TSTP Solution File: ARI359_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI359_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 : n017.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 17:47:45 EDT 2023

% Result   : Theorem 6.03s 1.52s
% Output   : Proof 9.85s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : ARI359_1 : TPTP v8.1.2. Released v5.0.0.
% 0.11/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue Aug 29 18:18:59 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.19/0.58  ________       _____
% 0.19/0.58  ___  __ \_________(_)________________________________
% 0.19/0.58  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.58  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.58  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.58  
% 0.19/0.58  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.58  (2023-06-19)
% 0.19/0.58  
% 0.19/0.58  (c) Philipp Rümmer, 2009-2023
% 0.19/0.58  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.58                Amanda Stjerna.
% 0.19/0.58  Free software under BSD-3-Clause.
% 0.19/0.58  
% 0.19/0.58  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.58  
% 0.19/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.60  Running up to 7 provers in parallel.
% 0.19/0.61  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.61  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.61  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.61  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.61  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.61  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.61  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.33/0.89  Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.33/0.89  Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.33/0.89  Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.33/0.89  Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.33/0.89  Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.33/0.89  Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.33/0.89  Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.97/0.95  Prover 4: Preprocessing ...
% 1.97/0.97  Prover 1: Preprocessing ...
% 2.48/1.02  Prover 0: Preprocessing ...
% 2.48/1.02  Prover 6: Preprocessing ...
% 3.10/1.08  Prover 3: Preprocessing ...
% 3.15/1.08  Prover 2: Preprocessing ...
% 3.15/1.08  Prover 5: Preprocessing ...
% 6.03/1.48  Prover 6: Constructing countermodel ...
% 6.03/1.50  Prover 1: Constructing countermodel ...
% 6.03/1.51  Prover 6: proved (903ms)
% 6.03/1.51  
% 6.03/1.52  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.03/1.52  
% 6.38/1.52  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.38/1.52  Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 6.38/1.54  Prover 0: Constructing countermodel ...
% 6.38/1.54  Prover 2: stopped
% 6.38/1.55  Prover 0: stopped
% 6.57/1.55  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.57/1.55  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.57/1.55  Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 6.57/1.55  Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 6.57/1.56  Prover 8: Preprocessing ...
% 6.57/1.57  Prover 4: Constructing countermodel ...
% 6.57/1.59  Prover 7: Preprocessing ...
% 6.57/1.60  Prover 10: Preprocessing ...
% 7.51/1.71  Prover 8: Warning: ignoring some quantifiers
% 7.51/1.73  Prover 8: Constructing countermodel ...
% 8.59/1.84  Prover 4: Found proof (size 7)
% 8.59/1.84  Prover 1: Found proof (size 7)
% 8.59/1.84  Prover 4: proved (1230ms)
% 8.59/1.84  Prover 8: stopped
% 8.59/1.84  Prover 1: proved (1236ms)
% 8.81/1.85  Prover 7: stopped
% 8.81/1.85  Prover 10: stopped
% 8.81/1.91  Prover 5: Constructing countermodel ...
% 8.81/1.91  Prover 5: stopped
% 8.81/1.96  Prover 3: Constructing countermodel ...
% 8.81/1.96  Prover 3: stopped
% 8.81/1.96  
% 8.81/1.96  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.81/1.96  
% 8.81/1.97  % SZS output start Proof for theBenchmark
% 8.81/1.97  Assumptions after simplification:
% 8.81/1.97  ---------------------------------
% 8.81/1.97  
% 8.81/1.97    (real_lesseq_problem_2)
% 9.47/1.99     ? [v0: int] : ( ~ (v0 = 0) & real_$lesseq(real_13/4, real_39/5) = v0)
% 9.47/1.99  
% 9.47/1.99    (input)
% 9.47/2.02     ~ (real_very_large = real_very_small) &  ~ (real_very_large = real_39/5) &  ~
% 9.47/2.02    (real_very_large = real_13/4) &  ~ (real_very_large = real_0) &  ~
% 9.47/2.02    (real_very_small = real_39/5) &  ~ (real_very_small = real_13/4) &  ~
