TSTP Solution File: ARI364_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI364_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 : n013.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 17:47:46 EDT 2023
% Result : Theorem 5.25s 1.49s
% Output : Proof 8.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI364_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 : n013.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 18:28:47 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.49/0.62 ________ _____
% 0.49/0.62 ___ __ \_________(_)________________________________
% 0.49/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.49/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.49/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.49/0.62
% 0.49/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.49/0.62 (2023-06-19)
% 0.49/0.62
% 0.49/0.62 (c) Philipp Rümmer, 2009-2023
% 0.49/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.49/0.62 Amanda Stjerna.
% 0.49/0.62 Free software under BSD-3-Clause.
% 0.49/0.62
% 0.49/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.49/0.62
% 0.49/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.49/0.63 Running up to 7 provers in parallel.
% 0.49/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.49/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.49/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.49/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.49/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.49/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.49/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.77/0.94 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.77/0.94 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.77/0.94 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.77/0.94 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.77/0.94 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.77/0.94 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.77/0.94 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 2.30/1.01 Prover 1: Preprocessing ...
% 2.30/1.01 Prover 4: Preprocessing ...
% 2.30/1.06 Prover 6: Preprocessing ...
% 2.30/1.06 Prover 5: Preprocessing ...
% 2.30/1.06 Prover 3: Preprocessing ...
% 2.30/1.06 Prover 2: Preprocessing ...
% 2.30/1.06 Prover 0: Preprocessing ...
% 5.25/1.45 Prover 2: Constructing countermodel ...
% 5.25/1.45 Prover 6: Constructing countermodel ...
% 5.25/1.48 Prover 6: proved (837ms)
% 5.25/1.48 Prover 2: proved (843ms)
% 5.25/1.48
% 5.25/1.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.25/1.49
% 5.25/1.49
% 5.25/1.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.25/1.49
% 5.25/1.49 Prover 5: Constructing countermodel ...
% 5.25/1.49 Prover 5: stopped
% 5.25/1.49 Prover 0: Constructing countermodel ...
% 5.25/1.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.25/1.49 Prover 0: stopped
% 5.25/1.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.25/1.50 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 5.25/1.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.25/1.50 Prover 3: Constructing countermodel ...
% 5.25/1.50 Prover 3: stopped
% 5.25/1.50 Prover 1: Constructing countermodel ...
% 5.25/1.50 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 5.25/1.50 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.25/1.51 Prover 8: Preprocessing ...
% 5.25/1.51 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation
% 5.25/1.51 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.87/1.51 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 5.87/1.51 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation
% 5.87/1.52 Prover 13: Preprocessing ...
% 5.87/1.52 Prover 7: Preprocessing ...
% 5.87/1.53 Prover 11: Preprocessing ...
% 5.87/1.53 Prover 10: Preprocessing ...
% 5.87/1.54 Prover 4: Constructing countermodel ...
% 6.36/1.62 Prover 8: Warning: ignoring some quantifiers
% 6.36/1.63 Prover 8: Constructing countermodel ...
% 6.36/1.65 Prover 13: Warning: ignoring some quantifiers
% 6.36/1.66 Prover 13: Constructing countermodel ...
% 7.31/1.71 Prover 4: Found proof (size 6)
% 7.31/1.71 Prover 4: proved (1073ms)
% 7.31/1.71 Prover 8: stopped
% 7.31/1.71 Prover 1: Found proof (size 7)
% 7.31/1.71 Prover 1: proved (1078ms)
% 7.31/1.72 Prover 13: Found proof (size 3)
% 7.31/1.72 Prover 13: proved (207ms)
% 7.31/1.73 Prover 10: Warning: ignoring some quantifiers
% 7.31/1.74 Prover 7: Warning: ignoring some quantifiers
% 7.31/1.74 Prover 10: Constructing countermodel ...
% 7.31/1.75 Prover 7: Constructing countermodel ...
% 7.31/1.76 Prover 10: stopped
% 7.31/1.76 Prover 7: stopped
% 7.54/1.81 Prover 11: Constructing countermodel ...
