TSTP Solution File: NUM905_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM905_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 : n029.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 11:50:39 EDT 2023
% Result : Theorem 5.93s 1.59s
% Output : Proof 7.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM905_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.35 % Computer : n029.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Fri Aug 25 14:20:39 EDT 2023
% 0.17/0.35 % 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.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.32/0.91 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.32/0.91 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.32/0.91 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.32/0.91 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.32/0.91 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.32/0.91 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.32/0.92 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.12/1.00 Prover 4: Preprocessing ...
% 2.12/1.00 Prover 1: Preprocessing ...
% 2.40/1.04 Prover 2: Preprocessing ...
% 2.40/1.04 Prover 0: Preprocessing ...
% 2.40/1.04 Prover 3: Preprocessing ...
% 2.40/1.04 Prover 6: Preprocessing ...
% 2.40/1.04 Prover 5: Preprocessing ...
% 4.51/1.35 Prover 5: Proving ...
% 4.51/1.36 Prover 6: Constructing countermodel ...
% 4.51/1.38 Prover 1: Constructing countermodel ...
% 4.51/1.41 Prover 3: Constructing countermodel ...
% 4.51/1.42 Prover 4: Constructing countermodel ...
% 4.51/1.44 Prover 2: Proving ...
% 5.35/1.48 Prover 0: Proving ...
% 5.93/1.59 Prover 3: proved (948ms)
% 5.93/1.59
% 5.93/1.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.93/1.59
% 5.93/1.59 Prover 6: stopped
% 5.93/1.59 Prover 0: stopped
% 5.93/1.59 Prover 2: stopped
% 5.93/1.60 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.93/1.60 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 5.93/1.60 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.93/1.60 Prover 5: proved (959ms)
% 5.93/1.60
% 5.93/1.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.93/1.60
% 5.93/1.60 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.93/1.60 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.93/1.60 Prover 7: Preprocessing ...
% 5.93/1.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.33/1.60 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.33/1.60 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.33/1.60 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.33/1.61 Prover 10: Preprocessing ...
% 6.33/1.61 Prover 11: Preprocessing ...
% 6.33/1.61 Prover 8: Preprocessing ...
% 6.33/1.61 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.33/1.63 Prover 13: Preprocessing ...
% 6.33/1.63 Prover 1: Found proof (size 15)
% 6.33/1.63 Prover 1: proved (1003ms)
% 6.33/1.63 Prover 10: stopped
% 6.33/1.64 Prover 11: stopped
% 6.33/1.65 Prover 4: stopped
% 6.67/1.65 Prover 7: stopped
% 6.67/1.66 Prover 13: stopped
% 6.67/1.71 Prover 8: Warning: ignoring some quantifiers
% 6.67/1.72 Prover 8: Constructing countermodel ...
% 6.67/1.73 Prover 8: stopped
% 6.67/1.73
% 6.67/1.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.67/1.73
% 6.67/1.74 % SZS output start Proof for theBenchmark
% 6.67/1.74 Assumptions after simplification:
% 6.67/1.74 ---------------------------------
% 6.67/1.74
% 6.67/1.74 (rat_uminus_problem_9)
% 7.16/1.77 ? [v0: $rat] : ? [v1: $rat] : (rat_$uminus(v0) = v1 & ((v1 = v0 & ~ (v0 =
% 7.16/1.77 rat_0)) | (v0 = rat_0 & ~ (v1 = rat_0))))
% 7.16/1.77
% 7.16/1.77 (input)
% 7.16/1.79 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_0) & ~
% 7.16/1.79 (rat_very_small = rat_0) & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_0) = 0 &
% 7.16/1.79 rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_0)
% 7.38/1.79 = rat_0 & rat_$round(rat_0) = rat_0 & rat_$to_int(rat_0) = 0 &
% 7.38/1.79 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_0) = real_0 & int_$to_rat(0) =
% 7.38/1.79 rat_0 & rat_$product(rat_0, rat_0) = rat_0 & rat_$difference(rat_0, rat_0) =
% 7.38/1.79 rat_0 & rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small,
% 7.38/1.79 rat_very_large) = 1 & rat_$greatereq(rat_0, rat_0) = 0 &
% 7.38/1.79 rat_$lesseq(rat_very_small, rat_very_large) = 0 & rat_$lesseq(rat_0, rat_0) =
% 7.38/1.79 0 & rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small,
% 7.38/1.79 rat_very_large) = 1 & rat_$greater(rat_0, rat_very_small) = 0 &
% 7.38/1.79 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0
% 7.38/1.79 & rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_0, rat_very_large) = 0
