TSTP Solution File: ARI339_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI339_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 : n023.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 17:47:41 EDT 2023

% Result   : Theorem 7.41s 1.70s
% Output   : Proof 22.72s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ARI339_1 : TPTP v8.1.2. Released v5.0.0.
% 0.03/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue Aug 29 18:57:25 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.66/0.65  ________       _____
% 0.66/0.65  ___  __ \_________(_)________________________________
% 0.66/0.65  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.66/0.65  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.66/0.65  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.66/0.65  
% 0.66/0.65  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.66/0.65  (2023-06-19)
% 0.66/0.65  
% 0.66/0.65  (c) Philipp Rümmer, 2009-2023
% 0.66/0.65  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.66/0.65                Amanda Stjerna.
% 0.66/0.65  Free software under BSD-3-Clause.
% 0.66/0.65  
% 0.66/0.65  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.66/0.65  
% 0.66/0.65  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.66  Running up to 7 provers in parallel.
% 0.76/0.67  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.76/0.67  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.76/0.67  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.76/0.67  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.76/0.67  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.76/0.67  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.76/0.67  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.84/0.93  Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.84/0.93  Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.84/0.93  Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.84/0.93  Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.84/0.93  Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.84/0.93  Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.84/0.93  Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.62/1.05  Prover 4: Preprocessing ...
% 2.62/1.05  Prover 1: Preprocessing ...
% 2.87/1.11  Prover 6: Preprocessing ...
% 2.87/1.12  Prover 0: Preprocessing ...
% 6.25/1.53  Prover 3: Preprocessing ...
% 6.25/1.53  Prover 2: Preprocessing ...
% 6.25/1.54  Prover 5: Preprocessing ...
% 7.09/1.66  Prover 6: Constructing countermodel ...
% 7.41/1.68  Prover 0: Constructing countermodel ...
% 7.41/1.69  Prover 1: Constructing countermodel ...
% 7.41/1.70  Prover 6: proved (1026ms)
% 7.41/1.70  Prover 0: proved (1028ms)
% 7.41/1.70  
% 7.41/1.70  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.41/1.70  
% 7.41/1.70  
% 7.41/1.70  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.41/1.70  
% 7.41/1.70  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.41/1.70  Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 7.41/1.70  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.41/1.71  Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 7.41/1.73  Prover 8: Preprocessing ...
% 8.07/1.79  Prover 4: Constructing countermodel ...
% 9.30/1.93  Prover 7: Preprocessing ...
% 9.69/1.99  Prover 8: Warning: ignoring some quantifiers
% 9.69/2.00  Prover 8: Constructing countermodel ...
% 10.24/2.05  Prover 1: Found proof (size 7)
% 10.24/2.05  Prover 1: proved (1388ms)
% 10.24/2.06  Prover 4: stopped
% 10.24/2.06  Prover 8: stopped
% 15.05/2.74  Prover 2: stopped
% 15.34/2.79  Prover 7: stopped
% 20.33/3.74  Prover 5: Constructing countermodel ...
% 20.33/3.74  Prover 5: stopped
% 21.71/4.20  Prover 3: Constructing countermodel ...