% 7.54/1.83 Prover 11: stopped
% 7.54/1.83
% 7.54/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.54/1.83
% 7.54/1.83 % SZS output start Proof for theBenchmark
% 7.54/1.83 Assumptions after simplification:
% 7.54/1.83 ---------------------------------
% 7.54/1.83
% 7.54/1.83 (real_lesseq_problem_7)
% 7.54/1.85 ? [v0: int] : ( ~ (v0 = 0) & real_$lesseq(real_-13/4, real_-13/4) = v0)
% 7.54/1.85
% 7.54/1.85 (input)
% 8.19/1.88 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_-13/4) &
% 8.19/1.88 ~ (real_very_large = real_0) & ~ (real_very_small = real_-13/4) & ~
% 8.19/1.88 (real_very_small = real_0) & ~ (real_-13/4 = real_0) &
% 8.19/1.88 real_$is_int(real_-13/4) = 1 & real_$is_int(real_0) = 0 &
% 8.19/1.88 real_$is_rat(real_-13/4) = 0 & real_$is_rat(real_0) = 0 & real_$floor(real_0)
% 8.19/1.88 = real_0 & real_$ceiling(real_0) = real_0 & real_$truncate(real_0) = real_0 &
% 8.19/1.88 real_$round(real_0) = real_0 & real_$to_int(real_-13/4) = -4 &
% 8.19/1.88 real_$to_int(real_0) = 0 & real_$to_rat(real_-13/4) = rat_-13/4 &
% 8.19/1.88 real_$to_rat(real_0) = rat_0 & real_$to_real(real_-13/4) = real_-13/4 &
% 8.19/1.88 real_$to_real(real_0) = real_0 & int_$to_real(0) = real_0 &
% 8.19/1.88 real_$quotient(real_0, real_-13/4) = real_0 & real_$product(real_-13/4,
% 8.19/1.88 real_0) = real_0 & real_$product(real_0, real_-13/4) = real_0 &
% 8.19/1.88 real_$product(real_0, real_0) = real_0 & real_$difference(real_-13/4,
% 8.19/1.88 real_-13/4) = real_0 & real_$difference(real_-13/4, real_0) = real_-13/4 &
% 8.19/1.88 real_$difference(real_0, real_0) = real_0 & real_$uminus(real_0) = real_0 &
% 8.19/1.88 real_$sum(real_-13/4, real_0) = real_-13/4 & real_$sum(real_0, real_-13/4) =
% 8.19/1.88 real_-13/4 & real_$sum(real_0, real_0) = real_0 &
% 8.19/1.88 real_$greatereq(real_very_small, real_very_large) = 1 &
% 8.19/1.88 real_$greatereq(real_-13/4, real_-13/4) = 0 & real_$greatereq(real_-13/4,
% 8.19/1.88 real_0) = 1 & real_$greatereq(real_0, real_-13/4) = 0 &
% 8.19/1.88 real_$greatereq(real_0, real_0) = 0 & real_$greater(real_very_large,
% 8.19/1.88 real_-13/4) = 0 & real_$greater(real_very_large, real_0) = 0 &
% 8.19/1.88 real_$greater(real_very_small, real_very_large) = 1 &
% 8.19/1.88 real_$greater(real_-13/4, real_very_small) = 0 & real_$greater(real_-13/4,
% 8.19/1.88 real_-13/4) = 1 & real_$greater(real_-13/4, real_0) = 1 &
% 8.19/1.88 real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0, real_-13/4)
% 8.19/1.88 = 0 & real_$greater(real_0, real_0) = 1 & real_$less(real_very_small,
% 8.19/1.88 real_very_large) = 0 & real_$less(real_very_small, real_-13/4) = 0 &
% 8.19/1.88 real_$less(real_very_small, real_0) = 0 & real_$less(real_-13/4,
% 8.19/1.88 real_very_large) = 0 & real_$less(real_-13/4, real_-13/4) = 1 &
% 8.19/1.88 real_$less(real_-13/4, real_0) = 0 & real_$less(real_0, real_very_large) = 0 &
% 8.19/1.88 real_$less(real_0, real_-13/4) = 1 & real_$less(real_0, real_0) = 1 &
% 8.19/1.88 real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_-13/4,
% 8.19/1.88 real_-13/4) = 0 & real_$lesseq(real_-13/4, real_0) = 0 &
% 8.19/1.89 real_$lesseq(real_0, real_-13/4) = 1 & real_$lesseq(real_0, real_0) = 0 & !
% 8.19/1.89 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4:
% 8.19/1.89 $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ?
% 8.19/1.89 [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0:
% 8.19/1.89 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] :
% 8.19/1.89 ( ~ (real_$sum(v2, v3) = v4) | ~ (real_$sum(v1, v0) = v3) | ? [v5: $real] :
% 8.19/1.89 (real_$sum(v5, v0) = v4 & real_$sum(v2, v1) = v5)) & ! [v0: $real] : !
