TSTP Solution File: ARI423_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI423_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 : n019.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 17:47:59 EDT 2023
% Result : Theorem 8.04s 1.87s
% Output : Proof 10.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI423_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 18:52:12 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.63/0.88 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.63/0.88 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.63/0.88 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.63/0.88 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.63/0.88 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.63/0.88 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.63/0.88 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 2.14/0.98 Prover 4: Preprocessing ...
% 2.14/0.98 Prover 1: Preprocessing ...
% 2.58/1.03 Prover 0: Preprocessing ...
% 2.58/1.03 Prover 3: Preprocessing ...
% 2.58/1.03 Prover 2: Preprocessing ...
% 2.58/1.03 Prover 5: Preprocessing ...
% 2.58/1.03 Prover 6: Preprocessing ...
% 5.23/1.49 Prover 1: Constructing countermodel ...
% 5.86/1.53 Prover 6: Proving ...
% 5.86/1.54 Prover 4: Constructing countermodel ...
% 6.47/1.62 Prover 0: Proving ...
% 6.47/1.62 Prover 2: Proving ...
% 6.47/1.63 Prover 3: Constructing countermodel ...
% 7.16/1.69 Prover 5: Proving ...
% 8.04/1.82 Prover 1: gave up
% 8.04/1.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.04/1.84 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 8.04/1.86 Prover 7: Preprocessing ...
% 8.04/1.87 Prover 2: proved (1248ms)
% 8.04/1.87
% 8.04/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.04/1.87
% 8.04/1.87 Prover 3: stopped
% 8.04/1.87 Prover 6: stopped
% 8.04/1.88 Prover 5: proved (1248ms)
% 8.04/1.88
% 8.04/1.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.04/1.88
% 8.57/1.88 Prover 0: stopped
% 8.57/1.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.57/1.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.57/1.89 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 8.57/1.89 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 8.57/1.89 Prover 8: Preprocessing ...
% 8.57/1.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.57/1.89 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.57/1.89 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation
% 8.57/1.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.57/1.89 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation
% 8.57/1.89 Prover 16: Warning: Problem contains reals, using incomplete axiomatisation
% 8.57/1.89 Prover 10: Preprocessing ...
% 8.57/1.91 Prover 13: Preprocessing ...
% 8.57/1.91 Prover 11: Preprocessing ...
% 8.57/1.91 Prover 16: Preprocessing ...
% 9.30/2.08 Prover 13: Warning: ignoring some quantifiers
% 9.30/2.08 Prover 13: Constructing countermodel ...
% 9.82/2.08 Prover 8: Warning: ignoring some quantifiers
% 9.82/2.09 Prover 8: Constructing countermodel ...
% 9.82/2.10 Prover 4: Found proof (size 8)
% 9.82/2.10 Prover 4: proved (1476ms)
% 9.82/2.10 Prover 13: stopped
% 9.82/2.10 Prover 11: stopped
% 9.82/2.10 Prover 8: stopped
% 10.15/2.11 Prover 7: Warning: ignoring some quantifiers
% 10.19/2.11 Prover 7: Constructing countermodel ...
% 10.19/2.11 Prover 10: Warning: ignoring some quantifiers
% 10.19/2.12 Prover 7: stopped
% 10.19/2.12 Prover 10: Constructing countermodel ...
% 10.19/2.13 Prover 10: stopped
% 10.19/2.14 Prover 16: Warning: ignoring some quantifiers
% 10.19/2.14 Prover 16: Constructing countermodel ...
