TSTP Solution File: ARI239_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI239_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 : n002.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 17:47:24 EDT 2023
% Result : Theorem 6.05s 1.62s
% Output : Proof 8.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI239_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 18:12:50 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.66 ________ _____
% 0.21/0.66 ___ __ \_________(_)________________________________
% 0.21/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.66
% 0.21/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.66 (2023-06-19)
% 0.21/0.66
% 0.21/0.66 (c) Philipp Rümmer, 2009-2023
% 0.21/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.66 Amanda Stjerna.
% 0.21/0.66 Free software under BSD-3-Clause.
% 0.21/0.66
% 0.21/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.66
% 0.21/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.68 Running up to 7 provers in parallel.
% 0.21/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.87/1.00 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.87/1.00 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.87/1.00 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.87/1.00 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.87/1.00 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.87/1.00 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.87/1.00 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.31/1.06 Prover 1: Preprocessing ...
% 2.31/1.06 Prover 4: Preprocessing ...
% 2.67/1.13 Prover 5: Preprocessing ...
% 2.67/1.13 Prover 3: Preprocessing ...
% 2.67/1.13 Prover 2: Preprocessing ...
% 2.67/1.13 Prover 0: Preprocessing ...
% 2.91/1.14 Prover 6: Preprocessing ...
% 5.51/1.57 Prover 6: Constructing countermodel ...
% 6.05/1.60 Prover 1: Constructing countermodel ...
% 6.05/1.62 Prover 6: proved (933ms)
% 6.05/1.62
% 6.05/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.05/1.62
% 6.05/1.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.05/1.64 Prover 4: Constructing countermodel ...
% 6.05/1.64 Prover 0: Constructing countermodel ...
% 6.05/1.64 Prover 0: stopped
% 6.05/1.64 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.05/1.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.05/1.66 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.69/1.68 Prover 8: Preprocessing ...
% 6.86/1.70 Prover 7: Preprocessing ...
% 6.86/1.71 Prover 2: Constructing countermodel ...
% 6.86/1.71 Prover 2: stopped
% 7.06/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.10/1.73 Prover 5: Constructing countermodel ...
% 7.10/1.73 Prover 5: stopped
% 7.10/1.73 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.10/1.73 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation
% 7.10/1.74 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation
% 7.10/1.77 Prover 10: Preprocessing ...
% 7.10/1.79 Prover 11: Preprocessing ...
% 7.10/1.79 Prover 3: Constructing countermodel ...
% 7.10/1.79 Prover 3: stopped
% 7.10/1.79 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.10/1.80 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation
% 7.66/1.82 Prover 13: Preprocessing ...
% 7.66/1.82 Prover 8: Warning: ignoring some quantifiers
% 7.66/1.84 Prover 8: Constructing countermodel ...
% 7.66/1.87 Prover 4: Found proof (size 4)
% 7.66/1.87 Prover 4: proved (1185ms)
% 8.20/1.87 Prover 8: stopped
% 8.20/1.88 Prover 1: stopped
% 8.20/1.88 Prover 7: stopped
% 8.20/1.88 Prover 13: stopped
% 8.20/1.91 Prover 10: stopped
% 8.20/1.93 Prover 11: stopped
% 8.20/1.93
