%------------------------------------------------------------------------------ % 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 : n025.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 04:11:42 EDT 2023 % Result : Theorem 98.55s 14.10s % Output : Proof 206.37s % 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 % 0.11/0.32 % Computer : n025.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Sun Aug 27 16:32:38 EDT 2023 % 0.17/0.32 % CPUTime : % 0.17/0.61 ________ _____ % 0.17/0.61 ___ __ \_________(_)________________________________ % 0.17/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.61 % 0.17/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.61 (2023-06-19) % 0.17/0.61 % 0.17/0.61 (c) Philipp Rümmer, 2009-2023 % 0.17/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.61 Amanda Stjerna. % 0.17/0.61 Free software under BSD-3-Clause. % 0.17/0.61 % 0.17/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.61 % 0.17/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.17/0.63 Running up to 7 provers in parallel. % 0.17/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.13/1.11 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 2.13/1.11 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 2.13/1.12 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 2.13/1.12 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 2.13/1.12 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 2.71/1.15 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 2.71/1.16 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 20.39/3.76 Prover 2: Preprocessing ... % 20.39/3.77 Prover 6: Preprocessing ... % 20.39/3.77 Prover 3: Preprocessing ... % 20.39/3.78 Prover 0: Preprocessing ... % 20.39/3.78 Prover 5: Preprocessing ... % 20.39/3.78 Prover 4: Preprocessing ... % 22.19/3.92 Prover 1: Preprocessing ... % 48.83/7.55 Prover 1: Warning: ignoring some quantifiers % 51.42/7.89 Prover 1: Constructing countermodel ... % 52.07/7.94 Prover 6: Proving ... % 52.52/8.00 Prover 3: Warning: ignoring some quantifiers % 53.17/8.09 Prover 3: Constructing countermodel ... % 58.87/8.88 Prover 4: Warning: ignoring some quantifiers % 59.69/9.04 Prover 4: Constructing countermodel ... % 62.42/9.36 Prover 0: Proving ... % 65.73/9.78 Prover 5: Proving ... % 66.18/9.94 Prover 2: Proving ... % 83.26/12.13 Prover 2: stopped % 84.04/12.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 84.04/12.17 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 88.93/12.80 Prover 7: Preprocessing ... % 97.73/13.98 Prover 5: stopped % 97.73/13.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 97.73/13.99 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 98.55/14.09 Prover 6: proved (13436ms) % 98.55/14.10 % 98.55/14.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 98.55/14.10 % 98.55/14.10 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 98.55/14.10 Prover 0: stopped % 98.55/14.10 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 99.11/14.11 Prover 7: Warning: ignoring some quantifiers % 99.11/14.11 Prover 3: stopped % 99.11/14.12 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 99.11/14.12 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 99.11/14.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 99.11/14.14 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 100.53/14.29 Prover 7: Constructing countermodel ... % 105.09/14.92 Prover 8: Preprocessing ... % 106.34/15.08 Prover 13: Preprocessing ... % 107.06/15.17 Prover 11: Preprocessing ... % 107.44/15.20 Prover 10: Preprocessing ... % 112.28/15.93 Prover 8: Warning: ignoring some quantifiers % 112.28/15.99 Prover 1: stopped % 113.31/16.01 Prover 8: Constructing countermodel ... % 113.31/16.01 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 113.31/16.01 Prover 16: Warning: Problem contains reals, using incomplete axiomatisation % 115.60/16.32 Prover 10: Warning: ignoring some quantifiers % 116.72/16.41 Prover 10: Constructing countermodel ... % 117.66/16.59 Prover 13: Warning: ignoring some quantifiers % 117.66/16.68 Prover 11: Warning: ignoring some quantifiers % 118.76/16.73 Prover 13: Constructing countermodel ... % 119.61/16.80 Prover 16: Preprocessing ... % 119.78/16.81 Prover 11: Constructing countermodel ... % 126.04/17.65 Prover 16: Warning: ignoring some quantifiers % 126.64/17.73 Prover 16: Constructing countermodel ... % 127.61/17.95 Prover 13: stopped % 127.61/17.98 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 128.73/17.99 Prover 19: Warning: Problem contains reals, using incomplete axiomatisation % 133.13/18.64 Prover 19: Preprocessing ... % 143.34/19.86 Prover 19: Warning: ignoring some quantifiers % 143.34/19.94 Prover 19: Constructing countermodel ... % 149.37/20.72 Prover 16: stopped % 153.24/21.18 Prover 19: stopped % 204.29/27.99 Prover 4: stopped % 205.06/28.25 Prover 8: Found proof (size 70) % 205.06/28.25 Prover 8: proved (14198ms) % 205.47/28.25 Prover 11: stopped % 205.47/28.25 Prover 10: stopped % 205.47/28.25 Prover 7: stopped % 205.47/28.25 % 205.47/28.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 205.47/28.25 % 205.47/28.27 % SZS output start Proof for theBenchmark % 205.47/28.30 Assumptions after simplification: % 205.47/28.30 --------------------------------- % 205.47/28.30 % 205.47/28.30 (axiom206) % 205.47/28.31 Int_nat_fun$(nat$) & ? [v0: Nat$] : ? [v1: Nat_set$] : (fun_app$p(nat$, 1) = % 205.47/28.31 v0 & atLeastAtMost$(v0, v0) = v1 & Nat_set$(v1) & Nat$(v0) & ! [v2: % 205.47/28.31 Nat_complex_fun$] : ! [v3: Complex$] : ( ~ (prod$(v2, v1) = v3) | ~ % 205.47/28.31 Nat_complex_fun$(v2) | (fun_app$(v2, v0) = v3 & Complex$(v3)))) % 205.47/28.31 % 205.47/28.31 (axiom302) % 205.47/28.31 ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v0, v1) = 0) | % 205.47/28.31 ? [v2: int] : ( ~ (v2 = 0) & real_$lesseq(v1, v0) = v2)) & ! [v0: $real] : % 205.47/28.31 ! [v1: int] : (v1 = 0 | ~ (real_$lesseq(v0, v0) = v1)) % 205.47/28.31 % 205.47/28.31 (axiom316) % 205.47/28.31 ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v0, v1) = 0) | % 205.47/28.31 ? [v2: int] : ( ~ (v2 = 0) & real_$lesseq(v1, v0) = v2)) & ! [v0: $real] : % 205.47/28.31 ! [v1: int] : (v1 = 0 | ~ (real_$lesseq(v0, v0) = v1)) % 205.47/28.31 % 205.47/28.31 (axiom324) % 205.47/28.31 ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v0, v1) = 0) | % 205.47/28.31 ? [v2: int] : ( ~ (v2 = 0) & real_$lesseq(v1, v0) = v2)) & ! [v0: $real] : % 205.47/28.31 ! [v1: int] : (v1 = 0 | ~ (real_$lesseq(v0, v0) = v1)) % 205.47/28.31 % 205.47/28.31 (axiom35) % 205.47/28.32 Nat_complex_fun$(of_nat$) & Nat$(n$) & Complex$(zero$) & Int_nat_fun$(nat$) & % 205.47/28.32 Complex_real_fun$(norm$) & ? [v0: Complex$] : ? [v1: Complex_set$] : ? [v2: % 205.47/28.32 Nat$] : ? [v3: Nat_set$] : (closed_segment$(zero$, v0) = v1 & % 205.47/28.32 fun_app$p(nat$, 1) = v2 & atLeastAtMost$(v2, n$) = v3 & fun_app$(of_nat$, % 205.47/28.32 n$) = v0 & Nat_set$(v3) & Complex_set$(v1) & Nat$(v2) & Complex$(v0) & ! % 205.47/28.32 [v4: $real] : ( ~ (real_$lesseq(real_0, v4) = 0) | thesis$ | ? [v5: % 205.47/28.32 Complex$] : ? [v6: Nat_complex_fun$] : ? [v7: Complex$] : ? [v8: % 205.47/28.32 $real] : ? [v9: int] : ( ~ (v9 = 0) & real_$lesseq(v8, v4) = v9 & % 205.47/28.32 prod$(v6, v3) = v7 & fun_app$i(norm$, v7) = v8 & member$(v5, v1) = 0 & % 205.47/28.32 uu$(v5) = v6 & Nat_complex_fun$(v6) & Complex$(v7) & Complex$(v5)))) % 205.47/28.32 % 205.47/28.32 (axiom355) % 205.47/28.32 Nat_int_fun$(of_nat$a) & Int_nat_fun$(nat$) & ? [v0: Nat$] : (fun_app$p(nat$, % 205.47/28.32 1) = v0 & fun_app$m(of_nat$a, v0) = 1 & Nat$(v0)) % 205.47/28.32 % 205.47/28.32 (axiom40) % 205.47/28.32 real_$lesseq(real_0, c$) = 0 % 205.47/28.32 % 205.47/28.32 (axiom41) % 205.47/28.32 Nat_complex_fun$(of_nat$) & Nat$(n$) & Complex$(zero$) & Int_nat_fun$(nat$) & % 205.47/28.32 Complex_real_fun$(norm$) & ? [v0: Complex$] : ? [v1: Complex_set$] : ? [v2: % 205.47/28.32 Nat$] : ? [v3: Nat_set$] : (closed_segment$(zero$, v0) = v1 & % 205.47/28.32 fun_app$p(nat$, 1) = v2 & atLeastAtMost$(v2, n$) = v3 & fun_app$(of_nat$, % 205.47/28.32 n$) = v0 & Nat_set$(v3) & Complex_set$(v1) & Nat$(v2) & Complex$(v0) & ! % 205.47/28.32 [v4: Complex$] : ( ~ (member$(v4, v1) = 0) | ~ Complex$(v4) | ? [v5: % 205.47/28.32 Nat_complex_fun$] : ? [v6: Complex$] : ? [v7: $real] : % 205.47/28.32 (real_$lesseq(v7, c$) = 0 & prod$(v5, v3) = v6 & fun_app$i(norm$, v6) = v7 % 205.47/28.32 & uu$(v4) = v5 & Nat_complex_fun$(v5) & Complex$(v6)))) % 205.47/28.32 % 205.47/28.32 (axiom44) % 205.47/28.32 Nat_complex_fun$(of_nat$) & Complex$(one$) & Int_nat_fun$(nat$) & ? [v0: % 205.47/28.32 Nat$] : (fun_app$p(nat$, 1) = v0 & fun_app$(of_nat$, v0) = one$ & Nat$(v0)) % 205.47/28.32 % 205.47/28.32 (axiom45) % 205.47/28.32 Nat_int_fun$(of_nat$a) & Int_nat_fun$(nat$) & ? [v0: Nat$] : (fun_app$p(nat$, % 205.47/28.32 1) = v0 & fun_app$m(of_nat$a, v0) = 1 & Nat$(v0)) % 205.47/28.32 % 205.47/28.32 (axiom46) % 205.47/28.33 Nat_real_fun$(of_nat$b) & Int_nat_fun$(nat$) & ? [v0: Nat$] : % 205.47/28.33 (fun_app$p(nat$, 1) = v0 & fun_app$h(of_nat$b, v0) = real_1 & Nat$(v0)) % 205.47/28.33 % 205.47/28.33 (conjecture34) % 205.47/28.33 ~ thesis$ % 205.47/28.33 % 205.47/28.33 (input) % 205.47/28.35 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_2) & ~ % 205.47/28.35 (real_very_large = real_1) & ~ (real_very_large = real_0) & ~ % 205.47/28.35 (real_very_small = real_2) & ~ (real_very_small = real_1) & ~ % 205.47/28.35 (real_very_small = real_0) & ~ (real_2 = real_1) & ~ (real_2 = real_0) & ~ % 205.47/28.35 (real_1 = real_0) & real_$is_int(real_2) = 0 & real_$is_int(real_1) = 0 & % 205.47/28.35 real_$is_int(real_0) = 0 & real_$is_rat(real_2) = 