TSTP Solution File: ARI725_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI725_1 : TPTP v8.1.2. Released v6.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n001.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 17:48:56 EDT 2023

% Result   : Theorem 8.63s 1.97s
% Output   : Proof 13.49s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ARI725_1 : TPTP v8.1.2. Released v6.3.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.34  % Computer : n001.cluster.edu
% 0.17/0.34  % Model    : x86_64 x86_64
% 0.17/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34  % Memory   : 8042.1875MB
% 0.17/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34  % CPULimit : 300
% 0.17/0.34  % WCLimit  : 300
% 0.17/0.34  % DateTime : Tue Aug 29 18:50:08 EDT 2023
% 0.17/0.34  % CPUTime  : 
% 0.20/0.60  ________       _____
% 0.20/0.60  ___  __ \_________(_)________________________________
% 0.20/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60  
% 0.20/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60  (2023-06-19)
% 0.20/0.60  
% 0.20/0.60  (c) Philipp Rümmer, 2009-2023
% 0.20/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60                Amanda Stjerna.
% 0.20/0.60  Free software under BSD-3-Clause.
% 0.20/0.60  
% 0.20/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60  
% 0.20/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61  Running up to 7 provers in parallel.
% 0.20/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.60/0.93  Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.60/0.93  Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.60/0.93  Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.60/0.93  Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.60/0.93  Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.60/0.94  Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.60/0.94  Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 2.16/1.03  Prover 1: Preprocessing ...
% 2.16/1.03  Prover 4: Preprocessing ...
% 2.16/1.08  Prover 6: Preprocessing ...
% 2.16/1.08  Prover 3: Preprocessing ...
% 2.16/1.08  Prover 2: Preprocessing ...
% 2.16/1.08  Prover 0: Preprocessing ...
% 2.16/1.08  Prover 5: Preprocessing ...
% 4.84/1.55  Prover 6: Proving ...
% 4.84/1.58  Prover 1: Constructing countermodel ...
% 4.84/1.58  Prover 4: Constructing countermodel ...
% 6.33/1.62  Prover 0: Proving ...
% 6.46/1.66  Prover 3: Constructing countermodel ...
% 6.46/1.68  Prover 2: Proving ...
% 6.46/1.69  Prover 5: Proving ...
% 8.15/1.87  Prover 1: gave up
% 8.24/1.89  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.24/1.89  Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 8.24/1.90  Prover 7: Preprocessing ...
% 8.63/1.97  Prover 3: proved (1349ms)
% 8.63/1.97  
% 8.63/1.97  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.63/1.97  
% 8.63/1.97  Prover 0: stopped
% 8.63/1.97  Prover 5: stopped
% 8.63/1.98  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.63/1.98  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.63/1.98  Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 8.63/1.98  Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 8.63/1.98  Prover 2: stopped
% 8.63/1.98  Prover 8: Preprocessing ...
% 8.63/1.98  Prover 6: stopped
% 8.63/1.99  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.63/1.99  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.63/1.99  Prover 11: Warning: Problem contains reals, using incomplete axiomatisation
% 8.63/1.99  Prover 13: Warning: Problem contains reals, using incomplete axiomatisation
% 8.63/1.99  Prover 10: Preprocessing ...
% 8.63/1.99  Prover 13: Preprocessing ...
% 8.63/1.99  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.63/2.00  Prover 16: Warning: Problem contains reals, using incomplete axiomatisation
% 8.63/2.01  Prover 11: Preprocessing ...
% 8.63/2.01  Prover 16: Preprocessing ...
% 9.82/2.09  Prover 7: Warning: ignoring some quantifiers
% 9.82/2.10  Prover 7: Constructing countermodel ...
% 9.82/2.13  Prover 8: Warning: ignoring some quantifiers
% 9.82/2.14  Prover 8: Constructing countermodel ...
% 9.82/2.16  Prover 13: Warning: ignoring some quantifiers
% 9.82/2.18  Prover 10: Warning: ignoring some quantifiers
% 9.82/2.18  Prover 13: Constructing countermodel ...
% 9.82/2.19  Prover 10: Constructing countermodel ...
% 9.82/2.20  Prover 16: Warning: ignoring some quantifiers
% 9.82/2.21  Prover 16: Constructing countermodel ...
% 9.82/2.25  Prover 11: Constructing countermodel ...
% 11.48/2.34  Prover 8: gave up
% 11.48/2.34  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 11.48/2.34  Prover 19: Warning: Problem contains reals, using incomplete axiomatisation
% 11.73/2.36  Prover 19: Preprocessing ...
