TSTP Solution File: NUM908_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUM908_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 : Thu Aug 31 11:50:39 EDT 2023

% Result   : Theorem 5.76s 1.56s
% Output   : Proof 7.90s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : NUM908_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 : n017.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 : Fri Aug 25 07:52:10 EDT 2023
% 0.14/0.35  % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 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 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 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 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
% 1.60/0.90  Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.60/0.90  Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.60/0.90  Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.60/0.90  Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.60/0.90  Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.60/0.90  Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.60/0.90  Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 2.20/0.98  Prover 4: Preprocessing ...
% 2.20/0.98  Prover 1: Preprocessing ...
% 2.38/1.03  Prover 5: Preprocessing ...
% 2.38/1.03  Prover 2: Preprocessing ...
% 2.38/1.03  Prover 0: Preprocessing ...
% 2.38/1.03  Prover 3: Preprocessing ...
% 2.38/1.03  Prover 6: Preprocessing ...
% 4.94/1.39  Prover 5: Proving ...
% 4.99/1.40  Prover 1: Constructing countermodel ...
% 5.05/1.41  Prover 3: Constructing countermodel ...
% 5.05/1.43  Prover 6: Constructing countermodel ...
% 5.05/1.44  Prover 2: Proving ...
% 5.05/1.47  Prover 4: Constructing countermodel ...
% 5.05/1.48  Prover 0: Proving ...
% 5.76/1.56  Prover 5: proved (910ms)
% 5.76/1.56  
% 5.76/1.56  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.76/1.56  
% 5.76/1.56  Prover 3: stopped
% 5.76/1.56  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.76/1.56  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.76/1.56  Prover 6: stopped
% 5.76/1.57  Prover 2: stopped
% 5.76/1.57  Prover 0: stopped
% 5.76/1.57  Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 5.76/1.57  Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 5.76/1.57  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.76/1.57  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.76/1.57  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.76/1.57  Prover 8: Preprocessing ...
% 5.76/1.57  Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 5.76/1.57  Prover 13: Warning: Problem contains reals, using incomplete axiomatisation
% 5.76/1.58  Prover 7: Preprocessing ...
% 5.76/1.58  Prover 11: Warning: Problem contains reals, using incomplete axiomatisation
% 5.76/1.58  Prover 13: Preprocessing ...
% 5.76/1.58  Prover 11: Preprocessing ...
% 5.76/1.59  Prover 10: Preprocessing ...
% 6.42/1.60  Prover 1: gave up
% 6.42/1.60  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.42/1.61  Prover 16: Warning: Problem contains reals, using incomplete axiomatisation
% 6.42/1.61  Prover 16: Preprocessing ...
% 6.42/1.67  Prover 7: Warning: ignoring some quantifiers
% 6.42/1.67  Prover 7: Constructing countermodel ...
% 6.42/1.68  Prover 10: Warning: ignoring some quantifiers
% 6.42/1.68  Prover 16: Warning: ignoring some quantifiers
% 7.12/1.69  Prover 16: Constructing countermodel ...
% 7.12/1.70  Prover 10: Constructing countermodel ...
% 7.12/1.72  Prover 13: Warning: ignoring some quantifiers
% 7.12/1.73  Prover 13: Constructing countermodel ...
% 7.12/1.73  Prover 8: Warning: ignoring some quantifiers
% 7.12/1.74  Prover 8: Constructing countermodel ...
% 7.12/1.77  Prover 4: Found proof (size 12)
% 7.12/1.77  Prover 4: proved (1121ms)
% 7.12/1.77  Prover 11: Constructing countermodel ...
