TSTP Solution File: ARI518_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI518_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 : n027.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 17:48:15 EDT 2023
% Result : Theorem 5.96s 1.56s
% Output : Proof 8.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI518_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n027.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 19:11:38 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.55/0.63 ________ _____
% 0.55/0.63 ___ __ \_________(_)________________________________
% 0.55/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.55/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.55/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.55/0.63
% 0.55/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.55/0.63 (2023-06-19)
% 0.55/0.63
% 0.55/0.63 (c) Philipp Rümmer, 2009-2023
% 0.55/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.55/0.63 Amanda Stjerna.
% 0.55/0.63 Free software under BSD-3-Clause.
% 0.55/0.63
% 0.55/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.55/0.63
% 0.55/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.55/0.65 Running up to 7 provers in parallel.
% 0.55/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.55/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.55/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.55/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.55/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.55/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.55/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.71/0.99 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.71/0.99 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.71/0.99 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.71/0.99 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.71/0.99 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.71/0.99 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.71/0.99 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 2.32/1.05 Prover 4: Preprocessing ...
% 2.32/1.06 Prover 1: Preprocessing ...
% 2.32/1.09 Prover 5: Preprocessing ...
% 2.32/1.09 Prover 2: Preprocessing ...
% 2.32/1.09 Prover 3: Preprocessing ...
% 2.32/1.09 Prover 0: Preprocessing ...
% 2.32/1.10 Prover 6: Preprocessing ...
% 5.30/1.51 Prover 6: Constructing countermodel ...
% 5.72/1.54 Prover 1: Constructing countermodel ...
% 5.72/1.55 Prover 6: proved (888ms)
% 5.96/1.56
% 5.96/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.96/1.56
% 5.96/1.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.96/1.56 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 5.96/1.57 Prover 0: Constructing countermodel ...
% 5.96/1.57 Prover 0: stopped
% 5.96/1.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.96/1.58 Prover 3: Constructing countermodel ...
% 5.96/1.58 Prover 3: stopped
% 5.96/1.58 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.96/1.58 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 5.96/1.58 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 5.96/1.58 Prover 8: Preprocessing ...
% 5.96/1.59 Prover 7: Preprocessing ...
% 5.96/1.60 Prover 10: Preprocessing ...
% 5.96/1.62 Prover 4: Constructing countermodel ...
% 6.51/1.63 Prover 2: Constructing countermodel ...
% 6.51/1.63 Prover 2: stopped
% 6.51/1.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.51/1.65 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation
% 6.51/1.67 Prover 11: Preprocessing ...
% 6.85/1.69 Prover 5: Constructing countermodel ...
% 6.85/1.69 Prover 5: stopped
% 6.85/1.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.85/1.71 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation
% 6.85/1.71 Prover 13: Preprocessing ...
% 6.85/1.73 Prover 8: Warning: ignoring some quantifiers
% 7.35/1.76 Prover 8: Constructing countermodel ...
% 7.49/1.79 Prover 1: Found proof (size 7)
% 7.49/1.79 Prover 1: proved (1133ms)
% 7.49/1.79 Prover 4: Found proof (size 7)
% 7.49/1.79 Prover 4: proved (1132ms)
% 7.49/1.79 Prover 8: stopped
% 7.49/1.83 Prover 7: Warning: ignoring some quantifiers
% 7.49/1.83 Prover 10: Warning: ignoring some quantifiers
% 7.49/1.83 Prover 13: Warning: ignoring some quantifiers
% 7.49/1.83 Prover 13: Constructing countermodel ...
% 7.49/1.84 Prover 7: Constructing countermodel ...
% 7.49/1.84 Prover 10: Constructing countermodel ...
% 7.49/1.85 Prover 13: stopped
% 7.49/1.86 Prover 10: stopped
% 7.49/1.86 Prover 7: stopped
% 8.44/1.93 Prover 11: Constructing countermodel ...
