TSTP Solution File: ARI555_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI555_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 : n008.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 17:48:22 EDT 2023

% Result   : Theorem 7.69s 1.75s
% Output   : Proof 16.65s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ARI555_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n008.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 18:28:47 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.58  ________       _____
% 0.20/0.58  ___  __ \_________(_)________________________________
% 0.20/0.58  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.58  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.58  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.58  
% 0.20/0.58  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.58  (2023-06-19)
% 0.20/0.58  
% 0.20/0.58  (c) Philipp Rümmer, 2009-2023
% 0.20/0.58  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.58                Amanda Stjerna.
% 0.20/0.58  Free software under BSD-3-Clause.
% 0.20/0.58  
% 0.20/0.58  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.58  
% 0.20/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.59  Running up to 7 provers in parallel.
% 0.20/0.61  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.61  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.61  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.61  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.61  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.61  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.61  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.74/0.92  Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.74/0.92  Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.74/0.92  Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.74/0.92  Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.74/0.92  Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.74/0.92  Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.74/0.92  Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.88/1.01  Prover 4: Preprocessing ...
% 1.88/1.01  Prover 1: Preprocessing ...
% 2.54/1.07  Prover 0: Preprocessing ...
% 2.54/1.07  Prover 6: Preprocessing ...
% 3.97/1.31  Prover 5: Preprocessing ...
% 3.97/1.33  Prover 3: Preprocessing ...
% 3.97/1.37  Prover 2: Preprocessing ...
% 7.15/1.72  Prover 1: Constructing countermodel ...
% 7.15/1.72  Prover 6: Constructing countermodel ...
% 7.53/1.75  Prover 6: proved (1141ms)
% 7.53/1.75  
% 7.69/1.75  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.69/1.75  
% 7.69/1.75  Prover 0: Constructing countermodel ...
% 7.69/1.75  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.69/1.75  Prover 0: stopped
% 7.69/1.75  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.69/1.76  Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 7.69/1.76  Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 7.69/1.80  Prover 8: Preprocessing ...
% 7.69/1.81  Prover 4: Constructing countermodel ...
