TSTP Solution File: ARI742_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI742_1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n007.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 17:48:59 EDT 2023
% Result : Theorem 6.68s 1.68s
% Output : Proof 9.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ARI742_1 : TPTP v8.1.2. Released v7.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n007.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 : Tue Aug 29 17:58:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.68/0.65 ________ _____
% 0.68/0.65 ___ __ \_________(_)________________________________
% 0.68/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.68/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.68/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.68/0.65
% 0.68/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.68/0.65 (2023-06-19)
% 0.68/0.65
% 0.68/0.65 (c) Philipp Rümmer, 2009-2023
% 0.68/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.68/0.65 Amanda Stjerna.
% 0.68/0.65 Free software under BSD-3-Clause.
% 0.68/0.65
% 0.68/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.68/0.65
% 0.68/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.67 Running up to 7 provers in parallel.
% 0.68/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.68/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.68/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.68/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.68/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.68/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.68/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.67/0.94 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.67/0.94 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.67/0.94 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.67/0.94 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.67/0.94 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.67/0.94 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.67/0.94 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 2.62/1.08 Prover 4: Preprocessing ...
% 2.62/1.08 Prover 1: Preprocessing ...
% 2.62/1.12 Prover 3: Preprocessing ...
% 2.62/1.12 Prover 6: Preprocessing ...
% 2.62/1.12 Prover 5: Preprocessing ...
% 2.62/1.12 Prover 0: Preprocessing ...
% 2.62/1.12 Prover 2: Preprocessing ...
% 5.76/1.51 Prover 5: Proving ...
% 5.76/1.52 Prover 3: Constructing countermodel ...
% 5.76/1.52 Prover 1: Constructing countermodel ...
% 5.96/1.53 Prover 6: Constructing countermodel ...
% 5.96/1.56 Prover 2: Proving ...
% 6.68/1.63 Prover 4: Constructing countermodel ...
% 6.68/1.65 Prover 0: Proving ...
% 6.68/1.68 Prover 3: proved (994ms)
% 6.68/1.68
% 6.68/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.68/1.68
% 6.68/1.68 Prover 6: stopped
% 6.68/1.68 Prover 0: stopped
% 6.68/1.68 Prover 2: stopped
% 6.68/1.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.68/1.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.68/1.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.68/1.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.68/1.69 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 6.68/1.69 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 6.68/1.69 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation
% 6.68/1.69 Prover 5: proved (1005ms)
% 6.68/1.69
% 6.68/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.68/1.69
% 7.26/1.71 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 7.26/1.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.26/1.71 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation
% 7.26/1.72 Prover 7: Preprocessing ...
% 7.26/1.72 Prover 11: Preprocessing ...
% 7.26/1.72 Prover 10: Preprocessing ...
% 7.26/1.72 Prover 8: Preprocessing ...
% 7.26/1.73 Prover 13: Preprocessing ...
% 7.95/1.80 Prover 10: Warning: ignoring some quantifiers
% 8.08/1.82 Prover 10: Constructing countermodel ...
% 8.08/1.83 Prover 7: Warning: ignoring some quantifiers
% 8.08/1.84 Prover 7: Constructing countermodel ...
% 8.08/1.84 Prover 1: Found proof (size 23)
% 8.08/1.85 Prover 1: proved (1163ms)
% 8.08/1.85 Prover 4: stopped
% 8.08/1.85 Prover 10: stopped
% 8.08/1.85 Prover 7: stopped
% 8.08/1.86 Prover 8: Warning: ignoring some quantifiers
% 8.08/1.86 Prover 13: Warning: ignoring some quantifiers
% 8.08/1.86 Prover 8: Constructing countermodel ...
% 8.08/1.87 Prover 13: Constructing countermodel ...
% 8.08/1.87 Prover 8: stopped
% 8.08/1.88 Prover 13: stopped
% 8.08/1.91 Prover 11: Constructing countermodel ...
