TSTP Solution File: ARI491_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI491_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 : n024.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 17:48:09 EDT 2023

% Result   : Theorem 6.59s 1.63s
% Output   : Proof 21.42s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : ARI491_1 : TPTP v8.1.2. Released v5.0.0.
% 0.13/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n024.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 18:38:52 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.62  ________       _____
% 0.20/0.62  ___  __ \_________(_)________________________________
% 0.20/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62  
% 0.20/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62  (2023-06-19)
% 0.20/0.62  
% 0.20/0.62  (c) Philipp Rümmer, 2009-2023
% 0.20/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62                Amanda Stjerna.
% 0.20/0.62  Free software under BSD-3-Clause.
% 0.20/0.62  
% 0.20/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62  
% 0.20/0.62  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 0.20/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.25/0.91  Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.25/0.91  Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.25/0.91  Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.25/0.91  Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.25/0.91  Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.25/0.91  Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.25/0.91  Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 2.29/1.02  Prover 4: Preprocessing ...
% 2.29/1.03  Prover 1: Preprocessing ...
% 2.90/1.09  Prover 6: Preprocessing ...
% 2.90/1.10  Prover 0: Preprocessing ...
% 4.11/1.35  Prover 5: Preprocessing ...
% 4.66/1.37  Prover 3: Preprocessing ...
% 4.66/1.38  Prover 2: Preprocessing ...
% 6.59/1.58  Prover 6: Constructing countermodel ...
% 6.59/1.63  Prover 6: proved (984ms)
% 6.59/1.63  
% 6.59/1.63  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.59/1.63  
% 6.59/1.64  Prover 1: Constructing countermodel ...
% 6.59/1.64  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.59/1.64  Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 6.59/1.64  Prover 0: Constructing countermodel ...
% 6.59/1.64  Prover 0: stopped
% 6.59/1.64  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.29/1.66  Prover 4: Constructing countermodel ...
% 7.29/1.66  Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 7.29/1.67  Prover 8: Preprocessing ...
% 8.43/1.86  Prover 8: Warning: ignoring some quantifiers
% 8.88/1.87  Prover 8: Constructing countermodel ...
% 8.88/1.89  Prover 7: Preprocessing ...
% 8.88/1.96  Prover 4: Found proof (size 7)
% 8.88/1.96  Prover 1: Found proof (size 7)
% 8.88/1.96  Prover 1: proved (1319ms)
% 8.88/1.96  Prover 4: proved (1317ms)
% 8.88/1.96  Prover 8: stopped
% 13.86/2.66  Prover 2: stopped
% 15.01/2.76  Prover 7: stopped
% 19.13/3.46  Prover 5: Constructing countermodel ...
% 19.13/3.47  Prover 5: stopped
% 20.86/4.10  Prover 3: Constructing countermodel ...
% 20.86/4.10  Prover 3: stopped
% 20.86/4.10  
% 20.86/4.10  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.86/4.10  
% 20.86/4.11  % SZS output start Proof for theBenchmark
% 20.86/4.11  Assumptions after simplification:
% 20.86/4.11  ---------------------------------
% 20.86/4.11  
% 20.86/4.11    (real_combined_problem_6)
% 20.97/4.15     ? [v0: int] : ( ~ (v0 = 0) & real_$less(real_15/2, real_77/10) = v0)
% 20.97/4.15  
% 20.97/4.16    (input)