% 7.12/1.77  Prover 7: stopped
% 7.12/1.77  Prover 13: stopped
% 7.12/1.77  Prover 16: stopped
% 7.12/1.77  Prover 10: stopped
% 7.12/1.77  Prover 8: stopped
% 7.12/1.78  Prover 11: stopped
% 7.12/1.78  
% 7.12/1.78  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.12/1.78  
% 7.12/1.78  % SZS output start Proof for theBenchmark
% 7.12/1.78  Assumptions after simplification:
% 7.12/1.78  ---------------------------------
% 7.12/1.78  
% 7.12/1.78    (real_difference_problem_12)
% 7.90/1.81     ? [v0: $real] :  ? [v1: $real] : ( ~ (v1 = real_0) & real_$difference(v0, v0)
% 7.90/1.81      = v1)
% 7.90/1.81  
% 7.90/1.81    (input)
% 7.90/1.84     ~ (real_very_large = real_very_small) &  ~ (real_very_large = real_0) &  ~
% 7.90/1.84    (real_very_small = real_0) & real_$is_int(real_0) = 0 & real_$is_rat(real_0) =
% 7.90/1.84    0 & real_$floor(real_0) = real_0 & real_$ceiling(real_0) = real_0 &
% 7.90/1.84    real_$truncate(real_0) = real_0 & real_$round(real_0) = real_0 &
% 7.90/1.84    real_$to_int(real_0) = 0 & real_$to_rat(real_0) = rat_0 &
% 7.90/1.84    real_$to_real(real_0) = real_0 & int_$to_real(0) = real_0 &
% 7.90/1.84    real_$product(real_0, real_0) = real_0 & real_$uminus(real_0) = real_0 &
% 7.90/1.84    real_$sum(real_0, real_0) = real_0 & real_$greatereq(real_very_small,
% 7.90/1.84      real_very_large) = 1 & real_$greatereq(real_0, real_0) = 0 &
% 7.90/1.84    real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_0,
% 7.90/1.84      real_0) = 0 & real_$greater(real_very_large, real_0) = 0 &
% 7.90/1.84    real_$greater(real_very_small, real_very_large) = 1 & real_$greater(real_0,
% 7.90/1.84      real_very_small) = 0 & real_$greater(real_0, real_0) = 1 &
% 7.90/1.84    real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small,
% 7.90/1.84      real_0) = 0 & real_$less(real_0, real_very_large) = 0 & real_$less(real_0,
% 7.90/1.84      real_0) = 1 & real_$difference(real_0, real_0) = real_0 &  ! [v0: $real] : 
% 7.90/1.84    ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] :  ! [v4: $real] : ( ~
% 7.90/1.84      (real_$sum(v3, v0) = v4) |  ~ (real_$sum(v2, v1) = v3) |  ? [v5: $real] :
% 7.90/1.84      (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) &  ! [v0: $real] :  !
% 7.90/1.84    [v1: $real] :  ! [v2: $real] :  ! [v3: $real] :  ! [v4: $real] : ( ~
% 7.90/1.84      (real_$sum(v2, v3) = v4) |  ~ (real_$sum(v1, v0) = v3) |  ? [v5: $real] :
% 7.90/1.84      (real_$sum(v5, v0) = v4 & real_$sum(v2, v1) = v5)) &  ! [v0: $real] :  !
% 7.90/1.84    [v1: $real] :  ! [v2: $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$lesseq(v2,
% 7.90/1.84          v1) = 0) |  ~ (real_$lesseq(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0)
% 7.90/1.84        & real_$lesseq(v1, v0) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 7.90/1.84      $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$lesseq(v2, v1) = 0) |  ~
% 7.90/1.84      (real_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0)
% 7.90/1.84        = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: int] :
% 7.90/1.84    (v3 = 0 |  ~ (real_$lesseq(v2, v0) = v3) |  ~ (real_$lesseq(v1, v0) = 0) |  ?
% 7.90/1.84      [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) &  ! [v0: $real] :  !
% 7.90/1.84    [v1: $real] :  ! [v2: $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$lesseq(v1,
% 7.90/1.84          v0) = 0) |  ~ (real_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) &
% 7.90/1.84        real_$less(v2, v1) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 7.90/1.84      $real] :  ! [v3: int] : (v3 = 0 |  ~ (real_$less(v2, v1) = 0) |  ~
% 7.90/1.84      (real_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1,
% 7.90/1.84          v0) = v4)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3:
% 7.90/1.84      int] : (v3 = 0 |  ~ (real_$less(v2, v0) = v3) |  ~ (real_$less(v1, v0) = 0)
% 7.90/1.84      |  ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) &  ! [v0: $real]
% 7.90/1.84    :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : ( ~ (real_$uminus(v0) =
% 7.90/1.84        v2) |  ~ (real_$sum(v1, v2) = v3) | real_$difference(v1, v0) = v3) &  !