% 21.71/4.21  Prover 3: stopped
% 21.71/4.21  
% 21.71/4.21  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.71/4.21  
% 21.71/4.21  % SZS output start Proof for theBenchmark
% 21.71/4.22  Assumptions after simplification:
% 21.71/4.22  ---------------------------------
% 21.71/4.22  
% 21.71/4.22    (rat_combined_problem_5)
% 22.01/4.26     ? [v0: int] : ( ~ (v0 = 0) & rat_$less(rat_61/10, rat_7) = v0)
% 22.01/4.26  
% 22.01/4.26    (input)
% 22.50/4.34     ~ (rat_very_large = rat_very_small) &  ~ (rat_very_large = rat_7) &  ~
% 22.50/4.34    (rat_very_large = rat_61/10) &  ~ (rat_very_large = rat_37/10) &  ~
% 22.50/4.34    (rat_very_large = rat_12/5) &  ~ (rat_very_large = rat_0) &  ~ (rat_very_small
% 22.50/4.34      = rat_7) &  ~ (rat_very_small = rat_61/10) &  ~ (rat_very_small = rat_37/10)
% 22.50/4.34    &  ~ (rat_very_small = rat_12/5) &  ~ (rat_very_small = rat_0) &  ~ (rat_7 =
% 22.50/4.34      rat_61/10) &  ~ (rat_7 = rat_37/10) &  ~ (rat_7 = rat_12/5) &  ~ (rat_7 =
% 22.50/4.34      rat_0) &  ~ (rat_61/10 = rat_37/10) &  ~ (rat_61/10 = rat_12/5) &  ~
% 22.50/4.34    (rat_61/10 = rat_0) &  ~ (rat_37/10 = rat_12/5) &  ~ (rat_37/10 = rat_0) &  ~
% 22.50/4.34    (rat_12/5 = rat_0) & rat_$is_int(rat_7) = 0 & rat_$is_int(rat_61/10) = 1 &
% 22.50/4.34    rat_$is_int(rat_37/10) = 1 & rat_$is_int(rat_12/5) = 1 & rat_$is_int(rat_0) =
% 22.50/4.34    0 & rat_$is_rat(rat_7) = 0 & rat_$is_rat(rat_61/10) = 0 &
% 22.50/4.34    rat_$is_rat(rat_37/10) = 0 & rat_$is_rat(rat_12/5) = 0 & rat_$is_rat(rat_0) =
% 22.50/4.34    0 & rat_$floor(rat_7) = rat_7 & rat_$floor(rat_0) = rat_0 &
% 22.50/4.34    rat_$ceiling(rat_7) = rat_7 & rat_$ceiling(rat_61/10) = rat_7 &
% 22.50/4.34    rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_7) = rat_7 &
% 22.50/4.34    rat_$truncate(rat_0) = rat_0 & rat_$round(rat_7) = rat_7 & rat_$round(rat_0) =
% 22.50/4.34    rat_0 & rat_$to_int(rat_7) = 7 & rat_$to_int(rat_61/10) = 6 &
% 22.50/4.34    rat_$to_int(rat_37/10) = 3 & rat_$to_int(rat_12/5) = 2 & rat_$to_int(rat_0) =
% 22.50/4.34    0 & rat_$to_rat(rat_7) = rat_7 & rat_$to_rat(rat_61/10) = rat_61/10 &
% 22.50/4.34    rat_$to_rat(rat_37/10) = rat_37/10 & rat_$to_rat(rat_12/5) = rat_12/5 &
% 22.50/4.34    rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_7) = real_7 &
% 22.50/4.34    rat_$to_real(rat_61/10) = real_61/10 & rat_$to_real(rat_37/10) = real_37/10 &
% 22.50/4.34    rat_$to_real(rat_12/5) = real_12/5 & rat_$to_real(rat_0) = real_0 &
% 22.50/4.34    int_$to_rat(7) = rat_7 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_0, rat_7)
% 22.50/4.34    = rat_0 & rat_$quotient(rat_0, rat_61/10) = rat_0 & rat_$quotient(rat_0,
% 22.50/4.34      rat_37/10) = rat_0 & rat_$quotient(rat_0, rat_12/5) = rat_0 &
% 22.50/4.34    rat_$product(rat_7, rat_0) = rat_0 & rat_$product(rat_61/10, rat_0) = rat_0 &
% 22.50/4.34    rat_$product(rat_37/10, rat_0) = rat_0 & rat_$product(rat_12/5, rat_0) = rat_0
% 22.50/4.34    & rat_$product(rat_0, rat_7) = rat_0 & rat_$product(rat_0, rat_61/10) = rat_0
