TSTP Solution File: ARI255_1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI255_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 : 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 17:47:27 EDT 2023
% Result : Theorem 10.53s 2.32s
% Output : Proof 13.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI255_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 18:35:38 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.56/0.96 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.56/0.96 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.56/0.96 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.56/0.96 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.56/0.96 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.56/0.96 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.56/0.96 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.08/1.07 Prover 1: Preprocessing ...
% 2.08/1.07 Prover 4: Preprocessing ...
% 2.54/1.12 Prover 6: Preprocessing ...
% 2.54/1.12 Prover 0: Preprocessing ...
% 3.19/1.21 Prover 5: Preprocessing ...
% 3.41/1.22 Prover 3: Preprocessing ...
% 3.41/1.22 Prover 2: Preprocessing ...
% 6.17/1.62 Prover 1: Constructing countermodel ...
% 6.40/1.63 Prover 4: Constructing countermodel ...
% 6.40/1.64 Prover 6: Proving ...
% 6.40/1.65 Prover 0: Proving ...
% 9.11/2.02 Prover 1: gave up
% 9.11/2.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.11/2.02 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 9.28/2.08 Prover 7: Preprocessing ...
% 9.98/2.14 Prover 2: Proving ...
% 9.98/2.15 Prover 3: Constructing countermodel ...
% 10.53/2.32 Prover 0: proved (1680ms)
% 10.53/2.32
% 10.53/2.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.53/2.32
% 10.53/2.34 Prover 2: stopped
% 10.53/2.34 Prover 6: stopped
% 10.53/2.35 Prover 3: stopped
% 10.53/2.37 Prover 5: Proving ...
% 10.53/2.37 Prover 5: stopped
% 10.53/2.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.53/2.37 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 10.53/2.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.53/2.37 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation
% 10.53/2.37 Prover 8: Preprocessing ...
% 10.53/2.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.53/2.37 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation
% 10.53/2.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.53/2.37 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation
% 10.53/2.37 Prover 13: Preprocessing ...
% 10.53/2.38 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 10.53/2.38 Prover 16: Warning: Problem contains rationals, using incomplete axiomatisation
% 11.91/2.40 Prover 11: Preprocessing ...
% 11.91/2.42 Prover 10: Preprocessing ...
% 12.18/2.44 Prover 16: Preprocessing ...
% 12.18/2.44 Prover 4: Found proof (size 10)
% 12.18/2.44 Prover 4: proved (1800ms)
% 12.18/2.45 Prover 13: stopped
% 12.18/2.47 Prover 8: Warning: ignoring some quantifiers
% 12.18/2.47 Prover 8: Constructing countermodel ...
% 12.18/2.49 Prover 8: stopped
% 12.73/2.50 Prover 7: Warning: ignoring some quantifiers
% 12.73/2.51 Prover 7: Constructing countermodel ...
% 12.73/2.53 Prover 7: stopped
% 13.23/2.60 Prover 10: stopped
% 13.23/2.64 Prover 11: stopped
% 13.23/2.65 Prover 16: stopped
% 13.23/2.66
% 13.23/2.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.23/2.66
% 13.23/2.66 % SZS output start Proof for theBenchmark
% 13.23/2.66 Assumptions after simplification:
% 13.23/2.66 ---------------------------------
% 13.23/2.66
% 13.23/2.66 (rat_sum_problem_10)
% 13.76/2.68 ! [v0: $rat] : ~ (rat_$sum(rat_5/16, v0) = rat_1/2)
% 13.76/2.68
% 13.76/2.68 (input)
% 13.89/2.71 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_1/2) & ~
% 13.89/2.71 (rat_very_large = rat_5/16) & ~ (rat_very_large = rat_0) & ~ (rat_very_small
% 13.89/2.71 = rat_1/2) & ~ (rat_very_small = rat_5/16) & ~ (rat_very_small = rat_0) &
% 13.89/2.71 ~ (rat_1/2 = rat_5/16) & ~ (rat_1/2 = rat_0) & ~ (rat_5/16 = rat_0) &
