TSTP Solution File: SWW824_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW824_1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n016.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 : Fri Sep 1 00:51:29 EDT 2023
% Result : Unsatisfiable 24.40s 4.28s
% Output : Proof 64.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW824_1 : TPTP v8.1.2. Released v7.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.36 % Computer : n016.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun Aug 27 18:04:59 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.14/1.00 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 2.14/1.00 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 2.14/1.00 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 2.14/1.00 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 2.14/1.00 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 2.14/1.01 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 2.14/1.02 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 10.59/2.20 Prover 6: Preprocessing ...
% 10.59/2.20 Prover 4: Preprocessing ...
% 10.59/2.20 Prover 1: Preprocessing ...
% 10.59/2.26 Prover 0: Preprocessing ...
% 11.24/2.35 Prover 3: Preprocessing ...
% 12.18/2.49 Prover 5: Preprocessing ...
% 12.93/2.52 Prover 2: Preprocessing ...
% 24.40/4.21 Prover 6: Constructing countermodel ...
% 24.40/4.26 Prover 6: proved (3602ms)
% 24.40/4.27
% 24.40/4.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.40/4.28
% 24.40/4.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 24.91/4.29 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 26.17/4.36 Prover 0: Constructing countermodel ...
% 26.17/4.36 Prover 0: stopped
% 26.17/4.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 26.17/4.38 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 27.75/4.56 Prover 1: Warning: ignoring some quantifiers
% 29.02/4.72 Prover 1: Constructing countermodel ...
% 29.02/4.74 Prover 3: Constructing countermodel ...
% 29.02/4.74 Prover 3: stopped
% 29.02/4.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 29.02/4.74 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 32.08/5.11 Prover 7: Preprocessing ...
% 32.44/5.14 Prover 4: Warning: ignoring some quantifiers
% 32.48/5.16 Prover 8: Preprocessing ...
% 32.96/5.25 Prover 10: Preprocessing ...
% 33.39/5.33 Prover 4: Constructing countermodel ...
% 38.55/5.98 Prover 2: Constructing countermodel ...
% 38.55/5.98 Prover 2: stopped
% 38.89/5.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 38.89/6.00 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation
% 40.21/6.36 Prover 8: Warning: ignoring some quantifiers
% 42.39/6.46 Prover 8: Constructing countermodel ...
% 42.83/6.55 Prover 11: Preprocessing ...
% 48.25/7.23 Prover 10: Warning: ignoring some quantifiers
% 48.25/7.26 Prover 7: Warning: ignoring some quantifiers
% 48.70/7.35 Prover 10: Constructing countermodel ...
% 49.81/7.43 Prover 7: Constructing countermodel ...
% 51.08/7.78 Prover 5: Proving ...
% 51.08/7.78 Prover 5: stopped
% 51.08/7.79 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 51.08/7.79 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation
% 56.18/8.33 Prover 13: Preprocessing ...
% 60.70/8.91 Prover 1: Found proof (size 80)
% 60.70/8.91 Prover 1: proved (8262ms)
% 60.70/8.91 Prover 8: stopped
% 61.30/8.92 Prover 4: stopped
% 61.30/8.92 Prover 7: stopped
% 61.30/8.93 Prover 10: stopped
% 61.60/9.02 Prover 11: Warning: ignoring some quantifiers
% 62.00/9.10 Prover 11: Constructing countermodel ...
% 63.12/9.29 Prover 11: stopped
% 64.04/9.53 Prover 13: Warning: ignoring some quantifiers
% 64.37/9.59 Prover 13: Constructing countermodel ...
% 64.81/9.67 Prover 13: stopped
% 64.81/9.67
% 64.81/9.67 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 64.81/9.67
% 64.81/9.70 % SZS output start Proof for theBenchmark
% 64.81/9.72 Assumptions after simplification:
% 64.81/9.72 ---------------------------------
% 64.81/9.72
% 64.81/9.72 (formula_13)
% 64.81/9.74 S2(f4) & ? [v0: $real] : (real_$product(real_2, f7) = v0 & ! [v1: $real] :
% 64.81/9.74 ! [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | ? [v3: $real] : (f3(f4, v2)
% 64.81/9.74 = v3 & f3(f4, v1) = v3)))
% 64.81/9.74
% 64.81/9.74 (formula_14)
% 64.81/9.74 S2(f4) & ? [v0: $real] : (real_$product(real_2, f7) = v0 & f3(f4, v0) =
% 64.81/9.74 real_1)
% 64.81/9.74
% 64.81/9.74 (formula_147)
% 64.81/9.74 S2(f31) & ? [v0: $real] : (real_$product(real_2, f7) = v0 & ! [v1: $real] :
% 64.81/9.74 ! [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | ? [v3: $real] : (f3(f31, v2)
% 64.81/9.74 = v3 & f3(f31, v1) = v3)))
% 64.81/9.74
% 64.81/9.74 (formula_148)
% 64.81/9.74 S2(f31) & ? [v0: $real] : (real_$product(real_2, f7) = v0 & f3(f31, v0) =
% 64.81/9.74 real_0)
% 64.81/9.74
% 64.81/9.74 (formula_183)
% 64.81/9.75 S2(f4) & S2(f31) & ? [v0: $real] : (real_$product(real_2, f7) = v0 & ! [v1:
% 64.81/9.75 $real] : ! [v2: any] : ( ~ (real_$less(v1, v0) = v2) | ? [v3: $real] :
% 64.81/9.75 ? [v4: $real] : (f3(f4, v1) = v4 & f3(f31, v1) = v3 & ? [v5: any] :
% 64.81/9.75 (real_$less(real_0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = real_1) | ~ (v3
% 64.81/9.75 = real_0) | ~ (v2 = 0))))))
% 64.81/9.75
% 64.81/9.75 (formula_3)
% 64.81/9.75 S3(f6) & S5(f10) & S4(f9) & S2(f4) & ? [v0: $real] : ? [v1: S2] : ? [v2:
% 64.81/9.75 $real] : ? [v3: $real] : (real_$product(real_2, f7) = v0 & f5(f6, v0) = v1
% 64.81/9.75 & f8(f9, f10) = v2 & f3(v1, v2) = v3 & f3(f4, v3) = real_0 & S2(v1))
% 64.81/9.75
% 64.81/9.75 (formula_4)
% 64.81/9.75 S3(f6) & S5(f10) & S4(f9) & S2(f4) & ? [v0: $real] : ? [v1: S2] : ? [v2:
% 64.81/9.75 $real] : ? [v3: $real] : ? [v4: $real] : (real_$product(real_2, f7) = v0 &
% 64.81/9.75 f5(f6, v0) = v1 & f8(f9, f10) = v2 & f3(v1, v2) = v3 & f3(f4, v3) = v4 &
% 64.81/9.75 S2(v1) & ? [v5: any] : ? [v6: $real] : (real_$less(v4, real_0) = v5 &
% 64.81/9.75 real_$uminus(v4) = v6 & ( ~ (v5 = 0) | v6 = real_1) & (v5 = 0 | v4 =
% 64.81/9.75 real_1)))
% 64.81/9.75
% 64.81/9.75 (formula_46)
% 64.81/9.75 ? [v0: $real] : ? [v1: $real] : (real_$less(v1, f7) = 0 & real_$uminus(v0) =
% 64.81/9.75 v1 & real_$product(real_2, f7) = v0)
% 64.81/9.75
% 64.81/9.75 (formula_64)
% 64.81/9.76 S3(f6) & S4(f9) & S10(f18) & S8(f16) & ? [v0: $real] : ? [v1: S2] :
% 64.81/9.76 (real_$product(real_2, f7) = v0 & f5(f6, v0) = v1 & S2(v1) & ! [v2: S5] : !