% 9.47/2.02    (real_very_small = real_0) &  ~ (real_39/5 = real_13/4) &  ~ (real_39/5 =
% 9.47/2.02      real_0) &  ~ (real_13/4 = real_0) & real_$is_int(real_39/5) = 1 &
% 9.47/2.02    real_$is_int(real_13/4) = 1 & real_$is_int(real_0) = 0 &
% 9.47/2.02    real_$is_rat(real_39/5) = 0 & real_$is_rat(real_13/4) = 0 &
% 9.47/2.02    real_$is_rat(real_0) = 0 & real_$floor(real_0) = real_0 &
% 9.47/2.02    real_$ceiling(real_0) = real_0 & real_$truncate(real_0) = real_0 &
% 9.47/2.02    real_$round(real_0) = real_0 & real_$to_int(real_39/5) = 7 &
% 9.47/2.02    real_$to_int(real_13/4) = 3 & real_$to_int(real_0) = 0 &
% 9.47/2.02    real_$to_rat(real_39/5) = rat_39/5 & real_$to_rat(real_13/4) = rat_13/4 &
% 9.47/2.02    real_$to_rat(real_0) = rat_0 & real_$to_real(real_39/5) = real_39/5 &
% 9.47/2.02    real_$to_real(real_13/4) = real_13/4 & real_$to_real(real_0) = real_0 &
% 9.47/2.02    int_$to_real(0) = real_0 & real_$quotient(real_0, real_39/5) = real_0 &
% 9.47/2.02    real_$quotient(real_0, real_13/4) = real_0 & real_$product(real_39/5, real_0)
% 9.47/2.02    = real_0 & real_$product(real_13/4, real_0) = real_0 & real_$product(real_0,
% 9.47/2.02      real_39/5) = real_0 & real_$product(real_0, real_13/4) = real_0 &
% 9.47/2.02    real_$product(real_0, real_0) = real_0 & real_$difference(real_39/5,
% 9.47/2.02      real_39/5) = real_0 & real_$difference(real_39/5, real_0) = real_39/5 &
% 9.47/2.02    real_$difference(real_13/4, real_13/4) = real_0 & real_$difference(real_13/4,
% 9.47/2.02      real_0) = real_13/4 & real_$difference(real_0, real_0) = real_0 &
% 9.47/2.02    real_$uminus(real_0) = real_0 & real_$sum(real_39/5, real_0) = real_39/5 &
% 9.47/2.02    real_$sum(real_13/4, real_0) = real_13/4 & real_$sum(real_0, real_39/5) =
% 9.47/2.02    real_39/5 & real_$sum(real_0, real_13/4) = real_13/4 & real_$sum(real_0,
% 9.47/2.02      real_0) = real_0 & real_$greatereq(real_very_small, real_very_large) = 1 &
% 9.47/2.02    real_$greatereq(real_39/5, real_39/5) = 0 & real_$greatereq(real_39/5,
% 9.47/2.02      real_13/4) = 0 & real_$greatereq(real_39/5, real_0) = 0 &
% 9.47/2.02    real_$greatereq(real_13/4, real_39/5) = 1 & real_$greatereq(real_13/4,
% 9.47/2.02      real_13/4) = 0 & real_$greatereq(real_13/4, real_0) = 0 &
% 9.47/2.02    real_$greatereq(real_0, real_39/5) = 1 & real_$greatereq(real_0, real_13/4) =
% 9.47/2.02    1 & real_$greatereq(real_0, real_0) = 0 & real_$greater(real_very_large,
% 9.47/2.02      real_39/5) = 0 & real_$greater(real_very_large, real_13/4) = 0 &
% 9.47/2.02    real_$greater(real_very_large, real_0) = 0 & real_$greater(real_very_small,
% 9.47/2.02      real_very_large) = 1 & real_$greater(real_39/5, real_very_small) = 0 &
% 9.47/2.02    real_$greater(real_39/5, real_39/5) = 1 & real_$greater(real_39/5, real_13/4)
% 9.47/2.02    = 0 & real_$greater(real_39/5, real_0) = 0 & real_$greater(real_13/4,
% 9.47/2.02      real_very_small) = 0 & real_$greater(real_13/4, real_39/5) = 1 &
% 9.47/2.02    real_$greater(real_13/4, real_13/4) = 1 & real_$greater(real_13/4, real_0) = 0
% 9.47/2.02    & real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0,
% 9.47/2.02      real_39/5) = 1 & real_$greater(real_0, real_13/4) = 1 &
% 9.47/2.02    real_$greater(real_0, real_0) = 1 & real_$less(real_very_small,
% 9.47/2.02      real_very_large) = 0 & real_$less(real_very_small, real_39/5) = 0 &
% 9.47/2.02    real_$less(real_very_small, real_13/4) = 0 & real_$less(real_very_small,
% 9.47/2.02      real_0) = 0 & real_$less(real_39/5, real_very_large) = 0 &
% 9.47/2.02    real_$less(real_39/5, real_39/5) = 1 & real_$less(real_39/5, real_13/4) = 1 &
% 9.47/2.02    real_$less(real_39/5, real_0) = 1 & real_$less(real_13/4, real_very_large) = 0
% 9.47/2.03    & real_$less(real_13/4, real_39/5) = 0 & real_$less(real_13/4, real_13/4) = 1
% 9.47/2.03    & real_$less(real_13/4, real_0) = 1 & real_$less(real_0, real_very_large) = 0
% 9.47/2.03    & real_$less(real_0, real_39/5) = 0 & real_$less(real_0, real_13/4) = 0 &
% 9.47/2.03    real_$less(real_0, real_0) = 1 & real_$lesseq(real_very_small,
% 9.47/2.03      real_very_large) = 0 & real_$lesseq(real_39/5, real_39/5) = 0 &
% 9.47/2.03    real_$lesseq(real_39/5, real_13/4) = 1 & real_$lesseq(real_39/5, real_0) = 1 &
% 9.47/2.03    real_$lesseq(real_13/4, real_39/5) = 0 & real_$lesseq(real_13/4, real_13/4) =
% 9.47/2.03    0 & real_$lesseq(real_13/4, real_0) = 1 & real_$lesseq(real_0, real_39/5) = 0
% 9.47/2.03    & real_$lesseq(real_0, real_13/4) = 0 & real_$lesseq(real_0, real_0) = 0 &  !