% 21.42/4.23     ~ (real_very_large = real_very_small) &  ~ (real_very_large = real_15/2) &  ~
% 21.42/4.23    (real_very_large = real_77/10) &  ~ (real_very_large = real_24/5) &  ~
% 21.42/4.23    (real_very_large = real_29/10) &  ~ (real_very_large = real_0) &  ~
% 21.42/4.23    (real_very_small = real_15/2) &  ~ (real_very_small = real_77/10) &  ~
% 21.42/4.23    (real_very_small = real_24/5) &  ~ (real_very_small = real_29/10) &  ~
% 21.42/4.23    (real_very_small = real_0) &  ~ (real_15/2 = real_77/10) &  ~ (real_15/2 =
% 21.42/4.23      real_24/5) &  ~ (real_15/2 = real_29/10) &  ~ (real_15/2 = real_0) &  ~
% 21.42/4.23    (real_77/10 = real_24/5) &  ~ (real_77/10 = real_29/10) &  ~ (real_77/10 =
% 21.42/4.23      real_0) &  ~ (real_24/5 = real_29/10) &  ~ (real_24/5 = real_0) &  ~
% 21.42/4.23    (real_29/10 = real_0) & real_$is_int(real_15/2) = 1 & real_$is_int(real_77/10)
% 21.42/4.23    = 1 & real_$is_int(real_24/5) = 1 & real_$is_int(real_29/10) = 1 &
% 21.42/4.23    real_$is_int(real_0) = 0 & real_$is_rat(real_15/2) = 0 &
% 21.42/4.23    real_$is_rat(real_77/10) = 0 & real_$is_rat(real_24/5) = 0 &
% 21.42/4.23    real_$is_rat(real_29/10) = 0 & real_$is_rat(real_0) = 0 & real_$floor(real_0)
% 21.42/4.23    = real_0 & real_$ceiling(real_0) = real_0 & real_$truncate(real_0) = real_0 &
% 21.42/4.23    real_$round(real_0) = real_0 & real_$to_int(real_15/2) = 7 &
% 21.42/4.23    real_$to_int(real_77/10) = 7 & real_$to_int(real_24/5) = 4 &
% 21.42/4.23    real_$to_int(real_29/10) = 2 & real_$to_int(real_0) = 0 &
% 21.42/4.23    real_$to_rat(real_15/2) = rat_15/2 & real_$to_rat(real_77/10) = rat_77/10 &
% 21.42/4.23    real_$to_rat(real_24/5) = rat_24/5 & real_$to_rat(real_29/10) = rat_29/10 &
% 21.42/4.23    real_$to_rat(real_0) = rat_0 & real_$to_real(real_15/2) = real_15/2 &
% 21.42/4.23    real_$to_real(real_77/10) = real_77/10 & real_$to_real(real_24/5) = real_24/5
% 21.42/4.23    & real_$to_real(real_29/10) = real_29/10 & real_$to_real(real_0) = real_0 &
% 21.42/4.23    int_$to_real(0) = real_0 & real_$quotient(real_0, real_15/2) = real_0 &
% 21.42/4.23    real_$quotient(real_0, real_77/10) = real_0 & real_$quotient(real_0,
% 21.42/4.23      real_24/5) = real_0 & real_$quotient(real_0, real_29/10) = real_0 &
% 21.42/4.23    real_$product(real_15/2, real_0) = real_0 & real_$product(real_77/10, real_0)
% 21.42/4.23    = real_0 & real_$product(real_24/5, real_0) = real_0 &
% 21.42/4.23    real_$product(real_29/10, real_0) = real_0 & real_$product(real_0, real_15/2)
% 21.42/4.23    = real_0 & real_$product(real_0, real_77/10) = real_0 & real_$product(real_0,
% 21.42/4.23      real_24/5) = real_0 & real_$product(real_0, real_29/10) = real_0 &
% 21.42/4.23    real_$product(real_0, real_0) = real_0 & real_$difference(real_15/2,
% 21.42/4.23      real_15/2) = real_0 & real_$difference(real_15/2, real_0) = real_15/2 &
% 21.42/4.23    real_$difference(real_77/10, real_77/10) = real_0 &
% 21.42/4.23    real_$difference(real_77/10, real_24/5) = real_29/10 &
% 21.42/4.23    real_$difference(real_77/10, real_29/10) = real_24/5 &
% 21.42/4.23    real_$difference(real_77/10, real_0) = real_77/10 &
% 21.42/4.23    real_$difference(real_24/5, real_24/5) = real_0 & real_$difference(real_24/5,
% 21.42/4.23      real_0) = real_24/5 & real_$difference(real_29/10, real_29/10) = real_0 &
% 21.42/4.23    real_$difference(real_29/10, real_0) = real_29/10 & real_$difference(real_0,
% 21.42/4.23      real_0) = real_0 & real_$uminus(real_0) = real_0 & real_$sum(real_15/2,
% 21.42/4.23      real_0) = real_15/2 & real_$sum(real_77/10, real_0) = real_77/10 &