% 8.16/1.86  Prover 7: Preprocessing ...
% 9.12/1.95  Prover 8: Warning: ignoring some quantifiers
% 9.12/1.98  Prover 8: Constructing countermodel ...
% 9.78/2.05  Prover 1: Found proof (size 7)
% 9.78/2.05  Prover 1: proved (1449ms)
% 9.78/2.05  Prover 4: stopped
% 9.78/2.06  Prover 8: stopped
% 9.78/2.12  Prover 2: stopped
% 12.34/2.49  Prover 7: stopped
% 14.04/2.87  Prover 5: Constructing countermodel ...
% 14.04/2.87  Prover 5: stopped
% 15.71/3.19  Prover 3: Constructing countermodel ...
% 15.71/3.19  Prover 3: stopped
% 15.71/3.19  
% 15.71/3.19  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.71/3.19  
% 15.71/3.19  % SZS output start Proof for theBenchmark
% 16.13/3.20  Assumptions after simplification:
% 16.13/3.20  ---------------------------------
% 16.13/3.20  
% 16.13/3.20    (rat_combined_problem_15)
% 16.13/3.24     ? [v0: int] : ( ~ (v0 = 0) & rat_$greatereq(rat_-9/50, rat_-9/50) = v0)
% 16.13/3.24  
% 16.13/3.24    (input)
% 16.65/3.31     ~ (rat_very_large = rat_very_small) &  ~ (rat_very_large = rat_-9/50) &  ~
% 16.65/3.31    (rat_very_large = rat_9/50) &  ~ (rat_very_large = rat_-1/4) &  ~
% 16.65/3.31    (rat_very_large = rat_-18/25) &  ~ (rat_very_large = rat_0) &  ~
% 16.65/3.31    (rat_very_small = rat_-9/50) &  ~ (rat_very_small = rat_9/50) &  ~
% 16.65/3.31    (rat_very_small = rat_-1/4) &  ~ (rat_very_small = rat_-18/25) &  ~
% 16.65/3.31    (rat_very_small = rat_0) &  ~ (rat_-9/50 = rat_9/50) &  ~ (rat_-9/50 =
% 16.65/3.31      rat_-1/4) &  ~ (rat_-9/50 = rat_-18/25) &  ~ (rat_-9/50 = rat_0) &  ~
% 16.65/3.31    (rat_9/50 = rat_-1/4) &  ~ (rat_9/50 = rat_-18/25) &  ~ (rat_9/50 = rat_0) & 
% 16.65/3.31    ~ (rat_-1/4 = rat_-18/25) &  ~ (rat_-1/4 = rat_0) &  ~ (rat_-18/25 = rat_0) &
% 16.65/3.31    rat_$is_int(rat_-9/50) = 1 & rat_$is_int(rat_9/50) = 1 & rat_$is_int(rat_-1/4)
% 16.65/3.31    = 1 & rat_$is_int(rat_-18/25) = 1 & rat_$is_int(rat_0) = 0 &
% 16.65/3.31    rat_$is_rat(rat_-9/50) = 0 & rat_$is_rat(rat_9/50) = 0 & rat_$is_rat(rat_-1/4)
% 16.65/3.31    = 0 & rat_$is_rat(rat_-18/25) = 0 & rat_$is_rat(rat_0) = 0 &
% 16.65/3.31    rat_$floor(rat_9/50) = rat_0 & rat_$floor(rat_0) = rat_0 &
% 16.65/3.31    rat_$ceiling(rat_-9/50) = rat_0 & rat_$ceiling(rat_-1/4) = rat_0 &
% 16.65/3.31    rat_$ceiling(rat_-18/25) = rat_0 & rat_$ceiling(rat_0) = rat_0 &
% 16.65/3.31    rat_$truncate(rat_-9/50) = rat_0 & rat_$truncate(rat_9/50) = rat_0 &
% 16.65/3.31    rat_$truncate(rat_-1/4) = rat_0 & rat_$truncate(rat_-18/25) = rat_0 &
% 16.65/3.31    rat_$truncate(rat_0) = rat_0 & rat_$round(rat_-9/50) = rat_0 &
% 16.65/3.31    rat_$round(rat_9/50) = rat_0 & rat_$round(rat_-1/4) = rat_0 &
% 16.65/3.31    rat_$round(rat_0) = rat_0 & rat_$to_int(rat_-9/50) = -1 &
% 16.65/3.31    rat_$to_int(rat_9/50) = 0 & rat_$to_int(rat_-1/4) = -1 &
% 16.65/3.31    rat_$to_int(rat_-18/25) = -1 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_-9/50)
% 16.65/3.31    = rat_-9/50 & rat_$to_rat(rat_9/50) = rat_9/50 & rat_$to_rat(rat_-1/4) =
% 16.65/3.31    rat_-1/4 & rat_$to_rat(rat_-18/25) = rat_-18/25 & rat_$to_rat(rat_0) = rat_0 &
