TSTP Solution File: ARI385_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI385_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 : n018.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 17:47:51 EDT 2023

% Result   : Theorem 5.68s 1.52s
% Output   : Proof 8.02s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : ARI385_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35  % Computer : n018.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Tue Aug 29 18:18:48 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.61  ________       _____
% 0.21/0.61  ___  __ \_________(_)________________________________
% 0.21/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61  
% 0.21/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61  (2023-06-19)
% 0.21/0.61  
% 0.21/0.61  (c) Philipp Rümmer, 2009-2023
% 0.21/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61                Amanda Stjerna.
% 0.21/0.61  Free software under BSD-3-Clause.
% 0.21/0.61  
% 0.21/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61  
% 0.21/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63  Running up to 7 provers in parallel.
% 0.21/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.66/0.98  Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.66/0.98  Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.66/0.98  Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.66/0.98  Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.66/0.98  Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.66/0.98  Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.66/0.98  Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 2.02/1.03  Prover 1: Preprocessing ...
% 2.02/1.03  Prover 4: Preprocessing ...
% 2.57/1.07  Prover 6: Preprocessing ...
% 2.57/1.07  Prover 3: Preprocessing ...
% 2.57/1.07  Prover 5: Preprocessing ...
% 2.57/1.07  Prover 0: Preprocessing ...
% 2.57/1.07  Prover 2: Preprocessing ...
% 5.36/1.49  Prover 6: Constructing countermodel ...
% 5.36/1.49  Prover 2: Constructing countermodel ...
% 5.36/1.49  Prover 5: Constructing countermodel ...
% 5.36/1.51  Prover 1: Constructing countermodel ...
% 5.68/1.52  Prover 2: proved (882ms)
% 5.68/1.52  Prover 6: proved (878ms)
% 5.68/1.52  
% 5.68/1.52  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.68/1.52  
% 5.68/1.52  
% 5.68/1.52  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.68/1.52  
% 5.68/1.54  Prover 5: proved (880ms)
% 5.68/1.54  
% 5.68/1.54  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.68/1.54  
% 5.68/1.54  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.68/1.54  Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 5.68/1.54  Prover 0: Constructing countermodel ...
% 5.68/1.54  Prover 0: stopped
% 5.68/1.54  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.68/1.54  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.68/1.54  Prover 3: Constructing countermodel ...
% 5.68/1.54  Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 5.68/1.54  Prover 3: stopped
% 5.92/1.55  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.92/1.55  Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 5.92/1.55  Prover 11: Warning: Problem contains reals, using incomplete axiomatisation
% 5.92/1.55  Prover 8: Preprocessing ...
% 5.92/1.56  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.92/1.56  Prover 4: Constructing countermodel ...
% 5.92/1.56  Prover 7: Preprocessing ...
% 5.92/1.56  Prover 10: Preprocessing ...
% 5.92/1.57  Prover 11: Preprocessing ...
% 5.92/1.57  Prover 13: Warning: Problem contains reals, using incomplete axiomatisation
% 5.92/1.59  Prover 13: Preprocessing ...
% 6.90/1.71  Prover 8: Warning: ignoring some quantifiers
% 6.90/1.73  Prover 8: Constructing countermodel ...
% 6.90/1.75  Prover 4: Found proof (size 7)
% 6.90/1.75  Prover 4: proved (1116ms)
% 7.43/1.76  Prover 13: Warning: ignoring some quantifiers
% 7.52/1.77  Prover 8: stopped
% 7.52/1.77  Prover 1: Found proof (size 7)
% 7.52/1.77  Prover 1: proved (1133ms)
% 7.52/1.77  Prover 13: Constructing countermodel ...
% 7.52/1.78  Prover 13: stopped
% 7.52/1.78  Prover 10: Warning: ignoring some quantifiers
% 7.52/1.79  Prover 10: Constructing countermodel ...
% 7.52/1.80  Prover 10: stopped
% 7.52/1.80  Prover 7: Warning: ignoring some quantifiers
% 7.84/1.81  Prover 7: Constructing countermodel ...
% 7.84/1.82  Prover 7: stopped
% 8.02/1.86  Prover 11: Constructing countermodel ...
