_3, % 117.10/16.23 | all_1100_2))) | ~ ($lesseq(1, all_1100_4))) % 117.10/16.23 | % 117.10/16.23 | ALPHA: (371) implies: % 117.10/16.23 | (372) fun_app$a(of_nat$, all_724_8) = all_1100_1 % 117.10/16.23 | (373) fun_app$a(of_nat$, all_724_7) = all_1100_3 % 117.10/16.23 | (374) fun_app$a(of_nat$, all_724_7) = all_1100_0 % 117.10/16.23 | (375) fun_app$a(of_nat$, all_724_6) = all_1100_2 % 117.10/16.23 | % 117.10/16.23 | DELTA: instantiating (210) with fresh symbols all_1102_0, all_1102_1, % 117.10/16.23 | all_1102_2, all_1102_3, all_1102_4 gives: % 117.10/16.23 | (376) fun_app$a(of_nat$, all_724_6) = all_1102_2 & fun_app$a(of_nat$, % 117.10/16.23 | all_724_6) = all_1102_3 & fun_app$a(of_nat$, all_724_7) = % 117.10/16.23 | all_1102_0 & fun_app$a(of_nat$, all_724_7) = all_1102_1 & % 117.10/16.23 | fun_app$a(of_nat$, all_520_0) = all_1102_4 & ( ~ ($lesseq(all_1102_1, % 117.10/16.23 | all_1102_0)) | ~ ($lesseq(1, $difference(all_1102_3, % 117.10/16.23 | all_1102_2))) | ~ ($lesseq(1, all_1102_4))) % 117.10/16.23 | % 117.10/16.23 | ALPHA: (376) implies: % 117.10/16.23 | (377) fun_app$a(of_nat$, all_724_7) = all_1102_1 % 117.10/16.23 | (378) fun_app$a(of_nat$, all_724_7) = all_1102_0 % 117.10/16.23 | (379) fun_app$a(of_nat$, all_724_6) = all_1102_3 % 117.10/16.23 | (380) fun_app$a(of_nat$, all_724_6) = all_1102_2 % 117.10/16.23 | % 117.10/16.23 | DELTA: instantiating (212) with fresh symbols all_1108_0, all_1108_1, % 117.10/16.23 | all_1108_2, all_1108_3, all_1108_4 gives: % 117.10/16.23 | (381) fun_app$a(of_nat$, all_724_6) = all_1108_3 & fun_app$a(of_nat$, % 117.10/16.23 | all_724_7) = all_1108_1 & fun_app$a(of_nat$, all_724_7) = % 117.10/16.23 | all_1108_2 & fun_app$a(of_nat$, all_724_8) = all_1108_0 & % 117.10/16.23 | fun_app$a(of_nat$, all_520_0) = all_1108_4 & ( ~ ($lesseq(all_1108_1, % 117.10/16.23 | all_1108_0)) | ~ ($lesseq(1, $difference(all_1108_3, % 117.10/16.23 | all_1108_2))) | ~ ($lesseq(1, all_1108_4))) % 117.10/16.23 | % 117.10/16.23 | ALPHA: (381) implies: % 117.10/16.24 | (382) fun_app$a(of_nat$, all_724_8) = all_1108_0 % 117.10/16.24 | (383) fun_app$a(of_nat$, all_724_7) = all_1108_2 % 117.10/16.24 | (384) fun_app$a(of_nat$, all_724_7) = all_1108_1 % 117.10/16.24 | (385) fun_app$a(of_nat$, all_724_6) = all_1108_3 % 117.10/16.24 | % 117.10/16.24 | DELTA: instantiating (241) with fresh symbols all_1110_0, all_1110_1, % 117.10/16.24 | all_1110_2, all_1110_3, all_1110_4 gives: % 117.10/16.24 | (386) fun_app$a(of_nat$, all_724_4) = all_1110_2 & fun_app$a(of_nat$, % 117.10/16.24 | all_724_4) = all_1110_3 & fun_app$a(of_nat$, all_724_6) = % 117.10/16.24 | all_1110_4 & fun_app$a(of_nat$, n$) = all_1110_0 & fun_app$a(of_nat$, % 117.10/16.24 | n$) = all_1110_1 & ( ~ ($lesseq(all_1110_1, all_1110_0)) | ~ % 117.10/16.24 | ($lesseq(1, $difference(all_1110_3, all_1110_2))) | ~ ($lesseq(1, % 117.10/16.24 | all_1110_4))) % 117.10/16.24 | % 117.10/16.24 | ALPHA: (386) implies: % 117.10/16.24 | (387) fun_app$a(of_nat$, n$) = all_1110_1 % 117.10/16.24 | (388) fun_app$a(of_nat$, n$) = all_1110_0 % 117.10/16.24 | (389) fun_app$a(of_nat$, all_724_6) = all_1110_4 % 117.10/16.24 | (390) fun_app$a(of_nat$, all_724_4) = all_1110_3 % 117.10/16.24 | (391) fun_app$a(of_nat$, all_724_4) = all_1110_2 % 117.10/16.24 | % 117.10/16.24 | DELTA: instantiating (223) with fresh symbols all_1112_0, all_1112_1, % 117.10/16.24 | all_1112_2, all_1112_3, all_1112_4 gives: % 117.10/16.24 | (392) fun_app$a(of_nat$, all_724_7) = all_1112_2 & fun_app$a(of_nat$, % 117.10/16.24 | all_724_7) = all_1112_3 & fun_app$a(of_nat$, all_724_8) = % 117.10/16.24 | all_1112_0 & fun_app$a(of_nat$, all_724_8) = all_1112_1 & % 117.10/16.24 | fun_app$a(of_nat$, all_520_0) = all_1112_4 & ( ~ ($lesseq(all_1112_1, % 117.10/16.24 | all_1112_0)) | ~ ($lesseq(1, $difference(all_1112_3, % 117.10/16.24 | all_1112_2))) | ~ ($lesseq(1, all_1112_4))) % 117.10/16.24 | % 117.10/16.24 | ALPHA: (392) implies: % 117.10/16.24 | (393) fun_app$a(of_nat$, all_724_8) = all_1112_1 % 117.10/16.24 | (394) fun_app$a(of_nat$, all_724_8) = all_1112_0 % 117.10/16.24 | (395) fun_app$a(of_nat$, all_724_7) = all_1112_3 % 117.10/16.24 | (396) fun_app$a(of_nat$, all_724_7) = all_1112_2 % 117.10/16.24 | % 117.10/16.24 | DELTA: instantiating (232) with fresh symbols all_1114_0, all_1114_1, % 117.10/16.24 | all_1114_2, all_1114_3, all_1114_4 gives: % 117.10/16.24 | (397) fun_app$a(of_nat$, all_724_1) = all_1114_3 & fun_app$a(of_nat$, % 117.10/16.24 | all_724_4) = all_1114_2 & fun_app$a(of_nat$, all_724_6) = % 117.10/16.24 | all_1114_4 & fun_app$a(of_nat$, all_539_1) = all_1114_1 & % 117.10/16.24 | fun_app$a(of_nat$, n$) = all_1114_0 & ( ~ ($lesseq(all_1114_1, % 117.10/16.24 | all_1114_0)) | ~ ($lesseq(1, $difference(all_1114_3, % 117.10/16.24 | all_1114_2))) | ~ ($lesseq(1, all_1114_4))) % 117.10/16.24 | % 117.10/16.24 | ALPHA: (397) implies: % 117.10/16.24 | (398) fun_app$a(of_nat$, n$) = all_1114_0 % 117.10/16.24 | (399) fun_app$a(of_nat$, all_539_1) = all_1114_1 % 117.10/16.24 | (400) fun_app$a(of_nat$, all_724_6) = all_1114_4 % 117.10/16.24 | (401) fun_app$a(of_nat$, all_724_4) = all_1114_2 % 117.10/16.24 | (402) fun_app$a(of_nat$, all_724_1) = all_1114_3 % 117.10/16.24 | (403) ~ ($lesseq(all_1114_1, all_1114_0)) | ~ ($lesseq(1, % 117.10/16.24 | $difference(all_1114_3, all_1114_2))) | ~ ($lesseq(1, % 117.10/16.24 | all_1114_4)) % 117.10/16.24 | % 117.10/16.24 | DELTA: instantiating (231) with fresh symbols all_1118_0, all_1118_1, % 117.10/16.24 | all_1118_2, all_1118_3, all_1118_4 gives: % 117.10/16.24 | (404) fun_app$a(of_nat$, all_724_1) = all_1118_2 & fun_app$a(of_nat$, % 117.10/16.24 | all_724_1) = all_1118_3 & fun_app$a(of_nat$, all_724_6) = % 117.10/16.24 | all_1118_4 & fun_app$a(of_nat$, all_539_1) = all_1118_0 & % 117.10/16.24 | fun_app$a(of_nat$, all_539_1) = all_1118_1 & ( ~ ($lesseq(all_1118_1, % 117.10/16.24 | all_1118_0)) | ~ ($lesseq(1, $difference(all_1118_3, % 117.10/16.24 | all_1118_2))) | ~ ($lesseq(1, all_1118_4))) % 117.10/16.24 | % 117.10/16.24 | ALPHA: (404) implies: % 117.10/16.24 | (405) fun_app$a(of_nat$, all_539_1) = all_1118_1 % 117.10/16.24 | (406) fun_app$a(of_nat$, all_539_1) = all_1118_0 % 117.10/16.24 | (407) fun_app$a(of_nat$, all_724_6) = all_1118_4 % 117.10/16.24 | (408) fun_app$a(of_nat$, all_724_1) = all_1118_3 % 117.10/16.24 | (409) fun_app$a(of_nat$, all_724_1) = all_1118_2 % 117.10/16.24 | % 117.10/16.24 | COMBINE_INEQS: (34), (206) imply: % 117.10/16.24 | (410) $lesseq(0, all_539_2) % 117.10/16.24 | % 117.10/16.24 | BETA: splitting (248) gives: % 117.10/16.24 | % 117.10/16.24 | Case 1: % 117.10/16.24 | | % 117.10/16.24 | | (411) fun_app$a(of_nat$, all_724_8) = $sum(all_539_2, 1) % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_994_1, all_1008_0, n$, of_nat$, % 117.10/16.24 | | simplifying with (299), (308) gives: % 117.10/16.24 | | (412) all_1008_0 = all_994_1 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_539_2, all_1094_2, n$, of_nat$, % 117.10/16.24 | | simplifying with (35), (362) gives: % 117.10/16.24 | | (413) all_1094_2 = all_539_2 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_994_1, all_1094_2, n$, of_nat$, % 117.10/16.24 | | simplifying with (299), (362) gives: % 117.10/16.24 | | (414) all_1094_2 = all_994_1 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_1008_0, all_1096_1, n$, of_nat$, % 117.10/16.24 | | simplifying with (308), (367) gives: % 117.10/16.24 | | (415) all_1096_1 = all_1008_0 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_1096_1, all_1110_1, n$, of_nat$, % 117.10/16.24 | | simplifying with (367), (387) gives: % 117.10/16.24 | | (416) all_1110_1 = all_1096_1 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_1012_1, all_1110_1, n$, of_nat$, % 117.10/16.24 | | simplifying with (312), (387) gives: % 117.10/16.24 | | (417) all_1110_1 = all_1012_1 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_1094_2, all_1110_0, n$, of_nat$, % 117.10/16.24 | | simplifying with (362), (388) gives: % 117.10/16.24 | | (418) all_1110_0 = all_1094_2 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_976_2, all_1110_0, n$, of_nat$, % 117.10/16.24 | | simplifying with (288), (388) gives: % 117.10/16.24 | | (419) all_1110_0 = all_976_2 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_1096_1, all_1114_0, n$, of_nat$, % 117.10/16.24 | | simplifying with (367), (398) gives: % 117.10/16.24 | | (420) all_1114_0 = all_1096_1 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_946_0, all_1114_0, n$, of_nat$, % 117.10/16.24 | | simplifying with (270), (398) gives: % 117.10/16.24 | | (421) all_1114_0 = all_946_0 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_978_2, all_1018_1, all_539_1, % 117.10/16.24 | | of_nat$, simplifying with (291), (316) gives: % 117.10/16.24 | | (422) all_1018_1 = all_978_2 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_978_2, all_1032_0, all_539_1, % 117.10/16.24 | | of_nat$, simplifying with (291), (320) gives: % 117.10/16.24 | | (423) all_1032_0 = all_978_2 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_1094_3, all_1096_0, all_539_1, % 117.10/16.24 | | of_nat$, simplifying with (363), (368) gives: % 117.10/16.24 | | (424) all_1096_0 = all_1094_3 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_990_1, all_1096_0, all_539_1, % 117.10/16.24 | | of_nat$, simplifying with (295), (368) gives: % 117.10/16.24 | | (425) all_1096_0 = all_990_1 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_978_2, all_1096_0, all_539_1, % 117.10/16.24 | | of_nat$, simplifying with (291), (368) gives: % 117.10/16.24 | | (426) all_1096_0 = all_978_2 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_1094_3, all_1114_1, all_539_1, % 117.10/16.24 | | of_nat$, simplifying with (363), (399) gives: % 117.10/16.24 | | (427) all_1114_1 = all_1094_3 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_954_0, all_1114_1, all_539_1, % 117.10/16.24 | | of_nat$, simplifying with (277), (399) gives: % 117.10/16.24 | | (428) all_1114_1 = all_954_0 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_539_0, all_1118_1, all_539_1, % 117.10/16.24 | | of_nat$, simplifying with (36), (405) gives: % 117.10/16.24 | | (429) all_1118_1 = all_539_0 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_1018_1, all_1118_1, all_539_1, % 117.10/16.24 | | of_nat$, simplifying with (316), (405) gives: % 117.10/16.24 | | (430) all_1118_1 = all_1018_1 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_1032_0, all_1118_0, all_539_1, % 117.10/16.24 | | of_nat$, simplifying with (320), (406) gives: % 117.10/16.24 | | (431) all_1118_0 = all_1032_0 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_952_0, all_1118_0, all_539_1, % 117.10/16.24 | | of_nat$, simplifying with (273), (406) gives: % 117.10/16.24 | | (432) all_1118_0 = all_952_0 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_1036_2, all_1038_1, all_724_8, % 117.10/16.24 | | of_nat$, simplifying with (324), (327) gives: % 117.10/16.24 | | (433) all_1038_1 = all_1036_2 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with all_819_0, all_1038_1, all_724_8, % 117.10/16.24 | | of_nat$, simplifying with (251), (327) gives: % 117.10/16.24 | | (434) all_1038_1 = all_819_0 % 117.10/16.24 | | % 117.10/16.24 | | GROUND_INST: instantiating (27) with $sum(all_539_2, 1), all_1038_1, % 117.10/16.24 | | all_724_8, of_nat$, simplifying with (327), (411) gives: % 117.10/16.25 | | (435) $difference(all_1038_1, all_539_2) = 1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1038_1, all_1042_1, all_724_8, % 117.10/16.25 | | of_nat$, simplifying with (327), (330) gives: % 117.10/16.25 | | (436) all_1042_1 = all_1038_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1036_2, all_1070_3, all_724_8, % 117.10/16.25 | | of_nat$, simplifying with (324), (342) gives: % 117.10/16.25 | | (437) all_1070_3 = all_1036_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_962_0, all_1070_3, all_724_8, % 117.10/16.25 | | of_nat$, simplifying with (282), (342) gives: % 117.10/16.25 | | (438) all_1070_3 = all_962_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1042_1, all_1083_3, all_724_8, % 117.10/16.25 | | of_nat$, simplifying with (330), (352) gives: % 117.10/16.25 | | (439) all_1083_3 = all_1042_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_964_0, all_1083_3, all_724_8, % 117.10/16.25 | | of_nat$, simplifying with (285), (352) gives: % 117.10/16.25 | | (440) all_1083_3 = all_964_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1100_1, all_1108_0, all_724_8, % 117.10/16.25 | | of_nat$, simplifying with (372), (382) gives: % 117.10/16.25 | | (441) all_1108_0 = all_1100_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1083_3, all_1108_0, all_724_8, % 117.10/16.25 | | of_nat$, simplifying with (352), (382) gives: % 117.10/16.25 | | (442) all_1108_0 = all_1083_3 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1108_0, all_1112_1, all_724_8, % 117.10/16.25 | | of_nat$, simplifying with (382), (393) gives: % 117.10/16.25 | | (443) all_1112_1 = all_1108_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1072_2, all_1112_1, all_724_8, % 117.10/16.25 | | of_nat$, simplifying with (347), (393) gives: % 117.10/16.25 | | (444) all_1112_1 = all_1072_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1070_2, all_1112_0, all_724_8, % 117.10/16.25 | | of_nat$, simplifying with (343), (394) gives: % 117.10/16.25 | | (445) all_1112_0 = all_1070_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1070_3, all_1112_0, all_724_8, % 117.10/16.25 | | of_nat$, simplifying with (342), (394) gives: % 117.10/16.25 | | (446) all_1112_0 = all_1070_3 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1044_0, all_1112_0, all_724_8, % 117.10/16.25 | | of_nat$, simplifying with (333), (394) gives: % 117.10/16.25 | | (447) all_1112_0 = all_1044_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_819_1, all_910_0, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (252), (258) gives: % 117.10/16.25 | | (448) all_910_0 = all_819_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_910_0, all_938_0, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (258), (262) gives: % 117.10/16.25 | | (449) all_938_0 = all_910_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_938_0, all_962_1, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (262), (283) gives: % 117.10/16.25 | | (450) all_962_1 = all_938_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_962_1, all_964_1, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (283), (286) gives: % 117.10/16.25 | | (451) all_964_1 = all_962_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_962_1, all_1000_2, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (283), (302) gives: % 117.10/16.25 | | (452) all_1000_2 = all_962_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_964_1, all_1002_1, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (286), (305) gives: % 117.10/16.25 | | (453) all_1002_1 = all_964_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1002_1, all_1036_0, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (305), (325) gives: % 