% 16.65/3.31    rat_$to_real(rat_-9/50) = real_-9/50 & rat_$to_real(rat_9/50) = real_9/50 &
% 16.65/3.31    rat_$to_real(rat_-1/4) = real_-1/4 & rat_$to_real(rat_-18/25) = real_-18/25 &
% 16.65/3.31    rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 &
% 16.65/3.31    rat_$quotient(rat_9/50, rat_-1/4) = rat_-18/25 & rat_$quotient(rat_9/50,
% 16.65/3.31      rat_-18/25) = rat_-1/4 & rat_$quotient(rat_0, rat_-9/50) = rat_0 &
% 16.65/3.31    rat_$quotient(rat_0, rat_9/50) = rat_0 & rat_$quotient(rat_0, rat_-1/4) =
% 16.65/3.31    rat_0 & rat_$quotient(rat_0, rat_-18/25) = rat_0 & rat_$product(rat_-9/50,
% 16.65/3.31      rat_0) = rat_0 & rat_$product(rat_9/50, rat_0) = rat_0 &
% 16.65/3.31    rat_$product(rat_-1/4, rat_-18/25) = rat_9/50 & rat_$product(rat_-1/4, rat_0)
% 16.65/3.31    = rat_0 & rat_$product(rat_-18/25, rat_-1/4) = rat_9/50 &
% 16.65/3.31    rat_$product(rat_-18/25, rat_0) = rat_0 & rat_$product(rat_0, rat_-9/50) =
% 16.65/3.31    rat_0 & rat_$product(rat_0, rat_9/50) = rat_0 & rat_$product(rat_0, rat_-1/4)
% 16.65/3.31    = rat_0 & rat_$product(rat_0, rat_-18/25) = rat_0 & rat_$product(rat_0, rat_0)
% 16.65/3.31    = rat_0 & rat_$difference(rat_-9/50, rat_-9/50) = rat_0 &
% 16.65/3.31    rat_$difference(rat_-9/50, rat_0) = rat_-9/50 & rat_$difference(rat_9/50,
% 16.65/3.31      rat_9/50) = rat_0 & rat_$difference(rat_9/50, rat_0) = rat_9/50 &
% 16.65/3.31    rat_$difference(rat_-1/4, rat_-1/4) = rat_0 & rat_$difference(rat_-1/4, rat_0)
% 16.65/3.31    = rat_-1/4 & rat_$difference(rat_-18/25, rat_-18/25) = rat_0 &
% 16.65/3.31    rat_$difference(rat_-18/25, rat_0) = rat_-18/25 & rat_$difference(rat_0,
% 16.65/3.31      rat_-9/50) = rat_9/50 & rat_$difference(rat_0, rat_9/50) = rat_-9/50 &
% 16.65/3.31    rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_-9/50) = rat_9/50 &
% 16.65/3.31    rat_$uminus(rat_9/50) = rat_-9/50 & rat_$uminus(rat_0) = rat_0 &
% 16.65/3.31    rat_$sum(rat_-9/50, rat_9/50) = rat_0 & rat_$sum(rat_-9/50, rat_0) = rat_-9/50
% 16.65/3.31    & rat_$sum(rat_9/50, rat_-9/50) = rat_0 & rat_$sum(rat_9/50, rat_0) = rat_9/50
% 16.65/3.31    & rat_$sum(rat_-1/4, rat_0) = rat_-1/4 & rat_$sum(rat_-18/25, rat_0) =
% 16.65/3.31    rat_-18/25 & rat_$sum(rat_0, rat_-9/50) = rat_-9/50 & rat_$sum(rat_0,
% 16.65/3.31      rat_9/50) = rat_9/50 & rat_$sum(rat_0, rat_-1/4) = rat_-1/4 &
% 16.65/3.31    rat_$sum(rat_0, rat_-18/25) = rat_-18/25 & rat_$sum(rat_0, rat_0) = rat_0 &
% 16.65/3.31    rat_$lesseq(rat_very_small, rat_very_large) = 0 & rat_$lesseq(rat_-9/50,
% 16.65/3.31      rat_-9/50) = 0 & rat_$lesseq(rat_-9/50, rat_9/50) = 0 &
% 16.65/3.31    rat_$lesseq(rat_-9/50, rat_-1/4) = 1 & rat_$lesseq(rat_-9/50, rat_-18/25) = 1
% 16.65/3.31    & rat_$lesseq(rat_-9/50, rat_0) = 0 & rat_$lesseq(rat_9/50, rat_-9/50) = 1 &
% 16.65/3.31    rat_$lesseq(rat_9/50, rat_9/50) = 0 & rat_$lesseq(rat_9/50, rat_-1/4) = 1 &
% 16.65/3.31    rat_$lesseq(rat_9/50, rat_-18/25) = 1 & rat_$lesseq(rat_9/50, rat_0) = 1 &
% 16.65/3.31    rat_$lesseq(rat_-1/4, rat_-9/50) = 0 & rat_$lesseq(rat_-1/4, rat_9/50) = 0 &
