TSTP Solution File: NUM901_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM901_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 : n024.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 6.46s 1.60s
% Output : Proof 8.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM901_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 16:36:24 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.75/0.95 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.75/0.95 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.75/0.95 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.75/0.95 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.75/0.95 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.75/0.95 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.75/0.95 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.26/1.04 Prover 1: Preprocessing ...
% 2.26/1.04 Prover 4: Preprocessing ...
% 2.39/1.08 Prover 2: Preprocessing ...
% 2.39/1.08 Prover 3: Preprocessing ...
% 2.39/1.08 Prover 5: Preprocessing ...
% 2.39/1.08 Prover 0: Preprocessing ...
% 2.39/1.08 Prover 6: Preprocessing ...
% 5.13/1.44 Prover 1: Constructing countermodel ...
% 5.13/1.44 Prover 6: Constructing countermodel ...
% 5.13/1.44 Prover 5: Proving ...
% 5.13/1.47 Prover 3: Constructing countermodel ...
% 5.13/1.49 Prover 2: Proving ...
% 5.62/1.50 Prover 4: Constructing countermodel ...
% 5.62/1.53 Prover 0: Proving ...
% 6.46/1.60 Prover 5: proved (963ms)
% 6.46/1.60
% 6.46/1.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.46/1.60
% 6.46/1.61 Prover 2: stopped
% 6.46/1.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.46/1.61 Prover 0: stopped
% 6.46/1.61 Prover 3: stopped
% 6.46/1.61 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.46/1.61 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.46/1.61 Prover 6: stopped
% 6.46/1.62 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.46/1.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.46/1.62 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.46/1.62 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.46/1.62 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.46/1.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.46/1.62 Prover 7: Preprocessing ...
% 6.46/1.62 Prover 8: Preprocessing ...
% 6.46/1.62 Prover 11: Preprocessing ...
% 6.46/1.62 Prover 10: Preprocessing ...
% 6.46/1.62 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.64/1.63 Prover 13: Preprocessing ...
% 6.64/1.63 Prover 1: gave up
% 6.64/1.64 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.64/1.64 Prover 16: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.64/1.65 Prover 16: Preprocessing ...
% 6.64/1.71 Prover 7: Warning: ignoring some quantifiers
% 6.64/1.72 Prover 7: Constructing countermodel ...
% 6.64/1.72 Prover 10: Warning: ignoring some quantifiers
% 7.37/1.73 Prover 10: Constructing countermodel ...
% 7.37/1.74 Prover 16: Warning: ignoring some quantifiers
% 7.37/1.74 Prover 8: Warning: ignoring some quantifiers
% 7.37/1.75 Prover 16: Constructing countermodel ...
% 7.37/1.75 Prover 13: Warning: ignoring some quantifiers
% 7.37/1.76 Prover 8: Constructing countermodel ...
% 7.37/1.77 Prover 13: Constructing countermodel ...
% 7.37/1.78 Prover 11: Constructing countermodel ...
% 7.89/1.81 Prover 10: gave up
% 7.89/1.81 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 7.89/1.81 Prover 19: Warning: Problem contains rationals, using incomplete axiomatisation
% 7.89/1.82 Prover 19: Preprocessing ...
% 7.89/1.84 Prover 4: Found proof (size 12)
% 7.89/1.84 Prover 4: proved (1201ms)
% 7.89/1.84 Prover 13: stopped
% 7.89/1.84 Prover 16: stopped
% 7.89/1.84 Prover 8: stopped
% 7.89/1.84 Prover 7: stopped
% 7.89/1.84 Prover 11: stopped
% 8.41/1.91 Prover 19: Warning: ignoring some quantifiers
% 8.41/1.91 Prover 19: Constructing countermodel ...
