TSTP Solution File: ARI411_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI411_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 : n023.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 17:47:57 EDT 2023

% Result   : Theorem 13.89s 2.64s
% Output   : Proof 18.46s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ARI411_1 : TPTP v8.1.2. Released v5.0.0.
% 0.03/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue Aug 29 18:11:24 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.68/0.63  ________       _____
% 0.68/0.63  ___  __ \_________(_)________________________________
% 0.68/0.63  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.68/0.63  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.68/0.63  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.68/0.63  
% 0.68/0.63  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.68/0.63  (2023-06-19)
% 0.68/0.63  
% 0.68/0.63  (c) Philipp Rümmer, 2009-2023
% 0.68/0.63  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.68/0.63                Amanda Stjerna.
% 0.68/0.63  Free software under BSD-3-Clause.
% 0.68/0.63  
% 0.68/0.63  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.68/0.63  
% 0.68/0.63  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.64  Running up to 7 provers in parallel.
% 0.68/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.68/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.68/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.68/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.68/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.68/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.68/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 1.71/0.95  Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.71/0.95  Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.71/0.95  Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.71/0.95  Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.71/0.95  Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.71/0.95  Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.71/0.95  Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 2.37/1.07  Prover 1: Preprocessing ...
% 2.37/1.07  Prover 4: Preprocessing ...
% 2.64/1.13  Prover 0: Preprocessing ...
% 3.10/1.15  Prover 6: Preprocessing ...
% 3.92/1.29  Prover 2: Preprocessing ...
% 3.92/1.30  Prover 5: Preprocessing ...
% 3.92/1.31  Prover 3: Preprocessing ...
% 6.93/1.70  Prover 1: Constructing countermodel ...
% 6.93/1.70  Prover 6: Constructing countermodel ...
% 6.93/1.71  Prover 4: Constructing countermodel ...
% 7.45/1.76  Prover 0: Proving ...
% 10.49/2.20  Prover 1: gave up
% 10.49/2.22  Prover 6: gave up
% 10.49/2.23  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.49/2.23  Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 10.49/2.23  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.15/2.23  Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 11.15/2.27  Prover 8: Preprocessing ...
% 11.58/2.31  Prover 7: Preprocessing ...
% 12.41/2.41  Prover 8: Warning: ignoring some quantifiers
% 12.41/2.41  Prover 8: Constructing countermodel ...
% 13.89/2.64  Prover 0: proved (1992ms)
% 13.89/2.64  
% 13.89/2.64  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.89/2.64  
% 13.89/2.64  Prover 8: gave up
% 13.89/2.65  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.89/2.65  Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 14.39/2.66  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.39/2.66  Prover 11: Warning: Problem contains reals, using incomplete axiomatisation
% 14.39/2.69  Prover 10: Preprocessing ...
% 14.81/2.74  Prover 3: Constructing countermodel ...
% 14.81/2.74  Prover 3: stopped
% 15.14/2.75  Prover 11: Preprocessing ...
% 15.14/2.75  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.14/2.76  Prover 13: Warning: Problem contains reals, using incomplete axiomatisation
% 15.14/2.76  Prover 13: Preprocessing ...
% 15.14/2.82  Prover 2: Proving ...
% 15.14/2.82  Prover 2: stopped
% 15.14/2.82  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 15.14/2.83  Prover 16: Warning: Problem contains reals, using incomplete axiomatisation
% 15.85/2.85  Prover 13: Warning: ignoring some quantifiers
% 15.85/2.85  Prover 13: Constructing countermodel ...
% 15.85/2.89  Prover 16: Preprocessing ...
% 16.60/2.98  Prover 4: Found proof (size 22)
% 16.60/2.98  Prover 4: proved (2327ms)
% 16.60/2.98  Prover 13: stopped
% 16.60/2.98  Prover 10: stopped
% 17.38/3.07  Prover 5: Proving ...
% 17.38/3.07  Prover 5: stopped
% 17.38/3.12  Prover 7: Warning: ignoring some quantifiers
% 17.38/3.12  Prover 16: stopped
% 17.38/3.13  Prover 7: Constructing countermodel ...
