TSTP Solution File: ARI449_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI449_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 : n022.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 17:48:05 EDT 2023
% Result : Theorem 10.69s 2.15s
% Output : Proof 15.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ARI449_1 : TPTP v8.1.2. Released v5.0.0.
% 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n022.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 18:07:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.70/0.67 ________ _____
% 0.70/0.67 ___ __ \_________(_)________________________________
% 0.70/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.70/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.70/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.70/0.67
% 0.70/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.70/0.67 (2023-06-19)
% 0.70/0.67
% 0.70/0.67 (c) Philipp Rümmer, 2009-2023
% 0.70/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.70/0.67 Amanda Stjerna.
% 0.70/0.67 Free software under BSD-3-Clause.
% 0.70/0.67
% 0.70/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.70/0.67
% 0.70/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.68 Running up to 7 provers in parallel.
% 0.70/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.70/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.70/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.70/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.70/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.70/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.70/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.69/0.94 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.69/0.94 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.69/0.94 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.69/0.94 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.69/0.94 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.69/0.94 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.69/0.94 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 2.31/1.06 Prover 4: Preprocessing ...
% 2.31/1.06 Prover 1: Preprocessing ...
% 2.68/1.13 Prover 0: Preprocessing ...
% 2.68/1.13 Prover 6: Preprocessing ...
% 3.94/1.28 Prover 2: Preprocessing ...
% 3.94/1.29 Prover 3: Preprocessing ...
% 3.94/1.30 Prover 5: Preprocessing ...
% 7.18/1.69 Prover 4: Constructing countermodel ...
% 7.18/1.69 Prover 6: Constructing countermodel ...
% 7.18/1.70 Prover 1: Constructing countermodel ...
% 7.18/1.76 Prover 0: Proving ...
% 10.51/2.14 Prover 6: proved (1448ms)
% 10.51/2.14
% 10.69/2.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.69/2.15
% 10.69/2.15 Prover 2: stopped
% 10.69/2.15 Prover 0: stopped
% 10.69/2.16 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.69/2.16 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.69/2.16 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 10.69/2.16 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 10.69/2.16 Prover 1: Found proof (size 10)
% 10.69/2.16 Prover 1: proved (1468ms)
% 10.69/2.16 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.69/2.16 Prover 4: stopped
% 10.69/2.16 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 10.69/2.17 Prover 8: Preprocessing ...
% 10.69/2.22 Prover 7: Preprocessing ...
% 11.30/2.23 Prover 10: Preprocessing ...
% 11.30/2.28 Prover 8: Warning: ignoring some quantifiers
% 11.81/2.30 Prover 8: Constructing countermodel ...
% 11.81/2.32 Prover 8: stopped
% 14.62/2.69 Prover 3: Constructing countermodel ...
% 14.62/2.70 Prover 3: stopped
% 15.11/2.74 Prover 5: Proving ...
% 15.11/2.75 Prover 5: stopped
% 15.11/2.75 Prover 10: stopped
% 15.11/2.75 Prover 7: stopped
% 15.11/2.75
% 15.11/2.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.11/2.75
