%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWW822_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 : n029.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 00:51:28 EDT 2023

% Result   : Unsatisfiable 49.45s 7.30s
% Output   : Proof 269.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWW822_1 : TPTP v8.1.2. Released v7.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.34  % Computer : n029.cluster.edu
% 0.17/0.34  % Model    : x86_64 x86_64
% 0.17/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34  % Memory   : 8042.1875MB
% 0.17/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34  % CPULimit : 300
% 0.17/0.34  % WCLimit  : 300
% 0.17/0.34  % DateTime : Sun Aug 27 17:59:10 EDT 2023
% 0.17/0.34  % CPUTime  : 
% 0.20/0.67  ________       _____
% 0.20/0.67  ___  __ \_________(_)________________________________
% 0.20/0.67  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.67  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.67  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.67  
% 0.20/0.67  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.67  (2023-06-19)
% 0.20/0.67  
% 0.20/0.67  (c) Philipp Rümmer, 2009-2023
% 0.20/0.67  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.67                Amanda Stjerna.
% 0.20/0.67  Free software under BSD-3-Clause.
% 0.20/0.67  
% 0.20/0.67  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.67  
% 0.20/0.67  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.68  Running up to 7 provers in parallel.
% 0.20/0.69  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.69  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.69  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.69  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.69  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.69  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.70  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.03/1.07  Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 2.03/1.07  Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 2.03/1.07  Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 2.03/1.07  Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 2.03/1.07  Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 2.50/1.08  Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 2.50/1.08  Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 12.65/2.53  Prover 0: Preprocessing ...
% 12.65/2.53  Prover 1: Preprocessing ...
% 12.65/2.55  Prover 5: Preprocessing ...
% 12.65/2.55  Prover 4: Preprocessing ...
% 13.36/2.58  Prover 2: Preprocessing ...
% 13.36/2.58  Prover 6: Preprocessing ...
% 13.53/2.59  Prover 3: Preprocessing ...
% 31.37/4.95  Prover 1: Warning: ignoring some quantifiers
% 32.05/5.07  Prover 3: Warning: ignoring some quantifiers
% 32.05/5.14  Prover 3: Constructing countermodel ...
% 32.05/5.15  Prover 1: Constructing countermodel ...
% 32.05/5.18  Prover 6: Proving ...
% 34.09/5.31  Prover 4: Warning: ignoring some quantifiers
% 35.15/5.49  Prover 4: Constructing countermodel ...
% 36.51/5.61  Prover 0: Proving ...
% 47.09/7.01  Prover 5: Proving ...
% 47.65/7.05  Prover 2: Proving ...
% 49.45/7.30  Prover 6: proved (6605ms)
% 49.45/7.30  
% 49.45/7.30  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.45/7.30  
% 49.45/7.30  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 49.45/7.31  Prover 5: stopped
% 49.45/7.31  Prover 2: stopped
% 49.45/7.32  Prover 0: stopped
% 49.45/7.33  Prover 3: stopped
% 49.45/7.34  Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 49.45/7.34  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 49.45/7.34  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 49.45/7.34  Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 49.45/7.34  Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 49.45/7.34  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 49.45/7.34  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 49.45/7.34  Prover 11: Warning: Problem contains reals, using incomplete axiomatisation
% 49.45/7.36  Prover 13: Warning: Problem contains reals, using incomplete axiomatisation
% 56.47/8.22  Prover 13: Preprocessing ...
% 56.63/8.22  Prover 8: Preprocessing ...
% 56.63/8.23  Prover 11: Preprocessing ...
% 56.63/8.23  Prover 10: Preprocessing ...
% 56.63/8.24  Prover 7: Preprocessing ...
% 65.18/9.35  Prover 8: Warning: ignoring some quantifiers
% 65.18/9.47  Prover 8: Constructing countermodel ...
% 66.44/9.52  Prover 10: Warning: ignoring some quantifiers
% 67.49/9.64  Prover 10: Constructing countermodel ...
% 69.44/9.92  Prover 11: Warning: ignoring some quantifiers
% 70.01/9.98  Prover 7: Warning: ignoring some quantifiers
% 70.56/10.10  Prover 11: Constructing countermodel ...
% 70.56/10.18  Prover 7: Constructing countermodel ...
% 72.79/10.32  Prover 13: Warning: ignoring some quantifiers
% 73.47/10.46  Prover 13: Constructing countermodel ...
% 84.84/11.93  Prover 13: stopped
% 84.84/11.96  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 84.84/11.96  Prover 16: Warning: Problem contains reals, using incomplete axiomatisation
% 88.80/12.42  Prover 16: Preprocessing ...
% 95.29/13.28  Prover 16: Warning: ignoring some quantifiers
% 95.88/13.33  Prover 16: Constructing countermodel ...
% 116.57/16.04  Prover 1: stopped
% 116.57/16.05  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 116.57/16.05  Prover 19: Warning: Problem contains reals, using incomplete axiomatisation
% 120.41/16.54  Prover 19: Preprocessing ...
% 139.33/19.05  Prover 19: Warning: ignoring some quantifiers
% 140.95/19.20  Prover 19: Constructing countermodel ...
% 167.05/22.73  Prover 19: stopped
% 177.31/24.16  Prover 16: stopped
% 202.12/28.03  Prover 4: stopped
% 205.39/28.71  Prover 7: stopped
% 255.29/40.32  Prover 11: stopped
% 256.56/40.83  Prover 8: stopped
% 268.93/47.71  Prover 10: Found proof (size 46)
% 268.93/47.71  Prover 10: proved (40395ms)
% 268.93/47.71  
% 268.93/47.71  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 268.93/47.71  
% 268.93/47.73  % SZS output start Proof for theBenchmark
% 268.93/47.74  Assumptions after simplification:
% 268.93/47.74  ---------------------------------
% 268.93/47.74  
% 268.93/47.74    (formula_12)
% 269.22/47.76    S16(f28) & S13(f20) & S9(f14) &  ! [v0: S2] :  ! [v1: S10] : ( ~ (f13(f14, v0)
% 269.22/47.76        = v1) |  ~ S2(v0) |  ? [v2: $real] : (f27(f28, v1) = v2 & f19(f20, v0) =
% 269.22/47.76        v2))
% 269.22/47.76  
% 269.22/47.76    (formula_16)
% 269.22/47.76    S16(f31) & S13(f20) & S9(f14) &  ! [v0: S2] :  ! [v1: S10] : ( ~ (f13(f14, v0)
% 269.22/47.76        = v1) |  ~ S2(v0) |  ? [v2: $real] : (f27(f31, v1) = v2 & f19(f20, v0) =
% 269.22/47.76        v2))
% 269.22/47.76  
% 269.22/47.76    (formula_17)
% 269.22/47.76    S11(f32) & S13(f20) & S9(f14) &  ! [v0: S2] :  ! [v1: S10] : ( ~ (f13(f14, v0)
% 269.22/47.76        = v1) |  ~ S2(v0) |  ? [v2: $real] : (f19(f20, v0) = v2 & f16(f32, v2) =
% 269.22/47.76        v1 & S10(v1)))
% 269.22/47.76  
% 269.22/47.76    (formula_3)
% 269.22/47.76    S13(f20) & S12(f18) & S9(f14) & S2(f15) &  ? [v0: S10] :  ? [v1: $real] :  ?
% 269.22/47.76    [v2: S11] :  ? [v3: S10] : ( ~ (v3 = v0) & f13(f14, f15) = v0 & f19(f20, f15)
% 269.22/47.76      = v1 & f17(f18, v1) = v2 & f16(v2, real_0) = v3 & S11(v2) & S10(v3) &
% 269.22/47.76      S10(v0))
% 269.22/47.76  
% 269.22/47.76    (formula_38)
% 269.22/47.77    S11(f32) & S12(f18) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  !
% 269.22/47.77    [v3: S11] :  ! [v4: S10] : (v2 = v0 |  ~ (f17(f18, v0) = v3) |  ~ (f16(v3, v1)
% 269.22/47.77        = v4) |  ~ (f16(f32, v2) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  !
% 269.22/47.77    [v2: $real] :  ! [v3: S11] :  ! [v4: S10] : (v1 = real_0 |  ~ (f17(f18, v0) =
% 269.22/47.77        v3) |  ~ (f16(v3, v1) = v4) |  ~ (f16(f32, v2) = v4)) &  ! [v0: $real] : 
% 269.22/47.77    ! [v1: S11] :  ! [v2: S10] :  ! [v3: S10] : (v3 = v2 |  ~ (f17(f18, v0) = v1)
% 269.22/47.77      |  ~ (f16(v1, real_0) = v2) |  ~ (f16(f32, v0) = v3))
% 269.22/47.77  
% 269.22/47.77    (formula_39)
% 269.22/47.77    S11(f32) & S12(f18) &  ! [v0: $real] :  ! [v1: S11] : ( ~ (f17(f18, v0) = v1)
% 269.22/47.77      |  ? [v2: S10] : (f16(v1, real_0) = v2 & f16(f32, v0) = v2 & S10(v2)))
% 269.22/47.77  
% 269.22/47.77    (formula_41)
% 269.22/47.77    S17(f35) & S12(f18) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: S11] :  ! [v3:
% 269.22/47.77      $real] : ( ~ (real_$uminus(v1) = v3) |  ~ (f17(f18, v0) = v2) |  ? [v4: S10]
% 269.22/47.77      :  ? [v5: S10] : (f34(f35, v4) = v5 & f16(v2, v3) = v5 & f16(v2, v1) = v4 &
% 269.22/47.77        S11(v2) & S10(v5) & S10(v4)))
% 269.22/47.77  
% 269.22/47.77    (input)
% 269.47/47.85     ~ (real_very_large = real_very_small) &  ~ (real_very_large = real_-3) &  ~
% 269.47/47.85    (real_very_large = real_-1/2) &  ~ (real_very_large = real_4) &  ~
% 269.47/47.85    (real_very_large = real_1/2) &  ~ (real_very_large = real_-2) &  ~
% 269.47/47.85    (real_very_large = real_3) &  ~ (real_very_large = real_-1) &  ~
% 269.47/47.85    (real_very_large = real_1) &  ~ (real_very_large = real_2) &  ~
% 269.47/47.85    (real_very_large = real_0) &  ~ (real_very_small = real_-3) &  ~
% 269.47/47.85    (real_very_small = real_-1/2) &  ~ (real_very_small = real_4) &  ~
% 269.47/47.85    (real_very_small = real_1/2) &  ~ (real_very_small = real_-2) &  ~
% 269.47/47.85    (real_very_small = real_3) &  ~ (real_very_small = real_-1) &  ~
% 269.47/47.85    (real_very_small = real_1) &  ~ (real_very_small = real_2) &  ~
% 269.47/47.85    (real_very_small = real_0) &  ~ (real_-3 = real_-1/2) &  ~ (real_-3 = real_4)
% 269.47/47.85    &  ~ (real_-3 = real_1/2) &  ~ (real_-3 = real_-2) &  ~ (real_-3 = real_3) & 