% 22.50/4.34    & rat_$product(rat_0, rat_37/10) = rat_0 & rat_$product(rat_0, rat_12/5) =
% 22.50/4.34    rat_0 & rat_$product(rat_0, rat_0) = rat_0 & rat_$difference(rat_7, rat_7) =
% 22.50/4.34    rat_0 & rat_$difference(rat_7, rat_0) = rat_7 & rat_$difference(rat_61/10,
% 22.50/4.34      rat_61/10) = rat_0 & rat_$difference(rat_61/10, rat_37/10) = rat_12/5 &
% 22.50/4.34    rat_$difference(rat_61/10, rat_12/5) = rat_37/10 & rat_$difference(rat_61/10,
% 22.50/4.34      rat_0) = rat_61/10 & rat_$difference(rat_37/10, rat_37/10) = rat_0 &
% 22.50/4.34    rat_$difference(rat_37/10, rat_0) = rat_37/10 & rat_$difference(rat_12/5,
% 22.50/4.34      rat_12/5) = rat_0 & rat_$difference(rat_12/5, rat_0) = rat_12/5 &
% 22.50/4.34    rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 &
% 22.50/4.34    rat_$sum(rat_7, rat_0) = rat_7 & rat_$sum(rat_61/10, rat_0) = rat_61/10 &
% 22.50/4.34    rat_$sum(rat_37/10, rat_12/5) = rat_61/10 & rat_$sum(rat_37/10, rat_0) =
% 22.50/4.34    rat_37/10 & rat_$sum(rat_12/5, rat_37/10) = rat_61/10 & rat_$sum(rat_12/5,
% 22.50/4.34      rat_0) = rat_12/5 & rat_$sum(rat_0, rat_7) = rat_7 & rat_$sum(rat_0,
% 22.50/4.34      rat_61/10) = rat_61/10 & rat_$sum(rat_0, rat_37/10) = rat_37/10 &
% 22.50/4.34    rat_$sum(rat_0, rat_12/5) = rat_12/5 & rat_$sum(rat_0, rat_0) = rat_0 &
% 22.50/4.34    rat_$greatereq(rat_very_small, rat_very_large) = 1 & rat_$greatereq(rat_7,
% 22.50/4.34      rat_7) = 0 & rat_$greatereq(rat_7, rat_61/10) = 0 & rat_$greatereq(rat_7,
% 22.50/4.34      rat_37/10) = 0 & rat_$greatereq(rat_7, rat_12/5) = 0 & rat_$greatereq(rat_7,
% 22.50/4.34      rat_0) = 0 & rat_$greatereq(rat_61/10, rat_7) = 1 &
% 22.50/4.34    rat_$greatereq(rat_61/10, rat_61/10) = 0 & rat_$greatereq(rat_61/10,
% 22.50/4.34      rat_37/10) = 0 & rat_$greatereq(rat_61/10, rat_12/5) = 0 &
% 22.50/4.34    rat_$greatereq(rat_61/10, rat_0) = 0 & rat_$greatereq(rat_37/10, rat_7) = 1 &
% 22.50/4.34    rat_$greatereq(rat_37/10, rat_61/10) = 1 & rat_$greatereq(rat_37/10,
% 22.50/4.34      rat_37/10) = 0 & rat_$greatereq(rat_37/10, rat_12/5) = 0 &
% 22.50/4.35    rat_$greatereq(rat_37/10, rat_0) = 0 & rat_$greatereq(rat_12/5, rat_7) = 1 &
% 22.50/4.35    rat_$greatereq(rat_12/5, rat_61/10) = 1 & rat_$greatereq(rat_12/5, rat_37/10)
% 22.50/4.35    = 1 & rat_$greatereq(rat_12/5, rat_12/5) = 0 & rat_$greatereq(rat_12/5, rat_0)
% 22.50/4.35    = 0 & rat_$greatereq(rat_0, rat_7) = 1 & rat_$greatereq(rat_0, rat_61/10) = 1
% 22.50/4.35    & rat_$greatereq(rat_0, rat_37/10) = 1 & rat_$greatereq(rat_0, rat_12/5) = 1 &
% 22.50/4.35    rat_$greatereq(rat_0, rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large)
% 22.50/4.35    = 0 & rat_$lesseq(rat_7, rat_7) = 0 & rat_$lesseq(rat_7, rat_61/10) = 1 &
% 22.50/4.35    rat_$lesseq(rat_7, rat_37/10) = 1 & rat_$lesseq(rat_7, rat_12/5) = 1 &
% 22.50/4.35    rat_$lesseq(rat_7, rat_0) = 1 & rat_$lesseq(rat_61/10, rat_7) = 0 &
% 22.50/4.35    rat_$lesseq(rat_61/10, rat_61/10) = 0 & rat_$lesseq(rat_61/10, rat_37/10) = 1
% 22.50/4.35    & rat_$lesseq(rat_61/10, rat_12/5) = 1 & rat_$lesseq(rat_61/10, rat_0) = 1 &
