TSTP Solution File: ARI513_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI513_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 : n021.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 17:48:14 EDT 2023
% Result : Theorem 6.79s 1.65s
% Output : Proof 11.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ARI513_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n021.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 : Tue Aug 29 18:19:44 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
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.54/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.54/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.54/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.54/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.54/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.54/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.54/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.61/0.91 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.61/0.91 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.61/0.91 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.61/0.91 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.61/0.91 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.61/0.91 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.61/0.91 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.61/0.92 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.61/0.92 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.61/0.92 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.61/0.92 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.61/0.92 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.61/0.92 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.61/0.92 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.98/0.98 Prover 1: Preprocessing ...
% 1.98/0.98 Prover 4: Preprocessing ...
% 2.48/1.04 Prover 0: Preprocessing ...
% 2.48/1.04 Prover 3: Preprocessing ...
% 2.48/1.04 Prover 2: Preprocessing ...
% 2.48/1.04 Prover 5: Preprocessing ...
% 2.48/1.04 Prover 6: Preprocessing ...
% 6.30/1.59 Prover 2: Constructing countermodel ...
% 6.79/1.60 Prover 6: Constructing countermodel ...
% 6.79/1.65 Prover 6: proved (1005ms)
% 6.79/1.65 Prover 2: proved (1007ms)
% 6.79/1.65
% 6.79/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.79/1.65
% 6.79/1.65
% 6.79/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.79/1.65
% 6.79/1.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.79/1.66 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 7.29/1.66 Prover 5: Constructing countermodel ...
% 7.29/1.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.29/1.66 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 7.29/1.66 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 7.31/1.67 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 7.31/1.67 Prover 5: stopped
% 7.31/1.68 Prover 1: Constructing countermodel ...
% 7.31/1.68 Prover 8: Preprocessing ...
% 7.31/1.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.31/1.68 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 7.31/1.69 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation
% 7.31/1.70 Prover 3: Constructing countermodel ...
% 7.31/1.70 Prover 3: stopped
% 7.57/1.70 Prover 7: Preprocessing ...
% 7.57/1.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.57/1.71 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation
% 7.57/1.71 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation
% 7.57/1.71 Prover 0: Constructing countermodel ...
% 7.57/1.71 Prover 0: stopped
% 7.57/1.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.57/1.72 Prover 10: Preprocessing ...
% 7.57/1.72 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation
% 7.57/1.72 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation
% 7.57/1.73 Prover 13: Preprocessing ...
% 7.57/1.73 Prover 11: Preprocessing ...
% 7.57/1.78 Prover 4: Constructing countermodel ...
% 9.53/2.00 Prover 8: Warning: ignoring some quantifiers
% 9.84/2.02 Prover 8: Constructing countermodel ...
% 9.84/2.03 Prover 13: Warning: ignoring some quantifiers
% 10.07/2.04 Prover 1: Found proof (size 7)
% 10.07/2.04 Prover 13: Constructing countermodel ...
% 10.07/2.04 Prover 1: proved (1409ms)
% 10.07/2.04 Prover 4: Found proof (size 6)
% 10.07/2.04 Prover 4: proved (1410ms)
% 10.07/2.05 Prover 8: stopped
% 10.07/2.06 Prover 13: stopped
% 10.07/2.10 Prover 7: Warning: ignoring some quantifiers
% 10.07/2.11 Prover 10: Warning: ignoring some quantifiers
% 10.07/2.11 Prover 7: Constructing countermodel ...
% 10.07/2.12 Prover 10: Constructing countermodel ...
% 10.67/2.13 Prover 7: stopped
% 10.67/2.14 Prover 10: stopped
% 10.67/2.17 Prover 11: Constructing countermodel ...