% 269.47/47.85    ~ (real_-3 = real_-1) &  ~ (real_-3 = real_1) &  ~ (real_-3 = real_2) &  ~
% 269.47/47.85    (real_-3 = real_0) &  ~ (real_-1/2 = real_4) &  ~ (real_-1/2 = real_1/2) &  ~
% 269.47/47.85    (real_-1/2 = real_-2) &  ~ (real_-1/2 = real_3) &  ~ (real_-1/2 = real_-1) & 
% 269.47/47.85    ~ (real_-1/2 = real_1) &  ~ (real_-1/2 = real_2) &  ~ (real_-1/2 = real_0) & 
% 269.47/47.85    ~ (real_4 = real_1/2) &  ~ (real_4 = real_-2) &  ~ (real_4 = real_3) &  ~
% 269.70/47.85    (real_4 = real_-1) &  ~ (real_4 = real_1) &  ~ (real_4 = real_2) &  ~ (real_4
% 269.70/47.85      = real_0) &  ~ (real_1/2 = real_-2) &  ~ (real_1/2 = real_3) &  ~ (real_1/2
% 269.70/47.85      = real_-1) &  ~ (real_1/2 = real_1) &  ~ (real_1/2 = real_2) &  ~ (real_1/2
% 269.70/47.85      = real_0) &  ~ (real_-2 = real_3) &  ~ (real_-2 = real_-1) &  ~ (real_-2 =
% 269.70/47.85      real_1) &  ~ (real_-2 = real_2) &  ~ (real_-2 = real_0) &  ~ (real_3 =
% 269.70/47.85      real_-1) &  ~ (real_3 = real_1) &  ~ (real_3 = real_2) &  ~ (real_3 =
% 269.70/47.85      real_0) &  ~ (real_-1 = real_1) &  ~ (real_-1 = real_2) &  ~ (real_-1 =
% 269.70/47.85      real_0) &  ~ (real_1 = real_2) &  ~ (real_1 = real_0) &  ~ (real_2 = real_0)
% 269.70/47.85    & real_$floor(real_-3) = real_-3 & real_$floor(real_-1/2) = real_-1 &
% 269.70/47.85    real_$floor(real_4) = real_4 & real_$floor(real_1/2) = real_0 &
% 269.70/47.85    real_$floor(real_-2) = real_-2 & real_$floor(real_3) = real_3 &
% 269.70/47.85    real_$floor(real_-1) = real_-1 & real_$floor(real_1) = real_1 &
% 269.70/47.85    real_$floor(real_2) = real_2 & real_$floor(real_0) = real_0 &
% 269.70/47.85    real_$ceiling(real_-3) = real_-3 & real_$ceiling(real_-1/2) = real_0 &
% 269.70/47.85    real_$ceiling(real_4) = real_4 & real_$ceiling(real_1/2) = real_1 &
% 269.70/47.85    real_$ceiling(real_-2) = real_-2 & real_$ceiling(real_3) = real_3 &
% 269.70/47.85    real_$ceiling(real_-1) = real_-1 & real_$ceiling(real_1) = real_1 &
% 269.70/47.85    real_$ceiling(real_2) = real_2 & real_$ceiling(real_0) = real_0 &
% 269.70/47.85    real_$truncate(real_-3) = real_-3 & real_$truncate(real_-1/2) = real_0 &
% 269.70/47.85    real_$truncate(real_4) = real_4 & real_$truncate(real_1/2) = real_0 &
% 269.70/47.85    real_$truncate(real_-2) = real_-2 & real_$truncate(real_3) = real_3 &
% 269.70/47.85    real_$truncate(real_-1) = real_-1 & real_$truncate(real_1) = real_1 &
% 269.70/47.85    real_$truncate(real_2) = real_2 & real_$truncate(real_0) = real_0 &
% 269.70/47.85    real_$round(real_-3) = real_-3 & real_$round(real_-1/2) = real_0 &
% 269.70/47.85    real_$round(real_4) = real_4 & real_$round(real_1/2) = real_1 &
% 269.70/47.85    real_$round(real_-2) = real_-2 & real_$round(real_3) = real_3 &
% 269.70/47.85    real_$round(real_-1) = real_-1 & real_$round(real_1) = real_1 &
% 269.70/47.85    real_$round(real_2) = real_2 & real_$round(real_0) = real_0 &
% 269.70/47.85    real_$to_int(real_-3) = -3 & real_$to_int(real_-1/2) = -1 &
% 269.70/47.85    real_$to_int(real_4) = 4 & real_$to_int(real_1/2) = 0 & real_$to_int(real_-2)
% 269.70/47.85    = -2 & real_$to_int(real_3) = 3 & real_$to_int(real_-1) = -1 &
% 269.70/47.85    real_$to_int(real_1) = 1 & real_$to_int(real_2) = 2 & real_$to_int(real_0) = 0
% 269.70/47.85    & real_$to_rat(real_-3) = rat_-3 & real_$to_rat(real_-1/2) = rat_-1/2 &
% 269.70/47.85    real_$to_rat(real_4) = rat_4 & real_$to_rat(real_1/2) = rat_1/2 &
% 269.70/47.85    real_$to_rat(real_-2) = rat_-2 & real_$to_rat(real_3) = rat_3 &
% 269.70/47.85    real_$to_rat(real_-1) = rat_-1 & real_$to_rat(real_1) = rat_1 &
% 269.70/47.85    real_$to_rat(real_2) = rat_2 & real_$to_rat(real_0) = rat_0 &
% 269.70/47.85    real_$to_real(real_-3) = real_-3 & real_$to_real(real_-1/2) = real_-1/2 &
% 269.70/47.85    real_$to_real(real_4) = real_4 & real_$to_real(real_1/2) = real_1/2 &
% 269.70/47.85    real_$to_real(real_-2) = real_-2 & real_$to_real(real_3) = real_3 &
% 269.70/47.85    real_$to_real(real_-1) = real_-1 & real_$to_real(real_1) = real_1 &
% 269.70/47.85    real_$to_real(real_2) = real_2 & real_$to_real(real_0) = real_0 &
% 269.70/47.85    int_$to_real(4) = real_4 & int_$to_real(-3) = real_-3 & int_$to_real(3) =
% 269.70/47.85    real_3 & int_$to_real(-2) = real_-2 & int_$to_real(2) = real_2 &
% 269.70/47.85    int_$to_real(-1) = real_-1 & int_$to_real(1) = real_1 & int_$to_real(0) =
% 269.70/47.85    real_0 & real_$quotient(real_-3, real_-3) = real_1 & real_$quotient(real_-3,
% 269.70/47.85      real_3) = real_-1 & real_$quotient(real_-3, real_-1) = real_3 &
% 269.70/47.85    real_$quotient(real_-3, real_1) = real_-3 & real_$quotient(real_-1/2,
% 269.70/47.85      real_-1/2) = real_1 & real_$quotient(real_-1/2, real_1/2) = real_-1 &
% 269.70/47.85    real_$quotient(real_-1/2, real_-1) = real_1/2 & real_$quotient(real_-1/2,
% 269.70/47.85      real_1) = real_-1/2 & real_$quotient(real_4, real_4) = real_1 &
% 269.70/47.85    real_$quotient(real_4, real_-2) = real_-2 & real_$quotient(real_4, real_1) =
% 269.70/47.85    real_4 & real_$quotient(real_4, real_2) = real_2 & real_$quotient(real_1/2,
% 269.70/47.85      real_-1/2) = real_-1 & real_$quotient(real_1/2, real_1/2) = real_1 &
% 269.70/47.85    real_$quotient(real_1/2, real_-1) = real_-1/2 & real_$quotient(real_1/2,
% 269.70/47.85      real_1) = real_1/2 & real_$quotient(real_-2, real_-1/2) = real_4 &
% 269.70/47.85    real_$quotient(real_-2, real_4) = real_-1/2 & real_$quotient(real_-2, real_-2)
% 269.70/47.85    = real_1 & real_$quotient(real_-2, real_-1) = real_2 & real_$quotient(real_-2,
% 269.70/47.85      real_1) = real_-2 & real_$quotient(real_-2, real_2) = real_-1 &
% 269.70/47.85    real_$quotient(real_3, real_-3) = real_-1 & real_$quotient(real_3, real_3) =
% 269.70/47.85    real_1 & real_$quotient(real_3, real_-1) = real_-3 & real_$quotient(real_3,
% 269.70/47.85      real_1) = real_3 & real_$quotient(real_-1, real_-1/2) = real_2 &
% 269.70/47.85    real_$quotient(real_-1, real_1/2) = real_-2 & real_$quotient(real_-1, real_-2)
% 269.70/47.85    = real_1/2 & real_$quotient(real_-1, real_-1) = real_1 &
% 269.70/47.85    real_$quotient(real_-1, real_1) = real_-1 & real_$quotient(real_-1, real_2) =
% 269.70/47.85    real_-1/2 & real_$quotient(real_1, real_-1/2) = real_-2 &
% 269.70/47.85    real_$quotient(real_1, real_1/2) = real_2 & real_$quotient(real_1, real_-2) =
% 269.70/47.85    real_-1/2 & real_$quotient(real_1, real_-1) = real_-1 & real_$quotient(real_1,
% 269.70/47.85      real_1) = real_1 & real_$quotient(real_1, real_2) = real_1/2 &
% 269.70/47.85    real_$quotient(real_2, real_4) = real_1/2 & real_$quotient(real_2, real_1/2) =
% 269.70/47.85    real_4 & real_$quotient(real_2, real_-2) = real_-1 & real_$quotient(real_2,
% 269.70/47.85      real_-1) = real_-2 & real_$quotient(real_2, real_1) = real_2 &
% 269.70/47.85    real_$quotient(real_2, real_2) = real_1 & real_$quotient(real_0, real_-3) =
% 269.70/47.85    real_0 & real_$quotient(real_0, real_-1/2) = real_0 & real_$quotient(real_0,
% 269.70/47.85      real_4) = real_0 & real_$quotient(real_0, real_1/2) = real_0 &
% 269.70/47.85    real_$quotient(real_0, real_-2) = real_0 & real_$quotient(real_0, real_3) =
% 269.70/47.85    real_0 & real_$quotient(real_0, real_-1) = real_0 & real_$quotient(real_0,
% 269.70/47.85      real_1) = real_0 & real_$quotient(real_0, real_2) = real_0 &
% 269.70/47.85    real_$difference(real_-3, real_-3) = real_0 & real_$difference(real_-3,
% 269.70/47.85      real_-2) = real_-1 & real_$difference(real_-3, real_-1) = real_-2 &
% 269.70/47.85    real_$difference(real_-3, real_0) = real_-3 & real_$difference(real_-1/2,
% 269.70/47.85      real_-1/2) = real_0 & real_$difference(real_-1/2, real_1/2) = real_-1 &
% 269.70/47.85    real_$difference(real_-1/2, real_-1) = real_1/2 & real_$difference(real_-1/2,
% 269.70/47.85      real_0) = real_-1/2 & real_$difference(real_4, real_4) = real_0 &
% 269.70/47.85    real_$difference(real_4, real_3) = real_1 & real_$difference(real_4, real_1) =
% 269.70/47.85    real_3 & real_$difference(real_4, real_2) = real_2 & real_$difference(real_4,
% 269.70/47.85      real_0) = real_4 & real_$difference(real_1/2, real_-1/2) = real_1 &
% 269.70/47.85    real_$difference(real_1/2, real_1/2) = real_0 & real_$difference(real_1/2,
% 269.70/47.85      real_1) = real_-1/2 & real_$difference(real_1/2, real_0) = real_1/2 &
% 269.70/47.85    real_$difference(real_-2, real_-3) = real_1 & real_$difference(real_-2,
% 269.70/47.85      real_-2) = real_0 & real_$difference(real_-2, real_-1) = real_-1 &
% 269.70/47.85    real_$difference(real_-2, real_1) = real_-3 & real_$difference(real_-2,
% 269.70/47.85      real_0) = real_-2 & real_$difference(real_3, real_4) = real_-1 &
% 269.70/47.85    real_$difference(real_3, real_3) = real_0 & real_$difference(real_3, real_-1)
% 269.70/47.85    = real_4 & real_$difference(real_3, real_1) = real_2 &
% 269.70/47.85    real_$difference(real_3, real_2) = real_1 & real_$difference(real_3, real_0) =
% 269.70/47.85    real_3 & real_$difference(real_-1, real_-3) = real_2 &
% 269.70/47.85    real_$difference(real_-1, real_-1/2) = real_-1/2 & real_$difference(real_-1,
% 269.70/47.85      real_-2) = real_1 & real_$difference(real_-1, real_-1) = real_0 &
% 269.70/47.85    real_$difference(real_-1, real_1) = real_-2 & real_$difference(real_-1,
% 269.70/47.85      real_2) = real_-3 & real_$difference(real_-1, real_0) = real_-1 &
% 269.70/47.85    real_$difference(real_1, real_-3) = real_4 & real_$difference(real_1, real_4)
% 269.70/47.85    = real_-3 & real_$difference(real_1, real_1/2) = real_1/2 &
% 269.70/47.85    real_$difference(real_1, real_-2) = real_3 & real_$difference(real_1, real_3)
% 269.70/47.85    = real_-2 & real_$difference(real_1, real_-1) = real_2 &
% 269.70/47.85    real_$difference(real_1, real_1) = real_0 & real_$difference(real_1, real_2) =
