TSTP Solution File: ARI406_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI406_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n009.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 : Wed Aug 30 17:47:56 EDT 2023

% Result   : Theorem 14.43s 2.68s
% Output   : Proof 22.56s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem  : ARI406_1 : TPTP v8.1.2. Released v5.0.0.
% 0.10/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue Aug 29 17:56:35 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.56/0.62  ________       _____
% 0.56/0.62  ___  __ \_________(_)________________________________
% 0.56/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.56/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.56/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.56/0.62  
% 0.56/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.56/0.62  (2023-06-19)
% 0.56/0.62  
% 0.56/0.62  (c) Philipp Rümmer, 2009-2023
% 0.56/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.56/0.62                Amanda Stjerna.
% 0.56/0.62  Free software under BSD-3-Clause.
% 0.56/0.62  
% 0.56/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.56/0.62  
% 0.56/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.65/0.64  Running up to 7 provers in parallel.
% 0.65/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.65/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.65/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.65/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.65/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.65/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.65/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.68/0.90  Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.68/0.90  Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.68/0.90  Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.68/0.90  Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.68/0.90  Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.68/0.90  Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.68/0.90  Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 2.38/1.00  Prover 1: Preprocessing ...
% 2.38/1.01  Prover 4: Preprocessing ...
% 2.96/1.08  Prover 0: Preprocessing ...
% 2.96/1.08  Prover 6: Preprocessing ...
% 2.96/1.13  Prover 2: Preprocessing ...
% 2.96/1.13  Prover 3: Preprocessing ...
% 2.96/1.14  Prover 5: Preprocessing ...
% 6.18/1.61  Prover 1: Constructing countermodel ...
% 6.89/1.64  Prover 6: Proving ...
% 6.89/1.66  Prover 4: Constructing countermodel ...
% 7.51/1.72  Prover 0: Proving ...
% 9.11/1.97  Prover 1: gave up
% 9.11/1.98  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.74/2.00  Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 9.74/2.08  Prover 7: Preprocessing ...
% 11.47/2.22  Prover 3: Constructing countermodel ...
% 11.47/2.27  Prover 2: Proving ...
% 11.47/2.28  Prover 5: Proving ...
% 13.70/2.56  Prover 7: Warning: ignoring some quantifiers
% 13.70/2.57  Prover 7: Constructing countermodel ...
% 14.43/2.68  Prover 0: proved (2034ms)
% 14.43/2.68  
% 14.43/2.68  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.43/2.68  
% 14.43/2.68  Prover 3: stopped
% 14.43/2.68  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.43/2.68  Prover 6: stopped
% 14.43/2.68  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.43/2.68  Prover 2: stopped
% 14.43/2.68  Prover 5: stopped
% 15.14/2.69  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.14/2.69  Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 15.14/2.69  Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 15.14/2.69  Prover 11: Warning: Problem contains reals, using incomplete axiomatisation
% 15.14/2.69  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.14/2.69  Prover 8: Preprocessing ...
% 15.14/2.69  Prover 13: Warning: Problem contains reals, using incomplete axiomatisation
% 15.14/2.69  Prover 13: Preprocessing ...
% 15.14/2.71  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 15.14/2.71  Prover 16: Warning: Problem contains reals, using incomplete axiomatisation
% 15.14/2.74  Prover 10: Preprocessing ...
% 15.14/2.74  Prover 11: Preprocessing ...
% 15.14/2.76  Prover 16: Preprocessing ...
% 15.89/2.79  Prover 8: Warning: ignoring some quantifiers
% 15.94/2.80  Prover 8: Constructing countermodel ...
% 15.94/2.80  Prover 13: Warning: ignoring some quantifiers
% 15.94/2.81  Prover 13: Constructing countermodel ...
% 16.82/2.95  Prover 8: gave up
% 16.82/2.95  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 16.82/2.95  Prover 19: Warning: Problem contains reals, using incomplete axiomatisation
% 17.44/2.99  Prover 13: gave up
% 17.44/3.00  Prover 19: Preprocessing ...
% 18.44/3.15  Prover 10: Warning: ignoring some quantifiers
% 18.44/3.17  Prover 10: Constructing countermodel ...