% 10.67/2.18 Prover 11: stopped
% 10.67/2.18
% 10.67/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.67/2.18
% 10.67/2.18 % SZS output start Proof for theBenchmark
% 10.67/2.18 Assumptions after simplification:
% 10.67/2.18 ---------------------------------
% 10.67/2.18
% 10.67/2.18 (mixed_types_problem_18)
% 10.99/2.20 ? [v0: int] : ( ~ (v0 = 0) & real_$lesseq(real_1/2, real_1/2) = v0)
% 10.99/2.20
% 10.99/2.20 (input)
% 10.99/2.23 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_1/2) & ~
% 10.99/2.23 (real_very_large = real_0) & ~ (real_very_small = real_1/2) & ~
% 10.99/2.23 (real_very_small = real_0) & ~ (rat_very_large = rat_very_small) & ~
% 10.99/2.23 (rat_very_large = rat_1/2) & ~ (rat_very_large = rat_0) & ~ (rat_very_small
% 10.99/2.23 = rat_1/2) & ~ (rat_very_small = rat_0) & ~ (real_1/2 = real_0) & ~
% 10.99/2.23 (rat_1/2 = rat_0) & rat_$is_int(rat_1/2) = 1 & rat_$is_int(rat_0) = 0 &
% 10.99/2.23 rat_$is_rat(rat_1/2) = 0 & rat_$is_rat(rat_0) = 0 & rat_$floor(rat_1/2) =
% 10.99/2.23 rat_0 & rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = rat_0 &
% 10.99/2.23 rat_$truncate(rat_1/2) = rat_0 & rat_$truncate(rat_0) = rat_0 &
% 10.99/2.23 rat_$round(rat_0) = rat_0 & rat_$to_int(rat_1/2) = 0 & rat_$to_int(rat_0) = 0
% 10.99/2.23 & rat_$to_rat(rat_1/2) = rat_1/2 & rat_$to_rat(rat_0) = rat_0 &
% 10.99/2.23 rat_$to_real(rat_1/2) = real_1/2 & rat_$to_real(rat_0) = real_0 &
% 10.99/2.23 int_$to_rat(0) = rat_0 & real_$is_int(real_1/2) = 1 & real_$is_int(real_0) = 0
% 10.99/2.23 & real_$is_rat(real_1/2) = 0 & real_$is_rat(real_0) = 0 &
% 10.99/2.23 real_$floor(real_1/2) = real_0 & real_$floor(real_0) = real_0 &
% 10.99/2.23 real_$ceiling(real_0) = real_0 & real_$truncate(real_1/2) = real_0 &
% 10.99/2.23 real_$truncate(real_0) = real_0 & real_$round(real_0) = real_0 &
% 10.99/2.23 real_$to_int(real_1/2) = 0 & real_$to_int(real_0) = 0 & real_$to_rat(real_1/2)
% 10.99/2.23 = rat_1/2 & real_$to_rat(real_0) = rat_0 & real_$to_real(real_1/2) = real_1/2
% 10.99/2.23 & real_$to_real(real_0) = real_0 & int_$to_real(0) = real_0 &
% 10.99/2.23 real_$quotient(real_0, real_1/2) = real_0 & real_$product(real_1/2, real_0) =
% 10.99/2.23 real_0 & real_$product(real_0, real_1/2) = real_0 & real_$product(real_0,
% 10.99/2.23 real_0) = real_0 & real_$difference(real_1/2, real_1/2) = real_0 &
% 10.99/2.23 real_$difference(real_1/2, real_0) = real_1/2 & real_$difference(real_0,
% 10.99/2.23 real_0) = real_0 & real_$uminus(real_0) = real_0 & real_$sum(real_1/2,
% 10.99/2.23 real_0) = real_1/2 & real_$sum(real_0, real_1/2) = real_1/2 &
% 10.99/2.23 real_$sum(real_0, real_0) = real_0 & real_$greatereq(real_very_small,
% 10.99/2.23 real_very_large) = 1 & real_$greatereq(real_1/2, real_1/2) = 0 &
% 10.99/2.23 real_$greatereq(real_1/2, real_0) = 0 & real_$greatereq(real_0, real_1/2) = 1
% 10.99/2.23 & real_$greatereq(real_0, real_0) = 0 & real_$greater(real_very_large,
% 10.99/2.23 real_1/2) = 0 & real_$greater(real_very_large, real_0) = 0 &
% 10.99/2.23 real_$greater(real_very_small, real_very_large) = 1 & real_$greater(real_1/2,
% 10.99/2.23 real_very_small) = 0 & real_$greater(real_1/2, real_1/2) = 1 &
% 10.99/2.23 real_$greater(real_1/2, real_0) = 0 & real_$greater(real_0, real_very_small) =
% 10.99/2.23 0 & real_$greater(real_0, real_1/2) = 1 & real_$greater(real_0, real_0) = 1 &
% 10.99/2.23 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small,
% 10.99/2.23 real_1/2) = 0 & real_$less(real_very_small, real_0) = 0 &
% 10.99/2.23 real_$less(real_1/2, real_very_large) = 0 & real_$less(real_1/2, real_1/2) = 1