0 & real_$is_rat(real_1) = 0 % 205.47/28.35 & real_$is_rat(real_0) = 0 & real_$floor(real_2) = real_2 & % 205.47/28.35 real_$floor(real_1) = real_1 & real_$floor(real_0) = real_0 & % 205.47/28.35 real_$ceiling(real_2) = real_2 & real_$ceiling(real_1) = real_1 & % 205.47/28.35 real_$ceiling(real_0) = real_0 & real_$truncate(real_2) = real_2 & % 205.47/28.35 real_$truncate(real_1) = real_1 & real_$truncate(real_0) = real_0 & % 205.47/28.35 real_$round(real_2) = real_2 & real_$round(real_1) = real_1 & % 205.47/28.35 real_$round(real_0) = real_0 & real_$to_int(real_2) = 2 & real_$to_int(real_1) % 205.47/28.35 = 1 & real_$to_int(real_0) = 0 & real_$to_rat(real_2) = rat_2 & % 205.47/28.35 real_$to_rat(real_1) = rat_1 & real_$to_rat(real_0) = rat_0 & % 205.47/28.35 real_$to_real(real_2) = real_2 & real_$to_real(real_1) = real_1 & % 205.47/28.35 real_$to_real(real_0) = real_0 & int_$to_real(2) = real_2 & int_$to_real(1) = % 205.47/28.35 real_1 & int_$to_real(0) = real_0 & real_$quotient(real_2, real_2) = real_1 & % 205.47/28.35 real_$quotient(real_2, real_1) = real_2 & real_$quotient(real_1, real_1) = % 205.47/28.35 real_1 & real_$quotient(real_0, real_2) = real_0 & real_$quotient(real_0, % 205.47/28.35 real_1) = real_0 & real_$product(real_2, real_1) = real_2 & % 205.47/28.35 real_$product(real_2, real_0) = real_0 & real_$product(real_1, real_2) = % 205.47/28.35 real_2 & real_$product(real_1, real_1) = real_1 & real_$product(real_1, % 205.47/28.35 real_0) = real_0 & real_$product(real_0, real_2) = real_0 & % 205.47/28.35 real_$product(real_0, real_1) = real_0 & real_$product(real_0, real_0) = % 205.47/28.35 real_0 & real_$uminus(real_0) = real_0 & real_$greatereq(real_very_small, % 205.47/28.35 real_very_large) = 1 & real_$greatereq(real_2, real_2) = 0 & % 205.47/28.35 real_$greatereq(real_2, real_1) = 0 & real_$greatereq(real_2, real_0) = 0 & % 205.47/28.35 real_$greatereq(real_1, real_2) = 1 & real_$greatereq(real_1, real_1) = 0 & % 205.47/28.35 real_$greatereq(real_1, real_0) = 0 & real_$greatereq(real_0, real_2) = 1 & % 205.47/28.35 real_$greatereq(real_0, real_1) = 1 & real_$greatereq(real_0, real_0) = 0 & % 205.47/28.35 real_$greater(real_very_large, real_2) = 0 & real_$greater(real_very_large, % 205.47/28.35 real_1) = 0 & real_$greater(real_very_large, real_0) = 0 & % 205.47/28.35 real_$greater(real_very_small, real_very_large) = 1 & real_$greater(real_2, % 205.47/28.35 real_very_small) = 0 & real_$greater(real_2, real_2) = 1 & % 205.47/28.35 real_$greater(real_2, real_1) = 0 & real_$greater(real_2, real_0) = 0 & % 205.47/28.35 real_$greater(real_1, real_very_small) = 0 & real_$greater(real_1, real_2) = 1 % 205.47/28.35 & real_$greater(real_1, real_1) = 1 & real_$greater(real_1, real_0) = 0 & % 205.47/28.35 real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0, real_2) = 1 % 205.47/28.35 & real_$greater(real_0, real_1) = 1 & real_$greater(real_0, real_0) = 1 & % 205.47/28.35 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small, % 205.47/28.35 real_2) = 0 & real_$less(real_very_small, real_1) = 0 & % 205.47/28.35 real_$less(real_very_small, real_0) = 0 & real_$less(real_2, real_very_large) % 205.47/28.35 = 0 & real_$less(real_2, real_2) = 1 & real_$less(real_2, real_1) = 1 & % 205.47/28.35 real_$less(real_2, real_0) = 1 & real_$less(real_1, real_very_large) = 0 & % 205.47/28.35 real_$less(real_1, real_2) = 0 & real_$less(real_1, real_1) = 1 & % 205.47/28.35 real_$less(real_1, real_0) = 1 & real_$less(real_0, real_very_large) = 0 & % 205.47/28.35 real_$less(real_0, real_2) = 0 & real_$less(real_0, real_1) = 0 & % 205.47/28.35 real_$less(real_0, real_0) = 1 & real_$sum(real_2, real_0) = real_2 & % 205.47/28.35 real_$sum(real_1, real_1) = real_2 & real_$sum(real_1, real_0) = real_1 & % 205.47/28.35 real_$sum(real_0, real_2) = real_2 & real_$sum(real_0, real_1) = real_1 & % 205.47/28.35 real_$sum(real_0, real_0) = real_0 & real_$lesseq(real_very_small, % 205.47/28.35 real_very_large) = 0 & real_$lesseq(real_2, real_2) = 0 & % 205.47/28.35 real_$lesseq(real_2, real_1) = 1 & real_$lesseq(real_2, real_0) = 1 & % 205.47/28.35 real_$lesseq(real_1, real_2) = 0 & real_$lesseq(real_1, real_1) = 0 & % 205.47/28.35 real_$lesseq(real_1, real_0) = 1 & real_$lesseq(real_0, real_2) = 0 & % 205.47/28.35 real_$lesseq(real_0, real_1) = 0 & real_$lesseq(real_0, real_0) = 0 & % 205.47/28.35 real_$difference(real_2, real_2) = real_0 & real_$difference(real_2, real_1) = % 205.47/28.35 real_1 & real_$difference(real_2, real_0) = real_2 & real_$difference(real_1, % 205.47/28.35 real_1) = real_0 & real_$difference(real_1, real_0) = real_1 & % 205.47/28.35 real_$difference(real_0, real_0) = real_0 & ! [v0: $real] : ! [v1: $real] : % 205.47/28.35 ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) % 205.47/28.35 | ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 & % 205.47/28.35 real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 205.47/28.35 $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~ (real_$quotient(v2, % 205.47/28.35 v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0: $real] : ! [v1: % 205.47/28.35 $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v1) = % 205.47/28.35 0) | ~ (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & % 205.47/28.35 real_$lesseq(v1, v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 205.47/28.35 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~ % 205.47/28.35 (real_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, % 205.47/28.35 v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: % 205.47/28.35 int] : (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = % 205.47/28.35 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: % 205.47/28.35 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ( ~ % 205.47/28.35 (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) | real_$difference(v1, % 205.47/28.35 v0) = v3) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v2 = % 205.47/28.35 real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) = v2)) & ! [v0: % 205.47/28.35 $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 205.47/28.35 (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, % 205.47/28.35 v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | % 205.47/28.35 ~ (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 205.47/28.35 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 205.47/28.35 int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = % 205.47/28.35 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! % 205.47/28.35 [v2: $real] : ( ~ (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2) & % 205.47/28.35 ! [v0: $real] : ! [v1: $real] : ! [v2: any] : ( ~ (real_$less(v1, v0) = v2) % 205.47/28.35 | real_$lesseq(v1, v0) = 0 | ( ~ (v2 = 0) & ~ (v1 = v0))) & ! [v0: $real] % 205.47/28.35 : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) | % 205.47/28.35 real_$sum(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ % 205.47/28.35 (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : ! [v1: $real] : ( ~ % 205.47/28.35 (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: % 205.47/28.35 $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & ! % 205.47/28.35 [v0: $real] : ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | % 205.47/28.35 real_$less(v1, v0) = 0) & ! [v0: $real] : (v0 = real_0 | ~ % 205.47/28.35 (real_$uminus(v0) = v0)) % 205.47/28.35 % 205.47/28.35 (function-axioms) % 206.00/28.42 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 206.00/28.42 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 206.00/28.42 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 206.00/28.42 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0: % 206.00/28.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 206.00/28.42 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~ % 206.00/28.42 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 206.00/28.42 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 206.00/28.42 (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, v2) = v0)) & ! [v0: % 206.00/28.42 Nat$] : ! [v1: Nat$] : ! [v2: Int_set$] : ! [v3: Int_nat_fun$] : (v1 = v0 % 206.00/28.42 | ~ (prod$k(v3, v2) = v1) | ~ (prod$k(v3, v2) = v0)) & ! [v0: Nat$] : ! % 206.00/28.42 [v1: Nat$] : ! [v2: Complex_set$] : ! [v3: Complex_nat_fun$] : (v1 = v0 | ~ % 206.00/28.42 (prod$j(v3, v2) = v1) | ~ (prod$j(v3, v2) = v0)) & ! [v0: Complex$] : ! % 206.00/28.42 [v1: Complex$] : ! [v2: Int_set$] : ! [v3: Int_complex_fun$] : (v1 = v0 | ~ % 206.00/28.42 (prod$i(v3, v2) = v1) | ~ (prod$i(v3, v2) = v0)) & ! [v0: Complex$] : ! % 206.00/28.42 [v1: Complex$] : ! [v2: int] : ! [v3: Int_complex_fun$] : (v1 = v0 | ~ % 206.00/28.42 (fun_app$w(v3, v2) = v1) | ~ (fun_app$w(v3, v2) = v0)) & ! [v0: % 206.00/28.