% 21.42/4.23    real_$sum(real_24/5, real_29/10) = real_77/10 & real_$sum(real_24/5, real_0) =
% 21.42/4.23    real_24/5 & real_$sum(real_29/10, real_24/5) = real_77/10 &
% 21.42/4.23    real_$sum(real_29/10, real_0) = real_29/10 & real_$sum(real_0, real_15/2) =
% 21.42/4.23    real_15/2 & real_$sum(real_0, real_77/10) = real_77/10 & real_$sum(real_0,
% 21.42/4.23      real_24/5) = real_24/5 & real_$sum(real_0, real_29/10) = real_29/10 &
% 21.42/4.23    real_$sum(real_0, real_0) = real_0 & real_$greatereq(real_very_small,
% 21.42/4.23      real_very_large) = 1 & real_$greatereq(real_15/2, real_15/2) = 0 &
% 21.42/4.23    real_$greatereq(real_15/2, real_77/10) = 1 & real_$greatereq(real_15/2,
% 21.42/4.23      real_24/5) = 0 & real_$greatereq(real_15/2, real_29/10) = 0 &
% 21.42/4.23    real_$greatereq(real_15/2, real_0) = 0 & real_$greatereq(real_77/10,
% 21.42/4.23      real_15/2) = 0 & real_$greatereq(real_77/10, real_77/10) = 0 &
% 21.42/4.23    real_$greatereq(real_77/10, real_24/5) = 0 & real_$greatereq(real_77/10,
% 21.42/4.23      real_29/10) = 0 & real_$greatereq(real_77/10, real_0) = 0 &
% 21.42/4.23    real_$greatereq(real_24/5, real_15/2) = 1 & real_$greatereq(real_24/5,
% 21.42/4.23      real_77/10) = 1 & real_$greatereq(real_24/5, real_24/5) = 0 &
% 21.42/4.23    real_$greatereq(real_24/5, real_29/10) = 0 & real_$greatereq(real_24/5,
% 21.42/4.24      real_0) = 0 & real_$greatereq(real_29/10, real_15/2) = 1 &
% 21.42/4.24    real_$greatereq(real_29/10, real_77/10) = 1 & real_$greatereq(real_29/10,
% 21.42/4.24      real_24/5) = 1 & real_$greatereq(real_29/10, real_29/10) = 0 &
% 21.42/4.24    real_$greatereq(real_29/10, real_0) = 0 & real_$greatereq(real_0, real_15/2) =
% 21.42/4.24    1 & real_$greatereq(real_0, real_77/10) = 1 & real_$greatereq(real_0,
% 21.42/4.24      real_24/5) = 1 & real_$greatereq(real_0, real_29/10) = 1 &
% 21.42/4.24    real_$greatereq(real_0, real_0) = 0 & real_$lesseq(real_very_small,
% 21.42/4.24      real_very_large) = 0 & real_$lesseq(real_15/2, real_15/2) = 0 &
% 21.42/4.24    real_$lesseq(real_15/2, real_77/10) = 0 & real_$lesseq(real_15/2, real_24/5) =
% 21.42/4.24    1 & real_$lesseq(real_15/2, real_29/10) = 1 & real_$lesseq(real_15/2, real_0)
% 21.42/4.24    = 1 & real_$lesseq(real_77/10, real_15/2) = 1 & real_$lesseq(real_77/10,
% 21.42/4.24      real_77/10) = 0 & real_$lesseq(real_77/10, real_24/5) = 1 &
% 21.42/4.24    real_$lesseq(real_77/10, real_29/10) = 1 & real_$lesseq(real_77/10, real_0) =
% 21.42/4.24    1 & real_$lesseq(real_24/5, real_15/2) = 0 & real_$lesseq(real_24/5,
% 21.42/4.24      real_77/10) = 0 & real_$lesseq(real_24/5, real_24/5) = 0 &
% 21.42/4.24    real_$lesseq(real_24/5, real_29/10) = 1 & real_$lesseq(real_24/5, real_0) = 1
% 21.42/4.24    & real_$lesseq(real_29/10, real_15/2) = 0 & real_$lesseq(real_29/10,
% 21.42/4.24      real_77/10) = 0 & real_$lesseq(real_29/10, real_24/5) = 0 &
% 21.42/4.24    real_$lesseq(real_29/10, real_29/10) = 0 & real_$lesseq(real_29/10, real_0) =
% 21.42/4.24    1 & real_$lesseq(real_0, real_15/2) = 0 & real_$lesseq(real_0, real_77/10) = 0
% 21.42/4.24    & real_$lesseq(real_0, real_24/5) = 0 & real_$lesseq(real_0, real_29/10) = 0 &
% 21.42/4.24    real_$lesseq(real_0, real_0) = 0 & real_$greater(real_very_large, real_15/2) =
% 21.42/4.24    0 & real_$greater(real_very_large, real_77/10) = 0 &
% 21.42/4.24    real_$greater(real_very_large, real_24/5) = 0 & real_$greater(real_very_large,
% 21.42/4.24      real_29/10) = 0 & real_$greater(real_very_large, real_0) = 0 &
% 21.42/4.24    real_$greater(real_very_small, real_very_large) = 1 & real_$greater(real_15/2,
