TSTP Solution File: ARI360_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI360_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 : n028.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 17:47:45 EDT 2023
% Result : Theorem 6.89s 1.71s
% Output : Proof 10.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ARI360_1 : TPTP v8.1.2. Released v5.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 18:29:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.64/0.65 ________ _____
% 0.64/0.65 ___ __ \_________(_)________________________________
% 0.64/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.64/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.64/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.64/0.65
% 0.64/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.64/0.65 (2023-06-19)
% 0.64/0.65
% 0.64/0.65 (c) Philipp Rümmer, 2009-2023
% 0.64/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.64/0.65 Amanda Stjerna.
% 0.64/0.65 Free software under BSD-3-Clause.
% 0.64/0.65
% 0.64/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.64/0.65
% 0.64/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.64/0.67 Running up to 7 provers in parallel.
% 0.64/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.64/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.64/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.64/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.64/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.64/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.64/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.79/1.00 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.79/1.00 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.79/1.00 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.79/1.00 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.79/1.00 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.79/1.00 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.79/1.00 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 2.35/1.07 Prover 1: Preprocessing ...
% 2.35/1.07 Prover 4: Preprocessing ...
% 2.82/1.14 Prover 6: Preprocessing ...
% 2.82/1.14 Prover 0: Preprocessing ...
% 3.13/1.20 Prover 5: Preprocessing ...
% 3.13/1.21 Prover 3: Preprocessing ...
% 3.13/1.21 Prover 2: Preprocessing ...
% 6.41/1.64 Prover 6: Constructing countermodel ...
% 6.41/1.67 Prover 0: Constructing countermodel ...
% 6.41/1.69 Prover 1: Constructing countermodel ...
% 6.89/1.71 Prover 0: proved (1018ms)
% 6.89/1.71 Prover 6: proved (1012ms)
% 6.89/1.71
% 6.89/1.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.89/1.71
% 6.89/1.72
% 6.89/1.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.89/1.72
% 6.89/1.72 Prover 2: stopped
% 6.89/1.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.89/1.72 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.89/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.89/1.72 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 6.89/1.73 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 6.89/1.73 Prover 4: Constructing countermodel ...
% 6.89/1.73 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 6.89/1.74 Prover 8: Preprocessing ...
% 7.40/1.79 Prover 7: Preprocessing ...
% 7.40/1.80 Prover 10: Preprocessing ...
% 8.28/1.94 Prover 8: Warning: ignoring some quantifiers
% 8.28/1.95 Prover 8: Constructing countermodel ...
% 8.28/1.97 Prover 4: Found proof (size 4)
% 8.28/1.97 Prover 1: Found proof (size 4)
% 8.28/1.97 Prover 4: proved (1294ms)
% 8.28/1.97 Prover 1: proved (1297ms)
% 8.28/1.98 Prover 8: stopped
% 9.14/2.09 Prover 5: Constructing countermodel ...
% 9.14/2.09 Prover 5: stopped
% 9.88/2.15 Prover 3: Constructing countermodel ...
% 9.88/2.15 Prover 3: stopped
% 9.88/2.16 Prover 10: Warning: ignoring some quantifiers
% 9.88/2.17 Prover 7: Warning: ignoring some quantifiers
% 9.88/2.18 Prover 10: Constructing countermodel ...
% 9.88/2.18 Prover 7: Constructing countermodel ...
% 10.50/2.21 Prover 10: stopped
% 10.50/2.22 Prover 7: stopped
% 10.50/2.22
% 10.50/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.50/2.22
% 10.50/2.22 % SZS output start Proof for theBenchmark
% 10.50/2.22 Assumptions after simplification:
% 10.50/2.22 ---------------------------------
% 10.50/2.22
% 10.50/2.22 (real_lesseq_problem_3)
% 10.50/2.24 real_$lesseq(real_39/5, real_13/4) = 0
% 10.50/2.24
% 10.50/2.24 (input)
% 10.50/2.27 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_13/4) & ~
% 10.50/2.27 (real_very_large = real_39/5) & ~ (real_very_large = real_0) & ~
