TSTP Solution File: NUM902_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM902_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 : n012.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 : Thu Aug 31 11:50:38 EDT 2023
% Result : Theorem 8.75s 1.92s
% Output : Proof 10.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM902_1 : TPTP v8.1.2. Released v5.0.0.
% 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 13:57:11 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 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 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 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 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
% 1.70/0.89 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.70/0.89 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.70/0.89 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.70/0.89 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.70/0.89 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.70/0.89 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.70/0.89 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.86/0.97 Prover 1: Preprocessing ...
% 1.86/0.97 Prover 4: Preprocessing ...
% 2.38/1.02 Prover 5: Preprocessing ...
% 2.38/1.02 Prover 3: Preprocessing ...
% 2.38/1.02 Prover 2: Preprocessing ...
% 2.38/1.02 Prover 6: Preprocessing ...
% 2.38/1.02 Prover 0: Preprocessing ...
% 3.99/1.41 Prover 5: Proving ...
% 3.99/1.42 Prover 3: Constructing countermodel ...
% 3.99/1.42 Prover 6: Constructing countermodel ...
% 4.95/1.42 Prover 1: Constructing countermodel ...
% 4.95/1.44 Prover 2: Proving ...
% 4.95/1.47 Prover 4: Constructing countermodel ...
% 5.85/1.54 Prover 0: Proving ...
% 5.85/1.58 Prover 6: gave up
% 5.85/1.58 Prover 3: gave up
% 5.85/1.59 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.85/1.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.85/1.59 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 5.85/1.59 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 5.85/1.59 Prover 1: gave up
% 5.85/1.59 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 5.85/1.59 Prover 9: Warning: Problem contains rationals, using incomplete axiomatisation
% 5.85/1.59 Prover 7: Preprocessing ...
% 5.85/1.60 Prover 8: Preprocessing ...
% 6.53/1.60 Prover 9: Preprocessing ...
% 6.53/1.69 Prover 7: Warning: ignoring some quantifiers
% 7.26/1.69 Prover 7: Constructing countermodel ...
% 7.32/1.70 Prover 8: Warning: ignoring some quantifiers
% 7.35/1.71 Prover 8: Constructing countermodel ...
% 7.35/1.77 Prover 9: Constructing countermodel ...
% 8.07/1.88 Prover 8: gave up
% 8.07/1.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.07/1.89 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation
% 8.75/1.90 Prover 0: proved (1265ms)
% 8.75/1.90
% 8.75/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.75/1.92
% 8.75/1.92 Prover 10: Preprocessing ...
% 8.75/1.92 Prover 9: stopped
% 8.75/1.93 Prover 2: stopped
% 8.75/1.93 Prover 5: stopped
% 8.75/1.95 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.75/1.95 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation
% 8.75/1.95 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.75/1.95 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation
% 8.75/1.95 Prover 11: Preprocessing ...
% 8.75/1.95 Prover 13: Preprocessing ...
% 8.75/1.95 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.75/1.95 Prover 16: Warning: Problem contains rationals, using incomplete axiomatisation
% 8.75/1.95 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 8.75/1.95 Prover 19: Warning: Problem contains rationals, using incomplete axiomatisation
% 8.75/1.95 Prover 10: Warning: ignoring some quantifiers
% 8.75/1.96 Prover 19: Preprocessing ...
% 8.75/1.96 Prover 16: Preprocessing ...
% 8.75/1.96 Prover 10: Constructing countermodel ...
% 8.75/1.99 Prover 4: Found proof (size 52)
% 8.75/1.99 Prover 4: proved (1350ms)
% 8.75/1.99 Prover 10: stopped
% 8.75/1.99 Prover 13: stopped
% 9.47/1.99 Prover 7: stopped
% 9.48/1.99 Prover 16: stopped
% 9.48/2.04 Prover 19: Warning: ignoring some quantifiers
% 9.48/2.04 Prover 19: Constructing countermodel ...
% 9.48/2.04 Prover 11: Constructing countermodel ...