% 17.38/3.14  Prover 11: stopped
% 17.97/3.17  Prover 7: stopped
% 17.97/3.17  
% 17.97/3.17  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.97/3.17  
% 17.97/3.17  % SZS output start Proof for theBenchmark
% 17.97/3.18  Assumptions after simplification:
% 17.97/3.18  ---------------------------------
% 17.97/3.18  
% 17.97/3.18    (real_sum_problem_11)
% 18.16/3.19     ? [v0: $real] : ( ~ (v0 = real_23/4) & real_$sum(real_17/4, v0) = real_10)
% 18.16/3.19  
% 18.16/3.20    (input)
% 18.16/3.23     ~ (real_very_large = real_very_small) &  ~ (real_very_large = real_23/4) &  ~
% 18.16/3.23    (real_very_large = real_10) &  ~ (real_very_large = real_17/4) &  ~
% 18.16/3.23    (real_very_large = real_0) &  ~ (real_very_small = real_23/4) &  ~
% 18.16/3.23    (real_very_small = real_10) &  ~ (real_very_small = real_17/4) &  ~
% 18.16/3.23    (real_very_small = real_0) &  ~ (real_23/4 = real_10) &  ~ (real_23/4 =
% 18.16/3.23      real_17/4) &  ~ (real_23/4 = real_0) &  ~ (real_10 = real_17/4) &  ~
% 18.16/3.23    (real_10 = real_0) &  ~ (real_17/4 = real_0) & real_$is_int(real_23/4) = 1 &
% 18.16/3.23    real_$is_int(real_10) = 0 & real_$is_int(real_17/4) = 1 & real_$is_int(real_0)
% 18.16/3.23    = 0 & real_$is_rat(real_23/4) = 0 & real_$is_rat(real_10) = 0 &
% 18.16/3.23    real_$is_rat(real_17/4) = 0 & real_$is_rat(real_0) = 0 & real_$floor(real_10)
% 18.16/3.23    = real_10 & real_$floor(real_0) = real_0 & real_$ceiling(real_10) = real_10 &
% 18.16/3.23    real_$ceiling(real_0) = real_0 & real_$truncate(real_10) = real_10 &
% 18.16/3.23    real_$truncate(real_0) = real_0 & real_$round(real_10) = real_10 &
% 18.16/3.23    real_$round(real_0) = real_0 & real_$to_int(real_23/4) = 5 &
% 18.16/3.23    real_$to_int(real_10) = 10 & real_$to_int(real_17/4) = 4 &
% 18.16/3.23    real_$to_int(real_0) = 0 & real_$to_rat(real_23/4) = rat_23/4 &
% 18.16/3.23    real_$to_rat(real_10) = rat_10 & real_$to_rat(real_17/4) = rat_17/4 &
% 18.16/3.23    real_$to_rat(real_0) = rat_0 & real_$to_real(real_23/4) = real_23/4 &
% 18.16/3.23    real_$to_real(real_10) = real_10 & real_$to_real(real_17/4) = real_17/4 &
% 18.16/3.23    real_$to_real(real_0) = real_0 & int_$to_real(10) = real_10 & int_$to_real(0)
% 18.16/3.23    = real_0 & real_$quotient(real_0, real_23/4) = real_0 & real_$quotient(real_0,
% 18.16/3.23      real_10) = real_0 & real_$quotient(real_0, real_17/4) = real_0 &
% 18.16/3.23    real_$product(real_23/4, real_0) = real_0 & real_$product(real_10, real_0) =
% 18.16/3.23    real_0 & real_$product(real_17/4, real_0) = real_0 & real_$product(real_0,
% 18.16/3.23      real_23/4) = real_0 & real_$product(real_0, real_10) = real_0 &
% 18.16/3.23    real_$product(real_0, real_17/4) = real_0 & real_$product(real_0, real_0) =
% 18.16/3.23    real_0 & real_$difference(real_23/4, real_23/4) = real_0 &
% 18.16/3.23    real_$difference(real_23/4, real_0) = real_23/4 & real_$difference(real_10,
% 18.16/3.23      real_23/4) = real_17/4 & real_$difference(real_10, real_10) = real_0 &
% 18.16/3.23    real_$difference(real_10, real_17/4) = real_23/4 & real_$difference(real_10,