% 10.19/2.15 Prover 16: stopped
% 10.19/2.15
% 10.19/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.19/2.15
% 10.19/2.15 % SZS output start Proof for theBenchmark
% 10.19/2.15 Assumptions after simplification:
% 10.19/2.15 ---------------------------------
% 10.19/2.15
% 10.19/2.15 (real_sum_problem_23)
% 10.19/2.17 ! [v0: $real] : ~ (real_$sum(v0, real_-3500000) = real_0)
% 10.19/2.17
% 10.19/2.17 (input)
% 10.19/2.20 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_-3500000)
% 10.19/2.20 & ~ (real_very_large = real_0) & ~ (real_very_small = real_-3500000) & ~
% 10.19/2.20 (real_very_small = real_0) & ~ (real_-3500000 = real_0) &
% 10.19/2.20 real_$is_int(real_-3500000) = 0 & real_$is_int(real_0) = 0 &
% 10.19/2.20 real_$is_rat(real_-3500000) = 0 & real_$is_rat(real_0) = 0 &
% 10.19/2.20 real_$floor(real_-3500000) = real_-3500000 & real_$floor(real_0) = real_0 &
% 10.19/2.20 real_$ceiling(real_-3500000) = real_-3500000 & real_$ceiling(real_0) = real_0
% 10.19/2.20 & real_$truncate(real_-3500000) = real_-3500000 & real_$truncate(real_0) =
% 10.19/2.20 real_0 & real_$round(real_-3500000) = real_-3500000 & real_$round(real_0) =
% 10.19/2.20 real_0 & real_$to_int(real_-3500000) = -3500000 & real_$to_int(real_0) = 0 &
% 10.19/2.20 real_$to_rat(real_-3500000) = rat_-3500000 & real_$to_rat(real_0) = rat_0 &
% 10.19/2.20 real_$to_real(real_-3500000) = real_-3500000 & real_$to_real(real_0) = real_0
% 10.19/2.20 & int_$to_real(-3500000) = real_-3500000 & int_$to_real(0) = real_0 &
% 10.19/2.20 real_$quotient(real_0, real_-3500000) = real_0 & real_$product(real_-3500000,
% 10.19/2.20 real_0) = real_0 & real_$product(real_0, real_-3500000) = real_0 &
% 10.19/2.20 real_$product(real_0, real_0) = real_0 & real_$difference(real_-3500000,
% 10.19/2.20 real_-3500000) = real_0 & real_$difference(real_-3500000, real_0) =
% 10.19/2.20 real_-3500000 & real_$difference(real_0, real_0) = real_0 &
% 10.19/2.20 real_$uminus(real_0) = real_0 & real_$greatereq(real_very_small,
% 10.19/2.20 real_very_large) = 1 & real_$greatereq(real_-3500000, real_-3500000) = 0 &
% 10.19/2.20 real_$greatereq(real_-3500000, real_0) = 1 & real_$greatereq(real_0,
% 10.19/2.20 real_-3500000) = 0 & real_$greatereq(real_0, real_0) = 0 &
% 10.19/2.20 real_$lesseq(real_very_small, real_very_large) = 0 &
% 10.19/2.20 real_$lesseq(real_-3500000, real_-3500000) = 0 & real_$lesseq(real_-3500000,
% 10.19/2.20 real_0) = 0 & real_$lesseq(real_0, real_-3500000) = 1 & real_$lesseq(real_0,
% 10.19/2.20 real_0) = 0 & real_$greater(real_very_large, real_-3500000) = 0 &
% 10.19/2.20 real_$greater(real_very_large, real_0) = 0 & real_$greater(real_very_small,
% 10.19/2.20 real_very_large) = 1 & real_$greater(real_-3500000, real_very_small) = 0 &
% 10.19/2.20 real_$greater(real_-3500000, real_-3500000) = 1 & real_$greater(real_-3500000,
% 10.19/2.20 real_0) = 1 & real_$greater(real_0, real_very_small) = 0 &
% 10.19/2.20 real_$greater(real_0, real_-3500000) = 0 & real_$greater(real_0, real_0) = 1 &
% 10.19/2.20 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small,
% 10.19/2.20 real_-3500000) = 0 & real_$less(real_very_small, real_0) = 0 &
% 10.19/2.20 real_$less(real_-3500000, real_very_large) = 0 & real_$less(real_-3500000,
% 10.19/2.20 real_-3500000) = 1 & real_$less(real_-3500000, real_0) = 0 &
% 10.19/2.20 real_$less(real_0, real_very_large) = 0 & real_$less(real_0, real_-3500000) =
% 10.19/2.20 1 & real_$less(real_0, real_0) = 1 & real_$sum(real_-3500000, real_0) =
% 10.19/2.20 real_-3500000 & real_$sum(real_0, real_-3500000) = real_-3500000 &
% 10.19/2.20 real_$sum(real_0, real_0) = real_0 & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.19/2.20 $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~
% 10.19/2.20 (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 &