% 7.90/1.84    [v0: $real] :  ! [v1: $real] :  ! [v2: int] : (v2 = 0 | v1 = v0 |  ~
% 7.90/1.84      (real_$less(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1,
% 7.90/1.84          v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: int] : (v2 = 0 | 
% 7.90/1.84      ~ (real_$greatereq(v0, v1) = v2) |  ? [v3: int] : ( ~ (v3 = 0) &
% 7.90/1.84        real_$lesseq(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 7.90/1.84      int] : (v2 = 0 |  ~ (real_$lesseq(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3 =
% 7.90/1.84          0) & real_$greatereq(v0, v1) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 7.90/1.84    ! [v2: int] : (v2 = 0 |  ~ (real_$lesseq(v1, v0) = v2) |  ? [v3: int] : ( ~
% 7.90/1.84        (v3 = 0) & real_$less(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 7.90/1.84    ! [v2: int] : (v2 = 0 |  ~ (real_$greater(v0, v1) = v2) |  ? [v3: int] : ( ~
% 7.90/1.84        (v3 = 0) & real_$less(v1, v0) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 7.90/1.84    ! [v2: int] : (v2 = 0 |  ~ (real_$less(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3
% 7.90/1.84          = 0) & real_$greater(v0, v1) = v3)) &  ! [v0: $real] :  ! [v1: $real] : 
% 7.90/1.84    ! [v2: $real] : (v0 = real_0 |  ~ (real_$product(v1, v0) = v2) |
% 7.90/1.84      real_$quotient(v2, v0) = v1) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 7.90/1.84      $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) &  !
% 7.90/1.84    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ (real_$product(v0, v1) =
% 7.90/1.84        v2) | real_$product(v1, v0) = v2) &  ! [v0: $real] :  ! [v1: $real] :  !
% 7.90/1.84    [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0, v1) = v2) &  ! [v0:
% 7.90/1.84      $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) |
% 7.90/1.84      real_$sum(v1, v0) = v2) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :
% 7.90/1.84    ( ~ (real_$lesseq(v2, v1) = 0) |  ~ (real_$lesseq(v1, v0) = 0) |
% 7.90/1.84      real_$lesseq(v2, v0) = 0) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real]
% 7.90/1.84    : ( ~ (real_$lesseq(v2, v1) = 0) |  ~ (real_$less(v1, v0) = 0) |
% 7.90/1.84      real_$less(v2, v0) = 0) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :
% 7.90/1.84    ( ~ (real_$lesseq(v1, v0) = 0) |  ~ (real_$less(v2, v1) = 0) | real_$less(v2,
% 7.90/1.84        v0) = 0) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~
% 7.90/1.84      (real_$difference(v1, v0) = v2) |  ? [v3: $real] : (real_$uminus(v0) = v3 &
% 7.90/1.84        real_$sum(v1, v3) = v2)) &  ! [v0: $real] :  ! [v1: $real] : (v1 = v0 |  ~
% 7.90/1.84      (real_$sum(v0, real_0) = v1)) &  ! [v0: $real] :  ! [v1: $real] : (v1 = v0 |
% 7.90/1.84       ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = 0) &  ! [v0: $real] : 
% 7.90/1.84    ! [v1: int] : (v1 = 0 |  ~ (real_$lesseq(v0, v0) = v1)) &  ! [v0: $real] :  !
% 7.90/1.84    [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) &  ! [v0:
% 7.90/1.84      $real] :  ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$sum(v0, v1) =
% 7.90/1.84      real_0) &  ! [v0: $real] :  ! [v1: $real] : ( ~ (real_$greatereq(v0, v1) =
% 7.90/1.84        0) | real_$lesseq(v1, v0) = 0) &  ! [v0: $real] :  ! [v1: $real] : ( ~
% 7.90/1.84      (real_$lesseq(v1, v0) = 0) | real_$greatereq(v0, v1) = 0) &  ! [v0: $real] :
% 7.90/1.84     ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & 
% 7.90/1.84    ! [v0: $real] :  ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) |
% 7.90/1.84      real_$lesseq(v1, v0) = 0) &  ! [v0: $real] :  ! [v1: $real] : ( ~
% 7.90/1.84      (real_$less(v1, v0) = 0) | real_$greater(v0, v1) = 0) &  ! [v0: $real] :  !
