TSTP Solution File: ARI558_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI558_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 : n023.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 17:48:23 EDT 2023
% Result : Theorem 10.69s 2.18s
% Output : Proof 11.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ARI558_1 : TPTP v8.1.2. Released v5.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 19:05:40 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.62/0.61 ________ _____
% 0.62/0.61 ___ __ \_________(_)________________________________
% 0.62/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.62/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.62/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.62/0.61
% 0.62/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.62/0.61 (2023-06-19)
% 0.62/0.61
% 0.62/0.61 (c) Philipp Rümmer, 2009-2023
% 0.62/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.62/0.61 Amanda Stjerna.
% 0.62/0.61 Free software under BSD-3-Clause.
% 0.62/0.61
% 0.62/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.62/0.61
% 0.62/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.62/0.62 Running up to 7 provers in parallel.
% 0.72/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.72/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.72/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.72/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.72/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.72/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.72/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.48/0.89 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.48/0.89 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.48/0.89 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.48/0.89 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.48/0.89 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.48/0.89 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.48/0.89 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.04/0.99 Prover 1: Preprocessing ...
% 2.48/1.00 Prover 4: Preprocessing ...
% 2.48/1.07 Prover 0: Preprocessing ...
% 2.48/1.07 Prover 6: Preprocessing ...
% 2.94/1.10 Prover 2: Preprocessing ...
% 2.94/1.10 Prover 3: Preprocessing ...
% 2.94/1.10 Prover 5: Preprocessing ...
% 6.39/1.58 Prover 1: Constructing countermodel ...
% 6.39/1.62 Prover 4: Constructing countermodel ...
% 7.08/1.63 Prover 6: Proving ...
% 7.08/1.67 Prover 0: Proving ...
% 9.90/2.02 Prover 1: Found proof (size 10)
% 9.90/2.02 Prover 1: proved (1387ms)
% 9.90/2.03 Prover 4: stopped
% 9.90/2.03 Prover 6: stopped
% 9.90/2.03 Prover 0: stopped
% 9.90/2.07 Prover 3: Constructing countermodel ...
% 9.90/2.07 Prover 3: stopped
% 10.60/2.10 Prover 2: Proving ...
% 10.60/2.10 Prover 2: stopped
% 10.69/2.18 Prover 5: Proving ...
% 10.69/2.18 Prover 5: stopped
% 10.69/2.18
% 10.69/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.69/2.18
% 10.69/2.18 % SZS output start Proof for theBenchmark
% 10.69/2.18 Assumptions after simplification:
% 10.69/2.18 ---------------------------------
% 10.69/2.18
% 10.69/2.18 (rat_combined_problem_18)
% 10.69/2.21 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$product(v0, rat_-1/20) = v1) | ?
% 10.69/2.21 [v2: $rat] : ? [v3: int] : ( ~ (v3 = 0) & rat_$difference(rat_-1/4, v1) =
% 10.69/2.21 v2 & rat_$lesseq(v2, rat_0) = v3))
% 10.69/2.21
% 10.69/2.21 (input)
% 11.18/2.23 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_-1/20) & ~
% 11.18/2.23 (rat_very_large = rat_-1/4) & ~ (rat_very_large = rat_0) & ~ (rat_very_small
% 11.18/2.23 = rat_-1/20) & ~ (rat_very_small = rat_-1/4) & ~ (rat_very_small = rat_0)
% 11.18/2.23 & ~ (rat_-1/20 = rat_-1/4) & ~ (rat_-1/20 = rat_0) & ~ (rat_-1/4 = rat_0) &