% 64.81/9.76 [v3: S9] : ( ~ (f15(f16, v2) = v3) | ~ S5(v2) | ? [v4: $real] : ? [v5:
% 64.81/9.76 $real] : (f17(f18, v5) = v3 & f8(f9, v2) = v4 & f3(v1, v4) = v5 &
% 64.81/9.76 S9(v3))))
% 64.81/9.76
% 64.81/9.76 (input)
% 64.81/9.79 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_6) & ~
% 64.81/9.79 (real_very_large = real_4) & ~ (real_very_large = real_-1) & ~
% 64.81/9.79 (real_very_large = real_3) & ~ (real_very_large = real_1) & ~
% 64.81/9.79 (real_very_large = real_2) & ~ (real_very_large = real_0) & ~
% 64.81/9.79 (real_very_small = real_6) & ~ (real_very_small = real_4) & ~
% 64.81/9.79 (real_very_small = real_-1) & ~ (real_very_small = real_3) & ~
% 64.81/9.79 (real_very_small = real_1) & ~ (real_very_small = real_2) & ~
% 64.81/9.79 (real_very_small = real_0) & ~ (real_6 = real_4) & ~ (real_6 = real_-1) & ~
% 64.81/9.79 (real_6 = real_3) & ~ (real_6 = real_1) & ~ (real_6 = real_2) & ~ (real_6 =
% 64.81/9.79 real_0) & ~ (real_4 = real_-1) & ~ (real_4 = real_3) & ~ (real_4 =
% 64.81/9.79 real_1) & ~ (real_4 = real_2) & ~ (real_4 = real_0) & ~ (real_-1 =
% 64.81/9.79 real_3) & ~ (real_-1 = real_1) & ~ (real_-1 = real_2) & ~ (real_-1 =
% 64.81/9.79 real_0) & ~ (real_3 = real_1) & ~ (real_3 = real_2) & ~ (real_3 = real_0)
% 64.81/9.79 & ~ (real_1 = real_2) & ~ (real_1 = real_0) & ~ (real_2 = real_0) &
% 64.81/9.79 real_$is_int(real_6) = 0 & real_$is_int(real_4) = 0 & real_$is_int(real_-1) =
% 64.81/9.79 0 & real_$is_int(real_3) = 0 & real_$is_int(real_1) = 0 & real_$is_int(real_2)
% 64.81/9.79 = 0 & real_$is_int(real_0) = 0 & real_$is_rat(real_6) = 0 &
% 64.81/9.79 real_$is_rat(real_4) = 0 & real_$is_rat(real_-1) = 0 & real_$is_rat(real_3) =
% 64.81/9.79 0 & real_$is_rat(real_1) = 0 & real_$is_rat(real_2) = 0 & real_$is_rat(real_0)
% 64.81/9.79 = 0 & real_$floor(real_6) = real_6 & real_$floor(real_4) = real_4 &
% 64.81/9.79 real_$floor(real_-1) = real_-1 & real_$floor(real_3) = real_3 &
% 64.81/9.79 real_$floor(real_1) = real_1 & real_$floor(real_2) = real_2 &
% 64.81/9.79 real_$floor(real_0) = real_0 & real_$ceiling(real_6) = real_6 &
% 64.81/9.79 real_$ceiling(real_4) = real_4 & real_$ceiling(real_-1) = real_-1 &
% 64.81/9.79 real_$ceiling(real_3) = real_3 & real_$ceiling(real_1) = real_1 &
% 64.81/9.79 real_$ceiling(real_2) = real_2 & real_$ceiling(real_0) = real_0 &
% 64.81/9.79 real_$truncate(real_6) = real_6 & real_$truncate(real_4) = real_4 &
% 64.81/9.79 real_$truncate(real_-1) = real_-1 & real_$truncate(real_3) = real_3 &
% 64.81/9.79 real_$truncate(real_1) = real_1 & real_$truncate(real_2) = real_2 &
% 64.81/9.79 real_$truncate(real_0) = real_0 & real_$round(real_6) = real_6 &
% 64.81/9.79 real_$round(real_4) = real_4 & real_$round(real_-1) = real_-1 &
% 64.81/9.79 real_$round(real_3) = real_3 & real_$round(real_1) = real_1 &
% 64.81/9.79 real_$round(real_2) = real_2 & real_$round(real_0) = real_0 &
% 64.81/9.79 real_$to_int(real_6) = 6 & real_$to_int(real_4) = 4 & real_$to_int(real_-1) =
% 64.81/9.79 -1 & real_$to_int(real_3) = 3 & real_$to_int(real_1) = 1 &
% 64.81/9.79 real_$to_int(real_2) = 2 & real_$to_int(real_0) = 0 & real_$to_rat(real_6) =
% 64.81/9.79 rat_6 & real_$to_rat(real_4) = rat_4 & real_$to_rat(real_-1) = rat_-1 &
% 64.81/9.79 real_$to_rat(real_3) = rat_3 & real_$to_rat(real_1) = rat_1 &
% 64.81/9.79 real_$to_rat(real_2) = rat_2 & real_$to_rat(real_0) = rat_0 &
% 64.81/9.79 real_$to_real(real_6) = real_6 & real_$to_real(real_4) = real_4 &
% 64.81/9.79 real_$to_real(real_-1) = real_-1 & real_$to_real(real_3) = real_3 &
% 64.81/9.79 real_$to_real(real_1) = real_1 & real_$to_real(real_2) = real_2 &
% 64.81/9.79 real_$to_real(real_0) = real_0 & int_$to_real(6) = real_6 & int_$to_real(4) =
% 64.81/9.79 real_4 & int_$to_real(3) = real_3 & int_$to_real(2) = real_2 &
% 64.81/9.79 int_$to_real(-1) = real_-1 & int_$to_real(1) = real_1 & int_$to_real(0) =
% 64.81/9.79 real_0 & real_$quotient(real_6, real_6) = real_1 & real_$quotient(real_6,
% 64.81/9.79 real_3) = real_2 & real_$quotient(real_6, real_1) = real_6 &
% 64.81/9.79 real_$quotient(real_6, real_2) = real_3 & real_$quotient(real_4, real_4) =
% 64.81/9.79 real_1 & real_$quotient(real_4, real_1) = real_4 & real_$quotient(real_4,
% 64.81/9.79 real_2) = real_2 & real_$quotient(real_-1, real_-1) = real_1 &
% 64.81/9.79 real_$quotient(real_-1, real_1) = real_-1 & real_$quotient(real_3, real_3) =
% 64.81/9.79 real_1 & real_$quotient(real_3, real_1) = real_3 & real_$quotient(real_1,
% 64.81/9.79 real_-1) = real_-1 & real_$quotient(real_1, real_1) = real_1 &
% 64.81/9.79 real_$quotient(real_2, real_1) = real_2 & real_$quotient(real_2, real_2) =
% 64.81/9.80 real_1 & real_$quotient(real_0, real_6) = real_0 & real_$quotient(real_0,
% 64.81/9.80 real_4) = real_0 & real_$quotient(real_0, real_-1) = real_0 &
% 64.81/9.80 real_$quotient(real_0, real_3) = real_0 & real_$quotient(real_0, real_1) =
% 64.81/9.80 real_0 & real_$quotient(real_0, real_2) = real_0 &
% 64.81/9.80 real_$greatereq(real_very_small, real_very_large) = 1 &
% 64.81/9.80 real_$greatereq(real_6, real_6) = 0 & real_$greatereq(real_6, real_4) = 0 &
% 64.81/9.80 real_$greatereq(real_6, real_-1) = 0 & real_$greatereq(real_6, real_3) = 0 &
% 64.81/9.80 real_$greatereq(real_6, real_1) = 0 & real_$greatereq(real_6, real_2) = 0 &
% 64.81/9.80 real_$greatereq(real_6, real_0) = 0 & real_$greatereq(real_4, real_6) = 1 &
% 64.81/9.80 real_$greatereq(real_4, real_4) = 0 & real_$greatereq(real_4, real_-1) = 0 &
% 64.81/9.80 real_$greatereq(real_4, real_3) = 0 & real_$greatereq(real_4, real_1) = 0 &
% 64.81/9.80 real_$greatereq(real_4, real_2) = 0 & real_$greatereq(real_4, real_0) = 0 &
% 64.81/9.80 real_$greatereq(real_-1, real_6) = 1 & real_$greatereq(real_-1, real_4) = 1 &
% 64.81/9.80 real_$greatereq(real_-1, real_-1) = 0 & real_$greatereq(real_-1, real_3) = 1 &
% 64.81/9.80 real_$greatereq(real_-1, real_1) = 1 & real_$greatereq(real_-1, real_2) = 1 &
% 64.81/9.80 real_$greatereq(real_-1, real_0) = 1 & real_$greatereq(real_3, real_6) = 1 &
% 64.81/9.80 real_$greatereq(real_3, real_4) = 1 & real_$greatereq(real_3, real_-1) = 0 &
% 64.81/9.80 real_$greatereq(real_3, real_3) = 0 & real_$greatereq(real_3, real_1) = 0 &
% 64.81/9.80 real_$greatereq(real_3, real_2) = 0 & real_$greatereq(real_3, real_0) = 0 &
% 64.81/9.80 real_$greatereq(real_1, real_6) = 1 & real_$greatereq(real_1, real_4) = 1 &
% 64.81/9.80 real_$greatereq(real_1, real_-1) = 0 & real_$greatereq(real_1, real_3) = 1 &
% 64.81/9.80 real_$greatereq(real_1, real_1) = 0 & real_$greatereq(real_1, real_2) = 1 &
% 64.81/9.80 real_$greatereq(real_1, real_0) = 0 & real_$greatereq(real_2, real_6) = 1 &
% 64.81/9.80 real_$greatereq(real_2, real_4) = 1 & real_$greatereq(real_2, real_-1) = 0 &
% 64.81/9.80 real_$greatereq(real_2, real_3) = 1 & real_$greatereq(real_2, real_1) = 0 &
% 64.81/9.80 real_$greatereq(real_2, real_2) = 0 & real_$greatereq(real_2, real_0) = 0 &
% 64.81/9.80 real_$greatereq(real_0, real_6) = 1 & real_$greatereq(real_0, real_4) = 1 &
% 64.81/9.80 real_$greatereq(real_0, real_-1) = 0 & real_$greatereq(real_0, real_3) = 1 &