% 10.68/2.20 real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.68/2.20 $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v2, v3) = v4) | ~
% 10.68/2.20 (real_$sum(v1, v0) = v3) | ? [v5: $real] : (real_$sum(v5, v0) = v4 &
% 10.68/2.20 real_$sum(v2, v1) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.68/2.20 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~
% 10.68/2.20 (real_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1,
% 10.68/2.20 v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3:
% 10.68/2.20 int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$less(v2, v0) =
% 10.68/2.20 v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0) = v4)) & ! [v0:
% 10.68/2.20 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~
% 10.68/2.20 (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] :
% 10.68/2.20 ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real]
% 10.68/2.20 : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, v0) = 0) | ~
% 10.68/2.20 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2, v1)
% 10.68/2.20 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] :
% 10.68/2.20 (v3 = 0 | ~ (real_$less(v2, v1) = 0) | ~ (real_$less(v2, v0) = v3) | ? [v4:
% 10.68/2.20 int] : ( ~ (v4 = 0) & real_$lesseq(v1, v0) = v4)) & ! [v0: $real] : !
% 10.68/2.20 [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v0)
% 10.68/2.20 = v3) | ~ (real_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) &
% 10.68/2.20 real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.68/2.20 $real] : ! [v3: $real] : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1,
% 10.68/2.20 v2) = v3) | real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1:
% 10.68/2.20 $real] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (real_$less(v1, v0) = v2) |
% 10.68/2.20 ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: $real] :
% 10.68/2.20 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greatereq(v0, v1) = v2) |
% 10.68/2.20 ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: $real] :
% 10.68/2.20 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ?
% 10.68/2.20 [v3: int] : ( ~ (v3 = 0) & real_$greatereq(v0, v1) = v3)) & ! [v0: $real] :
% 10.68/2.20 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ?
% 10.68/2.20 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : !
% 10.68/2.20 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ?
% 10.68/2.20 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : !
% 10.68/2.20 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$less(v1, v0) = v2) | ? [v3:
% 10.68/2.20 int] : ( ~ (v3 = 0) & real_$greater(v0, v1) = v3)) & ! [v0: $real] : !
% 10.68/2.20 [v1: $real] : ! [v2: $real] : (v0 = real_0 | ~ (real_$product(v1, v0) = v2)
% 10.68/2.20 | real_$quotient(v2, v0) = v1) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.68/2.20 $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) & !
% 10.68/2.20 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) =
% 10.68/2.20 v2) | real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : !
% 10.68/2.20 [v2: $real] : ( ~ (real_$difference(v1, v0) = v2) | ? [v3: $real] :
% 10.68/2.20 (real_$uminus(v0) = v3 & real_$sum(v1, v3) = v2)) & ! [v0: $real] : ! [v1:
% 10.68/2.20 $real] : ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) | ~
% 10.68/2.20 (real_$lesseq(v1, v0) = 0) | real_$lesseq(v2, v0) = 0) & ! [v0: $real] : !
% 10.68/2.20 [v1: $real] : ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) | ~
% 10.68/2.20 (real_$less(v1, v0) = 0) | real_$less(v2, v0) = 0) & ! [v0: $real] : !
% 10.68/2.20 [v1: $real] : ! [v2: $real] : ( ~ (real_$lesseq(v1, v0) = 0) | ~
% 10.68/2.20 (real_$less(v2, v1) = 0) | real_$less(v2, v0) = 0) & ! [v0: $real] : !