% 18.16/3.23      real_0) = real_10 & real_$difference(real_17/4, real_17/4) = real_0 &
% 18.16/3.23    real_$difference(real_17/4, real_0) = real_17/4 & real_$difference(real_0,
% 18.16/3.23      real_0) = real_0 & real_$uminus(real_0) = real_0 &
% 18.16/3.23    real_$greatereq(real_very_small, real_very_large) = 1 &
% 18.16/3.23    real_$greatereq(real_23/4, real_23/4) = 0 & real_$greatereq(real_23/4,
% 18.16/3.23      real_10) = 1 & real_$greatereq(real_23/4, real_17/4) = 0 &
% 18.16/3.23    real_$greatereq(real_23/4, real_0) = 0 & real_$greatereq(real_10, real_23/4) =
% 18.16/3.23    0 & real_$greatereq(real_10, real_10) = 0 & real_$greatereq(real_10,
% 18.16/3.23      real_17/4) = 0 & real_$greatereq(real_10, real_0) = 0 &
% 18.16/3.23    real_$greatereq(real_17/4, real_23/4) = 1 & real_$greatereq(real_17/4,
% 18.16/3.23      real_10) = 1 & real_$greatereq(real_17/4, real_17/4) = 0 &
% 18.16/3.23    real_$greatereq(real_17/4, real_0) = 0 & real_$greatereq(real_0, real_23/4) =
% 18.16/3.23    1 & real_$greatereq(real_0, real_10) = 1 & real_$greatereq(real_0, real_17/4)
% 18.16/3.23    = 1 & real_$greatereq(real_0, real_0) = 0 & real_$lesseq(real_very_small,
% 18.16/3.23      real_very_large) = 0 & real_$lesseq(real_23/4, real_23/4) = 0 &
% 18.16/3.23    real_$lesseq(real_23/4, real_10) = 0 & real_$lesseq(real_23/4, real_17/4) = 1
% 18.16/3.23    & real_$lesseq(real_23/4, real_0) = 1 & real_$lesseq(real_10, real_23/4) = 1 &
% 18.16/3.23    real_$lesseq(real_10, real_10) = 0 & real_$lesseq(real_10, real_17/4) = 1 &
% 18.16/3.23    real_$lesseq(real_10, real_0) = 1 & real_$lesseq(real_17/4, real_23/4) = 0 &
% 18.16/3.23    real_$lesseq(real_17/4, real_10) = 0 & real_$lesseq(real_17/4, real_17/4) = 0
% 18.16/3.23    & real_$lesseq(real_17/4, real_0) = 1 & real_$lesseq(real_0, real_23/4) = 0 &
% 18.16/3.23    real_$lesseq(real_0, real_10) = 0 & real_$lesseq(real_0, real_17/4) = 0 &
% 18.16/3.23    real_$lesseq(real_0, real_0) = 0 & real_$greater(real_very_large, real_23/4) =
% 18.16/3.23    0 & real_$greater(real_very_large, real_10) = 0 &
% 18.16/3.23    real_$greater(real_very_large, real_17/4) = 0 & real_$greater(real_very_large,
% 18.16/3.23      real_0) = 0 & real_$greater(real_very_small, real_very_large) = 1 &
% 18.16/3.23    real_$greater(real_23/4, real_very_small) = 0 & real_$greater(real_23/4,
% 18.16/3.23      real_23/4) = 1 & real_$greater(real_23/4, real_10) = 1 &
% 18.16/3.23    real_$greater(real_23/4, real_17/4) = 0 & real_$greater(real_23/4, real_0) = 0
% 18.16/3.23    & real_$greater(real_10, real_very_small) = 0 & real_$greater(real_10,
% 18.16/3.23      real_23/4) = 0 & real_$greater(real_10, real_10) = 1 &
% 18.16/3.23    real_$greater(real_10, real_17/4) = 0 & real_$greater(real_10, real_0) = 0 &
% 18.16/3.23    real_$greater(real_17/4, real_very_small) = 0 & real_$greater(real_17/4,
% 18.16/3.23      real_23/4) = 1 & real_$greater(real_17/4, real_10) = 1 &
% 18.16/3.23    real_$greater(real_17/4, real_17/4) = 1 & real_$greater(real_17/4, real_0) = 0