% 64.81/9.80 real_$greatereq(real_0, real_1) = 1 & real_$greatereq(real_0, real_2) = 1 &
% 64.81/9.80 real_$greatereq(real_0, real_0) = 0 & real_$greater(real_very_large, real_6) =
% 64.81/9.80 0 & real_$greater(real_very_large, real_4) = 0 &
% 64.81/9.80 real_$greater(real_very_large, real_-1) = 0 & real_$greater(real_very_large,
% 64.81/9.80 real_3) = 0 & real_$greater(real_very_large, real_1) = 0 &
% 64.81/9.80 real_$greater(real_very_large, real_2) = 0 & real_$greater(real_very_large,
% 64.81/9.80 real_0) = 0 & real_$greater(real_very_small, real_very_large) = 1 &
% 64.81/9.80 real_$greater(real_6, real_very_small) = 0 & real_$greater(real_6, real_6) = 1
% 64.81/9.80 & real_$greater(real_6, real_4) = 0 & real_$greater(real_6, real_-1) = 0 &
% 64.81/9.80 real_$greater(real_6, real_3) = 0 & real_$greater(real_6, real_1) = 0 &
% 64.81/9.80 real_$greater(real_6, real_2) = 0 & real_$greater(real_6, real_0) = 0 &
% 64.81/9.80 real_$greater(real_4, real_very_small) = 0 & real_$greater(real_4, real_6) = 1
% 64.81/9.80 & real_$greater(real_4, real_4) = 1 & real_$greater(real_4, real_-1) = 0 &
% 64.81/9.80 real_$greater(real_4, real_3) = 0 & real_$greater(real_4, real_1) = 0 &
% 64.81/9.80 real_$greater(real_4, real_2) = 0 & real_$greater(real_4, real_0) = 0 &
% 64.81/9.80 real_$greater(real_-1, real_very_small) = 0 & real_$greater(real_-1, real_6) =
% 64.81/9.80 1 & real_$greater(real_-1, real_4) = 1 & real_$greater(real_-1, real_-1) = 1 &
% 64.81/9.80 real_$greater(real_-1, real_3) = 1 & real_$greater(real_-1, real_1) = 1 &
% 64.81/9.80 real_$greater(real_-1, real_2) = 1 & real_$greater(real_-1, real_0) = 1 &
% 64.81/9.80 real_$greater(real_3, real_very_small) = 0 & real_$greater(real_3, real_6) = 1
% 64.81/9.80 & real_$greater(real_3, real_4) = 1 & real_$greater(real_3, real_-1) = 0 &
% 64.81/9.80 real_$greater(real_3, real_3) = 1 & real_$greater(real_3, real_1) = 0 &
% 64.81/9.80 real_$greater(real_3, real_2) = 0 & real_$greater(real_3, real_0) = 0 &
% 64.81/9.80 real_$greater(real_1, real_very_small) = 0 & real_$greater(real_1, real_6) = 1
% 64.81/9.80 & real_$greater(real_1, real_4) = 1 & real_$greater(real_1, real_-1) = 0 &
% 64.81/9.80 real_$greater(real_1, real_3) = 1 & real_$greater(real_1, real_1) = 1 &
% 64.81/9.80 real_$greater(real_1, real_2) = 1 & real_$greater(real_1, real_0) = 0 &
% 64.81/9.80 real_$greater(real_2, real_very_small) = 0 & real_$greater(real_2, real_6) = 1
% 64.81/9.80 & real_$greater(real_2, real_4) = 1 & real_$greater(real_2, real_-1) = 0 &
% 64.81/9.80 real_$greater(real_2, real_3) = 1 & real_$greater(real_2, real_1) = 0 &
% 64.81/9.80 real_$greater(real_2, real_2) = 1 & real_$greater(real_2, real_0) = 0 &
% 64.81/9.80 real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0, real_6) = 1
% 64.81/9.80 & real_$greater(real_0, real_4) = 1 & real_$greater(real_0, real_-1) = 0 &
% 64.81/9.80 real_$greater(real_0, real_3) = 1 & real_$greater(real_0, real_1) = 1 &
% 64.81/9.80 real_$greater(real_0, real_2) = 1 & real_$greater(real_0, real_0) = 1 &
% 64.81/9.80 real_$difference(real_6, real_6) = real_0 & real_$difference(real_6, real_4) =
% 64.81/9.80 real_2 & real_$difference(real_6, real_3) = real_3 & real_$difference(real_6,
% 64.81/9.80 real_2) = real_4 & real_$difference(real_6, real_0) = real_6 &
% 64.81/9.80 real_$difference(real_4, real_4) = real_0 & real_$difference(real_4, real_3) =
% 64.81/9.80 real_1 & real_$difference(real_4, real_1) = real_3 & real_$difference(real_4,
% 64.81/9.80 real_2) = real_2 & real_$difference(real_4, real_0) = real_4 &
% 64.81/9.80 real_$difference(real_-1, real_-1) = real_0 & real_$difference(real_-1,
% 64.81/9.80 real_0) = real_-1 & real_$difference(real_3, real_4) = real_-1 &
% 64.81/9.80 real_$difference(real_3, real_-1) = real_4 & real_$difference(real_3, real_3)
% 64.81/9.80 = real_0 & real_$difference(real_3, real_1) = real_2 &
% 64.81/9.80 real_$difference(real_3, real_2) = real_1 & real_$difference(real_3, real_0) =
% 64.81/9.80 real_3 & real_$difference(real_1, real_-1) = real_2 & real_$difference(real_1,
% 64.81/9.80 real_1) = real_0 & real_$difference(real_1, real_2) = real_-1 &
% 64.81/9.80 real_$difference(real_1, real_0) = real_1 & real_$difference(real_2, real_-1)
% 64.81/9.80 = real_3 & real_$difference(real_2, real_3) = real_-1 &
% 64.81/9.80 real_$difference(real_2, real_1) = real_1 & real_$difference(real_2, real_2) =
% 64.81/9.80 real_0 & real_$difference(real_2, real_0) = real_2 & real_$difference(real_0,
% 64.81/9.80 real_-1) = real_1 & real_$difference(real_0, real_1) = real_-1 &
% 64.81/9.80 real_$difference(real_0, real_0) = real_0 & real_$sum(real_6, real_0) = real_6
% 64.81/9.80 & real_$sum(real_4, real_-1) = real_3 & real_$sum(real_4, real_2) = real_6 &
% 64.81/9.80 real_$sum(real_4, real_0) = real_4 & real_$sum(real_-1, real_4) = real_3 &
% 64.81/9.80 real_$sum(real_-1, real_3) = real_2 & real_$sum(real_-1, real_1) = real_0 &
% 64.81/9.80 real_$sum(real_-1, real_2) = real_1 & real_$sum(real_-1, real_0) = real_-1 &
% 64.81/9.80 real_$sum(real_3, real_-1) = real_2 & real_$sum(real_3, real_3) = real_6 &
% 64.81/9.80 real_$sum(real_3, real_1) = real_4 & real_$sum(real_3, real_0) = real_3 &
% 64.81/9.80 real_$sum(real_1, real_-1) = real_0 & real_$sum(real_1, real_3) = real_4 &
% 64.81/9.80 real_$sum(real_1, real_1) = real_2 & real_$sum(real_1, real_2) = real_3 &
% 64.81/9.80 real_$sum(real_1, real_0) = real_1 & real_$sum(real_2, real_4) = real_6 &
% 64.81/9.80 real_$sum(real_2, real_-1) = real_1 & real_$sum(real_2, real_1) = real_3 &
% 64.81/9.80 real_$sum(real_2, real_2) = real_4 & real_$sum(real_2, real_0) = real_2 &
% 64.81/9.80 real_$sum(real_0, real_6) = real_6 & real_$sum(real_0, real_4) = real_4 &
% 64.81/9.80 real_$sum(real_0, real_-1) = real_-1 & real_$sum(real_0, real_3) = real_3 &
% 64.81/9.80 real_$sum(real_0, real_1) = real_1 & real_$sum(real_0, real_2) = real_2 &
% 64.81/9.80 real_$sum(real_0, real_0) = real_0 & real_$lesseq(real_very_small,
% 64.81/9.80 real_very_large) = 0 & real_$lesseq(real_6, real_6) = 0 &
% 64.81/9.80 real_$lesseq(real_6, real_4) = 1 & real_$lesseq(real_6, real_-1) = 1 &
% 64.81/9.80 real_$lesseq(real_6, real_3) = 1 & real_$lesseq(real_6, real_1) = 1 &
% 64.81/9.80 real_$lesseq(real_6, real_2) = 1 & real_$lesseq(real_6, real_0) = 1 &
% 64.81/9.80 real_$lesseq(real_4, real_6) = 0 & real_$lesseq(real_4, real_4) = 0 &
% 64.81/9.80 real_$lesseq(real_4, real_-1) = 1 & real_$lesseq(real_4, real_3) = 1 &
% 64.81/9.80 real_$lesseq(real_4, real_1) = 1 & real_$lesseq(real_4, real_2) = 1 &
% 64.81/9.80 real_$lesseq(real_4, real_0) = 1 & real_$lesseq(real_-1, real_6) = 0 &
% 64.81/9.80 real_$lesseq(real_-1, real_4) = 0 & real_$lesseq(real_-1, real_-1) = 0 &
% 64.81/9.80 real_$lesseq(real_-1, real_3) = 0 & real_$lesseq(real_-1, real_1) = 0 &
% 64.81/9.80 real_$lesseq(real_-1, real_2) = 0 & real_$lesseq(real_-1, real_0) = 0 &
% 64.81/9.80 real_$lesseq(real_3, real_6) = 0 & real_$lesseq(real_3, real_4) = 0 &
% 64.81/9.80 real_$lesseq(real_3, real_-1) = 1 & real_$lesseq(real_3, real_3) = 0 &