% 8.20/1.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.20/1.93
% 8.20/1.93 % SZS output start Proof for theBenchmark
% 8.20/1.94 Assumptions after simplification:
% 8.20/1.94 ---------------------------------
% 8.20/1.94
% 8.20/1.94 (rat_greatereq_problem_10)
% 8.20/1.96 rat_$greatereq(rat_-3/4, rat_3/4) = 0
% 8.20/1.96
% 8.20/1.96 (input)
% 8.20/1.99 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_3/4) & ~
% 8.20/1.99 (rat_very_large = rat_-3/4) & ~ (rat_very_large = rat_0) & ~ (rat_very_small
% 8.20/1.99 = rat_3/4) & ~ (rat_very_small = rat_-3/4) & ~ (rat_very_small = rat_0) &
% 8.20/1.99 ~ (rat_3/4 = rat_-3/4) & ~ (rat_3/4 = rat_0) & ~ (rat_-3/4 = rat_0) &
% 8.20/1.99 rat_$is_int(rat_3/4) = 1 & rat_$is_int(rat_-3/4) = 1 & rat_$is_int(rat_0) = 0
% 8.20/1.99 & rat_$is_rat(rat_3/4) = 0 & rat_$is_rat(rat_-3/4) = 0 & rat_$is_rat(rat_0) =
% 8.20/1.99 0 & rat_$floor(rat_3/4) = rat_0 & rat_$floor(rat_0) = rat_0 &
% 8.20/1.99 rat_$ceiling(rat_-3/4) = rat_0 & rat_$ceiling(rat_0) = rat_0 &
% 8.20/1.99 rat_$truncate(rat_3/4) = rat_0 & rat_$truncate(rat_-3/4) = rat_0 &
% 8.20/1.99 rat_$truncate(rat_0) = rat_0 & rat_$round(rat_0) = rat_0 &
% 8.20/1.99 rat_$to_int(rat_3/4) = 0 & rat_$to_int(rat_-3/4) = -1 & rat_$to_int(rat_0) = 0
% 8.20/1.99 & rat_$to_rat(rat_3/4) = rat_3/4 & rat_$to_rat(rat_-3/4) = rat_-3/4 &
% 8.20/1.99 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_3/4) = real_3/4 &
% 8.20/1.99 rat_$to_real(rat_-3/4) = real_-3/4 & rat_$to_real(rat_0) = real_0 &
% 8.20/1.99 int_$to_rat(0) = rat_0 & rat_$quotient(rat_0, rat_3/4) = rat_0 &
% 8.20/1.99 rat_$quotient(rat_0, rat_-3/4) = rat_0 & rat_$product(rat_3/4, rat_0) = rat_0
% 8.20/1.99 & rat_$product(rat_-3/4, rat_0) = rat_0 & rat_$product(rat_0, rat_3/4) = rat_0
% 8.20/1.99 & rat_$product(rat_0, rat_-3/4) = rat_0 & rat_$product(rat_0, rat_0) = rat_0 &
% 8.20/1.99 rat_$difference(rat_3/4, rat_3/4) = rat_0 & rat_$difference(rat_3/4, rat_0) =
% 8.20/1.99 rat_3/4 & rat_$difference(rat_-3/4, rat_-3/4) = rat_0 &
% 8.20/1.99 rat_$difference(rat_-3/4, rat_0) = rat_-3/4 & rat_$difference(rat_0, rat_3/4)
% 8.20/1.99 = rat_-3/4 & rat_$difference(rat_0, rat_-3/4) = rat_3/4 &
% 8.20/1.99 rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_3/4) = rat_-3/4 &
% 8.20/1.99 rat_$uminus(rat_-3/4) = rat_3/4 & rat_$uminus(rat_0) = rat_0 &
% 8.20/1.99 rat_$sum(rat_3/4, rat_-3/4) = rat_0 & rat_$sum(rat_3/4, rat_0) = rat_3/4 &
% 8.20/1.99 rat_$sum(rat_-3/4, rat_3/4) = rat_0 & rat_$sum(rat_-3/4, rat_0) = rat_-3/4 &
% 8.20/1.99 rat_$sum(rat_0, rat_3/4) = rat_3/4 & rat_$sum(rat_0, rat_-3/4) = rat_-3/4 &
% 8.20/1.99 rat_$sum(rat_0, rat_0) = rat_0 & rat_$lesseq(rat_very_small, rat_very_large) =
% 8.20/1.99 0 & rat_$lesseq(rat_3/4, rat_3/4) = 0 & rat_$lesseq(rat_3/4, rat_-3/4) = 1 &
% 8.20/1.99 rat_$lesseq(rat_3/4, rat_0) = 1 & rat_$lesseq(rat_-3/4, rat_3/4) = 0 &
% 8.20/1.99 rat_$lesseq(rat_-3/4, rat_-3/4) = 0 & rat_$lesseq(rat_-3/4, rat_0) = 0 &
% 8.20/1.99 rat_$lesseq(rat_0, rat_3/4) = 0 & rat_$lesseq(rat_0, rat_-3/4) = 1 &
% 8.20/1.99 rat_$lesseq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, rat_3/4) = 0 &
% 8.20/1.99 rat_$greater(rat_very_large, rat_-3/4) = 0 & rat_$greater(rat_very_large,
% 8.20/1.99 rat_0) = 0 & rat_$greater(rat_very_small, rat_very_large) = 1 &
% 8.20/1.99 rat_$greater(rat_3/4, rat_very_small) = 0 & rat_$greater(rat_3/4, rat_3/4) = 1
% 8.20/1.99 & rat_$greater(rat_3/4, rat_-3/4) = 0 & rat_$greater(rat_3/4, rat_0) = 0 &
% 8.20/1.99 rat_$greater(rat_-3/4, rat_very_small) = 0 & rat_$greater(rat_-3/4, rat_3/4) =
% 8.20/1.99 1 & rat_$greater(rat_-3/4, rat_-3/4) = 1 & rat_$greater(rat_-3/4, rat_0) = 1 &
