TSTP Solution File: ARI740_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI740_1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n004.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 17:48:59 EDT 2023
% Result : Theorem 12.66s 2.36s
% Output : Proof 14.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.07 % Problem : ARI740_1 : TPTP v8.1.2. Released v7.0.0.
% 0.04/0.07 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.07/0.26 % Computer : n004.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Tue Aug 29 18:06:07 EDT 2023
% 0.07/0.26 % CPUTime :
% 0.11/0.45 ________ _____
% 0.11/0.45 ___ __ \_________(_)________________________________
% 0.11/0.45 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.11/0.45 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.11/0.45 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.11/0.45
% 0.11/0.45 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.11/0.45 (2023-06-19)
% 0.11/0.45
% 0.11/0.45 (c) Philipp Rümmer, 2009-2023
% 0.11/0.45 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.11/0.45 Amanda Stjerna.
% 0.11/0.45 Free software under BSD-3-Clause.
% 0.11/0.45
% 0.11/0.45 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.11/0.45
% 0.11/0.46 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.11/0.47 Running up to 7 provers in parallel.
% 0.11/0.48 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.11/0.48 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.11/0.48 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.11/0.48 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.11/0.48 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.11/0.48 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.11/0.48 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.43/0.76 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.76 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.76 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.76 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.76 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.76 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.76 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 2.79/0.98 Prover 6: Preprocessing ...
% 2.79/0.98 Prover 1: Preprocessing ...
% 2.79/0.98 Prover 0: Preprocessing ...
% 2.79/0.99 Prover 4: Preprocessing ...
% 3.38/1.06 Prover 5: Preprocessing ...
% 3.38/1.07 Prover 2: Preprocessing ...
% 3.38/1.07 Prover 3: Preprocessing ...
% 6.89/1.60 Prover 6: Constructing countermodel ...
% 6.89/1.61 Prover 1: Constructing countermodel ...
% 7.54/1.67 Prover 4: Warning: ignoring some quantifiers
% 7.97/1.70 Prover 4: Constructing countermodel ...
% 7.97/1.72 Prover 0: Proving ...
% 10.35/2.02 Prover 2: Proving ...
% 10.35/2.03 Prover 3: Constructing countermodel ...
% 11.95/2.22 Prover 1: gave up
% 11.95/2.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.95/2.22 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 11.95/2.27 Prover 6: gave up
% 11.95/2.29 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.95/2.29 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 11.95/2.30 Prover 7: Preprocessing ...
% 11.95/2.31 Prover 8: Preprocessing ...
% 12.66/2.33 Prover 5: Proving ...
% 12.66/2.36 Prover 0: proved (1886ms)
% 12.66/2.36
% 12.66/2.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.66/2.36
% 12.66/2.36 Prover 3: stopped
% 12.66/2.36 Prover 5: stopped
% 12.66/2.37 Prover 2: stopped
% 12.66/2.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.66/2.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.66/2.37 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 12.66/2.37 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 12.66/2.37 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation
% 12.66/2.37 Prover 16: Warning: Problem contains reals, using incomplete axiomatisation
% 12.66/2.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.66/2.38 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation
% 13.18/2.41 Prover 4: Found proof (size 14)
% 13.18/2.41 Prover 4: proved (1933ms)
% 13.18/2.41 Prover 13: Preprocessing ...
% 13.18/2.43 Prover 7: stopped
% 13.18/2.43 Prover 10: Preprocessing ...
% 13.18/2.44 Prover 16: Preprocessing ...
% 13.18/2.44 Prover 11: Preprocessing ...
% 13.18/2.46 Prover 8: Warning: ignoring some quantifiers
% 13.18/2.46 Prover 8: Constructing countermodel ...