% 11.18/2.23 rat_$is_int(rat_-1/20) = 1 & rat_$is_int(rat_-1/4) = 1 & rat_$is_int(rat_0) =
% 11.18/2.23 0 & rat_$is_rat(rat_-1/20) = 0 & rat_$is_rat(rat_-1/4) = 0 &
% 11.18/2.23 rat_$is_rat(rat_0) = 0 & rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_-1/20) =
% 11.18/2.23 rat_0 & rat_$ceiling(rat_-1/4) = rat_0 & rat_$ceiling(rat_0) = rat_0 &
% 11.18/2.23 rat_$truncate(rat_-1/20) = rat_0 & rat_$truncate(rat_-1/4) = rat_0 &
% 11.18/2.23 rat_$truncate(rat_0) = rat_0 & rat_$round(rat_-1/20) = rat_0 &
% 11.18/2.23 rat_$round(rat_-1/4) = rat_0 & rat_$round(rat_0) = rat_0 &
% 11.18/2.23 rat_$to_int(rat_-1/20) = -1 & rat_$to_int(rat_-1/4) = -1 & rat_$to_int(rat_0)
% 11.18/2.23 = 0 & rat_$to_rat(rat_-1/20) = rat_-1/20 & rat_$to_rat(rat_-1/4) = rat_-1/4 &
% 11.18/2.23 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_-1/20) = real_-1/20 &
% 11.18/2.23 rat_$to_real(rat_-1/4) = real_-1/4 & rat_$to_real(rat_0) = real_0 &
% 11.18/2.23 int_$to_rat(0) = rat_0 & rat_$quotient(rat_0, rat_-1/20) = rat_0 &
% 11.18/2.23 rat_$quotient(rat_0, rat_-1/4) = rat_0 & rat_$uminus(rat_0) = rat_0 &
% 11.18/2.23 rat_$sum(rat_-1/20, rat_0) = rat_-1/20 & rat_$sum(rat_-1/4, rat_0) = rat_-1/4
% 11.18/2.23 & rat_$sum(rat_0, rat_-1/20) = rat_-1/20 & rat_$sum(rat_0, rat_-1/4) =
% 11.18/2.23 rat_-1/4 & rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small,
% 11.18/2.23 rat_very_large) = 1 & rat_$greatereq(rat_-1/20, rat_-1/20) = 0 &
% 11.18/2.23 rat_$greatereq(rat_-1/20, rat_-1/4) = 0 & rat_$greatereq(rat_-1/20, rat_0) = 1
% 11.18/2.23 & rat_$greatereq(rat_-1/4, rat_-1/20) = 1 & rat_$greatereq(rat_-1/4, rat_-1/4)
% 11.18/2.23 = 0 & rat_$greatereq(rat_-1/4, rat_0) = 1 & rat_$greatereq(rat_0, rat_-1/20) =
% 11.18/2.23 0 & rat_$greatereq(rat_0, rat_-1/4) = 0 & rat_$greatereq(rat_0, rat_0) = 0 &
% 11.18/2.23 rat_$greater(rat_very_large, rat_-1/20) = 0 & rat_$greater(rat_very_large,
% 11.18/2.23 rat_-1/4) = 0 & rat_$greater(rat_very_large, rat_0) = 0 &
% 11.18/2.23 rat_$greater(rat_very_small, rat_very_large) = 1 & rat_$greater(rat_-1/20,
% 11.18/2.23 rat_very_small) = 0 & rat_$greater(rat_-1/20, rat_-1/20) = 1 &
% 11.18/2.23 rat_$greater(rat_-1/20, rat_-1/4) = 0 & rat_$greater(rat_-1/20, rat_0) = 1 &
% 11.18/2.23 rat_$greater(rat_-1/4, rat_very_small) = 0 & rat_$greater(rat_-1/4, rat_-1/20)
% 11.18/2.23 = 1 & rat_$greater(rat_-1/4, rat_-1/4) = 1 & rat_$greater(rat_-1/4, rat_0) = 1
% 11.18/2.23 & rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_-1/20) = 0
% 11.18/2.23 & rat_$greater(rat_0, rat_-1/4) = 0 & rat_$greater(rat_0, rat_0) = 1 &
% 11.18/2.23 rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small,
% 11.18/2.23 rat_-1/20) = 0 & rat_$less(rat_very_small, rat_-1/4) = 0 &
% 11.18/2.23 rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_-1/20, rat_very_large) =
% 11.18/2.23 0 & rat_$less(rat_-1/20, rat_-1/20) = 1 & rat_$less(rat_-1/20, rat_-1/4) = 1 &
% 11.18/2.23 rat_$less(rat_-1/20, rat_0) = 0 & rat_$less(rat_-1/4, rat_very_large) = 0 &
% 11.18/2.23 rat_$less(rat_-1/4, rat_-1/20) = 0 & rat_$less(rat_-1/4, rat_-1/4) = 1 &
% 11.18/2.23 rat_$less(rat_-1/4, rat_0) = 0 & rat_$less(rat_0, rat_very_large) = 0 &
% 11.18/2.23 rat_$less(rat_0, rat_-1/20) = 1 & rat_$less(rat_0, rat_-1/4) = 1 &
% 11.18/2.23 rat_$less(rat_0, rat_0) = 1 & rat_$product(rat_-1/20, rat_0) = rat_0 &
% 11.18/2.23 rat_$product(rat_-1/4, rat_0) = rat_0 & rat_$product(rat_0, rat_-1/20) = rat_0
% 11.18/2.23 & rat_$product(rat_0, rat_-1/4) = rat_0 & rat_$product(rat_0, rat_0) = rat_0 &
% 11.18/2.23 rat_$difference(rat_-1/20, rat_-1/20) = rat_0 & rat_$difference(rat_-1/20,
% 11.18/2.23 rat_0) = rat_-1/20 & rat_$difference(rat_-1/4, rat_-1/4) = rat_0 &
% 11.18/2.23 rat_$difference(rat_-1/4, rat_0) = rat_-1/4 & rat_$difference(rat_0, rat_0) =