% 12.34/2.45  Prover 10: Found proof (size 13)
% 12.34/2.45  Prover 10: proved (482ms)
% 12.34/2.45  Prover 7: stopped
% 12.34/2.45  Prover 16: stopped
% 12.34/2.45  Prover 11: stopped
% 12.34/2.45  Prover 4: stopped
% 12.34/2.45  Prover 13: stopped
% 12.94/2.55  Prover 19: Warning: ignoring some quantifiers
% 12.94/2.55  Prover 19: Constructing countermodel ...
% 12.94/2.56  Prover 19: stopped
% 12.94/2.56  
% 12.94/2.56  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.94/2.56  
% 13.04/2.56  % SZS output start Proof for theBenchmark
% 13.04/2.57  Assumptions after simplification:
% 13.04/2.57  ---------------------------------
% 13.04/2.57  
% 13.04/2.57    (prove)
% 13.04/2.59     ! [v0: $real] :  ! [v1: $real] : ( ~ (real_$product(real_2, v0) = v1) |  ?
% 13.04/2.59      [v2: $real] :  ? [v3: $real] :  ? [v4: $real] : (real_$floor(v1) = v2 &
% 13.04/2.59        real_$floor(v0) = v3 & real_$product(real_2, v3) = v4 &  ~
% 13.04/2.59        real_$greater(v2, v4)))
% 13.04/2.59  
% 13.04/2.59    (input)
% 13.04/2.62     ~ (real_very_large = real_very_small) &  ~ (real_very_large = real_1) &  ~
% 13.04/2.62    (real_very_large = real_1/2) &  ~ (real_very_large = real_4) &  ~
% 13.32/2.62    (real_very_large = real_-2) &  ~ (real_very_large = real_2) &  ~
% 13.32/2.62    (real_very_large = real_0) &  ~ (real_very_small = real_1) &  ~
% 13.32/2.62    (real_very_small = real_1/2) &  ~ (real_very_small = real_4) &  ~
% 13.32/2.62    (real_very_small = real_-2) &  ~ (real_very_small = real_2) &  ~
% 13.32/2.62    (real_very_small = real_0) &  ~ (real_1 = real_1/2) &  ~ (real_1 = real_4) & 
% 13.32/2.62    ~ (real_1 = real_-2) &  ~ (real_1 = real_2) &  ~ (real_1 = real_0) &  ~
% 13.32/2.62    (real_1/2 = real_4) &  ~ (real_1/2 = real_-2) &  ~ (real_1/2 = real_2) &  ~
% 13.32/2.62    (real_1/2 = real_0) &  ~ (real_4 = real_-2) &  ~ (real_4 = real_2) &  ~
% 13.32/2.62    (real_4 = real_0) &  ~ (real_-2 = real_2) &  ~ (real_-2 = real_0) &  ~ (real_2
% 13.32/2.62      = real_0) & real_$ceiling(real_1) = real_1 & real_$ceiling(real_1/2) =
% 13.32/2.62    real_1 & real_$ceiling(real_4) = real_4 & real_$ceiling(real_-2) = real_-2 &
% 13.32/2.62    real_$ceiling(real_2) = real_2 & real_$ceiling(real_0) = real_0 &
% 13.32/2.62    real_$truncate(real_1) = real_1 & real_$truncate(real_1/2) = real_0 &
% 13.32/2.62    real_$truncate(real_4) = real_4 & real_$truncate(real_-2) = real_-2 &
% 13.32/2.62    real_$truncate(real_2) = real_2 & real_$truncate(real_0) = real_0 &
% 13.32/2.62    real_$round(real_1) = real_1 & real_$round(real_1/2) = real_1 &
% 13.32/2.62    real_$round(real_4) = real_4 & real_$round(real_-2) = real_-2 &
% 13.32/2.62    real_$round(real_2) = real_2 & real_$round(real_0) = real_0 &
% 13.32/2.62    real_$to_int(real_1) = 1 & real_$to_int(real_1/2) = 0 & real_$to_int(real_4) =
% 13.32/2.62    4 & real_$to_int(real_-2) = -2 & real_$to_int(real_2) = 2 &
% 13.32/2.62    real_$to_int(real_0) = 0 & real_$to_rat(real_1) = rat_1 &
% 13.32/2.62    real_$to_rat(real_1/2) = rat_1/2 & real_$to_rat(real_4) = rat_4 &
% 13.32/2.62    real_$to_rat(real_-2) = rat_-2 & real_$to_rat(real_2) = rat_2 &
% 13.32/2.62    real_$to_rat(real_0) = rat_0 & real_$to_real(real_1) = real_1 &