% 13.18/2.47 Prover 13: stopped
% 13.84/2.48 Prover 8: stopped
% 13.84/2.52 Prover 10: stopped
% 14.04/2.56 Prover 11: stopped
% 14.41/2.57 Prover 16: stopped
% 14.41/2.57
% 14.41/2.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.41/2.57
% 14.41/2.57 % SZS output start Proof for theBenchmark
% 14.41/2.58 Assumptions after simplification:
% 14.41/2.58 ---------------------------------
% 14.41/2.58
% 14.41/2.58 (pow_2_2)
% 14.48/2.59 ? [v0: $real] : ( ~ (v0 = real_4) & power(real_2, 2) = v0)
% 14.48/2.59
% 14.48/2.59 (power_1)
% 14.48/2.59 ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (power(v0, 1) = v1))
% 14.48/2.59
% 14.48/2.59 (power_s_alt)
% 14.48/2.59 ! [v0: $real] : ! [v1: int] : ! [v2: $real] : ( ~ ($lesseq(1, v1)) | ~
% 14.48/2.59 (power(v0, $sum(v1, -1)) = v2) | ? [v3: $real] : (real_$product(v0, v2) =
% 14.48/2.59 v3 & power(v0, v1) = v3)) & ! [v0: $real] : ! [v1: int] : ! [v2: $real]
% 14.48/2.59 : ( ~ ($lesseq(1, v1)) | ~ (power(v0, v1) = v2) | ? [v3: $real] :
% 14.48/2.59 (real_$product(v0, v3) = v2 & power(v0, $sum(v1, -1)) = v3))
% 14.48/2.59
% 14.48/2.59 (input)
% 14.65/2.62 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_4) & ~
% 14.65/2.62 (real_very_large = real_2) & ~ (real_very_large = real_1) & ~
% 14.65/2.62 (real_very_large = real_0) & ~ (real_very_small = real_4) & ~
% 14.65/2.62 (real_very_small = real_2) & ~ (real_very_small = real_1) & ~
% 14.65/2.62 (real_very_small = real_0) & ~ (real_4 = real_2) & ~ (real_4 = real_1) & ~
% 14.65/2.62 (real_4 = real_0) & ~ (real_2 = real_1) & ~ (real_2 = real_0) & ~ (real_1 =
% 14.65/2.62 real_0) & real_$is_int(real_4) = 0 & real_$is_int(real_2) = 0 &
% 14.65/2.62 real_$is_int(real_1) = 0 & real_$is_int(real_0) = 0 & real_$is_rat(real_4) = 0
% 14.65/2.62 & real_$is_rat(real_2) = 0 & real_$is_rat(real_1) = 0 & real_$is_rat(real_0) =
% 14.65/2.62 0 & real_$floor(real_4) = real_4 & real_$floor(real_2) = real_2 &
% 14.65/2.62 real_$floor(real_1) = real_1 & real_$floor(real_0) = real_0 &
% 14.65/2.62 real_$ceiling(real_4) = real_4 & real_$ceiling(real_2) = real_2 &
% 14.65/2.62 real_$ceiling(real_1) = real_1 & real_$ceiling(real_0) = real_0 &
% 14.65/2.62 real_$truncate(real_4) = real_4 & real_$truncate(real_2) = real_2 &
% 14.65/2.62 real_$truncate(real_1) = real_1 & real_$truncate(real_0) = real_0 &
% 14.65/2.62 real_$round(real_4) = real_4 & real_$round(real_2) = real_2 &
% 14.65/2.62 real_$round(real_1) = real_1 & real_$round(real_0) = real_0 &
% 14.65/2.62 real_$to_int(real_4) = 4 & real_$to_int(real_2) = 2 & real_$to_int(real_1) = 1
% 14.65/2.62 & real_$to_int(real_0) = 0 & real_$to_rat(real_4) = rat_4 &
% 14.65/2.62 real_$to_rat(real_2) = rat_2 & real_$to_rat(real_1) = rat_1 &
% 14.65/2.62 real_$to_rat(real_0) = rat_0 & real_$to_real(real_4) = real_4 &
% 14.65/2.62 real_$to_real(real_2) = real_2 & real_$to_real(real_1) = real_1 &
% 14.65/2.62 real_$to_real(real_0) = real_0 & int_$to_real(4) = real_4 & int_$to_real(2) =
% 14.65/2.62 real_2 & int_$to_real(1) = real_1 & int_$to_real(0) = real_0 &
% 14.65/2.62 real_$quotient(real_4, real_4) = real_1 & real_$quotient(real_4, real_2) =
% 14.65/2.62 real_2 & real_$quotient(real_4, real_1) = real_4 & real_$quotient(real_2,
% 14.65/2.62 real_2) = real_1 & real_$quotient(real_2, real_1) = real_2 &
% 14.65/2.62 real_$quotient(real_1, real_1) = real_1 & real_$quotient(real_0, real_4) =
% 14.65/2.62 real_0 & real_$quotient(real_0, real_2) = real_0 & real_$quotient(real_0,
% 14.65/2.62 real_1) = real_0 & real_$difference(real_4, real_4) = real_0 &
% 14.65/2.62 real_$difference(real_4, real_2) = real_2 & real_$difference(real_4, real_0) =
% 14.65/2.62 real_4 & real_$difference(real_2, real_2) = real_0 & real_$difference(real_2,
% 14.65/2.62 real_1) = real_1 & real_$difference(real_2, real_0) = real_2 &
% 14.65/2.62 real_$difference(real_1, real_1) = real_0 & real_$difference(real_1, real_0) =
% 14.65/2.62 real_1 & real_$difference(real_0, real_0) = real_0 & real_$uminus(real_0) =
% 14.65/2.62 real_0 & real_$sum(real_4, real_0) = real_4 & real_$sum(real_2, real_2) =