% 269.70/47.85    real_-1 & real_$difference(real_1, real_0) = real_1 & real_$difference(real_2,
% 269.70/47.85      real_4) = real_-2 & real_$difference(real_2, real_-2) = real_4 &
% 269.70/47.85    real_$difference(real_2, real_3) = real_-1 & real_$difference(real_2, real_-1)
% 269.70/47.85    = real_3 & real_$difference(real_2, real_1) = real_1 &
% 269.70/47.85    real_$difference(real_2, real_2) = real_0 & real_$difference(real_2, real_0) =
% 269.70/47.85    real_2 & real_$difference(real_0, real_-3) = real_3 & real_$difference(real_0,
% 269.70/47.85      real_-1/2) = real_1/2 & real_$difference(real_0, real_1/2) = real_-1/2 &
% 269.70/47.85    real_$difference(real_0, real_-2) = real_2 & real_$difference(real_0, real_3)
% 269.70/47.85    = real_-3 & real_$difference(real_0, real_-1) = real_1 &
% 269.70/47.85    real_$difference(real_0, real_1) = real_-1 & real_$difference(real_0, real_2)
% 269.70/47.85    = real_-2 & real_$difference(real_0, real_0) = real_0 & real_$sum(real_-3,
% 269.70/47.85      real_4) = real_1 & real_$sum(real_-3, real_3) = real_0 & real_$sum(real_-3,
% 269.70/47.85      real_1) = real_-2 & real_$sum(real_-3, real_2) = real_-1 &
% 269.70/47.85    real_$sum(real_-3, real_0) = real_-3 & real_$sum(real_-1/2, real_-1/2) =
% 269.70/47.85    real_-1 & real_$sum(real_-1/2, real_1/2) = real_0 & real_$sum(real_-1/2,
% 269.70/47.85      real_1) = real_1/2 & real_$sum(real_-1/2, real_0) = real_-1/2 &
% 269.70/47.85    real_$sum(real_4, real_-3) = real_1 & real_$sum(real_4, real_-2) = real_2 &
% 269.70/47.85    real_$sum(real_4, real_-1) = real_3 & real_$sum(real_4, real_0) = real_4 &
% 269.70/47.85    real_$sum(real_1/2, real_-1/2) = real_0 & real_$sum(real_1/2, real_1/2) =
% 269.70/47.85    real_1 & real_$sum(real_1/2, real_-1) = real_-1/2 & real_$sum(real_1/2,
% 269.70/47.85      real_0) = real_1/2 & real_$sum(real_-2, real_4) = real_2 &
% 269.70/47.85    real_$sum(real_-2, real_3) = real_1 & real_$sum(real_-2, real_-1) = real_-3 &
% 269.70/47.85    real_$sum(real_-2, real_1) = real_-1 & real_$sum(real_-2, real_2) = real_0 &
% 269.70/47.85    real_$sum(real_-2, real_0) = real_-2 & real_$sum(real_3, real_-3) = real_0 &
% 269.70/47.85    real_$sum(real_3, real_-2) = real_1 & real_$sum(real_3, real_-1) = real_2 &
% 269.70/47.85    real_$sum(real_3, real_1) = real_4 & real_$sum(real_3, real_0) = real_3 &
% 269.70/47.85    real_$sum(real_-1, real_4) = real_3 & real_$sum(real_-1, real_1/2) = real_-1/2
% 269.70/47.85    & real_$sum(real_-1, real_-2) = real_-3 & real_$sum(real_-1, real_3) = real_2
% 269.70/47.85    & real_$sum(real_-1, real_-1) = real_-2 & real_$sum(real_-1, real_1) = real_0
% 269.70/47.85    & real_$sum(real_-1, real_2) = real_1 & real_$sum(real_-1, real_0) = real_-1 &
% 269.70/47.85    real_$sum(real_1, real_-3) = real_-2 & real_$sum(real_1, real_-1/2) = real_1/2
% 269.70/47.85    & real_$sum(real_1, real_-2) = real_-1 & real_$sum(real_1, real_3) = real_4 &
% 269.70/47.85    real_$sum(real_1, real_-1) = real_0 & real_$sum(real_1, real_1) = real_2 &
% 269.70/47.85    real_$sum(real_1, real_2) = real_3 & real_$sum(real_1, real_0) = real_1 &
% 269.70/47.85    real_$sum(real_2, real_-3) = real_-1 & real_$sum(real_2, real_-2) = real_0 &
% 269.70/47.85    real_$sum(real_2, real_-1) = real_1 & real_$sum(real_2, real_1) = real_3 &
% 269.70/47.85    real_$sum(real_2, real_2) = real_4 & real_$sum(real_2, real_0) = real_2 &
% 269.70/47.85    real_$sum(real_0, real_-3) = real_-3 & real_$sum(real_0, real_-1/2) =
% 269.70/47.85    real_-1/2 & real_$sum(real_0, real_4) = real_4 & real_$sum(real_0, real_1/2) =
% 269.70/47.85    real_1/2 & real_$sum(real_0, real_-2) = real_-2 & real_$sum(real_0, real_3) =
% 269.70/47.85    real_3 & real_$sum(real_0, real_-1) = real_-1 & real_$sum(real_0, real_1) =
% 269.70/47.85    real_1 & real_$sum(real_0, real_2) = real_2 & real_$sum(real_0, real_0) =
% 269.70/47.86    real_0 & real_$product(real_-3, real_-1) = real_3 & real_$product(real_-3,
% 269.70/47.86      real_1) = real_-3 & real_$product(real_-3, real_0) = real_0 &
% 269.70/47.86    real_$product(real_-1/2, real_4) = real_-2 & real_$product(real_-1/2, real_-2)
% 269.70/47.86    = real_1 & real_$product(real_-1/2, real_-1) = real_1/2 &
% 269.70/47.86    real_$product(real_-1/2, real_1) = real_-1/2 & real_$product(real_-1/2,
% 269.70/47.86      real_2) = real_-1 & real_$product(real_-1/2, real_0) = real_0 &
% 269.70/47.86    real_$product(real_4, real_-1/2) = real_-2 & real_$product(real_4, real_1/2) =
% 269.70/47.86    real_2 & real_$product(real_4, real_1) = real_4 & real_$product(real_4,
% 269.70/47.86      real_0) = real_0 & real_$product(real_1/2, real_4) = real_2 &
% 269.70/47.86    real_$product(real_1/2, real_-2) = real_-1 & real_$product(real_1/2, real_-1)
% 269.70/47.86    = real_-1/2 & real_$product(real_1/2, real_1) = real_1/2 &
% 269.70/47.86    real_$product(real_1/2, real_2) = real_1 & real_$product(real_1/2, real_0) =
% 269.70/47.86    real_0 & real_$product(real_-2, real_-1/2) = real_1 & real_$product(real_-2,
% 269.70/47.86      real_1/2) = real_-1 & real_$product(real_-2, real_-2) = real_4 &
% 269.70/47.86    real_$product(real_-2, real_-1) = real_2 & real_$product(real_-2, real_1) =
% 269.70/47.86    real_-2 & real_$product(real_-2, real_0) = real_0 & real_$product(real_3,
% 269.70/47.86      real_-1) = real_-3 & real_$product(real_3, real_1) = real_3 &
% 269.70/47.86    real_$product(real_3, real_0) = real_0 & real_$product(real_-1, real_-3) =
% 269.70/47.86    real_3 & real_$product(real_-1, real_-1/2) = real_1/2 & real_$product(real_-1,
% 269.70/47.86      real_1/2) = real_-1/2 & real_$product(real_-1, real_-2) = real_2 &
% 269.70/47.86    real_$product(real_-1, real_3) = real_-3 & real_$product(real_-1, real_-1) =
% 269.70/47.86    real_1 & real_$product(real_-1, real_1) = real_-1 & real_$product(real_-1,
% 269.70/47.86      real_2) = real_-2 & real_$product(real_-1, real_0) = real_0 &
% 269.70/47.86    real_$product(real_1, real_-3) = real_-3 & real_$product(real_1, real_-1/2) =
% 269.70/47.86    real_-1/2 & real_$product(real_1, real_4) = real_4 & real_$product(real_1,
% 269.70/47.86      real_1/2) = real_1/2 & real_$product(real_1, real_-2) = real_-2 &
% 269.70/47.86    real_$product(real_1, real_3) = real_3 & real_$product(real_1, real_-1) =
% 269.70/47.86    real_-1 & real_$product(real_1, real_1) = real_1 & real_$product(real_1,
% 269.70/47.86      real_2) = real_2 & real_$product(real_1, real_0) = real_0 &
% 269.70/47.86    real_$product(real_2, real_-1/2) = real_-1 & real_$product(real_2, real_1/2) =
% 269.70/47.86    real_1 & real_$product(real_2, real_-1) = real_-2 & real_$product(real_2,
% 269.70/47.86      real_1) = real_2 & real_$product(real_2, real_2) = real_4 &
% 269.70/47.86    real_$product(real_2, real_0) = real_0 & real_$product(real_0, real_-3) =
% 269.70/47.86    real_0 & real_$product(real_0, real_-1/2) = real_0 & real_$product(real_0,
% 269.70/47.86      real_4) = real_0 & real_$product(real_0, real_1/2) = real_0 &
% 269.70/47.86    real_$product(real_0, real_-2) = real_0 & real_$product(real_0, real_3) =
% 269.70/47.86    real_0 & real_$product(real_0, real_-1) = real_0 & real_$product(real_0,
% 269.70/47.86      real_1) = real_0 & real_$product(real_0, real_2) = real_0 &
% 269.70/47.86    real_$product(real_0, real_0) = real_0 & real_$uminus(real_-3) = real_3 &
% 269.70/47.86    real_$uminus(real_-1/2) = real_1/2 & real_$uminus(real_1/2) = real_-1/2 &
% 269.70/47.86    real_$uminus(real_-2) = real_2 & real_$uminus(real_3) = real_-3 &
% 269.70/47.86    real_$uminus(real_-1) = real_1 & real_$uminus(real_1) = real_-1 &
% 269.70/47.86    real_$uminus(real_2) = real_-2 & real_$uminus(real_0) = real_0 &
% 269.70/47.86    real_$is_rat(real_-3) & real_$is_rat(real_-1/2) & real_$is_rat(real_4) &
% 269.70/47.86    real_$is_rat(real_1/2) & real_$is_rat(real_-2) & real_$is_rat(real_3) &
% 269.70/47.86    real_$is_rat(real_-1) & real_$is_rat(real_1) & real_$is_rat(real_2) &
% 269.70/47.86    real_$is_rat(real_0) & real_$is_int(real_-3) & real_$is_int(real_4) &
% 269.70/47.86    real_$is_int(real_-2) & real_$is_int(real_3) & real_$is_int(real_-1) &
% 269.70/47.86    real_$is_int(real_1) & real_$is_int(real_2) & real_$is_int(real_0) &
% 269.70/47.86    real_$greatereq(real_-3, real_-3) & real_$greatereq(real_-1/2, real_-3) &
% 269.70/47.86    real_$greatereq(real_-1/2, real_-1/2) & real_$greatereq(real_-1/2, real_-2) &
% 269.70/47.86    real_$greatereq(real_-1/2, real_-1) & real_$greatereq(real_4, real_-3) &
% 269.70/47.86    real_$greatereq(real_4, real_-1/2) & real_$greatereq(real_4, real_4) &
% 269.70/47.86    real_$greatereq(real_4, real_1/2) & real_$greatereq(real_4, real_-2) &
% 269.70/47.86    real_$greatereq(real_4, real_3) & real_$greatereq(real_4, real_-1) &
% 269.70/47.86    real_$greatereq(real_4, real_1) & real_$greatereq(real_4, real_2) &
% 269.70/47.86    real_$greatereq(real_4, real_0) & real_$greatereq(real_1/2, real_-3) &
% 269.70/47.86    real_$greatereq(real_1/2, real_-1/2) & real_$greatereq(real_1/2, real_1/2) &
% 269.70/47.86    real_$greatereq(real_1/2, real_-2) & real_$greatereq(real_1/2, real_-1) &
% 269.70/47.86    real_$greatereq(real_1/2, real_0) & real_$greatereq(real_-2, real_-3) &
% 269.70/47.86    real_$greatereq(real_-2, real_-2) & real_$greatereq(real_3, real_-3) &
% 269.70/47.86    real_$greatereq(real_3, real_-1/2) & real_$greatereq(real_3, real_1/2) &
% 269.70/47.86    real_$greatereq(real_3, real_-2) & real_$greatereq(real_3, real_3) &
% 269.70/47.86    real_$greatereq(real_3, real_-1) & real_$greatereq(real_3, real_1) &
% 269.70/47.86    real_$greatereq(real_3, real_2) & real_$greatereq(real_3, real_0) &
% 269.70/47.86    real_$greatereq(real_-1, real_-3) & real_$greatereq(real_-1, real_-2) &
% 269.70/47.86    real_$greatereq(real_-1, real_-1) & real_$greatereq(real_1, real_-3) &