% 13.89/2.71 rat_$is_int(rat_1/2) = 1 & rat_$is_int(rat_5/16) = 1 & rat_$is_int(rat_0) = 0
% 13.89/2.71 & rat_$is_rat(rat_1/2) = 0 & rat_$is_rat(rat_5/16) = 0 & rat_$is_rat(rat_0) =
% 13.89/2.71 0 & rat_$floor(rat_1/2) = rat_0 & rat_$floor(rat_5/16) = rat_0 &
% 13.89/2.71 rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = rat_0 &
% 13.89/2.71 rat_$truncate(rat_1/2) = rat_0 & rat_$truncate(rat_5/16) = rat_0 &
% 13.89/2.71 rat_$truncate(rat_0) = rat_0 & rat_$round(rat_5/16) = rat_0 &
% 13.89/2.71 rat_$round(rat_0) = rat_0 & rat_$to_int(rat_1/2) = 0 & rat_$to_int(rat_5/16) =
% 13.89/2.71 0 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_1/2) = rat_1/2 &
% 13.89/2.71 rat_$to_rat(rat_5/16) = rat_5/16 & rat_$to_rat(rat_0) = rat_0 &
% 13.89/2.71 rat_$to_real(rat_1/2) = real_1/2 & rat_$to_real(rat_5/16) = real_5/16 &
% 13.89/2.71 rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_0,
% 13.89/2.71 rat_1/2) = rat_0 & rat_$quotient(rat_0, rat_5/16) = rat_0 &
% 13.89/2.71 rat_$product(rat_1/2, rat_0) = rat_0 & rat_$product(rat_5/16, rat_0) = rat_0 &
% 13.89/2.71 rat_$product(rat_0, rat_1/2) = rat_0 & rat_$product(rat_0, rat_5/16) = rat_0 &
% 13.89/2.71 rat_$product(rat_0, rat_0) = rat_0 & rat_$difference(rat_1/2, rat_1/2) = rat_0
% 13.89/2.71 & rat_$difference(rat_1/2, rat_0) = rat_1/2 & rat_$difference(rat_5/16,
% 13.89/2.71 rat_5/16) = rat_0 & rat_$difference(rat_5/16, rat_0) = rat_5/16 &
% 13.89/2.71 rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 &
% 13.89/2.71 rat_$greatereq(rat_very_small, rat_very_large) = 1 & rat_$greatereq(rat_1/2,
% 13.89/2.71 rat_1/2) = 0 & rat_$greatereq(rat_1/2, rat_5/16) = 0 &
% 13.89/2.71 rat_$greatereq(rat_1/2, rat_0) = 0 & rat_$greatereq(rat_5/16, rat_1/2) = 1 &
% 13.89/2.71 rat_$greatereq(rat_5/16, rat_5/16) = 0 & rat_$greatereq(rat_5/16, rat_0) = 0 &
% 13.89/2.71 rat_$greatereq(rat_0, rat_1/2) = 1 & rat_$greatereq(rat_0, rat_5/16) = 1 &
% 13.89/2.71 rat_$greatereq(rat_0, rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large)
% 13.89/2.71 = 0 & rat_$lesseq(rat_1/2, rat_1/2) = 0 & rat_$lesseq(rat_1/2, rat_5/16) = 1 &
% 13.89/2.71 rat_$lesseq(rat_1/2, rat_0) = 1 & rat_$lesseq(rat_5/16, rat_1/2) = 0 &
% 13.89/2.71 rat_$lesseq(rat_5/16, rat_5/16) = 0 & rat_$lesseq(rat_5/16, rat_0) = 1 &
% 13.89/2.71 rat_$lesseq(rat_0, rat_1/2) = 0 & rat_$lesseq(rat_0, rat_5/16) = 0 &
% 13.89/2.71 rat_$lesseq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, rat_1/2) = 0 &
% 13.89/2.71 rat_$greater(rat_very_large, rat_5/16) = 0 & rat_$greater(rat_very_large,
% 13.89/2.71 rat_0) = 0 & rat_$greater(rat_very_small, rat_very_large) = 1 &
% 13.89/2.71 rat_$greater(rat_1/2, rat_very_small) = 0 & rat_$greater(rat_1/2, rat_1/2) = 1
% 13.89/2.71 & rat_$greater(rat_1/2, rat_5/16) = 0 & rat_$greater(rat_1/2, rat_0) = 0 &
% 13.89/2.71 rat_$greater(rat_5/16, rat_very_small) = 0 & rat_$greater(rat_5/16, rat_1/2) =
% 13.89/2.71 1 & rat_$greater(rat_5/16, rat_5/16) = 1 & rat_$greater(rat_5/16, rat_0) = 0 &
% 13.89/2.71 rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_1/2) = 1 &
% 13.89/2.71 rat_$greater(rat_0, rat_5/16) = 1 & rat_$greater(rat_0, rat_0) = 1 &
% 13.89/2.71 rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small,
% 13.89/2.71 rat_1/2) = 0 & rat_$less(rat_very_small, rat_5/16) = 0 &
% 13.89/2.71 rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_1/2, rat_very_large) = 0
% 13.89/2.71 & rat_$less(rat_1/2, rat_1/2) = 1 & rat_$less(rat_1/2, rat_5/16) = 1 &
% 13.89/2.71 rat_$less(rat_1/2, rat_0) = 1 & rat_$less(rat_5/16, rat_very_large) = 0 &
% 13.89/2.71 rat_$less(rat_5/16, rat_1/2) = 0 & rat_$less(rat_5/16, rat_5/16) = 1 &
% 13.89/2.71 rat_$less(rat_5/16, rat_0) = 1 & rat_$less(rat_0, rat_very_large) = 0 &
% 13.89/2.71 rat_$less(rat_0, rat_1/2) = 0 & rat_$less(rat_0, rat_5/16) = 0 &
% 13.89/2.71 rat_$less(rat_0, rat_0) = 1 & rat_$sum(rat_1/2, rat_0) = rat_1/2 &
