TSTP Solution File: ARI446_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI446_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 : n007.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 17:48:04 EDT 2023

% Result   : Theorem 6.59s 1.57s
% Output   : Proof 16.15s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : ARI446_1 : TPTP v8.1.2. Released v5.0.0.
% 0.04/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n007.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % 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 17:43:44 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.51/0.61  ________       _____
% 0.51/0.61  ___  __ \_________(_)________________________________
% 0.51/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.51/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.51/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.51/0.61  
% 0.51/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.51/0.61  (2023-06-19)
% 0.51/0.61  
% 0.51/0.61  (c) Philipp Rümmer, 2009-2023
% 0.51/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.51/0.61                Amanda Stjerna.
% 0.51/0.61  Free software under BSD-3-Clause.
% 0.51/0.61  
% 0.51/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.51/0.61  
% 0.51/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.51/0.62  Running up to 7 provers in parallel.
% 0.73/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.73/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.73/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.73/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.73/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.73/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.73/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.49/0.91  Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.49/0.91  Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.49/0.91  Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.49/0.91  Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.49/0.92  Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.49/0.92  Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.49/0.92  Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 2.29/1.00  Prover 4: Preprocessing ...
% 2.29/1.01  Prover 1: Preprocessing ...
% 2.94/1.09  Prover 0: Preprocessing ...
% 2.94/1.09  Prover 6: Preprocessing ...
% 5.12/1.40  Prover 5: Preprocessing ...
% 5.12/1.40  Prover 2: Preprocessing ...
% 5.12/1.42  Prover 3: Preprocessing ...
% 5.89/1.53  Prover 0: Constructing countermodel ...
% 5.89/1.53  Prover 6: Constructing countermodel ...
% 6.59/1.57  Prover 6: proved (931ms)
% 6.59/1.57  
% 6.59/1.57  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.59/1.57  
% 6.59/1.58  Prover 0: proved (938ms)
% 6.59/1.58  
% 6.59/1.58  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.59/1.58  
% 6.59/1.59  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.59/1.59  Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 6.59/1.59  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.59/1.59  Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 6.59/1.60  Prover 8: Preprocessing ...
% 7.29/1.70  Prover 4: Constructing countermodel ...
% 7.29/1.70  Prover 1: Constructing countermodel ...
% 8.03/1.81  Prover 8: Warning: ignoring some quantifiers
% 8.03/1.82  Prover 1: Found proof (size 3)
% 8.03/1.82  Prover 1: proved (1189ms)
% 8.03/1.82  Prover 8: Constructing countermodel ...
% 8.46/1.83  Prover 4: Found proof (size 3)
% 8.46/1.83  Prover 4: proved (1196ms)
% 8.46/1.83  Prover 8: stopped
% 8.46/1.83  Prover 7: Preprocessing ...
% 10.69/2.14  Prover 2: stopped
% 11.69/2.30  Prover 7: stopped
% 14.31/2.80  Prover 5: Constructing countermodel ...
% 14.31/2.80  Prover 5: stopped
% 15.35/3.06  Prover 3: Constructing countermodel ...
% 15.35/3.06  Prover 3: stopped
% 15.35/3.06  
% 15.35/3.06  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.35/3.06  