% 14.65/2.62 real_4 & real_$sum(real_2, real_0) = real_2 & real_$sum(real_1, real_1) =
% 14.65/2.62 real_2 & real_$sum(real_1, real_0) = real_1 & real_$sum(real_0, real_4) =
% 14.65/2.62 real_4 & real_$sum(real_0, real_2) = real_2 & real_$sum(real_0, real_1) =
% 14.65/2.62 real_1 & real_$sum(real_0, real_0) = real_0 & real_$greatereq(real_very_small,
% 14.65/2.62 real_very_large) = 1 & real_$greatereq(real_4, real_4) = 0 &
% 14.65/2.62 real_$greatereq(real_4, real_2) = 0 & real_$greatereq(real_4, real_1) = 0 &
% 14.65/2.62 real_$greatereq(real_4, real_0) = 0 & real_$greatereq(real_2, real_4) = 1 &
% 14.65/2.62 real_$greatereq(real_2, real_2) = 0 & real_$greatereq(real_2, real_1) = 0 &
% 14.65/2.62 real_$greatereq(real_2, real_0) = 0 & real_$greatereq(real_1, real_4) = 1 &
% 14.65/2.62 real_$greatereq(real_1, real_2) = 1 & real_$greatereq(real_1, real_1) = 0 &
% 14.65/2.62 real_$greatereq(real_1, real_0) = 0 & real_$greatereq(real_0, real_4) = 1 &
% 14.65/2.62 real_$greatereq(real_0, real_2) = 1 & real_$greatereq(real_0, real_1) = 1 &
% 14.65/2.62 real_$greatereq(real_0, real_0) = 0 & real_$greater(real_very_large, real_4) =
% 14.65/2.62 0 & real_$greater(real_very_large, real_2) = 0 &
% 14.65/2.62 real_$greater(real_very_large, real_1) = 0 & real_$greater(real_very_large,
% 14.65/2.62 real_0) = 0 & real_$greater(real_very_small, real_very_large) = 1 &
% 14.65/2.62 real_$greater(real_4, real_very_small) = 0 & real_$greater(real_4, real_4) = 1
% 14.65/2.62 & real_$greater(real_4, real_2) = 0 & real_$greater(real_4, real_1) = 0 &
% 14.65/2.62 real_$greater(real_4, real_0) = 0 & real_$greater(real_2, real_very_small) = 0
% 14.65/2.62 & real_$greater(real_2, real_4) = 1 & real_$greater(real_2, real_2) = 1 &
% 14.65/2.62 real_$greater(real_2, real_1) = 0 & real_$greater(real_2, real_0) = 0 &
% 14.65/2.62 real_$greater(real_1, real_very_small) = 0 & real_$greater(real_1, real_4) = 1
% 14.65/2.62 & real_$greater(real_1, real_2) = 1 & real_$greater(real_1, real_1) = 1 &
% 14.65/2.62 real_$greater(real_1, real_0) = 0 & real_$greater(real_0, real_very_small) = 0
% 14.65/2.63 & real_$greater(real_0, real_4) = 1 & real_$greater(real_0, real_2) = 1 &
% 14.65/2.63 real_$greater(real_0, real_1) = 1 & real_$greater(real_0, real_0) = 1 &
% 14.65/2.63 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small,
% 14.65/2.63 real_4) = 0 & real_$less(real_very_small, real_2) = 0 &
% 14.65/2.63 real_$less(real_very_small, real_1) = 0 & real_$less(real_very_small, real_0)
% 14.65/2.63 = 0 & real_$less(real_4, real_very_large) = 0 & real_$less(real_4, real_4) = 1
% 14.65/2.63 & real_$less(real_4, real_2) = 1 & real_$less(real_4, real_1) = 1 &
% 14.65/2.63 real_$less(real_4, real_0) = 1 & real_$less(real_2, real_very_large) = 0 &
% 14.65/2.63 real_$less(real_2, real_4) = 0 & real_$less(real_2, real_2) = 1 &
% 14.65/2.63 real_$less(real_2, real_1) = 1 & real_$less(real_2, real_0) = 1 &
% 14.65/2.63 real_$less(real_1, real_very_large) = 0 & real_$less(real_1, real_4) = 0 &
% 14.65/2.63 real_$less(real_1, real_2) = 0 & real_$less(real_1, real_1) = 1 &
% 14.65/2.63 real_$less(real_1, real_0) = 1 & real_$less(real_0, real_very_large) = 0 &
% 14.65/2.63 real_$less(real_0, real_4) = 0 & real_$less(real_0, real_2) = 0 &
% 14.65/2.63 real_$less(real_0, real_1) = 0 & real_$less(real_0, real_0) = 1 &
% 14.65/2.63 real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_4,
% 14.65/2.63 real_4) = 0 & real_$lesseq(real_4, real_2) = 1 & real_$lesseq(real_4,
% 14.65/2.63 real_1) = 1 & real_$lesseq(real_4, real_0) = 1 & real_$lesseq(real_2,
% 14.65/2.63 real_4) = 0 & real_$lesseq(real_2, real_2) = 0 & real_$lesseq(real_2,
% 14.65/2.63 real_1) = 1 & real_$lesseq(real_2, real_0) = 1 & real_$lesseq(real_1,
% 14.65/2.63 real_4) = 0 & real_$lesseq(real_1, real_2) = 0 & real_$lesseq(real_1,
% 14.65/2.63 real_1) = 0 & real_$lesseq(real_1, real_0) = 1 & real_$lesseq(real_0,
% 14.65/2.63 real_4) = 0 & real_$lesseq(real_0, real_2) = 0 & real_$lesseq(real_0,
% 14.65/2.63 real_1) = 0 & real_$lesseq(real_0, real_0) = 0 & real_$product(real_4,