% 269.70/47.86    real_$greatereq(real_1, real_-1/2) & real_$greatereq(real_1, real_1/2) &
% 269.70/47.86    real_$greatereq(real_1, real_-2) & real_$greatereq(real_1, real_-1) &
% 269.70/47.86    real_$greatereq(real_1, real_1) & real_$greatereq(real_1, real_0) &
% 269.70/47.86    real_$greatereq(real_2, real_-3) & real_$greatereq(real_2, real_-1/2) &
% 269.70/47.86    real_$greatereq(real_2, real_1/2) & real_$greatereq(real_2, real_-2) &
% 269.70/47.86    real_$greatereq(real_2, real_-1) & real_$greatereq(real_2, real_1) &
% 269.70/47.86    real_$greatereq(real_2, real_2) & real_$greatereq(real_2, real_0) &
% 269.70/47.86    real_$greatereq(real_0, real_-3) & real_$greatereq(real_0, real_-1/2) &
% 269.70/47.86    real_$greatereq(real_0, real_-2) & real_$greatereq(real_0, real_-1) &
% 269.70/47.86    real_$greatereq(real_0, real_0) & real_$greater(real_very_large, real_-3) &
% 269.70/47.86    real_$greater(real_very_large, real_-1/2) & real_$greater(real_very_large,
% 269.70/47.86      real_4) & real_$greater(real_very_large, real_1/2) &
% 269.70/47.86    real_$greater(real_very_large, real_-2) & real_$greater(real_very_large,
% 269.70/47.86      real_3) & real_$greater(real_very_large, real_-1) &
% 269.70/47.86    real_$greater(real_very_large, real_1) & real_$greater(real_very_large,
% 269.70/47.86      real_2) & real_$greater(real_very_large, real_0) & real_$greater(real_-3,
% 269.70/47.86      real_very_small) & real_$greater(real_-1/2, real_very_small) &
% 269.70/47.86    real_$greater(real_-1/2, real_-3) & real_$greater(real_-1/2, real_-2) &
% 269.70/47.86    real_$greater(real_-1/2, real_-1) & real_$greater(real_4, real_very_small) &
% 269.70/47.86    real_$greater(real_4, real_-3) & real_$greater(real_4, real_-1/2) &
% 269.70/47.86    real_$greater(real_4, real_1/2) & real_$greater(real_4, real_-2) &
% 269.70/47.86    real_$greater(real_4, real_3) & real_$greater(real_4, real_-1) &
% 269.70/47.86    real_$greater(real_4, real_1) & real_$greater(real_4, real_2) &
% 269.70/47.86    real_$greater(real_4, real_0) & real_$greater(real_1/2, real_very_small) &
% 269.70/47.86    real_$greater(real_1/2, real_-3) & real_$greater(real_1/2, real_-1/2) &
% 269.70/47.86    real_$greater(real_1/2, real_-2) & real_$greater(real_1/2, real_-1) &
% 269.70/47.86    real_$greater(real_1/2, real_0) & real_$greater(real_-2, real_very_small) &
% 269.70/47.86    real_$greater(real_-2, real_-3) & real_$greater(real_3, real_very_small) &
% 269.70/47.86    real_$greater(real_3, real_-3) & real_$greater(real_3, real_-1/2) &
% 269.70/47.86    real_$greater(real_3, real_1/2) & real_$greater(real_3, real_-2) &
% 269.70/47.86    real_$greater(real_3, real_-1) & real_$greater(real_3, real_1) &
% 269.70/47.86    real_$greater(real_3, real_2) & real_$greater(real_3, real_0) &
% 269.70/47.86    real_$greater(real_-1, real_very_small) & real_$greater(real_-1, real_-3) &
% 269.70/47.86    real_$greater(real_-1, real_-2) & real_$greater(real_1, real_very_small) &
% 269.70/47.86    real_$greater(real_1, real_-3) & real_$greater(real_1, real_-1/2) &
% 269.70/47.86    real_$greater(real_1, real_1/2) & real_$greater(real_1, real_-2) &
% 269.70/47.86    real_$greater(real_1, real_-1) & real_$greater(real_1, real_0) &
% 269.70/47.86    real_$greater(real_2, real_very_small) & real_$greater(real_2, real_-3) &
% 269.70/47.86    real_$greater(real_2, real_-1/2) & real_$greater(real_2, real_1/2) &
% 269.70/47.86    real_$greater(real_2, real_-2) & real_$greater(real_2, real_-1) &
% 269.70/47.86    real_$greater(real_2, real_1) & real_$greater(real_2, real_0) &
% 269.70/47.86    real_$greater(real_0, real_very_small) & real_$greater(real_0, real_-3) &
% 269.70/47.86    real_$greater(real_0, real_-1/2) & real_$greater(real_0, real_-2) &
% 269.70/47.86    real_$greater(real_0, real_-1) & real_$lesseq(real_very_small,
% 269.70/47.86      real_very_large) & real_$lesseq(real_-3, real_-3) & real_$lesseq(real_-3,
% 269.70/47.86      real_-1/2) & real_$lesseq(real_-3, real_4) & real_$lesseq(real_-3, real_1/2)
% 269.70/47.86    & real_$lesseq(real_-3, real_-2) & real_$lesseq(real_-3, real_3) &
% 269.70/47.86    real_$lesseq(real_-3, real_-1) & real_$lesseq(real_-3, real_1) &
% 269.70/47.86    real_$lesseq(real_-3, real_2) & real_$lesseq(real_-3, real_0) &
% 269.70/47.86    real_$lesseq(real_-1/2, real_-1/2) & real_$lesseq(real_-1/2, real_4) &
% 269.70/47.86    real_$lesseq(real_-1/2, real_1/2) & real_$lesseq(real_-1/2, real_3) &
% 269.70/47.86    real_$lesseq(real_-1/2, real_1) & real_$lesseq(real_-1/2, real_2) &
% 269.70/47.86    real_$lesseq(real_-1/2, real_0) & real_$lesseq(real_4, real_4) &
% 269.70/47.86    real_$lesseq(real_1/2, real_4) & real_$lesseq(real_1/2, real_1/2) &
% 269.70/47.86    real_$lesseq(real_1/2, real_3) & real_$lesseq(real_1/2, real_1) &
% 269.70/47.86    real_$lesseq(real_1/2, real_2) & real_$lesseq(real_-2, real_-1/2) &
% 269.70/47.86    real_$lesseq(real_-2, real_4) & real_$lesseq(real_-2, real_1/2) &
% 269.70/47.86    real_$lesseq(real_-2, real_-2) & real_$lesseq(real_-2, real_3) &
% 269.70/47.86    real_$lesseq(real_-2, real_-1) & real_$lesseq(real_-2, real_1) &
% 269.70/47.86    real_$lesseq(real_-2, real_2) & real_$lesseq(real_-2, real_0) &
% 269.70/47.86    real_$lesseq(real_3, real_4) & real_$lesseq(real_3, real_3) &
% 269.70/47.86    real_$lesseq(real_-1, real_-1/2) & real_$lesseq(real_-1, real_4) &
% 269.70/47.86    real_$lesseq(real_-1, real_1/2) & real_$lesseq(real_-1, real_3) &
% 269.70/47.86    real_$lesseq(real_-1, real_-1) & real_$lesseq(real_-1, real_1) &
% 269.70/47.86    real_$lesseq(real_-1, real_2) & real_$lesseq(real_-1, real_0) &
% 269.70/47.86    real_$lesseq(real_1, real_4) & real_$lesseq(real_1, real_3) &
% 269.70/47.86    real_$lesseq(real_1, real_1) & real_$lesseq(real_1, real_2) &
% 269.70/47.86    real_$lesseq(real_2, real_4) & real_$lesseq(real_2, real_3) &
% 269.70/47.86    real_$lesseq(real_2, real_2) & real_$lesseq(real_0, real_4) &
% 269.70/47.86    real_$lesseq(real_0, real_1/2) & real_$lesseq(real_0, real_3) &
% 269.70/47.86    real_$lesseq(real_0, real_1) & real_$lesseq(real_0, real_2) &
% 269.70/47.86    real_$lesseq(real_0, real_0) & real_$less(real_very_small, real_very_large) &
% 269.70/47.86    real_$less(real_very_small, real_-3) & real_$less(real_very_small, real_-1/2)
% 269.70/47.86    & real_$less(real_very_small, real_4) & real_$less(real_very_small, real_1/2)
% 269.70/47.86    & real_$less(real_very_small, real_-2) & real_$less(real_very_small, real_3) &
% 269.70/47.86    real_$less(real_very_small, real_-1) & real_$less(real_very_small, real_1) &
% 269.70/47.86    real_$less(real_very_small, real_2) & real_$less(real_very_small, real_0) &
% 269.70/47.86    real_$less(real_-3, real_very_large) & real_$less(real_-3, real_-1/2) &
% 269.70/47.86    real_$less(real_-3, real_4) & real_$less(real_-3, real_1/2) &
% 269.70/47.86    real_$less(real_-3, real_-2) & real_$less(real_-3, real_3) &
% 269.70/47.86    real_$less(real_-3, real_-1) & real_$less(real_-3, real_1) &
% 269.70/47.86    real_$less(real_-3, real_2) & real_$less(real_-3, real_0) &
% 269.70/47.86    real_$less(real_-1/2, real_very_large) & real_$less(real_-1/2, real_4) &
% 269.70/47.86    real_$less(real_-1/2, real_1/2) & real_$less(real_-1/2, real_3) &
% 269.70/47.86    real_$less(real_-1/2, real_1) & real_$less(real_-1/2, real_2) &
% 269.70/47.86    real_$less(real_-1/2, real_0) & real_$less(real_4, real_very_large) &
% 269.70/47.86    real_$less(real_1/2, real_very_large) & real_$less(real_1/2, real_4) &
% 269.70/47.86    real_$less(real_1/2, real_3) & real_$less(real_1/2, real_1) &
% 269.70/47.86    real_$less(real_1/2, real_2) & real_$less(real_-2, real_very_large) &
% 269.70/47.86    real_$less(real_-2, real_-1/2) & real_$less(real_-2, real_4) &
% 269.70/47.86    real_$less(real_-2, real_1/2) & real_$less(real_-2, real_3) &
% 269.70/47.86    real_$less(real_-2, real_-1) & real_$less(real_-2, real_1) &
% 269.70/47.86    real_$less(real_-2, real_2) & real_$less(real_-2, real_0) & real_$less(real_3,
% 269.70/47.86      real_very_large) & real_$less(real_3, real_4) & real_$less(real_-1,
% 269.70/47.86      real_very_large) & real_$less(real_-1, real_-1/2) & real_$less(real_-1,
% 269.70/47.86      real_4) & real_$less(real_-1, real_1/2) & real_$less(real_-1, real_3) &
% 269.70/47.86    real_$less(real_-1, real_1) & real_$less(real_-1, real_2) &
% 269.70/47.86    real_$less(real_-1, real_0) & real_$less(real_1, real_very_large) &
% 269.70/47.86    real_$less(real_1, real_4) & real_$less(real_1, real_3) & real_$less(real_1,
% 269.70/47.86      real_2) & real_$less(real_2, real_very_large) & real_$less(real_2, real_4) &
% 269.70/47.86    real_$less(real_2, real_3) & real_$less(real_0, real_very_large) &
% 269.70/47.86    real_$less(real_0, real_4) & real_$less(real_0, real_1/2) & real_$less(real_0,
% 269.70/47.86      real_3) & real_$less(real_0, real_1) & real_$less(real_0, real_2) &  ~
% 269.70/47.86    real_$is_int(real_-1/2) &  ~ real_$is_int(real_1/2) &  ~
% 269.70/47.86    real_$greatereq(real_very_small, real_very_large) &  ~
% 269.70/47.86    real_$greatereq(real_-3, real_-1/2) &  ~ real_$greatereq(real_-3, real_4) &  ~
% 269.70/47.86    real_$greatereq(real_-3, real_1/2) &  ~ real_$greatereq(real_-3, real_-2) &  ~
% 269.70/47.86    real_$greatereq(real_-3, real_3) &  ~ real_$greatereq(real_-3, real_-1) &  ~
% 269.70/47.86    real_$greatereq(real_-3, real_1) &  ~ real_$greatereq(real_-3, real_2) &  ~
% 269.70/47.86    real_$greatereq(real_-3, real_0) &  ~ real_$greatereq(real_-1/2, real_4) &  ~
% 269.70/47.86    real_$greatereq(real_-1/2, real_1/2) &  ~ real_$greatereq(real_-1/2, real_3) &
% 269.70/47.86     ~ real_$greatereq(real_-1/2, real_1) &  ~ real_$greatereq(real_-1/2, real_2)
% 269.70/47.86    &  ~ real_$greatereq(real_-1/2, real_0) &  ~ real_$greatereq(real_1/2, real_4)