% 8.41/1.92 Prover 19: stopped
% 8.41/1.92
% 8.41/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.41/1.92
% 8.41/1.92 % SZS output start Proof for theBenchmark
% 8.41/1.92 Assumptions after simplification:
% 8.41/1.92 ---------------------------------
% 8.41/1.92
% 8.41/1.92 (rat_difference_problem_12)
% 8.41/1.95 ? [v0: $rat] : ? [v1: $rat] : ( ~ (v1 = rat_0) & rat_$difference(v0, v0) =
% 8.41/1.95 v1)
% 8.41/1.95
% 8.41/1.95 (input)
% 8.71/1.97 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_0) & ~
% 8.71/1.97 (rat_very_small = rat_0) & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_0) = 0 &
% 8.71/1.97 rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_0)
% 8.71/1.97 = rat_0 & rat_$round(rat_0) = rat_0 & rat_$to_int(rat_0) = 0 &
% 8.71/1.97 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_0) = real_0 & int_$to_rat(0) =
% 8.71/1.97 rat_0 & rat_$product(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 &
% 8.71/1.97 rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small,
% 8.71/1.97 rat_very_large) = 1 & rat_$greatereq(rat_0, rat_0) = 0 &
% 8.71/1.97 rat_$lesseq(rat_very_small, rat_very_large) = 0 & rat_$lesseq(rat_0, rat_0) =
% 8.71/1.97 0 & rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small,
% 8.71/1.97 rat_very_large) = 1 & rat_$greater(rat_0, rat_very_small) = 0 &
% 8.71/1.97 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0
% 8.71/1.97 & rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_0, rat_very_large) = 0
% 8.71/1.97 & rat_$less(rat_0, rat_0) = 1 & rat_$difference(rat_0, rat_0) = rat_0 & !
% 8.71/1.97 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : (
% 8.71/1.97 ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] :
% 8.71/1.97 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1:
% 8.71/1.97 $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2,
% 8.71/1.97 v3) = v4) | ~ (rat_$sum(v1, v0) = v3) | ? [v5: $rat] : (rat_$sum(v5,
% 8.71/1.97 v0) = v4 & rat_$sum(v2, v1) = v5)) & ! [v0: $rat] : ! [v1: $rat] : !
% 8.71/1.97 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~
% 8.71/1.97 (rat_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1,
% 8.71/1.97 v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3:
% 8.71/1.97 int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3)
% 8.71/1.97 | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v1, v0) = v4)) & ! [v0: $rat] :
% 8.71/1.97 ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2,
% 8.71/1.97 v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) &
% 8.71/1.97 rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat]
% 8.71/1.97 : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2,
% 8.71/1.97 v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = v4)) & !
% 8.71/1.97 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~
% 8.71/1.97 (rat_$less(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~
% 8.71/1.97 (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : !
% 8.71/1.97 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~
% 8.71/1.97 (rat_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1)
% 8.71/1.97 = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (
% 8.71/1.97 ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1,
% 8.71/1.97 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | v1 =
% 8.71/1.97 v0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 8.71/1.97 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int]
% 8.71/1.97 : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 8.71/1.97 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int]
% 8.71/1.97 : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 8.71/1.97 rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 8.71/1.97 int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0)
% 8.71/1.97 & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int]
% 8.71/1.97 : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 8.71/1.97 rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] :
% 8.71/1.97 (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 8.71/1.97 rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 8.71/1.97 $rat] : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, v0)
% 8.71/1.97 = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 8.71/1.97 (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] :
% 8.71/1.97 ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) |
% 8.71/1.97 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 8.71/1.97 ( ~ (rat_$sum(v1, v0) = v2) | rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1:
% 8.71/1.97 $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2)
% 8.71/1.97 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) =
% 8.71/1.97 0) | ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2, v0) = 0) & ! [v0:
% 8.71/1.97 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) | ~
% 8.71/1.97 (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1:
% 8.71/1.97 $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2,
% 8.71/1.97 v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : !
% 8.71/1.97 [v2: $rat] : ( ~ (rat_$difference(v1, v0) = v2) | ? [v3: $rat] :
% 8.71/1.97 (rat_$uminus(v0) = v3 & rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1:
% 8.71/1.97 $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1:
% 8.71/1.97 $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) &
% 8.71/1.97 ! [v0: $rat] : ! [v1: int] : (v1 = 0 | ~ (rat_$lesseq(v0, v0) = v1)) & !
% 8.71/1.97 [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) =
% 8.71/1.97 v0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) |
% 8.71/1.97 rat_$sum(v0, v1) = rat_0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 8.71/1.97 (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : !
% 8.71/1.97 [v1: $rat] : ( ~ (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) & !
% 8.71/1.98 [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1,
% 8.71/1.98 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) |
% 8.71/1.98 rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 8.71/1.98 (rat_$less(v1, v0) = 0) | rat_$greater(v0, v1) = 0) & ! [v0: $rat] : !