% 8.72/1.92 Prover 11: stopped
% 8.72/1.92
% 8.72/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.72/1.92
% 8.72/1.93 % SZS output start Proof for theBenchmark
% 8.72/1.93 Assumptions after simplification:
% 8.72/1.93 ---------------------------------
% 8.72/1.93
% 8.72/1.93 (sqrt_positive)
% 8.72/1.95 ! [v0: $real] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $real] :
% 8.72/1.95 (sqrt(v0) = v1 & real_$lesseq(real_0, v1) = 0))
% 8.72/1.95
% 8.72/1.95 (sqrt_square)
% 8.72/1.95 ! [v0: $real] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $real] :
% 8.72/1.95 (sqrt(v0) = v1 & sqr(v1) = v0))
% 8.72/1.95
% 8.72/1.95 (sqrt_zero)
% 8.72/1.95 ? [v0: $real] : ( ~ (v0 = real_0) & sqrt(real_0) = v0)
% 8.72/1.95
% 8.72/1.96 (square_sqrt)
% 8.72/1.96 ! [v0: $real] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $real] :
% 8.72/1.96 (sqrt(v1) = v0 & real_$product(v0, v0) = v1))
% 8.72/1.96
% 8.72/1.96 (input)
% 8.72/1.97 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_0) & ~
% 8.72/1.97 (real_very_small = real_0) & real_$is_int(real_0) = 0 & real_$is_rat(real_0) =
% 8.72/1.97 0 & real_$floor(real_0) = real_0 & real_$ceiling(real_0) = real_0 &
% 8.72/1.97 real_$truncate(real_0) = real_0 & real_$round(real_0) = real_0 &
% 8.72/1.97 real_$to_int(real_0) = 0 & real_$to_rat(real_0) = rat_0 &
% 8.72/1.97 real_$to_real(real_0) = real_0 & int_$to_real(0) = real_0 &
% 8.72/1.97 real_$difference(real_0, real_0) = real_0 & real_$uminus(real_0) = real_0 &
% 8.72/1.97 real_$sum(real_0, real_0) = real_0 & real_$greatereq(real_very_small,
% 8.72/1.97 real_very_large) = 1 & real_$greatereq(real_0, real_0) = 0 &
% 8.72/1.97 real_$greater(real_very_large, real_0) = 0 & real_$greater(real_very_small,
% 8.72/1.97 real_very_large) = 1 & real_$greater(real_0, real_very_small) = 0 &
% 8.72/1.97 real_$greater(real_0, real_0) = 1 & real_$less(real_very_small,
% 8.72/1.97 real_very_large) = 0 & real_$less(real_very_small, real_0) = 0 &
% 8.72/1.97 real_$less(real_0, real_very_large) = 0 & real_$less(real_0, real_0) = 1 &
% 8.72/1.97 real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_0,
% 8.72/1.97 real_0) = 0 & real_$product(real_0, real_0) = real_0 & ! [v0: $real] : !
% 8.72/1.97 [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~
% 8.72/1.97 (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] :
% 8.72/1.97 (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0: $real] : !
% 8.72/1.97 [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~
% 8.72/1.97 (real_$quotient(v2, v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0:
% 8.72/1.97 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~
% 8.72/1.97 (real_$less(v2, v1) = 0) | ~ (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~
% 8.72/1.97 (v4 = 0) & real_$lesseq(v1, v0) = v4)) & ! [v0: $real] : ! [v1: $real] :
% 8.72/1.97 ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~
% 8.72/1.97 (real_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2,
% 8.72/1.97 v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3:
% 8.72/1.97 int] : (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) =
% 8.72/1.97 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0:
% 8.72/1.97 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ( ~
% 8.72/1.97 (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) | real_$difference(v1,
% 8.72/1.97 v0) = v3) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v2 =
% 8.72/1.97 real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) = v2)) & ! [v0:
% 8.72/1.97 $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~
% 8.72/1.97 (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1,
% 8.72/1.97 v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 |
% 8.72/1.97 ~ (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 8.72/1.97 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 8.72/1.97 int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 =
% 8.72/1.97 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : !
% 8.72/1.98 [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0:
% 8.72/1.98 $real] : ! [v1: $real] : ! [v2: any] : ( ~ (real_$less(v1, v0) = v2) |
% 8.72/1.98 real_$lesseq(v1, v0) = 0 | ( ~ (v2 = 0) & ~ (v1 = v0))) & ! [v0: $real] :
% 8.72/1.98 ! [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = v2) |
% 8.72/1.98 real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 |
% 8.72/1.98 ~ (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : ! [v1: $real] : ( ~
% 8.72/1.98 (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1:
% 8.72/1.98 $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & !
% 8.72/1.98 [v0: $real] : ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) |
% 8.72/1.98 real_$less(v1, v0) = 0) & ! [v0: $real] : (v0 = real_0 | ~
% 8.72/1.98 (real_$uminus(v0) = v0))
% 8.72/1.98
% 8.72/1.98 (function-axioms)
% 8.72/1.98 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 |
% 8.72/1.98 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & !
% 8.72/1.98 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 8.72/1.98 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & !
% 8.72/1.98 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 8.72/1.98 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0:
% 8.72/1.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 8.72/1.98 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~
% 8.72/1.98 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.72/1.98 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 8.72/1.98 (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, v2) = v0)) & ! [v0:
% 8.72/1.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 8.72/1.98 $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) =
% 8.72/1.98 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.72/1.98 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | ~
% 8.72/1.98 (real_$lesseq(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 8.72/1.98 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$product(v3, v2) = v1) | ~
% 8.72/1.98 (real_$product(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.72/1.98 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1)
% 8.72/1.98 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.72/1.98 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1)
% 8.72/1.98 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 8.72/1.98 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) &
% 8.72/1.98 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 8.72/1.98 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] :
% 8.72/1.98 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~
% 8.72/1.98 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 8.72/1.98 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) &
% 8.72/1.98 ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2)
% 8.72/1.98 = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : !
% 8.72/1.98 [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) =
% 8.72/1.98 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 8.72/1.98 (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] :
% 8.72/1.98 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~
% 8.72/1.98 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real]
% 8.72/1.98 : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) & !
% 8.72/1.98 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (sqrt(v2) = v1)
% 8.72/1.98 | ~ (sqrt(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 8.72/1.98 (v1 = v0 | ~ (sqr(v2) = v1) | ~ (sqr(v2) = v0))
% 8.72/1.98
% 8.72/1.98 Further assumptions not needed in the proof:
% 8.72/1.98 --------------------------------------------
% 8.72/1.98 sqr_def, sqrt_le, sqrt_mul
% 8.72/1.98
