TSTP Solution File: ARI295_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI295_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 : n019.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 17:47:36 EDT 2023

% Result   : Theorem 6.28s 1.64s
% Output   : Proof 16.37s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : ARI295_1 : TPTP v8.1.2. Released v5.0.0.
% 0.08/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n019.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
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue Aug 29 18:22:43 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.54/0.66  ________       _____
% 0.54/0.66  ___  __ \_________(_)________________________________
% 0.54/0.66  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.54/0.66  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.54/0.66  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.54/0.66  
% 0.54/0.66  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.54/0.66  (2023-06-19)
% 0.54/0.66  
% 0.54/0.66  (c) Philipp Rümmer, 2009-2023
% 0.54/0.66  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.54/0.66                Amanda Stjerna.
% 0.54/0.66  Free software under BSD-3-Clause.
% 0.54/0.66  
% 0.54/0.66  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.54/0.66  
% 0.54/0.66  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.54/0.68  Running up to 7 provers in parallel.
% 0.54/0.70  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.54/0.70  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.54/0.70  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.54/0.70  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.54/0.70  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.54/0.70  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.54/0.70  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.72/0.97  Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.72/0.97  Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.72/0.97  Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.72/0.97  Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.72/0.97  Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.72/0.97  Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.72/0.97  Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.11/1.05  Prover 4: Preprocessing ...
% 2.49/1.06  Prover 1: Preprocessing ...
% 2.49/1.11  Prover 6: Preprocessing ...
% 2.49/1.11  Prover 0: Preprocessing ...
% 5.18/1.49  Prover 5: Preprocessing ...
% 5.43/1.50  Prover 2: Preprocessing ...
% 5.43/1.52  Prover 3: Preprocessing ...
% 5.76/1.59  Prover 6: Constructing countermodel ...
% 6.28/1.62  Prover 0: Constructing countermodel ...
% 6.28/1.64  Prover 0: proved (954ms)
% 6.28/1.64  
% 6.28/1.64  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.28/1.64  
% 6.28/1.64  Prover 6: proved (944ms)
% 6.28/1.64  
% 6.28/1.64  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.28/1.64  
% 6.28/1.65  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.28/1.65  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.28/1.65  Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.73/1.67  Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.73/1.68  Prover 8: Preprocessing ...
% 6.73/1.71  Prover 1: Constructing countermodel ...
% 7.70/1.79  Prover 4: Constructing countermodel ...
% 7.70/1.82  Prover 7: Preprocessing ...
% 7.70/1.84  Prover 1: Found proof (size 3)
% 7.70/1.84  Prover 1: proved (1160ms)
% 7.70/1.87  Prover 4: stopped
% 8.44/1.96  Prover 8: Warning: ignoring some quantifiers
% 8.97/1.97  Prover 8: Constructing countermodel ...
% 8.97/1.99  Prover 8: stopped
% 10.99/2.25  Prover 2: stopped
% 11.42/2.36  Prover 7: stopped
% 15.09/2.99  Prover 5: Constructing countermodel ...
% 15.09/2.99  Prover 5: stopped
% 15.47/3.17  Prover 3: Constructing countermodel ...