% 15.11/2.76 % SZS output start Proof for theBenchmark
% 15.11/2.76 Assumptions after simplification:
% 15.11/2.76 ---------------------------------
% 15.11/2.76
% 15.11/2.76 (real_product_problem_14)
% 15.11/2.78 ? [v0: $real] : ( ~ (v0 = real_4) & real_$product(real_29/4, v0) = real_29)
% 15.11/2.78
% 15.11/2.78 (input)
% 15.11/2.80 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_4) & ~
% 15.11/2.80 (real_very_large = real_29) & ~ (real_very_large = real_29/4) & ~
% 15.11/2.80 (real_very_large = real_0) & ~ (real_very_small = real_4) & ~
% 15.11/2.80 (real_very_small = real_29) & ~ (real_very_small = real_29/4) & ~
% 15.11/2.80 (real_very_small = real_0) & ~ (real_4 = real_29) & ~ (real_4 = real_29/4) &
% 15.11/2.80 ~ (real_4 = real_0) & ~ (real_29 = real_29/4) & ~ (real_29 = real_0) & ~
% 15.11/2.80 (real_29/4 = real_0) & real_$is_int(real_4) = 0 & real_$is_int(real_29) = 0 &
% 15.11/2.80 real_$is_int(real_29/4) = 1 & real_$is_int(real_0) = 0 & real_$is_rat(real_4)
% 15.11/2.80 = 0 & real_$is_rat(real_29) = 0 & real_$is_rat(real_29/4) = 0 &
% 15.11/2.80 real_$is_rat(real_0) = 0 & real_$floor(real_4) = real_4 & real_$floor(real_29)
% 15.11/2.80 = real_29 & real_$floor(real_0) = real_0 & real_$ceiling(real_4) = real_4 &
% 15.11/2.80 real_$ceiling(real_29) = real_29 & real_$ceiling(real_0) = real_0 &
% 15.11/2.80 real_$truncate(real_4) = real_4 & real_$truncate(real_29) = real_29 &
% 15.11/2.80 real_$truncate(real_0) = real_0 & real_$round(real_4) = real_4 &
% 15.11/2.80 real_$round(real_29) = real_29 & real_$round(real_0) = real_0 &
% 15.11/2.80 real_$to_int(real_4) = 4 & real_$to_int(real_29) = 29 &
% 15.11/2.80 real_$to_int(real_29/4) = 7 & real_$to_int(real_0) = 0 & real_$to_rat(real_4)
% 15.11/2.80 = rat_4 & real_$to_rat(real_29) = rat_29 & real_$to_rat(real_29/4) = rat_29/4
% 15.11/2.80 & real_$to_rat(real_0) = rat_0 & real_$to_real(real_4) = real_4 &
% 15.11/2.80 real_$to_real(real_29) = real_29 & real_$to_real(real_29/4) = real_29/4 &
% 15.11/2.80 real_$to_real(real_0) = real_0 & int_$to_real(29) = real_29 & int_$to_real(4)
% 15.11/2.80 = real_4 & int_$to_real(0) = real_0 & real_$quotient(real_29, real_4) =
% 15.11/2.80 real_29/4 & real_$quotient(real_29, real_29/4) = real_4 &
% 15.11/2.80 real_$quotient(real_0, real_4) = real_0 & real_$quotient(real_0, real_29) =
% 15.11/2.80 real_0 & real_$quotient(real_0, real_29/4) = real_0 & real_$difference(real_4,
% 15.11/2.80 real_4) = real_0 & real_$difference(real_4, real_0) = real_4 &
% 15.11/2.80 real_$difference(real_29, real_29) = real_0 & real_$difference(real_29,
% 15.11/2.80 real_0) = real_29 & real_$difference(real_29/4, real_29/4) = real_0 &
% 15.11/2.80 real_$difference(real_29/4, real_0) = real_29/4 & real_$difference(real_0,
% 15.11/2.80 real_0) = real_0 & real_$uminus(real_0) = real_0 & real_$sum(real_4, real_0)
% 15.11/2.81 = real_4 & real_$sum(real_29, real_0) = real_29 & real_$sum(real_29/4, real_0)
% 15.11/2.81 = real_29/4 & real_$sum(real_0, real_4) = real_4 & real_$sum(real_0, real_29)
% 15.11/2.81 = real_29 & real_$sum(real_0, real_29/4) = real_29/4 & real_$sum(real_0,
% 15.11/2.81 real_0) = real_0 & real_$greatereq(real_very_small, real_very_large) = 1 &
% 15.11/2.81 real_$greatereq(real_4, real_4) = 0 & real_$greatereq(real_4, real_29) = 1 &
% 15.11/2.81 real_$greatereq(real_4, real_29/4) = 1 & real_$greatereq(real_4, real_0) = 0 &
% 15.11/2.81 real_$greatereq(real_29, real_4) = 0 & real_$greatereq(real_29, real_29) = 0 &
% 15.11/2.81 real_$greatereq(real_29, real_29/4) = 0 & real_$greatereq(real_29, real_0) = 0
% 15.11/2.81 & real_$greatereq(real_29/4, real_4) = 0 & real_$greatereq(real_29/4, real_29)
% 15.11/2.81 = 1 & real_$greatereq(real_29/4, real_29/4) = 0 & real_$greatereq(real_29/4,