% 13.32/2.62    real_$to_real(real_1/2) = real_1/2 & real_$to_real(real_4) = real_4 &
% 13.32/2.62    real_$to_real(real_-2) = real_-2 & real_$to_real(real_2) = real_2 &
% 13.32/2.62    real_$to_real(real_0) = real_0 & int_$to_real(4) = real_4 & int_$to_real(-2) =
% 13.32/2.62    real_-2 & int_$to_real(2) = real_2 & int_$to_real(1) = real_1 &
% 13.32/2.62    int_$to_real(0) = real_0 & real_$quotient(real_1, real_1) = real_1 &
% 13.32/2.62    real_$quotient(real_1, real_1/2) = real_2 & real_$quotient(real_1, real_2) =
% 13.32/2.62    real_1/2 & real_$quotient(real_1/2, real_1) = real_1/2 &
% 13.32/2.62    real_$quotient(real_1/2, real_1/2) = real_1 & real_$quotient(real_4, real_1) =
% 13.32/2.62    real_4 & real_$quotient(real_4, real_4) = real_1 & real_$quotient(real_4,
% 13.32/2.62      real_-2) = real_-2 & real_$quotient(real_4, real_2) = real_2 &
% 13.32/2.62    real_$quotient(real_-2, real_1) = real_-2 & real_$quotient(real_-2, real_-2) =
% 13.32/2.62    real_1 & real_$quotient(real_2, real_1) = real_2 & real_$quotient(real_2,
% 13.32/2.62      real_1/2) = real_4 & real_$quotient(real_2, real_4) = real_1/2 &
% 13.32/2.62    real_$quotient(real_2, real_2) = real_1 & real_$quotient(real_0, real_1) =
% 13.32/2.62    real_0 & real_$quotient(real_0, real_1/2) = real_0 & real_$quotient(real_0,
% 13.32/2.62      real_4) = real_0 & real_$quotient(real_0, real_-2) = real_0 &
% 13.32/2.62    real_$quotient(real_0, real_2) = real_0 & real_$difference(real_1, real_1) =
% 13.32/2.62    real_0 & real_$difference(real_1, real_1/2) = real_1/2 &
% 13.32/2.62    real_$difference(real_1, real_0) = real_1 & real_$difference(real_1/2,
% 13.32/2.62      real_1/2) = real_0 & real_$difference(real_1/2, real_0) = real_1/2 &
% 13.32/2.62    real_$difference(real_4, real_4) = real_0 & real_$difference(real_4, real_2) =
% 13.32/2.62    real_2 & real_$difference(real_4, real_0) = real_4 & real_$difference(real_-2,
% 13.32/2.62      real_-2) = real_0 & real_$difference(real_-2, real_0) = real_-2 &
% 13.32/2.62    real_$difference(real_2, real_1) = real_1 & real_$difference(real_2, real_4) =
% 13.32/2.62    real_-2 & real_$difference(real_2, real_-2) = real_4 &
% 13.32/2.62    real_$difference(real_2, real_2) = real_0 & real_$difference(real_2, real_0) =
% 13.32/2.62    real_2 & real_$difference(real_0, real_-2) = real_2 & real_$difference(real_0,
% 13.32/2.62      real_2) = real_-2 & real_$difference(real_0, real_0) = real_0 &
% 13.32/2.62    real_$uminus(real_-2) = real_2 & real_$uminus(real_2) = real_-2 &
% 13.32/2.62    real_$uminus(real_0) = real_0 & real_$sum(real_1, real_1) = real_2 &
% 13.32/2.62    real_$sum(real_1, real_0) = real_1 & real_$sum(real_1/2, real_1/2) = real_1 &
% 13.32/2.62    real_$sum(real_1/2, real_0) = real_1/2 & real_$sum(real_4, real_-2) = real_2 &
% 13.32/2.62    real_$sum(real_4, real_0) = real_4 & real_$sum(real_-2, real_4) = real_2 &
% 13.32/2.62    real_$sum(real_-2, real_2) = real_0 & real_$sum(real_-2, real_0) = real_-2 &
% 13.32/2.62    real_$sum(real_2, real_-2) = real_0 & real_$sum(real_2, real_2) = real_4 &
% 13.32/2.62    real_$sum(real_2, real_0) = real_2 & real_$sum(real_0, real_1) = real_1 &
% 13.32/2.62    real_$sum(real_0, real_1/2) = real_1/2 & real_$sum(real_0, real_4) = real_4 &
% 13.32/2.62    real_$sum(real_0, real_-2) = real_-2 & real_$sum(real_0, real_2) = real_2 &