% 269.70/47.86    &  ~ real_$greatereq(real_1/2, real_3) &  ~ real_$greatereq(real_1/2, real_1)
% 269.70/47.86    &  ~ real_$greatereq(real_1/2, real_2) &  ~ real_$greatereq(real_-2,
% 269.70/47.86      real_-1/2) &  ~ real_$greatereq(real_-2, real_4) &  ~
% 269.70/47.86    real_$greatereq(real_-2, real_1/2) &  ~ real_$greatereq(real_-2, real_3) &  ~
% 269.70/47.86    real_$greatereq(real_-2, real_-1) &  ~ real_$greatereq(real_-2, real_1) &  ~
% 269.70/47.86    real_$greatereq(real_-2, real_2) &  ~ real_$greatereq(real_-2, real_0) &  ~
% 269.70/47.86    real_$greatereq(real_3, real_4) &  ~ real_$greatereq(real_-1, real_-1/2) &  ~
% 269.70/47.86    real_$greatereq(real_-1, real_4) &  ~ real_$greatereq(real_-1, real_1/2) &  ~
% 269.70/47.86    real_$greatereq(real_-1, real_3) &  ~ real_$greatereq(real_-1, real_1) &  ~
% 269.70/47.86    real_$greatereq(real_-1, real_2) &  ~ real_$greatereq(real_-1, real_0) &  ~
% 269.70/47.86    real_$greatereq(real_1, real_4) &  ~ real_$greatereq(real_1, real_3) &  ~
% 269.70/47.86    real_$greatereq(real_1, real_2) &  ~ real_$greatereq(real_2, real_4) &  ~
% 269.70/47.86    real_$greatereq(real_2, real_3) &  ~ real_$greatereq(real_0, real_4) &  ~
% 269.70/47.86    real_$greatereq(real_0, real_1/2) &  ~ real_$greatereq(real_0, real_3) &  ~
% 269.70/47.86    real_$greatereq(real_0, real_1) &  ~ real_$greatereq(real_0, real_2) &  ~
% 269.70/47.86    real_$greater(real_very_small, real_very_large) &  ~ real_$greater(real_-3,
% 269.70/47.86      real_-3) &  ~ real_$greater(real_-3, real_-1/2) &  ~ real_$greater(real_-3,
% 269.70/47.86      real_4) &  ~ real_$greater(real_-3, real_1/2) &  ~ real_$greater(real_-3,
% 269.70/47.86      real_-2) &  ~ real_$greater(real_-3, real_3) &  ~ real_$greater(real_-3,
% 269.70/47.86      real_-1) &  ~ real_$greater(real_-3, real_1) &  ~ real_$greater(real_-3,
% 269.70/47.86      real_2) &  ~ real_$greater(real_-3, real_0) &  ~ real_$greater(real_-1/2,
% 269.70/47.86      real_-1/2) &  ~ real_$greater(real_-1/2, real_4) &  ~
% 269.70/47.86    real_$greater(real_-1/2, real_1/2) &  ~ real_$greater(real_-1/2, real_3) &  ~
% 269.70/47.86    real_$greater(real_-1/2, real_1) &  ~ real_$greater(real_-1/2, real_2) &  ~
% 269.70/47.86    real_$greater(real_-1/2, real_0) &  ~ real_$greater(real_4, real_4) &  ~
% 269.70/47.86    real_$greater(real_1/2, real_4) &  ~ real_$greater(real_1/2, real_1/2) &  ~
% 269.70/47.86    real_$greater(real_1/2, real_3) &  ~ real_$greater(real_1/2, real_1) &  ~
% 269.70/47.86    real_$greater(real_1/2, real_2) &  ~ real_$greater(real_-2, real_-1/2) &  ~
% 269.70/47.86    real_$greater(real_-2, real_4) &  ~ real_$greater(real_-2, real_1/2) &  ~
% 269.70/47.86    real_$greater(real_-2, real_-2) &  ~ real_$greater(real_-2, real_3) &  ~
% 269.70/47.86    real_$greater(real_-2, real_-1) &  ~ real_$greater(real_-2, real_1) &  ~
% 269.70/47.86    real_$greater(real_-2, real_2) &  ~ real_$greater(real_-2, real_0) &  ~
% 269.70/47.86    real_$greater(real_3, real_4) &  ~ real_$greater(real_3, real_3) &  ~
% 269.70/47.86    real_$greater(real_-1, real_-1/2) &  ~ real_$greater(real_-1, real_4) &  ~
% 269.70/47.86    real_$greater(real_-1, real_1/2) &  ~ real_$greater(real_-1, real_3) &  ~
% 269.70/47.86    real_$greater(real_-1, real_-1) &  ~ real_$greater(real_-1, real_1) &  ~
% 269.70/47.86    real_$greater(real_-1, real_2) &  ~ real_$greater(real_-1, real_0) &  ~
% 269.70/47.86    real_$greater(real_1, real_4) &  ~ real_$greater(real_1, real_3) &  ~
% 269.70/47.86    real_$greater(real_1, real_1) &  ~ real_$greater(real_1, real_2) &  ~
% 269.70/47.86    real_$greater(real_2, real_4) &  ~ real_$greater(real_2, real_3) &  ~
% 269.70/47.86    real_$greater(real_2, real_2) &  ~ real_$greater(real_0, real_4) &  ~
% 269.70/47.86    real_$greater(real_0, real_1/2) &  ~ real_$greater(real_0, real_3) &  ~
% 269.70/47.86    real_$greater(real_0, real_1) &  ~ real_$greater(real_0, real_2) &  ~
% 269.70/47.86    real_$greater(real_0, real_0) &  ~ real_$lesseq(real_-1/2, real_-3) &  ~
% 269.70/47.86    real_$lesseq(real_-1/2, real_-2) &  ~ real_$lesseq(real_-1/2, real_-1) &  ~
% 269.70/47.86    real_$lesseq(real_4, real_-3) &  ~ real_$lesseq(real_4, real_-1/2) &  ~
% 269.70/47.86    real_$lesseq(real_4, real_1/2) &  ~ real_$lesseq(real_4, real_-2) &  ~
% 269.70/47.86    real_$lesseq(real_4, real_3) &  ~ real_$lesseq(real_4, real_-1) &  ~
% 269.70/47.86    real_$lesseq(real_4, real_1) &  ~ real_$lesseq(real_4, real_2) &  ~
% 269.70/47.86    real_$lesseq(real_4, real_0) &  ~ real_$lesseq(real_1/2, real_-3) &  ~
% 269.70/47.86    real_$lesseq(real_1/2, real_-1/2) &  ~ real_$lesseq(real_1/2, real_-2) &  ~
% 269.70/47.86    real_$lesseq(real_1/2, real_-1) &  ~ real_$lesseq(real_1/2, real_0) &  ~
% 269.70/47.86    real_$lesseq(real_-2, real_-3) &  ~ real_$lesseq(real_3, real_-3) &  ~
% 269.70/47.86    real_$lesseq(real_3, real_-1/2) &  ~ real_$lesseq(real_3, real_1/2) &  ~
% 269.70/47.86    real_$lesseq(real_3, real_-2) &  ~ real_$lesseq(real_3, real_-1) &  ~
% 269.70/47.86    real_$lesseq(real_3, real_1) &  ~ real_$lesseq(real_3, real_2) &  ~
% 269.70/47.86    real_$lesseq(real_3, real_0) &  ~ real_$lesseq(real_-1, real_-3) &  ~
% 269.70/47.86    real_$lesseq(real_-1, real_-2) &  ~ real_$lesseq(real_1, real_-3) &  ~
% 269.70/47.86    real_$lesseq(real_1, real_-1/2) &  ~ real_$lesseq(real_1, real_1/2) &  ~
% 269.70/47.86    real_$lesseq(real_1, real_-2) &  ~ real_$lesseq(real_1, real_-1) &  ~
% 269.70/47.86    real_$lesseq(real_1, real_0) &  ~ real_$lesseq(real_2, real_-3) &  ~
% 269.70/47.86    real_$lesseq(real_2, real_-1/2) &  ~ real_$lesseq(real_2, real_1/2) &  ~
% 269.70/47.86    real_$lesseq(real_2, real_-2) &  ~ real_$lesseq(real_2, real_-1) &  ~
% 269.70/47.86    real_$lesseq(real_2, real_1) &  ~ real_$lesseq(real_2, real_0) &  ~
% 269.70/47.86    real_$lesseq(real_0, real_-3) &  ~ real_$lesseq(real_0, real_-1/2) &  ~
% 269.70/47.86    real_$lesseq(real_0, real_-2) &  ~ real_$lesseq(real_0, real_-1) &  ~
% 269.70/47.86    real_$less(real_-3, real_-3) &  ~ real_$less(real_-1/2, real_-3) &  ~
% 269.70/47.86    real_$less(real_-1/2, real_-1/2) &  ~ real_$less(real_-1/2, real_-2) &  ~
% 269.70/47.86    real_$less(real_-1/2, real_-1) &  ~ real_$less(real_4, real_-3) &  ~
% 269.70/47.86    real_$less(real_4, real_-1/2) &  ~ real_$less(real_4, real_4) &  ~
% 269.70/47.86    real_$less(real_4, real_1/2) &  ~ real_$less(real_4, real_-2) &  ~
% 269.70/47.86    real_$less(real_4, real_3) &  ~ real_$less(real_4, real_-1) &  ~
% 269.70/47.86    real_$less(real_4, real_1) &  ~ real_$less(real_4, real_2) &  ~
% 269.70/47.86    real_$less(real_4, real_0) &  ~ real_$less(real_1/2, real_-3) &  ~
% 269.70/47.86    real_$less(real_1/2, real_-1/2) &  ~ real_$less(real_1/2, real_1/2) &  ~
% 269.70/47.86    real_$less(real_1/2, real_-2) &  ~ real_$less(real_1/2, real_-1) &  ~
% 269.70/47.86    real_$less(real_1/2, real_0) &  ~ real_$less(real_-2, real_-3) &  ~
% 269.70/47.86    real_$less(real_-2, real_-2) &  ~ real_$less(real_3, real_-3) &  ~
% 269.70/47.86    real_$less(real_3, real_-1/2) &  ~ real_$less(real_3, real_1/2) &  ~
% 269.70/47.86    real_$less(real_3, real_-2) &  ~ real_$less(real_3, real_3) &  ~
% 269.70/47.86    real_$less(real_3, real_-1) &  ~ real_$less(real_3, real_1) &  ~
% 269.70/47.87    real_$less(real_3, real_2) &  ~ real_$less(real_3, real_0) &  ~
% 269.70/47.87    real_$less(real_-1, real_-3) &  ~ real_$less(real_-1, real_-2) &  ~
% 269.70/47.87    real_$less(real_-1, real_-1) &  ~ real_$less(real_1, real_-3) &  ~
% 269.70/47.87    real_$less(real_1, real_-1/2) &  ~ real_$less(real_1, real_1/2) &  ~
% 269.70/47.87    real_$less(real_1, real_-2) &  ~ real_$less(real_1, real_-1) &  ~
% 269.70/47.87    real_$less(real_1, real_1) &  ~ real_$less(real_1, real_0) &  ~
% 269.70/47.87    real_$less(real_2, real_-3) &  ~ real_$less(real_2, real_-1/2) &  ~
% 269.70/47.87    real_$less(real_2, real_1/2) &  ~ real_$less(real_2, real_-2) &  ~
% 269.70/47.87    real_$less(real_2, real_-1) &  ~ real_$less(real_2, real_1) &  ~
% 269.70/47.87    real_$less(real_2, real_2) &  ~ real_$less(real_2, real_0) &  ~
% 269.70/47.87    real_$less(real_0, real_-3) &  ~ real_$less(real_0, real_-1/2) &  ~
% 269.70/47.87    real_$less(real_0, real_-2) &  ~ real_$less(real_0, real_-1) &  ~
% 269.70/47.87    real_$less(real_0, real_0) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real]
% 269.70/47.87    :  ! [v3: $real] :  ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) |  ~
% 269.70/47.87      (real_$sum(v2, v1) = v3) |  ? [v5: $real] : (real_$sum(v2, v5) = v4 &
% 269.70/47.87        real_$sum(v1, v0) = v5)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 269.70/47.87      $real] :  ! [v3: $real] : (v3 = v1 | v0 = real_0 |  ~ (real_$quotient(v2,
% 269.70/47.87          v0) = v3) |  ~ (real_$product(v1, v0) = v2)) &  ! [v0: $real] :  ! [v1:
% 269.70/47.87      $real] :  ! [v2: $real] :  ! [v3: $real] : ( ~ (real_$sum(v1, v2) = v3) |  ~
% 269.70/47.87      (real_$uminus(v0) = v2) | real_$difference(v1, v0) = v3) &  ! [v0: $real] : 
% 269.70/47.87    ! [v1: $real] :  ! [v2: $real] : (v2 = real_0 |  ~ (real_$sum(v0, v1) = v2) | 
% 269.70/47.87      ~ (real_$uminus(v0) = v1)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 269.70/47.87      $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) &  ! [v0:
% 269.70/47.87      $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ (real_$product(v0, v1) = v2)
% 269.70/47.87      | real_$product(v1, v0) = v2) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 269.70/47.87      $real] : ( ~ real_$lesseq(v2, v1) |  ~ real_$lesseq(v1, v0) |
% 269.70/47.87      real_$lesseq(v2, v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (
% 269.70/47.87      ~ real_$lesseq(v2, v1) |  ~ real_$less(v1, v0) | real_$less(v2, v0)) &  !