% 19.78/3.32  Prover 4: Found proof (size 34)
% 19.78/3.32  Prover 4: proved (2669ms)
% 19.78/3.32  Prover 10: stopped
% 19.78/3.32  Prover 16: Warning: ignoring some quantifiers
% 19.78/3.33  Prover 16: Constructing countermodel ...
% 19.78/3.35  Prover 16: stopped
% 19.78/3.36  Prover 7: Found proof (size 3)
% 19.78/3.36  Prover 7: proved (1375ms)
% 20.47/3.39  Prover 11: Constructing countermodel ...
% 20.47/3.41  Prover 11: stopped
% 21.87/3.75  Prover 19: Warning: ignoring some quantifiers
% 21.87/3.76  Prover 19: Constructing countermodel ...
% 21.87/3.78  Prover 19: stopped
% 21.87/3.78  
% 21.87/3.78  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.87/3.78  
% 21.87/3.79  % SZS output start Proof for theBenchmark
% 21.87/3.79  Assumptions after simplification:
% 21.87/3.79  ---------------------------------
% 21.87/3.79  
% 21.87/3.79    (real_sum_problem_6)
% 22.24/3.82     ! [v0: $real] :  ~ (real_$sum(v0, real_407/100) = real_4769/250)
% 22.24/3.82  
% 22.24/3.83    (input)
% 22.56/3.88     ~ (real_very_large = real_very_small) &  ~ (real_very_large = real_4769/250)
% 22.56/3.88    &  ~ (real_very_large = real_407/100) &  ~ (real_very_large = real_0) &  ~
% 22.56/3.88    (real_very_small = real_4769/250) &  ~ (real_very_small = real_407/100) &  ~
% 22.56/3.88    (real_very_small = real_0) &  ~ (real_4769/250 = real_407/100) &  ~
% 22.56/3.88    (real_4769/250 = real_0) &  ~ (real_407/100 = real_0) &
% 22.56/3.88    real_$is_int(real_4769/250) = 1 & real_$is_int(real_407/100) = 1 &
% 22.56/3.88    real_$is_int(real_0) = 0 & real_$is_rat(real_4769/250) = 0 &
% 22.56/3.88    real_$is_rat(real_407/100) = 0 & real_$is_rat(real_0) = 0 &
% 22.56/3.88    real_$floor(real_0) = real_0 & real_$ceiling(real_0) = real_0 &
% 22.56/3.88    real_$truncate(real_0) = real_0 & real_$round(real_0) = real_0 &
% 22.56/3.88    real_$to_int(real_4769/250) = 19 & real_$to_int(real_407/100) = 4 &
% 22.56/3.88    real_$to_int(real_0) = 0 & real_$to_rat(real_4769/250) = rat_4769/250 &
% 22.56/3.88    real_$to_rat(real_407/100) = rat_407/100 & real_$to_rat(real_0) = rat_0 &
% 22.56/3.88    real_$to_real(real_4769/250) = real_4769/250 & real_$to_real(real_407/100) =
% 22.56/3.89    real_407/100 & real_$to_real(real_0) = real_0 & int_$to_real(0) = real_0 &
% 22.56/3.89    real_$quotient(real_0, real_4769/250) = real_0 & real_$quotient(real_0,
% 22.56/3.89      real_407/100) = real_0 & real_$product(real_4769/250, real_0) = real_0 &
% 22.56/3.89    real_$product(real_407/100, real_0) = real_0 & real_$product(real_0,
% 22.56/3.89      real_4769/250) = real_0 & real_$product(real_0, real_407/100) = real_0 &
% 22.56/3.89    real_$product(real_0, real_0) = real_0 & real_$difference(real_4769/250,
% 22.56/3.89      real_4769/250) = real_0 & real_$difference(real_4769/250, real_0) =
% 22.56/3.89    real_4769/250 & real_$difference(real_407/100, real_407/100) = real_0 &
% 22.56/3.89    real_$difference(real_407/100, real_0) = real_407/100 &
% 22.56/3.89    real_$difference(real_0, real_0) = real_0 & real_$uminus(real_0) = real_0 &
% 22.56/3.89    real_$greatereq(real_very_small, real_very_large) = 1 &
% 22.56/3.89    real_$greatereq(real_4769/250, real_4769/250) = 0 &
% 22.56/3.89    real_$greatereq(real_4769/250, real_407/100) = 0 &
% 22.56/3.89    real_$greatereq(real_4769/250, real_0) = 0 & real_$greatereq(real_407/100,
% 22.56/3.89      real_4769/250) = 1 & real_$greatereq(real_407/100, real_407/100) = 0 &