% 13.32/2.62    real_$sum(real_0, real_0) = real_0 & real_$floor(real_1) = real_1 &
% 13.32/2.62    real_$floor(real_1/2) = real_0 & real_$floor(real_4) = real_4 &
% 13.32/2.62    real_$floor(real_-2) = real_-2 & real_$floor(real_2) = real_2 &
% 13.32/2.62    real_$floor(real_0) = real_0 & real_$product(real_1, real_1) = real_1 &
% 13.32/2.62    real_$product(real_1, real_1/2) = real_1/2 & real_$product(real_1, real_4) =
% 13.32/2.62    real_4 & real_$product(real_1, real_-2) = real_-2 & real_$product(real_1,
% 13.32/2.62      real_2) = real_2 & real_$product(real_1, real_0) = real_0 &
% 13.32/2.62    real_$product(real_1/2, real_1) = real_1/2 & real_$product(real_1/2, real_4) =
% 13.32/2.62    real_2 & real_$product(real_1/2, real_2) = real_1 & real_$product(real_1/2,
% 13.32/2.62      real_0) = real_0 & real_$product(real_4, real_1) = real_4 &
% 13.32/2.62    real_$product(real_4, real_1/2) = real_2 & real_$product(real_4, real_0) =
% 13.32/2.62    real_0 & real_$product(real_-2, real_1) = real_-2 & real_$product(real_-2,
% 13.32/2.62      real_-2) = real_4 & real_$product(real_-2, real_0) = real_0 &
% 13.32/2.62    real_$product(real_2, real_1) = real_2 & real_$product(real_2, real_1/2) =
% 13.32/2.62    real_1 & real_$product(real_2, real_2) = real_4 & real_$product(real_2,
% 13.32/2.62      real_0) = real_0 & real_$product(real_0, real_1) = real_0 &
% 13.32/2.62    real_$product(real_0, real_1/2) = real_0 & real_$product(real_0, real_4) =
% 13.32/2.62    real_0 & real_$product(real_0, real_-2) = real_0 & real_$product(real_0,
% 13.32/2.62      real_2) = real_0 & real_$product(real_0, real_0) = real_0 &
% 13.32/2.62    real_$is_rat(real_1) & real_$is_rat(real_1/2) & real_$is_rat(real_4) &
% 13.32/2.62    real_$is_rat(real_-2) & real_$is_rat(real_2) & real_$is_rat(real_0) &
% 13.32/2.62    real_$is_int(real_1) & real_$is_int(real_4) & real_$is_int(real_-2) &
% 13.32/2.62    real_$is_int(real_2) & real_$is_int(real_0) & real_$greatereq(real_1, real_1)
% 13.32/2.62    & real_$greatereq(real_1, real_1/2) & real_$greatereq(real_1, real_-2) &
% 13.32/2.62    real_$greatereq(real_1, real_0) & real_$greatereq(real_1/2, real_1/2) &
% 13.32/2.62    real_$greatereq(real_1/2, real_-2) & real_$greatereq(real_1/2, real_0) &
% 13.32/2.62    real_$greatereq(real_4, real_1) & real_$greatereq(real_4, real_1/2) &
% 13.32/2.62    real_$greatereq(real_4, real_4) & real_$greatereq(real_4, real_-2) &
% 13.32/2.62    real_$greatereq(real_4, real_2) & real_$greatereq(real_4, real_0) &
% 13.32/2.62    real_$greatereq(real_-2, real_-2) & real_$greatereq(real_2, real_1) &
% 13.32/2.62    real_$greatereq(real_2, real_1/2) & real_$greatereq(real_2, real_-2) &
% 13.32/2.62    real_$greatereq(real_2, real_2) & real_$greatereq(real_2, real_0) &
% 13.32/2.62    real_$greatereq(real_0, real_-2) & real_$greatereq(real_0, real_0) &
% 13.32/2.62    real_$greater(real_very_large, real_1) & real_$greater(real_very_large,
% 13.32/2.62      real_1/2) & real_$greater(real_very_large, real_4) &
% 13.32/2.62    real_$greater(real_very_large, real_-2) & real_$greater(real_very_large,
% 13.32/2.62      real_2) & real_$greater(real_very_large, real_0) & real_$greater(real_1,