% 16.65/3.31    rat_$lesseq(rat_-1/4, rat_-1/4) = 0 & rat_$lesseq(rat_-1/4, rat_-18/25) = 1 &
% 16.65/3.31    rat_$lesseq(rat_-1/4, rat_0) = 0 & rat_$lesseq(rat_-18/25, rat_-9/50) = 0 &
% 16.65/3.31    rat_$lesseq(rat_-18/25, rat_9/50) = 0 & rat_$lesseq(rat_-18/25, rat_-1/4) = 0
% 16.65/3.31    & rat_$lesseq(rat_-18/25, rat_-18/25) = 0 & rat_$lesseq(rat_-18/25, rat_0) = 0
% 16.65/3.31    & rat_$lesseq(rat_0, rat_-9/50) = 1 & rat_$lesseq(rat_0, rat_9/50) = 0 &
% 16.65/3.31    rat_$lesseq(rat_0, rat_-1/4) = 1 & rat_$lesseq(rat_0, rat_-18/25) = 1 &
% 16.65/3.32    rat_$lesseq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, rat_-9/50) = 0 &
% 16.65/3.32    rat_$greater(rat_very_large, rat_9/50) = 0 & rat_$greater(rat_very_large,
% 16.65/3.32      rat_-1/4) = 0 & rat_$greater(rat_very_large, rat_-18/25) = 0 &
% 16.65/3.32    rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small,
% 16.65/3.32      rat_very_large) = 1 & rat_$greater(rat_-9/50, rat_very_small) = 0 &
% 16.65/3.32    rat_$greater(rat_-9/50, rat_-9/50) = 1 & rat_$greater(rat_-9/50, rat_9/50) = 1
% 16.65/3.32    & rat_$greater(rat_-9/50, rat_-1/4) = 0 & rat_$greater(rat_-9/50, rat_-18/25)
% 16.65/3.32    = 0 & rat_$greater(rat_-9/50, rat_0) = 1 & rat_$greater(rat_9/50,
% 16.65/3.32      rat_very_small) = 0 & rat_$greater(rat_9/50, rat_-9/50) = 0 &
% 16.65/3.32    rat_$greater(rat_9/50, rat_9/50) = 1 & rat_$greater(rat_9/50, rat_-1/4) = 0 &
% 16.65/3.32    rat_$greater(rat_9/50, rat_-18/25) = 0 & rat_$greater(rat_9/50, rat_0) = 0 &
% 16.65/3.32    rat_$greater(rat_-1/4, rat_very_small) = 0 & rat_$greater(rat_-1/4, rat_-9/50)
% 16.65/3.32    = 1 & rat_$greater(rat_-1/4, rat_9/50) = 1 & rat_$greater(rat_-1/4, rat_-1/4)
% 16.65/3.32    = 1 & rat_$greater(rat_-1/4, rat_-18/25) = 0 & rat_$greater(rat_-1/4, rat_0) =
% 16.65/3.32    1 & rat_$greater(rat_-18/25, rat_very_small) = 0 & rat_$greater(rat_-18/25,
% 16.65/3.32      rat_-9/50) = 1 & rat_$greater(rat_-18/25, rat_9/50) = 1 &
% 16.65/3.32    rat_$greater(rat_-18/25, rat_-1/4) = 1 & rat_$greater(rat_-18/25, rat_-18/25)
% 16.65/3.32    = 1 & rat_$greater(rat_-18/25, rat_0) = 1 & rat_$greater(rat_0,
% 16.65/3.32      rat_very_small) = 0 & rat_$greater(rat_0, rat_-9/50) = 0 &
% 16.65/3.32    rat_$greater(rat_0, rat_9/50) = 1 & rat_$greater(rat_0, rat_-1/4) = 0 &
% 16.65/3.32    rat_$greater(rat_0, rat_-18/25) = 0 & rat_$greater(rat_0, rat_0) = 1 &
% 16.65/3.32    rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small,
% 16.65/3.32      rat_-9/50) = 0 & rat_$less(rat_very_small, rat_9/50) = 0 &
% 16.65/3.32    rat_$less(rat_very_small, rat_-1/4) = 0 & rat_$less(rat_very_small,
% 16.65/3.32      rat_-18/25) = 0 & rat_$less(rat_very_small, rat_0) = 0 &
% 16.65/3.32    rat_$less(rat_-9/50, rat_very_large) = 0 & rat_$less(rat_-9/50, rat_-9/50) = 1
% 16.65/3.32    & rat_$less(rat_-9/50, rat_9/50) = 0 & rat_$less(rat_-9/50, rat_-1/4) = 1 &
% 16.65/3.32    rat_$less(rat_-9/50, rat_-18/25) = 1 & rat_$less(rat_-9/50, rat_0) = 0 &
% 16.65/3.32    rat_$less(rat_9/50, rat_very_large) = 0 & rat_$less(rat_9/50, rat_-9/50) = 1 &