% 269.70/47.87    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ real_$lesseq(v1, v0) |  ~
% 269.70/47.87      real_$less(v2, v1) | real_$less(v2, v0)) &  ! [v0: $real] :  ! [v1: $real] :
% 269.70/47.87    (v1 = v0 |  ~ (real_$sum(v0, real_0) = v1)) &  ! [v0: $real] :  ! [v1: $real]
% 269.70/47.87    : (v1 = v0 |  ~ real_$lesseq(v1, v0) | real_$less(v1, v0)) &  ! [v0: $real] : 
% 269.70/47.87    ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) &  ! [v0:
% 269.70/47.87      $real] :  ! [v1: $real] : ( ~ real_$greatereq(v0, v1) | real_$lesseq(v1,
% 269.70/47.87        v0)) &  ! [v0: $real] :  ! [v1: $real] : ( ~ real_$greater(v0, v1) |
% 269.70/47.87      real_$less(v1, v0)) &  ! [v0: $real] :  ! [v1: $real] : ( ~ real_$lesseq(v1,
% 269.70/47.87        v0) | real_$greatereq(v0, v1)) &  ! [v0: $real] :  ! [v1: $real] : ( ~
% 269.70/47.87      real_$less(v1, v0) | real_$greater(v0, v1)) &  ! [v0: $real] :  ! [v1:
% 269.70/47.87      $real] : ( ~ real_$less(v1, v0) | real_$lesseq(v1, v0)) &  ! [v0: $real] :
% 269.70/47.87    (v0 = real_0 |  ~ (real_$uminus(v0) = v0)) &  ? [v0: $real] : real_$lesseq(v0,
% 269.70/47.87      v0)
% 269.70/47.87  
% 269.70/47.87    (function-axioms)
% 269.70/47.88     ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |
% 269.70/47.88       ~ (real_$quotient(v3, v2) = v1) |  ~ (real_$quotient(v3, v2) = v0)) &  !
% 269.70/47.88    [v0: S9] :  ! [v1: S9] :  ! [v2: S10] :  ! [v3: S26] : (v1 = v0 |  ~ (f66(v3,
% 269.70/47.88          v2) = v1) |  ~ (f66(v3, v2) = v0)) &  ! [v0: S8] :  ! [v1: S8] :  ! [v2:
% 269.70/47.88      int] :  ! [v3: S25] : (v1 = v0 |  ~ (f63(v3, v2) = v1) |  ~ (f63(v3, v2) =
% 269.70/47.88        v0)) &  ! [v0: S13] :  ! [v1: S13] :  ! [v2: $real] :  ! [v3: S24] : (v1 =
% 269.70/47.88      v0 |  ~ (f59(v3, v2) = v1) |  ~ (f59(v3, v2) = v0)) &  ! [v0: S1] :  ! [v1:
% 269.70/47.88      S1] :  ! [v2: S2] :  ! [v3: S22] : (v1 = v0 |  ~ (f58(v3, v2) = v1) |  ~
% 269.70/47.88      (f58(v3, v2) = v0)) &  ! [v0: S1] :  ! [v1: S1] :  ! [v2: S10] :  ! [v3:
% 269.70/47.88      S21] : (v1 = v0 |  ~ (f57(v3, v2) = v1) |  ~ (f57(v3, v2) = v0)) &  ! [v0:
% 269.70/47.88      S1] :  ! [v1: S1] :  ! [v2: $real] :  ! [v3: S20] : (v1 = v0 |  ~ (f56(v3,
% 269.70/47.88          v2) = v1) |  ~ (f56(v3, v2) = v0)) &  ! [v0: S1] :  ! [v1: S1] :  ! [v2:
% 269.70/47.88      int] :  ! [v3: S19] : (v1 = v0 |  ~ (f55(v3, v2) = v1) |  ~ (f55(v3, v2) =
% 269.70/47.88        v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] :
% 269.70/47.88    (v1 = v0 |  ~ (real_$difference(v3, v2) = v1) |  ~ (real_$difference(v3, v2) =
% 269.70/47.88        v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] :
% 269.70/47.88    (v1 = v0 |  ~ (real_$sum(v3, v2) = v1) |  ~ (real_$sum(v3, v2) = v0)) &  !
% 269.70/47.88    [v0: S14] :  ! [v1: S14] :  ! [v2: $real] :  ! [v3: S23] : (v1 = v0 |  ~
% 269.70/47.88      (f49(v3, v2) = v1) |  ~ (f49(v3, v2) = v0)) &  ! [v0: S1] :  ! [v1: S1] :  !
% 269.70/47.88    [v2: S22] :  ! [v3: S2] : (v1 = v0 |  ~ (f47(v3, v2) = v1) |  ~ (f47(v3, v2) =
% 269.70/47.88        v0)) &  ! [v0: S1] :  ! [v1: S1] :  ! [v2: S21] :  ! [v3: S10] : (v1 = v0
% 269.70/47.88      |  ~ (f45(v3, v2) = v1) |  ~ (f45(v3, v2) = v0)) &  ! [v0: S1] :  ! [v1: S1]
% 269.70/47.88    :  ! [v2: S20] :  ! [v3: $real] : (v1 = v0 |  ~ (f43(v3, v2) = v1) |  ~
% 269.70/47.88      (f43(v3, v2) = v0)) &  ! [v0: S1] :  ! [v1: S1] :  ! [v2: S19] :  ! [v3:
% 269.70/47.88      int] : (v1 = v0 |  ~ (f41(v3, v2) = v1) |  ~ (f41(v3, v2) = v0)) &  ! [v0:
% 269.70/47.88      S17] :  ! [v1: S17] :  ! [v2: S10] :  ! [v3: S18] : (v1 = v0 |  ~ (f39(v3,
% 269.70/47.88          v2) = v1) |  ~ (f39(v3, v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] : 
% 269.70/47.88    ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~ (real_$product(v3, v2) = v1) | 
% 269.70/47.88      ~ (real_$product(v3, v2) = v0)) &  ! [v0: S10] :  ! [v1: S10] :  ! [v2: S10]
% 269.70/47.88    :  ! [v3: S17] : (v1 = v0 |  ~ (f34(v3, v2) = v1) |  ~ (f34(v3, v2) = v0)) & 
% 269.70/47.88    ! [v0: $real] :  ! [v1: $real] :  ! [v2: S10] :  ! [v3: S16] : (v1 = v0 |  ~
% 269.70/47.88      (f27(v3, v2) = v1) |  ~ (f27(v3, v2) = v0)) &  ! [v0: S2] :  ! [v1: S2] :  !
% 269.70/47.88    [v2: S10] :  ! [v3: S15] : (v1 = v0 |  ~ (f25(v3, v2) = v1) |  ~ (f25(v3, v2)
% 269.70/47.88        = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: S14] :
% 269.70/47.88    (v1 = v0 |  ~ (f22(v3, v2) = v1) |  ~ (f22(v3, v2) = v0)) &  ! [v0: S10] :  !
% 269.70/47.88    [v1: S10] :  ! [v2: S2] :  ! [v3: S9] : (v1 = v0 |  ~ (f13(v3, v2) = v1) |  ~
% 269.70/47.88      (f13(v3, v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: S2] :  !
% 269.70/47.88    [v3: S13] : (v1 = v0 |  ~ (f19(v3, v2) = v1) |  ~ (f19(v3, v2) = v0)) &  !
% 269.70/47.88    [v0: S11] :  ! [v1: S11] :  ! [v2: $real] :  ! [v3: S12] : (v1 = v0 |  ~
% 269.70/47.88      (f17(v3, v2) = v1) |  ~ (f17(v3, v2) = v0)) &  ! [v0: S10] :  ! [v1: S10] : 
% 269.70/47.88    ! [v2: $real] :  ! [v3: S11] : (v1 = v0 |  ~ (f16(v3, v2) = v1) |  ~ (f16(v3,
% 269.70/47.88          v2) = v0)) &  ! [v0: S6] :  ! [v1: S6] :  ! [v2: int] :  ! [v3: S7] :
% 269.70/47.88    (v1 = v0 |  ~ (f9(v3, v2) = v1) |  ~ (f9(v3, v2) = v0)) &  ! [v0: int] :  !
% 269.70/47.88    [v1: int] :  ! [v2: S2] :  ! [v3: S8] : (v1 = v0 |  ~ (f11(v3, v2) = v1) |  ~
% 269.70/47.88      (f11(v3, v2) = v0)) &  ! [v0: int] :  ! [v1: int] :  ! [v2: int] :  ! [v3:
% 269.70/47.88      S6] : (v1 = v0 |  ~ (f8(v3, v2) = v1) |  ~ (f8(v3, v2) = v0)) &  ! [v0: S3]
% 269.70/47.88    :  ! [v1: S3] :  ! [v2: S2] :  ! [v3: S4] : (v1 = v0 |  ~ (f4(v3, v2) = v1) | 
% 269.70/47.88      ~ (f4(v3, v2) = v0)) &  ! [v0: S2] :  ! [v1: S2] :  ! [v2: S2] :  ! [v3: S3]
% 269.70/47.88    : (v1 = v0 |  ~ (f3(v3, v2) = v1) |  ~ (f3(v3, v2) = v0)) &  ! [v0: S2] :  !
