TSTP Solution File: ARI509_1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI509_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 17:48:13 EDT 2023
% Result : Theorem 8.83s 1.88s
% Output : Proof 14.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : ARI509_1 : TPTP v8.1.2. Released v5.0.0.
% 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 18:12:43 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.58/0.91 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.58/0.91 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.58/0.91 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.58/0.91 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.58/0.91 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.58/0.91 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.58/0.91 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.58/0.92 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.58/0.92 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.58/0.92 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.58/0.92 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.58/0.92 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.58/0.92 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.58/0.92 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 2.33/1.02 Prover 1: Preprocessing ...
% 2.56/1.03 Prover 4: Preprocessing ...
% 2.65/1.06 Prover 6: Preprocessing ...
% 2.65/1.06 Prover 0: Preprocessing ...
% 3.62/1.19 Prover 2: Preprocessing ...
% 3.62/1.19 Prover 3: Preprocessing ...
% 3.62/1.20 Prover 5: Preprocessing ...
% 8.28/1.83 Prover 6: Constructing countermodel ...
% 8.28/1.88 Prover 0: Constructing countermodel ...
% 8.83/1.88 Prover 6: proved (1247ms)
% 8.83/1.88
% 8.83/1.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.83/1.88
% 8.83/1.89 Prover 0: proved (1252ms)
% 8.83/1.89
% 8.83/1.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.83/1.89
% 8.83/1.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.83/1.89 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 8.83/1.89 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 8.83/1.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.83/1.90 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 8.83/1.90 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 8.83/1.94 Prover 8: Preprocessing ...
% 8.83/1.97 Prover 1: Constructing countermodel ...
% 8.83/2.00 Prover 4: Constructing countermodel ...
% 8.83/2.02 Prover 7: Preprocessing ...
% 9.89/2.06 Prover 2: stopped
% 9.89/2.06 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.89/2.06 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation
% 9.89/2.07 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 10.39/2.12 Prover 10: Preprocessing ...
% 10.60/2.19 Prover 8: Warning: ignoring some quantifiers
% 10.60/2.21 Prover 8: Constructing countermodel ...
% 11.94/2.31 Prover 1: Found proof (size 4)
% 11.94/2.31 Prover 4: Found proof (size 4)
% 11.94/2.31 Prover 1: proved (1687ms)
% 11.94/2.31 Prover 4: proved (1686ms)
% 11.94/2.31 Prover 8: stopped
% 12.74/2.41 Prover 5: Constructing countermodel ...
% 12.74/2.41 Prover 5: stopped
% 13.58/2.60 Prover 3: Constructing countermodel ...
% 13.58/2.60 Prover 3: stopped
% 13.58/2.60 Prover 7: stopped
% 13.58/2.61 Prover 10: stopped
% 13.58/2.61
% 13.58/2.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.58/2.61
% 13.58/2.61 % SZS output start Proof for theBenchmark
% 13.58/2.61 Assumptions after simplification:
% 13.58/2.61 ---------------------------------
% 13.58/2.61
% 13.58/2.61 (mixed_types_problem_14)