% 64.81/9.80 real_$lesseq(real_3, real_1) = 1 & real_$lesseq(real_3, real_2) = 1 &
% 64.81/9.80 real_$lesseq(real_3, real_0) = 1 & real_$lesseq(real_1, real_6) = 0 &
% 64.81/9.80 real_$lesseq(real_1, real_4) = 0 & real_$lesseq(real_1, real_-1) = 1 &
% 64.81/9.80 real_$lesseq(real_1, real_3) = 0 & real_$lesseq(real_1, real_1) = 0 &
% 64.81/9.80 real_$lesseq(real_1, real_2) = 0 & real_$lesseq(real_1, real_0) = 1 &
% 64.81/9.80 real_$lesseq(real_2, real_6) = 0 & real_$lesseq(real_2, real_4) = 0 &
% 64.81/9.80 real_$lesseq(real_2, real_-1) = 1 & real_$lesseq(real_2, real_3) = 0 &
% 64.81/9.80 real_$lesseq(real_2, real_1) = 1 & real_$lesseq(real_2, real_2) = 0 &
% 64.81/9.80 real_$lesseq(real_2, real_0) = 1 & real_$lesseq(real_0, real_6) = 0 &
% 64.81/9.80 real_$lesseq(real_0, real_4) = 0 & real_$lesseq(real_0, real_-1) = 1 &
% 64.81/9.80 real_$lesseq(real_0, real_3) = 0 & real_$lesseq(real_0, real_1) = 0 &
% 64.81/9.80 real_$lesseq(real_0, real_2) = 0 & real_$lesseq(real_0, real_0) = 0 &
% 64.81/9.80 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small,
% 64.81/9.80 real_6) = 0 & real_$less(real_very_small, real_4) = 0 &
% 64.81/9.80 real_$less(real_very_small, real_-1) = 0 & real_$less(real_very_small, real_3)
% 64.81/9.80 = 0 & real_$less(real_very_small, real_1) = 0 & real_$less(real_very_small,
% 64.81/9.80 real_2) = 0 & real_$less(real_very_small, real_0) = 0 & real_$less(real_6,
% 64.81/9.80 real_very_large) = 0 & real_$less(real_6, real_6) = 1 & real_$less(real_6,
% 64.81/9.80 real_4) = 1 & real_$less(real_6, real_-1) = 1 & real_$less(real_6, real_3) =
% 64.81/9.80 1 & real_$less(real_6, real_1) = 1 & real_$less(real_6, real_2) = 1 &
% 64.81/9.80 real_$less(real_6, real_0) = 1 & real_$less(real_4, real_very_large) = 0 &
% 64.81/9.80 real_$less(real_4, real_6) = 0 & real_$less(real_4, real_4) = 1 &
% 64.81/9.80 real_$less(real_4, real_-1) = 1 & real_$less(real_4, real_3) = 1 &
% 64.81/9.80 real_$less(real_4, real_1) = 1 & real_$less(real_4, real_2) = 1 &
% 64.81/9.80 real_$less(real_4, real_0) = 1 & real_$less(real_-1, real_very_large) = 0 &
% 64.81/9.80 real_$less(real_-1, real_6) = 0 & real_$less(real_-1, real_4) = 0 &
% 64.81/9.80 real_$less(real_-1, real_-1) = 1 & real_$less(real_-1, real_3) = 0 &
% 64.81/9.80 real_$less(real_-1, real_1) = 0 & real_$less(real_-1, real_2) = 0 &
% 64.81/9.80 real_$less(real_-1, real_0) = 0 & real_$less(real_3, real_very_large) = 0 &
% 64.81/9.80 real_$less(real_3, real_6) = 0 & real_$less(real_3, real_4) = 0 &
% 64.81/9.80 real_$less(real_3, real_-1) = 1 & real_$less(real_3, real_3) = 1 &
% 64.81/9.80 real_$less(real_3, real_1) = 1 & real_$less(real_3, real_2) = 1 &
% 64.81/9.80 real_$less(real_3, real_0) = 1 & real_$less(real_1, real_very_large) = 0 &
% 64.81/9.80 real_$less(real_1, real_6) = 0 & real_$less(real_1, real_4) = 0 &
% 64.81/9.80 real_$less(real_1, real_-1) = 1 & real_$less(real_1, real_3) = 0 &
% 64.81/9.80 real_$less(real_1, real_1) = 1 & real_$less(real_1, real_2) = 0 &
% 64.81/9.80 real_$less(real_1, real_0) = 1 & real_$less(real_2, real_very_large) = 0 &
% 64.81/9.80 real_$less(real_2, real_6) = 0 & real_$less(real_2, real_4) = 0 &
% 64.81/9.80 real_$less(real_2, real_-1) = 1 & real_$less(real_2, real_3) = 0 &
% 64.81/9.80 real_$less(real_2, real_1) = 1 & real_$less(real_2, real_2) = 1 &
% 64.81/9.80 real_$less(real_2, real_0) = 1 & real_$less(real_0, real_very_large) = 0 &
% 64.81/9.80 real_$less(real_0, real_6) = 0 & real_$less(real_0, real_4) = 0 &
% 64.81/9.80 real_$less(real_0, real_-1) = 1 & real_$less(real_0, real_3) = 0 &
% 64.81/9.80 real_$less(real_0, real_1) = 0 & real_$less(real_0, real_2) = 0 &
% 64.81/9.80 real_$less(real_0, real_0) = 1 & real_$uminus(real_-1) = real_1 &
% 64.81/9.80 real_$uminus(real_1) = real_-1 & real_$uminus(real_0) = real_0 &
% 64.81/9.80 real_$product(real_6, real_1) = real_6 & real_$product(real_6, real_0) =
% 64.81/9.80 real_0 & real_$product(real_4, real_1) = real_4 & real_$product(real_4,
% 64.81/9.80 real_0) = real_0 & real_$product(real_-1, real_-1) = real_1 &
% 64.81/9.80 real_$product(real_-1, real_1) = real_-1 & real_$product(real_-1, real_0) =
% 64.81/9.80 real_0 & real_$product(real_3, real_1) = real_3 & real_$product(real_3,
% 64.81/9.80 real_2) = real_6 & real_$product(real_3, real_0) = real_0 &
% 64.81/9.80 real_$product(real_1, real_6) = real_6 & real_$product(real_1, real_4) =
% 64.81/9.80 real_4 & real_$product(real_1, real_-1) = real_-1 & real_$product(real_1,
% 64.81/9.80 real_3) = real_3 & real_$product(real_1, real_1) = real_1 &
% 64.81/9.80 real_$product(real_1, real_2) = real_2 & real_$product(real_1, real_0) =
% 64.81/9.80 real_0 & real_$product(real_2, real_3) = real_6 & real_$product(real_2,
% 64.81/9.80 real_1) = real_2 & real_$product(real_2, real_2) = real_4 &
% 64.81/9.80 real_$product(real_2, real_0) = real_0 & real_$product(real_0, real_6) =
% 64.81/9.80 real_0 & real_$product(real_0, real_4) = real_0 & real_$product(real_0,
% 64.81/9.80 real_-1) = real_0 & real_$product(real_0, real_3) = real_0 &
% 64.81/9.80 real_$product(real_0, real_1) = real_0 & real_$product(real_0, real_2) =
% 64.81/9.80 real_0 & real_$product(real_0, real_0) = real_0 & ! [v0: $real] : ! [v1:
% 64.81/9.80 $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~
% 64.81/9.80 (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] :
% 64.81/9.80 (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0: $real] : !
% 64.81/9.80 [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~
% 64.81/9.80 (real_$quotient(v2, v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0:
% 64.81/9.80 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~
% 64.81/9.80 (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] :
% 64.81/9.80 ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real]
% 64.81/9.80 : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v1) = 0) | ~
% 64.81/9.80 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1,
% 64.81/9.80 v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3:
% 64.81/9.80 int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~ (real_$less(v1, v0) = 0)
% 64.81/9.80 | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real]
% 64.81/9.80 : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ( ~ (real_$sum(v1, v2) =
% 64.81/9.80 v3) | ~ (real_$uminus(v0) = v2) | real_$difference(v1, v0) = v3) & !
% 64.81/9.80 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v2 = real_0 | ~
% 64.81/9.80 (real_$sum(v0, v1) = v2) | ~ (real_$uminus(v0) = v1)) & ! [v0: $real] : !
% 64.81/9.80 [v1: $real] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (real_$less(v1, v0) = v2)
% 64.81/9.80 | ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: $real]
% 64.81/9.80 : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greatereq(v0, v1) = v2)
% 64.81/9.80 | ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: $real]
% 64.81/9.80 : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) |
% 64.81/9.80 ? [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : !
% 64.81/9.80 [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1,
% 64.81/9.80 v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: any] : ( ~
% 64.81/9.80 (real_$less(v1, v0) = v2) | real_$lesseq(v1, v0) = 0 | ( ~ (v2 = 0) & ~ (v1
% 64.81/9.80 = v0))) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~
% 64.81/9.80 (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2) & ! [v0: $real]
% 64.81/9.80 : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! [v0:
% 64.81/9.80 $real] : ! [v1: $real] : ( ~ (real_$greatereq(v0, v1) = 0) |
% 64.81/9.80 real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 64.81/9.80 (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & ! [v0: $real] : !
% 64.81/9.80 [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0:
% 64.81/9.80 $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0))
% 64.81/9.80
% 64.81/9.80 (function-axioms)
% 64.81/9.81 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 |
% 64.81/9.81 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & !
% 64.81/9.81 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : !
% 64.81/9.81 [v3: $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~
% 64.81/9.81 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 64.81/9.81 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 64.81/9.81 (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, v2) = v0)) & ! [v0:
% 64.81/9.81 $real] : ! [v1: $real] : ! [v2: S9] : ! [v3: S21] : (v1 = v0 | ~
% 64.81/9.81 (f44(v3, v2) = v1) | ~ (f44(v3, v2) = v0)) & ! [v0: S10] : ! [v1: S10] :
% 64.81/9.81 ! [v2: $real] : ! [v3: S20] : (v1 = v0 | ~ (f42(v3, v2) = v1) | ~ (f42(v3,
% 64.81/9.81 v2) = v0)) & ! [v0: S8] : ! [v1: S8] : ! [v2: S9] : ! [v3: S19] :
% 64.81/9.81 (v1 = v0 | ~ (f40(v3, v2) = v1) | ~ (f40(v3, v2) = v0)) & ! [v0: S17] : !
% 64.81/9.81 [v1: S17] : ! [v2: S5] : ! [v3: S18] : (v1 = v0 | ~ (f37(v3, v2) = v1) | ~
% 64.81/9.81 (f37(v3, v2) = v0)) & ! [v0: S5] : ! [v1: S5] : ! [v2: S5] : ! [v3: S17]
% 64.81/9.81 : (v1 = v0 | ~ (f36(v3, v2) = v1) | ~ (f36(v3, v2) = v0)) & ! [v0: S6] : !
% 64.81/9.81 [v1: S6] : ! [v2: int] : ! [v3: S16] : (v1 = v0 | ~ (f34(v3, v2) = v1) | ~
% 64.81/9.81 (f34(v3, v2) = v0)) & ! [v0: S4] : ! [v1: S4] : ! [v2: $real] : ! [v3:
% 64.81/9.81 S15] : (v1 = v0 | ~ (f32(v3, v2) = v1) | ~ (f32(v3, v2) = v0)) & ! [v0:
% 64.81/9.81 S13] : ! [v1: S13] : ! [v2: int] : ! [v3: S14] : (v1 = v0 | ~ (f28(v3,
% 64.81/9.81 v2) = v1) | ~ (f28(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : !
% 64.81/9.81 [v2: int] : ! [v3: S13] : (v1 = v0 | ~ (f27(v3, v2) = v1) | ~ (f27(v3, v2)
% 64.81/9.81 = v0)) & ! [v0: S11] : ! [v1: S11] : ! [v2: S9] : ! [v3: S12] : (v1 =
% 64.81/9.81 v0 | ~ (f23(v3, v2) = v1) | ~ (f23(v3, v2) = v0)) & ! [v0: S9] : ! [v1:
% 64.81/9.81 S9] : ! [v2: S9] : ! [v3: S11] : (v1 = v0 | ~ (f22(v3, v2) = v1) | ~
% 64.81/9.81 (f22(v3, v2) = v0)) & ! [v0: S9] : ! [v1: S9] : ! [v2: S5] : ! [v3: S8]
% 64.81/9.81 : (v1 = v0 | ~ (f15(v3, v2) = v1) | ~ (f15(v3, v2) = v0)) & ! [v0: S9] : !
% 64.81/9.81 [v1: S9] : ! [v2: $real] : ! [v3: S10] : (v1 = v0 | ~ (f17(v3, v2) = v1) |
% 64.81/9.81 ~ (f17(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 64.81/9.81 ! [v3: $real] : (v1 = v0 | ~ (real_$difference(v3, v2) = v1) | ~
% 64.81/9.81 (real_$difference(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: S5]
% 64.81/9.81 : ! [v3: S6] : (v1 = v0 | ~ (f11(v3, v2) = v1) | ~ (f11(v3, v2) = v0)) & !
% 64.81/9.81 [v0: S5] : ! [v1: S5] : ! [v2: int] : ! [v3: S7] : (v1 = v0 | ~ (f13(v3,
% 64.81/9.81 v2) = v1) | ~ (f13(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] :
% 64.81/9.81 ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$sum(v3, v2) = v1) | ~
% 64.81/9.81 (real_$sum(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 64.81/9.81 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 64.81/9.81 (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, v2) = v0)) & ! [v0:
% 64.81/9.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 64.81/9.81 $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) =
% 64.81/9.81 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] :
% 64.81/9.81 (v1 = v0 | ~ (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0))
% 64.81/9.81 & ! [v0: S2] : ! [v1: S2] : ! [v2: $real] : ! [v3: S3] : (v1 = v0 | ~
% 64.81/9.81 (f5(v3, v2) = v1) | ~ (f5(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real]
% 64.81/9.81 : ! [v2: S5] : ! [v3: S4] : (v1 = v0 | ~ (f8(v3, v2) = v1) | ~ (f8(v3, v2)
% 64.81/9.81 = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: S2] :
% 64.81/9.81 (v1 = v0 | ~ (f3(v3, v2) = v1) | ~ (f3(v3, v2) = v0)) & ! [v0:
% 64.81/9.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : (v1 = v0
% 64.81/9.81 | ~ (real_$is_int(v2) = v1) | ~ (real_$is_int(v2) = v0)) & ! [v0:
% 64.81/9.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : (v1 = v0
% 64.81/9.81 | ~ (real_$is_rat(v2) = v1) | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real]
% 64.81/9.81 : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~
% 64.81/9.81 (real_$floor(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 64.81/9.81 (v1 = v0 | ~ (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & !
% 64.81/9.81 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 64.81/9.81 (real_$truncate(v2) = v1) | ~ (real_$truncate(v2) = v0)) & ! [v0: $real] :
% 64.81/9.81 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~
% 64.81/9.81 (real_$round(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1
% 64.81/9.81 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0:
% 64.81/9.81 $rat] : ! [v1: $rat] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) =
% 64.81/9.81 v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : !
% 64.81/9.81 [v2: $real] : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) =
% 64.81/9.81 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~
% 64.81/9.81 (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = v0)) & ! [v0: S1] : !