% 15.47/3.17  Prover 3: stopped
% 15.47/3.17  
% 15.47/3.17  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.47/3.17  
% 15.97/3.18  % SZS output start Proof for theBenchmark
% 15.97/3.18  Assumptions after simplification:
% 15.97/3.18  ---------------------------------
% 15.97/3.18  
% 15.97/3.18    (rat_product_problem_12)
% 15.97/3.19    rat_35/64 = rat_9/16
% 15.97/3.19  
% 15.97/3.19    (input)
% 16.37/3.27     ~ (rat_very_large = rat_very_small) &  ~ (rat_very_large = rat_35/64) &  ~
% 16.37/3.27    (rat_very_large = rat_9/16) &  ~ (rat_very_large = rat_7/8) &  ~
% 16.37/3.27    (rat_very_large = rat_5/8) &  ~ (rat_very_large = rat_0) &  ~ (rat_very_small
% 16.37/3.27      = rat_35/64) &  ~ (rat_very_small = rat_9/16) &  ~ (rat_very_small =
% 16.37/3.27      rat_7/8) &  ~ (rat_very_small = rat_5/8) &  ~ (rat_very_small = rat_0) &  ~
% 16.37/3.27    (rat_35/64 = rat_9/16) &  ~ (rat_35/64 = rat_7/8) &  ~ (rat_35/64 = rat_5/8) &
% 16.37/3.27     ~ (rat_35/64 = rat_0) &  ~ (rat_9/16 = rat_7/8) &  ~ (rat_9/16 = rat_5/8) & 
% 16.37/3.27    ~ (rat_9/16 = rat_0) &  ~ (rat_7/8 = rat_5/8) &  ~ (rat_7/8 = rat_0) &  ~
% 16.37/3.27    (rat_5/8 = rat_0) & rat_$is_int(rat_35/64) = 1 & rat_$is_int(rat_9/16) = 1 &
% 16.37/3.27    rat_$is_int(rat_7/8) = 1 & rat_$is_int(rat_5/8) = 1 & rat_$is_int(rat_0) = 0 &
% 16.37/3.27    rat_$is_rat(rat_35/64) = 0 & rat_$is_rat(rat_9/16) = 0 & rat_$is_rat(rat_7/8)
% 16.37/3.27    = 0 & rat_$is_rat(rat_5/8) = 0 & rat_$is_rat(rat_0) = 0 &
% 16.37/3.27    rat_$floor(rat_35/64) = rat_0 & rat_$floor(rat_9/16) = rat_0 &
% 16.37/3.27    rat_$floor(rat_7/8) = rat_0 & rat_$floor(rat_5/8) = rat_0 & rat_$floor(rat_0)
% 16.37/3.27    = rat_0 & rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_35/64) = rat_0 &
% 16.37/3.27    rat_$truncate(rat_9/16) = rat_0 & rat_$truncate(rat_7/8) = rat_0 &
% 16.37/3.27    rat_$truncate(rat_5/8) = rat_0 & rat_$truncate(rat_0) = rat_0 &
% 16.37/3.27    rat_$round(rat_0) = rat_0 & rat_$to_int(rat_35/64) = 0 & rat_$to_int(rat_9/16)
% 16.37/3.27    = 0 & rat_$to_int(rat_7/8) = 0 & rat_$to_int(rat_5/8) = 0 & rat_$to_int(rat_0)
% 16.37/3.27    = 0 & rat_$to_rat(rat_35/64) = rat_35/64 & rat_$to_rat(rat_9/16) = rat_9/16 &
% 16.37/3.27    rat_$to_rat(rat_7/8) = rat_7/8 & rat_$to_rat(rat_5/8) = rat_5/8 &
% 16.37/3.27    rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_35/64) = real_35/64 &
% 16.37/3.27    rat_$to_real(rat_9/16) = real_9/16 & rat_$to_real(rat_7/8) = real_7/8 &
% 16.37/3.27    rat_$to_real(rat_5/8) = real_5/8 & rat_$to_real(rat_0) = real_0 &
% 16.37/3.27    int_$to_rat(0) = rat_0 & rat_$quotient(rat_35/64, rat_7/8) = rat_5/8 &
% 16.37/3.27    rat_$quotient(rat_35/64, rat_5/8) = rat_7/8 & rat_$quotient(rat_0, rat_35/64)
