TSTP Solution File: ARI297_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI297_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 : n008.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 17:47:37 EDT 2023
% Result : Theorem 10.42s 2.43s
% Output : Proof 19.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ARI297_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.09/0.33 % Computer : n008.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8042.1875MB
% 0.09/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.33 % CPULimit : 300
% 0.09/0.33 % WCLimit : 300
% 0.09/0.33 % DateTime : Tue Aug 29 18:17:17 EDT 2023
% 0.09/0.33 % CPUTime :
% 0.14/0.58 ________ _____
% 0.14/0.58 ___ __ \_________(_)________________________________
% 0.14/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.14/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.14/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.14/0.58
% 0.14/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.58 (2023-06-19)
% 0.14/0.58
% 0.14/0.58 (c) Philipp Rümmer, 2009-2023
% 0.14/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.58 Amanda Stjerna.
% 0.14/0.58 Free software under BSD-3-Clause.
% 0.14/0.58
% 0.14/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.58
% 0.14/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.60 Running up to 7 provers in parallel.
% 0.14/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.14/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.13/0.89 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.13/0.89 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.13/0.89 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.13/0.89 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.13/0.89 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.13/0.89 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.13/0.89 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.08/1.03 Prover 4: Preprocessing ...
% 2.08/1.04 Prover 1: Preprocessing ...
% 2.43/1.10 Prover 6: Preprocessing ...
% 2.43/1.10 Prover 0: Preprocessing ...
% 4.47/1.39 Prover 5: Preprocessing ...
% 4.92/1.40 Prover 3: Preprocessing ...
% 4.92/1.42 Prover 2: Preprocessing ...
% 8.66/1.93 Prover 1: Constructing countermodel ...
% 8.66/1.93 Prover 6: Constructing countermodel ...
% 8.89/1.96 Prover 4: Constructing countermodel ...
% 8.89/2.02 Prover 0: Proving ...
% 10.42/2.43 Prover 6: proved (1811ms)
% 10.42/2.43
% 10.42/2.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.42/2.43
% 11.27/2.45 Prover 0: stopped
% 11.27/2.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.27/2.46 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 11.27/2.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.27/2.47 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 11.27/2.48 Prover 2: stopped
% 11.27/2.48 Prover 8: Preprocessing ...
% 12.68/2.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.68/2.50 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation
% 13.43/2.59 Prover 7: Preprocessing ...
% 13.43/2.61 Prover 10: Preprocessing ...
% 13.87/2.71 Prover 1: Found proof (size 9)
% 13.87/2.71 Prover 1: proved (2106ms)
% 13.87/2.72 Prover 4: stopped
% 14.53/2.77 Prover 8: Warning: ignoring some quantifiers
% 15.01/2.80 Prover 8: Constructing countermodel ...
% 15.01/2.82 Prover 8: stopped
% 15.91/2.97 Prover 7: stopped
% 15.91/3.02 Prover 10: stopped
% 17.95/3.31 Prover 3: Constructing countermodel ...
% 17.95/3.32 Prover 3: stopped
% 19.34/3.62 Prover 5: Proving ...
% 19.34/3.62 Prover 5: stopped