% 8.02/1.87  Prover 11: stopped
% 8.02/1.87  
% 8.02/1.87  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.02/1.87  
% 8.02/1.87  % SZS output start Proof for theBenchmark
% 8.02/1.88  Assumptions after simplification:
% 8.02/1.88  ---------------------------------
% 8.02/1.88  
% 8.02/1.88    (real_greatereq_problem_1)
% 8.02/1.90     ? [v0: int] : ( ~ (v0 = 0) & real_$greatereq(real_13/4, real_13/4) = v0)
% 8.02/1.90  
% 8.02/1.90    (input)
% 8.02/1.93     ~ (real_very_large = real_very_small) &  ~ (real_very_large = real_13/4) &  ~
% 8.02/1.93    (real_very_large = real_0) &  ~ (real_very_small = real_13/4) &  ~
% 8.02/1.93    (real_very_small = real_0) &  ~ (real_13/4 = real_0) & real_$is_int(real_13/4)
% 8.02/1.93    = 1 & real_$is_int(real_0) = 0 & real_$is_rat(real_13/4) = 0 &
% 8.02/1.93    real_$is_rat(real_0) = 0 & real_$floor(real_0) = real_0 &
% 8.02/1.93    real_$ceiling(real_0) = real_0 & real_$truncate(real_0) = real_0 &
% 8.02/1.93    real_$round(real_0) = real_0 & real_$to_int(real_13/4) = 3 &
% 8.02/1.93    real_$to_int(real_0) = 0 & real_$to_rat(real_13/4) = rat_13/4 &
% 8.02/1.93    real_$to_rat(real_0) = rat_0 & real_$to_real(real_13/4) = real_13/4 &
% 8.02/1.93    real_$to_real(real_0) = real_0 & int_$to_real(0) = real_0 &
% 8.02/1.93    real_$quotient(real_0, real_13/4) = real_0 & real_$product(real_13/4, real_0)
% 8.02/1.93    = real_0 & real_$product(real_0, real_13/4) = real_0 & real_$product(real_0,
% 8.02/1.93      real_0) = real_0 & real_$difference(real_13/4, real_13/4) = real_0 &
% 8.02/1.93    real_$difference(real_13/4, real_0) = real_13/4 & real_$difference(real_0,
% 8.02/1.93      real_0) = real_0 & real_$uminus(real_0) = real_0 & real_$sum(real_13/4,
% 8.02/1.93      real_0) = real_13/4 & real_$sum(real_0, real_13/4) = real_13/4 &
% 8.02/1.93    real_$sum(real_0, real_0) = real_0 & real_$lesseq(real_very_small,
% 8.02/1.93      real_very_large) = 0 & real_$lesseq(real_13/4, real_13/4) = 0 &
% 8.02/1.93    real_$lesseq(real_13/4, real_0) = 1 & real_$lesseq(real_0, real_13/4) = 0 &
% 8.02/1.93    real_$lesseq(real_0, real_0) = 0 & real_$greater(real_very_large, real_13/4) =
% 8.02/1.93    0 & real_$greater(real_very_large, real_0) = 0 &
% 8.02/1.93    real_$greater(real_very_small, real_very_large) = 1 & real_$greater(real_13/4,
% 8.02/1.93      real_very_small) = 0 & real_$greater(real_13/4, real_13/4) = 1 &
% 8.02/1.93    real_$greater(real_13/4, real_0) = 0 & real_$greater(real_0, real_very_small)
% 8.02/1.93    = 0 & real_$greater(real_0, real_13/4) = 1 & real_$greater(real_0, real_0) = 1
% 8.02/1.93    & real_$less(real_very_small, real_very_large) = 0 &
% 8.02/1.93    real_$less(real_very_small, real_13/4) = 0 & real_$less(real_very_small,
% 8.02/1.93      real_0) = 0 & real_$less(real_13/4, real_very_large) = 0 &
% 8.02/1.93    real_$less(real_13/4, real_13/4) = 1 & real_$less(real_13/4, real_0) = 1 &
% 8.02/1.93    real_$less(real_0, real_very_large) = 0 & real_$less(real_0, real_13/4) = 0 &
% 8.02/1.93    real_$less(real_0, real_0) = 1 & real_$greatereq(real_very_small,
% 8.02/1.93      real_very_large) = 1 & real_$greatereq(real_13/4, real_13/4) = 0 &
% 8.02/1.93    real_$greatereq(real_13/4, real_0) = 0 & real_$greatereq(real_0, real_13/4) =
% 8.02/1.93    1 & real_$greatereq(real_0, real_0) = 0 &  ! [v0: $real] :  ! [v1: $real] :  !