% 269.70/47.88    [v1: S2] :  ! [v2: int] :  ! [v3: S5] : (v1 = v0 |  ~ (f6(v3, v2) = v1) |  ~
% 269.70/47.88      (f6(v3, v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1
% 269.70/47.88      = v0 |  ~ (real_$floor(v2) = v1) |  ~ (real_$floor(v2) = v0)) &  ! [v0:
% 269.70/47.88      $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$ceiling(v2)
% 269.70/47.88        = v1) |  ~ (real_$ceiling(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] : 
% 269.70/47.88    ! [v2: $real] : (v1 = v0 |  ~ (real_$truncate(v2) = v1) |  ~
% 269.70/47.88      (real_$truncate(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 269.70/47.88      $real] : (v1 = v0 |  ~ (real_$round(v2) = v1) |  ~ (real_$round(v2) = v0)) &
% 269.70/47.88     ! [v0: int] :  ! [v1: int] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$to_int(v2)
% 269.70/47.88        = v1) |  ~ (real_$to_int(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 269.70/47.88    [v2: $real] : (v1 = v0 |  ~ (real_$to_rat(v2) = v1) |  ~ (real_$to_rat(v2) =
% 269.70/47.88        v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~
% 269.70/47.88      (real_$to_real(v2) = v1) |  ~ (real_$to_real(v2) = v0)) &  ! [v0: $real] : 
% 269.70/47.88    ! [v1: $real] :  ! [v2: int] : (v1 = v0 |  ~ (int_$to_real(v2) = v1) |  ~
% 269.70/47.88      (int_$to_real(v2) = v0)) &  ! [v0: S1] :  ! [v1: S1] :  ! [v2: S16] : (v1 =
% 269.70/47.88      v0 |  ~ (f38(v2) = v1) |  ~ (f38(v2) = v0)) &  ! [v0: S1] :  ! [v1: S1] :  !
% 269.70/47.88    [v2: S17] : (v1 = v0 |  ~ (f37(v2) = v1) |  ~ (f37(v2) = v0)) &  ! [v0: $real]
% 269.70/47.88    :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$uminus(v2) = v1) |  ~
% 269.70/47.88      (real_$uminus(v2) = v0))
% 269.70/47.88  
% 269.70/47.88  Further assumptions not needed in the proof:
% 269.70/47.88  --------------------------------------------
% 269.70/47.89  formula_1, formula_10, formula_100, formula_101, formula_102, formula_103,
% 269.70/47.89  formula_104, formula_105, formula_106, formula_107, formula_108, formula_109,
% 269.70/47.89  formula_11, formula_110, formula_111, formula_112, formula_113, formula_114,
% 269.70/47.89  formula_115, formula_116, formula_117, formula_118, formula_119, formula_120,
% 269.70/47.89  formula_121, formula_122, formula_123, formula_124, formula_125, formula_126,
% 269.70/47.89  formula_127, formula_128, formula_129, formula_13, formula_130, formula_131,
% 269.70/47.89  formula_132, formula_133, formula_134, formula_135, formula_136, formula_137,
% 269.70/47.89  formula_138, formula_139, formula_14, formula_140, formula_141, formula_142,
% 269.70/47.89  formula_143, formula_144, formula_145, formula_146, formula_147, formula_148,
% 269.70/47.89  formula_149, formula_15, formula_150, formula_151, formula_152, formula_153,
% 269.70/47.89  formula_154, formula_155, formula_156, formula_157, formula_158, formula_159,
% 269.70/47.89  formula_160, formula_161, formula_162, formula_163, formula_164, formula_165,
% 269.70/47.89  formula_166, formula_167, formula_168, formula_169, formula_170, formula_171,
% 269.70/47.89  formula_172, formula_173, formula_174, formula_175, formula_176, formula_177,
% 269.70/47.89  formula_178, formula_179, formula_18, formula_180, formula_181, formula_182,
% 269.70/47.89  formula_183, formula_184, formula_185, formula_186, formula_187, formula_188,
% 269.70/47.89  formula_189, formula_19, formula_190, formula_191, formula_192, formula_193,
% 269.70/47.89  formula_194, formula_195, formula_196, formula_197, formula_198, formula_199,
% 269.70/47.89  formula_2, formula_20, formula_200, formula_201, formula_202, formula_203,
% 269.70/47.89  formula_204, formula_205, formula_206, formula_207, formula_208, formula_209,
% 269.70/47.89  formula_21, formula_210, formula_211, formula_212, formula_213, formula_214,
% 269.70/47.89  formula_215, formula_216, formula_217, formula_218, formula_219, formula_22,
% 269.70/47.89  formula_220, formula_221, formula_222, formula_223, formula_224, formula_225,
% 269.70/47.89  formula_226, formula_227, formula_228, formula_229, formula_23, formula_230,
% 269.70/47.89  formula_231, formula_232, formula_233, formula_234, formula_235, formula_236,
% 269.70/47.89  formula_237, formula_238, formula_239, formula_24, formula_240, formula_241,
% 269.70/47.89  formula_242, formula_243, formula_244, formula_245, formula_246, formula_247,
% 269.70/47.89  formula_248, formula_249, formula_25, formula_250, formula_251, formula_252,
% 269.70/47.89  formula_253, formula_254, formula_255, formula_256, formula_257, formula_258,
% 269.70/47.89  formula_259, formula_26, formula_260, formula_261, formula_262, formula_263,
% 269.70/47.89  formula_264, formula_265, formula_266, formula_267, formula_268, formula_269,
% 269.70/47.89  formula_27, formula_270, formula_271, formula_272, formula_273, formula_274,
% 269.70/47.89  formula_275, formula_276, formula_277, formula_278, formula_279, formula_28,
% 269.70/47.89  formula_280, formula_281, formula_282, formula_283, formula_284, formula_285,
% 269.70/47.89  formula_286, formula_287, formula_288, formula_289, formula_29, formula_290,
% 269.70/47.89  formula_291, formula_292, formula_293, formula_294, formula_295, formula_296,
% 269.70/47.89  formula_297, formula_298, formula_299, formula_30, formula_300, formula_301,
% 269.70/47.89  formula_302, formula_303, formula_304, formula_305, formula_306, formula_307,
% 269.70/47.89  formula_308, formula_309, formula_31, formula_310, formula_311, formula_312,
% 269.70/47.89  formula_313, formula_314, formula_315, formula_316, formula_317, formula_318,
% 269.70/47.89  formula_319, formula_32, formula_320, formula_321, formula_322, formula_323,
% 269.70/47.89  formula_324, formula_325, formula_326, formula_327, formula_328, formula_329,
% 269.70/47.89  formula_33, formula_330, formula_331, formula_332, formula_333, formula_334,
% 269.70/47.89  formula_335, formula_336, formula_337, formula_338, formula_339, formula_34,
% 269.70/47.89  formula_340, formula_341, formula_342, formula_343, formula_344, formula_345,
% 269.70/47.89  formula_346, formula_347, formula_348, formula_349, formula_35, formula_350,
% 269.70/47.89  formula_351, formula_352, formula_353, formula_354, formula_355, formula_356,
% 269.70/47.89  formula_357, formula_358, formula_359, formula_36, formula_360, formula_361,
% 269.70/47.89  formula_362, formula_363, formula_364, formula_365, formula_366, formula_367,
% 269.70/47.89  formula_368, formula_369, formula_37, formula_370, formula_371, formula_372,
% 269.70/47.89  formula_373, formula_374, formula_375, formula_376, formula_377, formula_378,
% 269.70/47.89  formula_379, formula_380, formula_381, formula_382, formula_383, formula_384,
% 269.70/47.89  formula_385, formula_386, formula_387, formula_388, formula_389, formula_390,
% 269.70/47.89  formula_391, formula_392, formula_393, formula_394, formula_395, formula_396,
% 269.70/47.89  formula_397, formula_398, formula_399, formula_4, formula_40, formula_400,
% 269.70/47.89  formula_401, formula_402, formula_403, formula_404, formula_405, formula_406,
% 269.70/47.89  formula_407, formula_408, formula_409, formula_410, formula_411, formula_412,
% 269.70/47.89  formula_413, formula_414, formula_415, formula_416, formula_417, formula_418,
% 269.70/47.89  formula_419, formula_42, formula_420, formula_421, formula_422, formula_423,
% 269.70/47.89  formula_424, formula_425, formula_426, formula_427, formula_428, formula_429,
% 269.70/47.89  formula_43, formula_430, formula_431, formula_432, formula_433, formula_434,
% 269.70/47.89  formula_435, formula_436, formula_437, formula_438, formula_439, formula_44,
% 269.70/47.89  formula_440, formula_441, formula_442, formula_443, formula_444, formula_445,
% 269.70/47.89  formula_446, formula_447, formula_448, formula_449, formula_45, formula_450,
% 269.70/47.89  formula_451, formula_452, formula_453, formula_454, formula_455, formula_456,
% 269.70/47.89  formula_46, formula_47, formula_48, formula_49, formula_5, formula_50,
% 269.70/47.89  formula_51, formula_52, formula_53, formula_54, formula_55, formula_56,
% 269.70/47.89  formula_57, formula_58, formula_59, formula_6, formula_60, formula_61,
% 269.70/47.89  formula_62, formula_63, formula_64, formula_65, formula_66, formula_67,
% 269.70/47.89  formula_68, formula_69, formula_7, formula_70, formula_71, formula_72,
% 269.70/47.89  formula_73, formula_74, formula_75, formula_76, formula_77, formula_78,
% 269.70/47.89  formula_79, formula_8, formula_80, formula_81, formula_82, formula_83,
% 269.70/47.89  formula_84, formula_85, formula_86, formula_87, formula_88, formula_89,
% 269.70/47.89  formula_9, formula_90, formula_91, formula_92, formula_93, formula_94,
% 269.70/47.89  formula_95, formula_96, formula_97, formula_98, formula_99
% 269.70/47.89  
% 269.70/47.89  Those formulas are unsatisfiable:
% 269.70/47.89  ---------------------------------
% 269.70/47.89  
% 269.70/47.89  Begin of proof
% 269.70/47.89  | 
% 269.70/47.89  | ALPHA: (formula_3) implies:
% 269.70/47.89  |   (1)  S2(f15)
% 269.70/47.89  |   (2)   ? [v0: S10] :  ? [v1: $real] :  ? [v2: S11] :  ? [v3: S10] : ( ~ (v3 =
% 269.70/47.89  |            v0) & f13(f14, f15) = v0 & f19(f20, f15) = v1 & f17(f18, v1) = v2 &
% 269.70/47.89  |          f16(v2, real_0) = v3 & S11(v2) & S10(v3) & S10(v0))
% 269.70/47.89  | 
% 269.70/47.89  | ALPHA: (formula_12) implies:
% 269.70/47.89  |   (3)   ! [v0: S2] :  ! [v1: S10] : ( ~ (f13(f14, v0) = v1) |  ~ S2(v0) |  ?
% 269.70/47.89  |          [v2: $real] : (f27(f28, v1) = v2 & f19(f20, v0) = v2))
% 269.70/47.89  | 
% 269.70/47.89  | ALPHA: (formula_16) implies:
% 269.70/47.89  |   (4)   ! [v0: S2] :  ! [v1: S10] : ( ~ (f13(f14, v0) = v1) |  ~ S2(v0) |  ?
% 269.70/47.89  |          [v2: $real] : (f27(f31, v1) = v2 & f19(f20, v0) = v2))
% 269.70/47.89  | 
% 269.70/47.89  | ALPHA: (formula_17) implies:
% 269.70/47.89  |   (5)   ! [v0: S2] :  ! [v1: S10] : ( ~ (f13(f14, v0) = v1) |  ~ S2(v0) |  ?