% 64.81/9.81 [v1: S1] : ! [v2: S5] : (v1 = v0 | ~ (f26(v2) = v1) | ~ (f26(v2) = v0)) &
% 64.81/9.81 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 64.81/9.81 (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0))
% 64.81/9.81
% 64.81/9.81 Further assumptions not needed in the proof:
% 64.81/9.81 --------------------------------------------
% 64.81/9.81 formula_1, formula_10, formula_100, formula_101, formula_102, formula_103,
% 64.81/9.81 formula_104, formula_105, formula_106, formula_107, formula_108, formula_109,
% 64.81/9.81 formula_11, formula_110, formula_111, formula_112, formula_113, formula_114,
% 64.81/9.81 formula_115, formula_116, formula_117, formula_118, formula_119, formula_12,
% 64.81/9.81 formula_120, formula_121, formula_122, formula_123, formula_124, formula_125,
% 64.81/9.81 formula_126, formula_127, formula_128, formula_129, formula_130, formula_131,
% 64.81/9.81 formula_132, formula_133, formula_134, formula_135, formula_136, formula_137,
% 64.81/9.81 formula_138, formula_139, formula_140, formula_141, formula_142, formula_143,
% 64.81/9.81 formula_144, formula_145, formula_146, formula_149, formula_15, formula_150,
% 64.81/9.81 formula_151, formula_152, formula_153, formula_154, formula_155, formula_156,
% 64.81/9.81 formula_157, formula_158, formula_159, formula_16, formula_160, formula_161,
% 64.81/9.81 formula_162, formula_163, formula_164, formula_165, formula_166, formula_167,
% 64.81/9.81 formula_168, formula_169, formula_17, formula_170, formula_171, formula_172,
% 64.81/9.81 formula_173, formula_174, formula_175, formula_176, formula_177, formula_178,
% 64.81/9.81 formula_179, formula_18, formula_180, formula_181, formula_182, formula_184,
% 64.81/9.81 formula_185, formula_186, formula_187, formula_188, formula_189, formula_19,
% 64.81/9.81 formula_190, formula_191, formula_192, formula_193, formula_194, formula_195,
% 64.81/9.81 formula_196, formula_197, formula_198, formula_199, formula_2, formula_20,
% 64.81/9.81 formula_200, formula_201, formula_202, formula_203, formula_204, formula_205,
% 64.81/9.81 formula_206, formula_207, formula_208, formula_209, formula_21, formula_210,
% 64.81/9.81 formula_211, formula_212, formula_213, formula_214, formula_215, formula_216,
% 64.81/9.81 formula_217, formula_218, formula_219, formula_22, formula_220, formula_221,
% 64.81/9.81 formula_222, formula_223, formula_224, formula_225, formula_226, formula_227,
% 64.81/9.81 formula_228, formula_229, formula_23, formula_230, formula_231, formula_232,
% 64.81/9.81 formula_233, formula_234, formula_235, formula_236, formula_237, formula_238,
% 64.81/9.81 formula_239, formula_24, formula_240, formula_241, formula_242, formula_243,
% 64.81/9.81 formula_244, formula_245, formula_246, formula_247, formula_248, formula_249,
% 64.81/9.81 formula_25, formula_250, formula_251, formula_252, formula_253, formula_254,
% 64.81/9.81 formula_255, formula_256, formula_257, formula_258, formula_259, formula_26,
% 64.81/9.81 formula_260, formula_261, formula_262, formula_263, formula_264, formula_265,
% 64.81/9.81 formula_266, formula_267, formula_268, formula_269, formula_27, formula_270,
% 64.81/9.81 formula_271, formula_272, formula_273, formula_274, formula_275, formula_276,
% 64.81/9.81 formula_277, formula_278, formula_279, formula_28, formula_280, formula_281,
% 64.81/9.81 formula_282, formula_283, formula_284, formula_285, formula_286, formula_287,
% 64.81/9.81 formula_288, formula_289, formula_29, formula_290, formula_291, formula_292,
% 64.81/9.81 formula_293, formula_294, formula_295, formula_296, formula_297, formula_298,
% 64.81/9.81 formula_299, formula_30, formula_300, formula_301, formula_302, formula_303,
% 64.81/9.81 formula_304, formula_305, formula_306, formula_307, formula_308, formula_309,
% 64.81/9.81 formula_31, formula_310, formula_311, formula_312, formula_313, formula_314,
% 64.81/9.81 formula_315, formula_316, formula_317, formula_318, formula_319, formula_32,
% 64.81/9.81 formula_320, formula_321, formula_322, formula_323, formula_324, formula_325,
% 64.81/9.81 formula_326, formula_327, formula_328, formula_329, formula_33, formula_330,
% 64.81/9.81 formula_331, formula_332, formula_333, formula_334, formula_335, formula_336,
% 64.81/9.81 formula_337, formula_338, formula_339, formula_34, formula_340, formula_341,
% 64.81/9.81 formula_342, formula_343, formula_344, formula_345, formula_346, formula_347,
% 64.81/9.81 formula_348, formula_349, formula_35, formula_350, formula_351, formula_352,
% 64.81/9.81 formula_353, formula_354, formula_355, formula_356, formula_357, formula_358,
% 64.81/9.81 formula_359, formula_36, formula_37, formula_38, formula_39, formula_40,
% 64.81/9.81 formula_41, formula_42, formula_43, formula_44, formula_45, formula_47,
% 64.81/9.81 formula_48, formula_49, formula_5, formula_50, formula_51, formula_52,
% 64.81/9.81 formula_53, formula_54, formula_55, formula_56, formula_57, formula_58,
% 64.81/9.81 formula_59, formula_6, formula_60, formula_61, formula_62, formula_63,
% 64.81/9.81 formula_65, formula_66, formula_67, formula_68, formula_69, formula_7,
% 64.81/9.81 formula_70, formula_71, formula_72, formula_73, formula_74, formula_75,
% 64.81/9.81 formula_76, formula_77, formula_78, formula_79, formula_8, formula_80,
% 64.81/9.81 formula_81, formula_82, formula_83, formula_84, formula_85, formula_86,
% 64.81/9.81 formula_87, formula_88, formula_89, formula_9, formula_90, formula_91,
% 64.81/9.81 formula_92, formula_93, formula_94, formula_95, formula_96, formula_97,
% 64.81/9.81 formula_98, formula_99
% 64.81/9.81
% 64.81/9.81 Those formulas are unsatisfiable:
% 64.81/9.81 ---------------------------------
% 64.81/9.81
% 64.81/9.81 Begin of proof
% 64.81/9.82 |
% 64.81/9.82 | ALPHA: (formula_3) implies:
% 64.81/9.82 | (1) ? [v0: $real] : ? [v1: S2] : ? [v2: $real] : ? [v3: $real] :
% 64.81/9.82 | (real_$product(real_2, f7) = v0 & f5(f6, v0) = v1 & f8(f9, f10) = v2 &
% 64.81/9.82 | f3(v1, v2) = v3 & f3(f4, v3) = real_0 & S2(v1))
% 64.81/9.82 |
% 64.81/9.82 | ALPHA: (formula_4) implies:
% 64.81/9.82 | (2) ? [v0: $real] : ? [v1: S2] : ? [v2: $real] : ? [v3: $real] : ?
% 64.81/9.82 | [v4: $real] : (real_$product(real_2, f7) = v0 & f5(f6, v0) = v1 &
% 64.81/9.82 | f8(f9, f10) = v2 & f3(v1, v2) = v3 & f3(f4, v3) = v4 & S2(v1) & ?
% 64.81/9.82 | [v5: any] : ? [v6: $real] : (real_$less(v4, real_0) = v5 &
% 64.81/9.82 | real_$uminus(v4) = v6 & ( ~ (v5 = 0) | v6 = real_1) & (v5 = 0 | v4
% 64.81/9.82 | = real_1)))
% 64.81/9.82 |
% 64.81/9.82 | ALPHA: (formula_13) implies:
% 64.81/9.82 | (3) ? [v0: $real] : (real_$product(real_2, f7) = v0 & ! [v1: $real] : !
% 64.81/9.82 | [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | ? [v3: $real] : (f3(f4,
% 64.81/9.82 | v2) = v3 & f3(f4, v1) = v3)))
% 64.81/9.82 |
% 64.81/9.82 | ALPHA: (formula_14) implies:
% 64.81/9.82 | (4) ? [v0: $real] : (real_$product(real_2, f7) = v0 & f3(f4, v0) = real_1)
% 64.81/9.82 |
% 64.81/9.82 | ALPHA: (formula_64) implies:
% 64.81/9.82 | (5) ? [v0: $real] : ? [v1: S2] : (real_$product(real_2, f7) = v0 & f5(f6,
% 64.81/9.82 | v0) = v1 & S2(v1) & ! [v2: S5] : ! [v3: S9] : ( ~ (f15(f16, v2) =
% 64.81/9.82 | v3) | ~ S5(v2) | ? [v4: $real] : ? [v5: $real] : (f17(f18, v5)
% 64.81/9.82 | = v3 & f8(f9, v2) = v4 & f3(v1, v4) = v5 & S9(v3))))
% 64.81/9.82 |
% 64.81/9.82 | ALPHA: (formula_147) implies:
% 64.81/9.82 | (6) ? [v0: $real] : (real_$product(real_2, f7) = v0 & ! [v1: $real] : !
% 64.81/9.82 | [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | ? [v3: $real] :
% 64.81/9.82 | (f3(f31, v2) = v3 & f3(f31, v1) = v3)))
% 64.81/9.82 |
% 64.81/9.82 | ALPHA: (formula_148) implies:
% 64.81/9.82 | (7) ? [v0: $real] : (real_$product(real_2, f7) = v0 & f3(f31, v0) =
% 64.81/9.82 | real_0)
% 64.81/9.82 |
% 64.81/9.82 | ALPHA: (formula_183) implies:
% 64.81/9.82 | (8) ? [v0: $real] : (real_$product(real_2, f7) = v0 & ! [v1: $real] : !
