TSTP Solution File: ARI736_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI736_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 : n001.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 17:48:58 EDT 2023
% Result : Theorem 6.32s 1.64s
% Output : Proof 9.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI736_1 : TPTP v8.1.2. Released v7.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n001.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 18:48:07 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.65 ________ _____
% 0.20/0.65 ___ __ \_________(_)________________________________
% 0.20/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.65
% 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.65 (2023-06-19)
% 0.20/0.65
% 0.20/0.65 (c) Philipp Rümmer, 2009-2023
% 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.65 Amanda Stjerna.
% 0.20/0.65 Free software under BSD-3-Clause.
% 0.20/0.65
% 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.65
% 0.20/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.66 Running up to 7 provers in parallel.
% 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.43/0.99 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.99 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.99 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.99 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.99 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.99 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.99 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.98/1.06 Prover 1: Preprocessing ...
% 1.98/1.06 Prover 4: Preprocessing ...
% 2.58/1.12 Prover 6: Preprocessing ...
% 2.58/1.12 Prover 0: Preprocessing ...
% 2.58/1.15 Prover 2: Preprocessing ...
% 2.58/1.16 Prover 3: Preprocessing ...
% 2.58/1.16 Prover 5: Preprocessing ...
% 6.16/1.61 Prover 6: Constructing countermodel ...
% 6.32/1.63 Prover 6: proved (960ms)
% 6.32/1.63
% 6.32/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.32/1.64
% 6.32/1.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.32/1.64 Prover 1: Constructing countermodel ...
% 6.32/1.64 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 6.32/1.67 Prover 2: stopped
% 6.32/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.32/1.67 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 6.32/1.67 Prover 8: Preprocessing ...
% 6.32/1.67 Prover 7: Preprocessing ...
% 6.32/1.68 Prover 0: Constructing countermodel ...
% 6.32/1.68 Prover 0: stopped
% 6.32/1.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.32/1.69 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 7.02/1.74 Prover 10: Preprocessing ...
% 7.02/1.77 Prover 4: Constructing countermodel ...
% 7.56/1.87 Prover 1: Found proof (size 7)
% 8.16/1.87 Prover 1: proved (1206ms)
% 8.16/1.87 Prover 4: stopped
% 8.22/1.88 Prover 10: stopped
% 8.41/1.91 Prover 8: Warning: ignoring some quantifiers
% 8.55/1.92 Prover 8: Constructing countermodel ...
% 8.55/1.94 Prover 8: stopped
% 9.20/2.02 Prover 3: Constructing countermodel ...
% 9.20/2.02 Prover 3: stopped
% 9.20/2.05 Prover 7: Warning: ignoring some quantifiers
% 9.20/2.07 Prover 7: Constructing countermodel ...
% 9.67/2.10 Prover 7: stopped
% 9.67/2.14 Prover 5: Constructing countermodel ...
% 9.67/2.14 Prover 5: stopped
% 9.67/2.15
% 9.67/2.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.67/2.15
% 9.67/2.15 % SZS output start Proof for theBenchmark
% 9.67/2.15 Assumptions after simplification:
% 9.67/2.15 ---------------------------------
% 9.67/2.15
% 9.67/2.15 (g3)
% 9.67/2.17 ? [v0: int] : ( ~ (v0 = 2) & real_$to_int(real_2) = v0)
% 9.67/2.17
% 9.67/2.17 (input)
% 9.67/2.19 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_2) & ~
% 9.67/2.19 (real_very_large = real_3/2) & ~ (real_very_large = real_0) & ~
% 9.67/2.19 (real_very_small = real_2) & ~ (real_very_small = real_3/2) & ~
% 9.67/2.19 (real_very_small = real_0) & ~ (real_2 = real_3/2) & ~ (real_2 = real_0) &
% 9.67/2.19 ~ (real_3/2 = real_0) & real_$is_int(real_2) = 0 & real_$is_int(real_3/2) = 1
% 9.67/2.19 & real_$is_int(real_0) = 0 & real_$is_rat(real_2) = 0 & real_$is_rat(real_3/2)