% 16.37/3.27    = rat_0 & rat_$quotient(rat_0, rat_9/16) = rat_0 & rat_$quotient(rat_0,
% 16.37/3.27      rat_7/8) = rat_0 & rat_$quotient(rat_0, rat_5/8) = rat_0 &
% 16.37/3.27    rat_$product(rat_35/64, rat_0) = rat_0 & rat_$product(rat_9/16, rat_0) = rat_0
% 16.37/3.27    & rat_$product(rat_7/8, rat_5/8) = rat_35/64 & rat_$product(rat_7/8, rat_0) =
% 16.37/3.28    rat_0 & rat_$product(rat_5/8, rat_7/8) = rat_35/64 & rat_$product(rat_5/8,
% 16.37/3.28      rat_0) = rat_0 & rat_$product(rat_0, rat_35/64) = rat_0 &
% 16.37/3.28    rat_$product(rat_0, rat_9/16) = rat_0 & rat_$product(rat_0, rat_7/8) = rat_0 &
% 16.37/3.28    rat_$product(rat_0, rat_5/8) = rat_0 & rat_$product(rat_0, rat_0) = rat_0 &
% 16.37/3.28    rat_$difference(rat_35/64, rat_35/64) = rat_0 & rat_$difference(rat_35/64,
% 16.37/3.28      rat_0) = rat_35/64 & rat_$difference(rat_9/16, rat_9/16) = rat_0 &
% 16.37/3.28    rat_$difference(rat_9/16, rat_0) = rat_9/16 & rat_$difference(rat_7/8,
% 16.37/3.28      rat_7/8) = rat_0 & rat_$difference(rat_7/8, rat_0) = rat_7/8 &
% 16.37/3.28    rat_$difference(rat_5/8, rat_5/8) = rat_0 & rat_$difference(rat_5/8, rat_0) =
% 16.37/3.28    rat_5/8 & rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 &
% 16.37/3.28    rat_$sum(rat_35/64, rat_0) = rat_35/64 & rat_$sum(rat_9/16, rat_0) = rat_9/16
% 16.37/3.28    & rat_$sum(rat_7/8, rat_0) = rat_7/8 & rat_$sum(rat_5/8, rat_0) = rat_5/8 &
% 16.37/3.28    rat_$sum(rat_0, rat_35/64) = rat_35/64 & rat_$sum(rat_0, rat_9/16) = rat_9/16
% 16.37/3.28    & rat_$sum(rat_0, rat_7/8) = rat_7/8 & rat_$sum(rat_0, rat_5/8) = rat_5/8 &
% 16.37/3.28    rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small,
% 16.37/3.28      rat_very_large) = 1 & rat_$greatereq(rat_35/64, rat_35/64) = 0 &
% 16.37/3.28    rat_$greatereq(rat_35/64, rat_9/16) = 1 & rat_$greatereq(rat_35/64, rat_7/8) =
% 16.37/3.28    1 & rat_$greatereq(rat_35/64, rat_5/8) = 1 & rat_$greatereq(rat_35/64, rat_0)
% 16.37/3.28    = 0 & rat_$greatereq(rat_9/16, rat_35/64) = 0 & rat_$greatereq(rat_9/16,
% 16.37/3.28      rat_9/16) = 0 & rat_$greatereq(rat_9/16, rat_7/8) = 1 &
% 16.37/3.28    rat_$greatereq(rat_9/16, rat_5/8) = 1 & rat_$greatereq(rat_9/16, rat_0) = 0 &
% 16.37/3.28    rat_$greatereq(rat_7/8, rat_35/64) = 0 & rat_$greatereq(rat_7/8, rat_9/16) = 0
% 16.37/3.28    & rat_$greatereq(rat_7/8, rat_7/8) = 0 & rat_$greatereq(rat_7/8, rat_5/8) = 0
% 16.37/3.28    & rat_$greatereq(rat_7/8, rat_0) = 0 & rat_$greatereq(rat_5/8, rat_35/64) = 0
% 16.37/3.28    & rat_$greatereq(rat_5/8, rat_9/16) = 0 & rat_$greatereq(rat_5/8, rat_7/8) = 1
% 16.37/3.28    & rat_$greatereq(rat_5/8, rat_5/8) = 0 & rat_$greatereq(rat_5/8, rat_0) = 0 &
% 16.37/3.28    rat_$greatereq(rat_0, rat_35/64) = 1 & rat_$greatereq(rat_0, rat_9/16) = 1 &