% 64.81/9.82 | [v2: any] : ( ~ (real_$less(v1, v0) = v2) | ? [v3: $real] : ? [v4:
% 64.81/9.82 | $real] : (f3(f4, v1) = v4 & f3(f31, v1) = v3 & ? [v5: any] :
% 64.81/9.82 | (real_$less(real_0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = real_1) |
% 64.81/9.82 | ~ (v3 = real_0) | ~ (v2 = 0))))))
% 64.81/9.82 |
% 64.81/9.82 | ALPHA: (function-axioms) implies:
% 64.81/9.83 | (9) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: S2] : (v1 =
% 64.81/9.83 | v0 | ~ (f3(v3, v2) = v1) | ~ (f3(v3, v2) = v0))
% 64.81/9.83 | (10) ! [v0: $real] : ! [v1: $real] : ! [v2: S5] : ! [v3: S4] : (v1 = v0
% 64.81/9.83 | | ~ (f8(v3, v2) = v1) | ~ (f8(v3, v2) = v0))
% 64.81/9.83 | (11) ! [v0: S2] : ! [v1: S2] : ! [v2: $real] : ! [v3: S3] : (v1 = v0 |
% 64.81/9.83 | ~ (f5(v3, v2) = v1) | ~ (f5(v3, v2) = v0))
% 64.81/9.83 | (12) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] :
% 64.81/9.83 | (v1 = v0 | ~ (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2)
% 64.81/9.83 | = v0))
% 64.81/9.83 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 64.81/9.83 | $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) |
% 64.81/9.83 | ~ (real_$less(v3, v2) = v0))
% 64.81/9.83 |
% 64.81/9.83 | ALPHA: (input) implies:
% 64.81/9.83 | (14) ~ (real_1 = real_0)
% 64.81/9.83 | (15) real_$less(real_0, real_0) = 1
% 64.81/9.83 |
% 64.81/9.83 | DELTA: instantiating (7) with fresh symbol all_257_0 gives:
% 64.81/9.83 | (16) real_$product(real_2, f7) = all_257_0 & f3(f31, all_257_0) = real_0
% 64.81/9.83 |
% 64.81/9.83 | ALPHA: (16) implies:
% 64.81/9.83 | (17) real_$product(real_2, f7) = all_257_0
% 64.81/9.83 |
% 64.81/9.83 | DELTA: instantiating (4) with fresh symbol all_263_0 gives:
% 64.81/9.83 | (18) real_$product(real_2, f7) = all_263_0 & f3(f4, all_263_0) = real_1
% 64.81/9.83 |
% 64.81/9.83 | ALPHA: (18) implies:
% 64.81/9.83 | (19) real_$product(real_2, f7) = all_263_0
% 64.81/9.83 |
% 64.81/9.83 | DELTA: instantiating (formula_46) with fresh symbols all_273_0, all_273_1
% 64.81/9.83 | gives:
% 64.81/9.83 | (20) real_$less(all_273_0, f7) = 0 & real_$uminus(all_273_1) = all_273_0 &
% 64.81/9.83 | real_$product(real_2, f7) = all_273_1
% 64.81/9.83 |
% 64.81/9.83 | ALPHA: (20) implies:
% 64.81/9.83 | (21) real_$product(real_2, f7) = all_273_1
% 64.81/9.83 |
% 64.81/9.83 | DELTA: instantiating (6) with fresh symbol all_289_0 gives:
% 64.81/9.83 | (22) real_$product(real_2, f7) = all_289_0 & ! [v0: $real] : ! [v1:
% 64.81/9.83 | $real] : ( ~ (real_$sum(v0, all_289_0) = v1) | ? [v2: $real] :
% 64.81/9.83 | (f3(f31, v1) = v2 & f3(f31, v0) = v2))
% 64.81/9.83 |
% 64.81/9.83 | ALPHA: (22) implies:
% 64.81/9.83 | (23) real_$product(real_2, f7) = all_289_0
% 64.81/9.83 |
% 64.81/9.83 | DELTA: instantiating (3) with fresh symbol all_308_0 gives:
% 64.81/9.83 | (24) real_$product(real_2, f7) = all_308_0 & ! [v0: $real] : ! [v1:
% 64.81/9.83 | $real] : ( ~ (real_$sum(v0, all_308_0) = v1) | ? [v2: $real] :
% 64.81/9.83 | (f3(f4, v1) = v2 & f3(f4, v0) = v2))
% 64.81/9.83 |
% 64.81/9.83 | ALPHA: (24) implies:
% 64.81/9.83 | (25) real_$product(real_2, f7) = all_308_0
% 64.81/9.83 |
% 64.81/9.83 | DELTA: instantiating (1) with fresh symbols all_339_0, all_339_1, all_339_2,
% 64.81/9.83 | all_339_3 gives:
% 64.81/9.83 | (26) real_$product(real_2, f7) = all_339_3 & f5(f6, all_339_3) = all_339_2
% 64.81/9.83 | & f8(f9, f10) = all_339_1 & f3(all_339_2, all_339_1) = all_339_0 &
% 64.81/9.83 | f3(f4, all_339_0) = real_0 & S2(all_339_2)
% 64.81/9.83 |
% 64.81/9.83 | ALPHA: (26) implies:
% 64.81/9.83 | (27) f3(f4, all_339_0) = real_0
% 64.81/9.83 | (28) f3(all_339_2, all_339_1) = all_339_0
% 64.81/9.83 | (29) f8(f9, f10) = all_339_1
% 64.81/9.84 | (30) f5(f6, all_339_3) = all_339_2
% 64.81/9.84 | (31) real_$product(real_2, f7) = all_339_3
% 64.81/9.84 |
% 64.81/9.84 | DELTA: instantiating (5) with fresh symbols all_421_0, all_421_1 gives:
% 64.81/9.84 | (32) real_$product(real_2, f7) = all_421_1 & f5(f6, all_421_1) = all_421_0
% 64.81/9.84 | & S2(all_421_0) & ! [v0: S5] : ! [v1: S9] : ( ~ (f15(f16, v0) = v1)
% 64.81/9.84 | | ~ S5(v0) | ? [v2: $real] : ? [v3: $real] : (f17(f18, v3) = v1 &
% 64.81/9.84 | f8(f9, v0) = v2 & f3(all_421_0, v2) = v3 & S9(v1)))
% 64.81/9.84 |
% 64.81/9.84 | ALPHA: (32) implies:
% 64.81/9.84 | (33) f5(f6, all_421_1) = all_421_0
% 64.81/9.84 | (34) real_$product(real_2, f7) = all_421_1
% 64.81/9.84 |
% 64.81/9.84 | DELTA: instantiating (8) with fresh symbol all_424_0 gives:
% 64.81/9.84 | (35) real_$product(real_2, f7) = all_424_0 & ! [v0: $real] : ! [v1: any]
% 64.81/9.84 | : ( ~ (real_$less(v0, all_424_0) = v1) | ? [v2: $real] : ? [v3:
% 64.81/9.84 | $real] : (f3(f4, v0) = v3 & f3(f31, v0) = v2 & ? [v4: any] :
% 64.81/9.84 | (real_$less(real_0, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = real_1) |
% 64.81/9.84 | ~ (v2 = real_0) | ~ (v1 = 0)))))
% 64.81/9.84 |
% 64.81/9.84 | ALPHA: (35) implies:
% 64.81/9.84 | (36) real_$product(real_2, f7) = all_424_0
% 64.81/9.84 |
% 64.81/9.84 | DELTA: instantiating (2) with fresh symbols all_502_0, all_502_1, all_502_2,
% 64.81/9.84 | all_502_3, all_502_4 gives:
% 64.81/9.84 | (37) real_$product(real_2, f7) = all_502_4 & f5(f6, all_502_4) = all_502_3
% 64.81/9.84 | & f8(f9, f10) = all_502_2 & f3(all_502_3, all_502_2) = all_502_1 &
% 64.81/9.84 | f3(f4, all_502_1) = all_502_0 & S2(all_502_3) & ? [v0: any] : ? [v1:
% 64.81/9.84 | $real] : (real_$less(all_502_0, real_0) = v0 &
% 64.81/9.84 | real_$uminus(all_502_0) = v1 & ( ~ (v0 = 0) | v1 = real_1) & (v0 = 0
% 64.81/9.84 | | all_502_0 = real_1))
% 64.81/9.84 |
% 64.81/9.84 | ALPHA: (37) implies:
% 64.81/9.84 | (38) f3(f4, all_502_1) = all_502_0
% 64.81/9.84 | (39) f3(all_502_3, all_502_2) = all_502_1
% 64.81/9.84 | (40) f8(f9, f10) = all_502_2
% 64.81/9.84 | (41) f5(f6, all_502_4) = all_502_3
% 64.81/9.84 | (42) real_$product(real_2, f7) = all_502_4
% 64.81/9.84 | (43) ? [v0: any] : ? [v1: $real] : (real_$less(all_502_0, real_0) = v0 &
% 64.81/9.84 | real_$uminus(all_502_0) = v1 & ( ~ (v0 = 0) | v1 = real_1) & (v0 = 0
% 64.81/9.84 | | all_502_0 = real_1))
% 64.81/9.84 |
% 64.81/9.84 | DELTA: instantiating (43) with fresh symbols all_637_0, all_637_1 gives:
% 64.81/9.84 | (44) real_$less(all_502_0, real_0) = all_637_1 & real_$uminus(all_502_0) =
% 64.81/9.84 | all_637_0 & ( ~ (all_637_1 = 0) | all_637_0 = real_1) & (all_637_1 = 0
% 64.81/9.84 | | all_502_0 = real_1)