% 22.56/3.89    real_$greatereq(real_407/100, real_0) = 0 & real_$greatereq(real_0,
% 22.56/3.89      real_4769/250) = 1 & real_$greatereq(real_0, real_407/100) = 1 &
% 22.56/3.89    real_$greatereq(real_0, real_0) = 0 & real_$lesseq(real_very_small,
% 22.56/3.89      real_very_large) = 0 & real_$lesseq(real_4769/250, real_4769/250) = 0 &
% 22.56/3.89    real_$lesseq(real_4769/250, real_407/100) = 1 & real_$lesseq(real_4769/250,
% 22.56/3.89      real_0) = 1 & real_$lesseq(real_407/100, real_4769/250) = 0 &
% 22.56/3.89    real_$lesseq(real_407/100, real_407/100) = 0 & real_$lesseq(real_407/100,
% 22.56/3.89      real_0) = 1 & real_$lesseq(real_0, real_4769/250) = 0 & real_$lesseq(real_0,
% 22.56/3.89      real_407/100) = 0 & real_$lesseq(real_0, real_0) = 0 &
% 22.56/3.89    real_$greater(real_very_large, real_4769/250) = 0 &
% 22.56/3.89    real_$greater(real_very_large, real_407/100) = 0 &
% 22.56/3.89    real_$greater(real_very_large, real_0) = 0 & real_$greater(real_very_small,
% 22.56/3.89      real_very_large) = 1 & real_$greater(real_4769/250, real_very_small) = 0 &
% 22.56/3.89    real_$greater(real_4769/250, real_4769/250) = 1 & real_$greater(real_4769/250,
% 22.56/3.89      real_407/100) = 0 & real_$greater(real_4769/250, real_0) = 0 &
% 22.56/3.89    real_$greater(real_407/100, real_very_small) = 0 & real_$greater(real_407/100,
% 22.56/3.89      real_4769/250) = 1 & real_$greater(real_407/100, real_407/100) = 1 &
% 22.56/3.89    real_$greater(real_407/100, real_0) = 0 & real_$greater(real_0,
% 22.56/3.89      real_very_small) = 0 & real_$greater(real_0, real_4769/250) = 1 &
% 22.56/3.89    real_$greater(real_0, real_407/100) = 1 & real_$greater(real_0, real_0) = 1 &
% 22.56/3.89    real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small,
% 22.56/3.89      real_4769/250) = 0 & real_$less(real_very_small, real_407/100) = 0 &
% 22.56/3.89    real_$less(real_very_small, real_0) = 0 & real_$less(real_4769/250,
% 22.56/3.89      real_very_large) = 0 & real_$less(real_4769/250, real_4769/250) = 1 &
% 22.56/3.89    real_$less(real_4769/250, real_407/100) = 1 & real_$less(real_4769/250,
% 22.56/3.89      real_0) = 1 & real_$less(real_407/100, real_very_large) = 0 &
% 22.56/3.89    real_$less(real_407/100, real_4769/250) = 0 & real_$less(real_407/100,
% 22.56/3.89      real_407/100) = 1 & real_$less(real_407/100, real_0) = 1 &
% 22.56/3.89    real_$less(real_0, real_very_large) = 0 & real_$less(real_0, real_4769/250) =
% 22.56/3.89    0 & real_$less(real_0, real_407/100) = 0 & real_$less(real_0, real_0) = 1 &
% 22.56/3.89    real_$sum(real_4769/250, real_0) = real_4769/250 & real_$sum(real_407/100,
% 22.56/3.89      real_0) = real_407/100 & real_$sum(real_0, real_4769/250) = real_4769/250 &
% 22.56/3.89    real_$sum(real_0, real_407/100) = real_407/100 & real_$sum(real_0, real_0) =
% 22.56/3.89    real_0 &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : 
% 22.56/3.89    ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) |  ~ (real_$sum(v2, v1) = v3) | 
% 22.56/3.89      ? [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) &  ! [v0:
% 22.56/3.89      $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] :  ! [v4: $real] :
% 22.56/3.89    ( ~ (real_$sum(v2, v3) = v4) |  ~ (real_$sum(v1, v0) = v3) |  ? [v5: $real] :
% 22.56/3.89      (real_$sum(v5, v0) = v4 & real_$sum(v2, v1) = v5)) &  ! [v0: $real] :  !