% 21.42/4.24      real_very_small) = 0 & real_$greater(real_15/2, real_15/2) = 1 &
% 21.42/4.24    real_$greater(real_15/2, real_77/10) = 1 & real_$greater(real_15/2, real_24/5)
% 21.42/4.24    = 0 & real_$greater(real_15/2, real_29/10) = 0 & real_$greater(real_15/2,
% 21.42/4.24      real_0) = 0 & real_$greater(real_77/10, real_very_small) = 0 &
% 21.42/4.24    real_$greater(real_77/10, real_15/2) = 0 & real_$greater(real_77/10,
% 21.42/4.24      real_77/10) = 1 & real_$greater(real_77/10, real_24/5) = 0 &
% 21.42/4.24    real_$greater(real_77/10, real_29/10) = 0 & real_$greater(real_77/10, real_0)
% 21.42/4.24    = 0 & real_$greater(real_24/5, real_very_small) = 0 & real_$greater(real_24/5,
% 21.42/4.24      real_15/2) = 1 & real_$greater(real_24/5, real_77/10) = 1 &
% 21.42/4.24    real_$greater(real_24/5, real_24/5) = 1 & real_$greater(real_24/5, real_29/10)
% 21.42/4.24    = 0 & real_$greater(real_24/5, real_0) = 0 & real_$greater(real_29/10,
% 21.42/4.24      real_very_small) = 0 & real_$greater(real_29/10, real_15/2) = 1 &
% 21.42/4.24    real_$greater(real_29/10, real_77/10) = 1 & real_$greater(real_29/10,
% 21.42/4.24      real_24/5) = 1 & real_$greater(real_29/10, real_29/10) = 1 &
% 21.42/4.24    real_$greater(real_29/10, real_0) = 0 & real_$greater(real_0, real_very_small)
% 21.42/4.24    = 0 & real_$greater(real_0, real_15/2) = 1 & real_$greater(real_0, real_77/10)
% 21.42/4.24    = 1 & real_$greater(real_0, real_24/5) = 1 & real_$greater(real_0, real_29/10)
% 21.42/4.24    = 1 & real_$greater(real_0, real_0) = 1 & real_$less(real_very_small,
% 21.42/4.24      real_very_large) = 0 & real_$less(real_very_small, real_15/2) = 0 &
% 21.42/4.24    real_$less(real_very_small, real_77/10) = 0 & real_$less(real_very_small,
% 21.42/4.24      real_24/5) = 0 & real_$less(real_very_small, real_29/10) = 0 &
% 21.42/4.24    real_$less(real_very_small, real_0) = 0 & real_$less(real_15/2,
% 21.42/4.24      real_very_large) = 0 & real_$less(real_15/2, real_15/2) = 1 &
% 21.42/4.24    real_$less(real_15/2, real_77/10) = 0 & real_$less(real_15/2, real_24/5) = 1 &
% 21.42/4.24    real_$less(real_15/2, real_29/10) = 1 & real_$less(real_15/2, real_0) = 1 &
% 21.42/4.24    real_$less(real_77/10, real_very_large) = 0 & real_$less(real_77/10,
% 21.42/4.24      real_15/2) = 1 & real_$less(real_77/10, real_77/10) = 1 &
% 21.42/4.24    real_$less(real_77/10, real_24/5) = 1 & real_$less(real_77/10, real_29/10) = 1
% 21.42/4.24    & real_$less(real_77/10, real_0) = 1 & real_$less(real_24/5, real_very_large)
% 21.42/4.24    = 0 & real_$less(real_24/5, real_15/2) = 0 & real_$less(real_24/5, real_77/10)
% 21.42/4.24    = 0 & real_$less(real_24/5, real_24/5) = 1 & real_$less(real_24/5, real_29/10)
% 21.42/4.24    = 1 & real_$less(real_24/5, real_0) = 1 & real_$less(real_29/10,
% 21.42/4.24      real_very_large) = 0 & real_$less(real_29/10, real_15/2) = 0 &
% 21.42/4.24    real_$less(real_29/10, real_77/10) = 0 & real_$less(real_29/10, real_24/5) = 0
% 21.42/4.24    & real_$less(real_29/10, real_29/10) = 1 & real_$less(real_29/10, real_0) = 1
% 21.42/4.24    & real_$less(real_0, real_very_large) = 0 & real_$less(real_0, real_15/2) = 0
% 21.42/4.24    & real_$less(real_0, real_77/10) = 0 & real_$less(real_0, real_24/5) = 0 &
% 21.42/4.24    real_$less(real_0, real_29/10) = 0 & real_$less(real_0, real_0) = 1 &  ! [v0:
% 21.42/4.24      $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] :  ! [v4: $real] :
% 21.42/4.24    ( ~ (real_$sum(v3, v0) = v4) |  ~ (real_$sum(v2, v1) = v3) |  ? [v5: $real] :
% 21.42/4.24      (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) &  ! [v0: $real] :  !