% 9.48/2.05 Prover 19: stopped
% 9.48/2.05 Prover 11: stopped
% 9.48/2.05
% 9.48/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.48/2.05
% 9.48/2.06 % SZS output start Proof for theBenchmark
% 9.48/2.07 Assumptions after simplification:
% 9.48/2.07 ---------------------------------
% 9.48/2.07
% 9.48/2.07 (rat_difference_problem_13)
% 9.48/2.09 ? [v0: $rat] : ? [v1: $rat] : ( ~ (v1 = v0) & rat_$difference(v0, v1) =
% 9.48/2.09 rat_0)
% 9.48/2.09
% 9.48/2.09 (input)
% 9.86/2.12 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_0) & ~
% 9.86/2.12 (rat_very_small = rat_0) & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_0) = 0 &
% 9.86/2.12 rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_0)
% 9.86/2.12 = rat_0 & rat_$round(rat_0) = rat_0 & rat_$to_int(rat_0) = 0 &
% 9.86/2.12 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_0) = real_0 & int_$to_rat(0) =
% 9.86/2.12 rat_0 & rat_$product(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 &
% 9.86/2.12 rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small,
% 9.86/2.12 rat_very_large) = 1 & rat_$greatereq(rat_0, rat_0) = 0 &
% 9.86/2.12 rat_$lesseq(rat_very_small, rat_very_large) = 0 & rat_$lesseq(rat_0, rat_0) =
% 9.86/2.12 0 & rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small,
% 9.86/2.12 rat_very_large) = 1 & rat_$greater(rat_0, rat_very_small) = 0 &
% 9.86/2.12 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0
% 9.86/2.12 & rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_0, rat_very_large) = 0
% 9.86/2.12 & rat_$less(rat_0, rat_0) = 1 & rat_$difference(rat_0, rat_0) = rat_0 & !
% 9.86/2.12 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : (
% 9.86/2.12 ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] :
% 9.86/2.12 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1:
% 9.86/2.12 $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2,
% 9.86/2.12 v3) = v4) | ~ (rat_$sum(v1, v0) = v3) | ? [v5: $rat] : (rat_$sum(v5,
% 9.86/2.12 v0) = v4 & rat_$sum(v2, v1) = v5)) & ! [v0: $rat] : ! [v1: $rat] : !
% 9.86/2.12 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~
% 9.86/2.12 (rat_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1,
% 9.86/2.12 v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3:
% 9.86/2.12 int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3)
% 9.86/2.12 | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v1, v0) = v4)) & ! [v0: $rat] :
% 9.86/2.12 ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2,
% 9.86/2.12 v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) &
% 9.86/2.12 rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat]
% 9.86/2.12 : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2,
% 9.86/2.12 v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = v4)) & !
% 9.86/2.12 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~
% 9.86/2.12 (rat_$less(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~
% 9.86/2.12 (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : !
% 9.86/2.12 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~
% 9.86/2.12 (rat_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1)
% 9.86/2.12 = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (
% 9.86/2.12 ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1,
% 9.86/2.12 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | v1 =
% 9.86/2.12 v0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 9.86/2.12 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int]
% 9.86/2.12 : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 9.86/2.12 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int]
% 9.86/2.12 : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 9.86/2.12 rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 9.86/2.12 int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0)
% 9.86/2.12 & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int]
% 9.86/2.12 : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 9.86/2.12 rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] :
% 9.86/2.12 (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 9.86/2.12 rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 9.86/2.12 $rat] : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, v0)
% 9.86/2.12 = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 9.86/2.12 (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] :
% 9.86/2.12 ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) |
% 9.86/2.12 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 9.86/2.12 ( ~ (rat_$sum(v1, v0) = v2) | rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1:
% 9.86/2.12 $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2)
% 9.86/2.12 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) =
% 9.86/2.12 0) | ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2, v0) = 0) & ! [v0:
% 9.86/2.12 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) | ~
% 9.86/2.12 (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1:
% 10.18/2.12 $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2,
% 10.18/2.12 v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : !
% 10.18/2.12 [v2: $rat] : ( ~ (rat_$difference(v1, v0) = v2) | ? [v3: $rat] :
% 10.18/2.12 (rat_$uminus(v0) = v3 & rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1:
% 10.18/2.12 $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1:
% 10.18/2.12 $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) &
% 10.18/2.12 ! [v0: $rat] : ! [v1: int] : (v1 = 0 | ~ (rat_$lesseq(v0, v0) = v1)) & !
% 10.18/2.12 [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) =
% 10.18/2.12 v0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) |
% 10.18/2.12 rat_$sum(v0, v1) = rat_0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 10.18/2.12 (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : !
% 10.18/2.12 [v1: $rat] : ( ~ (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) & !
% 10.18/2.12 [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1,
% 10.18/2.12 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) |
% 10.18/2.12 rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 10.18/2.12 (rat_$less(v1, v0) = 0) | rat_$greater(v0, v1) = 0) & ! [v0: $rat] : !
% 10.18/2.12 [v1: MultipleValueBool] : ( ~ (rat_$less(v0, v0) = v1) | rat_$lesseq(v0, v0) =
% 10.18/2.12 0) & ! [v0: $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0) = v0))
% 10.18/2.12
% 10.18/2.12 (function-axioms)
% 10.18/2.13 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 10.18/2.13 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0:
% 10.18/2.13 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 10.18/2.13 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0:
% 10.18/2.13 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 10.18/2.13 (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0:
% 10.18/2.13 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 10.18/2.13 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3,
% 10.18/2.13 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 10.18/2.13 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~
% 10.18/2.13 (rat_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.18/2.13 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 10.18/2.13 (rat_$greater(v3, v2) = v1) | ~ (rat_$greater(v3, v2) = v0)) & ! [v0:
% 10.18/2.13 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 10.18/2.13 $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) =
% 10.18/2.13 v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1
% 10.18/2.13 = v0 | ~ (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) =
% 10.18/2.13 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.18/2.13 $rat] : (v1 = v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) &
% 10.18/2.13 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 =
% 10.18/2.13 v0 | ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat]
% 10.18/2.13 : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~
% 10.18/2.13 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1
% 10.18/2.13 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0:
% 10.18/2.13 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) =
% 10.18/2.13 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : !
% 10.18/2.13 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) &
% 10.18/2.13 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) =
% 10.18/2.13 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 10.18/2.13 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) &
% 10.18/2.13 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~
% 10.18/2.13 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : !
% 10.18/2.13 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~
% 10.18/2.13 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 10.18/2.13 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0))
% 10.18/2.13
% 10.18/2.13 Those formulas are unsatisfiable:
% 10.18/2.13 ---------------------------------
% 10.18/2.13
% 10.18/2.13 Begin of proof
% 10.18/2.13 |
% 10.18/2.13 | ALPHA: (function-axioms) implies:
% 10.18/2.13 | (1) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 =
% 10.18/2.13 | v0 | ~ (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0))
% 10.18/2.13 |
% 10.18/2.14 | ALPHA: (input) implies:
% 10.18/2.14 | (2) rat_$sum(rat_0, rat_0) = rat_0
% 10.18/2.14 | (3) ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) |
% 10.18/2.14 | rat_$sum(v0, v1) = rat_0)
% 10.18/2.14 | (4) ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) =
% 10.18/2.14 | v1))
% 10.18/2.14 | (5) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 10.18/2.14 | (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) =
% 10.18/2.14 | v3 & rat_$sum(v1, v3) = v2))
% 10.18/2.14 | (6) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) =
% 10.18/2.14 | v2) | rat_$sum(v0, v1) = v2)
% 10.18/2.14 | (7) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4:
% 10.18/2.14 | $rat] : ( ~ (rat_$sum(v2, v3) = v4) | ~ (rat_$sum(v1, v0) = v3) | ?
% 10.18/2.14 | [v5: $rat] : (rat_$sum(v5, v0) = v4 & rat_$sum(v2, v1) = v5))
% 10.18/2.14 | (8) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4:
% 10.18/2.14 | $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ?