% 13.58/2.63 rat_$less(rat_7/5, rat_6/5) = 0
% 13.58/2.63
% 13.58/2.63 (input)
% 14.23/2.67 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_6/5) & ~
% 14.23/2.67 (real_very_large = real_7/5) & ~ (real_very_large = real_0) & ~
% 14.23/2.67 (real_very_small = real_6/5) & ~ (real_very_small = real_7/5) & ~
% 14.23/2.67 (real_very_small = real_0) & ~ (rat_very_large = rat_very_small) & ~
% 14.23/2.67 (rat_very_large = rat_6/5) & ~ (rat_very_large = rat_7/5) & ~
% 14.23/2.67 (rat_very_large = rat_0) & ~ (rat_very_small = rat_6/5) & ~ (rat_very_small
% 14.23/2.67 = rat_7/5) & ~ (rat_very_small = rat_0) & ~ (real_6/5 = real_7/5) & ~
% 14.23/2.67 (real_6/5 = real_0) & ~ (rat_6/5 = rat_7/5) & ~ (rat_6/5 = rat_0) & ~
% 14.23/2.67 (real_7/5 = real_0) & ~ (rat_7/5 = rat_0) & rat_$is_int(rat_6/5) = 1 &
% 14.23/2.67 rat_$is_int(rat_7/5) = 1 & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_6/5) = 0 &
% 14.23/2.67 rat_$is_rat(rat_7/5) = 0 & rat_$is_rat(rat_0) = 0 & rat_$floor(rat_0) = rat_0
% 14.23/2.67 & rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_0) = rat_0 &
% 14.23/2.67 rat_$round(rat_0) = rat_0 & rat_$to_int(rat_6/5) = 1 & rat_$to_int(rat_7/5) =
% 14.23/2.67 1 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_6/5) = rat_6/5 &
% 14.23/2.67 rat_$to_rat(rat_7/5) = rat_7/5 & rat_$to_rat(rat_0) = rat_0 &
% 14.23/2.67 rat_$to_real(rat_6/5) = real_6/5 & rat_$to_real(rat_7/5) = real_7/5 &
% 14.23/2.67 rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & real_$is_int(real_6/5)
% 14.23/2.67 = 1 & real_$is_int(real_7/5) = 1 & real_$is_int(real_0) = 0 &
% 14.23/2.67 real_$is_rat(real_6/5) = 0 & real_$is_rat(real_7/5) = 0 & real_$is_rat(real_0)
% 14.23/2.67 = 0 & real_$floor(real_0) = real_0 & real_$ceiling(real_0) = real_0 &
% 14.23/2.67 real_$truncate(real_0) = real_0 & real_$round(real_0) = real_0 &
% 14.23/2.67 real_$to_int(real_6/5) = 1 & real_$to_int(real_7/5) = 1 & real_$to_int(real_0)
% 14.23/2.67 = 0 & real_$to_rat(real_6/5) = rat_6/5 & real_$to_rat(real_7/5) = rat_7/5 &
% 14.23/2.67 real_$to_rat(real_0) = rat_0 & real_$to_real(real_6/5) = real_6/5 &
% 14.23/2.67 real_$to_real(real_7/5) = real_7/5 & real_$to_real(real_0) = real_0 &
% 14.23/2.67 int_$to_real(0) = real_0 & real_$quotient(real_0, real_6/5) = real_0 &
% 14.23/2.67 real_$quotient(real_0, real_7/5) = real_0 & real_$product(real_6/5, real_0) =
% 14.23/2.67 real_0 & real_$product(real_7/5, real_0) = real_0 & real_$product(real_0,
% 14.23/2.67 real_6/5) = real_0 & real_$product(real_0, real_7/5) = real_0 &
% 14.23/2.67 real_$product(real_0, real_0) = real_0 & real_$difference(real_6/5, real_6/5)
% 14.23/2.67 = real_0 & real_$difference(real_6/5, real_0) = real_6/5 &
% 14.23/2.67 real_$difference(real_7/5, real_7/5) = real_0 & real_$difference(real_7/5,
% 14.23/2.67 real_0) = real_7/5 & real_$difference(real_0, real_0) = real_0 &
% 14.23/2.67 real_$uminus(real_0) = real_0 & real_$sum(real_6/5, real_0) = real_6/5 &
% 14.23/2.67 real_$sum(real_7/5, real_0) = real_7/5 & real_$sum(real_0, real_6/5) =
% 14.23/2.67 real_6/5 & real_$sum(real_0, real_7/5) = real_7/5 & real_$sum(real_0, real_0)
% 14.23/2.67 = real_0 & real_$greatereq(real_very_small, real_very_large) = 1 &
% 14.23/2.67 real_$greatereq(real_6/5, real_6/5) = 0 & real_$greatereq(real_6/5, real_7/5)
% 14.23/2.67 = 1 & real_$greatereq(real_6/5, real_0) = 0 & real_$greatereq(real_7/5,
% 14.23/2.67 real_6/5) = 0 & real_$greatereq(real_7/5, real_7/5) = 0 &
% 14.23/2.67 real_$greatereq(real_7/5, real_0) = 0 & real_$greatereq(real_0, real_6/5) = 1