% 9.47/2.03    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] :  ! [v4:
% 9.47/2.03      $real] : ( ~ (real_$sum(v3, v0) = v4) |  ~ (real_$sum(v2, v1) = v3) |  ?
% 9.47/2.03      [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) &  ! [v0:
% 9.47/2.03      $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] :  ! [v4: $real] :
% 9.47/2.03    ( ~ (real_$sum(v2, v3) = v4) |  ~ (real_$sum(v1, v0) = v3) |  ? [v5: $real] :
% 9.47/2.03      (real_$sum(v5, v0) = v4 & real_$sum(v2, v1) = v5)) &  ! [v0: $real] :  !
% 9.47/2.03    [v1: $real] :  ! [v2: $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$less(v2, v1)
% 9.47/2.03        = 0) |  ~ (real_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) &
% 9.47/2.03        real_$lesseq(v1, v0) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 9.47/2.03      $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$less(v2, v0) = v3) |  ~
% 9.47/2.03      (real_$less(v1, v0) = 0) |  ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2,
% 9.47/2.03          v1) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3:
% 9.47/2.03      int] : (v3 = 0 |  ~ (real_$less(v2, v0) = v3) |  ~ (real_$lesseq(v2, v1) =
% 9.47/2.03        0) |  ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0) = v4)) &  ! [v0:
% 9.47/2.03      $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: int] : (v3 = 0 |  ~
% 9.47/2.03      (real_$less(v2, v0) = v3) |  ~ (real_$lesseq(v1, v0) = 0) |  ? [v4: int] : (
% 9.47/2.03        ~ (v4 = 0) & real_$less(v2, v1) = v4)) &  ! [v0: $real] :  ! [v1: $real] :
% 9.47/2.03     ! [v2: $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$lesseq(v2, v1) = 0) |  ~
% 9.47/2.03      (real_$lesseq(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1,
% 9.47/2.03          v0) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3:
% 9.47/2.03      int] : (v3 = 0 |  ~ (real_$lesseq(v2, v0) = v3) |  ~ (real_$lesseq(v1, v0) =
% 9.47/2.03        0) |  ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) &  ! [v0:
% 9.47/2.03      $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : ( ~
% 9.47/2.03      (real_$uminus(v0) = v2) |  ~ (real_$sum(v1, v2) = v3) | real_$difference(v1,
% 9.47/2.03        v0) = v3) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: int] : (v2 = 0 | v1
% 9.47/2.03      = v0 |  ~ (real_$less(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3 = 0) &
% 9.47/2.03        real_$lesseq(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 9.47/2.03      int] : (v2 = 0 |  ~ (real_$greatereq(v0, v1) = v2) |  ? [v3: int] : ( ~ (v3
% 9.47/2.03          = 0) & real_$lesseq(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 9.47/2.03    ! [v2: int] : (v2 = 0 |  ~ (real_$greater(v0, v1) = v2) |  ? [v3: int] : ( ~
% 9.47/2.03        (v3 = 0) & real_$less(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 9.47/2.03    ! [v2: int] : (v2 = 0 |  ~ (real_$less(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3
% 9.47/2.03          = 0) & real_$greater(v0, v1) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 9.47/2.03    ! [v2: int] : (v2 = 0 |  ~ (real_$lesseq(v1, v0) = v2) |  ? [v3: int] : ( ~
% 9.47/2.03        (v3 = 0) & real_$greatereq(v0, v1) = v3)) &  ! [v0: $real] :  ! [v1:
% 9.47/2.03      $real] :  ! [v2: int] : (v2 = 0 |  ~ (real_$lesseq(v1, v0) = v2) |  ? [v3:
% 9.47/2.03        int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1:
% 9.47/2.03      $real] :  ! [v2: $real] : (v0 = real_0 |  ~ (real_$product(v1, v0) = v2) |
% 9.47/2.03      real_$quotient(v2, v0) = v1) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 9.47/2.03      $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) &  !