% 8.71/1.98 [v1: MultipleValueBool] : ( ~ (rat_$less(v0, v0) = v1) | rat_$lesseq(v0, v0) =
% 8.71/1.98 0) & ! [v0: $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0) = v0))
% 8.71/1.98
% 8.71/1.98 (function-axioms)
% 8.71/1.98 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 8.71/1.98 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0:
% 8.71/1.98 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 8.71/1.98 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0:
% 8.71/1.98 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 8.71/1.98 (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0:
% 8.71/1.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 8.71/1.98 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3,
% 8.71/1.98 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 8.71/1.98 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~
% 8.71/1.98 (rat_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.71/1.98 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 8.71/1.98 (rat_$greater(v3, v2) = v1) | ~ (rat_$greater(v3, v2) = v0)) & ! [v0:
% 8.71/1.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 8.71/1.98 $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) =
% 8.71/1.98 v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1
% 8.71/1.98 = v0 | ~ (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) =
% 8.71/1.98 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.71/1.98 $rat] : (v1 = v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) &
% 8.71/1.98 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 =
% 8.71/1.98 v0 | ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat]
% 8.71/1.98 : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~
% 8.71/1.98 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1
% 8.71/1.98 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0:
% 8.71/1.98 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) =
% 8.71/1.98 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : !
% 8.71/1.98 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) &
% 8.71/1.98 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) =
% 8.71/1.98 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 8.71/1.98 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) &
% 8.71/1.98 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~
% 8.71/1.98 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : !
% 8.71/1.98 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~
% 8.71/1.98 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 8.71/1.98 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0))
% 8.71/1.98
% 8.71/1.98 Those formulas are unsatisfiable:
% 8.71/1.98 ---------------------------------
% 8.71/1.98
% 8.71/1.98 Begin of proof
% 8.71/1.98 |
% 8.71/1.98 | ALPHA: (function-axioms) implies:
% 8.71/1.99 | (1) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 =
% 8.71/1.99 | v0 | ~ (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0))
% 8.99/1.99 |
% 8.99/1.99 | ALPHA: (input) implies:
% 8.99/1.99 | (2) ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) |
% 8.99/1.99 | rat_$sum(v0, v1) = rat_0)
% 8.99/1.99 | (3) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 8.99/1.99 | (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) =
% 8.99/1.99 | v3 & rat_$sum(v1, v3) = v2))
% 8.99/1.99 |
% 8.99/1.99 | DELTA: instantiating (rat_difference_problem_12) with fresh symbols all_5_0,
% 8.99/1.99 | all_5_1 gives:
% 8.99/1.99 | (4) ~ (all_5_0 = rat_0) & rat_$difference(all_5_1, all_5_1) = all_5_0
% 8.99/1.99 |
% 8.99/1.99 | ALPHA: (4) implies:
% 8.99/1.99 | (5) ~ (all_5_0 = rat_0)
% 8.99/1.99 | (6) rat_$difference(all_5_1, all_5_1) = all_5_0
% 8.99/1.99 |
% 8.99/1.99 | GROUND_INST: instantiating (3) with all_5_1, all_5_1, all_5_0, simplifying
% 8.99/1.99 | with (6) gives:
% 8.99/1.99 | (7) ? [v0: $rat] : (rat_$uminus(all_5_1) = v0 & rat_$sum(all_5_1, v0) =
% 8.99/1.99 | all_5_0)
% 8.99/1.99 |
% 8.99/1.99 | DELTA: instantiating (7) with fresh symbol all_17_0 gives:
% 8.99/1.99 | (8) rat_$uminus(all_5_1) = all_17_0 & rat_$sum(all_5_1, all_17_0) = all_5_0
% 8.99/1.99 |
% 8.99/1.99 | ALPHA: (8) implies:
% 8.99/1.99 | (9) rat_$sum(all_5_1, all_17_0) = all_5_0
% 8.99/1.99 | (10) rat_$uminus(all_5_1) = all_17_0
% 8.99/1.99 |
% 8.99/1.99 | GROUND_INST: instantiating (2) with all_5_1, all_17_0, simplifying with (10)
% 8.99/1.99 | gives:
% 8.99/1.99 | (11) rat_$sum(all_5_1, all_17_0) = rat_0
% 8.99/1.99 |
% 8.99/1.99 | GROUND_INST: instantiating (1) with all_5_0, rat_0, all_17_0, all_5_1,
% 8.99/1.99 | simplifying with (9), (11) gives:
% 8.99/1.99 | (12) all_5_0 = rat_0
% 8.99/1.99 |
% 8.99/1.99 | REDUCE: (5), (12) imply:
% 8.99/1.99 | (13) $false
% 8.99/1.99 |
% 8.99/1.99 | CLOSE: (13) is inconsistent.
% 8.99/1.99 |
% 8.99/1.99 End of proof
% 8.99/1.99 % SZS output end Proof for theBenchmark
% 8.99/2.00
% 8.99/2.00 1379ms
%------------------------------------------------------------------------------