% 7.90/1.84    [v1: MultipleValueBool] : ( ~ (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0)
% 7.90/1.84      = 0) &  ! [v0: $real] : (v0 = real_0 |  ~ (real_$uminus(v0) = v0))
% 7.90/1.84  
% 7.90/1.84    (function-axioms)
% 7.90/1.85     ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |
% 7.90/1.85       ~ (real_$quotient(v3, v2) = v1) |  ~ (real_$quotient(v3, v2) = v0)) &  !
% 7.90/1.85    [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 7.90/1.85      (real_$product(v3, v2) = v1) |  ~ (real_$product(v3, v2) = v0)) &  ! [v0:
% 7.90/1.85      $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 7.90/1.85      (real_$sum(v3, v2) = v1) |  ~ (real_$sum(v3, v2) = v0)) &  ! [v0:
% 7.90/1.85      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $real] :  ! [v3:
% 7.90/1.85      $real] : (v1 = v0 |  ~ (real_$greatereq(v3, v2) = v1) |  ~
% 7.90/1.85      (real_$greatereq(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 7.90/1.85      MultipleValueBool] :  ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~
% 7.90/1.85      (real_$lesseq(v3, v2) = v1) |  ~ (real_$lesseq(v3, v2) = v0)) &  ! [v0:
% 7.90/1.85      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $real] :  ! [v3:
% 7.90/1.85      $real] : (v1 = v0 |  ~ (real_$greater(v3, v2) = v1) |  ~ (real_$greater(v3,
% 7.90/1.85          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 7.90/1.85    ! [v2: $real] :  ! [v3: $real] : (v1 = v0 |  ~ (real_$less(v3, v2) = v1) |  ~
% 7.90/1.85      (real_$less(v3, v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 7.90/1.85      $real] :  ! [v3: $real] : (v1 = v0 |  ~ (real_$difference(v3, v2) = v1) |  ~
% 7.90/1.85      (real_$difference(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 7.90/1.85      MultipleValueBool] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$is_int(v2) = v1)
% 7.90/1.85      |  ~ (real_$is_int(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 7.90/1.85      MultipleValueBool] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$is_rat(v2) = v1)
% 7.90/1.85      |  ~ (real_$is_rat(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 7.90/1.85      $real] : (v1 = v0 |  ~ (real_$floor(v2) = v1) |  ~ (real_$floor(v2) = v0)) &
% 7.90/1.85     ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~
% 7.90/1.85      (real_$ceiling(v2) = v1) |  ~ (real_$ceiling(v2) = v0)) &  ! [v0: $real] : 
% 7.90/1.85    ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$truncate(v2) = v1) |  ~
% 7.90/1.85      (real_$truncate(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2:
% 7.90/1.85      $real] : (v1 = v0 |  ~ (real_$round(v2) = v1) |  ~ (real_$round(v2) = v0)) &
% 7.90/1.85     ! [v0: int] :  ! [v1: int] :  ! [v2: $real] : (v1 = v0 |  ~ (real_$to_int(v2)
% 7.90/1.85        = v1) |  ~ (real_$to_int(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 7.90/1.85    [v2: $real] : (v1 = v0 |  ~ (real_$to_rat(v2) = v1) |  ~ (real_$to_rat(v2) =
% 7.90/1.85        v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : (v1 = v0 |  ~