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 206.00/28.42 $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) = % 206.00/28.42 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : % 206.00/28.42 (v1 = v0 | ~ (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! % 206.00/28.42 [v0: int] : ! [v1: int] : ! [v2: Int_set$] : ! [v3: Int_int_fun$] : (v1 = % 206.00/28.42 v0 | ~ (prod$h(v3, v2) = v1) | ~ (prod$h(v3, v2) = v0)) & ! [v0: $real] : % 206.00/28.42 ! [v1: $real] : ! [v2: Int_set$] : ! [v3: Int_real_fun$] : (v1 = v0 | ~ % 206.00/28.42 (prod$g(v3, v2) = v1) | ~ (prod$g(v3, v2) = v0)) & ! [v0: int] : ! [v1: % 206.00/28.42 int] : ! [v2: $real] : ! [v3: Real_int_fun$] : (v1 = v0 | ~ % 206.00/28.42 (fun_app$v(v3, v2) = v1) | ~ (fun_app$v(v3, v2) = v0)) & ! [v0: % 206.00/28.42 Real_bool_fun$] : ! [v1: Real_bool_fun$] : ! [v2: $real] : ! [v3: % 206.00/28.42 Real_real_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$u(v3, v2) = v1) | ~ % 206.00/28.42 (fun_app$u(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 206.00/28.42 MultipleValueBool] : ! [v2: $real] : ! [v3: Real_bool_fun$] : (v1 = v0 | % 206.00/28.42 ~ (fun_app$t(v3, v2) = v1) | ~ (fun_app$t(v3, v2) = v0)) & ! [v0: % 206.00/28.42 Int_bool_fun$] : ! [v1: Int_bool_fun$] : ! [v2: Int_bool_fun$] : ! [v3: % 206.00/28.42 Int_bool_fun$] : (v1 = v0 | ~ (minus$f(v3, v2) = v1) | ~ (minus$f(v3, v2) % 206.00/28.42 = v0)) & ! [v0: Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: % 206.00/28.42 Nat_bool_fun$] : ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ (minus$e(v3, v2) = % 206.00/28.42 v1) | ~ (minus$e(v3, v2) = v0)) & ! [v0: Complex_bool_fun$] : ! [v1: % 206.00/28.42 Complex_bool_fun$] : ! [v2: Complex_bool_fun$] : ! [v3: Complex_bool_fun$] % 206.00/28.42 : (v1 = v0 | ~ (minus$d(v3, v2) = v1) | ~ (minus$d(v3, v2) = v0)) & ! [v0: % 206.00/28.42 Int_set$] : ! [v1: Int_set$] : ! [v2: Int_set$] : ! [v3: Int_set$] : (v1 % 206.00/28.42 = v0 | ~ (minus$c(v3, v2) = v1) | ~ (minus$c(v3, v2) = v0)) & ! [v0: % 206.00/28.42 Nat_set$] : ! [v1: Nat_set$] : ! [v2: Nat_set$] : ! [v3: Nat_set$] : (v1 % 206.00/28.42 = v0 | ~ (minus$b(v3, v2) = v1) | ~ (minus$b(v3, v2) = v0)) & ! [v0: % 206.00/28.42 Complex_set$] : ! [v1: Complex_set$] : ! [v2: Complex_set$] : ! [v3: % 206.00/28.42 Complex_set$] : (v1 = v0 | ~ (minus$a(v3, v2) = v1) | ~ (minus$a(v3, v2) = % 206.00/28.42 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 206.00/28.42 Nat_bool_fun$] : ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ (less_eq$f(v3, v2) = % 206.00/28.42 v1) | ~ (less_eq$f(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 206.00/28.42 MultipleValueBool] : ! [v2: Complex_bool_fun$] : ! [v3: Complex_bool_fun$] % 206.00/28.42 : (v1 = v0 | ~ (less_eq$e(v3, v2) = v1) | ~ (less_eq$e(v3, v2) = v0)) & ! % 206.00/28.42 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Int_set$] : ! % 206.00/28.42 [v3: Int_set$] : (v1 = v0 | ~ (less_eq$d(v3, v2) = v1) | ~ (less_eq$d(v3, % 206.00/28.42 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 206.00/28.42 ! [v2: Nat_set$] : ! [v3: Nat_set$] : (v1 = v0 | ~ (less_eq$c(v3, v2) = v1) % 206.00/28.42 | ~ (less_eq$c(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 206.00/28.42 MultipleValueBool] : ! [v2: Real_set$] : ! [v3: Real_set$] : (v1 = v0 | ~ % 206.00/28.42 (less_eq$b(v3, v2) = v1) | ~ (less_eq$b(v3, v2) = v0)) & ! [v0: % 206.00/28.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Complex_set$] : ! % 206.00/28.42 [v3: Complex_set$] : (v1 = v0 | ~ (less_eq$a(v3, v2) = v1) | ~ % 206.00/28.42 (less_eq$a(v3, v2) = v0)) & ! [v0: Real_set$] : ! [v1: Real_set$] : ! % 206.00/28.42 [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (atLeastAtMost$a(v3, v2) = v1) | % 206.00/28.42 ~ (atLeastAtMost$a(v3, v2) = v0)) & ! [v0: Nat_nat_fun$] : ! [v1: % 206.00/28.42 Nat_nat_fun$] : ! [v2: Nat_real_fun$] : ! [v3: % 206.00/28.42 Nat_real_fun_nat_nat_fun_fun$] : (v1 = v0 | ~ (fun_app$s(v3, v2) = v1) | ~ % 206.00/28.42 (fun_app$s(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 206.00/28.42 MultipleValueBool] : ! [v2: Nat_real_fun$] : ! [v3: % 206.00/28.42 Nat_real_fun_bool_fun$] : (v1 = v0 | ~ (fun_app$r(v3, v2) = v1) | ~ % 206.00/28.42 (fun_app$r(v3, v2) = v0)) & ! [v0: Real_set$] : ! [v1: Real_set$] : ! % 206.00/28.42 [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (closed_segment$a(v3, v2) = v1) | % 206.00/28.42 ~ (closed_segment$a(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 206.00/28.42 MultipleValueBool] : ! [v2: Real_set$] : ! [v3: $real] : (v1 = v0 | ~ % 206.00/28.42 (member$c(v3, v2) = v1) | ~ (member$c(v3, v2) = v0)) & ! [v0: $real] : ! % 206.00/28.42 [v1: $real] : ! [v2: Nat_set$] : ! [v3: Nat_real_fun$] : (v1 = v0 | ~ % 206.00/28.42 (prod$f(v3, v2) = v1) | ~ (prod$f(v3, v2) = v0)) & ! [v0: $real] : ! [v1: % 206.00/28.42 $real] : ! [v2: Complex_set$] : ! [v3: Complex_real_fun$] : (v1 = v0 | ~ % 206.00/28.42 (prod$e(v3, v2) = v1) | ~ (prod$e(v3, v2) = v0)) & ! [v0: int] : ! [v1: % 206.00/28.42 int] : ! [v2: Nat_set$] : ! [v3: Nat_int_fun$] : (v1 = v0 | ~ (prod$d(v3, % 206.00/28.42 v2) = v1) | ~ (prod$d(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! % 206.00/28.42 [v2: Complex_set$] : ! [v3: Complex_int_fun$] : (v1 = v0 | ~ (prod$c(v3, v2) % 206.00/28.42 = v1) | ~ (prod$c(v3, v2) = v0)) & ! [v0: Complex$] : ! [v1: Complex$] % 206.00/28.42 : ! [v2: Complex_set$] : ! [v3: Complex_complex_fun$] : (v1 = v0 | ~ % 206.00/28.42 (prod$b(v3, v2) = v1) | ~ (prod$b(v3, v2) = v0)) & ! [v0: Nat$] : ! [v1: % 206.00/28.42 Nat$] : ! [v2: Complex$] : ! [v3: Complex_nat_fun$] : (v1 = v0 | ~ % 206.00/28.42 (fun_app$q(v3, v2) = v1) | ~ (fun_app$q(v3, v2) = v0)) & ! [v0: Nat$] : ! % 206.00/28.42 [v1: Nat$] : ! [v2: Nat_set$] : ! [v3: Nat_nat_fun$] : (v1 = v0 | ~ % 206.00/28.42 (prod$a(v3, v2) = v1) | ~ (prod$a(v3, v2) = v0)) & ! [v0: Complex_set$] : % 206.00/28.42 ! [v1: Complex_set$] : ! [v2: Complex$] : ! [v3: Complex$] : (v1 = v0 | ~ % 206.00/28.42 (closed_segment$(v3, v2) = v1) | ~ (closed_segment$(v3, v2) = v0)) & ! % 206.00/28.42 [v0: Nat$] : ! [v1: Nat$] : ! [v2: int] : ! [v3: Int_nat_fun$] : (v1 = v0 | % 206.00/28.42 ~ (fun_app$p(v3, v2) = v1) | ~ (fun_app$p(v3, v2) = v0)) & ! [v0: % 206.00/28.42 Nat_set$] : ! [v1: Nat_set$] : ! [v2: Nat$] : ! [v3: Nat$] : (v1 = v0 | % 206.00/28.42 ~ (atLeastAtMost$(v3, v2) = v1) | ~ (atLeastAtMost$(v3, v2) = v0)) & ! % 206.00/28.42 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! % 206.00/28.42 [v3: $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, % 206.00/28.42 v2) = v0)) & ! [v0: Nat_complex_fun$] : ! [v1: Nat_complex_fun$] : ! % 206.00/28.42 [v2: Nat_set$] : ! [v3: Nat_nat_complex_fun_fun$] : (v1 = v0 | ~ (uuh$(v3, % 206.00/28.42 v2) = v1) | ~ (uuh$(v3, v2) = v0)) & ! [v0: Int_bool_fun$] : ! [v1: % 206.00/28.42 Int_bool_fun$] : ! [v2: Int_set$] : ! [v3: Int_set$] : (v1 = v0 | ~ % 206.00/28.42 (uuq$(v3, v2) = v1) | ~ (uuq$(v3, v2) = v0)) & ! [v0: Nat_bool_fun$] : ! % 206.00/28.42 [v1: Nat_bool_fun$] : ! [v2: Nat_set$] : ! [v3: Nat_set$] : (v1 = v0 | ~ % 206.00/28.42 (uup$(v3, v2) = v1) | ~ (uup$(v3, v2) = v0)) & ! [v0: Complex_bool_fun$] : % 206.00/28.42 ! [v1: Complex_bool_fun$] : ! [v2: Complex_set$] : ! [v3: Complex_set$] : % 206.00/28.42 (v1 = v0 | ~ (uuo$(v3, v2) = v1) | ~ (uuo$(v3, v2) = v0)) & ! [v0: % 206.00/28.42 Int_bool_fun$] : ! [v1: Int_bool_fun$] : ! [v2: Int_bool_fun$] : ! [v3: % 206.00/28.42 Int_set$] : (v1 = v0 | ~ (uun$(v3, v2) = v1) | ~ (uun$(v3, v2) = v0)) & ! % 206.00/28.42 [v0: Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: Nat_bool_fun$] : ! % 206.00/28.42 [v3: Nat_set$] : (v1 = v0 | ~ (uum$(v3, v2) = v1) | ~ (uum$(v3, v2) = v0)) & % 206.00/28.42 ! [v0: Complex_bool_fun$] : ! [v1: Complex_bool_fun$] : ! [v2: % 206.00/28.42 Complex_bool_fun$] : ! [v3: Complex_set$] : (v1 = v0 | ~ (uul$(v3, v2) = % 206.00/28.42 v1) | ~ (uul$(v3, v2) = v0)) & ! [v0: Complex$] : ! [v1: Complex$] : ! % 206.00/28.42 [v2: Nat_set$] : ! [v3: Nat_complex_fun$] : (v1 = v0 | ~ (prod$(v3, v2) = % 206.00/28.42 v1) | ~ (prod$(v3, v2) = v0)) & ! [v0: Nat_complex_fun$] : ! [v1: % 206.00/28.42 Nat_complex_fun$] : ! [v2: Nat_set$] : ! [v3: Nat_nat_complex_fun_fun$] : % 206.00/28.42 (v1 = v0 | ~ (uuj$(v3, v2) = v1) | ~ (uuj$(v3, v2) = v0)) & ! [v0: % 206.00/28.42 Nat_complex_fun$] : ! [v1: Nat_complex_fun$] : ! [v2: Nat$] : ! [v3: % 206.00/28.42 Nat_nat_complex_fun_fun$] : (v1 = v0 | ~ (fun_app$o(v3, v2) = v1) | ~ % 206.00/28.42 (fun_app$o(v3, v2) = v0)) & ! [v0: Int_int_fun$] : ! [v1: Int_int_fun$] : % 206.00/28.42 ! [v2: Int_int_fun$] : ! [v3: int] : (v1 = v0 | ~ (uvb$(v3, v2) = v1) | ~ % 206.00/28.42 (uvb$(v3, v2) = v0)) & ! [v0: Int_real_fun$] : ! [v1: Int_real_fun$] : ! % 206.00/28.42 [v2: Int_real_fun$] : ! [v3: int] : (v1 = v0 | ~ (uve$(v3, v2) = v1) | ~ % 206.00/28.42 (uve$(v3, v2) = v0)) & ! [v0: Nat_int_fun$] : ! [v1: Nat_int_fun$] : ! % 206.00/28.42 [v2: Nat_int_fun$] : ! [v3: Nat$] : (v1 = v0 | ~ (uva$(v3, v2) = v1) | ~ % 206.00/28.42 (uva$(v3, v2) = v0)) & ! [v0: Nat_complex_fun$] : ! [v1: Nat_complex_fun$] % 206.00/28.42 : ! [v2: Nat_complex_fun$] : ! [v3: Nat$] : (v1 = v0 | ~ (uvf$(v3, v2) = % 206.00/28.42 v1) | ~ (uvf$(v3, v2) = v0)) & ! [v0: Complex_int_fun$] : ! [v1: % 206.00/28.42 Complex_int_fun$] : ! [v2: Complex_int_fun$] : ! [v3: Complex$] : (v1 = v0 % 206.00/28.42 | ~ (uuz$(v3, v2) = v1) | ~ (uuz$(v3, v2) = v0)) & ! [v0: % 206.00/28.42 Complex_real_fun$] : ! [v1: Complex_real_fun$] : ! [v2: Complex_real_fun$] % 206.00/28.42 : ! [v3: Complex$] : (v1 = v0 | ~ (uvc$(v3, v2) = v1) | ~ (uvc$(v3, v2) = % 206.00/28.42 v0)) & ! [v0: Int_int_fun$] : ! [v1: Int_int_fun$] : ! [v2: % 206.00/28.42 Int_int_fun$] : ! [v3: int] : (v1 = v0 | ~ (uuu$(v3, v2) = v1) | ~ % 206.00/28.42 (uuu$(v3, v2) = v0)) & ! [v0: Int_real_fun$] : ! [v1: Int_real_fun$] : ! % 206.00/28.42 [v2: Int_real_fun$] : ! [v3: int] : (v1 = v0 | ~ (uux$(v3, v2) = v1) | ~ % 206.00/28.42 (uux$(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : ! % 206.00/28.42 [v3: Int_real_fun$] : (v1 = v0 | ~ (fun_app$n(v3, v2) = v1) | ~ % 206.00/28.42 (fun_app$n(v3, v2) = v0)) & ! [v0: Nat_int_fun$] : ! [v1: Nat_int_fun$] : % 206.00/28.42 ! [v2: Nat_int_fun$] : ! [v3: Nat$] : (v1 = v0 | ~ (uut$(v3, v2) = v1) | ~ % 206.00/28.42 (uut$(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: Nat$] : ! [v3: % 206.00/28.42 Nat_int_fun$] : (v1 = v0 | ~ (fun_app$m(v3, v2) = v1) | ~ (fun_app$m(v3, % 206.00/28.42 v2) = v0)) & ! [v0: Nat_real_fun$] : ! [v1: Nat_real_fun$] : ! [v2: % 206.00/28.42 Nat_real_fun$] : ! [v3: Nat_real_fun_nat_real_fun_fun$] : (v1 = v0 | ~ % 206.00/28.42 (fun_app$l(v3, v2) = v1) | ~ (fun_app$l(v3, v2) = v0)) & ! [v0: % 206.00/28.42 Nat_complex_fun$] : ! [v1: Nat_complex_fun$] : ! [v2: Nat_complex_fun$] : % 206.00/28.42 ! [v3: Nat$] : (v1 = v0 | ~ (uuy$(v3, v2) = v1) | ~ (uuy$(v3, v2) = v0)) & % 206.00/28.42 ! [v0: Complex_int_fun$] : ! [v1: Complex_int_fun$] : ! [v2: % 206.00/28.42 Complex_int_fun$] : ! [v3: Complex$] : (v1 = v0 | ~ (uus$(v3, v2) = v1) | % 206.00/28.42 ~ (uus$(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: Complex$] : % 206.00/28.42 ! [v3: Complex_int_fun$] : (v1 = v0 | ~ (fun_app$k(v3, v2) = v1) | ~ % 206.00/28.42 (fun_app$k(v3, v2) = v0)) & ! [v0: Complex_real_fun$] : ! [v1: % 206.00/28.42 Complex_real_fun$] : ! [v2: Complex_real_fun$] : ! [v3: Complex$] : (v1 = % 206.00/28.42 v0 | ~ (uuv$(v3, v2) = v1) | ~ (uuv$(v3, v2) = v0)) & ! [v0: Nat$] : ! % 206.00/28.42 [v1: Nat$] : ! [v2: Nat$] : ! [v3: Nat_nat_fun$] : (v1 = v0 | ~ % 206.00/28.42 (fun_app$j(v3, v2) = v1) | ~ (fun_app$j(v3, v2) = v0)) & ! [v0: $real] : % 206.00/28.42 ! [v1: $real] : ! [v2: Nat$] : ! [v3: Nat_real_fun$] : (v1 = v0 | ~ % 206.00/28.42 (fun_app$h(v3, v2) = v1) | ~ (fun_app$h(v3, v2) = v0)) & ! [v0: $real] : % 206.00/28.42 ! [v1: $real] : ! [v2: Complex$] : ! [v3: Complex_real_fun$] : (v1 = v0 | ~ % 206.00/28.42 (fun_app$i(v3, v2) = v1) | ~ (fun_app$i(v3, v2) = v0)) & ! [v0: % 206.00/28.