% 22.50/4.35    rat_$lesseq(rat_37/10, rat_7) = 0 & rat_$lesseq(rat_37/10, rat_61/10) = 0 &
% 22.50/4.35    rat_$lesseq(rat_37/10, rat_37/10) = 0 & rat_$lesseq(rat_37/10, rat_12/5) = 1 &
% 22.50/4.35    rat_$lesseq(rat_37/10, rat_0) = 1 & rat_$lesseq(rat_12/5, rat_7) = 0 &
% 22.50/4.35    rat_$lesseq(rat_12/5, rat_61/10) = 0 & rat_$lesseq(rat_12/5, rat_37/10) = 0 &
% 22.50/4.35    rat_$lesseq(rat_12/5, rat_12/5) = 0 & rat_$lesseq(rat_12/5, rat_0) = 1 &
% 22.50/4.35    rat_$lesseq(rat_0, rat_7) = 0 & rat_$lesseq(rat_0, rat_61/10) = 0 &
% 22.50/4.35    rat_$lesseq(rat_0, rat_37/10) = 0 & rat_$lesseq(rat_0, rat_12/5) = 0 &
% 22.50/4.35    rat_$lesseq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, rat_7) = 0 &
% 22.50/4.35    rat_$greater(rat_very_large, rat_61/10) = 0 & rat_$greater(rat_very_large,
% 22.50/4.35      rat_37/10) = 0 & rat_$greater(rat_very_large, rat_12/5) = 0 &
% 22.50/4.35    rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small,
% 22.50/4.35      rat_very_large) = 1 & rat_$greater(rat_7, rat_very_small) = 0 &
% 22.50/4.35    rat_$greater(rat_7, rat_7) = 1 & rat_$greater(rat_7, rat_61/10) = 0 &
% 22.50/4.35    rat_$greater(rat_7, rat_37/10) = 0 & rat_$greater(rat_7, rat_12/5) = 0 &
% 22.50/4.35    rat_$greater(rat_7, rat_0) = 0 & rat_$greater(rat_61/10, rat_very_small) = 0 &
% 22.50/4.35    rat_$greater(rat_61/10, rat_7) = 1 & rat_$greater(rat_61/10, rat_61/10) = 1 &
% 22.50/4.35    rat_$greater(rat_61/10, rat_37/10) = 0 & rat_$greater(rat_61/10, rat_12/5) = 0
% 22.50/4.35    & rat_$greater(rat_61/10, rat_0) = 0 & rat_$greater(rat_37/10, rat_very_small)
% 22.50/4.35    = 0 & rat_$greater(rat_37/10, rat_7) = 1 & rat_$greater(rat_37/10, rat_61/10)
% 22.50/4.35    = 1 & rat_$greater(rat_37/10, rat_37/10) = 1 & rat_$greater(rat_37/10,
% 22.50/4.35      rat_12/5) = 0 & rat_$greater(rat_37/10, rat_0) = 0 & rat_$greater(rat_12/5,
% 22.50/4.35      rat_very_small) = 0 & rat_$greater(rat_12/5, rat_7) = 1 &
% 22.50/4.35    rat_$greater(rat_12/5, rat_61/10) = 1 & rat_$greater(rat_12/5, rat_37/10) = 1
% 22.50/4.35    & rat_$greater(rat_12/5, rat_12/5) = 1 & rat_$greater(rat_12/5, rat_0) = 0 &
% 22.50/4.35    rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_7) = 1 &
% 22.50/4.35    rat_$greater(rat_0, rat_61/10) = 1 & rat_$greater(rat_0, rat_37/10) = 1 &
% 22.50/4.35    rat_$greater(rat_0, rat_12/5) = 1 & rat_$greater(rat_0, rat_0) = 1 &
% 22.50/4.35    rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small,
% 22.50/4.35      rat_7) = 0 & rat_$less(rat_very_small, rat_61/10) = 0 &
% 22.50/4.35    rat_$less(rat_very_small, rat_37/10) = 0 & rat_$less(rat_very_small, rat_12/5)
% 22.50/4.35    = 0 & rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_7, rat_very_large)
% 22.50/4.35    = 0 & rat_$less(rat_7, rat_7) = 1 & rat_$less(rat_7, rat_61/10) = 1 &
% 22.50/4.35    rat_$less(rat_7, rat_37/10) = 1 & rat_$less(rat_7, rat_12/5) = 1 &
% 22.50/4.35    rat_$less(rat_7, rat_0) = 1 & rat_$less(rat_61/10, rat_very_large) = 0 &
% 22.50/4.35    rat_$less(rat_61/10, rat_7) = 0 & rat_$less(rat_61/10, rat_61/10) = 1 &