% 10.18/2.14 | [v5: $rat] : (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5))
% 10.18/2.14 |
% 10.18/2.14 | DELTA: instantiating (rat_difference_problem_13) with fresh symbols all_5_0,
% 10.18/2.14 | all_5_1 gives:
% 10.18/2.14 | (9) ~ (all_5_0 = all_5_1) & rat_$difference(all_5_1, all_5_0) = rat_0
% 10.18/2.14 |
% 10.18/2.14 | ALPHA: (9) implies:
% 10.18/2.14 | (10) ~ (all_5_0 = all_5_1)
% 10.18/2.14 | (11) rat_$difference(all_5_1, all_5_0) = rat_0
% 10.18/2.14 |
% 10.18/2.14 | GROUND_INST: instantiating (5) with all_5_0, all_5_1, rat_0, simplifying with
% 10.18/2.14 | (11) gives:
% 10.18/2.14 | (12) ? [v0: $rat] : (rat_$uminus(all_5_0) = v0 & rat_$sum(all_5_1, v0) =
% 10.18/2.14 | rat_0)
% 10.18/2.14 |
% 10.18/2.14 | DELTA: instantiating (12) with fresh symbol all_17_0 gives:
% 10.18/2.14 | (13) rat_$uminus(all_5_0) = all_17_0 & rat_$sum(all_5_1, all_17_0) = rat_0
% 10.18/2.14 |
% 10.18/2.14 | ALPHA: (13) implies:
% 10.18/2.14 | (14) rat_$sum(all_5_1, all_17_0) = rat_0
% 10.18/2.14 | (15) rat_$uminus(all_5_0) = all_17_0
% 10.18/2.14 |
% 10.18/2.15 | GROUND_INST: instantiating (8) with rat_0, all_17_0, all_5_1, rat_0, rat_0,
% 10.18/2.15 | simplifying with (2), (14) gives:
% 10.18/2.15 | (16) ? [v0: $rat] : (rat_$sum(all_17_0, rat_0) = v0 & rat_$sum(all_5_1,
% 10.18/2.15 | v0) = rat_0)
% 10.18/2.15 |
% 10.18/2.15 | GROUND_INST: instantiating (7) with all_17_0, all_5_1, rat_0, rat_0, rat_0,
% 10.18/2.15 | simplifying with (2), (14) gives:
% 10.18/2.15 | (17) ? [v0: $rat] : (rat_$sum(v0, all_17_0) = rat_0 & rat_$sum(rat_0,
% 10.18/2.15 | all_5_1) = v0)
% 10.18/2.15 |
% 10.18/2.15 | GROUND_INST: instantiating (6) with all_17_0, all_5_1, rat_0, simplifying with
% 10.18/2.15 | (14) gives:
% 10.18/2.15 | (18) rat_$sum(all_17_0, all_5_1) = rat_0
% 10.18/2.15 |
% 10.18/2.15 | GROUND_INST: instantiating (3) with all_5_0, all_17_0, simplifying with (15)
% 10.18/2.15 | gives:
% 10.18/2.15 | (19) rat_$sum(all_5_0, all_17_0) = rat_0
% 10.18/2.15 |
% 10.18/2.15 | DELTA: instantiating (17) with fresh symbol all_29_0 gives:
% 10.18/2.15 | (20) rat_$sum(all_29_0, all_17_0) = rat_0 & rat_$sum(rat_0, all_5_1) =
% 10.18/2.15 | all_29_0
% 10.18/2.15 |
% 10.18/2.15 | ALPHA: (20) implies:
% 10.18/2.15 | (21) rat_$sum(rat_0, all_5_1) = all_29_0
% 10.18/2.15 | (22) rat_$sum(all_29_0, all_17_0) = rat_0
% 10.18/2.15 |
% 10.18/2.15 | DELTA: instantiating (16) with fresh symbol all_31_0 gives:
% 10.18/2.15 | (23) rat_$sum(all_17_0, rat_0) = all_31_0 & rat_$sum(all_5_1, all_31_0) =
% 10.18/2.15 | rat_0
% 10.18/2.15 |
% 10.18/2.15 | ALPHA: (23) implies:
% 10.18/2.15 | (24) rat_$sum(all_5_1, all_31_0) = rat_0
% 10.18/2.15 | (25) rat_$sum(all_17_0, rat_0) = all_31_0
% 10.18/2.15 |
% 10.18/2.15 | GROUND_INST: instantiating (4) with all_17_0, all_31_0, simplifying with (25)
% 10.18/2.15 | gives:
% 10.18/2.15 | (26) all_31_0 = all_17_0
% 10.18/2.15 |