% 18.16/3.23    & real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0,
% 18.16/3.23      real_23/4) = 1 & real_$greater(real_0, real_10) = 1 & real_$greater(real_0,
% 18.16/3.23      real_17/4) = 1 & real_$greater(real_0, real_0) = 1 &
% 18.16/3.23    real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small,
% 18.16/3.23      real_23/4) = 0 & real_$less(real_very_small, real_10) = 0 &
% 18.16/3.23    real_$less(real_very_small, real_17/4) = 0 & real_$less(real_very_small,
% 18.16/3.23      real_0) = 0 & real_$less(real_23/4, real_very_large) = 0 &
% 18.16/3.23    real_$less(real_23/4, real_23/4) = 1 & real_$less(real_23/4, real_10) = 0 &
% 18.16/3.24    real_$less(real_23/4, real_17/4) = 1 & real_$less(real_23/4, real_0) = 1 &
% 18.16/3.24    real_$less(real_10, real_very_large) = 0 & real_$less(real_10, real_23/4) = 1
% 18.16/3.24    & real_$less(real_10, real_10) = 1 & real_$less(real_10, real_17/4) = 1 &
% 18.16/3.24    real_$less(real_10, real_0) = 1 & real_$less(real_17/4, real_very_large) = 0 &
% 18.16/3.24    real_$less(real_17/4, real_23/4) = 0 & real_$less(real_17/4, real_10) = 0 &
% 18.16/3.24    real_$less(real_17/4, real_17/4) = 1 & real_$less(real_17/4, real_0) = 1 &
% 18.16/3.24    real_$less(real_0, real_very_large) = 0 & real_$less(real_0, real_23/4) = 0 &
% 18.16/3.24    real_$less(real_0, real_10) = 0 & real_$less(real_0, real_17/4) = 0 &
% 18.16/3.24    real_$less(real_0, real_0) = 1 & real_$sum(real_23/4, real_17/4) = real_10 &
% 18.16/3.24    real_$sum(real_23/4, real_0) = real_23/4 & real_$sum(real_10, real_0) =
% 18.16/3.24    real_10 & real_$sum(real_17/4, real_23/4) = real_10 & real_$sum(real_17/4,
% 18.16/3.24      real_0) = real_17/4 & real_$sum(real_0, real_23/4) = real_23/4 &
% 18.16/3.24    real_$sum(real_0, real_10) = real_10 & real_$sum(real_0, real_17/4) =
% 18.16/3.24    real_17/4 & real_$sum(real_0, real_0) = real_0 &  ! [v0: $real] :  ! [v1:
% 18.16/3.24      $real] :  ! [v2: $real] :  ! [v3: $real] :  ! [v4: $real] : ( ~
% 18.16/3.24      (real_$sum(v3, v0) = v4) |  ~ (real_$sum(v2, v1) = v3) |  ? [v5: $real] :
% 18.16/3.24      (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) &  ! [v0: $real] :  !
% 18.16/3.24    [v1: $real] :  ! [v2: $real] :  ! [v3: $real] :  ! [v4: $real] : ( ~
% 18.16/3.24      (real_$sum(v2, v3) = v4) |  ~ (real_$sum(v1, v0) = v3) |  ? [v5: $real] :
% 18.16/3.24      (real_$sum(v5, v0) = v4 & real_$sum(v2, v1) = v5)) &  ! [v0: $real] :  !
% 18.16/3.24    [v1: $real] :  ! [v2: $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$lesseq(v2,
% 18.16/3.24          v1) = 0) |  ~ (real_$lesseq(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0)
% 18.16/3.24        & real_$lesseq(v1, v0) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 18.16/3.24      $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$lesseq(v2, v1) = 0) |  ~
% 18.16/3.24      (real_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0)
% 18.16/3.24        = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: int] :
% 18.16/3.24    (v3 = 0 |  ~ (real_$lesseq(v2, v0) = v3) |  ~ (real_$lesseq(v1, v0) = 0) |  ?