% 9.47/2.03    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ (real_$product(v0, v1) =
% 9.47/2.03        v2) | real_$product(v1, v0) = v2) &  ! [v0: $real] :  ! [v1: $real] :  !
% 9.47/2.03    [v2: $real] : ( ~ (real_$difference(v1, v0) = v2) |  ? [v3: $real] :
% 9.47/2.03      (real_$uminus(v0) = v3 & real_$sum(v1, v3) = v2)) &  ! [v0: $real] :  ! [v1:
% 9.47/2.03      $real] :  ! [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0, v1) =
% 9.47/2.03      v2) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ (real_$sum(v0,
% 9.47/2.03          v1) = v2) | real_$sum(v1, v0) = v2) &  ! [v0: $real] :  ! [v1: $real] : 
% 9.47/2.03    ! [v2: $real] : ( ~ (real_$less(v2, v1) = 0) |  ~ (real_$lesseq(v1, v0) = 0) |
% 9.47/2.03      real_$less(v2, v0) = 0) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :
% 9.47/2.03    ( ~ (real_$less(v1, v0) = 0) |  ~ (real_$lesseq(v2, v1) = 0) | real_$less(v2,
% 9.47/2.03        v0) = 0) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~
% 9.47/2.03      (real_$lesseq(v2, v1) = 0) |  ~ (real_$lesseq(v1, v0) = 0) |
% 9.47/2.03      real_$lesseq(v2, v0) = 0) &  ! [v0: $real] :  ! [v1: $real] : (v1 = v0 |  ~
% 9.47/2.03      (real_$sum(v0, real_0) = v1)) &  ! [v0: $real] :  ! [v1: $real] : (v1 = v0 |
% 9.47/2.03       ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = 0) &  ! [v0: $real] : 
% 9.47/2.03    ! [v1: int] : (v1 = 0 |  ~ (real_$lesseq(v0, v0) = v1)) &  ! [v0: $real] :  !
% 9.47/2.03    [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) &  ! [v0:
% 9.47/2.03      $real] :  ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$sum(v0, v1) =
% 9.47/2.03      real_0) &  ! [v0: $real] :  ! [v1: $real] : ( ~ (real_$greatereq(v0, v1) =
% 9.47/2.03        0) | real_$lesseq(v1, v0) = 0) &  ! [v0: $real] :  ! [v1: $real] : ( ~
% 9.47/2.03      (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) &  ! [v0: $real] :  !
% 9.47/2.03    [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | real_$greater(v0, v1) = 0) &  !
% 9.47/2.03    [v0: $real] :  ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | real_$lesseq(v1,
% 9.47/2.03        v0) = 0) &  ! [v0: $real] :  ! [v1: MultipleValueBool] : ( ~
% 9.47/2.03      (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0) = 0) &  ! [v0: $real] :  !
% 9.47/2.03    [v1: $real] : ( ~ (real_$lesseq(v1, v0) = 0) | real_$greatereq(v0, v1) = 0) & 
% 9.47/2.03    ! [v0: $real] : (v0 = real_0 |  ~ (real_$uminus(v0) = v0))
% 9.47/2.03  
% 9.47/2.03    (function-axioms)
% 9.47/2.04     ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |
% 9.47/2.04       ~ (real_$quotient(v3, v2) = v1) |  ~ (real_$quotient(v3, v2) = v0)) &  !
% 9.47/2.04    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 9.47/2.04      (real_$product(v3, v2) = v1) |  ~ (real_$product(v3, v2) = v0)) &  ! [v0:
% 9.47/2.04      $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 9.47/2.04      (real_$difference(v3, v2) = v1) |  ~ (real_$difference(v3, v2) = v0)) &  !