% 10.18/2.15 | REDUCE: (25), (26) imply:
% 10.18/2.15 | (27) rat_$sum(all_17_0, rat_0) = all_17_0
% 10.18/2.15 |
% 10.18/2.15 | GROUND_INST: instantiating (8) with all_5_1, all_17_0, all_5_1, rat_0,
% 10.18/2.15 | all_29_0, simplifying with (14), (21) gives:
% 10.18/2.15 | (28) ? [v0: $rat] : (rat_$sum(all_17_0, all_5_1) = v0 & rat_$sum(all_5_1,
% 10.18/2.15 | v0) = all_29_0)
% 10.18/2.15 |
% 10.18/2.15 | GROUND_INST: instantiating (6) with all_5_1, rat_0, all_29_0, simplifying with
% 10.18/2.15 | (21) gives:
% 10.18/2.15 | (29) rat_$sum(all_5_1, rat_0) = all_29_0
% 10.18/2.15 |
% 10.18/2.15 | GROUND_INST: instantiating (8) with all_5_1, all_17_0, all_5_0, rat_0,
% 10.18/2.15 | all_29_0, simplifying with (19), (21) gives:
% 10.18/2.15 | (30) ? [v0: $rat] : (rat_$sum(all_17_0, all_5_1) = v0 & rat_$sum(all_5_0,
% 10.18/2.15 | v0) = all_29_0)
% 10.18/2.15 |
% 10.18/2.15 | GROUND_INST: instantiating (7) with all_17_0, all_5_1, all_17_0, rat_0,
% 10.18/2.15 | all_17_0, simplifying with (14), (27) gives:
% 10.18/2.15 | (31) ? [v0: $rat] : (rat_$sum(v0, all_17_0) = all_17_0 &
% 10.18/2.15 | rat_$sum(all_17_0, all_5_1) = v0)
% 10.18/2.15 |
% 10.18/2.15 | GROUND_INST: instantiating (8) with rat_0, all_5_1, all_17_0, rat_0, rat_0,
% 10.18/2.15 | simplifying with (2), (18) gives:
% 10.18/2.15 | (32) ? [v0: $rat] : (rat_$sum(all_17_0, v0) = rat_0 & rat_$sum(all_5_1,
% 10.18/2.15 | rat_0) = v0)
% 10.18/2.15 |
% 10.18/2.16 | GROUND_INST: instantiating (8) with all_5_1, all_17_0, all_29_0, rat_0,
% 10.18/2.16 | all_29_0, simplifying with (21), (22) gives:
% 10.18/2.16 | (33) ? [v0: $rat] : (rat_$sum(all_29_0, v0) = all_29_0 &
% 10.18/2.16 | rat_$sum(all_17_0, all_5_1) = v0)
% 10.18/2.16 |
% 10.18/2.16 | DELTA: instantiating (32) with fresh symbol all_60_0 gives:
% 10.18/2.16 | (34) rat_$sum(all_17_0, all_60_0) = rat_0 & rat_$sum(all_5_1, rat_0) =
% 10.18/2.16 | all_60_0
% 10.18/2.16 |
% 10.18/2.16 | ALPHA: (34) implies:
% 10.18/2.16 | (35) rat_$sum(all_5_1, rat_0) = all_60_0
% 10.18/2.16 |
% 10.18/2.16 | DELTA: instantiating (30) with fresh symbol all_62_0 gives:
% 10.18/2.16 | (36) rat_$sum(all_17_0, all_5_1) = all_62_0 & rat_$sum(all_5_0, all_62_0) =
% 10.18/2.16 | all_29_0
% 10.18/2.16 |
% 10.18/2.16 | ALPHA: (36) implies:
% 10.18/2.16 | (37) rat_$sum(all_5_0, all_62_0) = all_29_0
% 10.18/2.16 | (38) rat_$sum(all_17_0, all_5_1) = all_62_0
% 10.18/2.16 |
% 10.18/2.16 | DELTA: instantiating (31) with fresh symbol all_70_0 gives:
% 10.18/2.16 | (39) rat_$sum(all_70_0, all_17_0) = all_17_0 & rat_$sum(all_17_0, all_5_1)
% 10.18/2.16 | = all_70_0
% 10.18/2.16 |
% 10.18/2.16 | ALPHA: (39) implies:
% 10.18/2.16 | (40) rat_$sum(all_17_0, all_5_1) = all_70_0
% 10.18/2.16 |
% 10.18/2.16 | DELTA: instantiating (33) with fresh symbol all_72_0 gives:
% 10.18/2.16 | (41) rat_$sum(all_29_0, all_72_0) = all_29_0 & rat_$sum(all_17_0, all_5_1)