% 15.11/2.81 real_0) = 0 & real_$greatereq(real_0, real_4) = 1 & real_$greatereq(real_0,
% 15.11/2.81 real_29) = 1 & real_$greatereq(real_0, real_29/4) = 1 &
% 15.11/2.81 real_$greatereq(real_0, real_0) = 0 & real_$lesseq(real_very_small,
% 15.11/2.81 real_very_large) = 0 & real_$lesseq(real_4, real_4) = 0 &
% 15.11/2.81 real_$lesseq(real_4, real_29) = 0 & real_$lesseq(real_4, real_29/4) = 0 &
% 15.11/2.81 real_$lesseq(real_4, real_0) = 1 & real_$lesseq(real_29, real_4) = 1 &
% 15.11/2.81 real_$lesseq(real_29, real_29) = 0 & real_$lesseq(real_29, real_29/4) = 1 &
% 15.11/2.81 real_$lesseq(real_29, real_0) = 1 & real_$lesseq(real_29/4, real_4) = 1 &
% 15.11/2.81 real_$lesseq(real_29/4, real_29) = 0 & real_$lesseq(real_29/4, real_29/4) = 0
% 15.11/2.81 & real_$lesseq(real_29/4, real_0) = 1 & real_$lesseq(real_0, real_4) = 0 &
% 15.11/2.81 real_$lesseq(real_0, real_29) = 0 & real_$lesseq(real_0, real_29/4) = 0 &
% 15.11/2.81 real_$lesseq(real_0, real_0) = 0 & real_$greater(real_very_large, real_4) = 0
% 15.11/2.81 & real_$greater(real_very_large, real_29) = 0 & real_$greater(real_very_large,
% 15.11/2.81 real_29/4) = 0 & real_$greater(real_very_large, real_0) = 0 &
% 15.11/2.81 real_$greater(real_very_small, real_very_large) = 1 & real_$greater(real_4,
% 15.11/2.81 real_very_small) = 0 & real_$greater(real_4, real_4) = 1 &
% 15.11/2.81 real_$greater(real_4, real_29) = 1 & real_$greater(real_4, real_29/4) = 1 &
% 15.11/2.81 real_$greater(real_4, real_0) = 0 & real_$greater(real_29, real_very_small) =
% 15.11/2.81 0 & real_$greater(real_29, real_4) = 0 & real_$greater(real_29, real_29) = 1 &
% 15.11/2.81 real_$greater(real_29, real_29/4) = 0 & real_$greater(real_29, real_0) = 0 &
% 15.11/2.81 real_$greater(real_29/4, real_very_small) = 0 & real_$greater(real_29/4,
% 15.11/2.81 real_4) = 0 & real_$greater(real_29/4, real_29) = 1 &
% 15.11/2.81 real_$greater(real_29/4, real_29/4) = 1 & real_$greater(real_29/4, real_0) = 0
% 15.11/2.81 & real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0, real_4) =
% 15.11/2.81 1 & real_$greater(real_0, real_29) = 1 & real_$greater(real_0, real_29/4) = 1
% 15.11/2.81 & real_$greater(real_0, real_0) = 1 & real_$less(real_very_small,
% 15.11/2.81 real_very_large) = 0 & real_$less(real_very_small, real_4) = 0 &
% 15.11/2.81 real_$less(real_very_small, real_29) = 0 & real_$less(real_very_small,
% 15.11/2.81 real_29/4) = 0 & real_$less(real_very_small, real_0) = 0 &
% 15.11/2.81 real_$less(real_4, real_very_large) = 0 & real_$less(real_4, real_4) = 1 &
% 15.11/2.81 real_$less(real_4, real_29) = 0 & real_$less(real_4, real_29/4) = 0 &
% 15.11/2.81 real_$less(real_4, real_0) = 1 & real_$less(real_29, real_very_large) = 0 &
% 15.11/2.81 real_$less(real_29, real_4) = 1 & real_$less(real_29, real_29) = 1 &
% 15.11/2.81 real_$less(real_29, real_29/4) = 1 & real_$less(real_29, real_0) = 1 &
% 15.11/2.81 real_$less(real_29/4, real_very_large) = 0 & real_$less(real_29/4, real_4) = 1
% 15.11/2.81 & real_$less(real_29/4, real_29) = 0 & real_$less(real_29/4, real_29/4) = 1 &
% 15.11/2.81 real_$less(real_29/4, real_0) = 1 & real_$less(real_0, real_very_large) = 0 &
% 15.11/2.81 real_$less(real_0, real_4) = 0 & real_$less(real_0, real_29) = 0 &
% 15.11/2.81 real_$less(real_0, real_29/4) = 0 & real_$less(real_0, real_0) = 1 &
% 15.11/2.81 real_$product(real_4, real_29/4) = real_29 & real_$product(real_4, real_0) =
% 15.11/2.81 real_0 & real_$product(real_29, real_0) = real_0 & real_$product(real_29/4,
% 15.11/2.81 real_4) = real_29 & real_$product(real_29/4, real_0) = real_0 &
% 15.11/2.81 real_$product(real_0, real_4) = real_0 & real_$product(real_0, real_29) =
% 15.11/2.81 real_0 & real_$product(real_0, real_29/4) = real_0 & real_$product(real_0,
% 15.11/2.81 real_0) = real_0 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : !
% 15.11/2.81 [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~
% 15.11/2.81 (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 &
% 15.11/2.81 real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 15.11/2.81 $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~ (real_$quotient(v2,
% 15.11/2.81 v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0: $real] : ! [v1:
% 15.11/2.81 $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v0)
% 15.11/2.81 = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) &
% 15.11/2.81 real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 15.11/2.81 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, v0) = 0) | ~
% 15.11/2.81 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2, v1)
% 15.11/2.81 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real]
% 15.11/2.81 : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) |
% 15.11/2.81 real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 15.11/2.81 $real] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) =
% 15.11/2.81 v2)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~
% 15.11/2.81 (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 15.11/2.81 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 15.11/2.81 int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3:
% 15.11/2.81 int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & ! [v0: $real] : !
% 15.11/2.81 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ?
% 15.11/2.81 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : !
% 15.11/2.81 [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1,
% 15.11/2.81 v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~
% 15.11/2.81 (real_$lesseq(v2, v1) = 0) | ~ (real_$less(v1, v0) = 0) | real_$less(v2,
% 15.11/2.81 v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~
% 15.11/2.81 (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2) & ! [v0: $real]
% 15.11/2.81 : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! [v0:
% 15.11/2.81 $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) |
% 15.11/2.81 real_$less(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 15.11/2.81 (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1:
% 15.11/2.81 $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & !
% 15.11/2.81 [v0: $real] : ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) |
% 15.11/2.81 real_$less(v1, v0) = 0) & ! [v0: $real] : (v0 = real_0 | ~
% 15.11/2.81 (real_$uminus(v0) = v0))
% 15.11/2.81
% 15.11/2.81 Those formulas are unsatisfiable:
% 15.11/2.81 ---------------------------------
% 15.11/2.81
% 15.11/2.81 Begin of proof
% 15.11/2.81 |
% 15.11/2.81 | ALPHA: (input) implies:
% 15.11/2.81 | (1) ~ (real_29/4 = real_0)
% 15.11/2.81 | (2) real_$quotient(real_29, real_29/4) = real_4
% 15.11/2.82 | (3) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~
% 15.11/2.82 | (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2)
% 15.11/2.82 | (4) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v3
% 15.11/2.82 | = v1 | v0 = real_0 | ~ (real_$quotient(v2, v0) = v3) | ~
% 15.11/2.82 | (real_$product(v1, v0) = v2))
% 15.11/2.82 |
% 15.11/2.82 | DELTA: instantiating (real_product_problem_14) with fresh symbol all_5_0
% 15.11/2.82 | gives:
% 15.11/2.82 | (5) ~ (all_5_0 = real_4) & real_$product(real_29/4, all_5_0) = real_29
% 15.11/2.82 |
% 15.11/2.82 | ALPHA: (5) implies:
% 15.11/2.82 | (6) ~ (all_5_0 = real_4)
% 15.11/2.82 | (7) real_$product(real_29/4, all_5_0) = real_29
% 15.11/2.82 |
% 15.11/2.82 | GROUND_INST: instantiating (3) with real_29/4, all_5_0, real_29, simplifying
% 15.11/2.82 | with (7) gives:
% 15.11/2.82 | (8) real_$product(all_5_0, real_29/4) = real_29
% 15.11/2.82 |
% 15.11/2.82 | GROUND_INST: instantiating (4) with real_29/4, all_5_0, real_29, real_4,
% 15.11/2.82 | simplifying with (2), (8) gives:
% 15.11/2.82 | (9) all_5_0 = real_4 | real_29/4 = real_0
% 15.11/2.82 |
% 15.11/2.82 | BETA: splitting (9) gives:
% 15.11/2.82 |
% 15.11/2.82 | Case 1:
% 15.11/2.82 | |
% 15.11/2.82 | | (10) real_29/4 = real_0
% 15.11/2.82 | |
% 15.11/2.82 | | REDUCE: (1), (10) imply:
% 15.11/2.82 | | (11) $false
% 15.11/2.82 | |
% 15.11/2.82 | | CLOSE: (11) is inconsistent.
% 15.11/2.82 | |
% 15.11/2.82 | Case 2:
% 15.11/2.82 | |
% 15.11/2.82 | | (12) all_5_0 = real_4
% 15.11/2.82 | |
% 15.11/2.82 | | REDUCE: (6), (12) imply:
% 15.11/2.82 | | (13) $false
% 15.11/2.82 | |
% 15.11/2.82 | | CLOSE: (13) is inconsistent.
% 15.11/2.82 | |
% 15.11/2.82 | End of split
% 15.11/2.82 |
% 15.11/2.82 End of proof
% 15.11/2.82 % SZS output end Proof for theBenchmark
% 15.11/2.82
% 15.11/2.82 2151ms
%------------------------------------------------------------------------------