% 8.02/1.93    [v2: $real] :  ! [v3: $real] :  ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) |
% 8.02/1.93       ~ (real_$sum(v2, v1) = v3) |  ? [v5: $real] : (real_$sum(v2, v5) = v4 &
% 8.02/1.93        real_$sum(v1, v0) = v5)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 8.02/1.93      $real] :  ! [v3: $real] :  ! [v4: $real] : ( ~ (real_$sum(v2, v3) = v4) |  ~
% 8.02/1.93      (real_$sum(v1, v0) = v3) |  ? [v5: $real] : (real_$sum(v5, v0) = v4 &
% 8.02/1.93        real_$sum(v2, v1) = v5)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 8.02/1.93      $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$lesseq(v2, v1) = 0) |  ~
% 8.02/1.93      (real_$lesseq(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1,
% 8.02/1.93          v0) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3:
% 8.02/1.93      int] : (v3 = 0 |  ~ (real_$lesseq(v2, v1) = 0) |  ~ (real_$less(v2, v0) =
% 8.02/1.93        v3) |  ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0) = v4)) &  ! [v0:
% 8.02/1.93      $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: int] : (v3 = 0 |  ~
% 8.02/1.93      (real_$lesseq(v2, v0) = v3) |  ~ (real_$lesseq(v1, v0) = 0) |  ? [v4: int] :
% 8.02/1.93      ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) &  ! [v0: $real] :  ! [v1: $real]
% 8.02/1.93    :  ! [v2: $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$lesseq(v1, v0) = 0) |  ~
% 8.02/1.93      (real_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2, v1)
% 8.02/1.93        = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: int] :
% 8.02/1.93    (v3 = 0 |  ~ (real_$less(v2, v1) = 0) |  ~ (real_$less(v2, v0) = v3) |  ? [v4:
% 8.02/1.93        int] : ( ~ (v4 = 0) & real_$lesseq(v1, v0) = v4)) &  ! [v0: $real] :  !
% 8.02/1.93    [v1: $real] :  ! [v2: $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$less(v2, v0)
% 8.02/1.93        = v3) |  ~ (real_$less(v1, v0) = 0) |  ? [v4: int] : ( ~ (v4 = 0) &
% 8.02/1.93        real_$lesseq(v2, v1) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 8.02/1.93      $real] :  ! [v3: $real] : ( ~ (real_$uminus(v0) = v2) |  ~ (real_$sum(v1,
% 8.02/1.93          v2) = v3) | real_$difference(v1, v0) = v3) &  ! [v0: $real] :  ! [v1:
% 8.02/1.93      $real] :  ! [v2: int] : (v2 = 0 | v1 = v0 |  ~ (real_$less(v1, v0) = v2) | 
% 8.02/1.93      ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) &  ! [v0: $real] : 
% 8.02/1.93    ! [v1: $real] :  ! [v2: int] : (v2 = 0 |  ~ (real_$lesseq(v1, v0) = v2) |  ?
% 8.02/1.93      [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) &  ! [v0: $real] :  !
% 8.02/1.93    [v1: $real] :  ! [v2: int] : (v2 = 0 |  ~ (real_$lesseq(v1, v0) = v2) |  ?
% 8.02/1.93      [v3: int] : ( ~ (v3 = 0) & real_$greatereq(v0, v1) = v3)) &  ! [v0: $real] :
% 8.02/1.93     ! [v1: $real] :  ! [v2: int] : (v2 = 0 |  ~ (real_$greater(v0, v1) = v2) |  ?
% 8.02/1.93      [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) &  ! [v0: $real] :  !
% 8.02/1.93    [v1: $real] :  ! [v2: int] : (v2 = 0 |  ~ (real_$less(v1, v0) = v2) |  ? [v3:
% 8.02/1.93        int] : ( ~ (v3 = 0) & real_$greater(v0, v1) = v3)) &  ! [v0: $real] :  !
% 8.02/1.93    [v1: $real] :  ! [v2: int] : (v2 = 0 |  ~ (real_$greatereq(v0, v1) = v2) |  ?
% 8.02/1.93      [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) &  ! [v0: $real] :  !