% 7.90/1.85      (real_$to_real(v2) = v1) |  ~ (real_$to_real(v2) = v0)) &  ! [v0: $real] : 
% 7.90/1.85    ! [v1: $real] :  ! [v2: int] : (v1 = v0 |  ~ (int_$to_real(v2) = v1) |  ~
% 7.90/1.85      (int_$to_real(v2) = v0)) &  ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real]
% 7.90/1.85    : (v1 = v0 |  ~ (real_$uminus(v2) = v1) |  ~ (real_$uminus(v2) = v0))
% 7.90/1.85  
% 7.90/1.85  Those formulas are unsatisfiable:
% 7.90/1.85  ---------------------------------
% 7.90/1.85  
% 7.90/1.85  Begin of proof
% 7.90/1.85  | 
% 7.90/1.85  | ALPHA: (function-axioms) implies:
% 7.90/1.85  |   (1)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] :  ! [v3: $real] : (v1
% 7.90/1.85  |          = v0 |  ~ (real_$sum(v3, v2) = v1) |  ~ (real_$sum(v3, v2) = v0))
% 7.90/1.85  | 
% 7.90/1.85  | ALPHA: (input) implies:
% 7.90/1.86  |   (2)   ! [v0: $real] :  ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) |
% 7.90/1.86  |          real_$sum(v0, v1) = real_0)
% 7.90/1.86  |   (3)   ! [v0: $real] :  ! [v1: $real] :  ! [v2: $real] : ( ~
% 7.90/1.86  |          (real_$difference(v1, v0) = v2) |  ? [v3: $real] : (real_$uminus(v0)
% 7.90/1.86  |            = v3 & real_$sum(v1, v3) = v2))
% 7.90/1.86  | 
% 7.90/1.86  | DELTA: instantiating (real_difference_problem_12) with fresh symbols all_5_0,
% 7.90/1.86  |        all_5_1 gives:
% 7.90/1.86  |   (4)   ~ (all_5_0 = real_0) & real_$difference(all_5_1, all_5_1) = all_5_0
% 7.90/1.86  | 
% 7.90/1.86  | ALPHA: (4) implies:
% 7.90/1.86  |   (5)   ~ (all_5_0 = real_0)
% 7.90/1.86  |   (6)  real_$difference(all_5_1, all_5_1) = all_5_0
% 7.90/1.86  | 
% 7.90/1.86  | GROUND_INST: instantiating (3) with all_5_1, all_5_1, all_5_0, simplifying
% 7.90/1.86  |              with (6) gives:
% 7.90/1.86  |   (7)   ? [v0: $real] : (real_$uminus(all_5_1) = v0 & real_$sum(all_5_1, v0) =
% 7.90/1.86  |          all_5_0)
% 7.90/1.86  | 
% 7.90/1.86  | DELTA: instantiating (7) with fresh symbol all_17_0 gives:
% 7.90/1.86  |   (8)  real_$uminus(all_5_1) = all_17_0 & real_$sum(all_5_1, all_17_0) =
% 7.90/1.86  |        all_5_0
% 7.90/1.86  | 
% 7.90/1.86  | ALPHA: (8) implies:
% 7.90/1.86  |   (9)  real_$sum(all_5_1, all_17_0) = all_5_0
% 7.90/1.86  |   (10)  real_$uminus(all_5_1) = all_17_0
% 7.90/1.86  | 
% 7.90/1.86  | GROUND_INST: instantiating (2) with all_5_1, all_17_0, simplifying with (10)
% 7.90/1.86  |              gives:
% 7.90/1.86  |   (11)  real_$sum(all_5_1, all_17_0) = real_0
% 7.90/1.86  | 
% 7.90/1.86  | GROUND_INST: instantiating (1) with all_5_0, real_0, all_17_0, all_5_1,
% 7.90/1.86  |              simplifying with (9), (11) gives:
% 7.90/1.86  |   (12)  all_5_0 = real_0
% 7.90/1.86  | 
% 7.90/1.86  | REDUCE: (5), (12) imply:
% 7.90/1.86  |   (13)  $false
% 7.90/1.86  | 
% 7.90/1.86  | CLOSE: (13) is inconsistent.
% 7.90/1.86  | 
% 7.90/1.86  End of proof
% 7.90/1.86  % SZS output end Proof for theBenchmark
% 7.90/1.86  
% 7.90/1.86  1241ms
%------------------------------------------------------------------------------