% 22.50/4.35    rat_$less(rat_61/10, rat_37/10) = 1 & rat_$less(rat_61/10, rat_12/5) = 1 &
% 22.50/4.35    rat_$less(rat_61/10, rat_0) = 1 & rat_$less(rat_37/10, rat_very_large) = 0 &
% 22.50/4.35    rat_$less(rat_37/10, rat_7) = 0 & rat_$less(rat_37/10, rat_61/10) = 0 &
% 22.50/4.35    rat_$less(rat_37/10, rat_37/10) = 1 & rat_$less(rat_37/10, rat_12/5) = 1 &
% 22.50/4.35    rat_$less(rat_37/10, rat_0) = 1 & rat_$less(rat_12/5, rat_very_large) = 0 &
% 22.50/4.35    rat_$less(rat_12/5, rat_7) = 0 & rat_$less(rat_12/5, rat_61/10) = 0 &
% 22.50/4.35    rat_$less(rat_12/5, rat_37/10) = 0 & rat_$less(rat_12/5, rat_12/5) = 1 &
% 22.50/4.35    rat_$less(rat_12/5, rat_0) = 1 & rat_$less(rat_0, rat_very_large) = 0 &
% 22.50/4.35    rat_$less(rat_0, rat_7) = 0 & rat_$less(rat_0, rat_61/10) = 0 &
% 22.50/4.35    rat_$less(rat_0, rat_37/10) = 0 & rat_$less(rat_0, rat_12/5) = 0 &
% 22.50/4.35    rat_$less(rat_0, rat_0) = 1 &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] : 
% 22.50/4.35    ! [v3: $rat] :  ! [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) |  ~ (rat_$sum(v2,
% 22.50/4.35          v1) = v3) |  ? [v5: $rat] : (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) =
% 22.50/4.35        v5)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: $rat] : (v3
% 22.50/4.35      = v1 | v0 = rat_0 |  ~ (rat_$quotient(v2, v0) = v3) |  ~ (rat_$product(v1,
% 22.50/4.35          v0) = v2)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3:
% 22.50/4.35      int] : (v3 = 0 |  ~ (rat_$lesseq(v2, v0) = v3) |  ~ (rat_$lesseq(v1, v0) =
% 22.50/4.35        0) |  ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) &  ! [v0:
% 22.50/4.35      $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: int] : (v3 = 0 |  ~
% 22.50/4.35      (rat_$lesseq(v1, v0) = 0) |  ~ (rat_$less(v2, v0) = v3) |  ? [v4: int] : ( ~
% 22.50/4.35        (v4 = 0) & rat_$less(v2, v1) = v4)) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 22.50/4.35    [v2: $rat] :  ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) |  ~ (rat_$sum(v1, v2)
% 22.50/4.35        = v3) | rat_$difference(v1, v0) = v3) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 22.50/4.35    [v2: $rat] : (v2 = rat_0 |  ~ (rat_$uminus(v0) = v1) |  ~ (rat_$sum(v0, v1) =
% 22.50/4.35        v2)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: int] : (v2 = 0 |  ~
% 22.50/4.35      (rat_$greatereq(v0, v1) = v2) |  ? [v3: int] : ( ~ (v3 = 0) &
% 22.50/4.35        rat_$lesseq(v1, v0) = v3)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: int]
% 22.50/4.35    : (v2 = 0 |  ~ (rat_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) &  ? [v3: int] : ( ~
% 22.50/4.35          (v3 = 0) & rat_$less(v1, v0) = v3))) &  ! [v0: $rat] :  ! [v1: $rat] : 
% 22.50/4.35    ! [v2: int] : (v2 = 0 |  ~ (rat_$greater(v0, v1) = v2) |  ? [v3: int] : ( ~
% 22.50/4.35        (v3 = 0) & rat_$less(v1, v0) = v3)) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 22.50/4.35    [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) | rat_$product(v1, v0) = v2) &  !