% 21.42/4.24    [v1: $real] :  ! [v2: $real] :  ! [v3: $real] :  ! [v4: $real] : ( ~
% 21.42/4.24      (real_$sum(v2, v3) = v4) |  ~ (real_$sum(v1, v0) = v3) |  ? [v5: $real] :
% 21.42/4.24      (real_$sum(v5, v0) = v4 & real_$sum(v2, v1) = v5)) &  ! [v0: $real] :  !
% 21.42/4.24    [v1: $real] :  ! [v2: $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$lesseq(v2,
% 21.42/4.24          v1) = 0) |  ~ (real_$lesseq(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0)
% 21.42/4.24        & real_$lesseq(v1, v0) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 21.42/4.24      $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$lesseq(v2, v1) = 0) |  ~
% 21.42/4.25      (real_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0)
% 21.42/4.25        = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: int] :
% 21.42/4.25    (v3 = 0 |  ~ (real_$lesseq(v2, v0) = v3) |  ~ (real_$lesseq(v1, v0) = 0) |  ?
% 21.42/4.25      [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) &  ! [v0: $real] :  !
% 21.42/4.25    [v1: $real] :  ! [v2: $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$lesseq(v1,
% 21.42/4.25          v0) = 0) |  ~ (real_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) &
% 21.42/4.25        real_$less(v2, v1) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 21.42/4.25      $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$less(v2, v1) = 0) |  ~
% 21.42/4.25      (real_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1,
% 21.42/4.25          v0) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3:
% 21.42/4.25      int] : (v3 = 0 |  ~ (real_$less(v2, v0) = v3) |  ~ (real_$less(v1, v0) = 0)
% 21.42/4.25      |  ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) &  ! [v0: $real]
% 21.42/4.25    :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : ( ~ (real_$uminus(v0) =
% 21.42/4.25        v2) |  ~ (real_$sum(v1, v2) = v3) | real_$difference(v1, v0) = v3) &  !
% 21.42/4.25    [v0: $real] :  ! [v1: $real] :  ! [v2: int] : (v2 = 0 | v1 = v0 |  ~
% 21.42/4.25      (real_$less(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1,
% 21.42/4.25          v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: int] : (v2 = 0 | 
% 21.42/4.25      ~ (real_$greatereq(v0, v1) = v2) |  ? [v3: int] : ( ~ (v3 = 0) &
% 21.42/4.25        real_$lesseq(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 21.42/4.25      int] : (v2 = 0 |  ~ (real_$lesseq(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3 =
% 21.42/4.25          0) & real_$greatereq(v0, v1) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 21.42/4.25    ! [v2: int] : (v2 = 0 |  ~ (real_$lesseq(v1, v0) = v2) |  ? [v3: int] : ( ~
% 21.42/4.25        (v3 = 0) & real_$less(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 21.42/4.25    ! [v2: int] : (v2 = 0 |  ~ (real_$greater(v0, v1) = v2) |  ? [v3: int] : ( ~
% 21.42/4.25        (v3 = 0) & real_$less(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 21.42/4.25    ! [v2: int] : (v2 = 0 |  ~ (real_$less(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3
% 21.42/4.25          = 0) & real_$greater(v0, v1) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 21.42/4.25    ! [v2: $real] : (v0 = real_0 |  ~ (real_$product(v1, v0) = v2) |
% 21.42/4.25      real_$quotient(v2, v0) = v1) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 21.42/4.25      $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) &  !