% 19.34/3.62
% 19.34/3.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.34/3.62
% 19.34/3.63 % SZS output start Proof for theBenchmark
% 19.34/3.63 Assumptions after simplification:
% 19.34/3.63 ---------------------------------
% 19.34/3.63
% 19.34/3.63 (rat_product_problem_14)
% 19.70/3.67 ? [v0: $rat] : ( ~ (v0 = rat_5/8) & rat_$product(v0, rat_2/5) = rat_1/4)
% 19.70/3.67
% 19.70/3.67 (input)
% 19.70/3.71 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_5/8) & ~
% 19.70/3.71 (rat_very_large = rat_1/4) & ~ (rat_very_large = rat_2/5) & ~
% 19.70/3.71 (rat_very_large = rat_0) & ~ (rat_very_small = rat_5/8) & ~ (rat_very_small
% 19.70/3.71 = rat_1/4) & ~ (rat_very_small = rat_2/5) & ~ (rat_very_small = rat_0) &
% 19.70/3.71 ~ (rat_5/8 = rat_1/4) & ~ (rat_5/8 = rat_2/5) & ~ (rat_5/8 = rat_0) & ~
% 19.70/3.71 (rat_1/4 = rat_2/5) & ~ (rat_1/4 = rat_0) & ~ (rat_2/5 = rat_0) &
% 19.70/3.71 rat_$is_int(rat_5/8) = 1 & rat_$is_int(rat_1/4) = 1 & rat_$is_int(rat_2/5) = 1
% 19.70/3.71 & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_5/8) = 0 & rat_$is_rat(rat_1/4) = 0
% 19.70/3.71 & rat_$is_rat(rat_2/5) = 0 & rat_$is_rat(rat_0) = 0 & rat_$floor(rat_5/8) =
% 19.70/3.71 rat_0 & rat_$floor(rat_1/4) = rat_0 & rat_$floor(rat_2/5) = rat_0 &
% 19.70/3.71 rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = rat_0 &
% 19.70/3.71 rat_$truncate(rat_5/8) = rat_0 & rat_$truncate(rat_1/4) = rat_0 &
% 19.70/3.71 rat_$truncate(rat_2/5) = rat_0 & rat_$truncate(rat_0) = rat_0 &
% 19.70/3.71 rat_$round(rat_1/4) = rat_0 & rat_$round(rat_2/5) = rat_0 & rat_$round(rat_0)
% 19.70/3.71 = rat_0 & rat_$to_int(rat_5/8) = 0 & rat_$to_int(rat_1/4) = 0 &
% 19.70/3.71 rat_$to_int(rat_2/5) = 0 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_5/8) =
% 19.70/3.71 rat_5/8 & rat_$to_rat(rat_1/4) = rat_1/4 & rat_$to_rat(rat_2/5) = rat_2/5 &
% 19.70/3.71 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_5/8) = real_5/8 &
% 19.70/3.71 rat_$to_real(rat_1/4) = real_1/4 & rat_$to_real(rat_2/5) = real_2/5 &
% 19.70/3.71 rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_1/4,
% 19.70/3.71 rat_5/8) = rat_2/5 & rat_$quotient(rat_1/4, rat_2/5) = rat_5/8 &
% 19.70/3.71 rat_$quotient(rat_0, rat_5/8) = rat_0 & rat_$quotient(rat_0, rat_1/4) = rat_0
% 19.70/3.71 & rat_$quotient(rat_0, rat_2/5) = rat_0 & rat_$difference(rat_5/8, rat_5/8) =
% 19.70/3.71 rat_0 & rat_$difference(rat_5/8, rat_0) = rat_5/8 & rat_$difference(rat_1/4,
% 19.70/3.71 rat_1/4) = rat_0 & rat_$difference(rat_1/4, rat_0) = rat_1/4 &
% 19.70/3.71 rat_$difference(rat_2/5, rat_2/5) = rat_0 & rat_$difference(rat_2/5, rat_0) =
% 19.70/3.71 rat_2/5 & rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 &
% 19.70/3.71 rat_$sum(rat_5/8, rat_0) = rat_5/8 & rat_$sum(rat_1/4, rat_0) = rat_1/4 &
% 19.70/3.71 rat_$sum(rat_2/5, rat_0) = rat_2/5 & rat_$sum(rat_0, rat_5/8) = rat_5/8 &
% 19.70/3.71 rat_$sum(rat_0, rat_1/4) = rat_1/4 & rat_$sum(rat_0, rat_2/5) = rat_2/5 &
% 19.70/3.71 rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small,
% 19.70/3.71 rat_very_large) = 1 & rat_$greatereq(rat_5/8, rat_5/8) = 0 &
% 19.70/3.71 rat_$greatereq(rat_5/8, rat_1/4) = 0 & rat_$greatereq(rat_5/8, rat_2/5) = 0 &
% 19.70/3.71 rat_$greatereq(rat_5/8, rat_0) = 0 & rat_$greatereq(rat_1/4, rat_5/8) = 1 &
% 19.70/3.71 rat_$greatereq(rat_1/4, rat_1/4) = 0 & rat_$greatereq(rat_1/4, rat_2/5) = 1 &
% 19.70/3.71 rat_$greatereq(rat_1/4, rat_0) = 0 & rat_$greatereq(rat_2/5, rat_5/8) = 1 &
% 19.70/3.71 rat_$greatereq(rat_2/5, rat_1/4) = 0 & rat_$greatereq(rat_2/5, rat_2/5) = 0 &