% 11.18/2.23 rat_0 & rat_$lesseq(rat_very_small, rat_very_large) = 0 &
% 11.18/2.23 rat_$lesseq(rat_-1/20, rat_-1/20) = 0 & rat_$lesseq(rat_-1/20, rat_-1/4) = 1 &
% 11.18/2.23 rat_$lesseq(rat_-1/20, rat_0) = 0 & rat_$lesseq(rat_-1/4, rat_-1/20) = 0 &
% 11.18/2.23 rat_$lesseq(rat_-1/4, rat_-1/4) = 0 & rat_$lesseq(rat_-1/4, rat_0) = 0 &
% 11.18/2.23 rat_$lesseq(rat_0, rat_-1/20) = 1 & rat_$lesseq(rat_0, rat_-1/4) = 1 &
% 11.18/2.23 rat_$lesseq(rat_0, rat_0) = 0 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat]
% 11.18/2.23 : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~
% 11.18/2.23 (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : (rat_$sum(v2, v5) = v4 &
% 11.18/2.23 rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 11.18/2.23 ! [v3: $rat] : (v3 = v1 | v0 = rat_0 | ~ (rat_$quotient(v2, v0) = v3) | ~
% 11.18/2.23 (rat_$product(v1, v0) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat]
% 11.18/2.23 : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ (rat_$lesseq(v1,
% 11.18/2.23 v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = v4)) & !
% 11.18/2.23 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~
% 11.18/2.23 (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : (
% 11.18/2.23 ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] :
% 11.18/2.23 ! [v2: $rat] : ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1,
% 11.18/2.23 v2) = v3) | rat_$difference(v1, v0) = v3) & ! [v0: $rat] : ! [v1:
% 11.18/2.23 $rat] : ! [v2: $rat] : (v2 = rat_0 | ~ (rat_$uminus(v0) = v1) | ~
% 11.18/2.23 (rat_$sum(v0, v1) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] :
% 11.18/2.23 (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 11.18/2.23 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int]
% 11.18/2.23 : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 11.18/2.23 rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] :
% 11.18/2.23 (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3: int] : ( ~
% 11.18/2.23 (v3 = 0) & rat_$less(v1, v0) = v3))) & ! [v0: $rat] : ! [v1: $rat] :
% 11.18/2.23 ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) & ! [v0:
% 11.18/2.23 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$less(v1, v0) = 0) | ~
% 11.18/2.23 (rat_$lesseq(v2, v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1:
% 11.18/2.23 $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) | rat_$product(v1,
% 11.18/2.23 v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0,
% 11.18/2.23 rat_0) = v1)) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~
% 11.18/2.23 (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] : ! [v1:
% 11.18/2.23 $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0: $rat] :
% 11.18/2.23 ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1, v0) = 0) &
% 11.18/2.23 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1,
% 11.18/2.23 v0) = 0) & ! [v0: $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0) = v0))
% 11.18/2.23
% 11.18/2.24 (function-axioms)
% 11.18/2.24 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 11.18/2.24 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0:
% 11.18/2.24 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 11.18/2.24 (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0:
% 11.18/2.24 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 11.18/2.24 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3,
% 11.18/2.24 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 11.18/2.24 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$greater(v3, v2) = v1) | ~
% 11.18/2.24 (rat_$greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.18/2.24 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 11.18/2.24 (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) = v0)) & ! [v0: $rat] : !