% 18.16/3.24      [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) &  ! [v0: $real] :  !
% 18.16/3.24    [v1: $real] :  ! [v2: $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$lesseq(v1,
% 18.16/3.24          v0) = 0) |  ~ (real_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) &
% 18.16/3.24        real_$less(v2, v1) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 18.16/3.24      $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$less(v2, v1) = 0) |  ~
% 18.16/3.24      (real_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1,
% 18.16/3.24          v0) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3:
% 18.16/3.24      int] : (v3 = 0 |  ~ (real_$less(v2, v0) = v3) |  ~ (real_$less(v1, v0) = 0)
% 18.16/3.24      |  ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) &  ! [v0: $real]
% 18.16/3.24    :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : ( ~ (real_$uminus(v0) =
% 18.16/3.24        v2) |  ~ (real_$sum(v1, v2) = v3) | real_$difference(v1, v0) = v3) &  !
% 18.16/3.24    [v0: $real] :  ! [v1: $real] :  ! [v2: int] : (v2 = 0 | v1 = v0 |  ~
% 18.16/3.24      (real_$less(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1,
% 18.16/3.24          v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: int] : (v2 = 0 | 
% 18.16/3.24      ~ (real_$greatereq(v0, v1) = v2) |  ? [v3: int] : ( ~ (v3 = 0) &
% 18.16/3.24        real_$lesseq(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 18.16/3.24      int] : (v2 = 0 |  ~ (real_$lesseq(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3 =
% 18.16/3.24          0) & real_$greatereq(v0, v1) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 18.16/3.24    ! [v2: int] : (v2 = 0 |  ~ (real_$lesseq(v1, v0) = v2) |  ? [v3: int] : ( ~
% 18.16/3.24        (v3 = 0) & real_$less(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 18.16/3.24    ! [v2: int] : (v2 = 0 |  ~ (real_$greater(v0, v1) = v2) |  ? [v3: int] : ( ~
% 18.16/3.24        (v3 = 0) & real_$less(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 18.16/3.24    ! [v2: int] : (v2 = 0 |  ~ (real_$less(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3
% 18.16/3.24          = 0) & real_$greater(v0, v1) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 18.16/3.24    ! [v2: $real] : (v0 = real_0 |  ~ (real_$product(v1, v0) = v2) |
% 18.16/3.24      real_$quotient(v2, v0) = v1) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 18.16/3.24      $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) &  !
% 18.16/3.24    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ (real_$product(v0, v1) =
% 18.16/3.24        v2) | real_$product(v1, v0) = v2) &  ! [v0: $real] :  ! [v1: $real] :  !
% 18.16/3.24    [v2: $real] : ( ~ (real_$difference(v1, v0) = v2) |  ? [v3: $real] :
% 18.16/3.24      (real_$uminus(v0) = v3 & real_$sum(v1, v3) = v2)) &  ! [v0: $real] :  ! [v1:
% 18.16/3.24      $real] :  ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) |  ~
% 18.16/3.24      (real_$lesseq(v1, v0) = 0) | real_$lesseq(v2, v0) = 0) &  ! [v0: $real] :  !
% 18.16/3.24    [v1: $real] :  ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) |  ~
% 18.16/3.24      (real_$less(v1, v0) = 0) | real_$less(v2, v0) = 0) &  ! [v0: $real] :  !
% 18.16/3.24    [v1: $real] :  ! [v2: $real] : ( ~ (real_$lesseq(v1, v0) = 0) |  ~
% 18.16/3.24      (real_$less(v2, v1) = 0) | real_$less(v2, v0) = 0) &  ! [v0: $real] :  !
% 18.16/3.24    [v1: $real] :  ! [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0,
% 18.16/3.24        v1) = v2) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~
% 18.16/3.24      (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) &  ! [v0: $real] :  !