% 22.56/3.89    [v1: $real] :  ! [v2: $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$lesseq(v2,
% 22.56/3.89          v1) = 0) |  ~ (real_$lesseq(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0)
% 22.56/3.89        & real_$lesseq(v1, v0) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 22.56/3.89      $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$lesseq(v2, v1) = 0) |  ~
% 22.56/3.89      (real_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0)
% 22.56/3.89        = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: int] :
% 22.56/3.89    (v3 = 0 |  ~ (real_$lesseq(v2, v0) = v3) |  ~ (real_$lesseq(v1, v0) = 0) |  ?
% 22.56/3.89      [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) &  ! [v0: $real] :  !
% 22.56/3.89    [v1: $real] :  ! [v2: $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$lesseq(v1,
% 22.56/3.89          v0) = 0) |  ~ (real_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) &
% 22.56/3.90        real_$less(v2, v1) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 22.56/3.90      $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$less(v2, v1) = 0) |  ~
% 22.56/3.90      (real_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1,
% 22.56/3.90          v0) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3:
% 22.56/3.90      int] : (v3 = 0 |  ~ (real_$less(v2, v0) = v3) |  ~ (real_$less(v1, v0) = 0)
% 22.56/3.90      |  ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) &  ! [v0: $real]
% 22.56/3.90    :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : ( ~ (real_$uminus(v0) =
% 22.56/3.90        v2) |  ~ (real_$sum(v1, v2) = v3) | real_$difference(v1, v0) = v3) &  !
% 22.56/3.90    [v0: $real] :  ! [v1: $real] :  ! [v2: int] : (v2 = 0 | v1 = v0 |  ~
% 22.56/3.90      (real_$less(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1,
% 22.56/3.90          v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: int] : (v2 = 0 | 
% 22.56/3.90      ~ (real_$greatereq(v0, v1) = v2) |  ? [v3: int] : ( ~ (v3 = 0) &
% 22.56/3.90        real_$lesseq(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 22.56/3.90      int] : (v2 = 0 |  ~ (real_$lesseq(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3 =
% 22.56/3.90          0) & real_$greatereq(v0, v1) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 22.56/3.90    ! [v2: int] : (v2 = 0 |  ~ (real_$lesseq(v1, v0) = v2) |  ? [v3: int] : ( ~
% 22.56/3.90        (v3 = 0) & real_$less(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 22.56/3.90    ! [v2: int] : (v2 = 0 |  ~ (real_$greater(v0, v1) = v2) |  ? [v3: int] : ( ~
% 22.56/3.90        (v3 = 0) & real_$less(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 22.56/3.90    ! [v2: int] : (v2 = 0 |  ~ (real_$less(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3
% 22.56/3.90          = 0) & real_$greater(v0, v1) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 22.56/3.90    ! [v2: $real] : (v0 = real_0 |  ~ (real_$product(v1, v0) = v2) |
% 22.56/3.90      real_$quotient(v2, v0) = v1) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 22.56/3.90      $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) &  !
% 22.56/3.90    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ (real_$product(v0, v1) =
% 22.56/3.90        v2) | real_$product(v1, v0) = v2) &  ! [v0: $real] :  ! [v1: $real] :  !
% 22.56/3.90    [v2: $real] : ( ~ (real_$difference(v1, v0) = v2) |  ? [v3: $real] :
% 22.56/3.90      (real_$uminus(v0) = v3 & real_$sum(v1, v3) = v2)) &  ! [v0: $real] :  ! [v1:
% 22.56/3.90      $real] :  ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) |  ~
% 22.56/3.90      (real_$lesseq(v1, v0) = 0) | real_$lesseq(v2, v0) = 0) &  ! [v0: $real] :  !
% 22.56/3.90    [v1: $real] :  ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) |  ~
% 22.56/3.90      (real_$less(v1, v0) = 0) | real_$less(v2, v0) = 0) &  ! [v0: $real] :  !
% 22.56/3.90    [v1: $real] :  ! [v2: $real] : ( ~ (real_$lesseq(v1, v0) = 0) |  ~
% 22.56/3.90      (real_$less(v2, v1) = 0) | real_$less(v2, v0) = 0) &  ! [v0: $real] :  !