% 15.35/3.06  % SZS output start Proof for theBenchmark
% 15.35/3.07  Assumptions after simplification:
% 15.35/3.07  ---------------------------------
% 15.35/3.07  
% 15.35/3.07    (real_product_problem_11)
% 15.61/3.07    real_12500 = real_12000
% 15.61/3.07  
% 15.61/3.07    (input)
% 16.02/3.16     ~ (real_very_large = real_very_small) &  ~ (real_very_large = real_12500) & 
% 16.02/3.16    ~ (real_very_large = real_12000) &  ~ (real_very_large = real_5/2) &  ~
% 16.02/3.16    (real_very_large = real_5000) &  ~ (real_very_large = real_0) &  ~
% 16.02/3.16    (real_very_small = real_12500) &  ~ (real_very_small = real_12000) &  ~
% 16.02/3.16    (real_very_small = real_5/2) &  ~ (real_very_small = real_5000) &  ~
% 16.02/3.16    (real_very_small = real_0) &  ~ (real_12500 = real_12000) &  ~ (real_12500 =
% 16.02/3.16      real_5/2) &  ~ (real_12500 = real_5000) &  ~ (real_12500 = real_0) &  ~
% 16.02/3.16    (real_12000 = real_5/2) &  ~ (real_12000 = real_5000) &  ~ (real_12000 =
% 16.02/3.16      real_0) &  ~ (real_5/2 = real_5000) &  ~ (real_5/2 = real_0) &  ~ (real_5000
% 16.02/3.16      = real_0) & real_$is_int(real_12500) = 0 & real_$is_int(real_12000) = 0 &
% 16.02/3.16    real_$is_int(real_5/2) = 1 & real_$is_int(real_5000) = 0 &
% 16.02/3.16    real_$is_int(real_0) = 0 & real_$is_rat(real_12500) = 0 &
% 16.02/3.16    real_$is_rat(real_12000) = 0 & real_$is_rat(real_5/2) = 0 &
% 16.02/3.16    real_$is_rat(real_5000) = 0 & real_$is_rat(real_0) = 0 &
% 16.02/3.16    real_$floor(real_12500) = real_12500 & real_$floor(real_12000) = real_12000 &
% 16.02/3.16    real_$floor(real_5000) = real_5000 & real_$floor(real_0) = real_0 &
% 16.02/3.16    real_$ceiling(real_12500) = real_12500 & real_$ceiling(real_12000) =
% 16.02/3.16    real_12000 & real_$ceiling(real_5000) = real_5000 & real_$ceiling(real_0) =
% 16.02/3.16    real_0 & real_$truncate(real_12500) = real_12500 & real_$truncate(real_12000)
% 16.02/3.16    = real_12000 & real_$truncate(real_5000) = real_5000 & real_$truncate(real_0)
% 16.02/3.16    = real_0 & real_$round(real_12500) = real_12500 & real_$round(real_12000) =
% 16.02/3.16    real_12000 & real_$round(real_5000) = real_5000 & real_$round(real_0) = real_0
% 16.02/3.16    & real_$to_int(real_12500) = 12500 & real_$to_int(real_12000) = 12000 &
% 16.02/3.16    real_$to_int(real_5/2) = 2 & real_$to_int(real_5000) = 5000 &
% 16.02/3.16    real_$to_int(real_0) = 0 & real_$to_rat(real_12500) = rat_12500 &
% 16.02/3.16    real_$to_rat(real_12000) = rat_12000 & real_$to_rat(real_5/2) = rat_5/2 &
% 16.02/3.16    real_$to_rat(real_5000) = rat_5000 & real_$to_rat(real_0) = rat_0 &
% 16.02/3.16    real_$to_real(real_12500) = real_12500 & real_$to_real(real_12000) =
% 16.02/3.16    real_12000 & real_$to_real(real_5/2) = real_5/2 & real_$to_real(real_5000) =
% 16.02/3.16    real_5000 & real_$to_real(real_0) = real_0 & int_$to_real(12500) = real_12500
% 16.02/3.16    & int_$to_real(12000) = real_12000 & int_$to_real(5000) = real_5000 &
% 16.02/3.16    int_$to_real(0) = real_0 & real_$quotient(real_12500, real_5/2) = real_5000 &
% 16.02/3.16    real_$quotient(real_12500, real_5000) = real_5/2 & real_$quotient(real_0,
% 16.02/3.16      real_12500) = real_0 & real_$quotient(real_0, real_12000) = real_0 &
% 16.02/3.16    real_$quotient(real_0, real_5/2) = real_0 & real_$quotient(real_0, real_5000)
% 16.02/3.16    = real_0 & real_$product(real_12500, real_0) = real_0 &
% 16.02/3.16    real_$product(real_12000, real_0) = real_0 & real_$product(real_5/2,
% 16.02/3.16      real_5000) = real_12500 & real_$product(real_5/2, real_0) = real_0 &
% 16.02/3.16    real_$product(real_5000, real_5/2) = real_12500 & real_$product(real_5000,
% 16.02/3.16      real_0) = real_0 & real_$product(real_0, real_12500) = real_0 &
% 16.02/3.16    real_$product(real_0, real_12000) = real_0 & real_$product(real_0, real_5/2) =