117.10/16.25 | | (454) all_1036_0 = all_1002_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1036_0, all_1044_2, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (325), (334) gives: % 117.10/16.25 | | (455) all_1044_2 = all_1036_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1044_2, all_1048_1, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (334), (336) gives: % 117.10/16.25 | | (456) all_1048_1 = all_1044_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1048_1, all_1050_0, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (336), (339) gives: % 117.10/16.25 | | (457) all_1050_0 = all_1048_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1042_2, all_1070_1, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (331), (344) gives: % 117.10/16.25 | | (458) all_1070_1 = all_1042_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1070_1, all_1072_3, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (344), (348) gives: % 117.10/16.25 | | (459) all_1072_3 = all_1070_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1050_0, all_1072_1, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (339), (349) gives: % 117.10/16.25 | | (460) all_1072_1 = all_1050_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1072_3, all_1083_2, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (348), (353) gives: % 117.10/16.25 | | (461) all_1083_2 = all_1072_3 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1072_1, all_1083_0, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (349), (354) gives: % 117.10/16.25 | | (462) all_1083_0 = all_1072_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1083_2, all_1085_3, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (353), (357) gives: % 117.10/16.25 | | (463) all_1085_3 = all_1083_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1083_0, all_1085_2, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (354), (358) gives: % 117.10/16.25 | | (464) all_1085_2 = all_1083_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1085_2, all_1100_3, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (358), (373) gives: % 117.10/16.25 | | (465) all_1100_3 = all_1085_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1042_2, all_1100_0, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (331), (374) gives: % 117.10/16.25 | | (466) all_1100_0 = all_1042_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1038_0, all_1100_0, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (328), (374) gives: % 117.10/16.25 | | (467) all_1100_0 = all_1038_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1000_2, all_1100_0, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (302), (374) gives: % 117.10/16.25 | | (468) all_1100_0 = all_1000_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1085_3, all_1102_1, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (357), (377) gives: % 117.10/16.25 | | (469) all_1102_1 = all_1085_3 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1100_3, all_1102_0, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (373), (378) gives: % 117.10/16.25 | | (470) all_1102_0 = all_1100_3 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1108_2, all_1108_1, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (383), (384) gives: % 117.10/16.25 | | (471) all_1108_1 = all_1108_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1102_1, all_1108_1, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (377), (384) gives: % 117.10/16.25 | | (472) all_1108_1 = all_1102_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_828_0, all_1108_1, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (255), (384) gives: % 117.10/16.25 | | (473) all_1108_1 = all_828_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1102_0, all_1112_3, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (378), (395) gives: % 117.10/16.25 | | (474) all_1112_3 = all_1102_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_940_0, all_1112_3, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (265), (395) gives: % 117.10/16.25 | | (475) all_1112_3 = all_940_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1100_0, all_1112_2, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (374), (396) gives: % 117.10/16.25 | | (476) all_1112_2 = all_1100_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1070_0, all_1112_2, all_724_7, % 117.10/16.25 | | of_nat$, simplifying with (345), (396) gives: % 117.10/16.25 | | (477) all_1112_2 = all_1070_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_946_2, all_990_2, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (271), (296) gives: % 117.10/16.25 | | (478) all_990_2 = all_946_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_978_1, all_1000_0, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (292), (303) gives: % 117.10/16.25 | | (479) all_1000_0 = all_978_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_944_2, all_1000_0, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (268), (303) gives: % 117.10/16.25 | | (480) all_1000_0 = all_944_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_940_1, all_1012_0, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (266), (313) gives: % 117.10/16.25 | | (481) all_1012_0 = all_940_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_828_1, all_1012_0, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (256), (313) gives: % 117.10/16.25 | | (482) all_1012_0 = all_828_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1002_0, all_1018_0, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (306), (317) gives: % 117.10/16.25 | | (483) all_1018_0 = all_1002_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1000_0, all_1018_0, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (303), (317) gives: % 117.10/16.25 | | (484) all_1018_0 = all_1000_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_952_2, all_1018_0, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (274), (317) gives: % 117.10/16.25 | | (485) all_1018_0 = all_952_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_946_2, all_1018_0, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (271), (317) gives: % 117.10/16.25 | | (486) all_1018_0 = all_946_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_940_1, all_1018_0, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (266), (317) gives: % 117.10/16.25 | | (487) all_1018_0 = all_940_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_940_1, all_1032_1, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (266), (321) gives: % 117.10/16.25 | | (488) all_1032_1 = all_940_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1000_0, all_1050_2, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (303), (340) gives: % 117.10/16.25 | | (489) all_1050_2 = all_1000_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1050_2, all_1072_0, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (340), (350) gives: % 117.10/16.25 | | (490) all_1072_0 = all_1050_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_994_2, all_1072_0, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (300), (350) gives: % 117.10/16.25 | | (491) all_1072_0 = all_994_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_990_2, all_1083_1, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (296), (355) gives: % 117.10/16.25 | | (492) all_1083_1 = all_990_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_954_2, all_1083_1, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (278), (355) gives: % 117.10/16.25 | | (493) all_1083_1 = all_954_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1083_1, all_1085_1, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (355), (359) gives: % 117.10/16.25 | | (494) all_1085_1 = all_1083_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1032_1, all_1085_0, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (321), (360) gives: % 117.10/16.25 | | (495) all_1085_0 = all_1032_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1008_1, all_1096_4, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (309), (369) gives: % 117.10/16.25 | | (496) all_1096_4 = all_1008_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_990_2, all_1096_4, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (296), (369) gives: % 117.10/16.25 | | (497) all_1096_4 = all_990_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_976_1, all_1096_4, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (289), (369) gives: % 117.10/16.25 | | (498) all_1096_4 = all_976_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1102_3, all_1102_2, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (379), (380) gives: % 117.10/16.25 | | (499) all_1102_2 = all_1102_3 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1096_4, all_1102_2, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (369), (380) gives: % 117.10/16.25 | | (500) all_1102_2 = all_1096_4 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1085_1, all_1108_3, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (359), (385) gives: % 117.10/16.25 | | (501) all_1108_3 = all_1085_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1048_2, all_1108_3, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (337), (385) gives: % 117.10/16.25 | | (502) all_1108_3 = all_1048_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1102_2, all_1110_4, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (380), (389) gives: % 117.10/16.25 | | (503) all_1110_4 = all_1102_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_938_1, all_1110_4, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (263), (389) gives: % 117.10/16.25 | | (504) all_1110_4 = all_938_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1102_2, all_1114_4, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (380), (400) gives: % 117.10/16.25 | | (505) all_1114_4 = all_1102_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1100_2, all_1114_4, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (375), (400) gives: % 117.10/16.25 | | (506) all_1114_4 = all_1100_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1085_0, all_1118_4, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (360), (407) gives: % 117.10/16.25 | | (507) all_1118_4 = all_1085_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_916_0, all_1118_4, all_724_6, % 117.10/16.25 | | of_nat$, simplifying with (260), (407) gives: % 117.10/16.25 | | (508) all_1118_4 = all_916_0 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1094_1, all_1110_3, all_724_4, % 117.10/16.25 | | of_nat$, simplifying with (364), (390) gives: % 117.10/16.25 | | (509) all_1110_3 = all_1094_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1012_2, all_1110_3, all_724_4, % 117.10/16.25 | | of_nat$, simplifying with (314), (390) gives: % 117.10/16.25 | | (510) all_1110_3 = all_1012_2 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_724_3, all_1110_2, all_724_4, % 117.10/16.25 | | of_nat$, simplifying with (93), (391) gives: % 117.10/16.25 | | (511) all_1110_2 = all_724_3 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1110_3, all_1110_2, all_724_4, % 117.10/16.25 | | of_nat$, simplifying with (390), (391) gives: % 117.10/16.25 | | (512) all_1110_2 = all_1110_3 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1094_1, all_1114_2, all_724_4, % 117.10/16.25 | | of_nat$, simplifying with (364), (401) gives: % 117.10/16.25 | | (513) all_1114_2 = all_1094_1 % 117.10/16.25 | | % 117.10/16.25 | | GROUND_INST: instantiating (27) with all_1008_2, all_1114_2, all_724_4, % 117.10/16.25 | | of_nat$, simplifying with (310), (401) gives: % 117.10/16.25 | | (514) all_1114_2 = all_1008_2 % 117.10/16.25 | | % 117.10/16.26 | | GROUND_INST: instantiating (27) with all_724_0, all_990_0, all_724_1, % 117.10/16.26 | | of_nat$, simplifying with (94), (297) gives: % 117.10/16.26 | | (515) all_990_0 = all_724_0 % 117.10/16.26 | | % 117.10/16.26 | | GROUND_INST: instantiating (27) with all_990_0, all_1032_2, all_724_1, % 117.10/16.26 | | of_nat$, simplifying with (297), (322) gives: % 117.10/16.26 | | (516) all_1032_2 = all_990_0 % 117.10/16.26 | | % 117.10/16.26 | | GROUND_INST: instantiating (27) with all_1032_2, all_1094_0, all_724_1, % 117.10/16.26 | | of_nat$, simplifying with (322), (365) gives: % 117.10/16.26 | | (517) all_1094_0 = all_1032_2 % 117.10/16.26 | | % 117.10/16.26 | | GROUND_INST: instantiating (27) with all_1018_2, all_1094_0, all_724_1, % 117.10/16.26 | | of_nat$, simplifying with (318), (365) gives: % 117.10/16.26 | | (518) all_1094_0 = all_1018_2 % 117.10/16.26 | | % 117.10/16.26 | | GROUND_INST: instantiating (27) with all_990_0, all_1096_2, all_724_1, % 117.10/16.26 | | of_nat$, simplifying with (297), (370) gives: % 117.10/16.26 | | (519) all_1096_2 = all_990_0 % 117.10/16.26 | | % 117.10/16.26 | | GROUND_INST: instantiating (27) with all_1032_2, all_1114_3, all_724_1, % 117.10/16.26 | | of_nat$, simplifying with (322), (402) gives: % 117.10/16.26 | | (520) all_1114_3 = all_1032_2 % 117.10/16.26 | | % 117.10/16.26 | | GROUND_INST: instantiating (27) with all_978_0, all_1114_3, all_724_1, % 117.10/16.26 | | of_nat$, simplifying with (293), (402) gives: % 117.10/16.26 | | (521) all_1114_3 = all_978_0 % 117.10/16.26 | | % 117.10/16.26 | | GROUND_INST: instantiating (27) with all_1096_2, all_1118_3, all_724_1, % 117.10/16.26 | | of_nat$, simplifying with (370), (408) gives: % 117.10/16.26 | | (522) all_1118_3 = all_1096_2 % 117.10/16.26 | | % 117.10/16.26 | | GROUND_INST: instantiating (27) with all_954_1, all_1118_3, all_724_1, % 117.10/16.26 | | of_nat$, simplifying with (279), (408) gives: % 117.10/16.26 | | (523) all_1118_3 = all_954_1 % 117.10/16.26 | | % 117.10/16.26 | | GROUND_INST: instantiating (27) with all_990_0, all_1118_2, all_724_1, % 117.10/16.26 | | of_nat$, simplifying with (297), (409) gives: % 117.10/16.26 | | (524) all_1118_2 = all_990_0 % 117.10/16.26 | | % 117.10/16.26 | | GROUND_INST: instantiating (27) with all_952_1, all_1118_2, all_724_1, % 117.10/16.26 | | of_nat$, simplifying with (275), (409) gives: % 117.10/16.26 | | (525) all_1118_2 = all_952_1 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (431), (432) imply: % 117.10/16.26 | | (526) all_1032_0 = all_952_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (526) implies: % 117.10/16.26 | | (527) all_1032_0 = all_952_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (429), (430) imply: % 117.10/16.26 | | (528) all_1018_1 = all_539_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (528) implies: % 117.10/16.26 | | (529) all_1018_1 = all_539_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (524), (525) imply: % 117.10/16.26 | | (530) all_990_0 = all_952_1 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (530) implies: % 117.10/16.26 | | (531) all_990_0 = all_952_1 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (522), (523) imply: % 117.10/16.26 | | (532) all_1096_2 = all_954_1 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (532) implies: % 117.10/16.26 | | (533) all_1096_2 = all_954_1 