% 13.32/2.63      real_very_small) & real_$greater(real_1, real_1/2) & real_$greater(real_1,
% 13.32/2.63      real_-2) & real_$greater(real_1, real_0) & real_$greater(real_1/2,
% 13.32/2.63      real_very_small) & real_$greater(real_1/2, real_-2) &
% 13.32/2.63    real_$greater(real_1/2, real_0) & real_$greater(real_4, real_very_small) &
% 13.32/2.63    real_$greater(real_4, real_1) & real_$greater(real_4, real_1/2) &
% 13.32/2.63    real_$greater(real_4, real_-2) & real_$greater(real_4, real_2) &
% 13.32/2.63    real_$greater(real_4, real_0) & real_$greater(real_-2, real_very_small) &
% 13.32/2.63    real_$greater(real_2, real_very_small) & real_$greater(real_2, real_1) &
% 13.32/2.63    real_$greater(real_2, real_1/2) & real_$greater(real_2, real_-2) &
% 13.32/2.63    real_$greater(real_2, real_0) & real_$greater(real_0, real_very_small) &
% 13.32/2.63    real_$greater(real_0, real_-2) & real_$lesseq(real_very_small,
% 13.32/2.63      real_very_large) & real_$lesseq(real_1, real_1) & real_$lesseq(real_1,
% 13.32/2.63      real_4) & real_$lesseq(real_1, real_2) & real_$lesseq(real_1/2, real_1) &
% 13.32/2.63    real_$lesseq(real_1/2, real_1/2) & real_$lesseq(real_1/2, real_4) &
% 13.32/2.63    real_$lesseq(real_1/2, real_2) & real_$lesseq(real_4, real_4) &
% 13.32/2.63    real_$lesseq(real_-2, real_1) & real_$lesseq(real_-2, real_1/2) &
% 13.32/2.63    real_$lesseq(real_-2, real_4) & real_$lesseq(real_-2, real_-2) &
% 13.32/2.63    real_$lesseq(real_-2, real_2) & real_$lesseq(real_-2, real_0) &
% 13.32/2.63    real_$lesseq(real_2, real_4) & real_$lesseq(real_2, real_2) &
% 13.32/2.63    real_$lesseq(real_0, real_1) & real_$lesseq(real_0, real_1/2) &
% 13.32/2.63    real_$lesseq(real_0, real_4) & real_$lesseq(real_0, real_2) &
% 13.32/2.63    real_$lesseq(real_0, real_0) & real_$less(real_very_small, real_very_large) &
% 13.32/2.63    real_$less(real_very_small, real_1) & real_$less(real_very_small, real_1/2) &
% 13.32/2.63    real_$less(real_very_small, real_4) & real_$less(real_very_small, real_-2) &
% 13.32/2.63    real_$less(real_very_small, real_2) & real_$less(real_very_small, real_0) &
% 13.32/2.63    real_$less(real_1, real_very_large) & real_$less(real_1, real_4) &
% 13.32/2.63    real_$less(real_1, real_2) & real_$less(real_1/2, real_very_large) &
% 13.32/2.63    real_$less(real_1/2, real_1) & real_$less(real_1/2, real_4) &
% 13.32/2.63    real_$less(real_1/2, real_2) & real_$less(real_4, real_very_large) &
% 13.32/2.63    real_$less(real_-2, real_very_large) & real_$less(real_-2, real_1) &
% 13.32/2.63    real_$less(real_-2, real_1/2) & real_$less(real_-2, real_4) &
% 13.32/2.63    real_$less(real_-2, real_2) & real_$less(real_-2, real_0) & real_$less(real_2,
% 13.32/2.63      real_very_large) & real_$less(real_2, real_4) & real_$less(real_0,
% 13.32/2.63      real_very_large) & real_$less(real_0, real_1) & real_$less(real_0, real_1/2)
% 13.32/2.63    & real_$less(real_0, real_4) & real_$less(real_0, real_2) &  ~
% 13.32/2.63    real_$is_int(real_1/2) &  ~ real_$greatereq(real_very_small, real_very_large)
% 13.32/2.63    &  ~ real_$greatereq(real_1, real_4) &  ~ real_$greatereq(real_1, real_2) &  ~
% 13.32/2.63    real_$greatereq(real_1/2, real_1) &  ~ real_$greatereq(real_1/2, real_4) &  ~