% 16.02/3.16    real_0 & real_$product(real_0, real_5000) = real_0 & real_$product(real_0,
% 16.02/3.17      real_0) = real_0 & real_$difference(real_12500, real_12500) = real_0 &
% 16.02/3.17    real_$difference(real_12500, real_0) = real_12500 &
% 16.02/3.17    real_$difference(real_12000, real_12000) = real_0 &
% 16.02/3.17    real_$difference(real_12000, real_0) = real_12000 & real_$difference(real_5/2,
% 16.02/3.17      real_5/2) = real_0 & real_$difference(real_5/2, real_0) = real_5/2 &
% 16.02/3.17    real_$difference(real_5000, real_5000) = real_0 & real_$difference(real_5000,
% 16.02/3.17      real_0) = real_5000 & real_$difference(real_0, real_0) = real_0 &
% 16.02/3.17    real_$uminus(real_0) = real_0 & real_$sum(real_12500, real_0) = real_12500 &
% 16.02/3.17    real_$sum(real_12000, real_0) = real_12000 & real_$sum(real_5/2, real_0) =
% 16.02/3.17    real_5/2 & real_$sum(real_5000, real_0) = real_5000 & real_$sum(real_0,
% 16.02/3.17      real_12500) = real_12500 & real_$sum(real_0, real_12000) = real_12000 &
% 16.02/3.17    real_$sum(real_0, real_5/2) = real_5/2 & real_$sum(real_0, real_5000) =
% 16.02/3.17    real_5000 & real_$sum(real_0, real_0) = real_0 &
% 16.02/3.17    real_$greatereq(real_very_small, real_very_large) = 1 &
% 16.02/3.17    real_$greatereq(real_12500, real_12500) = 0 & real_$greatereq(real_12500,
% 16.02/3.17      real_12000) = 0 & real_$greatereq(real_12500, real_5/2) = 0 &
% 16.02/3.17    real_$greatereq(real_12500, real_5000) = 0 & real_$greatereq(real_12500,
% 16.02/3.17      real_0) = 0 & real_$greatereq(real_12000, real_12500) = 1 &
% 16.02/3.17    real_$greatereq(real_12000, real_12000) = 0 & real_$greatereq(real_12000,
% 16.02/3.17      real_5/2) = 0 & real_$greatereq(real_12000, real_5000) = 0 &
% 16.02/3.17    real_$greatereq(real_12000, real_0) = 0 & real_$greatereq(real_5/2,
% 16.02/3.17      real_12500) = 1 & real_$greatereq(real_5/2, real_12000) = 1 &
% 16.02/3.17    real_$greatereq(real_5/2, real_5/2) = 0 & real_$greatereq(real_5/2, real_5000)
% 16.02/3.17    = 1 & real_$greatereq(real_5/2, real_0) = 0 & real_$greatereq(real_5000,
% 16.02/3.17      real_12500) = 1 & real_$greatereq(real_5000, real_12000) = 1 &
% 16.02/3.17    real_$greatereq(real_5000, real_5/2) = 0 & real_$greatereq(real_5000,
% 16.02/3.17      real_5000) = 0 & real_$greatereq(real_5000, real_0) = 0 &
% 16.02/3.17    real_$greatereq(real_0, real_12500) = 1 & real_$greatereq(real_0, real_12000)
% 16.02/3.17    = 1 & real_$greatereq(real_0, real_5/2) = 1 & real_$greatereq(real_0,
% 16.02/3.17      real_5000) = 1 & real_$greatereq(real_0, real_0) = 0 &
% 16.02/3.17    real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_12500,
% 16.02/3.17      real_12500) = 0 & real_$lesseq(real_12500, real_12000) = 1 &
% 16.02/3.17    real_$lesseq(real_12500, real_5/2) = 1 & real_$lesseq(real_12500, real_5000) =
% 16.02/3.17    1 & real_$lesseq(real_12500, real_0) = 1 & real_$lesseq(real_12000,
% 16.02/3.17      real_12500) = 0 & real_$lesseq(real_12000, real_12000) = 0 &
% 16.02/3.17    real_$lesseq(real_12000, real_5/2) = 1 & real_$lesseq(real_12000, real_5000) =
% 16.02/3.17    1 & real_$lesseq(real_12000, real_0) = 1 & real_$lesseq(real_5/2, real_12500)
% 16.02/3.17    = 0 & real_$lesseq(real_5/2, real_12000) = 0 & real_$lesseq(real_5/2,
% 16.02/3.17      real_5/2) = 0 & real_$lesseq(real_5/2, real_5000) = 0 &
% 16.02/3.17    real_$lesseq(real_5/2, real_0) = 1 & real_$lesseq(real_5000, real_12500) = 0 &
% 16.02/3.17    real_$lesseq(real_5000, real_12000) = 0 & real_$lesseq(real_5000, real_5/2) =
% 16.02/3.17    1 & real_$lesseq(real_5000, real_5000) = 0 & real_$lesseq(real_5000, real_0) =
% 16.02/3.17    1 & real_$lesseq(real_0, real_12500) = 0 & real_$lesseq(real_0, real_12000) =
% 16.02/3.17    0 & real_$lesseq(real_0, real_5/2) = 0 & real_$lesseq(real_0, real_5000) = 0 &
% 16.02/3.17    real_$lesseq(real_0, real_0) = 0 & real_$greater(real_very_large, real_12500)