% 18.16/3.24    [v1: $real] : (v1 = v0 |  ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) =
% 18.16/3.24      0) &  ! [v0: $real] :  ! [v1: $real] : (v1 = v0 |  ~ (real_$sum(v0, real_0)
% 18.16/3.24        = v1)) &  ! [v0: $real] :  ! [v1: int] : (v1 = 0 |  ~ (real_$lesseq(v0,
% 18.16/3.24          v0) = v1)) &  ! [v0: $real] :  ! [v1: $real] : ( ~ (real_$uminus(v0) =
% 18.16/3.24        v1) | real_$uminus(v1) = v0) &  ! [v0: $real] :  ! [v1: $real] : ( ~
% 18.16/3.24      (real_$uminus(v0) = v1) | real_$sum(v0, v1) = real_0) &  ! [v0: $real] :  !
% 18.16/3.24    [v1: $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & 
% 18.16/3.24    ! [v0: $real] :  ! [v1: $real] : ( ~ (real_$lesseq(v1, v0) = 0) |
% 18.16/3.24      real_$greatereq(v0, v1) = 0) &  ! [v0: $real] :  ! [v1: $real] : ( ~
% 18.16/3.24      (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) &  ! [v0: $real] :  !
% 18.16/3.24    [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | real_$lesseq(v1, v0) = 0) &  !
% 18.16/3.24    [v0: $real] :  ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) |
% 18.16/3.24      real_$greater(v0, v1) = 0) &  ! [v0: $real] :  ! [v1: MultipleValueBool] : (
% 18.16/3.24      ~ (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0) = 0) &  ! [v0: $real] :
% 18.40/3.24    (v0 = real_0 |  ~ (real_$uminus(v0) = v0))
% 18.40/3.24  
% 18.40/3.24    (function-axioms)
% 18.40/3.25     ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |
% 18.40/3.25       ~ (real_$quotient(v3, v2) = v1) |  ~ (real_$quotient(v3, v2) = v0)) &  !
% 18.40/3.25    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 18.40/3.25      (real_$product(v3, v2) = v1) |  ~ (real_$product(v3, v2) = v0)) &  ! [v0:
% 18.40/3.25      $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 18.40/3.25      (real_$difference(v3, v2) = v1) |  ~ (real_$difference(v3, v2) = v0)) &  !
% 18.40/3.25    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $real] :  !
% 18.40/3.25    [v3: $real] : (v1 = v0 |  ~ (real_$greatereq(v3, v2) = v1) |  ~
% 18.40/3.25      (real_$greatereq(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 18.40/3.25      MultipleValueBool] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 18.40/3.25      (real_$lesseq(v3, v2) = v1) |  ~ (real_$lesseq(v3, v2) = v0)) &  ! [v0:
% 18.40/3.25      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $real] :  ! [v3:
% 18.40/3.25      $real] : (v1 = v0 |  ~ (real_$greater(v3, v2) = v1) |  ~ (real_$greater(v3,
% 18.40/3.25          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 18.40/3.25    ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~ (real_$less(v3, v2) = v1) |  ~
% 18.40/3.25      (real_$less(v3, v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 18.40/3.25      $real] :  ! [v3: $real] : (v1 = v0 |  ~ (real_$sum(v3, v2) = v1) |  ~
% 18.40/3.25      (real_$sum(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 18.40/3.25      MultipleValueBool] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$is_int(v2) = v1)
% 18.40/3.25      |  ~ (real_$is_int(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 18.40/3.25      MultipleValueBool] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$is_rat(v2) = v1)
% 18.40/3.25      |  ~ (real_$is_rat(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 18.40/3.25      $real] : (v1 = v0 |  ~ (real_$floor(v2) = v1) |  ~ (real_$floor(v2) = v0)) &