% 22.56/3.90    [v1: $real] :  ! [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0,
% 22.56/3.90        v1) = v2) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~
% 22.56/3.90      (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) &  ! [v0: $real] :  !
% 22.56/3.90    [v1: $real] : (v1 = v0 |  ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) =
% 22.56/3.90      0) &  ! [v0: $real] :  ! [v1: $real] : (v1 = v0 |  ~ (real_$sum(v0, real_0)
% 22.56/3.90        = v1)) &  ! [v0: $real] :  ! [v1: int] : (v1 = 0 |  ~ (real_$lesseq(v0,
% 22.56/3.90          v0) = v1)) &  ! [v0: $real] :  ! [v1: $real] : ( ~ (real_$uminus(v0) =
% 22.56/3.90        v1) | real_$uminus(v1) = v0) &  ! [v0: $real] :  ! [v1: $real] : ( ~
% 22.56/3.90      (real_$uminus(v0) = v1) | real_$sum(v0, v1) = real_0) &  ! [v0: $real] :  !
% 22.56/3.90    [v1: $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & 
% 22.56/3.90    ! [v0: $real] :  ! [v1: $real] : ( ~ (real_$lesseq(v1, v0) = 0) |
% 22.56/3.90      real_$greatereq(v0, v1) = 0) &  ! [v0: $real] :  ! [v1: $real] : ( ~
% 22.56/3.90      (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) &  ! [v0: $real] :  !
% 22.56/3.90    [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | real_$lesseq(v1, v0) = 0) &  !
% 22.56/3.90    [v0: $real] :  ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) |
% 22.56/3.90      real_$greater(v0, v1) = 0) &  ! [v0: $real] :  ! [v1: MultipleValueBool] : (
% 22.56/3.90      ~ (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0) = 0) &  ! [v0: $real] :
% 22.56/3.90    (v0 = real_0 |  ~ (real_$uminus(v0) = v0))
% 22.56/3.90  
% 22.56/3.90    (function-axioms)
% 22.56/3.91     ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |
% 22.56/3.91       ~ (real_$quotient(v3, v2) = v1) |  ~ (real_$quotient(v3, v2) = v0)) &  !
% 22.56/3.91    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 22.56/3.91      (real_$product(v3, v2) = v1) |  ~ (real_$product(v3, v2) = v0)) &  ! [v0:
% 22.56/3.91      $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 22.56/3.91      (real_$difference(v3, v2) = v1) |  ~ (real_$difference(v3, v2) = v0)) &  !
% 22.56/3.91    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $real] :  !
% 22.56/3.91    [v3: $real] : (v1 = v0 |  ~ (real_$greatereq(v3, v2) = v1) |  ~
% 22.56/3.91      (real_$greatereq(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 22.56/3.91      MultipleValueBool] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 22.56/3.91      (real_$lesseq(v3, v2) = v1) |  ~ (real_$lesseq(v3, v2) = v0)) &  ! [v0:
% 22.56/3.91      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $real] :  ! [v3:
% 22.56/3.91      $real] : (v1 = v0 |  ~ (real_$greater(v3, v2) = v1) |  ~ (real_$greater(v3,
% 22.56/3.91          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 22.56/3.91    ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~ (real_$less(v3, v2) = v1) |  ~
% 22.56/3.91      (real_$less(v3, v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 22.56/3.91      $real] :  ! [v3: $real] : (v1 = v0 |  ~ (real_$sum(v3, v2) = v1) |  ~
% 22.56/3.91      (real_$sum(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 22.56/3.91      MultipleValueBool] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$is_int(v2) = v1)
% 22.56/3.91      |  ~ (real_$is_int(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 22.56/3.91      MultipleValueBool] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$is_rat(v2) = v1)