% 14.65/2.63 real_1) = real_4 & real_$product(real_4, real_0) = real_0 &
% 14.65/2.63 real_$product(real_2, real_2) = real_4 & real_$product(real_2, real_1) =
% 14.65/2.63 real_2 & real_$product(real_2, real_0) = real_0 & real_$product(real_1,
% 14.65/2.63 real_4) = real_4 & real_$product(real_1, real_2) = real_2 &
% 14.65/2.63 real_$product(real_1, real_1) = real_1 & real_$product(real_1, real_0) =
% 14.65/2.63 real_0 & real_$product(real_0, real_4) = real_0 & real_$product(real_0,
% 14.65/2.63 real_2) = real_0 & real_$product(real_0, real_1) = real_0 &
% 14.65/2.63 real_$product(real_0, real_0) = real_0 & ! [v0: $real] : ! [v1: $real] : !
% 14.65/2.63 [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) |
% 14.65/2.63 ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 &
% 14.65/2.63 real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 14.65/2.63 $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v2, v3) = v4) | ~
% 14.65/2.63 (real_$sum(v1, v0) = v3) | ? [v5: $real] : (real_$sum(v5, v0) = v4 &
% 14.65/2.63 real_$sum(v2, v1) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 14.65/2.63 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v1) = 0) | ~
% 14.65/2.63 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1,
% 14.65/2.63 v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3:
% 14.65/2.63 int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~ (real_$less(v1, v0) = 0)
% 14.65/2.63 | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real]
% 14.65/2.63 : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~
% 14.65/2.63 (real_$less(v2, v0) = v3) | ~ (real_$lesseq(v2, v1) = 0) | ? [v4: int] : (
% 14.65/2.63 ~ (v4 = 0) & real_$less(v1, v0) = v4)) & ! [v0: $real] : ! [v1: $real] :
% 14.65/2.63 ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~
% 14.65/2.63 (real_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2,
% 14.65/2.63 v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3:
% 14.65/2.63 int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$lesseq(v2, v0) =
% 14.65/2.63 v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1, v0) = v4)) & ! [v0:
% 14.65/2.63 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~
% 14.65/2.63 (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] :
% 14.65/2.63 ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real]
% 14.65/2.63 : ! [v2: $real] : ! [v3: $real] : ( ~ (real_$uminus(v0) = v2) | ~
% 14.65/2.63 (real_$sum(v1, v2) = v3) | real_$difference(v1, v0) = v3) & ! [v0: $real] :
% 14.65/2.63 ! [v1: $real] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (real_$less(v1, v0) =
% 14.65/2.63 v2) | ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0:
% 14.65/2.63 $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greatereq(v0,
% 14.65/2.63 v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) &
% 14.65/2.63 ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~
% 14.65/2.63 (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & real_$less(v1,
% 14.65/2.63 v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 |
% 14.65/2.63 ~ (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 14.65/2.63 real_$greater(v0, v1) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 14.65/2.63 int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 =
% 14.65/2.63 0) & real_$greatereq(v0, v1) = v3)) & ! [v0: $real] : ! [v1: $real] :
% 14.74/2.63 ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~
% 14.74/2.63 (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] :
% 14.74/2.63 ! [v2: $real] : (v0 = real_0 | ~ (real_$product(v1, v0) = v2) |
% 14.74/2.63 real_$quotient(v2, v0) = v1) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 14.74/2.63 $real] : ( ~ (real_$difference(v1, v0) = v2) | ? [v3: $real] :
% 14.74/2.63 (real_$uminus(v0) = v3 & real_$sum(v1, v3) = v2)) & ! [v0: $real] : ! [v1:
% 14.74/2.63 $real] : ! [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0, v1) =
% 14.74/2.63 v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0,
% 14.74/2.63 v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] :