% 16.37/3.28    rat_$greatereq(rat_0, rat_7/8) = 1 & rat_$greatereq(rat_0, rat_5/8) = 1 &
% 16.37/3.28    rat_$greatereq(rat_0, rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large)
% 16.37/3.28    = 0 & rat_$lesseq(rat_35/64, rat_35/64) = 0 & rat_$lesseq(rat_35/64, rat_9/16)
% 16.37/3.28    = 0 & rat_$lesseq(rat_35/64, rat_7/8) = 0 & rat_$lesseq(rat_35/64, rat_5/8) =
% 16.37/3.28    0 & rat_$lesseq(rat_35/64, rat_0) = 1 & rat_$lesseq(rat_9/16, rat_35/64) = 1 &
% 16.37/3.28    rat_$lesseq(rat_9/16, rat_9/16) = 0 & rat_$lesseq(rat_9/16, rat_7/8) = 0 &
% 16.37/3.28    rat_$lesseq(rat_9/16, rat_5/8) = 0 & rat_$lesseq(rat_9/16, rat_0) = 1 &
% 16.37/3.28    rat_$lesseq(rat_7/8, rat_35/64) = 1 & rat_$lesseq(rat_7/8, rat_9/16) = 1 &
% 16.37/3.28    rat_$lesseq(rat_7/8, rat_7/8) = 0 & rat_$lesseq(rat_7/8, rat_5/8) = 1 &
% 16.37/3.28    rat_$lesseq(rat_7/8, rat_0) = 1 & rat_$lesseq(rat_5/8, rat_35/64) = 1 &
% 16.37/3.28    rat_$lesseq(rat_5/8, rat_9/16) = 1 & rat_$lesseq(rat_5/8, rat_7/8) = 0 &
% 16.37/3.28    rat_$lesseq(rat_5/8, rat_5/8) = 0 & rat_$lesseq(rat_5/8, rat_0) = 1 &
% 16.37/3.28    rat_$lesseq(rat_0, rat_35/64) = 0 & rat_$lesseq(rat_0, rat_9/16) = 0 &
% 16.37/3.28    rat_$lesseq(rat_0, rat_7/8) = 0 & rat_$lesseq(rat_0, rat_5/8) = 0 &
% 16.37/3.28    rat_$lesseq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, rat_35/64) = 0 &
% 16.37/3.28    rat_$greater(rat_very_large, rat_9/16) = 0 & rat_$greater(rat_very_large,
% 16.37/3.28      rat_7/8) = 0 & rat_$greater(rat_very_large, rat_5/8) = 0 &
% 16.37/3.28    rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small,
% 16.37/3.28      rat_very_large) = 1 & rat_$greater(rat_35/64, rat_very_small) = 0 &
% 16.37/3.28    rat_$greater(rat_35/64, rat_35/64) = 1 & rat_$greater(rat_35/64, rat_9/16) = 1
% 16.37/3.28    & rat_$greater(rat_35/64, rat_7/8) = 1 & rat_$greater(rat_35/64, rat_5/8) = 1
% 16.37/3.28    & rat_$greater(rat_35/64, rat_0) = 0 & rat_$greater(rat_9/16, rat_very_small)
% 16.37/3.28    = 0 & rat_$greater(rat_9/16, rat_35/64) = 0 & rat_$greater(rat_9/16, rat_9/16)
% 16.37/3.28    = 1 & rat_$greater(rat_9/16, rat_7/8) = 1 & rat_$greater(rat_9/16, rat_5/8) =
% 16.37/3.28    1 & rat_$greater(rat_9/16, rat_0) = 0 & rat_$greater(rat_7/8, rat_very_small)
% 16.37/3.28    = 0 & rat_$greater(rat_7/8, rat_35/64) = 0 & rat_$greater(rat_7/8, rat_9/16) =
% 16.37/3.28    0 & rat_$greater(rat_7/8, rat_7/8) = 1 & rat_$greater(rat_7/8, rat_5/8) = 0 &
% 16.37/3.28    rat_$greater(rat_7/8, rat_0) = 0 & rat_$greater(rat_5/8, rat_very_small) = 0 &
% 16.37/3.28    rat_$greater(rat_5/8, rat_35/64) = 0 & rat_$greater(rat_5/8, rat_9/16) = 0 &
% 16.37/3.28    rat_$greater(rat_5/8, rat_7/8) = 1 & rat_$greater(rat_5/8, rat_5/8) = 1 &