% 19.70/3.71 rat_$greatereq(rat_2/5, rat_0) = 0 & rat_$greatereq(rat_0, rat_5/8) = 1 &
% 19.70/3.71 rat_$greatereq(rat_0, rat_1/4) = 1 & rat_$greatereq(rat_0, rat_2/5) = 1 &
% 19.70/3.71 rat_$greatereq(rat_0, rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large)
% 19.70/3.71 = 0 & rat_$lesseq(rat_5/8, rat_5/8) = 0 & rat_$lesseq(rat_5/8, rat_1/4) = 1 &
% 19.70/3.71 rat_$lesseq(rat_5/8, rat_2/5) = 1 & rat_$lesseq(rat_5/8, rat_0) = 1 &
% 19.70/3.71 rat_$lesseq(rat_1/4, rat_5/8) = 0 & rat_$lesseq(rat_1/4, rat_1/4) = 0 &
% 19.70/3.71 rat_$lesseq(rat_1/4, rat_2/5) = 0 & rat_$lesseq(rat_1/4, rat_0) = 1 &
% 19.70/3.71 rat_$lesseq(rat_2/5, rat_5/8) = 0 & rat_$lesseq(rat_2/5, rat_1/4) = 1 &
% 19.70/3.71 rat_$lesseq(rat_2/5, rat_2/5) = 0 & rat_$lesseq(rat_2/5, rat_0) = 1 &
% 19.70/3.71 rat_$lesseq(rat_0, rat_5/8) = 0 & rat_$lesseq(rat_0, rat_1/4) = 0 &
% 19.70/3.71 rat_$lesseq(rat_0, rat_2/5) = 0 & rat_$lesseq(rat_0, rat_0) = 0 &
% 19.70/3.71 rat_$greater(rat_very_large, rat_5/8) = 0 & rat_$greater(rat_very_large,
% 19.70/3.71 rat_1/4) = 0 & rat_$greater(rat_very_large, rat_2/5) = 0 &
% 19.70/3.71 rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small,
% 19.70/3.71 rat_very_large) = 1 & rat_$greater(rat_5/8, rat_very_small) = 0 &
% 19.70/3.71 rat_$greater(rat_5/8, rat_5/8) = 1 & rat_$greater(rat_5/8, rat_1/4) = 0 &
% 19.70/3.71 rat_$greater(rat_5/8, rat_2/5) = 0 & rat_$greater(rat_5/8, rat_0) = 0 &
% 19.70/3.71 rat_$greater(rat_1/4, rat_very_small) = 0 & rat_$greater(rat_1/4, rat_5/8) = 1
% 19.70/3.71 & rat_$greater(rat_1/4, rat_1/4) = 1 & rat_$greater(rat_1/4, rat_2/5) = 1 &
% 19.70/3.71 rat_$greater(rat_1/4, rat_0) = 0 & rat_$greater(rat_2/5, rat_very_small) = 0 &
% 19.70/3.71 rat_$greater(rat_2/5, rat_5/8) = 1 & rat_$greater(rat_2/5, rat_1/4) = 0 &
% 19.70/3.71 rat_$greater(rat_2/5, rat_2/5) = 1 & rat_$greater(rat_2/5, rat_0) = 0 &
% 19.70/3.71 rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_5/8) = 1 &
% 19.70/3.71 rat_$greater(rat_0, rat_1/4) = 1 & rat_$greater(rat_0, rat_2/5) = 1 &
% 19.70/3.71 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0
% 19.70/3.71 & rat_$less(rat_very_small, rat_5/8) = 0 & rat_$less(rat_very_small, rat_1/4)
% 19.70/3.71 = 0 & rat_$less(rat_very_small, rat_2/5) = 0 & rat_$less(rat_very_small,
% 19.70/3.72 rat_0) = 0 & rat_$less(rat_5/8, rat_very_large) = 0 & rat_$less(rat_5/8,
% 19.70/3.72 rat_5/8) = 1 & rat_$less(rat_5/8, rat_1/4) = 1 & rat_$less(rat_5/8, rat_2/5)
% 19.70/3.72 = 1 & rat_$less(rat_5/8, rat_0) = 1 & rat_$less(rat_1/4, rat_very_large) = 0 &
% 19.70/3.72 rat_$less(rat_1/4, rat_5/8) = 0 & rat_$less(rat_1/4, rat_1/4) = 1 &
% 19.70/3.72 rat_$less(rat_1/4, rat_2/5) = 0 & rat_$less(rat_1/4, rat_0) = 1 &
% 19.70/3.72 rat_$less(rat_2/5, rat_very_large) = 0 & rat_$less(rat_2/5, rat_5/8) = 0 &
% 19.70/3.72 rat_$less(rat_2/5, rat_1/4) = 1 & rat_$less(rat_2/5, rat_2/5) = 1 &
% 19.70/3.72 rat_$less(rat_2/5, rat_0) = 1 & rat_$less(rat_0, rat_very_large) = 0 &
% 19.70/3.72 rat_$less(rat_0, rat_5/8) = 0 & rat_$less(rat_0, rat_1/4) = 0 &
% 19.70/3.72 rat_$less(rat_0, rat_2/5) = 0 & rat_$less(rat_0, rat_0) = 1 &
% 19.70/3.72 rat_$product(rat_5/8, rat_2/5) = rat_1/4 & rat_$product(rat_5/8, rat_0) =
% 19.70/3.72 rat_0 & rat_$product(rat_1/4, rat_0) = rat_0 & rat_$product(rat_2/5, rat_5/8)
% 19.70/3.72 = rat_1/4 & rat_$product(rat_2/5, rat_0) = rat_0 & rat_$product(rat_0,
% 19.70/3.72 rat_5/8) = rat_0 & rat_$product(rat_0, rat_1/4) = rat_0 &
% 19.70/3.72 rat_$product(rat_0, rat_2/5) = rat_0 & rat_$product(rat_0, rat_0) = rat_0 & !