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Int_set$] : ! % 206.00/28.42 [v3: int] : (v1 = v0 | ~ (member$b(v3, v2) = v1) | ~ (member$b(v3, v2) = % 206.00/28.42 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 206.00/28.42 Nat$] : ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ (fun_app$g(v3, v2) = v1) | ~ % 206.00/28.42 (fun_app$g(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 206.00/28.42 MultipleValueBool] : ! [v2: Nat_set$] : ! [v3: Nat$] : (v1 = v0 | ~ % 206.00/28.42 (member$a(v3, v2) = v1) | ~ (member$a(v3, v2) = v0)) & ! [v0: % 206.00/28.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Complex$] : ! % 206.00/28.42 [v3: Complex_bool_fun$] : (v1 = v0 | ~ (fun_app$f(v3, v2) = v1) | ~ % 206.00/28.42 (fun_app$f(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 206.00/28.42 MultipleValueBool] : ! [v2: Complex_set$] : ! [v3: Complex$] : (v1 = v0 | % 206.00/28.42 ~ (member$(v3, v2) = v1) | ~ (member$(v3, v2) = v0)) & ! [v0: int] : ! % 206.00/28.42 [v1: int] : ! [v2: int] : ! [v3: Int_int_fun$] : (v1 = v0 | ~ % 206.00/28.42 (fun_app$e(v3, v2) = v1) | ~ (fun_app$e(v3, v2) = v0)) & ! [v0: $real] : % 206.00/28.42 ! [v1: $real] : ! [v2: $real] : ! [v3: Real_real_fun$] : (v1 = v0 | ~ % 206.00/28.42 (fun_app$d(v3, v2) = v1) | ~ (fun_app$d(v3, v2) = v0)) & ! [v0: $real] : % 206.00/28.42 ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 206.00/28.42 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & ! % 206.00/28.42 [v0: Int_bool_fun$] : ! [v1: Int_bool_fun$] : ! [v2: int] : ! [v3: % 206.00/28.42 Int_int_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$c(v3, v2) = v1) | ~ % 206.00/28.42 (fun_app$c(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 206.00/28.42 MultipleValueBool] : ! [v2: int] : ! [v3: Int_bool_fun$] : (v1 = v0 | ~ % 206.00/28.42 (fun_app$b(v3, v2) = v1) | ~ (fun_app$b(v3, v2) = v0)) & ! [v0: Complex$] % 206.00/28.42 : ! [v1: Complex$] : ! [v2: Complex$] : ! [v3: Complex_complex_fun$] : (v1 % 206.00/28.42 = v0 | ~ (fun_app$a(v3, v2) = v1) | ~ (fun_app$a(v3, v2) = v0)) & ! [v0: % 206.00/28.42 Complex$] : ! [v1: Complex$] : ! [v2: Nat$] : ! [v3: Nat_complex_fun$] : % 206.00/28.42 (v1 = v0 | ~ (fun_app$(v3, v2) = v1) | ~ (fun_app$(v3, v2) = v0)) & ! [v0: % 206.00/28.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : (v1 = v0 % 206.00/28.42 | ~ (real_$is_int(v2) = v1) | ~ (real_$is_int(v2) = v0)) & ! [v0: % 206.00/28.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : (v1 = v0 % 206.00/28.42 | ~ (real_$is_rat(v2) = v1) | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] % 206.00/28.42 : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ % 206.00/28.42 (real_$floor(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : % 206.00/28.42 (v1 = v0 | ~ (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! % 206.00/28.42 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 206.00/28.42 (real_$truncate(v2) = v1) | ~ (real_$truncate(v2) = v0)) & ! [v0: $real] : % 206.00/28.42 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ % 206.00/28.42 (real_$round(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 % 206.00/28.42 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: % 206.00/28.42 $rat] : ! [v1: $rat] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = % 206.00/28.42 v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! % 206.00/28.42 [v2: $real] : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = % 206.00/28.42 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ % 206.00/28.42 (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = v0)) & ! [v0: $real] : ! % 206.00/28.42 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ % 206.00/28.42 (real_$uminus(v2) = v0)) & ! [v0: Complex_bool_fun$] : ! [v1: % 206.00/28.42 Complex_bool_fun$] : ! [v2: Complex$] : (v1 = v0 | ~ (less$(v2) = v1) | ~ % 206.00/28.42 (less$(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 206.00/28.42 : ! [v2: Real_set$] : (v1 = v0 | ~ (finite$c(v2) = v1) | ~ (finite$c(v2) = % 206.00/28.42 v0)) & ! [v0: Complex_complex_fun$] : ! [v1: Complex_complex_fun$] : ! % 206.00/28.42 [v2: Complex$] : (v1 = v0 | ~ (plus$(v2) = v1) | ~ (plus$(v2) = v0)) & ! % 206.00/28.42 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Int_set$] : (v1 % 206.00/28.42 = v0 | ~ (finite$b(v2) = v1) | ~ (finite$b(v2) = v0)) & ! [v0: % 206.00/28.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Nat_set$] : (v1 = % 206.00/28.42 v0 | ~ (finite$a(v2) = v1) | ~ (finite$a(v2) = v0)) & ! [v0: % 206.00/28.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Complex_set$] : % 206.00/28.42 (v1 = v0 | ~ (finite$(v2) = v1) | ~ (finite$(v2) = v0)) & ! [v0: Int_set$] % 206.00/28.42 : ! [v1: Int_set$] : ! [v2: Int_bool_fun$] : (v1 = v0 | ~ (collect$b(v2) = % 206.00/28.42 v1) | ~ (collect$b(v2) = v0)) & ! [v0: Nat_set$] : ! [v1: Nat_set$] : % 206.00/28.42 ! [v2: Nat_bool_fun$] : (v1 = v0 | ~ (collect$a(v2) = v1) | ~ (collect$a(v2) % 206.00/28.42 = v0)) & ! [v0: Complex_set$] : ! [v1: Complex_set$] : ! [v2: % 206.00/28.42 Complex_bool_fun$] : (v1 = v0 | ~ (collect$(v2) = v1) | ~ (collect$(v2) = % 206.00/28.42 v0)) & ! [v0: Complex_bool_fun$] : ! [v1: Complex_bool_fun$] : ! [v2: % 206.00/28.42 Complex$] : (v1 = v0 | ~ (less_eq$(v2) = v1) | ~ (less_eq$(v2) = v0)) & ! % 206.00/28.42 [v0: Complex_complex_fun$] : ! [v1: Complex_complex_fun$] : ! [v2: % 206.00/28.42 Complex_poly$] : (v1 = v0 | ~ (i$(v2) = v1) | ~ (i$(v2) = v0)) & ! [v0: % 206.00/28.42 Int_int_bool_fun_fun$] : ! [v1: Int_int_bool_fun_fun$] : ! [v2: int] : (v1 % 206.00/28.42 = v0 | ~ (uur$(v2) = v1) | ~ (uur$(v2) = v0)) & ! [v0: % 206.00/28.42 Nat_nat_complex_fun_fun$] : ! [v1: Nat_nat_complex_fun_fun$] : ! [v2: % 206.00/28.42 Nat_nat_complex_fun_fun$] : (v1 = v0 | ~ (uui$(v2) = v1) | ~ (uui$(v2) = % 206.00/28.42 v0)) & ! [v0: Nat_real_fun_nat_real_fun_fun$] : ! [v1: % 206.00/28.42 Nat_real_fun_nat_real_fun_fun$] : ! [v2: Nat$] : (v1 = v0 | ~ (uvd$(v2) = % 206.00/28.42 v1) | ~ (uvd$(v2) = v0)) & ! [v0: Nat_real_fun_nat_real_fun_fun$] : ! % 206.00/28.42 [v1: Nat_real_fun_nat_real_fun_fun$] : ! [v2: Nat$] : (v1 = v0 | ~ (uuw$(v2) % 206.00/28.42 = v1) | ~ (uuw$(v2) = v0)) & ! [v0: Nat_complex_fun$] : ! [v1: % 206.00/28.42 Nat_complex_fun$] : ! [v2: Nat_nat_fun$] : (v1 = v0 | ~ (uua$(v2) = v1) | % 206.00/28.42 ~ (uua$(v2) = v0)) & ! [v0: Nat_real_fun$] : ! [v1: Nat_real_fun$] : ! % 206.00/28.42 [v2: Nat_complex_fun$] : (v1 = v0 | ~ (uuk$(v2) = v1) | ~ (uuk$(v2) = v0)) & % 206.00/28.42 ! [v0: Int_bool_fun$] : ! [v1: Int_bool_fun$] : ! [v2: Int_set$] : (v1 = v0 % 206.00/28.42 | ~ (uug$(v2) = v1) | ~ (uug$(v2) = v0)) & ! [v0: Nat_bool_fun$] : ! % 206.00/28.42 [v1: Nat_bool_fun$] : ! [v2: Nat_set$] : (v1 = v0 | ~ (uuf$(v2) = v1) | ~ % 206.00/28.42 (uuf$(v2) = v0)) & ! [v0: Complex_bool_fun$] : ! [v1: Complex_bool_fun$] : % 206.00/28.42 ! [v2: Complex_set$] : (v1 = v0 | ~ (uue$(v2) = v1) | ~ (uue$(v2) = v0)) & % 206.00/28.42 ! [v0: Int_int_fun$] : ! [v1: Int_int_fun$] : ! [v2: int] : (v1 = v0 | ~ % 206.00/28.42 (uud$(v2) = v1) | ~ (uud$(v2) = v0)) & ! [v0: Real_real_fun$] : ! [v1: % 206.00/28.42 Real_real_fun$] : ! [v2: $real] : (v1 = v0 | ~ (uuc$(v2) = v1) | ~ % 206.00/28.42 (uuc$(v2) = v0)) & ! [v0: Complex_complex_fun$] : ! [v1: % 206.00/28.42 Complex_complex_fun$] : ! [v2: Complex$] : (v1 = v0 | ~ (minus$(v2) = v1) % 206.00/28.42 | ~ (minus$(v2) = v0)) & ! [v0: Nat_complex_fun$] : ! [v1: % 206.00/28.42 Nat_complex_fun$] : ! [v2: Complex$] : (v1 = v0 | ~ (uu$(v2) = v1) | ~ % 206.00/28.42 (uu$(v2) = v0)) & ? [v0: $real] : ? [v1: $real] : ? [v2: $real] : % 206.00/28.42 (real_$quotient(v1, v0) = v2) & ? [v0: $real] : ? [v1: $real] : ? [v2: % 206.00/28.42 $real] : (real_$product(v1, v0) = v2) & ? [v0: $real] : ? [v1: $real] : ? % 206.00/28.42 [v2: MultipleValueBool] : (real_$greatereq(v1, v0) = v2) & ? [v0: $real] : ? % 206.00/28.42 [v1: $real] : ? [v2: MultipleValueBool] : (real_$greater(v1, v0) = v2) & ? % 206.00/28.42 [v0: $real] : ? [v1: $real] : ? [v2: MultipleValueBool] : (real_$less(v1, % 206.00/28.42 v0) = v2) & ? [v0: $real] : ? [v1: $real] : ? [v2: $real] : % 206.00/28.42 (real_$sum(v1, v0) = v2) & ? [v0: Int_set$] : ? [v1: Int_int_fun$] : ? [v2: % 206.00/28.42 int] : (prod$h(v1, v0) = v2) & ? [v0: Int_set$] : ? [v1: Int_real_fun$] : % 206.00/28.42 ? [v2: $real] : (prod$g(v1, v0) = v2) & ? [v0: $real] : ? [v1: % 206.00/28.42 Real_int_fun$] : ? [v2: int] : (fun_app$v(v1, v0) = v2) & ? [v0: $real] : % 206.00/28.42 ? [v1: Real_bool_fun$] : ? [v2: MultipleValueBool] : (fun_app$t(v1, v0) = v2) % 206.00/28.42 & ? [v0: Nat_bool_fun$] : ? [v1: Nat_bool_fun$] : ? [v2: MultipleValueBool] % 206.00/28.42 : (less_eq$f(v1, v0) = v2) & ? [v0: Complex_bool_fun$] : ? [v1: % 206.00/28.42 Complex_bool_fun$] : ? [v2: MultipleValueBool] : (less_eq$e(v1, v0) = v2) & % 206.00/28.42 ? [v0: Int_set$] : ? [v1: Int_set$] : ? [v2: MultipleValueBool] : % 206.00/28.42 (less_eq$d(v1, v0) = v2) & ? [v0: Nat_set$] : ? [v1: Nat_set$] : ? [v2: % 206.00/28.42 MultipleValueBool] : (less_eq$c(v1, v0) = v2) & ? [v0: Real_set$] : ? [v1: % 206.00/28.42 Real_set$] : ? [v2: MultipleValueBool] : (less_eq$b(v1, v0) = v2) & ? [v0: % 206.00/28.42 Complex_set$] : ? [v1: Complex_set$] : ? [v2: MultipleValueBool] : % 206.00/28.42 (less_eq$a(v1, v0) = v2) & ? [v0: Nat_real_fun$] : ? [v1: % 206.00/28.42 Nat_real_fun_bool_fun$] : ? [v2: MultipleValueBool] : (fun_app$r(v1, v0) = % 206.00/28.42 v2) & ? [v0: Real_set$] : ? [v1: $real] : ? [v2: MultipleValueBool] : % 206.00/28.42 (member$c(v1, v0) = v2) & ? [v0: Nat_set$] : ? [v1: Nat_real_fun$] : ? [v2: % 206.00/28.42 $real] : (prod$f(v1, v0) = v2) & ? [v0: Complex_set$] : ? [v1: % 206.00/28.42 Complex_real_fun$] : ? [v2: $real] : (prod$e(v1, v0) = v2) & ? [v0: % 206.00/28.42 Nat_set$] : ? [v1: Nat_int_fun$] : ? [v2: int] : (prod$d(v1, v0) = v2) & % 206.00/28.42 ? [v0: Complex_set$] : ? [v1: Complex_int_fun$] : ? [v2: int] : (prod$c(v1, % 206.00/28.42 v0) = v2) & ? [v0: $real] : ? [v1: $real] : ? [v2: MultipleValueBool] : % 206.00/28.42 (real_$lesseq(v1, v0) = v2) & ? [v0: int] : ? [v1: Int_real_fun$] : ? [v2: % 206.00/28.42 $real] : (fun_app$n(v1, v0) = v2) & ? [v0: Nat$] : ? [v1: Nat_int_fun$] : % 206.00/28.42 ? [v2: int] : (fun_app$m(v1, v0) = v2) & ? [v0: Complex$] : ? [v1: % 206.00/28.42 Complex_int_fun$] : ? [v2: int] : (fun_app$k(v1, v0) = v2) & ? [v0: Nat$] % 206.00/28.42 : ? [v1: Nat_real_fun$] : ? [v2: $real] : (fun_app$h(v1, v0) = v2) & ? [v0: % 206.00/28.42 Complex$] : ? [v1: Complex_real_fun$] : ? [v2: $real] : (fun_app$i(v1, v0) % 206.00/28.42 = v2) & ? [v0: Int_set$] : ? [v1: int] : ? [v2: MultipleValueBool] : % 206.00/28.42 (member$b(v1, v0) = v2) & ? [v0: Nat$] : ? [v1: Nat_bool_fun$] : ? [v2: % 206.00/28.42 MultipleValueBool] : (fun_app$g(v1, v0) = v2) & ? [v0: Nat_set$] : ? [v1: % 206.00/28.42 Nat$] : ? [v2: MultipleValueBool] : (member$a(v1, v0) = v2) & ? [v0: % 206.00/28.42 Complex$] : ? [v1: Complex_bool_fun$] : ? [v2: MultipleValueBool] : % 206.00/28.42 (fun_app$f(v1, v0) = v2) & ? [v0: Complex_set$] : ? [v1: Complex$] : ? [v2: % 206.00/28.42 MultipleValueBool] : (member$(v1, v0) = v2) & ? [v0: int] : ? [v1: % 206.00/28.42 Int_int_fun$] : ? [v2: int] : (fun_app$e(v1, v0) = v2) & ? [v0: $real] : % 206.00/28.42 ? [v1: Real_real_fun$] : ? [v2: $real] : (fun_app$d(v1, v0) = v2) & ? [v0: % 206.00/28.42 $real] : ? [v1: $real] : ? [v2: $real] : (real_$difference(v1, v0) = v2) & % 206.00/28.42 ? [v0: int] : ? [v1: Int_bool_fun$] : ? [v2: MultipleValueBool] : % 206.00/28.42 (fun_app$b(v1, v0) = v2) & ? [v0: Int_set$] : ? [v1: Int_nat_fun$] : ? [v2: % 206.00/28.42 Nat$] : (prod$k(v1, v0) = v2 & Nat$(v2)) & ? [v0: Complex_set$] : ? [v1: % 206.00/28.42 Complex_nat_fun$] : ? [v2: Nat$] : (prod$j(v1, v0) = v2 & Nat$(v2)) & ? % 206.00/28.42 [v0: Int_set$] : ? [v1: Int_complex_fun$] : ? [v2: Complex$] : (prod$i(v1, % 206.00/28.42 v0) = v2 & Complex$(v2)) & ? [v0: int] : ? [v1: Int_complex_fun$] : ? % 206.00/28.42 [v2: Complex$] : (fun_app$w(v1, v0) = v2 & Complex$(v2)) & ? [v0: $real] : ? % 206.00/28.42 [v1: Real_real_bool_fun_fun$] : ? [v2: Real_bool_fun$] : (fun_app$u(v1, v0) = % 206.00/28.42 v2 & Real_bool_fun$(v2)) & ? [v0: Int_bool_fun$] : ? [v1: Int_bool_fun$] : % 206.00/28.42 ? [v2: Int_bool_fun$] : (minus$f(v1, v0) = v2 & Int_bool_fun$(v2)) & ? [v0: % 206.00/28.42 Nat_bool_fun$] : ? [v1: Nat_bool_fun$] : ? [v2: Nat_bool_fun$] : % 206.00/28.42 (minus$e(v1, v0) = v2 & Nat_bool_fun$(v2)) & ? [v0: Complex_bool_fun$] : ? % 206.00/28.42 [v1: Complex_bool_fun$] : ? [v2: Complex_bool_fun$] : (minus$d(v1, v0) = v2 & % 206.00/28.42 Complex_bool_fun$(v2)) & ? [v0: Int_set$] : ? [v1: Int_set$] : ? [v2: % 206.00/28.42 Int_set$] : (minus$c(v1, v0) = v2 & Int_set$(v2)) & ? [v0: Nat_set$] : ? % 206.00/28.42 [v1: Nat_set$] : ? [v2: Nat_set$] : (minus$b(v1, v0) = v2 & Nat_set$(v2)) & % 206.00/28.42 ? [v0: Complex_set$] : ? [v1: Complex_set$] : ? [v2: Complex_set$] : % 206.00/28.42 (minus$a(v1, v0) = v2 & Complex_set$(v2)) & ? [v0: $real] : ? [v1: $real] : % 206.00/28.42 ? [v2: Real_set$] : (atLeastAtMost$a(v1, v0) = v2 & Real_set$(v2)) & ? [v0: % 206.00/28.42 Nat_real_fun$] : ? [v1: Nat_real_fun_nat_nat_fun_fun$] : ? [v2: % 206.00/28.42 Nat_nat_fun$] : (fun_app$s(v1, v0) = v2 & Nat_nat_fun$(v2)) & ? [v0: $real] % 206.00/28.42 : ? [v1: $real] : ? [v2: Real_set$] : (closed_segment$a(v1, v0) = v2 & % 206.00/28.42 Real_set$(v2)) & ? [v0: Complex_set$] : ? [v1: Complex_complex_fun$] : ? % 206.00/28.42 [v2: Complex$] : (prod$b(v1, v0) = v2 & Complex$(v2)) & ? [v0: Complex$] : ? % 206.00/28.42 [v1: Complex_nat_fun$] : ? [v2: Nat$] : (fun_app$q(v1, v0) = v2 & Nat$(v2)) & % 206.00/28.42 ? [v0: Nat_set$] : ? [v1: Nat_nat_fun$] : ? [v2: Nat$] : (prod$a(v1, v0) = % 206.00/28.42 v2 & Nat$(v2)) & ? [v0: Complex$] : ? [v1: Complex$] : ? [v2: % 206.00/28.42 Complex_set$] : (closed_segment$(v1, v0) = v2 & Complex_set$(v2)) & ? [v0: % 206.00/28.42 int] : ? [v1: Int_nat_fun$] : ? [v2: Nat$] : (fun_app$p(v1, v0) = v2 & % 206.00/28.42 Nat$(v2)) & ? [v0: Nat$] : ? [v1: Nat$] : ? [v2: Nat_set$] : % 206.00/28.42 (atLeastAtMost$(v1, v0) = v2 & Nat_set$(v2)) & ? [v0: Nat_set$] : ? [v1: % 206.00/28.42 Nat_nat_complex_fun_fun$] : ? [v2: Nat_complex_fun$] : (uuh$(v1, v0) = v2 & % 206.00/28.42 Nat_complex_fun$(v2)) & ? [v0: Int_set$] : ? [v1: Int_set$] : ? [v2: % 206.00/28.42 Int_bool_fun$] : (uuq$(v1, v0) = v2 & Int_bool_fun$(v2)) & ? [v0: Nat_set$] % 206.00/28.42 : ? [v1: Nat_set$] : ? [v2: Nat_bool_fun$] : (uup$(v1, v0) = v2 & % 206.00/28.42 Nat_bool_fun$(v2)) & ? [v0: Complex_set$] : ? [v1: Complex_set$] : ? [v2: % 206.00/28.42 Complex_bool_fun$] : (uuo$(v1, v0) = v2 & Complex_bool_fun$(v2)) & ? [v0: % 206.00/28.42 Int_bool_fun$] : ? [v1: Int_set$] : ? [v2: Int_bool_fun$] : (uun$(v1, v0) % 206.00/28.42 = v2 & Int_bool_fun$(v2)) & ? [v0: Nat_bool_fun$] : ? [v1: Nat_set$] : ? % 206.00/28.42 [v2: Nat_bool_fun$] : (uum$(v1, v0) = v2 & Nat_bool_fun$(v2)) & ? [v0: % 206.00/28.42 Complex_bool_fun$] : ? [v1: Complex_set$] : ? [v2: Complex_bool_fun$] : % 206.00/28.42 (uul$(v1, v0) = v2 & Complex_bool_fun$(v2)) & ? [v0: Nat_set$] : ? [v1: % 206.00/28.42 Nat_complex_fun$] : ? [v2: Complex$] : (prod$(v1, v0) = v2 & Complex$(v2)) % 206.00/28.42 & ? [v0: Nat_set$] : ? [v1: Nat_nat_complex_fun_fun$] : ? [v2: % 206.00/28.42 Nat_complex_fun$] : (uuj$(v1, v0) = v2 & Nat_complex_fun$(v2)) & ? [v0: % 206.00/28.42 Nat$] : ? [v1: Nat_nat_complex_fun_fun$] : ? [v2: Nat_complex_fun$] : % 206.00/28.42 (fun_app$o(v1, v0) = v2 & Nat_complex_fun$(v2)) & ? [v0: Int_int_fun$] : ? % 206.00/28.42 [v1: int] : ? [v2: Int_int_fun$] : (uvb$(v1, v0) = v2 & Int_int_fun$(v2)) & % 206.00/28.42 ? [v0: Int_real_fun$] : ? [v1: int] : ? [v2: Int_real_fun$] : (uve$(v1, v0) % 206.00/28.42 = v2 & Int_real_fun$(v2)) & ? [v0: Nat_int_fun$] : ? [v1: Nat$] : ? [v2: % 206.00/28.42 Nat_int_fun$] : (uva$(v1, v0) = v2 & Nat_int_fun$(v2)) & ? [v0: % 206.00/28.42 Nat_complex_fun$] : ? [v1: Nat$] : ? [v2: Nat_complex_fun$] : (uvf$(v1, % 206.00/28.42 v0) = v2 & Nat_complex_fun$(v2)) & ? [v0: Complex_int_fun$] : ? [v1: % 206.00/28.42 Complex$] : ? [v2: Complex_int_fun$] : (uuz$(v1, v0) = v2 & % 206.00/28.42 Complex_int_fun$(v2)) & ? [v0: Complex_real_fun$] : ? [v1: Complex$] : ? % 206.00/28.42 [v2: Complex_real_fun$] : (uvc$(v1, v0) = v2 & Complex_real_fun$(v2)) & ? % 206.00/28.42 [v0: Int_int_fun$] : ? [v1: int] : ? [v2: Int_int_fun$] : (uuu$(v1, v0) = v2 % 206.00/28.42 & Int_int_fun$(v2)) & ? [v0: Int_real_fun$] : ? [v1: int] : ? [v2: % 206.00/28.42 Int_real_fun$] : (uux$(v1, v0) = v2 & Int_real_fun$(v2)) & ? [v0: % 206.00/28.42 Nat_int_fun$] : ? [v1: Nat$] : ? [v2: Nat_int_fun$] : (uut$(v1, v0) = v2 & % 206.00/28.42 Nat_int_fun$(v2)) & ? [v0: Nat_real_fun$] : ? [v1: % 206.00/28.42 Nat_real_fun_nat_real_fun_fun$] : ? [v2: Nat_real_fun$] : (fun_app$l(v1, % 206.00/28.42 v0) = v2 & Nat_real_fun$(v2)) & ? [v0: Nat_complex_fun$] : ? [v1: Nat$] % 206.00/28.42 : ? [v2: Nat_complex_fun$] : (uuy$(v1, v0) = v2 & Nat_complex_fun$(v2)) & ? % 206.00/28.42 [v0: Complex_int_fun$] : ? [v1: Complex$] : ? [v2: Complex_int_fun$] : % 206.00/28.42 (uus$(v1, v0) = v2 & Complex_int_fun$(v2)) & ? [v0: Complex_real_fun$] : ? % 206.00/28.42 [v1: Complex$] : ? [v2: Complex_real_fun$] : (uuv$(v1, v0) = v2 & % 206.00/28.42 Complex_real_fun$(v2)) & ? [v0: Nat$] : ? [v1: Nat_nat_fun$] : ? [v2: % 206.00/28.42 Nat$] : (fun_app$j(v1, v0) = v2 & Nat$(v2)) & ? [v0: int] : ? [v1: % 206.00/28.42 Int_int_bool_fun_fun$] : ? [v2: Int_bool_fun$] : (fun_app$c(v1, v0) = v2 & % 206.00/28.42 Int_bool_fun$(v2)) & ? [v0: Complex$] : ? [v1: Complex_complex_fun$] : ? % 206.00/28.42 [v2: Complex$] : (fun_app$a(v1, v0) = v2 & Complex$(v2)) & ? [v0: Nat$] : ? % 206.00/28.42 [v1: Nat_complex_fun$] : ? [v2: Complex$] : (fun_app$(v1, v0) = v2 & % 206.00/28.42 Complex$(v2)) & ? [v0: $real] : ? [v1: MultipleValueBool] : % 206.00/28.42 (real_$is_int(v0) = v1) & ? [v0: $real] : ? [v1: MultipleValueBool] : % 206.00/28.42 (real_$is_rat(v0) = v1) & ? [v0: $real] : ? [v1: $real] : (real_$floor(v0) = % 206.00/28.42 v1) & ? [v0: $real] : ? [v1: $real] : (real_$ceiling(v0) = v1) & ? [v0: % 206.00/28.43 $real] : ? [v1: $real] : (real_$truncate(v0) = v1) & ? [v0: $real] : ? % 206.00/28.43 [v1: $real] : (real_$round(v0) = v1) & ? [v0: $real] : ? [v1: int] : % 206.00/28.43 (real_$to_int(v0) = v1) & ? [v0: $real] : ? [v1: $rat] : (real_$to_rat(v0) = % 206.00/28.43 v1) & ? [v0: $real] : ? [v1: $real] : (real_$to_real(v0) = v1) & ? [v0: % 206.00/28.43 int] : ? [v1: $real] : (int_$to_real(v0) = v1) & ? [v0: $real] : ? [v1: % 206.00/28.43 $real] : (real_$uminus(v0) = v1) & ? [v0: Real_set$] : ? [v1: % 206.00/28.43 MultipleValueBool] : (finite$c(v0) = v1) & ? [v0: Int_set$] : ? [v1: % 206.00/28.43 MultipleValueBool] : (finite$b(v0) = v1) & ? [v0: Nat_set$] : ? [v1: % 206.00/28.43 MultipleValueBool] : (finite$a(v0) = v1) & ? [v0: Complex_set$] : ? [v1: % 206.00/28.43 MultipleValueBool] : (finite$(v0) = v1) & ? [v0: Complex$] : ? [v1: % 206.00/28.43 Complex_bool_fun$] : (less$(v0) = v1 & Complex_bool_fun$(v1)) & ? [v0: % 206.00/28.43 Complex$] : ? [v1: Complex_complex_fun$] : (plus$(v0) = v1 & % 206.00/28.43 Complex_complex_fun$(v1)) & ? [v0: Int_bool_fun$] : ? [v1: Int_set$] : % 206.00/28.43 (collect$b(v0) = v1 & Int_set$(v1)) & ? [v0: Nat_bool_fun$] : ? [v1: % 206.00/28.43 Nat_set$] : (collect$a(v0) = v1 & Nat_set$(v1)) & ? [v0: Complex_bool_fun$] % 206.00/28.43 : ? [v1: Complex_set$] : (collect$(v0) = v1 & Complex_set$(v1)) & ? [v0: % 206.00/28.43 Complex$] : ? [v1: Complex_bool_fun$] : (less_eq$(v0) = v1 & % 206.00/28.43 Complex_bool_fun$(v1)) & ? [v0: Complex_poly$] : ? [v1: % 206.00/28.43 Complex_complex_fun$] : (i$(v0) = v1 & Complex_complex_fun$(v1)) & ? [v0: % 206.00/28.43 int] : ? [v1: Int_int_bool_fun_fun$] : (uur$(v0) = v1 & % 206.00/28.43 Int_int_bool_fun_fun$(v1)) & ? [v0: Nat_nat_complex_fun_fun$] : ? [v1: % 206.00/28.43 Nat_nat_complex_fun_fun$] : (uui$(v0) = v1 & Nat_nat_complex_fun_fun$(v1)) & % 206.00/28.43 ? [v0: Nat$] : ? [v1: Nat_real_fun_nat_real_fun_fun$] : (uvd$(v0) = v1 & % 206.00/28.43 Nat_real_fun_nat_real_fun_fun$(v1)) & ? [v0: Nat$] : ? [v1: % 206.00/28.43 Nat_real_fun_nat_real_fun_fun$] : (uuw$(v0) = v1 & % 206.00/28.43 Nat_real_fun_nat_real_fun_fun$(v1)) & ? [v0: Nat_nat_fun$] : ? [v1: % 206.00/28.43 Nat_complex_fun$] : (uua$(v0) = v1 & Nat_complex_fun$(v1)) & ? [v0: % 206.00/28.43 Nat_complex_fun$] : ? [v1: Nat_real_fun$] : (uuk$(v0) = v1 & % 206.00/28.43 Nat_real_fun$(v1)) & ? [v0: Int_set$] : ? [v1: Int_bool_fun$] : (uug$(v0) % 206.00/28.43 = v1 & Int_bool_fun$(v1)) & ? [v0: Nat_set$] : ? [v1: Nat_bool_fun$] : % 206.00/28.43 (uuf$(v0) = v1 & Nat_bool_fun$(v1)) & ? [v0: Complex_set$] : ? [v1: % 206.00/28.43 Complex_bool_fun$] : (uue$(v0) = v1 & Complex_bool_fun$(v1)) & ? [v0: int] % 206.00/28.43 : ? [v1: Int_int_fun$] : (uud$(v0) = v1 & Int_int_fun$(v1)) & ? [v0: $real] % 206.00/28.43 : ? [v1: Real_real_fun$] : (uuc$(v0) = v1 & Real_real_fun$(v1)) & ? [v0: % 206.00/28.43 Complex$] : ? [v1: Complex_complex_fun$] : (minus$(v0) = v1 & % 206.00/28.43 Complex_complex_fun$(v1)) & ? [v0: Complex$] : ? [v1: Nat_complex_fun$] : % 206.00/28.43 (uu$(v0) = v1 & Nat_complex_fun$(v1)) % 206.00/28.43 % 206.00/28.43 Further assumptions not needed in the proof: % 206.00/28.43 -------------------------------------------- % 206.00/28.43 axiom0, axiom1, axiom10, axiom100, axiom101, axiom102, axiom103, axiom104, % 206.00/28.43 axiom105, axiom106, axiom107, axiom108, axiom109, axiom11, axiom110, axiom111, % 206.00/28.43 axiom112, axiom113, axiom114, axiom115, axiom116, axiom117, axiom118, axiom119, % 206.00/28.43 axiom12, axiom120, axiom121, axiom122, axiom123, axiom124, axiom125, axiom126, % 206.00/28.43 axiom127, axiom128, axiom129, axiom13, axiom130, axiom131, axiom132, axiom133, % 206.00/28.43 axiom134, axiom135, axiom136, axiom137, axiom138, axiom139, axiom14, axiom140, % 206.00/28.43 axiom141, axiom142, axiom143, axiom144, axiom145, axiom146, axiom147, axiom148, % 206.00/28.43 axiom149, axiom15, axiom150, axiom151, axiom152, axiom153, axiom154, axiom155, % 206.00/28.43 axiom156, axiom157, axiom158, axiom159, axiom16, axiom160, axiom161, axiom162, % 206.00/28.43 axiom163, axiom164, axiom165, axiom166, axiom167, axiom168, axiom169, axiom17, % 206.00/28.43 axiom170, axiom171, axiom172, axiom173, axiom174, axiom175, axiom176, axiom177, % 206.00/28.43 axiom178, axiom179, axiom18, axiom180, axiom181, axiom182, axiom183, axiom184, % 206.00/28.43 axiom185, axiom186, axiom187, axiom188, axiom189, axiom19, axiom190, axiom191, % 206.00/28.43 axiom192, axiom193, axiom194, axiom195, axiom196, axiom197, axiom198, axiom199, % 206.00/28.43 axiom2, axiom20, axiom200, axiom201, axiom202, axiom203, axiom204, axiom205, % 206.00/28.43 axiom207, axiom208, axiom209, axiom21, axiom210, axiom211, axiom212, axiom213, % 206.00/28.43 axiom214, axiom215, axiom216, axiom217, axiom218, axiom219, axiom22, axiom220, % 206.00/28.43 axiom221, axiom222, axiom223, axiom224, axiom225, axiom226, axiom227, axiom228, % 206.00/28.43 axiom229, axiom23, axiom230, axiom231, axiom232, axiom233, axiom234, axiom235, % 206.00/28.43 axiom236, axiom237, axiom238, axiom239, axiom24, axiom240, axiom241, axiom242, % 206.00/28.43 axiom243, axiom244, axiom245, axiom246, axiom247, axiom248, axiom249, axiom25, % 206.00/28.43 axiom250, axiom251, axiom252, axiom253, axiom254, axiom255, axiom256, axiom257, % 206.00/28.43 axiom258, axiom259, axiom26, axiom260, axiom261, axiom262, axiom263, axiom264, % 206.00/28.43 axiom265, axiom266, axiom267, axiom268, axiom269, axiom27, axiom270, axiom271, % 206.00/28.43 axiom272, axiom273, axiom274, axiom275, axiom276, axiom277, axiom278, axiom279, % 206.00/28.43 axiom28, axiom280, axiom281, axiom282, axiom283, axiom284, axiom285, axiom286, % 206.00/28.43 axiom287, axiom288, axiom289, axiom29, axiom290, axiom291, axiom292, axiom293, % 206.00/28.43 axiom294, axiom295, axiom296, axiom297, axiom298, axiom299, axiom3, axiom30, % 206.00/28.43 axiom300, axiom301, axiom303, axiom304, axiom305, axiom306, axiom307, axiom308, % 206.00/28.43 axiom309, axiom31, axiom310, axiom311, axiom312, axiom313, axiom314, axiom315, % 206.00/28.43 axiom317, axiom318, axiom319, axiom32, axiom320, axiom321, axiom322, axiom323, % 206.00/28.43 axiom325, axiom326, axiom327, axiom328, axiom329, axiom33, axiom330, axiom331, % 206.00/28.43 axiom332, axiom333, axiom334, axiom335, axiom336, axiom337, axiom338, axiom339, % 206.00/28.43 axiom340, axiom341, axiom342, axiom343, axiom344, axiom345, axiom346, axiom347, % 206.00/28.43 axiom348, axiom349, axiom350, axiom351, axiom352, axiom353, axiom354, axiom356, % 206.00/28.43 axiom357, axiom358, axiom359, axiom36, axiom360, axiom361, axiom362, axiom363, % 206.00/28.43 axiom364, axiom365, axiom366, axiom367, axiom368, axiom369, axiom37, axiom370, % 206.00/28.43 axiom371, axiom372, axiom373, axiom374, axiom375, axiom376, axiom377, axiom378, % 206.00/28.43 axiom379, axiom38, axiom380, axiom381, axiom382, axiom383, axiom384, axiom385, % 206.00/28.43 axiom386, axiom387, axiom388, axiom389, axiom39, axiom390, axiom391, axiom392, % 206.00/28.43 axiom393, axiom394, axiom395, axiom396, axiom397, axiom398, axiom399, axiom4, % 206.00/28.43 axiom400, axiom401, axiom402, axiom403, axiom404, axiom405, axiom406, axiom407, % 206.00/28.43 axiom408, axiom409, axiom410, axiom411, axiom412, axiom413, axiom414, axiom415, % 206.00/28.43 axiom416, axiom417, axiom418, axiom419, axiom42, axiom420, axiom421, axiom422, % 206.00/28.43 axiom423, axiom424, axiom425, axiom426, axiom427, axiom428, axiom429, axiom43, % 206.00/28.43 axiom430, axiom431, axiom432, axiom433, axiom434, axiom435, axiom436, axiom437, % 206.00/28.43 axiom438, axiom439, axiom440, axiom441, axiom442, axiom443, axiom444, axiom445, % 206.00/28.43 axiom446, axiom447, axiom448, axiom449, axiom450, axiom451, axiom452, axiom453, % 206.00/28.43 axiom454, axiom455, axiom456, axiom457, axiom458, axiom459, axiom460, axiom461, % 206.00/28.43 axiom462, axiom463, axiom464, axiom465, axiom466, axiom467, axiom468, axiom469, % 206.00/28.43 axiom47, axiom470, axiom471, axiom472, axiom473, axiom474, axiom475, axiom476, % 206.00/28.43 axiom477, axiom478, axiom479, axiom48, axiom480, axiom481, axiom482, axiom483, % 206.00/28.43 axiom484, axiom485, axiom486, axiom487, axiom488, axiom489, axiom49, axiom490, % 206.00/28.43 axiom491, axiom492, axiom493, axiom494, axiom495, axiom496, axiom497, axiom498, % 206.00/28.43 axiom499, axiom5, axiom50, axiom500, axiom501, axiom502, axiom503, axiom504, % 206.00/28.43 axiom505, axiom506, axiom507, axiom508, axiom509, axiom51, axiom510, axiom511, % 206.00/28.43 axiom512, axiom513, axiom514, axiom515, axiom516, axiom517, axiom518, axiom519, % 206.00/28.43 axiom52, axiom520, axiom521, axiom522, axiom523, axiom524, axiom525, axiom526, % 206.00/28.43 axiom527, axiom528, axiom529, axiom53, axiom530, axiom531, axiom532, axiom533, % 206.00/28.43 axiom534, axiom535, axiom536, axiom537, axiom538, axiom539, axiom54, axiom540, % 206.00/28.43 axiom541, axiom542, axiom543, axiom544, axiom545, axiom546, axiom547, axiom548, % 206.00/28.43 axiom549, axiom55, axiom550, axiom551, axiom552, axiom553, axiom554, axiom555, % 206.00/28.43 axiom556, axiom557, axiom558, axiom559, axiom56, axiom560, axiom561, axiom562, % 206.00/28.43 axiom563, axiom564, axiom565, axiom566, axiom567, axiom568, axiom569, axiom57, % 206.00/28.43 axiom570, axiom571, axiom572, axiom573, axiom574, axiom575, axiom576, axiom577, % 206.00/28.43 axiom578, axiom579, axiom58, axiom580, axiom581, axiom582, axiom583, axiom584, % 206.00/28.43 axiom585, axiom586, axiom587, axiom588, axiom589, axiom59, axiom590, axiom591, % 206.00/28.43 axiom592, axiom593, axiom594, axiom595, axiom596, axiom597, axiom598, axiom599, % 206.00/28.43 