% 16.02/3.17    = 0 & real_$greater(real_very_large, real_12000) = 0 &
% 16.02/3.17    real_$greater(real_very_large, real_5/2) = 0 & real_$greater(real_very_large,
% 16.02/3.17      real_5000) = 0 & real_$greater(real_very_large, real_0) = 0 &
% 16.02/3.17    real_$greater(real_very_small, real_very_large) = 1 &
% 16.02/3.17    real_$greater(real_12500, real_very_small) = 0 & real_$greater(real_12500,
% 16.02/3.17      real_12500) = 1 & real_$greater(real_12500, real_12000) = 0 &
% 16.02/3.17    real_$greater(real_12500, real_5/2) = 0 & real_$greater(real_12500, real_5000)
% 16.02/3.17    = 0 & real_$greater(real_12500, real_0) = 0 & real_$greater(real_12000,
% 16.02/3.17      real_very_small) = 0 & real_$greater(real_12000, real_12500) = 1 &
% 16.02/3.17    real_$greater(real_12000, real_12000) = 1 & real_$greater(real_12000,
% 16.02/3.17      real_5/2) = 0 & real_$greater(real_12000, real_5000) = 0 &
% 16.02/3.17    real_$greater(real_12000, real_0) = 0 & real_$greater(real_5/2,
% 16.02/3.17      real_very_small) = 0 & real_$greater(real_5/2, real_12500) = 1 &
% 16.02/3.17    real_$greater(real_5/2, real_12000) = 1 & real_$greater(real_5/2, real_5/2) =
% 16.02/3.17    1 & real_$greater(real_5/2, real_5000) = 1 & real_$greater(real_5/2, real_0) =
% 16.02/3.17    0 & real_$greater(real_5000, real_very_small) = 0 & real_$greater(real_5000,
% 16.02/3.17      real_12500) = 1 & real_$greater(real_5000, real_12000) = 1 &
% 16.02/3.17    real_$greater(real_5000, real_5/2) = 0 & real_$greater(real_5000, real_5000) =
% 16.02/3.17    1 & real_$greater(real_5000, real_0) = 0 & real_$greater(real_0,
% 16.02/3.17      real_very_small) = 0 & real_$greater(real_0, real_12500) = 1 &
% 16.02/3.17    real_$greater(real_0, real_12000) = 1 & real_$greater(real_0, real_5/2) = 1 &
% 16.02/3.17    real_$greater(real_0, real_5000) = 1 & real_$greater(real_0, real_0) = 1 &
% 16.02/3.18    real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small,
% 16.02/3.18      real_12500) = 0 & real_$less(real_very_small, real_12000) = 0 &
% 16.02/3.18    real_$less(real_very_small, real_5/2) = 0 & real_$less(real_very_small,
% 16.02/3.18      real_5000) = 0 & real_$less(real_very_small, real_0) = 0 &
% 16.02/3.18    real_$less(real_12500, real_very_large) = 0 & real_$less(real_12500,
% 16.02/3.18      real_12500) = 1 & real_$less(real_12500, real_12000) = 1 &
% 16.02/3.18    real_$less(real_12500, real_5/2) = 1 & real_$less(real_12500, real_5000) = 1 &
% 16.02/3.18    real_$less(real_12500, real_0) = 1 & real_$less(real_12000, real_very_large) =
% 16.02/3.18    0 & real_$less(real_12000, real_12500) = 0 & real_$less(real_12000,
% 16.02/3.18      real_12000) = 1 & real_$less(real_12000, real_5/2) = 1 &
% 16.02/3.18    real_$less(real_12000, real_5000) = 1 & real_$less(real_12000, real_0) = 1 &
% 16.02/3.18    real_$less(real_5/2, real_very_large) = 0 & real_$less(real_5/2, real_12500) =
% 16.02/3.18    0 & real_$less(real_5/2, real_12000) = 0 & real_$less(real_5/2, real_5/2) = 1
% 16.02/3.18    & real_$less(real_5/2, real_5000) = 0 & real_$less(real_5/2, real_0) = 1 &
% 16.02/3.18    real_$less(real_5000, real_very_large) = 0 & real_$less(real_5000, real_12500)
% 16.02/3.18    = 0 & real_$less(real_5000, real_12000) = 0 & real_$less(real_5000, real_5/2)
% 16.02/3.18    = 1 & real_$less(real_5000, real_5000) = 1 & real_$less(real_5000, real_0) = 1
% 16.02/3.18    & real_$less(real_0, real_very_large) = 0 & real_$less(real_0, real_12500) = 0
% 16.02/3.18    & real_$less(real_0, real_12000) = 0 & real_$less(real_0, real_5/2) = 0 &
% 16.02/3.18    real_$less(real_0, real_5000) = 0 & real_$less(real_0, real_0) = 1 &  ! [v0:
% 16.02/3.18      $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] :  ! [v4: $real] :
% 16.02/3.18    ( ~ (real_$sum(v3, v0) = v4) |  ~ (real_$sum(v2, v1) = v3) |  ? [v5: $real] :
% 16.02/3.18      (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) &  ! [v0: $real] :  !