% 8.02/1.93    [v1: $real] :  ! [v2: $real] : (v0 = real_0 |  ~ (real_$product(v1, v0) = v2)
% 8.02/1.93      | real_$quotient(v2, v0) = v1) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 8.02/1.93      $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) &  !
% 8.02/1.93    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ (real_$product(v0, v1) =
% 8.02/1.93        v2) | real_$product(v1, v0) = v2) &  ! [v0: $real] :  ! [v1: $real] :  !
% 8.02/1.93    [v2: $real] : ( ~ (real_$difference(v1, v0) = v2) |  ? [v3: $real] :
% 8.02/1.93      (real_$uminus(v0) = v3 & real_$sum(v1, v3) = v2)) &  ! [v0: $real] :  ! [v1:
% 8.02/1.93      $real] :  ! [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0, v1) =
% 8.02/1.93      v2) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ (real_$sum(v0,
% 8.02/1.93          v1) = v2) | real_$sum(v1, v0) = v2) &  ! [v0: $real] :  ! [v1: $real] : 
% 8.02/1.94    ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) |  ~ (real_$lesseq(v1, v0) = 0)
% 8.02/1.94      | real_$lesseq(v2, v0) = 0) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 8.02/1.94      $real] : ( ~ (real_$lesseq(v2, v1) = 0) |  ~ (real_$less(v1, v0) = 0) |
% 8.02/1.94      real_$less(v2, v0) = 0) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :
% 8.02/1.94    ( ~ (real_$lesseq(v1, v0) = 0) |  ~ (real_$less(v2, v1) = 0) | real_$less(v2,
% 8.02/1.94        v0) = 0) &  ! [v0: $real] :  ! [v1: $real] : (v1 = v0 |  ~ (real_$sum(v0,
% 8.02/1.94          real_0) = v1)) &  ! [v0: $real] :  ! [v1: $real] : (v1 = v0 |  ~
% 8.02/1.94      (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = 0) &  ! [v0: $real] :  !
% 8.02/1.94    [v1: int] : (v1 = 0 |  ~ (real_$lesseq(v0, v0) = v1)) &  ! [v0: $real] :  !
% 8.02/1.94    [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) &  ! [v0:
% 8.02/1.94      $real] :  ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$sum(v0, v1) =
% 8.02/1.94      real_0) &  ! [v0: $real] :  ! [v1: $real] : ( ~ (real_$lesseq(v1, v0) = 0) |
% 8.02/1.94      real_$greatereq(v0, v1) = 0) &  ! [v0: $real] :  ! [v1: $real] : ( ~
% 8.02/1.94      (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) &  ! [v0: $real] :  !
% 8.02/1.94    [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | real_$lesseq(v1, v0) = 0) &  !
% 8.02/1.94    [v0: $real] :  ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) |
% 8.02/1.94      real_$greater(v0, v1) = 0) &  ! [v0: $real] :  ! [v1: MultipleValueBool] : (
% 8.02/1.94      ~ (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0) = 0) &  ! [v0: $real] : 
% 8.02/1.94    ! [v1: $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0)
% 8.02/1.94    &  ! [v0: $real] : (v0 = real_0 |  ~ (real_$uminus(v0) = v0))
% 8.02/1.94  
% 8.02/1.94    (function-axioms)
% 8.02/1.94     ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |
% 8.02/1.94       ~ (real_$quotient(v3, v2) = v1) |  ~ (real_$quotient(v3, v2) = v0)) &  !
% 8.02/1.94    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 8.02/1.94      (real_$product(v3, v2) = v1) |  ~ (real_$product(v3, v2) = v0)) &  ! [v0:
% 8.02/1.94      $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 8.02/1.94      (real_$difference(v3, v2) = v1) |  ~ (real_$difference(v3, v2) = v0)) &  !