% 7.38/1.79 & rat_$less(rat_0, rat_0) = 1 & rat_$uminus(rat_0) = rat_0 & ! [v0: $rat] :
% 7.38/1.79 ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~
% 7.38/1.79 (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] :
% 7.38/1.79 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1:
% 7.38/1.79 $rat] : ! [v2: $rat] : ! [v3: $rat] : (v3 = v1 | v0 = rat_0 | ~
% 7.38/1.79 (rat_$quotient(v2, v0) = v3) | ~ (rat_$product(v1, v0) = v2)) & ! [v0:
% 7.38/1.79 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~
% 7.38/1.79 (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : (
% 7.38/1.79 ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] :
% 7.38/1.79 ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~
% 7.38/1.79 (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) =
% 7.38/1.79 v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~
% 7.38/1.79 (rat_$sum(v1, v2) = v3) | ~ (rat_$uminus(v0) = v2) | rat_$difference(v1,
% 7.38/1.79 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v2 = rat_0 |
% 7.38/1.79 ~ (rat_$sum(v0, v1) = v2) | ~ (rat_$uminus(v0) = v1)) & ! [v0: $rat] : !
% 7.38/1.79 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ?
% 7.38/1.80 [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : !
% 7.38/1.80 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ( ~ (v1
% 7.38/1.80 = v0) & ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3))) & !
% 7.38/1.80 [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greater(v0, v1)
% 7.38/1.80 = v2) | ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0:
% 7.38/1.80 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) |
% 7.38/1.80 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 7.38/1.80 ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1:
% 7.38/1.80 $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1,
% 7.38/1.80 v0) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : (v1
% 7.38/1.80 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1: $rat] : (v1
% 7.38/1.80 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat]
% 7.38/1.80 : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1, v0) = 0)
% 7.38/1.80 & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) |
% 7.38/1.80 rat_$less(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 7.38/1.80 (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0: $rat] : (v0 = rat_0
% 7.38/1.80 | ~ (rat_$uminus(v0) = v0))
% 7.38/1.80
% 7.38/1.80 (function-axioms)
% 7.38/1.81 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 7.38/1.81 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0:
% 7.38/1.81 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 7.38/1.81 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0:
% 7.38/1.81 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 7.38/1.81 (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & !
% 7.38/1.81 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 7.38/1.81 (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0:
% 7.38/1.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 7.38/1.81 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3,
% 7.38/1.81 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 7.38/1.81 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~
% 7.38/1.81 (rat_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.38/1.81 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 7.38/1.81 (rat_$greater(v3, v2) = v1) | ~ (rat_$greater(v3, v2) = v0)) & ! [v0:
% 7.38/1.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 7.38/1.81 $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) =
% 7.38/1.81 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 7.38/1.81 $rat] : (v1 = v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) &
% 7.38/1.81 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 =
% 7.38/1.81 v0 | ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat]
% 7.38/1.81 : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~
% 7.38/1.81 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1
% 7.38/1.81 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0:
% 7.38/1.81 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) =
% 7.38/1.81 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : !
% 7.38/1.81 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) &
% 7.38/1.81 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) =
% 7.38/1.81 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 7.38/1.81 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) &
% 7.38/1.81 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~
% 7.38/1.81 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : !
% 7.38/1.81 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~
% 7.38/1.81 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 7.38/1.81 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0))
% 7.38/1.81
% 7.38/1.81 Those formulas are unsatisfiable:
% 7.38/1.81 ---------------------------------
% 7.38/1.81
% 7.38/1.81 Begin of proof
% 7.38/1.81 |
% 7.38/1.81 | ALPHA: (function-axioms) implies:
% 7.38/1.81 | (1) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~
% 7.38/1.81 | (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0))
% 7.38/1.81 |
% 7.38/1.81 | ALPHA: (input) implies:
% 7.38/1.81 | (2) rat_$uminus(rat_0) = rat_0
% 7.38/1.81 | (3) ! [v0: $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0) = v0))
% 7.38/1.81 |
% 7.38/1.81 | DELTA: instantiating (rat_uminus_problem_9) with fresh symbols all_5_0,
% 7.38/1.81 | all_5_1 gives:
% 7.38/1.81 | (4) rat_$uminus(all_5_1) = all_5_0 & ((all_5_0 = all_5_1 & ~ (all_5_1 =
% 7.38/1.81 | rat_0)) | (all_5_1 = rat_0 & ~ (all_5_0 = rat_0)))
% 7.38/1.81 |
% 7.38/1.81 | ALPHA: (4) implies:
% 7.38/1.82 | (5) rat_$uminus(all_5_1) = all_5_0
% 7.38/1.82 | (6) (all_5_0 = all_5_1 & ~ (all_5_1 = rat_0)) | (all_5_1 = rat_0 & ~
% 7.38/1.82 | (all_5_0 = rat_0))
% 7.38/1.82 |
% 7.38/1.82 | BETA: splitting (6) gives:
% 7.38/1.82 |
% 7.38/1.82 | Case 1:
% 7.38/1.82 | |
% 7.38/1.82 | | (7) all_5_0 = all_5_1 & ~ (all_5_1 = rat_0)
% 7.38/1.82 | |
% 7.38/1.82 | | ALPHA: (7) implies:
% 7.38/1.82 | | (8) all_5_0 = all_5_1
% 7.38/1.82 | | (9) ~ (all_5_1 = rat_0)
% 7.38/1.82 | |
% 7.38/1.82 | | REDUCE: (5), (8) imply:
% 7.38/1.82 | | (10) rat_$uminus(all_5_1) = all_5_1
% 7.38/1.82 | |
% 7.38/1.82 | | GROUND_INST: instantiating (3) with all_5_1, simplifying with (10) gives:
% 7.38/1.82 | | (11) all_5_1 = rat_0
% 7.38/1.82 | |
% 7.38/1.82 | | REDUCE: (9), (11) imply:
% 7.38/1.82 | | (12) $false
% 7.38/1.82 | |
% 7.38/1.82 | | CLOSE: (12) is inconsistent.
% 7.38/1.82 | |
% 7.38/1.82 | Case 2:
% 7.38/1.82 | |
% 7.38/1.82 | | (13) all_5_1 = rat_0 & ~ (all_5_0 = rat_0)
% 7.38/1.82 | |
% 7.38/1.82 | | ALPHA: (13) implies:
% 7.38/1.82 | | (14) all_5_1 = rat_0
% 7.38/1.82 | | (15) ~ (all_5_0 = rat_0)
% 7.38/1.82 | |
% 7.38/1.82 | | REDUCE: (5), (14) imply:
% 7.38/1.82 | | (16) rat_$uminus(rat_0) = all_5_0
% 7.38/1.82 | |
% 7.38/1.82 | | GROUND_INST: instantiating (1) with rat_0, all_5_0, rat_0, simplifying with
% 7.38/1.82 | | (2), (16) gives:
% 7.38/1.82 | | (17) all_5_0 = rat_0
% 7.38/1.82 | |
% 7.38/1.82 | | REDUCE: (15), (17) imply:
% 7.38/1.82 | | (18) $false
% 7.38/1.82 | |
% 7.38/1.82 | | CLOSE: (18) is inconsistent.
% 7.38/1.82 | |
% 7.38/1.82 | End of split
% 7.38/1.82 |
% 7.38/1.82 End of proof
% 7.38/1.82 % SZS output end Proof for theBenchmark
% 7.38/1.82
% 7.38/1.82 1210ms
%------------------------------------------------------------------------------