% 10.68/2.20 [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0,
% 10.68/2.20 v1) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~
% 10.68/2.20 (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0: $real] : !
% 10.68/2.20 [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) =
% 10.68/2.20 0) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0)
% 10.68/2.20 = v1)) & ! [v0: $real] : ! [v1: int] : (v1 = 0 | ~ (real_$lesseq(v0,
% 10.68/2.20 v0) = v1)) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) =
% 10.68/2.20 v1) | real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 10.68/2.20 (real_$uminus(v0) = v1) | real_$sum(v0, v1) = real_0) & ! [v0: $real] : !
% 10.68/2.20 [v1: $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) &
% 10.68/2.20 ! [v0: $real] : ! [v1: $real] : ( ~ (real_$lesseq(v1, v0) = 0) |
% 10.68/2.20 real_$greatereq(v0, v1) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 10.68/2.20 (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & ! [v0: $real] : !
% 10.68/2.20 [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | real_$lesseq(v1, v0) = 0) & !
% 10.68/2.20 [v0: $real] : ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) |
% 10.68/2.20 real_$greater(v0, v1) = 0) & ! [v0: $real] : ! [v1: MultipleValueBool] : (
% 10.68/2.20 ~ (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0) = 0) & ! [v0: $real] :
% 10.68/2.20 (v0 = real_0 | ~ (real_$uminus(v0) = v0))
% 10.68/2.20
% 10.68/2.20 Those formulas are unsatisfiable:
% 10.68/2.20 ---------------------------------
% 10.68/2.20
% 10.68/2.20 Begin of proof
% 10.68/2.20 |
% 10.68/2.20 | ALPHA: (input) implies:
% 10.68/2.21 | (1) real_$difference(real_-3500000, real_-3500000) = real_0
% 10.68/2.21 | (2) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v1,
% 10.68/2.21 | v0) = v2) | real_$sum(v0, v1) = v2)
% 10.68/2.21 | (3) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~
% 10.68/2.21 | (real_$difference(v1, v0) = v2) | ? [v3: $real] : (real_$uminus(v0)
% 10.68/2.21 | = v3 & real_$sum(v1, v3) = v2))
% 10.68/2.21 |
% 10.68/2.21 | GROUND_INST: instantiating (3) with real_-3500000, real_-3500000, real_0,
% 10.68/2.21 | simplifying with (1) gives:
% 10.68/2.21 | (4) ? [v0: $real] : (real_$uminus(real_-3500000) = v0 &
% 10.68/2.21 | real_$sum(real_-3500000, v0) = real_0)
% 10.68/2.21 |
% 10.68/2.21 | DELTA: instantiating (4) with fresh symbol all_22_0 gives:
% 10.68/2.21 | (5) real_$uminus(real_-3500000) = all_22_0 & real_$sum(real_-3500000,
% 10.68/2.21 | all_22_0) = real_0
% 10.68/2.21 |
% 10.68/2.21 | ALPHA: (5) implies:
% 10.68/2.21 | (6) real_$sum(real_-3500000, all_22_0) = real_0
% 10.68/2.21 |
% 10.68/2.21 | GROUND_INST: instantiating (2) with all_22_0, real_-3500000, real_0,
% 10.68/2.21 | simplifying with (6) gives:
% 10.68/2.21 | (7) real_$sum(all_22_0, real_-3500000) = real_0
% 10.68/2.21 |
% 10.68/2.21 | GROUND_INST: instantiating (real_sum_problem_23) with all_22_0, simplifying
% 10.68/2.21 | with (7) gives:
% 10.68/2.21 | (8) $false
% 10.68/2.21 |
% 10.68/2.21 | CLOSE: (8) is inconsistent.
% 10.68/2.21 |
% 10.68/2.21 End of proof
% 10.68/2.21 % SZS output end Proof for theBenchmark
% 10.68/2.21
% 10.68/2.21 1611ms
%------------------------------------------------------------------------------