axiom6, axiom60, axiom600, axiom601, axiom602, axiom603, axiom604, axiom605, % 206.00/28.43 axiom606, axiom607, axiom608, axiom609, axiom61, axiom610, axiom611, axiom612, % 206.00/28.43 axiom613, axiom614, axiom615, axiom616, axiom617, axiom618, axiom619, axiom62, % 206.00/28.43 axiom620, axiom621, axiom622, axiom623, axiom624, axiom625, axiom626, axiom627, % 206.00/28.43 axiom628, axiom629, axiom63, axiom630, axiom631, axiom632, axiom633, axiom64, % 206.00/28.43 axiom65, axiom66, axiom67, axiom68, axiom69, axiom7, axiom70, axiom71, axiom72, % 206.00/28.43 axiom73, axiom74, axiom75, axiom76, axiom77, axiom78, axiom79, axiom8, axiom80, % 206.00/28.43 axiom81, axiom82, axiom83, axiom84, axiom85, axiom86, axiom87, axiom88, axiom89, % 206.00/28.43 axiom9, axiom90, axiom91, axiom92, axiom93, axiom94, axiom95, axiom96, axiom97, % 206.00/28.43 axiom98, axiom99, formula_635, formula_636 % 206.00/28.43 % 206.00/28.43 Those formulas are unsatisfiable: % 206.00/28.43 --------------------------------- % 206.00/28.43 % 206.00/28.43 Begin of proof % 206.00/28.43 | % 206.00/28.43 | ALPHA: (axiom35) implies: % 206.00/28.43 | (1) ? [v0: Complex$] : ? [v1: Complex_set$] : ? [v2: Nat$] : ? [v3: % 206.00/28.43 | Nat_set$] : (closed_segment$(zero$, v0) = v1 & fun_app$p(nat$, 1) = % 206.00/28.43 | v2 & atLeastAtMost$(v2, n$) = v3 & fun_app$(of_nat$, n$) = v0 & % 206.00/28.43 | Nat_set$(v3) & Complex_set$(v1) & Nat$(v2) & Complex$(v0) & ! [v4: % 206.00/28.43 | $real] : ( ~ (real_$lesseq(real_0, v4) = 0) | thesis$ | ? [v5: % 206.00/28.43 | Complex$] : ? [v6: Nat_complex_fun$] : ? [v7: Complex$] : ? % 206.00/28.43 | [v8: $real] : ? [v9: int] : ( ~ (v9 = 0) & real_$lesseq(v8, v4) = % 206.00/28.43 | v9 & prod$(v6, v3) = v7 & fun_app$i(norm$, v7) = v8 & member$(v5, % 206.00/28.43 | v1) = 0 & uu$(v5) = v6 & Nat_complex_fun$(v6) & Complex$(v7) & % 206.00/28.43 | Complex$(v5)))) % 206.00/28.43 | % 206.00/28.43 | ALPHA: (axiom41) implies: % 206.34/28.43 | (2) ? [v0: Complex$] : ? [v1: Complex_set$] : ? [v2: Nat$] : ? [v3: % 206.34/28.43 | Nat_set$] : (closed_segment$(zero$, v0) = v1 & fun_app$p(nat$, 1) = % 206.34/28.43 | v2 & atLeastAtMost$(v2, n$) = v3 & fun_app$(of_nat$, n$) = v0 & % 206.34/28.43 | Nat_set$(v3) & Complex_set$(v1) & Nat$(v2) & Complex$(v0) & ! [v4: % 206.34/28.43 | Complex$] : ( ~ (member$(v4, v1) = 0) | ~ Complex$(v4) | ? [v5: % 206.34/28.43 | Nat_complex_fun$] : ? [v6: Complex$] : ? [v7: $real] : % 206.34/28.43 | (real_$lesseq(v7, c$) = 0 & prod$(v5, v3) = v6 & fun_app$i(norm$, % 206.34/28.43 | v6) = v7 & uu$(v4) = v5 & Nat_complex_fun$(v5) & % 206.34/28.43 | Complex$(v6)))) % 206.34/28.43 | % 206.34/28.43 | ALPHA: (axiom44) implies: % 206.34/28.43 | (3) ? [v0: Nat$] : (fun_app$p(nat$, 1) = v0 & fun_app$(of_nat$, v0) = one$ % 206.34/28.43 | & Nat$(v0)) % 206.34/28.43 | % 206.34/28.43 | ALPHA: (axiom46) implies: % 206.34/28.43 | (4) ? [v0: Nat$] : (fun_app$p(nat$, 1) = v0 & fun_app$h(of_nat$b, v0) = % 206.34/28.43 | real_1 & Nat$(v0)) % 206.34/28.43 | % 206.34/28.43 | ALPHA: (axiom206) implies: % 206.34/28.44 | (5) ? [v0: Nat$] : ? [v1: Nat_set$] : (fun_app$p(nat$, 1) = v0 & % 206.34/28.44 | atLeastAtMost$(v0, v0) = v1 & Nat_set$(v1) & Nat$(v0) & ! [v2: % 206.34/28.44 | Nat_complex_fun$] : ! [v3: Complex$] : ( ~ (prod$(v2, v1) = v3) | % 206.34/28.44 | ~ Nat_complex_fun$(v2) | (fun_app$(v2, v0) = v3 & Complex$(v3)))) % 206.34/28.44 | % 206.34/28.44 | ALPHA: (axiom324) implies: % 206.34/28.44 | (6) ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v0, v1) = % 206.34/28.44 | 0) | ? [v2: int] : ( ~ (v2 = 0) & real_$lesseq(v1, v0) = v2)) % 206.34/28.44 | % 206.34/28.44 | ALPHA: (axiom45) implies: % 206.34/28.44 | (7) ? [v0: Nat$] : (fun_app$p(nat$, 1) = v0 & fun_app$m(of_nat$a, v0) = 1 % 206.34/28.44 | & Nat$(v0)) % 206.34/28.44 | % 206.34/28.44 | ALPHA: (function-axioms) implies: % 206.34/28.44 | (8) ! [v0: Nat_complex_fun$] : ! [v1: Nat_complex_fun$] : ! [v2: % 206.34/28.44 | Complex$] : (v1 = v0 | ~ (uu$(v2) = v1) | ~ (uu$(v2) = v0)) % 206.34/28.44 | (9) ! [v0: Complex$] : ! [v1: Complex$] : ! [v2: Nat$] : ! [v3: % 206.34/28.44 | Nat_complex_fun$] : (v1 = v0 | ~ (fun_app$(v3, v2) = v1) | ~ % 206.34/28.44 | (fun_app$(v3, v2) = v0)) % 206.34/28.44 | (10) ! [v0: $real] : ! [v1: $real] : ! [v2: Complex$] : ! [v3: % 206.34/28.44 | Complex_real_fun$] : (v1 = v0 | ~ (fun_app$i(v3, v2) = v1) | ~ % 206.34/28.44 | (fun_app$i(v3, v2) = v0)) % 206.37/28.44 | (11) ! [v0: Complex$] : ! [v1: Complex$] : ! [v2: Nat_set$] : ! [v3: % 206.37/28.44 | Nat_complex_fun$] : (v1 = v0 | ~ (prod$(v3, v2) = v1) | ~ % 206.37/28.44 | (prod$(v3, v2) = v0)) % 206.37/28.44 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 206.37/28.44 | $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) % 206.37/28.44 | | ~ (real_$lesseq(v3, v2) = v0)) % 206.37/28.44 | (13) ! [v0: Nat_set$] : ! [v1: Nat_set$] : ! [v2: Nat$] : ! [v3: Nat$] % 206.37/28.44 | : (v1 = v0 | ~ (atLeastAtMost$(v3, v2) = v1) | ~ (atLeastAtMost$(v3, % 206.37/28.44 | v2) = v0)) % 206.37/28.44 | (14) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: int] : ! [v3: Int_nat_fun$] : % 206.37/28.44 | (v1 = v0 | ~ (fun_app$p(v3, v2) = v1) | ~ (fun_app$p(v3, v2) = v0)) % 206.37/28.44 | (15) ! [v0: Complex_set$] : ! [v1: Complex_set$] : ! [v2: Complex$] : ! % 206.37/28.44 | [v3: Complex$] : (v1 = v0 | ~ (closed_segment$(v3, v2) = v1) | ~ % 206.37/28.44 | (closed_segment$(v3, v2) = v0)) % 206.37/28.44 | % 206.37/28.44 | ALPHA: (input) implies: % 206.37/28.44 | (16) ~ (real_very_large = real_very_small) % 206.37/28.44 | (17) real_$lesseq(real_very_small, real_very_large) = 0 % 206.37/28.44 | % 206.37/28.44 | DELTA: instantiating (3) with fresh symbol all_699_0 gives: % 206.37/28.44 | (18) fun_app$p(nat$, 1) = all_699_0 & fun_app$(of_nat$, all_699_0) = one$ & % 206.37/28.44 | Nat$(all_699_0) % 206.37/28.44 | % 206.37/28.44 | ALPHA: (18) implies: % 206.37/28.44 | (19) fun_app$p(nat$, 1) = all_699_0 % 206.37/28.44 | % 206.37/28.44 | DELTA: instantiating (4) with fresh symbol all_701_0 gives: % 206.37/28.44 | (20) fun_app$p(nat$, 1) = all_701_0 & fun_app$h(of_nat$b, all_701_0) = % 206.37/28.44 | real_1 & Nat$(all_701_0) % 206.37/28.44 | % 206.37/28.44 | ALPHA: (20) implies: % 206.37/28.44 | (21) fun_app$p(nat$, 1) = all_701_0 % 206.37/28.44 | % 206.37/28.44 | DELTA: instantiating (7) with fresh symbol all_709_0 gives: % 206.37/28.44 | (22) fun_app$p(nat$, 1) = all_709_0 & fun_app$m(of_nat$a, all_709_0) = 1 & % 206.37/28.44 | Nat$(all_709_0) % 206.37/28.44 | % 206.37/28.44 | ALPHA: (22) implies: % 206.37/28.44 | (23) fun_app$p(nat$, 1) = all_709_0 % 206.37/28.44 | % 206.37/28.44 | DELTA: instantiating (7) with fresh symbol all_713_0 gives: % 206.37/28.44 | (24) fun_app$p(nat$, 1) = all_713_0 & fun_app$m(of_nat$a, all_713_0) = 1 & % 206.37/28.44 | Nat$(all_713_0) % 206.37/28.44 | % 206.37/28.44 | ALPHA: (24) implies: % 206.37/28.44 | (25) fun_app$p(nat$, 1) = all_713_0 % 206.37/28.44 | % 206.37/28.44 | DELTA: instantiating (5) with fresh symbols all_722_0, all_722_1 gives: % 206.37/28.44 | (26) fun_app$p(nat$, 1) = all_722_1 & atLeastAtMost$(all_722_1, all_722_1) % 206.37/28.44 | = all_722_0 & Nat_set$(all_722_0) & Nat$(all_722_1) & ! [v0: % 206.37/28.44 | Nat_complex_fun$] : ! [v1: Complex$] : ( ~ (prod$(v0, all_722_0) = % 206.37/28.44 | v1) | ~ Nat_complex_fun$(v0) | (fun_app$(v0, all_722_1) = v1 & % 206.37/28.44 | Complex$(v1))) % 206.37/28.44 | % 206.37/28.44 | ALPHA: (26) implies: % 206.37/28.44 | (27) fun_app$p(nat$, 1) = all_722_1 % 206.37/28.44 | % 206.37/28.44 | DELTA: instantiating (2) with fresh symbols all_740_0, all_740_1, all_740_2, % 206.37/28.44 | all_740_3 gives: % 206.37/28.45 | (28) closed_segment$(zero$, all_740_3) = all_740_2 & fun_app$p(nat$, 1) = % 206.37/28.45 | all_740_1 & atLeastAtMost$(all_740_1, n$) = all_740_0 & % 206.37/28.45 | fun_app$(of_nat$, n$) = all_740_3 & Nat_set$(all_740_0) & % 206.37/28.45 | Complex_set$(all_740_2) & Nat$(all_740_1) & Complex$(all_740_3) & ! % 206.37/28.45 | [v0: Complex$] : ( ~ (member$(v0, all_740_2) = 0) | ~ Complex$(v0) | % 206.37/28.45 | ? [v1: Nat_complex_fun$] : ? [v2: Complex$] : ? [v3: $real] : % 206.37/28.45 | (real_$lesseq(v3, c$) = 0 & prod$(v1, all_740_0) = v2 & % 206.37/28.45 | fun_app$i(norm$, v2) = v3 & uu$(v0) = v1 & Nat_complex_fun$(v1) & % 206.37/28.45 | Complex$(v2))) % 206.37/28.45 | % 206.37/28.45 | ALPHA: (28) implies: % 206.37/28.45 | (29) fun_app$(of_nat$, n$) = all_740_3 % 206.37/28.45 | (30) atLeastAtMost$(all_740_1, n$) = all_740_0 % 206.37/28.45 | (31) fun_app$p(nat$, 1) = all_740_1 % 206.37/28.45 | (32) closed_segment$(zero$, all_740_3) = all_740_2 % 206.37/28.45 | (33) ! [v0: Complex$] : ( ~ (member$(v0, all_740_2) = 0) | ~ Complex$(v0) % 206.37/28.45 | | ? [v1: Nat_complex_fun$] : ? [v2: Complex$] : ? [v3: $real] : % 206.37/28.45 | (real_$lesseq(v3, c$) = 0 & prod$(v1, all_740_0) = v2 & % 206.37/28.45 | fun_app$i(norm$, v2) = v3 & uu$(v0) = v1 & Nat_complex_fun$(v1) & % 206.37/28.45 | Complex$(v2))) % 206.37/28.45 | % 206.37/28.45 | DELTA: instantiating (1) with fresh symbols all_764_0, all_764_1, all_764_2, % 206.37/28.45 | all_764_3 gives: % 206.37/28.45 | (34) closed_segment$(zero$, all_764_3) = all_764_2 & fun_app$p(nat$, 1) = % 206.37/28.45 | all_764_1 & atLeastAtMost$(all_764_1, n$) = all_764_0 & % 206.37/28.45 | fun_app$(of_nat$, n$) = all_764_3 & Nat_set$(all_764_0) & % 206.37/28.45 | Complex_set$(all_764_2) & Nat$(all_764_1) & Complex$(all_764_3) & ! % 206.37/28.45 | [v0: $real] : ( ~ (real_$lesseq(real_0, v0) = 0) | thesis$ | ? [v1: % 206.37/28.45 | Complex$] : ? [v2: Nat_complex_fun$] : ? [v3: Complex$] : ? % 206.37/28.45 | [v4: $real] : ? [v5: int] : ( ~ (v5 = 0) & real_$lesseq(v4, v0) = % 