% 10.99/2.23 & real_$less(real_1/2, real_0) = 1 & real_$less(real_0, real_very_large) = 0 &
% 10.99/2.23 real_$less(real_0, real_1/2) = 0 & real_$less(real_0, real_0) = 1 &
% 10.99/2.23 rat_$quotient(rat_0, rat_1/2) = rat_0 & rat_$product(rat_1/2, rat_0) = rat_0 &
% 10.99/2.23 rat_$product(rat_0, rat_1/2) = rat_0 & rat_$product(rat_0, rat_0) = rat_0 &
% 10.99/2.23 rat_$difference(rat_1/2, rat_1/2) = rat_0 & rat_$difference(rat_1/2, rat_0) =
% 10.99/2.23 rat_1/2 & rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 &
% 10.99/2.23 rat_$sum(rat_1/2, rat_0) = rat_1/2 & rat_$sum(rat_0, rat_1/2) = rat_1/2 &
% 10.99/2.24 rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small,
% 10.99/2.24 rat_very_large) = 1 & rat_$greatereq(rat_1/2, rat_1/2) = 0 &
% 10.99/2.24 rat_$greatereq(rat_1/2, rat_0) = 0 & rat_$greatereq(rat_0, rat_1/2) = 1 &
% 10.99/2.24 rat_$greatereq(rat_0, rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large)
% 10.99/2.24 = 0 & rat_$lesseq(rat_1/2, rat_1/2) = 0 & rat_$lesseq(rat_1/2, rat_0) = 1 &
% 10.99/2.24 rat_$lesseq(rat_0, rat_1/2) = 0 & rat_$lesseq(rat_0, rat_0) = 0 &
% 10.99/2.24 rat_$greater(rat_very_large, rat_1/2) = 0 & rat_$greater(rat_very_large,
% 10.99/2.24 rat_0) = 0 & rat_$greater(rat_very_small, rat_very_large) = 1 &
% 10.99/2.24 rat_$greater(rat_1/2, rat_very_small) = 0 & rat_$greater(rat_1/2, rat_1/2) = 1
% 10.99/2.24 & rat_$greater(rat_1/2, rat_0) = 0 & rat_$greater(rat_0, rat_very_small) = 0 &
% 10.99/2.24 rat_$greater(rat_0, rat_1/2) = 1 & rat_$greater(rat_0, rat_0) = 1 &
% 10.99/2.24 rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small,
% 10.99/2.24 rat_1/2) = 0 & rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_1/2,
% 10.99/2.24 rat_very_large) = 0 & rat_$less(rat_1/2, rat_1/2) = 1 & rat_$less(rat_1/2,
% 10.99/2.24 rat_0) = 1 & rat_$less(rat_0, rat_very_large) = 0 & rat_$less(rat_0,
% 10.99/2.24 rat_1/2) = 0 & rat_$less(rat_0, rat_0) = 1 & real_$lesseq(real_very_small,
% 10.99/2.24 real_very_large) = 0 & real_$lesseq(real_1/2, real_1/2) = 0 &
% 10.99/2.24 real_$lesseq(real_1/2, real_0) = 1 & real_$lesseq(real_0, real_1/2) = 0 &
% 10.99/2.24 real_$lesseq(real_0, real_0) = 0 & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.99/2.24 $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~
% 10.99/2.24 (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 &
% 10.99/2.24 real_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 10.99/2.24 ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2,
% 10.99/2.24 v1) = v3) | ? [v5: $rat] : (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) =
% 10.99/2.24 v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] :
% 10.99/2.24 (v3 = v1 | v0 = real_0 | ~ (real_$quotient(v2, v0) = v3) | ~
% 10.99/2.24 (real_$product(v1, v0) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 10.99/2.24 $rat] : ! [v3: $rat] : (v3 = v1 | v0 = rat_0 | ~ (rat_$quotient(v2, v0) =
% 10.99/2.24 v3) | ~ (rat_$product(v1, v0) = v2)) & ! [v0: $real] : ! [v1: $real] :
% 10.99/2.24 ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~
% 10.99/2.24 (real_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2,
% 10.99/2.24 v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3:
% 10.99/2.24 int] : (v3 = 0 | ~ (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) =
% 10.99/2.24 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0:
% 10.99/2.24 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~
% 10.99/2.24 (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~
% 10.99/2.24 (v4 = 0) & rat_$less(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : !
% 10.99/2.24 [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~
% 10.99/2.24 (real_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2,
% 10.99/2.24 v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3:
% 10.99/2.24 $real] : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) |
% 10.99/2.24 real_$difference(v1, v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 10.99/2.24 $rat] : ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) =
% 10.99/2.24 v3) | rat_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1: $real] : !
% 10.99/2.24 [v2: $real] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0,
% 10.99/2.24 v1) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v2 = rat_0
% 10.99/2.24 | ~ (rat_$uminus(v0) = v1) | ~ (rat_$sum(v0, v1) = v2)) & ! [v0: $real] :
% 10.99/2.24 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greatereq(v0, v1) = v2) |
% 10.99/2.24 ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: $real] :
% 10.99/2.24 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ?
% 10.99/2.24 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $rat] : !
% 10.99/2.24 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ?
% 10.99/2.24 [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : !
% 10.99/2.24 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ( ~ (v1
% 10.99/2.24 = v0) & ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3))) & !
% 10.99/2.24 [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greater(v0, v1)
% 10.99/2.24 = v2) | ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0:
% 10.99/2.24 $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0)
% 10.99/2.24 = v2) | ( ~ (v1 = v0) & ? [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) =
% 10.99/2.24 v3))) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~
% 10.99/2.24 (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2) & ! [v0: $real]
% 10.99/2.24 : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) |
% 10.99/2.24 real_$sum(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 10.99/2.24 ( ~ (real_$less(v1, v0) = 0) | ~ (real_$lesseq(v2, v1) = 0) | real_$less(v2,
% 10.99/2.24 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 10.99/2.24 (rat_$product(v0, v1) = v2) | rat_$product(v1, v0) = v2) & ! [v0: $rat] :
% 10.99/2.24 ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0)
% 10.99/2.24 = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2,
% 10.99/2.24 v1) = 0) | ~ (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = 0) & ! [v0:
% 10.99/2.24 $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & !
% 10.99/2.24 [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & !
% 10.99/2.24 [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) |
% 10.99/2.24 rat_$less(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~
% 10.99/2.24 (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = 0) & ! [v0: $real] : !
% 10.99/2.24 [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0:
% 10.99/2.24 $real] : ! [v1: $real] : ( ~ (real_$greatereq(v0, v1) = 0) |
% 10.99/2.24 real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 10.99/2.24 (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & ! [v0: $rat] : !
% 10.99/2.24 [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0:
% 10.99/2.24 $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1,
% 10.99/2.24 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0)
% 10.99/2.24 | rat_$less(v1, v0) = 0) & ! [v0: $real] : (v0 = real_0 | ~
% 10.99/2.24 (real_$uminus(v0) = v0)) & ! [v0: $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0)
% 10.99/2.24 = v0))
% 10.99/2.24
% 10.99/2.24 (function-axioms)
% 10.99/2.25 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 |
% 10.99/2.25 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & !
% 10.99/2.25 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 10.99/2.25 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0:
% 10.99/2.25 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 10.99/2.25 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & !
% 10.99/2.25 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 10.99/2.25 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0:
% 10.99/2.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 10.99/2.25 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~
% 10.99/2.25 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.99/2.25 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 10.99/2.25 (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, v2) = v0)) & ! [v0:
% 10.99/2.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 10.99/2.25 $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) =
% 10.99/2.25 v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1
% 10.99/2.25 = v0 | ~ (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) &
% 10.99/2.25 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 10.99/2.25 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0:
% 10.99/2.25 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 10.99/2.25 (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & !
% 10.99/2.25 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 10.99/2.25 (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0:
% 10.99/2.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 10.99/2.25 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3,
% 10.99/2.25 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 10.99/2.25 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~
% 10.99/2.25 (rat_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.99/2.25 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 10.99/2.25 (rat_$greater(v3, v2) = v1) | ~ (rat_$greater(v3, v2) = v0)) & ! [v0:
% 10.99/2.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 10.99/2.25 $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) =
% 10.99/2.26 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.99/2.26 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | ~
% 10.99/2.26 (real_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.99/2.26 MultipleValueBool] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$is_int(v2) = v1) |
% 10.99/2.26 ~ (rat_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.99/2.26 MultipleValueBool] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$is_rat(v2) = v1) |
% 10.99/2.26 ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 10.99/2.26 (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~ (rat_$floor(v2) = v0)) & ! [v0:
% 10.99/2.26 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$ceiling(v2) =
% 10.99/2.26 v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : !
% 11.34/2.26 [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) = v1) | ~ (rat_$truncate(v2) =
% 11.34/2.26 v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~
% 11.34/2.26 (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) & ! [v0: int] : ! [v1:
% 11.34/2.26 int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) = v1) | ~
% 11.34/2.26 (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 11.34/2.26 (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) & ! [v0:
% 11.34/2.26 $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_real(v2) =
% 11.34/2.26 v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : !
% 11.34/2.26 [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~ (int_$to_rat(v2) = v0))
% 11.34/2.26 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] :
% 11.34/2.26 (v1 = v0 | ~ (real_$is_int(v2) = v1) | ~ (real_$is_int(v2) = v0)) & ! [v0:
% 11.34/2.26 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : (v1 = v0
% 11.34/2.26 | ~ (real_$is_rat(v2) = v1) | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real]
% 11.34/2.26 : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~
% 11.34/2.26 (real_$floor(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 11.34/2.26 (v1 = v0 | ~ (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & !
% 11.34/2.26 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 11.34/2.26 (real_$truncate(v2) = v1) | ~ (real_$truncate(v2) = v0)) & ! [v0: $real] :
% 11.34/2.26 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~
% 11.34/2.26 (real_$round(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1
% 11.34/2.26 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0:
% 11.34/2.26 $rat] : ! [v1: $rat] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) =
% 11.34/2.26 v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : !
% 11.34/2.26 [v2: $real] : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) =
% 11.34/2.26 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~
% 11.34/2.26 (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = v0)) & ! [v0: $real] : !
% 11.34/2.26 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~
% 11.34/2.26 (real_$uminus(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 11.34/2.26 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0))
% 11.34/2.26
% 11.34/2.26 Those formulas are unsatisfiable:
% 11.34/2.26 ---------------------------------
% 11.34/2.26
% 11.34/2.26 Begin of proof
% 11.34/2.26 |
% 11.34/2.26 | ALPHA: (function-axioms) implies:
% 11.34/2.26 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.34/2.26 | $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) |
% 11.34/2.26 | ~ (real_$lesseq(v3, v2) = v0))
% 11.34/2.26 |
% 11.34/2.26 | ALPHA: (input) implies:
% 11.34/2.26 | (2) real_$lesseq(real_1/2, real_1/2) = 0
% 11.34/2.26 |
% 11.34/2.27 | DELTA: instantiating (mixed_types_problem_18) with fresh symbol all_5_0 gives:
% 11.34/2.27 | (3) ~ (all_5_0 = 0) & real_$lesseq(real_1/2, real_1/2) = all_5_0
% 11.34/2.27 |
% 11.34/2.27 | ALPHA: (3) implies:
% 11.34/2.27 | (4) ~ (all_5_0 = 0)
% 11.39/2.27 | (5) real_$lesseq(real_1/2, real_1/2) = all_5_0
% 11.39/2.27 |
% 11.39/2.27 | GROUND_INST: instantiating (1) with 0, all_5_0, real_1/2, real_1/2,
% 11.39/2.27 | simplifying with (2), (5) gives:
% 11.39/2.27 | (6) all_5_0 = 0
% 11.39/2.27 |
% 11.39/2.27 | REDUCE: (4), (6) imply:
% 11.39/2.27 | (7) $false
% 11.39/2.27 |
% 11.39/2.27 | CLOSE: (7) is inconsistent.
% 11.39/2.27 |
% 11.39/2.27 End of proof
% 11.39/2.27 % SZS output end Proof for theBenchmark
% 11.39/2.27
% 11.39/2.27 1661ms
%------------------------------------------------------------------------------