% 16.65/3.32    rat_$less(rat_9/50, rat_9/50) = 1 & rat_$less(rat_9/50, rat_-1/4) = 1 &
% 16.65/3.32    rat_$less(rat_9/50, rat_-18/25) = 1 & rat_$less(rat_9/50, rat_0) = 1 &
% 16.65/3.32    rat_$less(rat_-1/4, rat_very_large) = 0 & rat_$less(rat_-1/4, rat_-9/50) = 0 &
% 16.65/3.32    rat_$less(rat_-1/4, rat_9/50) = 0 & rat_$less(rat_-1/4, rat_-1/4) = 1 &
% 16.65/3.32    rat_$less(rat_-1/4, rat_-18/25) = 1 & rat_$less(rat_-1/4, rat_0) = 0 &
% 16.65/3.32    rat_$less(rat_-18/25, rat_very_large) = 0 & rat_$less(rat_-18/25, rat_-9/50) =
% 16.65/3.32    0 & rat_$less(rat_-18/25, rat_9/50) = 0 & rat_$less(rat_-18/25, rat_-1/4) = 0
% 16.65/3.32    & rat_$less(rat_-18/25, rat_-18/25) = 1 & rat_$less(rat_-18/25, rat_0) = 0 &
% 16.65/3.32    rat_$less(rat_0, rat_very_large) = 0 & rat_$less(rat_0, rat_-9/50) = 1 &
% 16.65/3.32    rat_$less(rat_0, rat_9/50) = 0 & rat_$less(rat_0, rat_-1/4) = 1 &
% 16.65/3.32    rat_$less(rat_0, rat_-18/25) = 1 & rat_$less(rat_0, rat_0) = 1 &
% 16.65/3.32    rat_$greatereq(rat_very_small, rat_very_large) = 1 & rat_$greatereq(rat_-9/50,
% 16.65/3.32      rat_-9/50) = 0 & rat_$greatereq(rat_-9/50, rat_9/50) = 1 &
% 16.65/3.32    rat_$greatereq(rat_-9/50, rat_-1/4) = 0 & rat_$greatereq(rat_-9/50,
% 16.65/3.32      rat_-18/25) = 0 & rat_$greatereq(rat_-9/50, rat_0) = 1 &
% 16.65/3.32    rat_$greatereq(rat_9/50, rat_-9/50) = 0 & rat_$greatereq(rat_9/50, rat_9/50) =
% 16.65/3.32    0 & rat_$greatereq(rat_9/50, rat_-1/4) = 0 & rat_$greatereq(rat_9/50,
% 16.65/3.32      rat_-18/25) = 0 & rat_$greatereq(rat_9/50, rat_0) = 0 &
% 16.65/3.32    rat_$greatereq(rat_-1/4, rat_-9/50) = 1 & rat_$greatereq(rat_-1/4, rat_9/50) =
% 16.65/3.32    1 & rat_$greatereq(rat_-1/4, rat_-1/4) = 0 & rat_$greatereq(rat_-1/4,
% 16.65/3.32      rat_-18/25) = 0 & rat_$greatereq(rat_-1/4, rat_0) = 1 &
% 16.65/3.32    rat_$greatereq(rat_-18/25, rat_-9/50) = 1 & rat_$greatereq(rat_-18/25,
% 16.65/3.32      rat_9/50) = 1 & rat_$greatereq(rat_-18/25, rat_-1/4) = 1 &
% 16.65/3.32    rat_$greatereq(rat_-18/25, rat_-18/25) = 0 & rat_$greatereq(rat_-18/25, rat_0)
% 16.65/3.32    = 1 & rat_$greatereq(rat_0, rat_-9/50) = 0 & rat_$greatereq(rat_0, rat_9/50) =
% 16.65/3.32    1 & rat_$greatereq(rat_0, rat_-1/4) = 0 & rat_$greatereq(rat_0, rat_-18/25) =
% 16.65/3.32    0 & rat_$greatereq(rat_0, rat_0) = 0 &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2:
% 16.65/3.32      $rat] :  ! [v3: $rat] :  ! [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) |  ~
% 16.65/3.32      (rat_$sum(v2, v1) = v3) |  ? [v5: $rat] : (rat_$sum(v2, v5) = v4 &
% 16.65/3.32        rat_$sum(v1, v0) = v5)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] : 
% 16.65/3.32    ! [v3: $rat] : (v3 = v1 | v0 = rat_0 |  ~ (rat_$quotient(v2, v0) = v3) |  ~
% 16.65/3.32      (rat_$product(v1, v0) = v2)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat]
% 16.65/3.32    :  ! [v3: int] : (v3 = 0 |  ~ (rat_$lesseq(v2, v0) = v3) |  ~ (rat_$lesseq(v1,
% 16.65/3.32          v0) = 0) |  ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) &  !