% 22.50/4.35    [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) |
% 22.50/4.35      rat_$sum(v1, v0) = v2) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] : ( ~
% 22.50/4.35      (rat_$lesseq(v2, v1) = 0) |  ~ (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) =
% 22.50/4.35      0) &  ! [v0: $rat] :  ! [v1: $rat] : (v1 = v0 |  ~ (rat_$sum(v0, rat_0) =
% 22.50/4.35        v1)) &  ! [v0: $rat] :  ! [v1: $rat] : (v1 = v0 |  ~ (rat_$lesseq(v1, v0)
% 22.50/4.35        = 0) | rat_$less(v1, v0) = 0) &  ! [v0: $rat] :  ! [v1: $rat] : ( ~
% 22.50/4.35      (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) &  ! [v0: $rat] :  ! [v1:
% 22.50/4.35      $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1, v0) = 0) &  !
% 22.50/4.35    [v0: $rat] :  ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1,
% 22.50/4.35        v0) = 0) &  ! [v0: $rat] : (v0 = rat_0 |  ~ (rat_$uminus(v0) = v0))
% 22.50/4.36  
% 22.50/4.36    (function-axioms)
% 22.50/4.37     ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~
% 22.50/4.37      (rat_$quotient(v3, v2) = v1) |  ~ (rat_$quotient(v3, v2) = v0)) &  ! [v0:
% 22.50/4.37      $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~
% 22.50/4.37      (rat_$product(v3, v2) = v1) |  ~ (rat_$product(v3, v2) = v0)) &  ! [v0:
% 22.50/4.37      $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~
% 22.50/4.37      (rat_$difference(v3, v2) = v1) |  ~ (rat_$difference(v3, v2) = v0)) &  !
% 22.50/4.37    [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~
% 22.50/4.37      (rat_$sum(v3, v2) = v1) |  ~ (rat_$sum(v3, v2) = v0)) &  ! [v0:
% 22.50/4.37      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $rat] :  ! [v3:
% 22.50/4.37      $rat] : (v1 = v0 |  ~ (rat_$greatereq(v3, v2) = v1) |  ~ (rat_$greatereq(v3,
% 22.50/4.37          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 22.50/4.37    ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~ (rat_$lesseq(v3, v2) = v1) |  ~
% 22.50/4.37      (rat_$lesseq(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 22.50/4.37      MultipleValueBool] :  ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~
% 22.50/4.37      (rat_$greater(v3, v2) = v1) |  ~ (rat_$greater(v3, v2) = v0)) &  ! [v0:
% 22.50/4.37      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $rat] :  ! [v3:
% 22.50/4.37      $rat] : (v1 = v0 |  ~ (rat_$less(v3, v2) = v1) |  ~ (rat_$less(v3, v2) =
% 22.50/4.37        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 22.50/4.37      $rat] : (v1 = v0 |  ~ (rat_$is_int(v2) = v1) |  ~ (rat_$is_int(v2) = v0)) & 
% 22.50/4.37    ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $rat] : (v1 =
% 22.50/4.37      v0 |  ~ (rat_$is_rat(v2) = v1) |  ~ (rat_$is_rat(v2) = v0)) &  ! [v0: $rat]