% 8.02/1.94    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 8.02/1.94      (real_$sum(v3, v2) = v1) |  ~ (real_$sum(v3, v2) = v0)) &  ! [v0:
% 8.02/1.95      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $real] :  ! [v3:
% 8.02/1.95      $real] : (v1 = v0 |  ~ (real_$lesseq(v3, v2) = v1) |  ~ (real_$lesseq(v3,
% 8.02/1.95          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 8.02/1.95    ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~ (real_$greater(v3, v2) = v1) | 
% 8.02/1.95      ~ (real_$greater(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 8.02/1.95      MultipleValueBool] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 8.02/1.95      (real_$less(v3, v2) = v1) |  ~ (real_$less(v3, v2) = v0)) &  ! [v0:
% 8.02/1.95      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $real] :  ! [v3:
% 8.02/1.95      $real] : (v1 = v0 |  ~ (real_$greatereq(v3, v2) = v1) |  ~
% 8.02/1.95      (real_$greatereq(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 8.02/1.95      MultipleValueBool] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$is_int(v2) = v1)
% 8.02/1.95      |  ~ (real_$is_int(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 8.02/1.95      MultipleValueBool] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$is_rat(v2) = v1)
% 8.02/1.95      |  ~ (real_$is_rat(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 8.02/1.95      $real] : (v1 = v0 |  ~ (real_$floor(v2) = v1) |  ~ (real_$floor(v2) = v0)) &
% 8.02/1.95     ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~
% 8.02/1.95      (real_$ceiling(v2) = v1) |  ~ (real_$ceiling(v2) = v0)) &  ! [v0: $real] : 
% 8.02/1.95    ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$truncate(v2) = v1) |  ~
% 8.02/1.95      (real_$truncate(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 8.02/1.95      $real] : (v1 = v0 |  ~ (real_$round(v2) = v1) |  ~ (real_$round(v2) = v0)) &
% 8.02/1.95     ! [v0: int] :  ! [v1: int] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$to_int(v2)
% 8.02/1.95        = v1) |  ~ (real_$to_int(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 8.02/1.95    [v2: $real] : (v1 = v0 |  ~ (real_$to_rat(v2) = v1) |  ~ (real_$to_rat(v2) =
% 8.02/1.95        v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~
% 8.02/1.95      (real_$to_real(v2) = v1) |  ~ (real_$to_real(v2) = v0)) &  ! [v0: $real] : 
% 8.02/1.95    ! [v1: $real] :  ! [v2: int] : (v1 = v0 |  ~ (int_$to_real(v2) = v1) |  ~
% 8.02/1.95      (int_$to_real(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real]
% 8.02/1.95    : (v1 = v0 |  ~ (real_$uminus(v2) = v1) |  ~ (real_$uminus(v2) = v0))
% 8.02/1.95  
% 8.02/1.95  Those formulas are unsatisfiable:
% 8.02/1.95  ---------------------------------
% 8.02/1.95  
% 8.02/1.95  Begin of proof
% 8.02/1.95  | 
% 8.02/1.95  | ALPHA: (function-axioms) implies:
% 8.02/1.95  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 8.02/1.95  |          $real] :  ! [v3: $real] : (v1 = v0 |  ~ (real_$greatereq(v3, v2) =
% 8.02/1.95  |            v1) |  ~ (real_$greatereq(v3, v2) = v0))
% 8.02/1.95  | 
% 8.02/1.95  | ALPHA: (input) implies:
% 8.02/1.95  |   (2)  real_$greatereq(real_13/4, real_13/4) = 0
% 8.02/1.95  | 
% 8.02/1.95  | DELTA: instantiating (real_greatereq_problem_1) with fresh symbol all_5_0
% 8.02/1.95  |        gives:
% 8.02/1.95  |   (3)   ~ (all_5_0 = 0) & real_$greatereq(real_13/4, real_13/4) = all_5_0
% 8.02/1.95  | 
% 8.02/1.95  | ALPHA: (3) implies:
% 8.02/1.96  |   (4)   ~ (all_5_0 = 0)
% 8.02/1.96  |   (5)  real_$greatereq(real_13/4, real_13/4) = all_5_0
% 8.02/1.96  | 
% 8.02/1.96  | GROUND_INST: instantiating (1) with 0, all_5_0, real_13/4, real_13/4,
% 8.02/1.96  |              simplifying with (2), (5) gives:
% 8.02/1.96  |   (6)  all_5_0 = 0
% 8.02/1.96  | 
% 8.02/1.96  | REDUCE: (4), (6) imply:
% 8.02/1.96  |   (7)  $false
% 8.02/1.96  | 
% 8.02/1.96  | CLOSE: (7) is inconsistent.
% 8.02/1.96  | 
% 8.02/1.96  End of proof
% 8.02/1.96  % SZS output end Proof for theBenchmark
% 8.02/1.96  
% 8.02/1.96  1344ms
%------------------------------------------------------------------------------