% 13.89/2.71 rat_$sum(rat_5/16, rat_0) = rat_5/16 & rat_$sum(rat_0, rat_1/2) = rat_1/2 &
% 13.89/2.71 rat_$sum(rat_0, rat_5/16) = rat_5/16 & rat_$sum(rat_0, rat_0) = rat_0 & !
% 13.89/2.71 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : (
% 13.89/2.71 ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] :
% 13.89/2.71 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1:
% 13.89/2.71 $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2,
% 13.89/2.71 v3) = v4) | ~ (rat_$sum(v1, v0) = v3) | ? [v5: $rat] : (rat_$sum(v5,
% 13.89/2.71 v0) = v4 & rat_$sum(v2, v1) = v5)) & ! [v0: $rat] : ! [v1: $rat] : !
% 13.89/2.71 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~
% 13.89/2.71 (rat_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1,
% 13.89/2.71 v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3:
% 13.89/2.71 int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3)
% 13.89/2.71 | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v1, v0) = v4)) & ! [v0: $rat] :
% 13.89/2.71 ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2,
% 13.89/2.71 v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) &
% 13.89/2.71 rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat]
% 13.89/2.71 : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2,
% 13.89/2.71 v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = v4)) & !
% 13.89/2.71 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~
% 13.89/2.71 (rat_$less(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~
% 13.89/2.71 (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : !
% 13.89/2.71 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~
% 13.89/2.71 (rat_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1)
% 13.89/2.71 = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (
% 13.89/2.71 ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1,
% 13.89/2.71 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | v1 =
% 13.89/2.71 v0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 13.89/2.71 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int]
% 13.89/2.71 : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 13.89/2.71 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int]
% 13.89/2.71 : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 13.89/2.71 rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 13.89/2.71 int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0)
% 13.89/2.71 & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int]
% 13.89/2.71 : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 13.89/2.71 rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] :
% 13.89/2.71 (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 13.89/2.71 rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 13.89/2.71 $rat] : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, v0)
% 13.89/2.71 = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 13.89/2.71 (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] :
% 13.89/2.71 ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) |
% 13.89/2.71 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 13.89/2.71 ( ~ (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = v3 &
% 13.89/2.71 rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 13.89/2.71 ( ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2,
% 13.89/2.71 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 13.89/2.71 (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) =
% 13.89/2.71 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v1,
% 13.89/2.71 v0) = 0) | ~ (rat_$less(v2, v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0:
% 13.89/2.71 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) = v2) |
% 13.89/2.71 rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 13.89/2.71 (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1:
% 13.89/2.71 $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) &
% 13.89/2.71 ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & !
% 13.89/2.71 [v0: $rat] : ! [v1: int] : (v1 = 0 | ~ (rat_$lesseq(v0, v0) = v1)) & ! [v0:
% 13.89/2.71 $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) &
% 13.89/2.71 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$sum(v0, v1)
% 13.89/2.71 = rat_0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0)
% 13.89/2.71 | rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 13.89/2.71 (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) & ! [v0: $rat] : !
% 13.89/2.71 [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) & ! [v0:
% 13.89/2.71 $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$lesseq(v1, v0) =
% 13.89/2.71 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) |
% 13.89/2.71 rat_$greater(v0, v1) = 0) & ! [v0: $rat] : ! [v1: MultipleValueBool] : ( ~
% 13.89/2.71 (rat_$less(v0, v0) = v1) | rat_$lesseq(v0, v0) = 0) & ! [v0: $rat] : (v0 =
% 13.89/2.71 rat_0 | ~ (rat_$uminus(v0) = v0))
% 13.89/2.71
% 13.89/2.71 Those formulas are unsatisfiable:
% 13.89/2.71 ---------------------------------
% 13.89/2.71
% 13.89/2.71 Begin of proof
% 13.89/2.71 |
% 13.89/2.71 | ALPHA: (input) implies:
% 13.89/2.71 | (1) rat_$sum(rat_0, rat_1/2) = rat_1/2
% 13.89/2.71 | (2) rat_$difference(rat_5/16, rat_5/16) = rat_0
% 13.89/2.71 | (3) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 13.89/2.71 | (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) =
% 13.89/2.71 | v3 & rat_$sum(v1, v3) = v2))
% 13.89/2.71 | (4) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4:
% 13.89/2.71 | $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ?
% 13.89/2.71 | [v5: $rat] : (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5))
% 13.89/2.71 |
% 13.89/2.71 | GROUND_INST: instantiating (3) with rat_5/16, rat_5/16, rat_0, simplifying
% 13.89/2.71 | with (2) gives:
% 13.89/2.72 | (5) ? [v0: $rat] : (rat_$uminus(rat_5/16) = v0 & rat_$sum(rat_5/16, v0) =
% 13.89/2.72 | rat_0)
% 13.89/2.72 |
% 13.89/2.72 | DELTA: instantiating (5) with fresh symbol all_22_0 gives:
% 13.89/2.72 | (6) rat_$uminus(rat_5/16) = all_22_0 & rat_$sum(rat_5/16, all_22_0) = rat_0
% 13.89/2.72 |
% 13.89/2.72 | ALPHA: (6) implies:
% 13.89/2.72 | (7) rat_$sum(rat_5/16, all_22_0) = rat_0
% 13.89/2.72 |
% 13.89/2.72 | GROUND_INST: instantiating (4) with rat_1/2, all_22_0, rat_5/16, rat_0,
% 13.89/2.72 | rat_1/2, simplifying with (1), (7) gives:
% 13.89/2.72 | (8) ? [v0: $rat] : (rat_$sum(all_22_0, rat_1/2) = v0 & rat_$sum(rat_5/16,
% 13.89/2.72 | v0) = rat_1/2)
% 13.89/2.72 |
% 13.89/2.72 | DELTA: instantiating (8) with fresh symbol all_44_0 gives:
% 13.89/2.72 | (9) rat_$sum(all_22_0, rat_1/2) = all_44_0 & rat_$sum(rat_5/16, all_44_0) =
% 13.89/2.72 | rat_1/2
% 13.89/2.72 |
% 13.89/2.72 | ALPHA: (9) implies:
% 13.89/2.72 | (10) rat_$sum(rat_5/16, all_44_0) = rat_1/2
% 13.89/2.72 |
% 13.89/2.72 | GROUND_INST: instantiating (rat_sum_problem_10) with all_44_0, simplifying
% 13.89/2.72 | with (10) gives:
% 13.89/2.72 | (11) $false
% 13.89/2.72 |
% 13.89/2.72 | CLOSE: (11) is inconsistent.
% 13.89/2.72 |
% 13.89/2.72 End of proof
% 13.89/2.72 % SZS output end Proof for theBenchmark
% 13.89/2.72
% 13.89/2.72 2099ms
%------------------------------------------------------------------------------