% 22.56/3.91      |  ~ (real_$is_rat(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 22.56/3.91      $real] : (v1 = v0 |  ~ (real_$floor(v2) = v1) |  ~ (real_$floor(v2) = v0)) &
% 22.56/3.91     ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~
% 22.56/3.91      (real_$ceiling(v2) = v1) |  ~ (real_$ceiling(v2) = v0)) &  ! [v0: $real] : 
% 22.56/3.91    ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$truncate(v2) = v1) |  ~
% 22.56/3.91      (real_$truncate(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 22.56/3.91      $real] : (v1 = v0 |  ~ (real_$round(v2) = v1) |  ~ (real_$round(v2) = v0)) &
% 22.56/3.91     ! [v0: int] :  ! [v1: int] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$to_int(v2)
% 22.56/3.92        = v1) |  ~ (real_$to_int(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 22.56/3.92    [v2: $real] : (v1 = v0 |  ~ (real_$to_rat(v2) = v1) |  ~ (real_$to_rat(v2) =
% 22.56/3.92        v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~
% 22.56/3.92      (real_$to_real(v2) = v1) |  ~ (real_$to_real(v2) = v0)) &  ! [v0: $real] : 
% 22.56/3.92    ! [v1: $real] :  ! [v2: int] : (v1 = v0 |  ~ (int_$to_real(v2) = v1) |  ~
% 22.56/3.92      (int_$to_real(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real]
% 22.56/3.92    : (v1 = v0 |  ~ (real_$uminus(v2) = v1) |  ~ (real_$uminus(v2) = v0))
% 22.56/3.92  
% 22.56/3.92  Those formulas are unsatisfiable:
% 22.56/3.92  ---------------------------------
% 22.56/3.92  
% 22.56/3.92  Begin of proof
% 22.56/3.92  | 
% 22.56/3.92  | ALPHA: (function-axioms) implies:
% 22.56/3.92  |   (1)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1
% 22.56/3.92  |          = v0 |  ~ (real_$sum(v3, v2) = v1) |  ~ (real_$sum(v3, v2) = v0))
% 22.56/3.92  | 
% 22.56/3.92  | ALPHA: (input) implies:
% 22.56/3.92  |   (2)  real_$sum(real_0, real_407/100) = real_407/100
% 22.56/3.92  |   (3)  real_$sum(real_0, real_4769/250) = real_4769/250
% 22.56/3.92  |   (4)  real_$less(real_4769/250, real_4769/250) = 1
% 22.56/3.92  |   (5)  real_$less(real_very_small, real_4769/250) = 0
% 22.56/3.92  |   (6)  real_$difference(real_407/100, real_407/100) = real_0
% 22.56/3.92  |   (7)  real_$difference(real_4769/250, real_4769/250) = real_0
% 22.56/3.92  |   (8)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ (real_$sum(v1,
% 22.56/3.92  |              v0) = v2) | real_$sum(v0, v1) = v2)
% 22.56/3.92  |   (9)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~
% 22.56/3.92  |          (real_$difference(v1, v0) = v2) |  ? [v3: $real] : (real_$uminus(v0)
% 22.56/3.92  |            = v3 & real_$sum(v1, v3) = v2))
% 22.56/3.92  |   (10)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: int] : (v2 = 0 |  ~
% 22.56/3.92  |           (real_$lesseq(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3 = 0) &
% 22.56/3.92  |             real_$greatereq(v0, v1) = v3))
% 22.56/3.92  |   (11)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: int] : (v3
% 22.56/3.92  |           = 0 |  ~ (real_$less(v2, v0) = v3) |  ~ (real_$less(v1, v0) = 0) | 
% 22.56/3.92  |           ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4))
% 22.56/3.93  |   (12)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] :  !
% 22.56/3.93  |         [v4: $real] : ( ~ (real_$sum(v2, v3) = v4) |  ~ (real_$sum(v1, v0) =
% 22.56/3.93  |             v3) |  ? [v5: $real] : (real_$sum(v5, v0) = v4 & real_$sum(v2, v1)
% 22.56/3.93  |             = v5))
% 22.56/3.93  |   (13)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] :  !