% 8.20/1.99 rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_3/4) = 1 &
% 8.20/1.99 rat_$greater(rat_0, rat_-3/4) = 0 & rat_$greater(rat_0, rat_0) = 1 &
% 8.20/1.99 rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small,
% 8.20/1.99 rat_3/4) = 0 & rat_$less(rat_very_small, rat_-3/4) = 0 &
% 8.20/1.99 rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_3/4, rat_very_large) = 0
% 8.20/1.99 & rat_$less(rat_3/4, rat_3/4) = 1 & rat_$less(rat_3/4, rat_-3/4) = 1 &
% 8.20/1.99 rat_$less(rat_3/4, rat_0) = 1 & rat_$less(rat_-3/4, rat_very_large) = 0 &
% 8.20/1.99 rat_$less(rat_-3/4, rat_3/4) = 0 & rat_$less(rat_-3/4, rat_-3/4) = 1 &
% 8.20/1.99 rat_$less(rat_-3/4, rat_0) = 0 & rat_$less(rat_0, rat_very_large) = 0 &
% 8.20/1.99 rat_$less(rat_0, rat_3/4) = 0 & rat_$less(rat_0, rat_-3/4) = 1 &
% 8.20/1.99 rat_$less(rat_0, rat_0) = 1 & rat_$greatereq(rat_very_small, rat_very_large) =
% 8.20/1.99 1 & rat_$greatereq(rat_3/4, rat_3/4) = 0 & rat_$greatereq(rat_3/4, rat_-3/4) =
% 8.20/1.99 0 & rat_$greatereq(rat_3/4, rat_0) = 0 & rat_$greatereq(rat_-3/4, rat_3/4) = 1
% 8.20/1.99 & rat_$greatereq(rat_-3/4, rat_-3/4) = 0 & rat_$greatereq(rat_-3/4, rat_0) = 1
% 8.20/1.99 & rat_$greatereq(rat_0, rat_3/4) = 1 & rat_$greatereq(rat_0, rat_-3/4) = 0 &
% 8.20/1.99 rat_$greatereq(rat_0, rat_0) = 0 & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 8.20/1.99 $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~
% 8.20/1.99 (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : (rat_$sum(v2, v5) = v4 &
% 8.20/1.99 rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 8.20/1.99 ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2, v3) = v4) | ~ (rat_$sum(v1,
% 8.20/1.99 v0) = v3) | ? [v5: $rat] : (rat_$sum(v5, v0) = v4 & rat_$sum(v2, v1) =
% 8.20/1.99 v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3
% 8.20/1.99 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v2, v0) = v3) | ? [v4:
% 8.20/1.99 int] : ( ~ (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1:
% 8.20/1.99 $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) =
% 8.20/1.99 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) &
% 8.20/1.99 rat_$less(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 8.20/1.99 ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1,
% 8.20/1.99 v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & !
% 8.20/1.99 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~
% 8.20/1.99 (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~
% 8.20/1.99 (v4 = 0) & rat_$less(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : !
% 8.20/1.99 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v1) = 0) | ~
% 8.20/1.99 (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1, v0)
% 8.20/1.99 = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] :
% 8.20/1.99 (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ (rat_$less(v1, v0) = 0) | ? [v4:
% 8.20/1.99 int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1:
% 8.20/1.99 $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) | ~
% 8.20/1.99 (rat_$sum(v1, v2) = v3) | rat_$difference(v1, v0) = v3) & ! [v0: $rat] : !
% 8.20/1.99 [v1: $rat] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (rat_$less(v1, v0) = v2) |
% 8.20/1.99 ? [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : !
% 8.20/1.99 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3:
% 8.20/1.99 int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1:
% 8.20/1.99 $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3:
% 8.20/1.99 int] : ( ~ (v3 = 0) & rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : !
% 8.20/1.99 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3:
% 8.20/1.99 int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1:
% 8.20/1.99 $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int]
% 8.20/1.99 : ( ~ (v3 = 0) & rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat]
% 8.20/1.99 : ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : (
% 8.20/1.99 ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] :
% 8.20/1.99 ! [v2: $rat] : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) |
% 8.20/1.99 rat_$quotient(v2, v0) = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat]
% 8.20/1.99 : ( ~ (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat]
% 8.20/1.99 : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) |
% 8.20/1.99 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 8.20/1.99 ( ~ (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = v3 &
% 8.20/1.99 rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 8.20/1.99 ( ~ (rat_$sum(v1, v0) = v2) | rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1:
% 8.20/1.99 $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2)
% 8.20/1.99 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) =
% 8.20/1.99 0) | ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2, v0) = 0) & ! [v0:
% 8.20/1.99 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) | ~
% 8.20/1.99 (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1:
% 8.20/1.99 $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2,
% 8.20/1.99 v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : (v1
% 8.20/1.99 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1: $rat] : (v1
% 8.20/1.99 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat]
% 8.20/1.99 : ! [v1: int] : (v1 = 0 | ~ (rat_$lesseq(v0, v0) = v1)) & ! [v0: $rat] : !
% 8.20/1.99 [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0:
% 8.20/1.99 $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$sum(v0, v1) =
% 8.20/1.99 rat_0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$lesseq(v1, v0) = 0) |
% 8.20/1.99 rat_$greatereq(v0, v1) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 8.20/1.99 (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] : !
% 8.20/1.99 [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$lesseq(v1, v0) = 0) & ! [v0:
% 8.20/1.99 $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$greater(v0, v1) =
% 8.20/1.99 0) & ! [v0: $rat] : ! [v1: MultipleValueBool] : ( ~ (rat_$less(v0, v0) =
% 8.20/1.99 v1) | rat_$lesseq(v0, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 8.20/1.99 (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] :
% 8.20/1.99 (v0 = rat_0 | ~ (rat_$uminus(v0) = v0))
% 8.20/1.99
% 8.20/1.99 (function-axioms)
% 8.20/2.00 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 8.20/2.00 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0:
% 8.20/2.00 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 8.20/2.00 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0:
% 8.20/2.00 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 8.20/2.00 (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & !
% 8.20/2.00 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 8.20/2.00 (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0:
% 8.20/2.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 8.20/2.00 $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ (rat_$lesseq(v3, v2) =
% 8.20/2.00 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.20/2.00 $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$greater(v3, v2) = v1) | ~
% 8.20/2.00 (rat_$greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.20/2.00 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 8.20/2.00 (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) = v0)) & ! [v0:
% 8.20/2.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 8.20/2.00 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3,
% 8.20/2.00 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 8.20/2.00 ! [v2: $rat] : (v1 = v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) =
% 8.20/2.00 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.20/2.00 $rat] : (v1 = v0 | ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) &
% 8.20/2.00 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) =
% 8.20/2.00 v1) | ~ (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 8.20/2.00 $rat] : (v1 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0))
% 8.20/2.00 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~
% 8.20/2.00 (rat_$truncate(v2) = v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : !
% 8.20/2.00 [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~
% 8.20/2.00 (rat_$round(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 =
% 8.20/2.00 v0 | ~ (rat_$to_int(v2) = v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat]
% 8.20/2.00 : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~
% 8.20/2.00 (rat_$to_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] :
% 8.20/2.00 (v1 = v0 | ~ (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0:
% 8.20/2.00 $rat] : ! [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1)
% 8.20/2.00 | ~ (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat]
% 8.20/2.00 : (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0))
% 8.20/2.00
% 8.20/2.00 Those formulas are unsatisfiable:
% 8.20/2.00 ---------------------------------
% 8.20/2.00
% 8.20/2.00 Begin of proof
% 8.20/2.00 |
% 8.20/2.00 | ALPHA: (function-axioms) implies:
% 8.20/2.00 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat]
% 8.20/2.00 | : ! [v3: $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~
% 8.20/2.00 | (rat_$greatereq(v3, v2) = v0))
% 8.20/2.00 |
% 8.20/2.00 | ALPHA: (input) implies:
% 8.20/2.00 | (2) rat_$greatereq(rat_-3/4, rat_3/4) = 1
% 8.20/2.00 |
% 8.20/2.00 | GROUND_INST: instantiating (1) with 0, 1, rat_3/4, rat_-3/4, simplifying with
% 8.20/2.00 | (2), (rat_greatereq_problem_10) gives:
% 8.20/2.00 | (3) $false
% 8.20/2.01 |
% 8.20/2.01 | CLOSE: (3) is inconsistent.
% 8.20/2.01 |
% 8.20/2.01 End of proof
% 8.20/2.01 % SZS output end Proof for theBenchmark
% 8.20/2.01
% 8.20/2.01 1342ms
%------------------------------------------------------------------------------