% 9.67/2.19 = 0 & real_$is_rat(real_0) = 0 & real_$floor(real_2) = real_2 &
% 9.67/2.19 real_$floor(real_0) = real_0 & real_$ceiling(real_2) = real_2 &
% 9.67/2.19 real_$ceiling(real_3/2) = real_2 & real_$ceiling(real_0) = real_0 &
% 9.67/2.19 real_$truncate(real_2) = real_2 & real_$truncate(real_0) = real_0 &
% 9.67/2.19 real_$round(real_2) = real_2 & real_$round(real_3/2) = real_2 &
% 9.67/2.19 real_$round(real_0) = real_0 & real_$to_rat(real_2) = rat_2 &
% 9.67/2.19 real_$to_rat(real_3/2) = rat_3/2 & real_$to_rat(real_0) = rat_0 &
% 9.67/2.19 real_$to_real(real_2) = real_2 & real_$to_real(real_3/2) = real_3/2 &
% 9.67/2.19 real_$to_real(real_0) = real_0 & int_$to_real(2) = real_2 & int_$to_real(0) =
% 9.67/2.19 real_0 & real_$quotient(real_0, real_2) = real_0 & real_$quotient(real_0,
% 9.67/2.19 real_3/2) = real_0 & real_$product(real_2, real_0) = real_0 &
% 9.67/2.19 real_$product(real_3/2, real_0) = real_0 & real_$product(real_0, real_2) =
% 9.67/2.19 real_0 & real_$product(real_0, real_3/2) = real_0 & real_$product(real_0,
% 9.67/2.19 real_0) = real_0 & real_$difference(real_2, real_2) = real_0 &
% 9.67/2.19 real_$difference(real_2, real_0) = real_2 & real_$difference(real_3/2,
% 9.67/2.19 real_3/2) = real_0 & real_$difference(real_3/2, real_0) = real_3/2 &
% 9.67/2.20 real_$difference(real_0, real_0) = real_0 & real_$uminus(real_0) = real_0 &
% 9.67/2.20 real_$sum(real_2, real_0) = real_2 & real_$sum(real_3/2, real_0) = real_3/2 &
% 9.67/2.20 real_$sum(real_0, real_2) = real_2 & real_$sum(real_0, real_3/2) = real_3/2 &
% 9.67/2.20 real_$sum(real_0, real_0) = real_0 & real_$greatereq(real_very_small,
% 9.67/2.20 real_very_large) = 1 & real_$greatereq(real_2, real_2) = 0 &
% 9.67/2.20 real_$greatereq(real_2, real_3/2) = 0 & real_$greatereq(real_2, real_0) = 0 &
% 9.67/2.20 real_$greatereq(real_3/2, real_2) = 1 & real_$greatereq(real_3/2, real_3/2) =
% 9.67/2.20 0 & real_$greatereq(real_3/2, real_0) = 0 & real_$greatereq(real_0, real_2) =
% 9.67/2.20 1 & real_$greatereq(real_0, real_3/2) = 1 & real_$greatereq(real_0, real_0) =
% 9.67/2.20 0 & real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_2,
% 9.67/2.20 real_2) = 0 & real_$lesseq(real_2, real_3/2) = 1 & real_$lesseq(real_2,
% 9.67/2.20 real_0) = 1 & real_$lesseq(real_3/2, real_2) = 0 & real_$lesseq(real_3/2,
% 9.67/2.20 real_3/2) = 0 & real_$lesseq(real_3/2, real_0) = 1 & real_$lesseq(real_0,
% 9.67/2.20 real_2) = 0 & real_$lesseq(real_0, real_3/2) = 0 & real_$lesseq(real_0,
% 9.67/2.20 real_0) = 0 & real_$greater(real_very_large, real_2) = 0 &
% 9.67/2.20 real_$greater(real_very_large, real_3/2) = 0 & real_$greater(real_very_large,
% 9.67/2.20 real_0) = 0 & real_$greater(real_very_small, real_very_large) = 1 &
% 9.67/2.20 real_$greater(real_2, real_very_small) = 0 & real_$greater(real_2, real_2) = 1
% 9.67/2.20 & real_$greater(real_2, real_3/2) = 0 & real_$greater(real_2, real_0) = 0 &
% 9.67/2.20 real_$greater(real_3/2, real_very_small) = 0 & real_$greater(real_3/2, real_2)
% 9.67/2.20 = 1 & real_$greater(real_3/2, real_3/2) = 1 & real_$greater(real_3/2, real_0)
% 9.67/2.20 = 0 & real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0,
% 9.67/2.20 real_2) = 1 & real_$greater(real_0, real_3/2) = 1 & real_$greater(real_0,
% 9.67/2.20 real_0) = 1 & real_$less(real_very_small, real_very_large) = 0 &
% 9.67/2.20 real_$less(real_very_small, real_2) = 0 & real_$less(real_very_small,
% 9.67/2.20 real_3/2) = 0 & real_$less(real_very_small, real_0) = 0 & real_$less(real_2,
% 9.67/2.20 real_very_large) = 0 & real_$less(real_2, real_2) = 1 & real_$less(real_2,
% 9.67/2.20 real_3/2) = 1 & real_$less(real_2, real_0) = 1 & real_$less(real_3/2,
% 9.67/2.20 real_very_large) = 0 & real_$less(real_3/2, real_2) = 0 &
% 9.67/2.20 real_$less(real_3/2, real_3/2) = 1 & real_$less(real_3/2, real_0) = 1 &
% 9.67/2.20 real_$less(real_0, real_very_large) = 0 & real_$less(real_0, real_2) = 0 &
% 9.67/2.20 real_$less(real_0, real_3/2) = 0 & real_$less(real_0, real_0) = 1 &
% 9.67/2.20 real_$to_int(real_2) = 2 & real_$to_int(real_3/2) = 1 & real_$to_int(real_0) =
% 9.67/2.20 0 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : !
% 9.67/2.20 [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ?
% 9.67/2.20 [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0:
% 9.67/2.20 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v3 = v1 | v0 =
% 9.67/2.20 real_0 | ~ (real_$quotient(v2, v0) = v3) | ~ (real_$product(v1, v0) = v2))
% 9.67/2.20 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 |
% 9.67/2.20 ~ (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int]
% 9.67/2.20 : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1:
% 9.67/2.20 $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, v0)
% 9.67/2.20 = 0) | ~ (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) &
% 9.67/2.20 real_$less(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 9.67/2.20 $real] : ! [v3: $real] : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1,
% 9.67/2.20 v2) = v3) | real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1:
% 9.67/2.20 $real] : ! [v2: $real] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | ~
% 9.67/2.20 (real_$sum(v0, v1) = v2)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] :
% 9.67/2.20 (v2 = 0 | ~ (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 9.67/2.20 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 9.67/2.20 int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3:
% 9.67/2.20 int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & ! [v0: $real] : !
% 9.67/2.20 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ?
% 9.67/2.20 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : !
% 9.67/2.20 [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = v2) |
% 9.67/2.20 real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 9.67/2.20 $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0:
% 9.67/2.20 $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) |
% 9.67/2.20 ~ (real_$less(v1, v0) = 0) | real_$less(v2, v0) = 0) & ! [v0: $real] : !
% 9.67/2.20 [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! [v0: $real] :
% 9.67/2.20 ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0)
% 9.67/2.20 = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) |
% 9.67/2.20 real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 9.67/2.20 (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $real] :
% 9.67/2.20 ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) &
% 9.67/2.20 ! [v0: $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0))
% 9.67/2.20
% 9.67/2.20 (function-axioms)
% 9.67/2.21 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 |
% 9.67/2.21 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & !
% 9.67/2.21 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 9.67/2.21 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0:
% 9.67/2.21 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 9.67/2.21 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & !
% 9.67/2.21 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 9.67/2.21 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0:
% 9.67/2.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 9.67/2.21 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~
% 9.67/2.21 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.67/2.21 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 9.67/2.21 (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, v2) = v0)) & ! [v0:
% 9.67/2.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 9.67/2.21 $real] : (v1 = v0 | ~ (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3,
% 9.67/2.21 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 9.67/2.21 ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~
% 9.67/2.21 (real_$less(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.67/2.21 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1)
% 9.67/2.21 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.67/2.21 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1)
% 9.67/2.21 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 9.67/2.21 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) &
% 9.67/2.21 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 9.67/2.21 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] :
% 9.67/2.21 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~
% 9.67/2.21 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 9.67/2.21 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) &
% 9.67/2.21 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $real] : (v1 = v0 | ~
% 9.67/2.21 (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: $real] : !
% 9.67/2.21 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~
% 9.67/2.21 (real_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] :
% 9.67/2.21 (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = v0)) & ! [v0:
% 9.67/2.21 $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$uminus(v2) =
% 9.67/2.21 v1) | ~ (real_$uminus(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2:
% 9.67/2.21 $real] : (v1 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0))
% 9.67/2.21
% 9.67/2.21 Those formulas are unsatisfiable:
% 9.67/2.21 ---------------------------------
% 9.67/2.21
% 9.67/2.21 Begin of proof
% 9.67/2.21 |
% 9.67/2.21 | ALPHA: (function-axioms) implies:
% 9.67/2.21 | (1) ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~
% 9.67/2.21 | (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0))
% 9.67/2.21 |
% 9.67/2.21 | ALPHA: (input) implies:
% 9.67/2.21 | (2) real_$to_int(real_2) = 2
% 9.67/2.21 |
% 9.67/2.21 | DELTA: instantiating (g3) with fresh symbol all_5_0 gives:
% 9.67/2.22 | (3) ~ (all_5_0 = 2) & real_$to_int(real_2) = all_5_0
% 9.67/2.22 |
% 9.67/2.22 | ALPHA: (3) implies:
% 9.67/2.22 | (4) ~ (all_5_0 = 2)
% 9.67/2.22 | (5) real_$to_int(real_2) = all_5_0
% 9.67/2.22 |
% 9.67/2.22 | GROUND_INST: instantiating (1) with 2, all_5_0, real_2, simplifying with (2),
% 9.67/2.22 | (5) gives:
% 9.67/2.22 | (6) all_5_0 = 2
% 9.67/2.22 |
% 9.67/2.22 | REDUCE: (4), (6) imply:
% 9.67/2.22 | (7) $false
% 9.67/2.22 |
% 9.67/2.22 | CLOSE: (7) is inconsistent.
% 9.67/2.22 |
% 9.67/2.22 End of proof
% 9.67/2.22 % SZS output end Proof for theBenchmark
% 9.67/2.22
% 9.67/2.22 1570ms
%------------------------------------------------------------------------------