% 14.74/2.63 ! [v2: $real] : ( ~ (real_$less(v2, v1) = 0) | ~ (real_$lesseq(v1, v0) = 0) |
% 14.74/2.63 real_$less(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 14.74/2.63 ( ~ (real_$less(v1, v0) = 0) | ~ (real_$lesseq(v2, v1) = 0) | real_$less(v2,
% 14.74/2.63 v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~
% 14.74/2.63 (real_$lesseq(v2, v1) = 0) | ~ (real_$lesseq(v1, v0) = 0) |
% 14.74/2.63 real_$lesseq(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real]
% 14.74/2.63 : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) & ! [v0:
% 14.74/2.63 $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = v2)
% 14.74/2.63 | real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 |
% 14.74/2.63 ~ (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : ! [v1: $real] : (v1 =
% 14.74/2.63 v0 | ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = 0) & ! [v0:
% 14.74/2.63 $real] : ! [v1: int] : (v1 = 0 | ~ (real_$lesseq(v0, v0) = v1)) & ! [v0:
% 14.74/2.63 $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) =
% 14.74/2.63 v0) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) |
% 14.74/2.63 real_$sum(v0, v1) = real_0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 14.74/2.63 (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $real] :
% 14.74/2.63 ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) &
% 14.74/2.63 ! [v0: $real] : ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) |
% 14.74/2.63 real_$greater(v0, v1) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 14.74/2.63 (real_$less(v1, v0) = 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $real] : !
% 14.74/2.63 [v1: MultipleValueBool] : ( ~ (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0)
% 14.74/2.63 = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$lesseq(v1, v0) = 0) |
% 14.74/2.63 real_$greatereq(v0, v1) = 0) & ! [v0: $real] : (v0 = real_0 | ~
% 14.74/2.63 (real_$uminus(v0) = v0))
% 14.74/2.63
% 14.74/2.63 (function-axioms)
% 14.74/2.64 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 |
% 14.74/2.64 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & !
% 14.74/2.64 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 14.74/2.64 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & !
% 14.74/2.64 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 14.74/2.64 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0:
% 14.74/2.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 14.74/2.64 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~
% 14.74/2.64 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.74/2.64 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 14.74/2.64 (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, v2) = v0)) & ! [v0:
% 14.74/2.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 14.74/2.64 $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) =
% 14.74/2.64 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.74/2.64 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | ~
% 14.74/2.64 (real_$lesseq(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 14.74/2.64 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$product(v3, v2) = v1) | ~
% 14.74/2.64 (real_$product(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 14.74/2.64 int] : ! [v3: $real] : (v1 = v0 | ~ (power(v3, v2) = v1) | ~ (power(v3,
% 14.74/2.64 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 14.74/2.64 ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1) | ~ (real_$is_int(v2) =
% 14.74/2.64 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.74/2.64 $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1) | ~ (real_$is_rat(v2) = v0))
% 14.74/2.64 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 14.74/2.64 (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) & ! [v0: $real] : !
% 14.74/2.64 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$ceiling(v2) = v1) | ~
% 14.74/2.64 (real_$ceiling(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real]
% 14.74/2.64 : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ (real_$truncate(v2) = v0)) & !