% 16.02/3.18    [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v3 = v1 | v0 = real_0 |  ~
% 16.02/3.18      (real_$quotient(v2, v0) = v3) |  ~ (real_$product(v1, v0) = v2)) &  ! [v0:
% 16.02/3.18      $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: int] : (v3 = 0 |  ~
% 16.02/3.18      (real_$lesseq(v2, v0) = v3) |  ~ (real_$lesseq(v1, v0) = 0) |  ? [v4: int] :
% 16.02/3.18      ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) &  ! [v0: $real] :  ! [v1: $real]
% 16.02/3.18    :  ! [v2: $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$lesseq(v1, v0) = 0) |  ~
% 16.02/3.18      (real_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2, v1)
% 16.02/3.18        = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real]
% 16.02/3.18    : ( ~ (real_$uminus(v0) = v2) |  ~ (real_$sum(v1, v2) = v3) |
% 16.02/3.18      real_$difference(v1, v0) = v3) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 16.02/3.18      $real] : (v2 = real_0 |  ~ (real_$uminus(v0) = v1) |  ~ (real_$sum(v0, v1) =
% 16.02/3.18        v2)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: int] : (v2 = 0 |  ~
% 16.02/3.18      (real_$greatereq(v0, v1) = v2) |  ? [v3: int] : ( ~ (v3 = 0) &
% 16.02/3.18        real_$lesseq(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 16.02/3.18      int] : (v2 = 0 |  ~ (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) &  ? [v3:
% 16.02/3.18          int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) &  ! [v0: $real] :  !
% 16.02/3.18    [v1: $real] :  ! [v2: int] : (v2 = 0 |  ~ (real_$greater(v0, v1) = v2) |  ?
% 16.15/3.18      [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) &  ! [v0: $real] :  !
% 16.15/3.18    [v1: $real] :  ! [v2: $real] : ( ~ (real_$product(v0, v1) = v2) |
% 16.15/3.18      real_$product(v1, v0) = v2) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 16.15/3.18      $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) &  ! [v0:
% 16.15/3.18      $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) | 
% 16.15/3.18      ~ (real_$less(v1, v0) = 0) | real_$less(v2, v0) = 0) &  ! [v0: $real] :  !
% 16.15/3.18    [v1: $real] : (v1 = v0 |  ~ (real_$sum(v0, real_0) = v1)) &  ! [v0: $real] : 
% 16.15/3.18    ! [v1: $real] : (v1 = v0 |  ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0)
% 16.15/3.18      = 0) &  ! [v0: $real] :  ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) |
% 16.15/3.18      real_$uminus(v1) = v0) &  ! [v0: $real] :  ! [v1: $real] : ( ~
% 16.15/3.18      (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) &  ! [v0: $real] :
% 16.15/3.18     ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & 
% 16.15/3.18    ! [v0: $real] : (v0 = real_0 |  ~ (real_$uminus(v0) = v0))
% 16.15/3.18  
% 16.15/3.18  Those formulas are unsatisfiable:
% 16.15/3.18  ---------------------------------
% 16.15/3.18  
% 16.15/3.18  Begin of proof
% 16.15/3.19  | 
% 16.15/3.19  | ALPHA: (input) implies:
% 16.15/3.19  |   (1)   ~ (real_12500 = real_12000)
% 16.15/3.19  | 
% 16.15/3.19  | REDUCE: (1), (real_product_problem_11) imply:
% 16.15/3.19  |   (2)  $false
% 16.15/3.19  | 
% 16.15/3.19  | CLOSE: (2) is inconsistent.
% 16.15/3.19  | 
% 16.15/3.19  End of proof
% 16.15/3.19  % SZS output end Proof for theBenchmark
% 16.15/3.19  
% 16.15/3.19  2582ms
%------------------------------------------------------------------------------