% 9.47/2.04    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 9.47/2.04      (real_$sum(v3, v2) = v1) |  ~ (real_$sum(v3, v2) = v0)) &  ! [v0:
% 9.47/2.04      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $real] :  ! [v3:
% 9.47/2.04      $real] : (v1 = v0 |  ~ (real_$greatereq(v3, v2) = v1) |  ~
% 9.47/2.04      (real_$greatereq(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.47/2.04      MultipleValueBool] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 9.47/2.04      (real_$greater(v3, v2) = v1) |  ~ (real_$greater(v3, v2) = v0)) &  ! [v0:
% 9.47/2.04      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $real] :  ! [v3:
% 9.47/2.04      $real] : (v1 = v0 |  ~ (real_$less(v3, v2) = v1) |  ~ (real_$less(v3, v2) =
% 9.47/2.04        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 9.47/2.04      $real] :  ! [v3: $real] : (v1 = v0 |  ~ (real_$lesseq(v3, v2) = v1) |  ~
% 9.47/2.04      (real_$lesseq(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.47/2.04      MultipleValueBool] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$is_int(v2) = v1)
% 9.47/2.04      |  ~ (real_$is_int(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.47/2.04      MultipleValueBool] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$is_rat(v2) = v1)
% 9.47/2.04      |  ~ (real_$is_rat(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 9.47/2.04      $real] : (v1 = v0 |  ~ (real_$floor(v2) = v1) |  ~ (real_$floor(v2) = v0)) &
% 9.47/2.04     ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~
% 9.47/2.04      (real_$ceiling(v2) = v1) |  ~ (real_$ceiling(v2) = v0)) &  ! [v0: $real] : 
% 9.47/2.04    ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$truncate(v2) = v1) |  ~
% 9.47/2.04      (real_$truncate(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 9.47/2.04      $real] : (v1 = v0 |  ~ (real_$round(v2) = v1) |  ~ (real_$round(v2) = v0)) &
% 9.47/2.04     ! [v0: int] :  ! [v1: int] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$to_int(v2)
% 9.47/2.04        = v1) |  ~ (real_$to_int(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 9.47/2.04    [v2: $real] : (v1 = v0 |  ~ (real_$to_rat(v2) = v1) |  ~ (real_$to_rat(v2) =
% 9.47/2.04        v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~
% 9.47/2.04      (real_$to_real(v2) = v1) |  ~ (real_$to_real(v2) = v0)) &  ! [v0: $real] : 
% 9.47/2.04    ! [v1: $real] :  ! [v2: int] : (v1 = v0 |  ~ (int_$to_real(v2) = v1) |  ~
% 9.47/2.04      (int_$to_real(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real]
% 9.47/2.04    : (v1 = v0 |  ~ (real_$uminus(v2) = v1) |  ~ (real_$uminus(v2) = v0))
% 9.47/2.04  
% 9.47/2.04  Those formulas are unsatisfiable:
% 9.47/2.04  ---------------------------------
% 9.47/2.04  
% 9.47/2.04  Begin of proof
% 9.47/2.04  | 
% 9.85/2.04  | ALPHA: (function-axioms) implies:
% 9.85/2.04  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 9.85/2.04  |          $real] :  ! [v3: $real] : (v1 = v0 |  ~ (real_$lesseq(v3, v2) = v1) |
% 9.85/2.04  |           ~ (real_$lesseq(v3, v2) = v0))
% 9.85/2.04  | 
% 9.85/2.04  | ALPHA: (input) implies:
% 9.85/2.04  |   (2)  real_$lesseq(real_13/4, real_39/5) = 0
% 9.85/2.04  | 
% 9.85/2.05  | DELTA: instantiating (real_lesseq_problem_2) with fresh symbol all_5_0 gives:
% 9.85/2.05  |   (3)   ~ (all_5_0 = 0) & real_$lesseq(real_13/4, real_39/5) = all_5_0
% 9.85/2.05  | 
% 9.85/2.05  | ALPHA: (3) implies:
% 9.85/2.05  |   (4)   ~ (all_5_0 = 0)
% 9.85/2.05  |   (5)  real_$lesseq(real_13/4, real_39/5) = all_5_0
% 9.85/2.05  | 
% 9.85/2.05  | GROUND_INST: instantiating (1) with 0, all_5_0, real_39/5, real_13/4,
% 9.85/2.05  |              simplifying with (2), (5) gives:
% 9.85/2.05  |   (6)  all_5_0 = 0
% 9.85/2.05  | 
% 9.85/2.05  | REDUCE: (4), (6) imply:
% 9.85/2.05  |   (7)  $false
% 9.85/2.05  | 
% 9.85/2.05  | CLOSE: (7) is inconsistent.
% 9.85/2.05  | 
% 9.85/2.05  End of proof
% 9.85/2.05  % SZS output end Proof for theBenchmark
% 9.85/2.05  
% 9.85/2.05  1464ms
%------------------------------------------------------------------------------