% 8.72/1.98 Those formulas are unsatisfiable:
% 8.72/1.98 ---------------------------------
% 8.72/1.98
% 8.72/1.98 Begin of proof
% 8.72/1.99 |
% 8.72/1.99 | ALPHA: (function-axioms) implies:
% 8.72/1.99 | (1) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 8.72/1.99 | (sqrt(v2) = v1) | ~ (sqrt(v2) = v0))
% 8.72/1.99 | (2) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1
% 8.72/1.99 | = v0 | ~ (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) =
% 8.72/1.99 | v0))
% 8.72/1.99 |
% 8.72/1.99 | ALPHA: (input) implies:
% 8.72/1.99 | (3) real_$product(real_0, real_0) = real_0
% 8.72/1.99 | (4) real_$lesseq(real_0, real_0) = 0
% 8.72/1.99 |
% 8.72/1.99 | DELTA: instantiating (sqrt_zero) with fresh symbol all_11_0 gives:
% 8.72/1.99 | (5) ~ (all_11_0 = real_0) & sqrt(real_0) = all_11_0
% 8.72/1.99 |
% 8.72/1.99 | ALPHA: (5) implies:
% 8.72/1.99 | (6) ~ (all_11_0 = real_0)
% 8.72/1.99 | (7) sqrt(real_0) = all_11_0
% 8.72/1.99 |
% 8.72/1.99 | GROUND_INST: instantiating (square_sqrt) with real_0, simplifying with (4)
% 8.72/1.99 | gives:
% 8.72/1.99 | (8) ? [v0: $real] : (sqrt(v0) = real_0 & real_$product(real_0, real_0) =
% 8.72/1.99 | v0)
% 8.72/1.99 |
% 8.72/1.99 | GROUND_INST: instantiating (sqrt_positive) with real_0, simplifying with (4)
% 8.72/1.99 | gives:
% 8.72/1.99 | (9) ? [v0: $real] : (sqrt(real_0) = v0 & real_$lesseq(real_0, v0) = 0)
% 8.72/1.99 |
% 8.72/1.99 | GROUND_INST: instantiating (sqrt_square) with real_0, simplifying with (4)
% 8.72/1.99 | gives:
% 8.72/1.99 | (10) ? [v0: $real] : (sqrt(real_0) = v0 & sqr(v0) = real_0)
% 8.72/1.99 |
% 8.72/1.99 | DELTA: instantiating (10) with fresh symbol all_25_0 gives:
% 8.72/1.99 | (11) sqrt(real_0) = all_25_0 & sqr(all_25_0) = real_0
% 8.72/1.99 |
% 9.12/1.99 | ALPHA: (11) implies:
% 9.12/1.99 | (12) sqrt(real_0) = all_25_0
% 9.12/1.99 |
% 9.12/1.99 | DELTA: instantiating (9) with fresh symbol all_27_0 gives:
% 9.12/1.99 | (13) sqrt(real_0) = all_27_0 & real_$lesseq(real_0, all_27_0) = 0
% 9.12/1.99 |
% 9.12/1.99 | ALPHA: (13) implies:
% 9.12/1.99 | (14) sqrt(real_0) = all_27_0
% 9.12/1.99 |
% 9.12/1.99 | DELTA: instantiating (8) with fresh symbol all_31_0 gives:
% 9.12/2.00 | (15) sqrt(all_31_0) = real_0 & real_$product(real_0, real_0) = all_31_0
% 9.12/2.00 |
% 9.12/2.00 | ALPHA: (15) implies:
% 9.12/2.00 | (16) real_$product(real_0, real_0) = all_31_0
% 9.12/2.00 | (17) sqrt(all_31_0) = real_0
% 9.12/2.00 |
% 9.12/2.00 | GROUND_INST: instantiating (2) with real_0, all_31_0, real_0, real_0,
% 9.12/2.00 | simplifying with (3), (16) gives:
% 9.12/2.00 | (18) all_31_0 = real_0
% 9.12/2.00 |
% 9.12/2.00 | GROUND_INST: instantiating (1) with all_11_0, all_27_0, real_0, simplifying
% 9.12/2.00 | with (7), (14) gives:
% 9.12/2.00 | (19) all_27_0 = all_11_0
% 9.12/2.00 |
% 9.12/2.00 | GROUND_INST: instantiating (1) with all_25_0, all_27_0, real_0, simplifying
% 9.12/2.00 | with (12), (14) gives:
% 9.12/2.00 | (20) all_27_0 = all_25_0
% 9.12/2.00 |
% 9.12/2.00 | COMBINE_EQS: (19), (20) imply:
% 9.12/2.00 | (21) all_25_0 = all_11_0
% 9.12/2.00 |
% 9.12/2.00 | SIMP: (21) implies:
% 9.12/2.00 | (22) all_25_0 = all_11_0
% 9.12/2.00 |
% 9.12/2.00 | REDUCE: (17), (18) imply:
% 9.12/2.00 | (23) sqrt(real_0) = real_0
% 9.12/2.00 |
% 9.12/2.00 | GROUND_INST: instantiating (1) with all_11_0, real_0, real_0, simplifying with
% 9.12/2.00 | (7), (23) gives:
% 9.12/2.00 | (24) all_11_0 = real_0
% 9.12/2.00 |
% 9.12/2.00 | REDUCE: (6), (24) imply:
% 9.12/2.00 | (25) $false
% 9.12/2.00 |
% 9.12/2.00 | CLOSE: (25) is inconsistent.
% 9.12/2.00 |
% 9.12/2.00 End of proof
% 9.12/2.00 % SZS output end Proof for theBenchmark
% 9.12/2.00
% 9.12/2.00 1348ms
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