% 8.19/1.89 [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v1)
% 8.19/1.89 = 0) | ~ (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) &
% 8.19/1.89 real_$lesseq(v1, v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 8.19/1.89 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~
% 8.19/1.89 (real_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2,
% 8.19/1.89 v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3:
% 8.19/1.89 int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~ (real_$lesseq(v2, v1) =
% 8.19/1.89 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0) = v4)) & ! [v0:
% 8.19/1.89 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~
% 8.19/1.89 (real_$less(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] : (
% 8.19/1.89 ~ (v4 = 0) & real_$less(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] :
% 8.19/1.89 ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~
% 8.19/1.89 (real_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1,
% 8.19/1.89 v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3:
% 8.19/1.89 int] : (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) =
% 8.19/1.89 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0:
% 8.19/1.89 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ( ~
% 8.19/1.89 (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) | real_$difference(v1,
% 8.19/1.89 v0) = v3) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | v1
% 8.19/1.89 = v0 | ~ (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 8.19/1.89 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 8.19/1.89 int] : (v2 = 0 | ~ (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3
% 8.19/1.89 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] :
% 8.19/1.89 ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~
% 8.19/1.89 (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] :
% 8.19/1.89 ! [v2: int] : (v2 = 0 | ~ (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3
% 8.19/1.89 = 0) & real_$greater(v0, v1) = v3)) & ! [v0: $real] : ! [v1: $real] :
% 8.19/1.89 ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~
% 8.19/1.89 (v3 = 0) & real_$greatereq(v0, v1) = v3)) & ! [v0: $real] : ! [v1:
% 8.19/1.89 $real] : ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? [v3:
% 8.19/1.89 int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1:
% 8.19/1.89 $real] : ! [v2: $real] : (v0 = real_0 | ~ (real_$product(v1, v0) = v2) |
% 8.19/1.89 real_$quotient(v2, v0) = v1) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 8.19/1.89 $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) & !
% 8.19/1.89 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) =
% 8.19/1.89 v2) | real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : !
% 8.19/1.89 [v2: $real] : ( ~ (real_$difference(v1, v0) = v2) | ? [v3: $real] :
% 8.19/1.89 (real_$uminus(v0) = v3 & real_$sum(v1, v3) = v2)) & ! [v0: $real] : ! [v1:
% 8.19/1.89 $real] : ! [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0, v1) =
% 8.19/1.89 v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0,
% 8.19/1.89 v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] :
% 8.19/1.89 ! [v2: $real] : ( ~ (real_$less(v2, v1) = 0) | ~ (real_$lesseq(v1, v0) = 0) |
% 8.19/1.89 real_$less(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 8.19/1.89 ( ~ (real_$less(v1, v0) = 0) | ~ (real_$lesseq(v2, v1) = 0) | real_$less(v2,
% 8.19/1.89 v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~
% 8.19/1.89 (real_$lesseq(v2, v1) = 0) | ~ (real_$lesseq(v1, v0) = 0) |
% 8.19/1.89 real_$lesseq(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~
% 8.19/1.89 (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 |
% 8.19/1.89 ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = 0) & ! [v0: $real] :
% 8.19/1.89 ! [v1: int] : (v1 = 0 | ~ (real_$lesseq(v0, v0) = v1)) & ! [v0: $real] : !
% 8.19/1.89 [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0:
% 8.19/1.89 $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$sum(v0, v1) =
% 8.19/1.89 real_0) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$greatereq(v0, v1) =
% 8.19/1.89 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 8.19/1.89 (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & ! [v0: $real] : !
% 8.19/1.89 [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | real_$greater(v0, v1) = 0) & !
% 8.19/1.89 [v0: $real] : ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | real_$lesseq(v1,
% 8.19/1.89 v0) = 0) & ! [v0: $real] : ! [v1: MultipleValueBool] : ( ~
% 8.19/1.89 (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0) = 0) & ! [v0: $real] : !
% 8.19/1.89 [v1: $real] : ( ~ (real_$lesseq(v1, v0) = 0) | real_$greatereq(v0, v1) = 0) &
% 8.19/1.89 ! [v0: $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0))
% 8.19/1.89
% 8.19/1.89 Those formulas are unsatisfiable:
% 8.19/1.89 ---------------------------------
% 8.19/1.89
% 8.19/1.89 Begin of proof
% 8.19/1.89 |
% 8.19/1.89 | ALPHA: (input) implies:
% 8.19/1.89 | (1) ! [v0: $real] : ! [v1: int] : (v1 = 0 | ~ (real_$lesseq(v0, v0) =
% 8.19/1.89 | v1))
% 8.19/1.89 |
% 8.19/1.90 | DELTA: instantiating (real_lesseq_problem_7) with fresh symbol all_5_0 gives:
% 8.19/1.90 | (2) ~ (all_5_0 = 0) & real_$lesseq(real_-13/4, real_-13/4) = all_5_0
% 8.19/1.90 |
% 8.19/1.90 | ALPHA: (2) implies:
% 8.19/1.90 | (3) ~ (all_5_0 = 0)
% 8.19/1.90 | (4) real_$lesseq(real_-13/4, real_-13/4) = all_5_0
% 8.19/1.90 |
% 8.19/1.90 | GROUND_INST: instantiating (1) with real_-13/4, all_5_0, simplifying with (4)
% 8.19/1.90 | gives:
% 8.19/1.90 | (5) all_5_0 = 0
% 8.19/1.90 |
% 8.19/1.90 | REDUCE: (3), (5) imply:
% 8.19/1.90 | (6) $false
% 8.19/1.90 |
% 8.19/1.90 | CLOSE: (6) is inconsistent.
% 8.19/1.90 |
% 8.19/1.90 End of proof
% 8.19/1.90 % SZS output end Proof for theBenchmark
% 8.19/1.90
% 8.19/1.90 1281ms
%------------------------------------------------------------------------------