% 21.42/4.25    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ (real_$product(v0, v1) =
% 21.42/4.25        v2) | real_$product(v1, v0) = v2) &  ! [v0: $real] :  ! [v1: $real] :  !
% 21.42/4.25    [v2: $real] : ( ~ (real_$difference(v1, v0) = v2) |  ? [v3: $real] :
% 21.42/4.25      (real_$uminus(v0) = v3 & real_$sum(v1, v3) = v2)) &  ! [v0: $real] :  ! [v1:
% 21.42/4.25      $real] :  ! [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0, v1) =
% 21.42/4.25      v2) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ (real_$sum(v0,
% 21.42/4.25          v1) = v2) | real_$sum(v1, v0) = v2) &  ! [v0: $real] :  ! [v1: $real] : 
% 21.42/4.25    ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) |  ~ (real_$lesseq(v1, v0) = 0)
% 21.42/4.25      | real_$lesseq(v2, v0) = 0) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 21.42/4.25      $real] : ( ~ (real_$lesseq(v2, v1) = 0) |  ~ (real_$less(v1, v0) = 0) |
% 21.42/4.25      real_$less(v2, v0) = 0) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :
% 21.42/4.25    ( ~ (real_$lesseq(v1, v0) = 0) |  ~ (real_$less(v2, v1) = 0) | real_$less(v2,
% 21.42/4.25        v0) = 0) &  ! [v0: $real] :  ! [v1: $real] : (v1 = v0 |  ~ (real_$sum(v0,
% 21.42/4.25          real_0) = v1)) &  ! [v0: $real] :  ! [v1: $real] : (v1 = v0 |  ~
% 21.42/4.25      (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = 0) &  ! [v0: $real] :  !
% 21.42/4.25    [v1: int] : (v1 = 0 |  ~ (real_$lesseq(v0, v0) = v1)) &  ! [v0: $real] :  !
% 21.42/4.25    [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) &  ! [v0:
% 21.42/4.25      $real] :  ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$sum(v0, v1) =
% 21.42/4.25      real_0) &  ! [v0: $real] :  ! [v1: $real] : ( ~ (real_$greatereq(v0, v1) =
% 21.42/4.25        0) | real_$lesseq(v1, v0) = 0) &  ! [v0: $real] :  ! [v1: $real] : ( ~
% 21.42/4.25      (real_$lesseq(v1, v0) = 0) | real_$greatereq(v0, v1) = 0) &  ! [v0: $real] :
% 21.42/4.25     ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & 
% 21.42/4.25    ! [v0: $real] :  ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) |
% 21.42/4.25      real_$lesseq(v1, v0) = 0) &  ! [v0: $real] :  ! [v1: $real] : ( ~
% 21.42/4.25      (real_$less(v1, v0) = 0) | real_$greater(v0, v1) = 0) &  ! [v0: $real] :  !
% 21.42/4.25    [v1: MultipleValueBool] : ( ~ (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0)
% 21.42/4.25      = 0) &  ! [v0: $real] : (v0 = real_0 |  ~ (real_$uminus(v0) = v0))
% 21.42/4.25  
% 21.42/4.25    (function-axioms)
% 21.42/4.26     ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |
% 21.42/4.26       ~ (real_$quotient(v3, v2) = v1) |  ~ (real_$quotient(v3, v2) = v0)) &  !
% 21.42/4.26    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 21.42/4.26      (real_$product(v3, v2) = v1) |  ~ (real_$product(v3, v2) = v0)) &  ! [v0:
% 21.42/4.26      $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 21.42/4.26      (real_$difference(v3, v2) = v1) |  ~ (real_$difference(v3, v2) = v0)) &  !