% 14.74/2.64 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$round(v2)
% 14.74/2.64 = v1) | ~ (real_$round(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2:
% 14.74/2.64 $real] : (v1 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0))
% 14.74/2.64 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $real] : (v1 = v0 | ~
% 14.74/2.64 (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: $real] : !
% 14.74/2.64 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~
% 14.74/2.64 (real_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] :
% 14.74/2.64 (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = v0)) & ! [v0:
% 14.74/2.64 $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$uminus(v2) =
% 14.74/2.64 v1) | ~ (real_$uminus(v2) = v0))
% 14.74/2.64
% 14.74/2.64 Further assumptions not needed in the proof:
% 14.74/2.64 --------------------------------------------
% 14.74/2.64 pow_ge_one, power_0, power_mult, power_mult2, power_s, power_sum
% 14.74/2.64
% 14.74/2.64 Those formulas are unsatisfiable:
% 14.74/2.64 ---------------------------------
% 14.74/2.64
% 14.74/2.64 Begin of proof
% 14.74/2.64 |
% 14.74/2.64 | ALPHA: (power_s_alt) implies:
% 14.74/2.64 | (1) ! [v0: $real] : ! [v1: int] : ! [v2: $real] : ( ~ ($lesseq(1, v1)) |
% 14.74/2.64 | ~ (power(v0, v1) = v2) | ? [v3: $real] : (real_$product(v0, v3) =
% 14.74/2.64 | v2 & power(v0, $sum(v1, -1)) = v3))
% 14.74/2.64 |
% 14.74/2.64 | ALPHA: (function-axioms) implies:
% 14.74/2.64 | (2) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1
% 14.74/2.64 | = v0 | ~ (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) =
% 14.74/2.64 | v0))
% 14.74/2.64 |
% 14.74/2.64 | ALPHA: (input) implies:
% 14.74/2.64 | (3) real_$product(real_2, real_2) = real_4
% 14.74/2.64 |
% 14.74/2.64 | DELTA: instantiating (pow_2_2) with fresh symbol all_13_0 gives:
% 14.74/2.64 | (4) ~ (all_13_0 = real_4) & power(real_2, 2) = all_13_0
% 14.74/2.64 |
% 14.74/2.64 | ALPHA: (4) implies:
% 14.74/2.65 | (5) ~ (all_13_0 = real_4)
% 14.74/2.65 | (6) power(real_2, 2) = all_13_0
% 14.74/2.65 |
% 14.74/2.65 | GROUND_INST: instantiating (1) with real_2, 2, all_13_0, simplifying with (6)
% 14.74/2.65 | gives:
% 14.74/2.65 | (7) ? [v0: $real] : (real_$product(real_2, v0) = all_13_0 & power(real_2,
% 14.74/2.65 | 1) = v0)
% 14.74/2.65 |
% 14.74/2.65 | DELTA: instantiating (7) with fresh symbol all_27_0 gives:
% 14.74/2.65 | (8) real_$product(real_2, all_27_0) = all_13_0 & power(real_2, 1) =
% 14.74/2.65 | all_27_0
% 14.74/2.65 |
% 14.74/2.65 | ALPHA: (8) implies:
% 14.74/2.65 | (9) power(real_2, 1) = all_27_0
% 14.74/2.65 | (10) real_$product(real_2, all_27_0) = all_13_0
% 14.74/2.65 |
% 14.74/2.65 | GROUND_INST: instantiating (power_1) with real_2, all_27_0, simplifying with
% 14.74/2.65 | (9) gives:
% 14.74/2.65 | (11) all_27_0 = real_2
% 14.74/2.65 |
% 14.74/2.65 | REDUCE: (10), (11) imply:
% 14.74/2.65 | (12) real_$product(real_2, real_2) = all_13_0
% 14.74/2.65 |
% 14.74/2.65 | GROUND_INST: instantiating (2) with real_4, all_13_0, real_2, real_2,
% 14.74/2.65 | simplifying with (3), (12) gives:
% 14.74/2.65 | (13) all_13_0 = real_4
% 14.74/2.65 |
% 14.74/2.65 | REDUCE: (5), (13) imply:
% 14.74/2.65 | (14) $false
% 14.74/2.65 |
% 14.74/2.65 | CLOSE: (14) is inconsistent.
% 14.74/2.65 |
% 14.74/2.65 End of proof
% 14.74/2.65 % SZS output end Proof for theBenchmark
% 14.74/2.65
% 14.74/2.65 2195ms
%------------------------------------------------------------------------------