% 11.18/2.24 [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$product(v3,
% 11.18/2.24 v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0: $rat] : ! [v1:
% 11.18/2.24 $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$difference(v3,
% 11.18/2.24 v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & ! [v0:
% 11.18/2.24 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 11.18/2.24 $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ (rat_$lesseq(v3, v2) =
% 11.18/2.24 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.18/2.24 $rat] : (v1 = v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) &
% 11.18/2.24 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 =
% 11.18/2.24 v0 | ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat]
% 11.18/2.24 : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~
% 11.18/2.24 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1
% 11.18/2.24 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0:
% 11.18/2.24 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) =
% 11.18/2.24 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : !
% 11.18/2.24 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) &
% 11.18/2.24 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) =
% 11.18/2.24 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 11.18/2.24 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) &
% 11.18/2.24 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~
% 11.18/2.24 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : !
% 11.18/2.24 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~
% 11.18/2.24 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 11.18/2.24 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0))
% 11.18/2.24
% 11.18/2.24 Those formulas are unsatisfiable:
% 11.18/2.24 ---------------------------------
% 11.18/2.24
% 11.18/2.24 Begin of proof
% 11.18/2.24 |
% 11.18/2.24 | ALPHA: (function-axioms) implies:
% 11.18/2.25 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat]
% 11.18/2.25 | : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~
% 11.18/2.25 | (rat_$lesseq(v3, v2) = v0))
% 11.18/2.25 | (2) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 =
% 11.18/2.25 | v0 | ~ (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2)
% 11.18/2.25 | = v0))
% 11.18/2.25 |
% 11.18/2.25 | ALPHA: (input) implies:
% 11.18/2.25 | (3) rat_$lesseq(rat_-1/4, rat_0) = 0
% 11.18/2.25 | (4) rat_$difference(rat_-1/4, rat_0) = rat_-1/4
% 11.18/2.25 | (5) rat_$product(rat_0, rat_-1/20) = rat_0
% 11.18/2.25 |
% 11.18/2.25 | GROUND_INST: instantiating (rat_combined_problem_18) with rat_0, rat_0,
% 11.18/2.25 | simplifying with (5) gives:
% 11.18/2.25 | (6) ? [v0: $rat] : ? [v1: int] : ( ~ (v1 = 0) & rat_$difference(rat_-1/4,
% 11.18/2.25 | rat_0) = v0 & rat_$lesseq(v0, rat_0) = v1)
% 11.18/2.25 |
% 11.18/2.25 | DELTA: instantiating (6) with fresh symbols all_15_0, all_15_1 gives:
% 11.18/2.25 | (7) ~ (all_15_0 = 0) & rat_$difference(rat_-1/4, rat_0) = all_15_1 &
% 11.18/2.25 | rat_$lesseq(all_15_1, rat_0) = all_15_0
% 11.18/2.25 |
% 11.18/2.25 | ALPHA: (7) implies:
% 11.18/2.25 | (8) ~ (all_15_0 = 0)
% 11.18/2.25 | (9) rat_$lesseq(all_15_1, rat_0) = all_15_0
% 11.18/2.25 | (10) rat_$difference(rat_-1/4, rat_0) = all_15_1
% 11.18/2.25 |
% 11.18/2.25 | GROUND_INST: instantiating (2) with rat_-1/4, all_15_1, rat_0, rat_-1/4,
% 11.18/2.25 | simplifying with (4), (10) gives:
% 11.18/2.25 | (11) all_15_1 = rat_-1/4
% 11.18/2.25 |
% 11.18/2.25 | REDUCE: (9), (11) imply:
% 11.18/2.25 | (12) rat_$lesseq(rat_-1/4, rat_0) = all_15_0
% 11.18/2.25 |
% 11.18/2.25 | GROUND_INST: instantiating (1) with 0, all_15_0, rat_0, rat_-1/4, simplifying
% 11.18/2.25 | with (3), (12) gives:
% 11.18/2.25 | (13) all_15_0 = 0
% 11.18/2.25 |
% 11.18/2.25 | REDUCE: (8), (13) imply:
% 11.18/2.25 | (14) $false
% 11.18/2.26 |
% 11.18/2.26 | CLOSE: (14) is inconsistent.
% 11.18/2.26 |
% 11.18/2.26 End of proof
% 11.18/2.26 % SZS output end Proof for theBenchmark
% 11.18/2.26
% 11.18/2.26 1646ms
%------------------------------------------------------------------------------