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (507), (508) imply: % 117.10/16.26 | | (534) all_1085_0 = all_916_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (534) implies: % 117.10/16.26 | | (535) all_1085_0 = all_916_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (420), (421) imply: % 117.10/16.26 | | (536) all_1096_1 = all_946_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (536) implies: % 117.10/16.26 | | (537) all_1096_1 = all_946_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (427), (428) imply: % 117.10/16.26 | | (538) all_1094_3 = all_954_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (538) implies: % 117.10/16.26 | | (539) all_1094_3 = all_954_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (513), (514) imply: % 117.10/16.26 | | (540) all_1094_1 = all_1008_2 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (540) implies: % 117.10/16.26 | | (541) all_1094_1 = all_1008_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (520), (521) imply: % 117.10/16.26 | | (542) all_1032_2 = all_978_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (542) implies: % 117.10/16.26 | | (543) all_1032_2 = all_978_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (505), (506) imply: % 117.10/16.26 | | (544) all_1102_2 = all_1100_2 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (544) implies: % 117.10/16.26 | | (545) all_1102_2 = all_1100_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (445), (447) imply: % 117.10/16.26 | | (546) all_1070_2 = all_1044_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (445), (446) imply: % 117.10/16.26 | | (547) all_1070_2 = all_1070_3 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (443), (444) imply: % 117.10/16.26 | | (548) all_1108_0 = all_1072_2 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (548) implies: % 117.10/16.26 | | (549) all_1108_0 = all_1072_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (476), (477) imply: % 117.10/16.26 | | (550) all_1100_0 = all_1070_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (550) implies: % 117.10/16.26 | | (551) all_1100_0 = all_1070_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (474), (475) imply: % 117.10/16.26 | | (552) all_1102_0 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (552) implies: % 117.10/16.26 | | (553) all_1102_0 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (418), (419) imply: % 117.10/16.26 | | (554) all_1094_2 = all_976_2 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (554) implies: % 117.10/16.26 | | (555) all_1094_2 = all_976_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (416), (417) imply: % 117.10/16.26 | | (556) all_1096_1 = all_1012_1 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (556) implies: % 117.10/16.26 | | (557) all_1096_1 = all_1012_1 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (511), (512) imply: % 117.10/16.26 | | (558) all_1110_3 = all_724_3 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (558) implies: % 117.10/16.26 | | (559) all_1110_3 = all_724_3 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (509), (510) imply: % 117.10/16.26 | | (560) all_1094_1 = all_1012_2 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (560) implies: % 117.10/16.26 | | (561) all_1094_1 = all_1012_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (510), (559) imply: % 117.10/16.26 | | (562) all_1012_2 = all_724_3 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (503), (504) imply: % 117.10/16.26 | | (563) all_1102_2 = all_938_1 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (563) implies: % 117.10/16.26 | | (564) all_1102_2 = all_938_1 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (441), (442) imply: % 117.10/16.26 | | (565) all_1100_1 = all_1083_3 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (441), (549) imply: % 117.10/16.26 | | (566) all_1100_1 = all_1072_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (471), (473) imply: % 117.10/16.26 | | (567) all_1108_2 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (471), (472) imply: % 117.10/16.26 | | (568) all_1108_2 = all_1102_1 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (567), (568) imply: % 117.10/16.26 | | (569) all_1102_1 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (569) implies: % 117.10/16.26 | | (570) all_1102_1 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (501), (502) imply: % 117.10/16.26 | | (571) all_1085_1 = all_1048_2 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (571) implies: % 117.10/16.26 | | (572) all_1085_1 = all_1048_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (470), (553) imply: % 117.10/16.26 | | (573) all_1100_3 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (573) implies: % 117.10/16.26 | | (574) all_1100_3 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (469), (570) imply: % 117.10/16.26 | | (575) all_1085_3 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (575) implies: % 117.10/16.26 | | (576) all_1085_3 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (499), (500) imply: % 117.10/16.26 | | (577) all_1102_3 = all_1096_4 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (499), (564) imply: % 117.10/16.26 | | (578) all_1102_3 = all_938_1 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (499), (545) imply: % 117.10/16.26 | | (579) all_1102_3 = all_1100_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (578), (579) imply: % 117.10/16.26 | | (580) all_1100_2 = all_938_1 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (577), (579) imply: % 117.10/16.26 | | (581) all_1100_2 = all_1096_4 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (468), (551) imply: % 117.10/16.26 | | (582) all_1070_0 = all_1000_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (466), (551) imply: % 117.10/16.26 | | (583) all_1070_0 = all_1042_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (467), (551) imply: % 117.10/16.26 | | (584) all_1070_0 = all_1038_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (565), (566) imply: % 117.10/16.26 | | (585) all_1083_3 = all_1072_2 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (585) implies: % 117.10/16.26 | | (586) all_1083_3 = all_1072_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (580), (581) imply: % 117.10/16.26 | | (587) all_1096_4 = all_938_1 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (587) implies: % 117.10/16.26 | | (588) all_1096_4 = all_938_1 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (465), (574) imply: % 117.10/16.26 | | (589) all_1085_2 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (589) implies: % 117.10/16.26 | | (590) all_1085_2 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (424), (425) imply: % 117.10/16.26 | | (591) all_1094_3 = all_990_1 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (591) implies: % 117.10/16.26 | | (592) all_1094_3 = all_990_1 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (425), (426) imply: % 117.10/16.26 | | (593) all_990_1 = all_978_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (415), (557) imply: % 117.10/16.26 | | (594) all_1012_1 = all_1008_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (537), (557) imply: % 117.10/16.26 | | (595) all_1012_1 = all_946_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (519), (533) imply: % 117.10/16.26 | | (596) all_990_0 = all_954_1 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (596) implies: % 117.10/16.26 | | (597) all_990_0 = all_954_1 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (496), (497) imply: % 117.10/16.26 | | (598) all_1008_1 = all_990_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (496), (588) imply: % 117.10/16.26 | | (599) all_1008_1 = all_938_1 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (496), (498) imply: % 117.10/16.26 | | (600) all_1008_1 = all_976_1 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (517), (518) imply: % 117.10/16.26 | | (601) all_1032_2 = all_1018_2 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (601) implies: % 117.10/16.26 | | (602) all_1032_2 = all_1018_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (541), (561) imply: % 117.10/16.26 | | (603) all_1012_2 = all_1008_2 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (603) implies: % 117.10/16.26 | | (604) all_1012_2 = all_1008_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (414), (555) imply: % 117.10/16.26 | | (605) all_994_1 = all_976_2 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (605) implies: % 117.10/16.26 | | (606) all_994_1 = all_976_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (413), (555) imply: % 117.10/16.26 | | (607) all_976_2 = all_539_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (539), (592) imply: % 117.10/16.26 | | (608) all_990_1 = all_954_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (608) implies: % 117.10/16.26 | | (609) all_990_1 = all_954_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (495), (535) imply: % 117.10/16.26 | | (610) all_1032_1 = all_916_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (610) implies: % 117.10/16.26 | | (611) all_1032_1 = all_916_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (494), (572) imply: % 117.10/16.26 | | (612) all_1083_1 = all_1048_2 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (612) implies: % 117.10/16.26 | | (613) all_1083_1 = all_1048_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (464), (590) imply: % 117.10/16.26 | | (614) all_1083_0 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (614) implies: % 117.10/16.26 | | (615) all_1083_0 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (463), (576) imply: % 117.10/16.26 | | (616) all_1083_2 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (616) implies: % 117.10/16.26 | | (617) all_1083_2 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (462), (615) imply: % 117.10/16.26 | | (618) all_1072_1 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (618) implies: % 117.10/16.26 | | (619) all_1072_1 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (492), (613) imply: % 117.10/16.26 | | (620) all_1048_2 = all_990_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (493), (613) imply: % 117.10/16.26 | | (621) all_1048_2 = all_954_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (461), (617) imply: % 117.10/16.26 | | (622) all_1072_3 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (622) implies: % 117.10/16.26 | | (623) all_1072_3 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (440), (586) imply: % 117.10/16.26 | | (624) all_1072_2 = all_964_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (439), (586) imply: % 117.10/16.26 | | (625) all_1072_2 = all_1042_1 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (490), (491) imply: % 117.10/16.26 | | (626) all_1050_2 = all_994_2 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (626) implies: % 117.10/16.26 | | (627) all_1050_2 = all_994_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (460), (619) imply: % 117.10/16.26 | | (628) all_1050_0 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (628) implies: % 117.10/16.26 | | (629) all_1050_0 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (624), (625) imply: % 117.10/16.26 | | (630) all_1042_1 = all_964_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (630) implies: % 117.10/16.26 | | (631) all_1042_1 = all_964_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (459), (623) imply: % 117.10/16.26 | | (632) all_1070_1 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (632) implies: % 117.10/16.26 | | (633) all_1070_1 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (582), (584) imply: % 117.10/16.26 | | (634) all_1038_0 = all_1000_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (583), (584) imply: % 117.10/16.26 | | (635) all_1042_2 = all_1038_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (635) implies: % 117.10/16.26 | | (636) all_1042_2 = all_1038_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (458), (633) imply: % 117.10/16.26 | | (637) all_1042_2 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (637) implies: % 117.10/16.26 | | (638) all_1042_2 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (546), (547) imply: % 117.10/16.26 | | (639) all_1070_3 = all_1044_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (639) implies: % 117.10/16.26 | | (640) all_1070_3 = all_1044_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (438), (640) imply: % 117.10/16.26 | | (641) all_1044_0 = all_962_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (437), (640) imply: % 117.10/16.26 | | (642) all_1044_0 = all_1036_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (457), (629) imply: % 117.10/16.26 | | (643) all_1048_1 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (643) implies: % 117.10/16.26 | | (644) all_1048_1 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (489), (627) imply: % 117.10/16.26 | | (645) all_1000_0 = all_994_2 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (645) implies: % 117.10/16.26 | | (646) all_1000_0 = all_994_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (456), (644) imply: % 117.10/16.26 | | (647) all_1044_2 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (647) implies: % 117.10/16.26 | | (648) all_1044_2 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (620), (621) imply: % 117.10/16.26 | | (649) all_990_2 = all_954_2 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (649) implies: % 117.10/16.26 | | (650) all_990_2 = all_954_2 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (641), (642) imply: % 117.10/16.26 | | (651) all_1036_2 = all_962_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (651) implies: % 117.10/16.26 | | (652) all_1036_2 = all_962_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (455), (648) imply: % 117.10/16.26 | | (653) all_1036_0 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (653) implies: % 117.10/16.26 | | (654) all_1036_0 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (436), (631) imply: % 117.10/16.26 | | (655) all_1038_1 = all_964_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (655) implies: % 117.10/16.26 | | (656) all_1038_1 = all_964_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (636), (638) imply: % 117.10/16.26 | | (657) all_1038_0 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (657) implies: % 117.10/16.26 | | (658) all_1038_0 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (634), (658) imply: % 117.10/16.26 | | (659) all_1000_2 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (659) implies: % 117.10/16.26 | | (660) all_1000_2 = all_828_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (435), (656) imply: % 117.10/16.26 | | (661) $difference(all_964_0, all_539_2) = 1 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (434), (656) imply: % 117.10/16.26 | | (662) all_964_0 = all_819_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (433), (656) imply: % 117.10/16.26 | | (663) all_1036_2 = all_964_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (663) implies: % 117.10/16.26 | | (664) all_1036_2 = all_964_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (454), (654) imply: % 117.10/16.26 | | (665) all_1002_1 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (665) implies: % 117.10/16.26 | | (666) all_1002_1 = all_940_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (652), (664) imply: % 117.10/16.26 | | (667) all_964_0 = all_962_0 % 117.10/16.26 | | % 117.10/16.26 | | SIMP: (667) implies: % 117.10/16.26 | | (668) all_964_0 = all_962_0 % 117.10/16.26 | | % 117.10/16.26 | | COMBINE_EQS: (423), (527) imply: % 117.10/16.26 | | (669) all_978_2 = all_952_0 % 117.10/16.27 | | % 117.10/16.27 | | SIMP: (669) implies: % 117.10/16.27 | | (670) all_978_2 = all_952_0 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (488), (611) imply: % 117.10/16.27 | | (671) all_940_1 = all_916_0 % 117.10/16.27 | | % 117.10/16.27 | | SIMP: (671) implies: % 117.10/16.27 | | (672) all_940_1 = all_916_0 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (516), (602) imply: % 117.10/16.27 | | (673) all_1018_2 = all_990_0 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (543), (602) imply: % 117.10/16.27 | | (674) all_1018_2 = all_978_0 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (483), (484) imply: % 117.10/16.27 | | (675) all_1002_0 = all_1000_0 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (483), (485) imply: % 117.10/16.27 | | (676) all_1002_0 = all_952_2 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (483), (486) imply: % 117.10/16.27 | | (677) all_1002_0 = all_946_2 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (483), (487) imply: % 117.10/16.27 | | (678) all_1002_0 = all_940_1 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (422), (529) imply: % 117.10/16.27 | | (679) all_978_2 = all_539_0 % 117.10/16.27 | | % 117.10/16.27 | | SIMP: (679) implies: % 117.10/16.27 | | (680) all_978_2 = all_539_0 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (673), (674) imply: % 117.10/16.27 | | (681) all_990_0 = all_978_0 % 117.10/16.27 | | % 117.10/16.27 | | SIMP: (681) implies: % 117.10/16.27 | | (682) all_990_0 = all_978_0 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (481), (482) imply: % 117.10/16.27 | | (683) all_940_1 = all_828_1 % 117.10/16.27 | | % 117.10/16.27 | | SIMP: (683) implies: % 117.10/16.27 | | (684) all_940_1 = all_828_1 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (594), (595) imply: % 117.10/16.27 | | (685) all_1008_0 = all_946_0 % 117.10/16.27 | | % 117.10/16.27 | | SIMP: (685) implies: % 117.10/16.27 | | (686) all_1008_0 = all_946_0 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (562), (604) imply: % 117.10/16.27 | | (687) all_1008_2 = all_724_3 % 117.10/16.27 | | % 117.10/16.27 | | SIMP: (687) implies: % 117.10/16.27 | | (688) all_1008_2 = all_724_3 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (412), (686) imply: % 117.10/16.27 | | (689) all_994_1 = all_946_0 % 117.10/16.27 | | % 117.10/16.27 | | SIMP: (689) implies: % 117.10/16.27 | | (690) all_994_1 = all_946_0 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (598), (600) imply: % 117.10/16.27 | | (691) all_990_2 = all_976_1 % 117.10/16.27 | | % 117.10/16.27 | | SIMP: (691) implies: % 117.10/16.27 | | (692) all_990_2 = all_976_1 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (599), (600) imply: % 117.10/16.27 | | (693) all_976_1 = all_938_1 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (676), (677) imply: % 117.10/16.27 | | (694) all_952_2 = all_946_2 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (676), (678) imply: % 117.10/16.27 | | (695) all_952_2 = all_940_1 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (675), (676) imply: % 117.10/16.27 | | (696) all_1000_0 = all_952_2 % 117.10/16.27 | | % 117.10/16.27 | | SIMP: (696) implies: % 117.10/16.27 | | (697) all_1000_0 = all_952_2 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (453), (666) imply: % 117.10/16.27 | | (698) all_964_1 = all_940_0 % 117.10/16.27 | | % 117.10/16.27 | | SIMP: (698) implies: % 117.10/16.27 | | (699) all_964_1 = all_940_0 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (646), (697) imply: % 117.10/16.27 | | (700) all_994_2 = all_952_2 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (480), (646) imply: % 117.10/16.27 | | (701) all_994_2 = all_944_2 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (479), (646) imply: % 117.10/16.27 | | (702) all_994_2 = all_978_1 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (452), (660) imply: % 117.10/16.27 | | (703) all_962_1 = all_828_0 % 117.10/16.27 | | % 117.10/16.27 | | SIMP: (703) implies: % 117.10/16.27 | | (704) all_962_1 = all_828_0 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (606), (690) imply: % 117.10/16.27 | | (705) all_976_2 = all_946_0 % 117.10/16.27 | | % 117.10/16.27 | | SIMP: (705) implies: % 117.10/16.27 | | (706) all_976_2 = all_946_0 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (700), (702) imply: % 117.10/16.27 | | (707) all_978_1 = all_952_2 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (701), (702) imply: % 117.10/16.27 | | (708) all_978_1 = all_944_2 % 117.10/16.27 | | % 117.10/16.27 | | COMBINE_EQS: (515), (682) imply: % 117.45/16.27 | | (709) all_978_0 = all_724_0 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (531), (682) imply: % 117.45/16.27 | | (710) all_978_0 = all_952_1 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (597), (682) imply: % 117.45/16.27 | | (711) all_978_0 = all_954_1 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (593), (609) imply: % 117.45/16.27 | | (712) all_978_2 = all_954_0 % 117.45/16.27 | | % 117.45/16.27 | | SIMP: (712) implies: % 117.45/16.27 | | (713) all_978_2 = all_954_0 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (478), (650) imply: % 117.45/16.27 | | (714) all_954_2 = all_946_2 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (650), (692) imply: % 117.45/16.27 | | (715) all_976_1 = all_954_2 % 117.45/16.27 | | % 117.45/16.27 | | SIMP: (715) implies: % 117.45/16.27 | | (716) all_976_1 = all_954_2 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (710), (711) imply: % 117.45/16.27 | | (717) all_954_1 = all_952_1 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (709), (711) imply: % 117.45/16.27 | | (718) all_954_1 = all_724_0 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (707), (708) imply: % 117.45/16.27 | | (719) all_952_2 = all_944_2 % 117.45/16.27 | | % 117.45/16.27 | | SIMP: (719) implies: % 117.45/16.27 | | (720) all_952_2 = all_944_2 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (680), (713) imply: % 117.45/16.27 | | (721) all_954_0 = all_539_0 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (670), (713) imply: % 117.45/16.27 | | (722) all_954_0 = all_952_0 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (693), (716) imply: % 117.45/16.27 | | (723) all_954_2 = all_938_1 % 117.45/16.27 | | % 117.45/16.27 | | SIMP: (723) implies: % 117.45/16.27 | | (724) all_954_2 = all_938_1 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (607), (706) imply: % 117.45/16.27 | | (725) all_946_0 = all_539_2 % 117.45/16.27 | | % 117.45/16.27 | | SIMP: (725) implies: % 117.45/16.27 | | (726) all_946_0 = all_539_2 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (661), (668) imply: % 117.45/16.27 | | (727) $difference(all_962_0, all_539_2) = 1 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (662), (668) imply: % 117.45/16.27 | | (728) all_962_0 = all_819_0 