% 22.56/3.93  |         [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) |  ~ (real_$sum(v2, v1) =
% 22.56/3.93  |             v3) |  ? [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0)
% 22.56/3.93  |             = v5))
% 22.56/3.93  | 
% 22.56/3.93  | GROUND_INST: instantiating (11) with real_4769/250, real_very_small,
% 22.56/3.93  |              real_4769/250, 1, simplifying with (4), (5) gives:
% 22.56/3.93  |   (14)   ? [v0: int] : ( ~ (v0 = 0) & real_$lesseq(real_4769/250,
% 22.56/3.93  |             real_very_small) = v0)
% 22.56/3.93  | 
% 22.56/3.93  | GROUND_INST: instantiating (9) with real_407/100, real_407/100, real_0,
% 22.56/3.93  |              simplifying with (6) gives:
% 22.56/3.93  |   (15)   ? [v0: $real] : (real_$uminus(real_407/100) = v0 &
% 22.56/3.93  |           real_$sum(real_407/100, v0) = real_0)
% 22.56/3.93  | 
% 22.56/3.93  | GROUND_INST: instantiating (9) with real_4769/250, real_4769/250, real_0,
% 22.56/3.93  |              simplifying with (7) gives:
% 22.56/3.93  |   (16)   ? [v0: $real] : (real_$uminus(real_4769/250) = v0 &
% 22.56/3.93  |           real_$sum(real_4769/250, v0) = real_0)
% 22.56/3.93  | 
% 22.56/3.93  | DELTA: instantiating (16) with fresh symbol all_20_0 gives:
% 22.56/3.93  |   (17)  real_$uminus(real_4769/250) = all_20_0 & real_$sum(real_4769/250,
% 22.56/3.93  |           all_20_0) = real_0
% 22.56/3.93  | 
% 22.56/3.93  | ALPHA: (17) implies:
% 22.56/3.93  |   (18)  real_$sum(real_4769/250, all_20_0) = real_0
% 22.56/3.93  | 
% 22.56/3.93  | DELTA: instantiating (15) with fresh symbol all_22_0 gives:
% 22.56/3.93  |   (19)  real_$uminus(real_407/100) = all_22_0 & real_$sum(real_407/100,
% 22.56/3.93  |           all_22_0) = real_0
% 22.56/3.93  | 
% 22.56/3.93  | ALPHA: (19) implies:
% 22.56/3.93  |   (20)  real_$sum(real_407/100, all_22_0) = real_0
% 22.56/3.93  | 
% 22.56/3.93  | DELTA: instantiating (14) with fresh symbol all_30_0 gives:
% 22.56/3.93  |   (21)   ~ (all_30_0 = 0) & real_$lesseq(real_4769/250, real_very_small) =
% 22.56/3.93  |         all_30_0
% 22.56/3.93  | 
% 22.56/3.93  | ALPHA: (21) implies:
% 22.56/3.93  |   (22)   ~ (all_30_0 = 0)
% 22.56/3.93  |   (23)  real_$lesseq(real_4769/250, real_very_small) = all_30_0
% 22.56/3.93  | 
% 22.56/3.93  | GROUND_INST: instantiating (13) with real_407/100, all_22_0, real_407/100,
% 22.56/3.93  |              real_0, real_407/100, simplifying with (2), (20) gives:
% 22.56/3.93  |   (24)   ? [v0: $real] : (real_$sum(all_22_0, real_407/100) = v0 &
% 22.56/3.93  |           real_$sum(real_407/100, v0) = real_407/100)
% 22.56/3.93  | 
% 22.56/3.93  | GROUND_INST: instantiating (8) with all_22_0, real_407/100, real_0,
% 22.56/3.93  |              simplifying with (20) gives:
% 22.56/3.93  |   (25)  real_$sum(all_22_0, real_407/100) = real_0
% 22.56/3.93  | 
% 22.56/3.93  | GROUND_INST: instantiating (13) with real_4769/250, all_20_0, real_4769/250,
% 22.56/3.93  |              real_0, real_4769/250, simplifying with (3), (18) gives:
% 22.56/3.93  |   (26)   ? [v0: $real] : (real_$sum(all_20_0, real_4769/250) = v0 &
% 22.56/3.93  |           real_$sum(real_4769/250, v0) = real_4769/250)
% 22.56/3.94  | 
% 22.56/3.94  | GROUND_INST: instantiating (8) with all_20_0, real_4769/250, real_0,
% 22.56/3.94  |              simplifying with (18) gives:
% 22.56/3.94  |   (27)  real_$sum(all_20_0, real_4769/250) = real_0