% 14.23/2.67 & real_$greatereq(real_0, real_7/5) = 1 & real_$greatereq(real_0, real_0) = 0
% 14.23/2.67 & real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_6/5,
% 14.23/2.67 real_6/5) = 0 & real_$lesseq(real_6/5, real_7/5) = 0 &
% 14.23/2.67 real_$lesseq(real_6/5, real_0) = 1 & real_$lesseq(real_7/5, real_6/5) = 1 &
% 14.23/2.67 real_$lesseq(real_7/5, real_7/5) = 0 & real_$lesseq(real_7/5, real_0) = 1 &
% 14.23/2.67 real_$lesseq(real_0, real_6/5) = 0 & real_$lesseq(real_0, real_7/5) = 0 &
% 14.23/2.67 real_$lesseq(real_0, real_0) = 0 & real_$greater(real_very_large, real_6/5) =
% 14.23/2.67 0 & real_$greater(real_very_large, real_7/5) = 0 &
% 14.23/2.67 real_$greater(real_very_large, real_0) = 0 & real_$greater(real_very_small,
% 14.23/2.67 real_very_large) = 1 & real_$greater(real_6/5, real_very_small) = 0 &
% 14.23/2.67 real_$greater(real_6/5, real_6/5) = 1 & real_$greater(real_6/5, real_7/5) = 1
% 14.23/2.67 & real_$greater(real_6/5, real_0) = 0 & real_$greater(real_7/5,
% 14.23/2.67 real_very_small) = 0 & real_$greater(real_7/5, real_6/5) = 0 &
% 14.23/2.67 real_$greater(real_7/5, real_7/5) = 1 & real_$greater(real_7/5, real_0) = 0 &
% 14.23/2.67 real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0, real_6/5) =
% 14.23/2.67 1 & real_$greater(real_0, real_7/5) = 1 & real_$greater(real_0, real_0) = 1 &
% 14.23/2.67 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small,
% 14.23/2.67 real_6/5) = 0 & real_$less(real_very_small, real_7/5) = 0 &
% 14.23/2.67 real_$less(real_very_small, real_0) = 0 & real_$less(real_6/5,
% 14.23/2.67 real_very_large) = 0 & real_$less(real_6/5, real_6/5) = 1 &
% 14.23/2.67 real_$less(real_6/5, real_7/5) = 0 & real_$less(real_6/5, real_0) = 1 &
% 14.23/2.67 real_$less(real_7/5, real_very_large) = 0 & real_$less(real_7/5, real_6/5) = 1
% 14.23/2.67 & real_$less(real_7/5, real_7/5) = 1 & real_$less(real_7/5, real_0) = 1 &
% 14.23/2.67 real_$less(real_0, real_very_large) = 0 & real_$less(real_0, real_6/5) = 0 &
% 14.23/2.67 real_$less(real_0, real_7/5) = 0 & real_$less(real_0, real_0) = 1 &
% 14.23/2.67 rat_$quotient(rat_0, rat_6/5) = rat_0 & rat_$quotient(rat_0, rat_7/5) = rat_0
% 14.23/2.67 & rat_$product(rat_6/5, rat_0) = rat_0 & rat_$product(rat_7/5, rat_0) = rat_0
% 14.23/2.67 & rat_$product(rat_0, rat_6/5) = rat_0 & rat_$product(rat_0, rat_7/5) = rat_0
% 14.23/2.67 & rat_$product(rat_0, rat_0) = rat_0 & rat_$difference(rat_6/5, rat_6/5) =
% 14.23/2.67 rat_0 & rat_$difference(rat_6/5, rat_0) = rat_6/5 & rat_$difference(rat_7/5,
% 14.23/2.67 rat_7/5) = rat_0 & rat_$difference(rat_7/5, rat_0) = rat_7/5 &
% 14.23/2.67 rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 &
% 14.23/2.67 rat_$sum(rat_6/5, rat_0) = rat_6/5 & rat_$sum(rat_7/5, rat_0) = rat_7/5 &
% 14.23/2.68 rat_$sum(rat_0, rat_6/5) = rat_6/5 & rat_$sum(rat_0, rat_7/5) = rat_7/5 &
% 14.23/2.68 rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small,
% 14.23/2.68 rat_very_large) = 1 & rat_$greatereq(rat_6/5, rat_6/5) = 0 &
% 14.23/2.68 rat_$greatereq(rat_6/5, rat_7/5) = 1 & rat_$greatereq(rat_6/5, rat_0) = 0 &
% 14.23/2.68 rat_$greatereq(rat_7/5, rat_6/5) = 0 & rat_$greatereq(rat_7/5, rat_7/5) = 0 &
% 14.23/2.68 rat_$greatereq(rat_7/5, rat_0) = 0 & rat_$greatereq(rat_0, rat_6/5) = 1 &
% 14.23/2.68 rat_$greatereq(rat_0, rat_7/5) = 1 & rat_$greatereq(rat_0, rat_0) = 0 &
% 14.23/2.68 rat_$lesseq(rat_very_small, rat_very_large) = 0 & rat_$lesseq(rat_6/5,
% 14.23/2.68 rat_6/5) = 0 & rat_$lesseq(rat_6/5, rat_7/5) = 0 & rat_$lesseq(rat_6/5,