% 64.81/9.84 |
% 64.81/9.84 | ALPHA: (44) implies:
% 64.81/9.84 | (45) real_$less(all_502_0, real_0) = all_637_1
% 64.81/9.84 | (46) all_637_1 = 0 | all_502_0 = real_1
% 64.81/9.84 |
% 64.81/9.84 | GROUND_INST: instantiating (10) with all_339_1, all_502_2, f10, f9,
% 64.81/9.84 | simplifying with (29), (40) gives:
% 64.81/9.84 | (47) all_502_2 = all_339_1
% 64.81/9.84 |
% 64.81/9.84 | GROUND_INST: instantiating (12) with all_263_0, all_339_3, f7, real_2,
% 64.81/9.84 | simplifying with (19), (31) gives:
% 64.81/9.84 | (48) all_339_3 = all_263_0
% 64.81/9.84 |
% 64.81/9.84 | GROUND_INST: instantiating (12) with all_289_0, all_421_1, f7, real_2,
% 64.81/9.84 | simplifying with (23), (34) gives:
% 64.81/9.84 | (49) all_421_1 = all_289_0
% 64.81/9.84 |
% 64.81/9.84 | GROUND_INST: instantiating (12) with all_257_0, all_421_1, f7, real_2,
% 64.81/9.84 | simplifying with (17), (34) gives:
% 64.81/9.84 | (50) all_421_1 = all_257_0
% 64.81/9.84 |
% 64.81/9.84 | GROUND_INST: instantiating (12) with all_339_3, all_424_0, f7, real_2,
% 64.81/9.84 | simplifying with (31), (36) gives:
% 64.81/9.85 | (51) all_424_0 = all_339_3
% 64.81/9.85 |
% 64.81/9.85 | GROUND_INST: instantiating (12) with all_308_0, all_424_0, f7, real_2,
% 64.81/9.85 | simplifying with (25), (36) gives:
% 64.81/9.85 | (52) all_424_0 = all_308_0
% 64.81/9.85 |
% 64.81/9.85 | GROUND_INST: instantiating (12) with all_289_0, all_424_0, f7, real_2,
% 64.81/9.85 | simplifying with (23), (36) gives:
% 64.81/9.85 | (53) all_424_0 = all_289_0
% 64.81/9.85 |
% 64.81/9.85 | GROUND_INST: instantiating (12) with all_421_1, all_502_4, f7, real_2,
% 64.81/9.85 | simplifying with (34), (42) gives:
% 64.81/9.85 | (54) all_502_4 = all_421_1
% 64.81/9.85 |
% 64.81/9.85 | GROUND_INST: instantiating (12) with all_273_1, all_502_4, f7, real_2,
% 64.81/9.85 | simplifying with (21), (42) gives:
% 64.81/9.85 | (55) all_502_4 = all_273_1
% 64.81/9.85 |
% 64.81/9.85 | COMBINE_EQS: (54), (55) imply:
% 64.81/9.85 | (56) all_421_1 = all_273_1
% 64.81/9.85 |
% 64.81/9.85 | SIMP: (56) implies:
% 64.81/9.85 | (57) all_421_1 = all_273_1
% 64.81/9.85 |
% 64.81/9.85 | COMBINE_EQS: (52), (53) imply:
% 64.81/9.85 | (58) all_308_0 = all_289_0
% 64.81/9.85 |
% 64.81/9.85 | COMBINE_EQS: (51), (52) imply:
% 64.81/9.85 | (59) all_339_3 = all_308_0
% 64.81/9.85 |
% 64.81/9.85 | SIMP: (59) implies:
% 64.81/9.85 | (60) all_339_3 = all_308_0
% 64.81/9.85 |
% 64.81/9.85 | COMBINE_EQS: (50), (57) imply:
% 64.81/9.85 | (61) all_273_1 = all_257_0
% 64.81/9.85 |
% 64.81/9.85 | COMBINE_EQS: (49), (57) imply:
% 64.81/9.85 | (62) all_289_0 = all_273_1
% 64.81/9.85 |
% 64.81/9.85 | SIMP: (62) implies:
% 64.81/9.85 | (63) all_289_0 = all_273_1
% 64.81/9.85 |
% 64.81/9.85 | COMBINE_EQS: (48), (60) imply:
% 64.81/9.85 | (64) all_308_0 = all_263_0
% 64.81/9.85 |
% 64.81/9.85 | SIMP: (64) implies:
% 64.81/9.85 | (65) all_308_0 = all_263_0
% 64.81/9.85 |
% 64.81/9.85 | COMBINE_EQS: (58), (65) imply:
% 64.81/9.85 | (66) all_289_0 = all_263_0
% 64.81/9.85 |
% 64.81/9.85 | SIMP: (66) implies:
% 64.81/9.85 | (67) all_289_0 = all_263_0
% 64.81/9.85 |
% 64.81/9.85 | COMBINE_EQS: (63), (67) imply:
% 64.81/9.85 | (68) all_273_1 = all_263_0
% 64.81/9.85 |
% 64.81/9.85 | SIMP: (68) implies:
% 64.81/9.85 | (69) all_273_1 = all_263_0
% 64.81/9.85 |
% 64.81/9.85 | COMBINE_EQS: (61), (69) imply:
% 64.81/9.85 | (70) all_263_0 = all_257_0
% 64.81/9.85 |
% 64.81/9.85 | COMBINE_EQS: (48), (70) imply:
% 64.81/9.85 | (71) all_339_3 = all_257_0
% 64.81/9.85 |
% 64.81/9.85 | COMBINE_EQS: (55), (61) imply:
% 64.81/9.85 | (72) all_502_4 = all_257_0
% 64.81/9.85 |
% 64.81/9.85 | REDUCE: (41), (72) imply:
% 64.81/9.85 | (73) f5(f6, all_257_0) = all_502_3
% 64.81/9.85 |
% 64.81/9.85 | REDUCE: (33), (50) imply:
% 64.81/9.85 | (74) f5(f6, all_257_0) = all_421_0
% 64.81/9.85 |
% 64.81/9.85 | REDUCE: (30), (71) imply:
% 64.81/9.85 | (75) f5(f6, all_257_0) = all_339_2
% 64.81/9.85 |
% 64.81/9.85 | REDUCE: (39), (47) imply:
% 64.81/9.85 | (76) f3(all_502_3, all_339_1) = all_502_1
% 64.81/9.85 |
% 64.81/9.85 | GROUND_INST: instantiating (11) with all_421_0, all_502_3, all_257_0, f6,
% 64.81/9.85 | simplifying with (73), (74) gives:
% 64.81/9.85 | (77) all_502_3 = all_421_0
% 64.81/9.85 |
% 64.81/9.85 | GROUND_INST: instantiating (11) with all_339_2, all_502_3, all_257_0, f6,
% 64.81/9.85 | simplifying with (73), (75) gives:
% 64.81/9.85 | (78) all_502_3 = all_339_2
% 64.81/9.85 |
% 64.81/9.85 | COMBINE_EQS: (77), (78) imply:
% 64.81/9.85 | (79) all_421_0 = all_339_2
% 64.81/9.85 |
% 64.81/9.85 | REDUCE: (76), (78) imply:
% 64.81/9.85 | (80) f3(all_339_2, all_339_1) = all_502_1
% 64.81/9.85 |
% 64.81/9.85 | GROUND_INST: instantiating (9) with all_339_0, all_502_1, all_339_1,
% 64.81/9.85 | all_339_2, simplifying with (28), (80) gives:
% 64.81/9.85 | (81) all_502_1 = all_339_0
% 64.81/9.85 |
% 64.81/9.85 | REDUCE: (38), (81) imply:
% 64.81/9.85 | (82) f3(f4, all_339_0) = all_502_0
% 64.81/9.85 |
% 64.81/9.85 | GROUND_INST: instantiating (9) with real_0, all_502_0, all_339_0, f4,
% 64.81/9.85 | simplifying with (27), (82) gives:
% 64.81/9.85 | (83) all_502_0 = real_0
% 64.81/9.85 |
% 64.81/9.85 | REDUCE: (45), (83) imply:
% 64.81/9.85 | (84) real_$less(real_0, real_0) = all_637_1
% 64.81/9.85 |
% 64.81/9.85 | BETA: splitting (46) gives:
% 64.81/9.85 |
% 64.81/9.86 | Case 1:
% 64.81/9.86 | |
% 64.81/9.86 | | (85) all_637_1 = 0
% 64.81/9.86 | |
% 64.81/9.86 | | REDUCE: (84), (85) imply:
% 64.81/9.86 | | (86) real_$less(real_0, real_0) = 0
% 64.81/9.86 | |
% 64.81/9.86 | | GROUND_INST: instantiating (13) with 1, 0, real_0, real_0, simplifying with
% 64.81/9.86 | | (15), (86) gives:
% 64.81/9.86 | | (87) $false
% 64.81/9.86 | |
% 64.81/9.86 | | CLOSE: (87) is inconsistent.
% 64.81/9.86 | |
% 64.81/9.86 | Case 2:
% 64.81/9.86 | |
% 64.81/9.86 | | (88) all_502_0 = real_1
% 64.81/9.86 | |
% 64.81/9.86 | | COMBINE_EQS: (83), (88) imply:
% 64.81/9.86 | | (89) real_1 = real_0
% 64.81/9.86 | |
% 64.81/9.86 | | REDUCE: (14), (89) imply:
% 64.81/9.86 | | (90) $false
% 64.81/9.86 | |
% 64.81/9.86 | | CLOSE: (90) is inconsistent.
% 64.81/9.86 | |
% 64.81/9.86 | End of split
% 64.81/9.86 |
% 64.81/9.86 End of proof
% 64.81/9.86 % SZS output end Proof for theBenchmark
% 64.81/9.86
% 64.81/9.86 9226ms
%------------------------------------------------------------------------------