% 22.56/3.94  | 
% 22.56/3.94  | GROUND_INST: instantiating (10) with real_very_small, real_4769/250, all_30_0,
% 22.56/3.94  |              simplifying with (23) gives:
% 22.56/3.94  |   (28)  all_30_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) &
% 22.56/3.94  |           real_$greatereq(real_very_small, real_4769/250) = v0)
% 22.56/3.94  | 
% 22.56/3.94  | DELTA: instantiating (24) with fresh symbol all_58_0 gives:
% 22.56/3.94  |   (29)  real_$sum(all_22_0, real_407/100) = all_58_0 & real_$sum(real_407/100,
% 22.56/3.94  |           all_58_0) = real_407/100
% 22.56/3.94  | 
% 22.56/3.94  | ALPHA: (29) implies:
% 22.56/3.94  |   (30)  real_$sum(all_22_0, real_407/100) = all_58_0
% 22.56/3.94  | 
% 22.56/3.94  | DELTA: instantiating (26) with fresh symbol all_72_0 gives:
% 22.56/3.94  |   (31)  real_$sum(all_20_0, real_4769/250) = all_72_0 &
% 22.56/3.94  |         real_$sum(real_4769/250, all_72_0) = real_4769/250
% 22.56/3.94  | 
% 22.56/3.94  | ALPHA: (31) implies:
% 22.56/3.94  |   (32)  real_$sum(real_4769/250, all_72_0) = real_4769/250
% 22.56/3.94  |   (33)  real_$sum(all_20_0, real_4769/250) = all_72_0
% 22.56/3.94  | 
% 22.56/3.94  | BETA: splitting (28) gives:
% 22.56/3.94  | 
% 22.56/3.94  | Case 1:
% 22.56/3.94  | | 
% 22.56/3.94  | |   (34)  all_30_0 = 0
% 22.56/3.94  | | 
% 22.56/3.94  | | REDUCE: (22), (34) imply:
% 22.56/3.94  | |   (35)  $false
% 22.56/3.94  | | 
% 22.56/3.94  | | CLOSE: (35) is inconsistent.
% 22.56/3.94  | | 
% 22.56/3.94  | Case 2:
% 22.56/3.94  | | 
% 22.56/3.94  | | 
% 22.56/3.94  | | GROUND_INST: instantiating (1) with real_0, all_72_0, real_4769/250,
% 22.56/3.94  | |              all_20_0, simplifying with (27), (33) gives:
% 22.56/3.94  | |   (36)  all_72_0 = real_0
% 22.56/3.94  | | 
% 22.56/3.94  | | GROUND_INST: instantiating (1) with real_0, all_58_0, real_407/100,
% 22.56/3.94  | |              all_22_0, simplifying with (25), (30) gives:
% 22.56/3.94  | |   (37)  all_58_0 = real_0
% 22.56/3.94  | | 
% 22.56/3.94  | | REDUCE: (32), (36) imply:
% 22.56/3.94  | |   (38)  real_$sum(real_4769/250, real_0) = real_4769/250
% 22.56/3.94  | | 
% 22.56/3.94  | | GROUND_INST: instantiating (12) with real_407/100, all_22_0, real_4769/250,
% 22.56/3.94  | |              real_0, real_4769/250, simplifying with (25), (38) gives:
% 22.56/3.94  | |   (39)   ? [v0: $real] : (real_$sum(v0, real_407/100) = real_4769/250 &
% 22.56/3.94  | |           real_$sum(real_4769/250, all_22_0) = v0)
% 22.56/3.94  | | 
% 22.56/3.94  | | DELTA: instantiating (39) with fresh symbol all_239_0 gives:
% 22.56/3.94  | |   (40)  real_$sum(all_239_0, real_407/100) = real_4769/250 &
% 22.56/3.94  | |         real_$sum(real_4769/250, all_22_0) = all_239_0
% 22.56/3.94  | | 
% 22.56/3.94  | | ALPHA: (40) implies:
% 22.56/3.94  | |   (41)  real_$sum(all_239_0, real_407/100) = real_4769/250
% 22.56/3.94  | | 
% 22.56/3.94  | | GROUND_INST: instantiating (real_sum_problem_6) with all_239_0, simplifying
% 22.56/3.94  | |              with (41) gives:
% 22.56/3.94  | |   (42)  $false
% 22.56/3.94  | | 
% 22.56/3.94  | | CLOSE: (42) is inconsistent.
% 22.56/3.94  | | 
% 22.56/3.94  | End of split
% 22.56/3.94  | 
% 22.56/3.94  End of proof
% 22.56/3.94  % SZS output end Proof for theBenchmark
% 22.56/3.94  
% 22.56/3.94  3318ms
%------------------------------------------------------------------------------