% 8.44/1.95 Prover 11: stopped
% 8.44/1.95
% 8.44/1.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.44/1.95
% 8.44/1.95 % SZS output start Proof for theBenchmark
% 8.44/1.95 Assumptions after simplification:
% 8.44/1.95 ---------------------------------
% 8.44/1.95
% 8.44/1.95 (mixed_types_problem_23)
% 8.44/1.97 ? [v0: int] : ($lesseq(v0, 12) & real_$to_int(real_131/10) = v0)
% 8.44/1.97
% 8.44/1.97 (input)
% 8.83/2.00 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_131/10) &
% 8.83/2.00 ~ (real_very_large = real_0) & ~ (real_very_small = real_131/10) & ~
% 8.83/2.00 (real_very_small = real_0) & ~ (real_131/10 = real_0) &
% 8.83/2.00 real_$is_int(real_131/10) = 1 & real_$is_int(real_0) = 0 &
% 8.83/2.00 real_$is_rat(real_131/10) = 0 & real_$is_rat(real_0) = 0 & real_$floor(real_0)
% 8.83/2.00 = real_0 & real_$ceiling(real_0) = real_0 & real_$truncate(real_0) = real_0 &
% 8.83/2.00 real_$round(real_0) = real_0 & real_$to_rat(real_131/10) = rat_131/10 &
% 8.83/2.00 real_$to_rat(real_0) = rat_0 & real_$to_real(real_131/10) = real_131/10 &
% 8.83/2.00 real_$to_real(real_0) = real_0 & int_$to_real(0) = real_0 &
% 8.83/2.00 real_$quotient(real_0, real_131/10) = real_0 & real_$product(real_131/10,
% 8.83/2.00 real_0) = real_0 & real_$product(real_0, real_131/10) = real_0 &
% 8.83/2.00 real_$product(real_0, real_0) = real_0 & real_$difference(real_131/10,
% 8.83/2.00 real_131/10) = real_0 & real_$difference(real_131/10, real_0) = real_131/10
% 8.83/2.00 & real_$difference(real_0, real_0) = real_0 & real_$uminus(real_0) = real_0 &
% 8.83/2.00 real_$sum(real_131/10, real_0) = real_131/10 & real_$sum(real_0, real_131/10)
% 8.83/2.00 = real_131/10 & real_$sum(real_0, real_0) = real_0 &
% 8.83/2.00 real_$greatereq(real_very_small, real_very_large) = 1 &
% 8.83/2.00 real_$greatereq(real_131/10, real_131/10) = 0 & real_$greatereq(real_131/10,
% 8.83/2.00 real_0) = 0 & real_$greatereq(real_0, real_131/10) = 1 &
% 8.83/2.00 real_$greatereq(real_0, real_0) = 0 & real_$lesseq(real_very_small,
% 8.83/2.00 real_very_large) = 0 & real_$lesseq(real_131/10, real_131/10) = 0 &
% 8.83/2.00 real_$lesseq(real_131/10, real_0) = 1 & real_$lesseq(real_0, real_131/10) = 0
% 8.83/2.00 & real_$lesseq(real_0, real_0) = 0 & real_$greater(real_very_large,
% 8.83/2.00 real_131/10) = 0 & real_$greater(real_very_large, real_0) = 0 &
% 8.83/2.00 real_$greater(real_very_small, real_very_large) = 1 &
% 8.83/2.00 real_$greater(real_131/10, real_very_small) = 0 & real_$greater(real_131/10,
% 8.83/2.00 real_131/10) = 1 & real_$greater(real_131/10, real_0) = 0 &
% 8.83/2.00 real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0,
% 8.83/2.00 real_131/10) = 1 & real_$greater(real_0, real_0) = 1 &
% 8.83/2.00 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small,
% 8.83/2.00 real_131/10) = 0 & real_$less(real_very_small, real_0) = 0 &
% 8.83/2.00 real_$less(real_131/10, real_very_large) = 0 & real_$less(real_131/10,
% 8.83/2.00 real_131/10) = 1 & real_$less(real_131/10, real_0) = 1 & real_$less(real_0,
% 8.83/2.00 real_very_large) = 0 & real_$less(real_0, real_131/10) = 0 &
% 8.83/2.00 real_$less(real_0, real_0) = 1 & real_$to_int(real_131/10) = 13 &
% 8.83/2.00 real_$to_int(real_0) = 0 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 8.83/2.00 ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~
% 8.83/2.00 (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 &
% 8.83/2.00 real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 8.83/2.00 $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v2, v3) = v4) | ~
% 8.83/2.00 (real_$sum(v1, v0) = v3) | ? [v5: $real] : (real_$sum(v5, v0) = v4 &
% 8.83/2.00 real_$sum(v2, v1) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 8.83/2.00 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~