% 21.42/4.26    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 21.42/4.26      (real_$sum(v3, v2) = v1) |  ~ (real_$sum(v3, v2) = v0)) &  ! [v0:
% 21.42/4.26      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $real] :  ! [v3:
% 21.42/4.26      $real] : (v1 = v0 |  ~ (real_$greatereq(v3, v2) = v1) |  ~
% 21.42/4.26      (real_$greatereq(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 21.42/4.26      MultipleValueBool] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 21.42/4.26      (real_$lesseq(v3, v2) = v1) |  ~ (real_$lesseq(v3, v2) = v0)) &  ! [v0:
% 21.42/4.26      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $real] :  ! [v3:
% 21.42/4.26      $real] : (v1 = v0 |  ~ (real_$greater(v3, v2) = v1) |  ~ (real_$greater(v3,
% 21.42/4.26          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 21.42/4.26    ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~ (real_$less(v3, v2) = v1) |  ~
% 21.42/4.26      (real_$less(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 21.42/4.26      MultipleValueBool] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$is_int(v2) = v1)
% 21.42/4.26      |  ~ (real_$is_int(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 21.42/4.26      MultipleValueBool] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$is_rat(v2) = v1)
% 21.42/4.26      |  ~ (real_$is_rat(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 21.42/4.26      $real] : (v1 = v0 |  ~ (real_$floor(v2) = v1) |  ~ (real_$floor(v2) = v0)) &
% 21.42/4.26     ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~
% 21.42/4.26      (real_$ceiling(v2) = v1) |  ~ (real_$ceiling(v2) = v0)) &  ! [v0: $real] : 
% 21.42/4.26    ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$truncate(v2) = v1) |  ~
% 21.42/4.26      (real_$truncate(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 21.42/4.26      $real] : (v1 = v0 |  ~ (real_$round(v2) = v1) |  ~ (real_$round(v2) = v0)) &
% 21.42/4.26     ! [v0: int] :  ! [v1: int] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$to_int(v2)
% 21.42/4.26        = v1) |  ~ (real_$to_int(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 21.42/4.26    [v2: $real] : (v1 = v0 |  ~ (real_$to_rat(v2) = v1) |  ~ (real_$to_rat(v2) =
% 21.42/4.26        v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~
% 21.42/4.26      (real_$to_real(v2) = v1) |  ~ (real_$to_real(v2) = v0)) &  ! [v0: $real] : 
% 21.42/4.26    ! [v1: $real] :  ! [v2: int] : (v1 = v0 |  ~ (int_$to_real(v2) = v1) |  ~
% 21.42/4.26      (int_$to_real(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real]
% 21.42/4.26    : (v1 = v0 |  ~ (real_$uminus(v2) = v1) |  ~ (real_$uminus(v2) = v0))
% 21.42/4.26  
% 21.42/4.26  Those formulas are unsatisfiable:
% 21.42/4.26  ---------------------------------
% 21.42/4.26  
% 21.42/4.26  Begin of proof
% 21.42/4.26  | 
% 21.42/4.27  | ALPHA: (function-axioms) implies:
% 21.42/4.27  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 21.42/4.27  |          $real] :  ! [v3: $real] : (v1 = v0 |  ~ (real_$less(v3, v2) = v1) | 
% 21.42/4.27  |          ~ (real_$less(v3, v2) = v0))
% 21.42/4.27  | 
% 21.42/4.27  | ALPHA: (input) implies:
% 21.42/4.27  |   (2)  real_$less(real_15/2, real_77/10) = 0
% 21.42/4.27  | 
% 21.42/4.27  | DELTA: instantiating (real_combined_problem_6) with fresh symbol all_5_0
% 21.42/4.27  |        gives:
% 21.42/4.27  |   (3)   ~ (all_5_0 = 0) & real_$less(real_15/2, real_77/10) = all_5_0
% 21.42/4.27  | 
% 21.42/4.27  | ALPHA: (3) implies:
% 21.42/4.27  |   (4)   ~ (all_5_0 = 0)
% 21.42/4.27  |   (5)  real_$less(real_15/2, real_77/10) = all_5_0
% 21.42/4.27  | 
% 21.42/4.27  | GROUND_INST: instantiating (1) with 0, all_5_0, real_77/10, real_15/2,
% 21.42/4.27  |              simplifying with (2), (5) gives:
% 21.42/4.27  |   (6)  all_5_0 = 0
% 21.42/4.27  | 
% 21.42/4.27  | REDUCE: (4), (6) imply:
% 21.42/4.27  |   (7)  $false
% 21.42/4.28  | 
% 21.42/4.28  | CLOSE: (7) is inconsistent.
% 21.42/4.28  | 
% 21.42/4.28  End of proof
% 21.42/4.28  % SZS output end Proof for theBenchmark
% 21.42/4.28  
% 21.42/4.28  3654ms
%------------------------------------------------------------------------------