% 22.50/4.37    :  ! [v1: $rat] :  ! [v2: $rat] : (v1 = v0 |  ~ (rat_$floor(v2) = v1) |  ~
% 22.50/4.37      (rat_$floor(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] : (v1
% 22.50/4.37      = v0 |  ~ (rat_$ceiling(v2) = v1) |  ~ (rat_$ceiling(v2) = v0)) &  ! [v0:
% 22.50/4.37      $rat] :  ! [v1: $rat] :  ! [v2: $rat] : (v1 = v0 |  ~ (rat_$truncate(v2) =
% 22.50/4.37        v1) |  ~ (rat_$truncate(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 22.50/4.37    [v2: $rat] : (v1 = v0 |  ~ (rat_$round(v2) = v1) |  ~ (rat_$round(v2) = v0)) &
% 22.50/4.37     ! [v0: int] :  ! [v1: int] :  ! [v2: $rat] : (v1 = v0 |  ~ (rat_$to_int(v2) =
% 22.50/4.37        v1) |  ~ (rat_$to_int(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2:
% 22.50/4.37      $rat] : (v1 = v0 |  ~ (rat_$to_rat(v2) = v1) |  ~ (rat_$to_rat(v2) = v0)) & 
% 22.50/4.37    ! [v0: $real] :  ! [v1: $real] :  ! [v2: $rat] : (v1 = v0 |  ~
% 22.50/4.37      (rat_$to_real(v2) = v1) |  ~ (rat_$to_real(v2) = v0)) &  ! [v0: $rat] :  !
% 22.50/4.37    [v1: $rat] :  ! [v2: int] : (v1 = v0 |  ~ (int_$to_rat(v2) = v1) |  ~
% 22.50/4.37      (int_$to_rat(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :
% 22.50/4.37    (v1 = v0 |  ~ (rat_$uminus(v2) = v1) |  ~ (rat_$uminus(v2) = v0))
% 22.50/4.37  
% 22.50/4.37  Those formulas are unsatisfiable:
% 22.50/4.37  ---------------------------------
% 22.50/4.37  
% 22.50/4.37  Begin of proof
% 22.50/4.37  | 
% 22.50/4.37  | ALPHA: (function-axioms) implies:
% 22.50/4.37  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $rat]
% 22.50/4.37  |        :  ! [v3: $rat] : (v1 = v0 |  ~ (rat_$less(v3, v2) = v1) |  ~
% 22.50/4.37  |          (rat_$less(v3, v2) = v0))
% 22.50/4.37  | 
% 22.50/4.37  | ALPHA: (input) implies:
% 22.50/4.37  |   (2)  rat_$less(rat_61/10, rat_7) = 0
% 22.50/4.37  | 
% 22.50/4.38  | DELTA: instantiating (rat_combined_problem_5) with fresh symbol all_5_0 gives:
% 22.50/4.38  |   (3)   ~ (all_5_0 = 0) & rat_$less(rat_61/10, rat_7) = all_5_0
% 22.50/4.38  | 
% 22.50/4.38  | ALPHA: (3) implies:
% 22.50/4.38  |   (4)   ~ (all_5_0 = 0)
% 22.50/4.38  |   (5)  rat_$less(rat_61/10, rat_7) = all_5_0
% 22.50/4.38  | 
% 22.50/4.38  | GROUND_INST: instantiating (1) with 0, all_5_0, rat_7, rat_61/10, simplifying
% 22.50/4.38  |              with (2), (5) gives:
% 22.72/4.38  |   (6)  all_5_0 = 0
% 22.72/4.38  | 
% 22.72/4.38  | REDUCE: (4), (6) imply:
% 22.72/4.38  |   (7)  $false
% 22.72/4.38  | 
% 22.72/4.38  | CLOSE: (7) is inconsistent.
% 22.72/4.38  | 
% 22.72/4.38  End of proof
% 22.72/4.38  % SZS output end Proof for theBenchmark
% 22.72/4.38  
% 22.72/4.38  3734ms
%------------------------------------------------------------------------------