% 10.50/2.27 (real_very_small = real_13/4) & ~ (real_very_small = real_39/5) & ~
% 10.50/2.27 (real_very_small = real_0) & ~ (real_13/4 = real_39/5) & ~ (real_13/4 =
% 10.50/2.27 real_0) & ~ (real_39/5 = real_0) & real_$is_int(real_13/4) = 1 &
% 10.50/2.27 real_$is_int(real_39/5) = 1 & real_$is_int(real_0) = 0 &
% 10.50/2.27 real_$is_rat(real_13/4) = 0 & real_$is_rat(real_39/5) = 0 &
% 10.50/2.27 real_$is_rat(real_0) = 0 & real_$floor(real_0) = real_0 &
% 10.50/2.27 real_$ceiling(real_0) = real_0 & real_$truncate(real_0) = real_0 &
% 10.50/2.27 real_$round(real_0) = real_0 & real_$to_int(real_13/4) = 3 &
% 10.50/2.27 real_$to_int(real_39/5) = 7 & real_$to_int(real_0) = 0 &
% 10.50/2.27 real_$to_rat(real_13/4) = rat_13/4 & real_$to_rat(real_39/5) = rat_39/5 &
% 10.50/2.27 real_$to_rat(real_0) = rat_0 & real_$to_real(real_13/4) = real_13/4 &
% 10.50/2.27 real_$to_real(real_39/5) = real_39/5 & real_$to_real(real_0) = real_0 &
% 10.50/2.27 int_$to_real(0) = real_0 & real_$quotient(real_0, real_13/4) = real_0 &
% 10.50/2.27 real_$quotient(real_0, real_39/5) = real_0 & real_$product(real_13/4, real_0)
% 10.50/2.27 = real_0 & real_$product(real_39/5, real_0) = real_0 & real_$product(real_0,
% 10.50/2.27 real_13/4) = real_0 & real_$product(real_0, real_39/5) = real_0 &
% 10.50/2.27 real_$product(real_0, real_0) = real_0 & real_$difference(real_13/4,
% 10.50/2.27 real_13/4) = real_0 & real_$difference(real_13/4, real_0) = real_13/4 &
% 10.50/2.27 real_$difference(real_39/5, real_39/5) = real_0 & real_$difference(real_39/5,
% 10.50/2.27 real_0) = real_39/5 & real_$difference(real_0, real_0) = real_0 &
% 10.50/2.27 real_$uminus(real_0) = real_0 & real_$sum(real_13/4, real_0) = real_13/4 &
% 10.50/2.27 real_$sum(real_39/5, real_0) = real_39/5 & real_$sum(real_0, real_13/4) =
% 10.50/2.27 real_13/4 & real_$sum(real_0, real_39/5) = real_39/5 & real_$sum(real_0,
% 10.50/2.27 real_0) = real_0 & real_$greatereq(real_very_small, real_very_large) = 1 &
% 10.50/2.27 real_$greatereq(real_13/4, real_13/4) = 0 & real_$greatereq(real_13/4,
% 10.50/2.27 real_39/5) = 1 & real_$greatereq(real_13/4, real_0) = 0 &
% 10.50/2.27 real_$greatereq(real_39/5, real_13/4) = 0 & real_$greatereq(real_39/5,
% 10.50/2.27 real_39/5) = 0 & real_$greatereq(real_39/5, real_0) = 0 &
% 10.50/2.27 real_$greatereq(real_0, real_13/4) = 1 & real_$greatereq(real_0, real_39/5) =
% 10.50/2.27 1 & real_$greatereq(real_0, real_0) = 0 & real_$greater(real_very_large,
% 10.50/2.27 real_13/4) = 0 & real_$greater(real_very_large, real_39/5) = 0 &
% 10.50/2.27 real_$greater(real_very_large, real_0) = 0 & real_$greater(real_very_small,
% 10.50/2.27 real_very_large) = 1 & real_$greater(real_13/4, real_very_small) = 0 &
% 10.50/2.27 real_$greater(real_13/4, real_13/4) = 1 & real_$greater(real_13/4, real_39/5)
% 10.50/2.27 = 1 & real_$greater(real_13/4, real_0) = 0 & real_$greater(real_39/5,
% 10.50/2.27 real_very_small) = 0 & real_$greater(real_39/5, real_13/4) = 0 &
% 10.50/2.27 real_$greater(real_39/5, real_39/5) = 1 & real_$greater(real_39/5, real_0) = 0
% 10.50/2.27 & real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0,
% 10.50/2.27 real_13/4) = 1 & real_$greater(real_0, real_39/5) = 1 &
% 10.50/2.27 real_$greater(real_0, real_0) = 1 & real_$less(real_very_small,
% 10.50/2.27 real_very_large) = 0 & real_$less(real_very_small, real_13/4) = 0 &
% 10.50/2.27 real_$less(real_very_small, real_39/5) = 0 & real_$less(real_very_small,
% 10.50/2.27 real_0) = 0 & real_$less(real_13/4, real_very_large) = 0 &
% 10.50/2.27 real_$less(real_13/4, real_13/4) = 1 & real_$less(real_13/4, real_39/5) = 0 &
% 10.50/2.27 real_$less(real_13/4, real_0) = 1 & real_$less(real_39/5, real_very_large) = 0
% 10.50/2.27 & real_$less(real_39/5, real_13/4) = 1 & real_$less(real_39/5, real_39/5) = 1
% 10.50/2.27 & real_$less(real_39/5, real_0) = 1 & real_$less(real_0, real_very_large) = 0
% 10.50/2.27 & real_$less(real_0, real_13/4) = 0 & real_$less(real_0, real_39/5) = 0 &
% 10.50/2.27 real_$less(real_0, real_0) = 1 & real_$lesseq(real_very_small,
% 10.50/2.27 real_very_large) = 0 & real_$lesseq(real_13/4, real_13/4) = 0 &
% 10.50/2.27 real_$lesseq(real_13/4, real_39/5) = 0 & real_$lesseq(real_13/4, real_0) = 1 &
% 10.50/2.27 real_$lesseq(real_39/5, real_13/4) = 1 & real_$lesseq(real_39/5, real_39/5) =
% 10.50/2.27 0 & real_$lesseq(real_39/5, real_0) = 1 & real_$lesseq(real_0, real_13/4) = 0
% 10.50/2.27 & real_$lesseq(real_0, real_39/5) = 0 & real_$lesseq(real_0, real_0) = 0 & !