% 16.37/3.28    rat_$greater(rat_5/8, rat_0) = 0 & rat_$greater(rat_0, rat_very_small) = 0 &
% 16.37/3.28    rat_$greater(rat_0, rat_35/64) = 1 & rat_$greater(rat_0, rat_9/16) = 1 &
% 16.37/3.28    rat_$greater(rat_0, rat_7/8) = 1 & rat_$greater(rat_0, rat_5/8) = 1 &
% 16.37/3.28    rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0
% 16.37/3.28    & rat_$less(rat_very_small, rat_35/64) = 0 & rat_$less(rat_very_small,
% 16.37/3.28      rat_9/16) = 0 & rat_$less(rat_very_small, rat_7/8) = 0 &
% 16.37/3.28    rat_$less(rat_very_small, rat_5/8) = 0 & rat_$less(rat_very_small, rat_0) = 0
% 16.37/3.28    & rat_$less(rat_35/64, rat_very_large) = 0 & rat_$less(rat_35/64, rat_35/64) =
% 16.37/3.28    1 & rat_$less(rat_35/64, rat_9/16) = 0 & rat_$less(rat_35/64, rat_7/8) = 0 &
% 16.37/3.28    rat_$less(rat_35/64, rat_5/8) = 0 & rat_$less(rat_35/64, rat_0) = 1 &
% 16.37/3.28    rat_$less(rat_9/16, rat_very_large) = 0 & rat_$less(rat_9/16, rat_35/64) = 1 &
% 16.37/3.28    rat_$less(rat_9/16, rat_9/16) = 1 & rat_$less(rat_9/16, rat_7/8) = 0 &
% 16.37/3.28    rat_$less(rat_9/16, rat_5/8) = 0 & rat_$less(rat_9/16, rat_0) = 1 &
% 16.37/3.28    rat_$less(rat_7/8, rat_very_large) = 0 & rat_$less(rat_7/8, rat_35/64) = 1 &
% 16.37/3.28    rat_$less(rat_7/8, rat_9/16) = 1 & rat_$less(rat_7/8, rat_7/8) = 1 &
% 16.37/3.28    rat_$less(rat_7/8, rat_5/8) = 1 & rat_$less(rat_7/8, rat_0) = 1 &
% 16.37/3.28    rat_$less(rat_5/8, rat_very_large) = 0 & rat_$less(rat_5/8, rat_35/64) = 1 &
% 16.37/3.28    rat_$less(rat_5/8, rat_9/16) = 1 & rat_$less(rat_5/8, rat_7/8) = 0 &
% 16.37/3.28    rat_$less(rat_5/8, rat_5/8) = 1 & rat_$less(rat_5/8, rat_0) = 1 &
% 16.37/3.28    rat_$less(rat_0, rat_very_large) = 0 & rat_$less(rat_0, rat_35/64) = 0 &
% 16.37/3.28    rat_$less(rat_0, rat_9/16) = 0 & rat_$less(rat_0, rat_7/8) = 0 &
% 16.37/3.28    rat_$less(rat_0, rat_5/8) = 0 & rat_$less(rat_0, rat_0) = 1 &  ! [v0: $rat] : 
% 16.37/3.28    ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: $rat] :  ! [v4: $rat] : ( ~
% 16.37/3.28      (rat_$sum(v3, v0) = v4) |  ~ (rat_$sum(v2, v1) = v3) |  ? [v5: $rat] :
% 16.37/3.28      (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) &  ! [v0: $rat] :  ! [v1:
% 16.37/3.28      $rat] :  ! [v2: $rat] :  ! [v3: $rat] : (v3 = v1 | v0 = rat_0 |  ~
% 16.37/3.28      (rat_$quotient(v2, v0) = v3) |  ~ (rat_$product(v1, v0) = v2)) &  ! [v0:
% 16.37/3.28      $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: int] : (v3 = 0 |  ~
% 16.37/3.28      (rat_$lesseq(v2, v0) = v3) |  ~ (rat_$lesseq(v1, v0) = 0) |  ? [v4: int] : (
% 16.37/3.28        ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) &  ! [v0: $rat] :  ! [v1: $rat] : 
% 16.37/3.28    ! [v2: $rat] :  ! [v3: int] : (v3 = 0 |  ~ (rat_$lesseq(v1, v0) = 0) |  ~