% 269.70/47.89  |          [v2: $real] : (f19(f20, v0) = v2 & f16(f32, v2) = v1 & S10(v1)))
% 269.70/47.89  | 
% 269.70/47.89  | ALPHA: (formula_38) implies:
% 269.70/47.89  |   (6)   ! [v0: $real] :  ! [v1: S11] :  ! [v2: S10] :  ! [v3: S10] : (v3 = v2
% 269.70/47.90  |          |  ~ (f17(f18, v0) = v1) |  ~ (f16(v1, real_0) = v2) |  ~ (f16(f32,
% 269.70/47.90  |              v0) = v3))
% 269.70/47.90  | 
% 269.70/47.90  | ALPHA: (formula_39) implies:
% 269.70/47.90  |   (7)   ! [v0: $real] :  ! [v1: S11] : ( ~ (f17(f18, v0) = v1) |  ? [v2: S10]
% 269.70/47.90  |          : (f16(v1, real_0) = v2 & f16(f32, v0) = v2 & S10(v2)))
% 269.70/47.90  | 
% 269.70/47.90  | ALPHA: (formula_41) implies:
% 269.70/47.90  |   (8)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: S11] :  ! [v3: $real] : ( ~
% 269.70/47.90  |          (real_$uminus(v1) = v3) |  ~ (f17(f18, v0) = v2) |  ? [v4: S10] :  ?
% 269.70/47.90  |          [v5: S10] : (f34(f35, v4) = v5 & f16(v2, v3) = v5 & f16(v2, v1) = v4
% 269.70/47.90  |            & S11(v2) & S10(v5) & S10(v4)))
% 269.70/47.90  | 
% 269.70/47.90  | ALPHA: (function-axioms) implies:
% 269.70/47.90  |   (9)   ! [v0: S10] :  ! [v1: S10] :  ! [v2: $real] :  ! [v3: S11] : (v1 = v0
% 269.70/47.90  |          |  ~ (f16(v3, v2) = v1) |  ~ (f16(v3, v2) = v0))
% 269.70/47.90  |   (10)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: S2] :  ! [v3: S13] : (v1 =
% 269.70/47.90  |           v0 |  ~ (f19(v3, v2) = v1) |  ~ (f19(v3, v2) = v0))
% 269.70/47.90  | 
% 269.70/47.90  | ALPHA: (input) implies:
% 269.70/47.90  |   (11)  real_$uminus(real_0) = real_0
% 269.70/47.90  | 
% 269.70/47.90  | DELTA: instantiating (2) with fresh symbols all_504_0, all_504_1, all_504_2,
% 269.70/47.90  |        all_504_3 gives:
% 269.70/47.90  |   (12)   ~ (all_504_0 = all_504_3) & f13(f14, f15) = all_504_3 & f19(f20, f15)
% 269.70/47.90  |         = all_504_2 & f17(f18, all_504_2) = all_504_1 & f16(all_504_1, real_0)
% 269.70/47.90  |         = all_504_0 & S11(all_504_1) & S10(all_504_0) & S10(all_504_3)
% 269.70/47.90  | 
% 269.70/47.90  | ALPHA: (12) implies:
% 269.70/47.90  |   (13)   ~ (all_504_0 = all_504_3)
% 269.70/47.90  |   (14)  f16(all_504_1, real_0) = all_504_0
% 269.70/47.90  |   (15)  f17(f18, all_504_2) = all_504_1
% 269.70/47.90  |   (16)  f19(f20, f15) = all_504_2
% 269.70/47.90  |   (17)  f13(f14, f15) = all_504_3
% 269.70/47.90  | 
% 269.70/47.90  | GROUND_INST: instantiating (7) with all_504_2, all_504_1, simplifying with
% 269.70/47.90  |              (15) gives:
% 269.70/47.91  |   (18)   ? [v0: S10] : (f16(all_504_1, real_0) = v0 & f16(f32, all_504_2) = v0
% 269.70/47.91  |           & S10(v0))
% 269.70/47.91  | 
% 269.70/47.91  | GROUND_INST: instantiating (3) with f15, all_504_3, simplifying with (1), (17)
% 269.70/47.91  |              gives:
% 269.70/47.91  |   (19)   ? [v0: $real] : (f27(f28, all_504_3) = v0 & f19(f20, f15) = v0)
% 269.70/47.91  | 
% 269.70/47.91  | GROUND_INST: instantiating (4) with f15, all_504_3, simplifying with (1), (17)
% 269.70/47.91  |              gives:
% 269.70/47.91  |   (20)   ? [v0: $real] : (f27(f31, all_504_3) = v0 & f19(f20, f15) = v0)
% 269.70/47.91  | 
% 269.70/47.91  | GROUND_INST: instantiating (5) with f15, all_504_3, simplifying with (1), (17)
% 269.70/47.91  |              gives:
% 269.70/47.91  |   (21)   ? [v0: $real] : (f19(f20, f15) = v0 & f16(f32, v0) = all_504_3 &
% 269.70/47.91  |           S10(all_504_3))
% 269.70/47.91  | 
% 269.70/47.91  | GROUND_INST: instantiating (8) with all_504_2, real_0, all_504_1, real_0,
% 269.70/47.91  |              simplifying with (11), (15) gives:
% 269.70/47.91  |   (22)   ? [v0: S10] :  ? [v1: S10] : (f34(f35, v0) = v1 & f16(all_504_1,
% 269.70/47.91  |             real_0) = v1 & f16(all_504_1, real_0) = v0 & S11(all_504_1) &
% 269.70/47.91  |           S10(v1) & S10(v0))
% 269.70/47.91  | 
% 269.70/47.91  | DELTA: instantiating (20) with fresh symbol all_725_0 gives:
% 269.70/47.91  |   (23)  f27(f31, all_504_3) = all_725_0 & f19(f20, f15) = all_725_0
% 269.70/47.91  | 
% 269.70/47.91  | ALPHA: (23) implies:
% 269.70/47.91  |   (24)  f19(f20, f15) = all_725_0
% 269.70/47.91  | 
% 269.70/47.91  | DELTA: instantiating (19) with fresh symbol all_867_0 gives:
% 269.70/47.91  |   (25)  f27(f28, all_504_3) = all_867_0 & f19(f20, f15) = all_867_0
% 269.70/47.91  | 
% 269.70/47.91  | ALPHA: (25) implies:
% 269.70/47.91  |   (26)  f19(f20, f15) = all_867_0
% 269.70/47.91  | 
% 269.70/47.91  | DELTA: instantiating (18) with fresh symbol all_1271_0 gives:
% 269.70/47.91  |   (27)  f16(all_504_1, real_0) = all_1271_0 & f16(f32, all_504_2) = all_1271_0
% 269.70/47.91  |         & S10(all_1271_0)
% 269.70/47.91  | 
% 269.70/47.91  | ALPHA: (27) implies:
% 269.70/47.91  |   (28)  f16(f32, all_504_2) = all_1271_0
% 269.70/47.91  | 
% 269.70/47.91  | DELTA: instantiating (21) with fresh symbol all_2643_0 gives:
% 269.70/47.91  |   (29)  f19(f20, f15) = all_2643_0 & f16(f32, all_2643_0) = all_504_3 &
% 269.70/47.91  |         S10(all_504_3)
% 269.70/47.91  | 
% 269.70/47.91  | ALPHA: (29) implies:
% 269.70/47.91  |   (30)  f16(f32, all_2643_0) = all_504_3
% 269.70/47.91  |   (31)  f19(f20, f15) = all_2643_0
% 269.70/47.91  | 
% 269.70/47.91  | DELTA: instantiating (22) with fresh symbols all_3291_0, all_3291_1 gives:
% 269.70/47.91  |   (32)  f34(f35, all_3291_1) = all_3291_0 & f16(all_504_1, real_0) =
% 269.70/47.91  |         all_3291_0 & f16(all_504_1, real_0) = all_3291_1 & S11(all_504_1) &
% 269.70/47.91  |         S10(all_3291_0) & S10(all_3291_1)
% 269.70/47.91  | 
% 269.70/47.91  | ALPHA: (32) implies:
% 269.70/47.91  |   (33)  f16(all_504_1, real_0) = all_3291_1
% 269.70/47.91  |   (34)  f16(all_504_1, real_0) = all_3291_0
% 269.70/47.91  | 
% 269.70/47.91  | GROUND_INST: instantiating (9) with all_504_0, all_3291_0, real_0, all_504_1,
% 269.70/47.91  |              simplifying with (14), (34) gives:
% 269.70/47.91  |   (35)  all_3291_0 = all_504_0
% 269.70/47.91  | 
% 269.70/47.91  | GROUND_INST: instantiating (9) with all_3291_1, all_3291_0, real_0, all_504_1,
% 269.70/47.91  |              simplifying with (33), (34) gives:
% 269.70/47.91  |   (36)  all_3291_0 = all_3291_1
% 269.70/47.91  | 
% 269.70/47.91  | GROUND_INST: instantiating (6) with all_504_2, all_504_1, all_3291_0,
% 269.70/47.91  |              all_1271_0, simplifying with (15), (28), (34) gives:
% 269.70/47.91  |   (37)  all_3291_0 = all_1271_0
% 269.70/47.91  | 
% 269.70/47.91  | GROUND_INST: instantiating (10) with all_504_2, all_867_0, f15, f20,
% 269.70/47.91  |              simplifying with (16), (26) gives:
% 269.70/47.91  |   (38)  all_867_0 = all_504_2
% 269.70/47.91  | 
% 269.70/47.91  | GROUND_INST: instantiating (10) with all_867_0, all_2643_0, f15, f20,
% 269.70/47.91  |              simplifying with (26), (31) gives:
% 269.70/47.91  |   (39)  all_2643_0 = all_867_0
% 269.70/47.91  | 
% 269.70/47.91  | GROUND_INST: instantiating (10) with all_725_0, all_2643_0, f15, f20,
% 269.70/47.91  |              simplifying with (24), (31) gives:
% 269.70/47.91  |   (40)  all_2643_0 = all_725_0
% 269.70/47.91  | 
% 269.70/47.91  | COMBINE_EQS: (35), (36) imply:
% 269.70/47.91  |   (41)  all_3291_1 = all_504_0
% 269.70/47.91  | 
% 269.70/47.91  | COMBINE_EQS: (36), (37) imply:
% 269.70/47.91  |   (42)  all_3291_1 = all_1271_0
% 269.70/47.91  | 
% 269.70/47.91  | COMBINE_EQS: (41), (42) imply:
% 269.70/47.91  |   (43)  all_1271_0 = all_504_0
% 269.70/47.91  | 
% 269.70/47.91  | COMBINE_EQS: (39), (40) imply:
% 269.70/47.91  |   (44)  all_867_0 = all_725_0
% 269.70/47.91  | 
% 269.70/47.91  | SIMP: (44) implies:
% 269.70/47.91  |   (45)  all_867_0 = all_725_0
% 269.70/47.91  | 
% 269.70/47.91  | COMBINE_EQS: (38), (45) imply:
% 269.70/47.91  |   (46)  all_725_0 = all_504_2
% 269.70/47.91  | 
% 269.70/47.91  | SIMP: (46) implies:
% 269.70/47.91  |   (47)  all_725_0 = all_504_2
% 269.70/47.91  | 
% 269.70/47.91  | COMBINE_EQS: (40), (47) imply:
% 269.70/47.91  |   (48)  all_2643_0 = all_504_2
% 269.70/47.91  | 
% 269.70/47.91  | REDUCE: (30), (48) imply:
% 269.70/47.91  |   (49)  f16(f32, all_504_2) = all_504_3
% 269.70/47.92  | 
% 269.70/47.92  | REDUCE: (28), (43) imply:
% 269.70/47.92  |   (50)  f16(f32, all_504_2) = all_504_0
% 269.70/47.92  | 
% 269.70/47.92  | GROUND_INST: instantiating (9) with all_504_3, all_504_0, all_504_2, f32,
% 269.70/47.92  |              simplifying with (49), (50) gives:
% 269.70/47.92  |   (51)  all_504_0 = all_504_3
% 269.70/47.92  | 
% 269.70/47.92  | REDUCE: (13), (51) imply:
% 269.70/47.92  |   (52)  $false
% 269.70/47.92  | 
% 269.70/47.92  | CLOSE: (52) is inconsistent.
% 269.70/47.92  | 
% 269.70/47.92  End of proof
% 269.70/47.92  % SZS output end Proof for theBenchmark
% 269.70/47.92  
% 269.70/47.92  47249ms
%------------------------------------------------------------------------------