% 10.18/2.16 | = all_72_0
% 10.18/2.16 |
% 10.18/2.16 | ALPHA: (41) implies:
% 10.18/2.16 | (42) rat_$sum(all_17_0, all_5_1) = all_72_0
% 10.18/2.16 |
% 10.18/2.16 | DELTA: instantiating (28) with fresh symbol all_74_0 gives:
% 10.18/2.16 | (43) rat_$sum(all_17_0, all_5_1) = all_74_0 & rat_$sum(all_5_1, all_74_0) =
% 10.18/2.16 | all_29_0
% 10.18/2.16 |
% 10.18/2.16 | ALPHA: (43) implies:
% 10.18/2.16 | (44) rat_$sum(all_17_0, all_5_1) = all_74_0
% 10.18/2.16 |
% 10.18/2.16 | GROUND_INST: instantiating (1) with all_29_0, all_60_0, rat_0, all_5_1,
% 10.18/2.16 | simplifying with (29), (35) gives:
% 10.18/2.16 | (45) all_60_0 = all_29_0
% 10.18/2.16 |
% 10.18/2.16 | GROUND_INST: instantiating (4) with all_5_1, all_60_0, simplifying with (35)
% 10.18/2.16 | gives:
% 10.18/2.16 | (46) all_60_0 = all_5_1
% 10.18/2.16 |
% 10.18/2.16 | GROUND_INST: instantiating (1) with all_62_0, all_70_0, all_5_1, all_17_0,
% 10.18/2.16 | simplifying with (38), (40) gives:
% 10.18/2.16 | (47) all_70_0 = all_62_0
% 10.18/2.16 |
% 10.18/2.16 | GROUND_INST: instantiating (1) with all_70_0, all_72_0, all_5_1, all_17_0,
% 10.18/2.16 | simplifying with (40), (42) gives:
% 10.18/2.16 | (48) all_72_0 = all_70_0
% 10.18/2.16 |
% 10.18/2.16 | GROUND_INST: instantiating (1) with rat_0, all_74_0, all_5_1, all_17_0,
% 10.18/2.16 | simplifying with (18), (44) gives:
% 10.18/2.16 | (49) all_74_0 = rat_0
% 10.18/2.16 |
% 10.18/2.16 | GROUND_INST: instantiating (1) with all_72_0, all_74_0, all_5_1, all_17_0,
% 10.18/2.16 | simplifying with (42), (44) gives:
% 10.18/2.16 | (50) all_74_0 = all_72_0
% 10.18/2.16 |
% 10.18/2.16 | COMBINE_EQS: (49), (50) imply:
% 10.18/2.16 | (51) all_72_0 = rat_0
% 10.18/2.16 |
% 10.18/2.16 | SIMP: (51) implies:
% 10.18/2.16 | (52) all_72_0 = rat_0
% 10.18/2.16 |
% 10.18/2.16 | COMBINE_EQS: (48), (52) imply:
% 10.18/2.16 | (53) all_70_0 = rat_0
% 10.18/2.16 |
% 10.18/2.16 | SIMP: (53) implies:
% 10.18/2.16 | (54) all_70_0 = rat_0
% 10.18/2.16 |
% 10.18/2.16 | COMBINE_EQS: (47), (54) imply:
% 10.18/2.16 | (55) all_62_0 = rat_0
% 10.18/2.16 |
% 10.18/2.16 | COMBINE_EQS: (45), (46) imply:
% 10.18/2.16 | (56) all_29_0 = all_5_1
% 10.18/2.16 |
% 10.18/2.16 | SIMP: (56) implies:
% 10.18/2.16 | (57) all_29_0 = all_5_1
% 10.18/2.17 |
% 10.18/2.17 | REDUCE: (37), (55), (57) imply:
% 10.18/2.17 | (58) rat_$sum(all_5_0, rat_0) = all_5_1
% 10.18/2.17 |
% 10.18/2.17 | GROUND_INST: instantiating (4) with all_5_0, all_5_1, simplifying with (58)
% 10.18/2.17 | gives:
% 10.18/2.17 | (59) all_5_0 = all_5_1
% 10.18/2.17 |
% 10.18/2.17 | REDUCE: (10), (59) imply:
% 10.18/2.17 | (60) $false
% 10.18/2.17 |
% 10.18/2.17 | CLOSE: (60) is inconsistent.
% 10.18/2.17 |
% 10.18/2.17 End of proof
% 10.18/2.17 % SZS output end Proof for theBenchmark
% 10.18/2.17
% 10.18/2.17 1554ms
%------------------------------------------------------------------------------