% 14.23/2.68 rat_0) = 1 & rat_$lesseq(rat_7/5, rat_6/5) = 1 & rat_$lesseq(rat_7/5,
% 14.23/2.68 rat_7/5) = 0 & rat_$lesseq(rat_7/5, rat_0) = 1 & rat_$lesseq(rat_0, rat_6/5)
% 14.23/2.68 = 0 & rat_$lesseq(rat_0, rat_7/5) = 0 & rat_$lesseq(rat_0, rat_0) = 0 &
% 14.23/2.68 rat_$greater(rat_very_large, rat_6/5) = 0 & rat_$greater(rat_very_large,
% 14.23/2.68 rat_7/5) = 0 & rat_$greater(rat_very_large, rat_0) = 0 &
% 14.23/2.68 rat_$greater(rat_very_small, rat_very_large) = 1 & rat_$greater(rat_6/5,
% 14.23/2.68 rat_very_small) = 0 & rat_$greater(rat_6/5, rat_6/5) = 1 &
% 14.23/2.68 rat_$greater(rat_6/5, rat_7/5) = 1 & rat_$greater(rat_6/5, rat_0) = 0 &
% 14.23/2.68 rat_$greater(rat_7/5, rat_very_small) = 0 & rat_$greater(rat_7/5, rat_6/5) = 0
% 14.23/2.68 & rat_$greater(rat_7/5, rat_7/5) = 1 & rat_$greater(rat_7/5, rat_0) = 0 &
% 14.23/2.68 rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_6/5) = 1 &
% 14.23/2.68 rat_$greater(rat_0, rat_7/5) = 1 & rat_$greater(rat_0, rat_0) = 1 &
% 14.23/2.68 rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small,
% 14.23/2.68 rat_6/5) = 0 & rat_$less(rat_very_small, rat_7/5) = 0 &
% 14.23/2.68 rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_6/5, rat_very_large) = 0
% 14.23/2.68 & rat_$less(rat_6/5, rat_6/5) = 1 & rat_$less(rat_6/5, rat_7/5) = 0 &
% 14.23/2.68 rat_$less(rat_6/5, rat_0) = 1 & rat_$less(rat_7/5, rat_very_large) = 0 &
% 14.23/2.68 rat_$less(rat_7/5, rat_6/5) = 1 & rat_$less(rat_7/5, rat_7/5) = 1 &
% 14.23/2.68 rat_$less(rat_7/5, rat_0) = 1 & rat_$less(rat_0, rat_very_large) = 0 &
% 14.23/2.68 rat_$less(rat_0, rat_6/5) = 0 & rat_$less(rat_0, rat_7/5) = 0 &
% 14.23/2.68 rat_$less(rat_0, rat_0) = 1 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real]
% 14.23/2.68 : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~
% 14.23/2.68 (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 &
% 14.23/2.68 real_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 14.23/2.68 ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2,
% 14.23/2.68 v1) = v3) | ? [v5: $rat] : (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) =
% 14.23/2.68 v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] :
% 14.23/2.68 (v3 = v1 | v0 = real_0 | ~ (real_$quotient(v2, v0) = v3) | ~
% 14.23/2.68 (real_$product(v1, v0) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 14.23/2.68 $rat] : ! [v3: $rat] : (v3 = v1 | v0 = rat_0 | ~ (rat_$quotient(v2, v0) =
% 14.23/2.68 v3) | ~ (rat_$product(v1, v0) = v2)) & ! [v0: $real] : ! [v1: $real] :
% 14.23/2.68 ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~
% 14.23/2.68 (real_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2,
% 14.23/2.68 v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3:
% 14.23/2.68 int] : (v3 = 0 | ~ (real_$lesseq(v1, v0) = 0) | ~ (real_$less(v2, v0) =
% 14.23/2.68 v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2, v1) = v4)) & ! [v0:
% 14.23/2.68 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~
% 14.23/2.68 (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : (
% 14.23/2.68 ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] :
% 14.23/2.68 ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~
% 14.23/2.68 (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) =
% 14.23/2.68 v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] :
% 14.23/2.68 ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) |
% 14.23/2.68 real_$difference(v1, v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 14.23/2.68 $rat] : ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) =