% 8.83/2.00 (real_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1,
% 8.83/2.00 v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3:
% 8.83/2.00 int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$less(v2, v0) =
% 8.83/2.00 v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0) = v4)) & ! [v0:
% 8.83/2.00 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~
% 8.83/2.00 (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] :
% 8.83/2.00 ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real]
% 8.83/2.00 : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, v0) = 0) | ~
% 8.83/2.00 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2, v1)
% 8.83/2.00 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] :
% 8.83/2.00 (v3 = 0 | ~ (real_$less(v2, v1) = 0) | ~ (real_$less(v2, v0) = v3) | ? [v4:
% 8.83/2.00 int] : ( ~ (v4 = 0) & real_$lesseq(v1, v0) = v4)) & ! [v0: $real] : !
% 8.83/2.00 [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v0)
% 8.83/2.00 = v3) | ~ (real_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) &
% 8.83/2.00 real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 8.83/2.00 $real] : ! [v3: $real] : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1,
% 8.83/2.00 v2) = v3) | real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1:
% 8.83/2.00 $real] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (real_$less(v1, v0) = v2) |
% 8.83/2.00 ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: $real] :
% 8.83/2.00 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greatereq(v0, v1) = v2) |
% 8.83/2.00 ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: $real] :
% 8.83/2.00 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ?
% 8.83/2.00 [v3: int] : ( ~ (v3 = 0) & real_$greatereq(v0, v1) = v3)) & ! [v0: $real] :
% 8.83/2.00 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ?
% 8.83/2.00 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : !
% 8.83/2.00 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ?
% 8.83/2.00 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : !
% 8.83/2.00 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$less(v1, v0) = v2) | ? [v3:
% 8.83/2.00 int] : ( ~ (v3 = 0) & real_$greater(v0, v1) = v3)) & ! [v0: $real] : !
% 8.83/2.00 [v1: $real] : ! [v2: $real] : (v0 = real_0 | ~ (real_$product(v1, v0) = v2)
% 8.83/2.00 | real_$quotient(v2, v0) = v1) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 8.83/2.00 $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) & !
% 8.83/2.00 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) =
% 8.83/2.00 v2) | real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : !
% 8.83/2.00 [v2: $real] : ( ~ (real_$difference(v1, v0) = v2) | ? [v3: $real] :
% 8.83/2.00 (real_$uminus(v0) = v3 & real_$sum(v1, v3) = v2)) & ! [v0: $real] : ! [v1:
% 8.83/2.00 $real] : ! [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0, v1) =
% 8.83/2.00 v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0,
% 8.83/2.00 v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] :
% 8.83/2.00 ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$lesseq(v1, v0) = 0)
% 8.83/2.00 | real_$lesseq(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 8.83/2.00 $real] : ( ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$less(v1, v0) = 0) |
% 8.83/2.00 real_$less(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 8.83/2.00 ( ~ (real_$lesseq(v1, v0) = 0) | ~ (real_$less(v2, v1) = 0) | real_$less(v2,
% 8.83/2.00 v0) = 0) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0,
% 8.83/2.00 real_0) = v1)) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~
% 8.83/2.00 (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = 0) & ! [v0: $real] : !
% 8.83/2.00 [v1: int] : (v1 = 0 | ~ (real_$lesseq(v0, v0) = v1)) & ! [v0: $real] : !