% 13.32/2.63    real_$greatereq(real_1/2, real_2) &  ~ real_$greatereq(real_-2, real_1) &  ~
% 13.32/2.63    real_$greatereq(real_-2, real_1/2) &  ~ real_$greatereq(real_-2, real_4) &  ~
% 13.32/2.63    real_$greatereq(real_-2, real_2) &  ~ real_$greatereq(real_-2, real_0) &  ~
% 13.32/2.63    real_$greatereq(real_2, real_4) &  ~ real_$greatereq(real_0, real_1) &  ~
% 13.32/2.63    real_$greatereq(real_0, real_1/2) &  ~ real_$greatereq(real_0, real_4) &  ~
% 13.32/2.63    real_$greatereq(real_0, real_2) &  ~ real_$greater(real_very_small,
% 13.32/2.63      real_very_large) &  ~ real_$greater(real_1, real_1) &  ~
% 13.32/2.63    real_$greater(real_1, real_4) &  ~ real_$greater(real_1, real_2) &  ~
% 13.32/2.63    real_$greater(real_1/2, real_1) &  ~ real_$greater(real_1/2, real_1/2) &  ~
% 13.32/2.63    real_$greater(real_1/2, real_4) &  ~ real_$greater(real_1/2, real_2) &  ~
% 13.32/2.63    real_$greater(real_4, real_4) &  ~ real_$greater(real_-2, real_1) &  ~
% 13.32/2.63    real_$greater(real_-2, real_1/2) &  ~ real_$greater(real_-2, real_4) &  ~
% 13.32/2.63    real_$greater(real_-2, real_-2) &  ~ real_$greater(real_-2, real_2) &  ~
% 13.32/2.63    real_$greater(real_-2, real_0) &  ~ real_$greater(real_2, real_4) &  ~
% 13.32/2.63    real_$greater(real_2, real_2) &  ~ real_$greater(real_0, real_1) &  ~
% 13.32/2.63    real_$greater(real_0, real_1/2) &  ~ real_$greater(real_0, real_4) &  ~
% 13.32/2.63    real_$greater(real_0, real_2) &  ~ real_$greater(real_0, real_0) &  ~
% 13.32/2.63    real_$lesseq(real_1, real_1/2) &  ~ real_$lesseq(real_1, real_-2) &  ~
% 13.32/2.63    real_$lesseq(real_1, real_0) &  ~ real_$lesseq(real_1/2, real_-2) &  ~
% 13.32/2.63    real_$lesseq(real_1/2, real_0) &  ~ real_$lesseq(real_4, real_1) &  ~
% 13.32/2.63    real_$lesseq(real_4, real_1/2) &  ~ real_$lesseq(real_4, real_-2) &  ~
% 13.32/2.63    real_$lesseq(real_4, real_2) &  ~ real_$lesseq(real_4, real_0) &  ~
% 13.32/2.63    real_$lesseq(real_2, real_1) &  ~ real_$lesseq(real_2, real_1/2) &  ~
% 13.32/2.63    real_$lesseq(real_2, real_-2) &  ~ real_$lesseq(real_2, real_0) &  ~
% 13.32/2.63    real_$lesseq(real_0, real_-2) &  ~ real_$less(real_1, real_1) &  ~
% 13.32/2.63    real_$less(real_1, real_1/2) &  ~ real_$less(real_1, real_-2) &  ~
% 13.32/2.63    real_$less(real_1, real_0) &  ~ real_$less(real_1/2, real_1/2) &  ~
% 13.32/2.63    real_$less(real_1/2, real_-2) &  ~ real_$less(real_1/2, real_0) &  ~
% 13.32/2.63    real_$less(real_4, real_1) &  ~ real_$less(real_4, real_1/2) &  ~
% 13.32/2.63    real_$less(real_4, real_4) &  ~ real_$less(real_4, real_-2) &  ~
% 13.32/2.63    real_$less(real_4, real_2) &  ~ real_$less(real_4, real_0) &  ~
% 13.32/2.63    real_$less(real_-2, real_-2) &  ~ real_$less(real_2, real_1) &  ~
% 13.32/2.63    real_$less(real_2, real_1/2) &  ~ real_$less(real_2, real_-2) &  ~
% 13.32/2.63    real_$less(real_2, real_2) &  ~ real_$less(real_2, real_0) &  ~
% 13.32/2.63    real_$less(real_0, real_-2) &  ~ real_$less(real_0, real_0) &  ! [v0: $real] :
% 13.32/2.63     ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] :  ! [v4: $real] : ( ~
% 13.32/2.63      (real_$sum(v3, v0) = v4) |  ~ (real_$sum(v2, v1) = v3) |  ? [v5: $real] :
% 13.32/2.63      (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) &  ! [v0: $real] :  !