% 16.65/3.32    [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: int] : (v3 = 0 |  ~
% 16.65/3.32      (rat_$lesseq(v1, v0) = 0) |  ~ (rat_$less(v2, v0) = v3) |  ? [v4: int] : ( ~
% 16.65/3.32        (v4 = 0) & rat_$less(v2, v1) = v4)) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 16.65/3.32    [v2: $rat] :  ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) |  ~ (rat_$sum(v1, v2)
% 16.65/3.32        = v3) | rat_$difference(v1, v0) = v3) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 16.65/3.32    [v2: $rat] : (v2 = rat_0 |  ~ (rat_$uminus(v0) = v1) |  ~ (rat_$sum(v0, v1) =
% 16.65/3.32        v2)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: int] : (v2 = 0 |  ~
% 16.65/3.32      (rat_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) &  ? [v3: int] : ( ~ (v3 = 0) &
% 16.65/3.32          rat_$less(v1, v0) = v3))) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: int]
% 16.65/3.32    : (v2 = 0 |  ~ (rat_$greater(v0, v1) = v2) |  ? [v3: int] : ( ~ (v3 = 0) &
% 16.65/3.32        rat_$less(v1, v0) = v3)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: int] :
% 16.65/3.32    (v2 = 0 |  ~ (rat_$greatereq(v0, v1) = v2) |  ? [v3: int] : ( ~ (v3 = 0) &
% 16.65/3.32        rat_$lesseq(v1, v0) = v3)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat]
% 16.65/3.32    : ( ~ (rat_$product(v0, v1) = v2) | rat_$product(v1, v0) = v2) &  ! [v0: $rat]
% 16.65/3.32    :  ! [v1: $rat] :  ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1,
% 16.65/3.32        v0) = v2) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] : ( ~
% 16.65/3.32      (rat_$lesseq(v2, v1) = 0) |  ~ (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) =
% 16.65/3.32      0) &  ! [v0: $rat] :  ! [v1: $rat] : (v1 = v0 |  ~ (rat_$sum(v0, rat_0) =
% 16.65/3.32        v1)) &  ! [v0: $rat] :  ! [v1: $rat] : (v1 = v0 |  ~ (rat_$lesseq(v1, v0)
% 16.65/3.32        = 0) | rat_$less(v1, v0) = 0) &  ! [v0: $rat] :  ! [v1: $rat] : ( ~
% 16.65/3.32      (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) &  ! [v0: $rat] :  ! [v1:
% 16.65/3.32      $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) &  ! [v0:
% 16.65/3.32      $rat] :  ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1,
% 16.65/3.32        v0) = 0) &  ! [v0: $rat] : (v0 = rat_0 |  ~ (rat_$uminus(v0) = v0))
% 16.65/3.32  
% 16.65/3.32    (function-axioms)
% 16.65/3.33     ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~
% 16.65/3.33      (rat_$quotient(v3, v2) = v1) |  ~ (rat_$quotient(v3, v2) = v0)) &  ! [v0:
% 16.65/3.33      $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~
% 16.65/3.33      (rat_$product(v3, v2) = v1) |  ~ (rat_$product(v3, v2) = v0)) &  ! [v0:
% 16.65/3.33      $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~
% 16.65/3.33      (rat_$difference(v3, v2) = v1) |  ~ (rat_$difference(v3, v2) = v0)) &  !
% 16.65/3.33    [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~
% 16.65/3.33      (rat_$sum(v3, v2) = v1) |  ~ (rat_$sum(v3, v2) = v0)) &  ! [v0:
% 16.65/3.33      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $rat] :  ! [v3:
% 16.65/3.33      $rat] : (v1 = v0 |  ~ (rat_$lesseq(v3, v2) = v1) |  ~ (rat_$lesseq(v3, v2) =
% 16.65/3.33        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 16.65/3.33      $rat] :  ! [v3: $rat] : (v1 = v0 |  ~ (rat_$greater(v3, v2) = v1) |  ~
% 16.65/3.33      (rat_$greater(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 16.65/3.33      MultipleValueBool] :  ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~
% 16.65/3.33      (rat_$less(v3, v2) = v1) |  ~ (rat_$less(v3, v2) = v0)) &  ! [v0:
% 16.65/3.33      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $rat] :  ! [v3:
% 16.65/3.33      $rat] : (v1 = v0 |  ~ (rat_$greatereq(v3, v2) = v1) |  ~ (rat_$greatereq(v3,
% 16.65/3.33          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 16.65/3.33    ! [v2: $rat] : (v1 = v0 |  ~ (rat_$is_int(v2) = v1) |  ~ (rat_$is_int(v2) =
% 16.65/3.33        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 16.65/3.33      $rat] : (v1 = v0 |  ~ (rat_$is_rat(v2) = v1) |  ~ (rat_$is_rat(v2) = v0)) & 
% 16.65/3.33    ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] : (v1 = v0 |  ~ (rat_$floor(v2) =
% 16.65/3.33        v1) |  ~ (rat_$floor(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2:
% 16.65/3.33      $rat] : (v1 = v0 |  ~ (rat_$ceiling(v2) = v1) |  ~ (rat_$ceiling(v2) = v0))
% 16.65/3.33    &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] : (v1 = v0 |  ~
% 16.65/3.33      (rat_$truncate(v2) = v1) |  ~ (rat_$truncate(v2) = v0)) &  ! [v0: $rat] :  !