% 16.37/3.28      (rat_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) =
% 16.37/3.28        v4)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: $rat] : ( ~
% 16.37/3.28      (rat_$uminus(v0) = v2) |  ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1,
% 16.37/3.28        v0) = v3) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] : (v2 = rat_0 | 
% 16.37/3.28      ~ (rat_$uminus(v0) = v1) |  ~ (rat_$sum(v0, v1) = v2)) &  ! [v0: $rat] :  !
% 16.37/3.28    [v1: $rat] :  ! [v2: int] : (v2 = 0 |  ~ (rat_$greatereq(v0, v1) = v2) |  ?
% 16.37/3.28      [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) &  ! [v0: $rat] :  !
% 16.37/3.28    [v1: $rat] :  ! [v2: int] : (v2 = 0 |  ~ (rat_$lesseq(v1, v0) = v2) | ( ~ (v1
% 16.37/3.28          = v0) &  ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3))) &  !
% 16.37/3.28    [v0: $rat] :  ! [v1: $rat] :  ! [v2: int] : (v2 = 0 |  ~ (rat_$greater(v0, v1)
% 16.37/3.28        = v2) |  ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) &  ! [v0:
% 16.37/3.28      $rat] :  ! [v1: $rat] :  ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) |
% 16.37/3.28      rat_$product(v1, v0) = v2) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :
% 16.37/3.28    ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) &  ! [v0: $rat] :  ! [v1:
% 16.37/3.28      $rat] :  ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) |  ~ (rat_$less(v1,
% 16.37/3.28          v0) = 0) | rat_$less(v2, v0) = 0) &  ! [v0: $rat] :  ! [v1: $rat] : (v1
% 16.37/3.28      = v0 |  ~ (rat_$sum(v0, rat_0) = v1)) &  ! [v0: $rat] :  ! [v1: $rat] : (v1
% 16.37/3.28      = v0 |  ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) &  ! [v0: $rat]
% 16.37/3.28    :  ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) &  ! [v0:
% 16.37/3.28      $rat] :  ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1,
% 16.37/3.28        v0) = 0) &  ! [v0: $rat] :  ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0)
% 16.37/3.28      | rat_$less(v1, v0) = 0) &  ! [v0: $rat] : (v0 = rat_0 |  ~ (rat_$uminus(v0)
% 16.37/3.28        = v0))
% 16.37/3.28  
% 16.37/3.28  Those formulas are unsatisfiable:
% 16.37/3.28  ---------------------------------
% 16.37/3.28  
% 16.37/3.28  Begin of proof
% 16.37/3.28  | 
% 16.37/3.28  | ALPHA: (input) implies:
% 16.37/3.28  |   (1)   ~ (rat_35/64 = rat_9/16)
% 16.37/3.28  | 
% 16.37/3.29  | REDUCE: (1), (rat_product_problem_12) imply:
% 16.37/3.29  |   (2)  $false
% 16.37/3.29  | 
% 16.37/3.29  | CLOSE: (2) is inconsistent.
% 16.37/3.29  | 
% 16.37/3.29  End of proof
% 16.37/3.29  % SZS output end Proof for theBenchmark
% 16.37/3.29  
% 16.37/3.29  2630ms
%------------------------------------------------------------------------------