% 13.32/2.63    [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v3 = v1 | v0 = real_0 |  ~
% 13.32/2.63      (real_$quotient(v2, v0) = v3) |  ~ (real_$product(v1, v0) = v2)) &  ! [v0:
% 13.32/2.63      $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : ( ~
% 13.32/2.63      (real_$uminus(v0) = v2) |  ~ (real_$sum(v1, v2) = v3) | real_$difference(v1,
% 13.32/2.63        v0) = v3) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v2 =
% 13.32/2.63      real_0 |  ~ (real_$uminus(v0) = v1) |  ~ (real_$sum(v0, v1) = v2)) &  ! [v0:
% 13.32/2.63      $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) |
% 13.32/2.63      real_$sum(v1, v0) = v2) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :
% 13.32/2.63    ( ~ (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2) &  ! [v0:
% 13.32/2.63      $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ real_$lesseq(v2, v1) |  ~
% 13.32/2.63      real_$lesseq(v1, v0) | real_$lesseq(v2, v0)) &  ! [v0: $real] :  ! [v1:
% 13.32/2.63      $real] :  ! [v2: $real] : ( ~ real_$lesseq(v2, v1) |  ~ real_$less(v1, v0) |
% 13.32/2.63      real_$less(v2, v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~
% 13.32/2.63      real_$lesseq(v1, v0) |  ~ real_$less(v2, v1) | real_$less(v2, v0)) &  ! [v0:
% 13.32/2.63      $real] :  ! [v1: $real] : (v1 = v0 |  ~ (real_$sum(v0, real_0) = v1)) &  !
% 13.32/2.63    [v0: $real] :  ! [v1: $real] : (v1 = v0 |  ~ real_$lesseq(v1, v0) |
% 13.32/2.63      real_$less(v1, v0)) &  ! [v0: $real] :  ! [v1: $real] : ( ~
% 13.32/2.63      (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) &  ! [v0: $real] :  ! [v1:
% 13.32/2.63      $real] : ( ~ real_$greatereq(v0, v1) | real_$lesseq(v1, v0)) &  ! [v0:
% 13.32/2.63      $real] :  ! [v1: $real] : ( ~ real_$greater(v0, v1) | real_$less(v1, v0)) & 
% 13.32/2.63    ! [v0: $real] :  ! [v1: $real] : ( ~ real_$lesseq(v1, v0) |
% 13.32/2.63      real_$greatereq(v0, v1)) &  ! [v0: $real] :  ! [v1: $real] : ( ~
% 13.32/2.63      real_$less(v1, v0) | real_$greater(v0, v1)) &  ! [v0: $real] :  ! [v1:
% 13.32/2.63      $real] : ( ~ real_$less(v1, v0) | real_$lesseq(v1, v0)) &  ! [v0: $real] :
% 13.32/2.63    (v0 = real_0 |  ~ (real_$uminus(v0) = v0)) &  ? [v0: $real] : real_$lesseq(v0,
% 13.32/2.63      v0)
% 13.32/2.63  
% 13.32/2.63    (function-axioms)
% 13.32/2.64     ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |
% 13.32/2.64       ~ (real_$quotient(v3, v2) = v1) |  ~ (real_$quotient(v3, v2) = v0)) &  !
% 13.32/2.64    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 13.32/2.64      (real_$difference(v3, v2) = v1) |  ~ (real_$difference(v3, v2) = v0)) &  !
% 13.32/2.64    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 13.32/2.64      (real_$sum(v3, v2) = v1) |  ~ (real_$sum(v3, v2) = v0)) &  ! [v0: $real] : 
% 13.32/2.64    ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 13.32/2.64      (real_$product(v3, v2) = v1) |  ~ (real_$product(v3, v2) = v0)) &  ! [v0:
% 13.32/2.64      $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$ceiling(v2)
% 13.32/2.64        = v1) |  ~ (real_$ceiling(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] : 
% 13.32/2.64    ! [v2: $real] : (v1 = v0 |  ~ (real_$truncate(v2) = v1) |  ~
% 13.32/2.64      (real_$truncate(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 13.32/2.64      $real] : (v1 = v0 |  ~ (real_$round(v2) = v1) |  ~ (real_$round(v2) = v0)) &
% 13.32/2.64     ! [v0: int] :  ! [v1: int] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$to_int(v2)
% 13.32/2.64        = v1) |  ~ (real_$to_int(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 13.32/2.64    [v2: $real] : (v1 = v0 |  ~ (real_$to_rat(v2) = v1) |  ~ (real_$to_rat(v2) =
% 13.32/2.64        v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~
% 13.32/2.64      (real_$to_real(v2) = v1) |  ~ (real_$to_real(v2) = v0)) &  ! [v0: $real] : 
% 13.32/2.64    ! [v1: $real] :  ! [v2: int] : (v1 = v0 |  ~ (int_$to_real(v2) = v1) |  ~
% 13.32/2.64      (int_$to_real(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real]
% 13.32/2.64    : (v1 = v0 |  ~ (real_$uminus(v2) = v1) |  ~ (real_$uminus(v2) = v0)) &  !