% 16.65/3.33    [v1: $rat] :  ! [v2: $rat] : (v1 = v0 |  ~ (rat_$round(v2) = v1) |  ~
% 16.65/3.33      (rat_$round(v2) = v0)) &  ! [v0: int] :  ! [v1: int] :  ! [v2: $rat] : (v1 =
% 16.65/3.33      v0 |  ~ (rat_$to_int(v2) = v1) |  ~ (rat_$to_int(v2) = v0)) &  ! [v0: $rat]
% 16.65/3.33    :  ! [v1: $rat] :  ! [v2: $rat] : (v1 = v0 |  ~ (rat_$to_rat(v2) = v1) |  ~
% 16.65/3.33      (rat_$to_rat(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $rat] :
% 16.65/3.33    (v1 = v0 |  ~ (rat_$to_real(v2) = v1) |  ~ (rat_$to_real(v2) = v0)) &  ! [v0:
% 16.65/3.33      $rat] :  ! [v1: $rat] :  ! [v2: int] : (v1 = v0 |  ~ (int_$to_rat(v2) = v1)
% 16.65/3.33      |  ~ (int_$to_rat(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat]
% 16.65/3.33    : (v1 = v0 |  ~ (rat_$uminus(v2) = v1) |  ~ (rat_$uminus(v2) = v0))
% 16.65/3.33  
% 16.65/3.33  Those formulas are unsatisfiable:
% 16.65/3.33  ---------------------------------
% 16.65/3.33  
% 16.65/3.33  Begin of proof
% 16.65/3.33  | 
% 16.65/3.33  | ALPHA: (function-axioms) implies:
% 16.65/3.33  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $rat]
% 16.65/3.33  |        :  ! [v3: $rat] : (v1 = v0 |  ~ (rat_$greatereq(v3, v2) = v1) |  ~
% 16.65/3.33  |          (rat_$greatereq(v3, v2) = v0))
% 16.65/3.33  | 
% 16.65/3.33  | ALPHA: (input) implies:
% 16.65/3.33  |   (2)  rat_$greatereq(rat_-9/50, rat_-9/50) = 0
% 16.65/3.33  | 
% 16.65/3.33  | DELTA: instantiating (rat_combined_problem_15) with fresh symbol all_5_0
% 16.65/3.33  |        gives:
% 16.65/3.33  |   (3)   ~ (all_5_0 = 0) & rat_$greatereq(rat_-9/50, rat_-9/50) = all_5_0
% 16.65/3.33  | 
% 16.65/3.33  | ALPHA: (3) implies:
% 16.65/3.33  |   (4)   ~ (all_5_0 = 0)
% 16.65/3.33  |   (5)  rat_$greatereq(rat_-9/50, rat_-9/50) = all_5_0
% 16.65/3.33  | 
% 16.65/3.33  | GROUND_INST: instantiating (1) with 0, all_5_0, rat_-9/50, rat_-9/50,
% 16.65/3.33  |              simplifying with (2), (5) gives:
% 16.65/3.33  |   (6)  all_5_0 = 0
% 16.65/3.33  | 
% 16.65/3.33  | REDUCE: (4), (6) imply:
% 16.65/3.33  |   (7)  $false
% 16.65/3.34  | 
% 16.65/3.34  | CLOSE: (7) is inconsistent.
% 16.65/3.34  | 
% 16.65/3.34  End of proof
% 16.65/3.34  % SZS output end Proof for theBenchmark
% 16.65/3.34  
% 16.65/3.34  2757ms
%------------------------------------------------------------------------------