% 14.23/2.68 v3) | rat_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1: $real] : !
% 14.23/2.68 [v2: $real] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0,
% 14.23/2.68 v1) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v2 = rat_0
% 14.23/2.68 | ~ (rat_$uminus(v0) = v1) | ~ (rat_$sum(v0, v1) = v2)) & ! [v0: $real] :
% 14.23/2.68 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greatereq(v0, v1) = v2) |
% 14.23/2.68 ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: $real] :
% 14.23/2.68 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~
% 14.23/2.68 (v1 = v0) & ? [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & !
% 14.23/2.68 [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0,
% 14.23/2.68 v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & !
% 14.23/2.68 [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0,
% 14.23/2.68 v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) &
% 14.23/2.68 ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1,
% 14.23/2.68 v0) = v2) | ( ~ (v1 = v0) & ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1,
% 14.23/2.68 v0) = v3))) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 |
% 14.23/2.68 ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1,
% 14.23/2.68 v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~
% 14.23/2.68 (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2) & ! [v0: $real]
% 14.23/2.68 : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) |
% 14.23/2.68 real_$sum(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 14.23/2.68 ( ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$less(v1, v0) = 0) | real_$less(v2,
% 14.23/2.68 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 14.23/2.68 (rat_$product(v0, v1) = v2) | rat_$product(v1, v0) = v2) & ! [v0: $rat] :
% 14.23/2.68 ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0)
% 14.23/2.68 = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2,
% 14.23/2.68 v1) = 0) | ~ (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = 0) & ! [v0:
% 14.23/2.68 $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & !
% 14.23/2.68 [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) |
% 14.23/2.68 real_$less(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~
% 14.23/2.68 (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~
% 14.23/2.68 (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $real] : !
% 14.23/2.68 [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0:
% 14.23/2.68 $real] : ! [v1: $real] : ( ~ (real_$greatereq(v0, v1) = 0) |
% 14.23/2.68 real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 14.23/2.68 (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & ! [v0: $rat] : !
% 14.23/2.68 [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0:
% 14.23/2.68 $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1,
% 14.23/2.68 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0)
% 14.23/2.68 | rat_$less(v1, v0) = 0) & ! [v0: $real] : (v0 = real_0 | ~
% 14.23/2.68 (real_$uminus(v0) = v0)) & ! [v0: $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0)
% 14.23/2.68 = v0))
% 14.23/2.68
% 14.23/2.68 (function-axioms)
% 14.23/2.69 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 |
% 14.23/2.69 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & !
% 14.23/2.69 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 14.23/2.69 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0:
% 14.23/2.69 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 14.23/2.69 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & !
% 14.23/2.69 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 14.23/2.69 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0:
% 14.23/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 14.23/2.69 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~
% 14.23/2.69 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.23/2.69 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 14.23/2.69 (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, v2) = v0)) & ! [v0:
% 14.23/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 14.23/2.69 $real] : (v1 = v0 | ~ (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3,
% 14.23/2.69 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 14.23/2.69 ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~
% 14.23/2.69 (real_$less(v3, v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 14.23/2.69 ! [v3: $rat] : (v1 = v0 | ~ (rat_$quotient(v3, v2) = v1) | ~
% 14.23/2.69 (rat_$quotient(v3, v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 14.23/2.69 $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$product(v3, v2) = v1) | ~
% 14.23/2.70 (rat_$product(v3, v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat]
% 14.23/2.70 : ! [v3: $rat] : (v1 = v0 | ~ (rat_$difference(v3, v2) = v1) | ~
% 14.23/2.70 (rat_$difference(v3, v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 14.23/2.70 $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$sum(v3, v2) = v1) | ~
% 14.23/2.70 (rat_$sum(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.23/2.70 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 14.23/2.70 (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3, v2) = v0)) & ! [v0:
% 14.23/2.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 14.23/2.70 $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ (rat_$lesseq(v3, v2) =
% 14.23/2.70 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.23/2.70 $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$greater(v3, v2) = v1) | ~
% 14.23/2.70 (rat_$greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.23/2.70 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 14.23/2.70 (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) = v0)) & ! [v0:
% 14.23/2.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = v0 |
% 14.23/2.70 ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) & ! [v0:
% 14.23/2.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = v0 |
% 14.23/2.70 ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat] : !
% 14.23/2.70 [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~
% 14.23/2.70 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1
% 14.23/2.70 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0:
% 14.23/2.70 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) =
% 14.23/2.70 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : !
% 14.23/2.70 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) &
% 14.23/2.70 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) =
% 14.23/2.70 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 14.23/2.70 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) &
% 14.23/2.70 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~
% 14.23/2.70 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : !
% 14.23/2.70 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~
% 14.23/2.70 (int_$to_rat(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.23/2.70 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1)
% 14.23/2.70 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.23/2.70 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1)
% 14.23/2.70 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 14.23/2.70 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) &
% 14.23/2.70 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 14.23/2.70 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] :
% 14.23/2.70 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~
% 14.23/2.70 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 14.23/2.70 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) &
% 14.23/2.70 ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2)
% 14.23/2.70 = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : !
% 14.23/2.70 [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) =
% 14.23/2.70 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 14.23/2.70 (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] :
% 14.23/2.70 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~
% 14.23/2.70 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real]
% 14.23/2.70 : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) & !
% 14.23/2.70 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$uminus(v2) =
% 14.23/2.70 v1) | ~ (rat_$uminus(v2) = v0))
% 14.23/2.70
% 14.23/2.70 Those formulas are unsatisfiable:
% 14.23/2.70 ---------------------------------
% 14.23/2.70
% 14.23/2.70 Begin of proof
% 14.23/2.70 |
% 14.23/2.70 | ALPHA: (function-axioms) implies:
% 14.23/2.70 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat]
% 14.23/2.70 | : ! [v3: $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~
% 14.23/2.70 | (rat_$less(v3, v2) = v0))
% 14.23/2.70 |
% 14.23/2.70 | ALPHA: (input) implies:
% 14.23/2.70 | (2) rat_$less(rat_7/5, rat_6/5) = 1
% 14.23/2.70 |
% 14.23/2.71 | GROUND_INST: instantiating (1) with 0, 1, rat_6/5, rat_7/5, simplifying with
% 14.23/2.71 | (2), (mixed_types_problem_14) gives:
% 14.23/2.71 | (3) $false
% 14.23/2.71 |
% 14.23/2.71 | CLOSE: (3) is inconsistent.
% 14.23/2.71 |
% 14.23/2.71 End of proof
% 14.23/2.71 % SZS output end Proof for theBenchmark
% 14.23/2.71
% 14.23/2.71 2100ms
%------------------------------------------------------------------------------