% 18.40/3.25     ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~
% 18.40/3.25      (real_$ceiling(v2) = v1) |  ~ (real_$ceiling(v2) = v0)) &  ! [v0: $real] : 
% 18.40/3.25    ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$truncate(v2) = v1) |  ~
% 18.40/3.25      (real_$truncate(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 18.40/3.25      $real] : (v1 = v0 |  ~ (real_$round(v2) = v1) |  ~ (real_$round(v2) = v0)) &
% 18.40/3.25     ! [v0: int] :  ! [v1: int] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$to_int(v2)
% 18.40/3.25        = v1) |  ~ (real_$to_int(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 18.40/3.25    [v2: $real] : (v1 = v0 |  ~ (real_$to_rat(v2) = v1) |  ~ (real_$to_rat(v2) =
% 18.40/3.25        v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~
% 18.40/3.25      (real_$to_real(v2) = v1) |  ~ (real_$to_real(v2) = v0)) &  ! [v0: $real] : 
% 18.40/3.25    ! [v1: $real] :  ! [v2: int] : (v1 = v0 |  ~ (int_$to_real(v2) = v1) |  ~
% 18.40/3.25      (int_$to_real(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real]
% 18.40/3.25    : (v1 = v0 |  ~ (real_$uminus(v2) = v1) |  ~ (real_$uminus(v2) = v0))
% 18.40/3.25  
% 18.40/3.25  Those formulas are unsatisfiable:
% 18.40/3.25  ---------------------------------
% 18.40/3.25  
% 18.40/3.25  Begin of proof
% 18.40/3.25  | 
% 18.40/3.25  | ALPHA: (function-axioms) implies:
% 18.40/3.25  |   (1)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~
% 18.40/3.25  |          (real_$uminus(v2) = v1) |  ~ (real_$uminus(v2) = v0))
% 18.40/3.25  |   (2)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1
% 18.40/3.25  |          = v0 |  ~ (real_$sum(v3, v2) = v1) |  ~ (real_$sum(v3, v2) = v0))
% 18.40/3.25  | 
% 18.40/3.25  | ALPHA: (input) implies:
% 18.40/3.25  |   (3)  real_$difference(real_17/4, real_17/4) = real_0
% 18.40/3.25  |   (4)  real_$difference(real_10, real_17/4) = real_23/4
% 18.40/3.26  |   (5)   ! [v0: $real] :  ! [v1: $real] : (v1 = v0 |  ~ (real_$sum(v0, real_0)
% 18.40/3.26  |            = v1))
% 18.40/3.26  |   (6)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ (real_$sum(v1,
% 18.40/3.26  |              v0) = v2) | real_$sum(v0, v1) = v2)
% 18.46/3.26  |   (7)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~
% 18.46/3.26  |          (real_$difference(v1, v0) = v2) |  ? [v3: $real] : (real_$uminus(v0)
% 18.46/3.26  |            = v3 & real_$sum(v1, v3) = v2))
% 18.46/3.26  |   (8)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] :  !
% 18.46/3.26  |        [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) |  ~ (real_$sum(v2, v1) =
% 18.46/3.26  |            v3) |  ? [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0)
% 18.46/3.26  |            = v5))
% 18.46/3.26  | 
% 18.46/3.26  | DELTA: instantiating (real_sum_problem_11) with fresh symbol all_5_0 gives:
% 18.46/3.26  |   (9)   ~ (all_5_0 = real_23/4) & real_$sum(real_17/4, all_5_0) = real_10
% 18.46/3.26  | 
% 18.46/3.26  | ALPHA: (9) implies:
% 18.46/3.26  |   (10)   ~ (all_5_0 = real_23/4)
% 18.46/3.26  |   (11)  real_$sum(real_17/4, all_5_0) = real_10
% 18.46/3.26  | 
% 18.46/3.26  | GROUND_INST: instantiating (6) with all_5_0, real_17/4, real_10, simplifying
% 18.46/3.26  |              with (11) gives:
% 18.46/3.26  |   (12)  real_$sum(all_5_0, real_17/4) = real_10