% 13.32/2.64    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$floor(v2)
% 13.32/2.64        = v1) |  ~ (real_$floor(v2) = v0))
% 13.32/2.64  
% 13.32/2.64  Those formulas are unsatisfiable:
% 13.32/2.64  ---------------------------------
% 13.32/2.64  
% 13.32/2.64  Begin of proof
% 13.32/2.64  | 
% 13.32/2.64  | ALPHA: (function-axioms) implies:
% 13.32/2.64  |   (1)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~
% 13.32/2.64  |          (real_$floor(v2) = v1) |  ~ (real_$floor(v2) = v0))
% 13.32/2.64  |   (2)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1
% 13.32/2.64  |          = v0 |  ~ (real_$product(v3, v2) = v1) |  ~ (real_$product(v3, v2) =
% 13.32/2.64  |            v0))
% 13.32/2.64  | 
% 13.32/2.64  | ALPHA: (input) implies:
% 13.32/2.64  |   (3)  real_$greater(real_1, real_0)
% 13.32/2.64  |   (4)  real_$product(real_2, real_0) = real_0
% 13.32/2.64  |   (5)  real_$product(real_2, real_1/2) = real_1
% 13.32/2.64  |   (6)  real_$floor(real_1/2) = real_0
% 13.32/2.64  |   (7)  real_$floor(real_1) = real_1
% 13.32/2.64  | 
% 13.32/2.65  | GROUND_INST: instantiating (prove) with real_1/2, real_1, simplifying with (5)
% 13.32/2.65  |              gives:
% 13.32/2.65  |   (8)   ? [v0: $real] :  ? [v1: $real] :  ? [v2: $real] : (real_$floor(real_1)
% 13.32/2.65  |          = v0 & real_$floor(real_1/2) = v1 & real_$product(real_2, v1) = v2 & 
% 13.32/2.65  |          ~ real_$greater(v0, v2))
% 13.32/2.65  | 
% 13.32/2.65  | DELTA: instantiating (8) with fresh symbols all_36_0, all_36_1, all_36_2
% 13.32/2.65  |        gives:
% 13.32/2.65  |   (9)  real_$floor(real_1) = all_36_2 & real_$floor(real_1/2) = all_36_1 &
% 13.32/2.65  |        real_$product(real_2, all_36_1) = all_36_0 &  ~ real_$greater(all_36_2,
% 13.32/2.65  |          all_36_0)
% 13.32/2.65  | 
% 13.32/2.65  | ALPHA: (9) implies:
% 13.32/2.65  |   (10)   ~ real_$greater(all_36_2, all_36_0)
% 13.32/2.65  |   (11)  real_$product(real_2, all_36_1) = all_36_0
% 13.32/2.65  |   (12)  real_$floor(real_1/2) = all_36_1
% 13.32/2.65  |   (13)  real_$floor(real_1) = all_36_2
% 13.32/2.65  | 
% 13.32/2.65  | GROUND_INST: instantiating (1) with real_0, all_36_1, real_1/2, simplifying
% 13.32/2.65  |              with (6), (12) gives:
% 13.32/2.65  |   (14)  all_36_1 = real_0
% 13.32/2.65  | 
% 13.32/2.65  | GROUND_INST: instantiating (1) with real_1, all_36_2, real_1, simplifying with
% 13.32/2.65  |              (7), (13) gives:
% 13.32/2.65  |   (15)  all_36_2 = real_1
% 13.32/2.65  | 
% 13.32/2.65  | REDUCE: (11), (14) imply:
% 13.32/2.65  |   (16)  real_$product(real_2, real_0) = all_36_0
% 13.32/2.65  | 
% 13.32/2.65  | REDUCE: (10), (15) imply:
% 13.32/2.65  |   (17)   ~ real_$greater(real_1, all_36_0)
% 13.32/2.65  | 
% 13.32/2.65  | GROUND_INST: instantiating (2) with real_0, all_36_0, real_0, real_2,
% 13.32/2.65  |              simplifying with (4), (16) gives:
% 13.32/2.65  |   (18)  all_36_0 = real_0
% 13.32/2.65  | 
% 13.32/2.65  | REDUCE: (17), (18) imply:
% 13.32/2.65  |   (19)   ~ real_$greater(real_1, real_0)
% 13.32/2.65  | 
% 13.32/2.65  | PRED_UNIFY: (3), (19) imply:
% 13.32/2.65  |   (20)  $false
% 13.49/2.65  | 
% 13.49/2.65  | CLOSE: (20) is inconsistent.
% 13.49/2.65  | 
% 13.49/2.65  End of proof
% 13.49/2.65  % SZS output end Proof for theBenchmark
% 13.49/2.65  
% 13.49/2.65  2055ms
%------------------------------------------------------------------------------