206.37/28.45 | v5 & prod$(v2, all_764_0) = v3 & fun_app$i(norm$, v3) = v4 & % 206.37/28.45 | member$(v1, all_764_2) = 0 & uu$(v1) = v2 & Nat_complex_fun$(v2) & % 206.37/28.45 | Complex$(v3) & Complex$(v1))) % 206.37/28.45 | % 206.37/28.45 | ALPHA: (34) implies: % 206.37/28.45 | (35) fun_app$(of_nat$, n$) = all_764_3 % 206.37/28.45 | (36) atLeastAtMost$(all_764_1, n$) = all_764_0 % 206.37/28.45 | (37) fun_app$p(nat$, 1) = all_764_1 % 206.37/28.45 | (38) closed_segment$(zero$, all_764_3) = all_764_2 % 206.37/28.45 | (39) ! [v0: $real] : ( ~ (real_$lesseq(real_0, v0) = 0) | thesis$ | ? % 206.37/28.45 | [v1: Complex$] : ? [v2: Nat_complex_fun$] : ? [v3: Complex$] : ? % 206.37/28.45 | [v4: $real] : ? [v5: int] : ( ~ (v5 = 0) & real_$lesseq(v4, v0) = % 206.37/28.45 | v5 & prod$(v2, all_764_0) = v3 & fun_app$i(norm$, v3) = v4 & % 206.37/28.45 | member$(v1, all_764_2) = 0 & uu$(v1) = v2 & Nat_complex_fun$(v2) & % 206.37/28.45 | Complex$(v3) & Complex$(v1))) % 206.37/28.45 | % 206.37/28.45 | GROUND_INST: instantiating (9) with all_740_3, all_764_3, n$, of_nat$, % 206.37/28.45 | simplifying with (29), (35) gives: % 206.37/28.45 | (40) all_764_3 = all_740_3 % 206.37/28.45 | % 206.37/28.45 | GROUND_INST: instantiating (14) with all_709_0, all_713_0, 1, nat$, % 206.37/28.45 | simplifying with (23), (25) gives: % 206.37/28.45 | (41) all_713_0 = all_709_0 % 206.37/28.45 | % 206.37/28.45 | GROUND_INST: instantiating (14) with all_699_0, all_713_0, 1, nat$, % 206.37/28.45 | simplifying with (19), (25) gives: % 206.37/28.45 | (42) all_713_0 = all_699_0 % 206.37/28.45 | % 206.37/28.45 | GROUND_INST: instantiating (14) with all_713_0, all_722_1, 1, nat$, % 206.37/28.45 | simplifying with (25), (27) gives: % 206.37/28.45 | (43) all_722_1 = all_713_0 % 206.37/28.45 | % 206.37/28.45 | GROUND_INST: instantiating (14) with all_740_1, all_764_1, 1, nat$, % 206.37/28.45 | simplifying with (31), (37) gives: % 206.37/28.45 | (44) all_764_1 = all_740_1 % 206.37/28.45 | % 206.37/28.45 | GROUND_INST: instantiating (14) with all_722_1, all_764_1, 1, nat$, % 206.37/28.45 | simplifying with (27), (37) gives: % 206.37/28.45 | (45) all_764_1 = all_722_1 % 206.37/28.45 | % 206.37/28.45 | GROUND_INST: instantiating (14) with all_701_0, all_764_1, 1, nat$, % 206.37/28.45 | simplifying with (21), (37) gives: % 206.37/28.45 | (46) all_764_1 = all_701_0 % 206.37/28.45 | % 206.37/28.45 | COMBINE_EQS: (44), (45) imply: % 206.37/28.45 | (47) all_740_1 = all_722_1 % 206.37/28.45 | % 206.37/28.45 | COMBINE_EQS: (44), (46) imply: % 206.37/28.45 | (48) all_740_1 = all_701_0 % 206.37/28.45 | % 206.37/28.45 | COMBINE_EQS: (47), (48) imply: % 206.37/28.45 | (49) all_722_1 = all_701_0 % 206.37/28.45 | % 206.37/28.45 | SIMP: (49) implies: % 206.37/28.45 | (50) all_722_1 = all_701_0 % 206.37/28.45 | % 206.37/28.45 | COMBINE_EQS: (43), (50) imply: % 206.37/28.45 | (51) all_713_0 = all_701_0 % 206.37/28.45 | % 206.37/28.45 | SIMP: (51) implies: % 206.37/28.45 | (52) all_713_0 = all_701_0 % 206.37/28.45 | % 206.37/28.45 | COMBINE_EQS: (41), (42) imply: % 206.37/28.45 | (53) all_709_0 = all_699_0 % 206.37/28.45 | % 206.37/28.45 | COMBINE_EQS: (41), (52) imply: % 206.37/28.45 | (54) all_709_0 = all_701_0 % 206.37/28.45 | % 206.37/28.45 | COMBINE_EQS: (53), (54) imply: % 206.37/28.45 | (55) all_701_0 = all_699_0 % 206.37/28.45 | % 206.37/28.45 | SIMP: (55) implies: % 206.37/28.45 | (56) all_701_0 = all_699_0 % 206.37/28.45 | % 206.37/28.45 | COMBINE_EQS: (48), (56) imply: % 206.37/28.45 | (57) all_740_1 = all_699_0 % 206.37/28.45 | % 206.37/28.45 | COMBINE_EQS: (44), (57) imply: % 206.37/28.45 | (58) all_764_1 = all_699_0 % 206.37/28.45 | % 206.37/28.45 | REDUCE: (38), (40) imply: % 206.37/28.45 | (59) closed_segment$(zero$, all_740_3) = all_764_2 % 206.37/28.45 | % 206.37/28.45 | REDUCE: (36), (58) imply: % 206.37/28.45 | (60) atLeastAtMost$(all_699_0, n$) = all_764_0 % 206.37/28.45 | % 206.37/28.45 | REDUCE: (30), (57) imply: % 206.37/28.45 | (61) atLeastAtMost$(all_699_0, n$) = all_740_0 % 206.37/28.45 | % 206.37/28.45 | GROUND_INST: instantiating (13) with all_740_0, all_764_0, n$, all_699_0, % 206.37/28.45 | simplifying with (60), (61) gives: % 206.37/28.45 | (62) all_764_0 = all_740_0 % 206.37/28.45 | % 206.37/28.46 | GROUND_INST: instantiating (15) with all_740_2, all_764_2, all_740_3, zero$, % 206.37/28.46 | simplifying with (32), (59) gives: % 206.37/28.46 | (63) all_764_2 = all_740_2 % 206.37/28.46 | % 206.37/28.46 | GROUND_INST: instantiating (39) with c$, simplifying with (axiom40), % 206.37/28.46 | (conjecture34) gives: % 206.37/28.46 | (64) ? [v0: Complex$] : ? [v1: Nat_complex_fun$] : ? [v2: Complex$] : ? % 206.37/28.46 | [v3: $real] : ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v3, c$) = v4 % 206.37/28.46 | & prod$(v1, all_764_0) = v2 & fun_app$i(norm$, v2) = v3 & % 206.37/28.46 | member$(v0, all_764_2) = 0 & uu$(v0) = v1 & Nat_complex_fun$(v1) & % 206.37/28.46 | Complex$(v2) & Complex$(v0)) % 206.37/28.46 | % 206.37/28.46 | GROUND_INST: instantiating (6) with real_very_small, real_very_large, % 206.37/28.46 | simplifying with (17) gives: % 206.37/28.46 | (65) real_very_large = real_very_small | ? [v0: int] : ( ~ (v0 = 0) & % 206.37/28.46 | real_$lesseq(real_very_large, real_very_small) = v0) % 206.37/28.46 | % 206.37/28.46 | DELTA: instantiating (64) with fresh symbols all_973_0, all_973_1, all_973_2, % 206.37/28.46 | all_973_3, all_973_4 gives: % 206.37/28.46 | (66) ~ (all_973_0 = 0) & real_$lesseq(all_973_1, c$) = all_973_0 & % 206.37/28.46 | prod$(all_973_3, all_764_0) = all_973_2 & fun_app$i(norm$, all_973_2) % 206.37/28.46 | = all_973_1 & member$(all_973_4, all_764_2) = 0 & uu$(all_973_4) = % 206.37/28.46 | all_973_3 & Nat_complex_fun$(all_973_3) & Complex$(all_973_2) & % 206.37/28.46 | Complex$(all_973_4) % 206.37/28.46 | % 206.37/28.46 | ALPHA: (66) implies: % 206.37/28.46 | (67) ~ (all_973_0 = 0) % 206.37/28.46 | (68) Complex$(all_973_4) % 206.37/28.46 | (69) uu$(all_973_4) = all_973_3 % 206.37/28.46 | (70) member$(all_973_4, all_764_2) = 0 % 206.37/28.46 | (71) fun_app$i(norm$, all_973_2) = all_973_1 % 206.37/28.46 | (72) prod$(all_973_3, all_764_0) = all_973_2 % 206.37/28.46 | (73) real_$lesseq(all_973_1, c$) = all_973_0 % 206.37/28.46 | % 206.37/28.46 | REDUCE: (62), (72) imply: % 206.37/28.46 | (74) prod$(all_973_3, all_740_0) = all_973_2 % 206.37/28.46 | % 206.37/28.46 | REDUCE: (63), (70) imply: % 206.37/28.46 | (75) member$(all_973_4, all_740_2) = 0 % 206.37/28.46 | % 206.37/28.46 | BETA: splitting (65) gives: % 206.37/28.46 | % 206.37/28.46 | Case 1: % 206.37/28.46 | | % 206.37/28.46 | | (76) real_very_large = real_very_small % 206.37/28.46 | | % 206.37/28.46 | | REDUCE: (16), (76) imply: % 206.37/28.46 | | (77) $false % 206.37/28.46 | | % 206.37/28.46 | | CLOSE: (77) is inconsistent. % 206.37/28.46 | | % 206.37/28.46 | Case 2: % 206.37/28.46 | | % 206.37/28.46 | | % 206.37/28.46 | | GROUND_INST: instantiating (33) with all_973_4, simplifying with (68), (75) % 206.37/28.46 | | gives: % 206.37/28.46 | | (78) ? [v0: Nat_complex_fun$] : ? [v1: Complex$] : ? [v2: $real] : % 206.37/28.46 | | (real_$lesseq(v2, c$) = 0 & prod$(v0, all_740_0) = v1 & % 206.37/28.46 | | fun_app$i(norm$, v1) = v2 & uu$(all_973_4) = v0 & % 206.37/28.46 | | Nat_complex_fun$(v0) & Complex$(v1)) % 206.37/28.46 | | % 206.37/28.46 | | DELTA: instantiating (78) with fresh symbols all_1785_0, all_1785_1, % 206.37/28.46 | | all_1785_2 gives: % 206.37/28.46 | | (79) real_$lesseq(all_1785_0, c$) = 0 & prod$(all_1785_2, all_740_0) = % 206.37/28.46 | | all_1785_1 & fun_app$i(norm$, all_1785_1) = all_1785_0 & % 206.37/28.46 | | uu$(all_973_4) = all_1785_2 & Nat_complex_fun$(all_1785_2) & % 206.37/28.46 | | Complex$(all_1785_1) % 206.37/28.46 | | % 206.37/28.46 | | ALPHA: (79) implies: % 206.37/28.46 | | (80) uu$(all_973_4) = all_1785_2 % 206.37/28.46 | | (81) fun_app$i(norm$, all_1785_1) = all_1785_0 % 206.37/28.46 | | (82) prod$(all_1785_2, all_740_0) = all_1785_1 % 206.37/28.46 | | (83) real_$lesseq(all_1785_0, c$) = 0 % 206.37/28.46 | | % 206.37/28.46 | | GROUND_INST: instantiating (8) with all_973_3, all_1785_2, all_973_4, % 206.37/28.46 | | simplifying with (69), (80) gives: % 206.37/28.46 | | (84) all_1785_2 = all_973_3 % 206.37/28.46 | | % 206.37/28.46 | | REDUCE: (82), (84) imply: % 206.37/28.46 | | (85) prod$(all_973_3, all_740_0) = all_1785_1 % 206.37/28.46 | | % 206.37/28.46 | | GROUND_INST: instantiating (11) with all_973_2, all_1785_1, all_740_0, % 206.37/28.46 | | all_973_3, simplifying with (74), (85) gives: % 206.37/28.46 | | (86) all_1785_1 = all_973_2 % 206.37/28.46 | | % 206.37/28.46 | | REDUCE: (81), (86) imply: % 206.37/28.46 | | (87) fun_app$i(norm$, all_973_2) = all_1785_0 % 206.37/28.46 | | % 206.37/28.46 | | GROUND_INST: instantiating (10) with all_973_1, all_1785_0, all_973_2, % 206.37/28.46 | | norm$, simplifying with (71), (87) gives: % 206.37/28.46 | | (88) all_1785_0 = all_973_1 % 206.37/28.46 | | % 206.37/28.46 | | REDUCE: (83), (88) imply: % 206.37/28.46 | | (89) real_$lesseq(all_973_1, c$) = 0 % 206.37/28.46 | | % 206.37/28.46 | | GROUND_INST: instantiating (12) with all_973_0, 0, c$, all_973_1, % 206.37/28.46 | | simplifying with (73), (89) gives: % 206.37/28.46 | | (90) all_973_0 = 0 % 206.37/28.46 | | % 206.37/28.46 | | REDUCE: (67), (90) imply: % 206.37/28.46 | | (91) $false % 206.37/28.46 | | % 206.37/28.46 | | CLOSE: (91) is inconsistent. % 206.37/28.46 | | % 206.37/28.46 | End of split % 206.37/28.46 | % 206.37/28.46 End of proof % 206.37/28.46 % SZS output end Proof for theBenchmark % 206.37/28.46 % 206.37/28.46 27850ms %------------------------------------------------------------------------------