% 18.46/3.26  | 
% 18.46/3.26  | GROUND_INST: instantiating (7) with real_17/4, real_17/4, real_0, simplifying
% 18.46/3.26  |              with (3) gives:
% 18.46/3.26  |   (13)   ? [v0: $real] : (real_$uminus(real_17/4) = v0 & real_$sum(real_17/4,
% 18.46/3.26  |             v0) = real_0)
% 18.46/3.26  | 
% 18.46/3.26  | GROUND_INST: instantiating (7) with real_17/4, real_10, real_23/4, simplifying
% 18.46/3.26  |              with (4) gives:
% 18.46/3.26  |   (14)   ? [v0: $real] : (real_$uminus(real_17/4) = v0 & real_$sum(real_10,
% 18.46/3.26  |             v0) = real_23/4)
% 18.46/3.26  | 
% 18.46/3.26  | DELTA: instantiating (13) with fresh symbol all_23_0 gives:
% 18.46/3.26  |   (15)  real_$uminus(real_17/4) = all_23_0 & real_$sum(real_17/4, all_23_0) =
% 18.46/3.26  |         real_0
% 18.46/3.26  | 
% 18.46/3.26  | ALPHA: (15) implies:
% 18.46/3.26  |   (16)  real_$sum(real_17/4, all_23_0) = real_0
% 18.46/3.26  |   (17)  real_$uminus(real_17/4) = all_23_0
% 18.46/3.26  | 
% 18.46/3.26  | DELTA: instantiating (14) with fresh symbol all_27_0 gives:
% 18.46/3.26  |   (18)  real_$uminus(real_17/4) = all_27_0 & real_$sum(real_10, all_27_0) =
% 18.46/3.26  |         real_23/4
% 18.46/3.26  | 
% 18.46/3.26  | ALPHA: (18) implies:
% 18.46/3.26  |   (19)  real_$sum(real_10, all_27_0) = real_23/4
% 18.46/3.26  |   (20)  real_$uminus(real_17/4) = all_27_0
% 18.46/3.26  | 
% 18.46/3.26  | GROUND_INST: instantiating (1) with all_23_0, all_27_0, real_17/4, simplifying
% 18.46/3.26  |              with (17), (20) gives:
% 18.46/3.26  |   (21)  all_27_0 = all_23_0
% 18.46/3.26  | 
% 18.46/3.26  | REDUCE: (19), (21) imply:
% 18.46/3.26  |   (22)  real_$sum(real_10, all_23_0) = real_23/4
% 18.46/3.26  | 
% 18.46/3.26  | GROUND_INST: instantiating (8) with all_23_0, real_17/4, all_5_0, real_10,
% 18.46/3.26  |              real_23/4, simplifying with (12), (22) gives:
% 18.46/3.26  |   (23)   ? [v0: $real] : (real_$sum(all_5_0, v0) = real_23/4 &
% 18.46/3.26  |           real_$sum(real_17/4, all_23_0) = v0)
% 18.46/3.26  | 
% 18.46/3.26  | DELTA: instantiating (23) with fresh symbol all_183_0 gives:
% 18.46/3.27  |   (24)  real_$sum(all_5_0, all_183_0) = real_23/4 & real_$sum(real_17/4,
% 18.46/3.27  |           all_23_0) = all_183_0
% 18.46/3.27  | 
% 18.46/3.27  | ALPHA: (24) implies:
% 18.46/3.27  |   (25)  real_$sum(real_17/4, all_23_0) = all_183_0
% 18.46/3.27  |   (26)  real_$sum(all_5_0, all_183_0) = real_23/4
% 18.46/3.27  | 
% 18.46/3.27  | GROUND_INST: instantiating (2) with real_0, all_183_0, all_23_0, real_17/4,
% 18.46/3.27  |              simplifying with (16), (25) gives:
% 18.46/3.27  |   (27)  all_183_0 = real_0
% 18.46/3.27  | 
% 18.46/3.27  | REDUCE: (26), (27) imply:
% 18.46/3.27  |   (28)  real_$sum(all_5_0, real_0) = real_23/4
% 18.46/3.27  | 
% 18.46/3.27  | GROUND_INST: instantiating (5) with all_5_0, real_23/4, simplifying with (28)
% 18.46/3.27  |              gives:
% 18.46/3.27  |   (29)  all_5_0 = real_23/4
% 18.46/3.27  | 
% 18.46/3.27  | REDUCE: (10), (29) imply:
% 18.46/3.27  |   (30)  $false
% 18.46/3.27  | 
% 18.46/3.27  | CLOSE: (30) is inconsistent.
% 18.46/3.27  | 
% 18.46/3.27  End of proof
% 18.46/3.27  % SZS output end Proof for theBenchmark
% 18.46/3.27  
% 18.46/3.27  2641ms
%------------------------------------------------------------------------------