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (451), (699) imply: % 117.45/16.27 | | (729) all_962_1 = all_940_0 % 117.45/16.27 | | % 117.45/16.27 | | SIMP: (729) implies: % 117.45/16.27 | | (730) all_962_1 = all_940_0 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (727), (728) imply: % 117.45/16.27 | | (731) $difference(all_819_0, all_539_2) = 1 % 117.45/16.27 | | % 117.45/16.27 | | SIMP: (731) implies: % 117.45/16.27 | | (732) $difference(all_819_0, all_539_2) = 1 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (450), (730) imply: % 117.45/16.27 | | (733) all_940_0 = all_938_0 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (704), (730) imply: % 117.45/16.27 | | (734) all_940_0 = all_828_0 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (721), (722) imply: % 117.45/16.27 | | (735) all_952_0 = all_539_0 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (717), (718) imply: % 117.45/16.27 | | (736) all_952_1 = all_724_0 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (714), (724) imply: % 117.45/16.27 | | (737) all_946_2 = all_938_1 % 117.45/16.27 | | % 117.45/16.27 | | SIMP: (737) implies: % 117.45/16.27 | | (738) all_946_2 = all_938_1 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (695), (720) imply: % 117.45/16.27 | | (739) all_944_2 = all_940_1 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (694), (720) imply: % 117.45/16.27 | | (740) all_946_2 = all_944_2 % 117.45/16.27 | | % 117.45/16.27 | | SIMP: (740) implies: % 117.45/16.27 | | (741) all_946_2 = all_944_2 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (738), (741) imply: % 117.45/16.27 | | (742) all_944_2 = all_938_1 % 117.45/16.27 | | % 117.45/16.27 | | SIMP: (742) implies: % 117.45/16.27 | | (743) all_944_2 = all_938_1 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (739), (743) imply: % 117.45/16.27 | | (744) all_940_1 = all_938_1 % 117.45/16.27 | | % 117.45/16.27 | | SIMP: (744) implies: % 117.45/16.27 | | (745) all_940_1 = all_938_1 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (733), (734) imply: % 117.45/16.27 | | (746) all_938_0 = all_828_0 % 117.45/16.27 | | % 117.45/16.27 | | SIMP: (746) implies: % 117.45/16.27 | | (747) all_938_0 = all_828_0 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (684), (745) imply: % 117.45/16.27 | | (748) all_938_1 = all_828_1 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (672), (745) imply: % 117.45/16.27 | | (749) all_938_1 = all_916_0 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (449), (747) imply: % 117.45/16.27 | | (750) all_910_0 = all_828_0 % 117.45/16.27 | | % 117.45/16.27 | | SIMP: (750) implies: % 117.45/16.27 | | (751) all_910_0 = all_828_0 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (748), (749) imply: % 117.45/16.27 | | (752) all_916_0 = all_828_1 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (448), (751) imply: % 117.45/16.27 | | (753) all_828_0 = all_819_1 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (724), (748) imply: % 117.45/16.27 | | (754) all_954_2 = all_828_1 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (580), (748) imply: % 117.45/16.27 | | (755) all_1100_2 = all_828_1 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (506), (755) imply: % 117.45/16.27 | | (756) all_1114_4 = all_828_1 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (521), (709) imply: % 117.45/16.27 | | (757) all_1114_3 = all_724_0 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (514), (688) imply: % 117.45/16.27 | | (758) all_1114_2 = all_724_3 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (428), (721) imply: % 117.45/16.27 | | (759) all_1114_1 = all_539_0 % 117.45/16.27 | | % 117.45/16.27 | | COMBINE_EQS: (421), (726) imply: % 117.45/16.27 | | (760) all_1114_0 = all_539_2 % 117.45/16.27 | | % 117.45/16.27 | | REDUCE: (254), (753) imply: % 117.45/16.27 | | (761) $lesseq(1, $difference(all_828_1, all_819_1)) % 117.45/16.27 | | % 117.45/16.27 | | REDUCE: (250), (732) imply: % 117.45/16.27 | | (762) $lesseq(2, $difference(all_819_1, all_539_2)) % 117.45/16.27 | | % 117.45/16.27 | | BETA: splitting (280) gives: % 117.45/16.27 | | % 117.45/16.27 | | Case 1: % 117.45/16.27 | | | % 117.45/16.27 | | | (763) $lesseq(all_954_2, 1) % 117.45/16.27 | | | % 117.45/16.27 | | | REDUCE: (754), (763) imply: % 117.45/16.27 | | | (764) $lesseq(all_828_1, 1) % 117.45/16.27 | | | % 117.45/16.27 | | | COMBINE_INEQS: (761), (764) imply: % 117.45/16.27 | | | (765) $lesseq(all_819_1, 0) % 117.45/16.27 | | | % 117.45/16.27 | | | COMBINE_INEQS: (762), (765) imply: % 117.45/16.27 | | | (766) $lesseq(all_539_2, -2) % 117.45/16.27 | | | % 117.45/16.27 | | | COMBINE_INEQS: (410), (766) imply: % 117.45/16.27 | | | (767) $false % 117.45/16.27 | | | % 117.45/16.27 | | | CLOSE: (767) is inconsistent. % 117.45/16.27 | | | % 117.45/16.27 | | Case 2: % 117.45/16.27 | | | % 117.45/16.27 | | | (768) $lesseq(2, all_954_2) % 117.45/16.27 | | | % 117.45/16.27 | | | REDUCE: (754), (768) imply: % 117.45/16.27 | | | (769) $lesseq(2, all_828_1) % 117.45/16.27 | | | % 117.45/16.27 | | | BETA: splitting (403) gives: % 117.45/16.27 | | | % 117.45/16.27 | | | Case 1: % 117.45/16.27 | | | | % 117.45/16.27 | | | | (770) $lesseq(1, $difference(all_1114_1, all_1114_0)) % 117.45/16.27 | | | | % 117.45/16.27 | | | | REDUCE: (759), (760), (770) imply: % 117.45/16.27 | | | | (771) $lesseq(1, $difference(all_539_0, all_539_2)) % 117.45/16.27 | | | | % 117.45/16.27 | | | | COMBINE_INEQS: (34), (771) imply: % 117.45/16.27 | | | | (772) $false % 117.45/16.27 | | | | % 117.45/16.27 | | | | CLOSE: (772) is inconsistent. % 117.45/16.27 | | | | % 117.45/16.27 | | | Case 2: % 117.45/16.27 | | | | % 117.45/16.27 | | | | (773) ~ ($lesseq(1, $difference(all_1114_3, all_1114_2))) | ~ % 117.45/16.27 | | | | ($lesseq(1, all_1114_4)) % 117.45/16.27 | | | | % 117.45/16.27 | | | | BETA: splitting (773) gives: % 117.45/16.27 | | | | % 117.45/16.27 | | | | Case 1: % 117.45/16.27 | | | | | % 117.45/16.27 | | | | | (774) $lesseq(all_1114_4, 0) % 117.45/16.27 | | | | | % 117.45/16.27 | | | | | REDUCE: (756), (774) imply: % 117.45/16.27 | | | | | (775) $lesseq(all_828_1, 0) % 117.45/16.27 | | | | | % 117.45/16.27 | | | | | COMBINE_INEQS: (769), (775) imply: % 117.45/16.27 | | | | | (776) $false % 117.45/16.27 | | | | | % 117.45/16.27 | | | | | CLOSE: (776) is inconsistent. % 117.45/16.27 | | | | | % 117.45/16.27 | | | | Case 2: % 117.45/16.27 | | | | | % 117.45/16.27 | | | | | (777) $lesseq(all_1114_3, all_1114_2) % 117.45/16.27 | | | | | % 117.45/16.27 | | | | | REDUCE: (757), (758), (777) imply: % 117.45/16.27 | | | | | (778) $lesseq(all_724_0, all_724_3) % 117.45/16.27 | | | | | % 117.45/16.27 | | | | | COMBINE_INEQS: (87), (778) imply: % 117.45/16.27 | | | | | (779) $false % 117.45/16.27 | | | | | % 117.45/16.27 | | | | | CLOSE: (779) is inconsistent. % 117.45/16.27 | | | | | % 117.45/16.27 | | | | End of split % 117.45/16.27 | | | | % 117.45/16.27 | | | End of split % 117.45/16.27 | | | % 117.45/16.27 | | End of split % 117.45/16.27 | | % 117.48/16.28 | Case 2: % 117.48/16.28 | | % 117.48/16.28 | | (780) $lesseq(all_539_2, -2) % 117.48/16.28 | | % 117.48/16.28 | | COMBINE_INEQS: (410), (780) imply: % 117.48/16.28 | | (781) $false % 117.48/16.28 | | % 117.48/16.28 | | CLOSE: (781) is inconsistent. % 117.48/16.28 | | % 117.48/16.28 | End of split % 117.48/16.28 | % 117.48/16.28 End of proof % 117.48/16.28 % SZS output end Proof for theBenchmark % 117.48/16.28 % 117.48/16.28 15751ms %------------------------------------------------------------------------------