% 10.50/2.27 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4:
% 10.50/2.27 $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ?
% 10.50/2.27 [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0:
% 10.50/2.27 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v3 = v1 | v0 =
% 10.50/2.27 real_0 | ~ (real_$quotient(v2, v0) = v3) | ~ (real_$product(v1, v0) = v2))
% 10.50/2.27 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 |
% 10.50/2.27 ~ (real_$less(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] :
% 10.50/2.27 ( ~ (v4 = 0) & real_$less(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] :
% 10.50/2.27 ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~
% 10.50/2.27 (real_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2,
% 10.50/2.27 v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3:
% 10.50/2.27 $real] : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) |
% 10.50/2.27 real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.50/2.27 $real] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) =
% 10.50/2.27 v2)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~
% 10.50/2.27 (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 10.50/2.27 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.50/2.27 int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 =
% 10.50/2.27 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : !
% 10.50/2.27 [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3:
% 10.50/2.27 int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & ! [v0: $real] : !
% 10.50/2.27 [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = v2) |
% 10.50/2.27 real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.50/2.27 $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0:
% 10.50/2.27 $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$less(v1, v0) = 0) | ~
% 10.50/2.27 (real_$lesseq(v2, v1) = 0) | real_$less(v2, v0) = 0) & ! [v0: $real] : !
% 10.50/2.27 [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! [v0: $real] :
% 10.50/2.27 ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0)
% 10.50/2.27 = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) |
% 10.50/2.27 real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 10.50/2.27 (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $real] :
% 10.50/2.27 ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) &
% 10.50/2.27 ! [v0: $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0))
% 10.50/2.27
% 10.50/2.27 (function-axioms)
% 10.50/2.28 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 |
% 10.50/2.28 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & !
% 10.50/2.28 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 10.50/2.28 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0:
% 10.50/2.28 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 10.50/2.28 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & !
% 10.50/2.28 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 10.50/2.28 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0:
% 10.50/2.28 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 10.50/2.28 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~
% 10.50/2.28 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.50/2.28 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 10.50/2.28 (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, v2) = v0)) & ! [v0:
% 10.50/2.28 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 10.50/2.28 $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) =
% 10.50/2.28 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.50/2.28 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | ~
% 10.50/2.28 (real_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.50/2.28 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1)
% 10.50/2.28 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.50/2.28 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1)
% 10.50/2.28 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.50/2.28 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) &
% 10.50/2.28 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 10.50/2.28 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] :
% 10.50/2.28 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~
% 10.50/2.28 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.50/2.28 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) &
% 10.50/2.28 ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2)
% 10.50/2.28 = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : !
% 10.50/2.28 [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) =
% 10.50/2.28 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 10.50/2.28 (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] :
% 10.50/2.28 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~
% 10.50/2.28 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real]
% 10.50/2.28 : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0))
% 10.50/2.28
% 10.50/2.28 Those formulas are unsatisfiable:
% 10.50/2.28 ---------------------------------
% 10.50/2.28
% 10.50/2.28 Begin of proof
% 10.50/2.28 |
% 10.50/2.28 | ALPHA: (function-axioms) implies:
% 10.50/2.28 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.50/2.28 | $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) |
% 10.50/2.28 | ~ (real_$lesseq(v3, v2) = v0))
% 10.50/2.29 |
% 10.50/2.29 | ALPHA: (input) implies:
% 10.50/2.29 | (2) real_$lesseq(real_39/5, real_13/4) = 1
% 10.50/2.29 |
% 10.50/2.29 | GROUND_INST: instantiating (1) with 0, 1, real_13/4, real_39/5, simplifying
% 10.50/2.29 | with (2), (real_lesseq_problem_3) gives:
% 10.50/2.29 | (3) $false
% 10.50/2.29 |
% 10.50/2.29 | CLOSE: (3) is inconsistent.
% 10.50/2.29 |
% 10.50/2.29 End of proof
% 10.50/2.29 % SZS output end Proof for theBenchmark
% 10.50/2.29
% 10.50/2.29 1641ms
%------------------------------------------------------------------------------