% 8.83/2.00 [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0:
% 8.83/2.00 $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$sum(v0, v1) =
% 8.83/2.00 real_0) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$greatereq(v0, v1) =
% 8.83/2.00 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 8.83/2.00 (real_$lesseq(v1, v0) = 0) | real_$greatereq(v0, v1) = 0) & ! [v0: $real] :
% 8.83/2.00 ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) &
% 8.83/2.00 ! [v0: $real] : ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) |
% 8.83/2.00 real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 8.83/2.00 (real_$less(v1, v0) = 0) | real_$greater(v0, v1) = 0) & ! [v0: $real] : !
% 8.83/2.00 [v1: MultipleValueBool] : ( ~ (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0)
% 8.83/2.00 = 0) & ! [v0: $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0))
% 8.83/2.00
% 8.83/2.00 (function-axioms)
% 8.83/2.01 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 |
% 8.83/2.01 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & !
% 8.83/2.01 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 8.83/2.01 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0:
% 8.83/2.01 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 8.83/2.01 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & !
% 8.83/2.01 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 8.83/2.01 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0:
% 8.83/2.01 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 8.83/2.01 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~
% 8.83/2.01 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.83/2.01 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 8.83/2.01 (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, v2) = v0)) & ! [v0:
% 8.83/2.01 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 8.83/2.01 $real] : (v1 = v0 | ~ (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3,
% 8.83/2.01 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 8.83/2.01 ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~
% 8.83/2.01 (real_$less(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.83/2.01 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1)
% 8.83/2.01 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.83/2.01 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1)
% 8.83/2.01 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 8.83/2.01 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) &
% 8.83/2.01 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 8.83/2.01 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] :
% 8.83/2.01 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~
% 8.83/2.01 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 8.83/2.01 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) &
% 8.83/2.01 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $real] : (v1 = v0 | ~
% 8.83/2.01 (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: $real] : !
% 8.83/2.01 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~
% 8.83/2.01 (real_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] :
% 8.83/2.01 (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = v0)) & ! [v0:
% 8.83/2.01 $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$uminus(v2) =
% 8.83/2.01 v1) | ~ (real_$uminus(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2:
% 8.83/2.01 $real] : (v1 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0))
% 8.83/2.01
% 8.83/2.01 Those formulas are unsatisfiable:
% 8.83/2.01 ---------------------------------
% 8.83/2.01
% 8.83/2.01 Begin of proof
% 8.83/2.01 |
% 8.83/2.01 | ALPHA: (function-axioms) implies:
% 8.83/2.01 | (1) ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~
% 8.83/2.01 | (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0))
% 8.83/2.01 |
% 8.83/2.01 | ALPHA: (input) implies:
% 8.83/2.01 | (2) real_$to_int(real_131/10) = 13
% 8.83/2.01 |
% 8.83/2.01 | DELTA: instantiating (mixed_types_problem_23) with fresh symbol all_5_0 gives:
% 8.83/2.01 | (3) $lesseq(all_5_0, 12) & real_$to_int(real_131/10) = all_5_0
% 8.83/2.01 |
% 8.83/2.01 | ALPHA: (3) implies:
% 8.83/2.01 | (4) $lesseq(all_5_0, 12)
% 8.83/2.01 | (5) real_$to_int(real_131/10) = all_5_0
% 8.83/2.01 |
% 8.83/2.01 | GROUND_INST: instantiating (1) with 13, all_5_0, real_131/10, simplifying with
% 8.83/2.01 | (2), (5) gives:
% 8.83/2.01 | (6) all_5_0 = 13
% 8.83/2.01 |
% 8.83/2.01 | REDUCE: (4), (6) imply:
% 8.83/2.01 | (7) $false
% 8.83/2.02 |
% 8.83/2.02 | CLOSE: (7) is inconsistent.
% 8.83/2.02 |
% 8.83/2.02 End of proof
% 8.83/2.02 % SZS output end Proof for theBenchmark
% 8.83/2.02
% 8.83/2.02 1380ms
%------------------------------------------------------------------------------