% 19.70/3.72 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : (
% 19.70/3.72 ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] :
% 19.70/3.72 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1:
% 19.70/3.72 $rat] : ! [v2: $rat] : ! [v3: $rat] : (v3 = v1 | v0 = rat_0 | ~
% 19.70/3.72 (rat_$quotient(v2, v0) = v3) | ~ (rat_$product(v1, v0) = v2)) & ! [v0:
% 19.70/3.72 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~
% 19.70/3.72 (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : (
% 19.70/3.72 ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] :
% 19.70/3.72 ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~
% 19.70/3.72 (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) =
% 19.70/3.72 v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~
% 19.70/3.72 (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1,
% 19.70/3.72 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v2 = rat_0 |
% 19.70/3.72 ~ (rat_$uminus(v0) = v1) | ~ (rat_$sum(v0, v1) = v2)) & ! [v0: $rat] : !
% 19.70/3.72 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ?
% 19.70/3.72 [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : !
% 19.70/3.72 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ( ~ (v1
% 19.70/3.72 = v0) & ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3))) & !
% 19.70/3.72 [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greater(v0, v1)
% 19.70/3.72 = v2) | ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0:
% 19.70/3.72 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) |
% 19.70/3.72 rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 19.70/3.72 (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) =
% 19.70/3.72 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0,
% 19.70/3.72 v1) = v2) | rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] :
% 19.70/3.72 (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1: $rat] :
% 19.70/3.72 (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & ! [v0:
% 19.70/3.72 $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) &
% 19.70/3.72 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) |
% 19.70/3.72 rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 19.70/3.72 (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] : (v0 =
% 19.70/3.72 rat_0 | ~ (rat_$uminus(v0) = v0))
% 19.70/3.72
% 19.70/3.72 Those formulas are unsatisfiable:
% 19.70/3.72 ---------------------------------
% 19.70/3.72
% 19.70/3.72 Begin of proof
% 19.70/3.72 |
% 19.70/3.72 | ALPHA: (input) implies:
% 19.70/3.73 | (1) ~ (rat_2/5 = rat_0)
% 19.70/3.73 | (2) rat_$quotient(rat_1/4, rat_2/5) = rat_5/8
% 19.70/3.73 | (3) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v3 =
% 19.70/3.73 | v1 | v0 = rat_0 | ~ (rat_$quotient(v2, v0) = v3) | ~
% 19.70/3.73 | (rat_$product(v1, v0) = v2))
% 19.70/3.73 |
% 19.70/3.73 | DELTA: instantiating (rat_product_problem_14) with fresh symbol all_5_0 gives:
% 19.70/3.73 | (4) ~ (all_5_0 = rat_5/8) & rat_$product(all_5_0, rat_2/5) = rat_1/4
% 19.70/3.73 |
% 19.70/3.73 | ALPHA: (4) implies:
% 19.70/3.73 | (5) ~ (all_5_0 = rat_5/8)
% 19.70/3.73 | (6) rat_$product(all_5_0, rat_2/5) = rat_1/4
% 19.70/3.73 |
% 19.70/3.73 | GROUND_INST: instantiating (3) with rat_2/5, all_5_0, rat_1/4, rat_5/8,
% 19.70/3.73 | simplifying with (2), (6) gives:
% 19.70/3.73 | (7) all_5_0 = rat_5/8 | rat_2/5 = rat_0
% 19.70/3.73 |
% 19.70/3.73 | BETA: splitting (7) gives:
% 19.70/3.73 |
% 19.70/3.73 | Case 1:
% 19.70/3.73 | |
% 19.70/3.73 | | (8) rat_2/5 = rat_0
% 19.70/3.73 | |
% 19.70/3.73 | | REDUCE: (1), (8) imply:
% 19.70/3.73 | | (9) $false
% 19.70/3.74 | |
% 19.70/3.74 | | CLOSE: (9) is inconsistent.
% 19.70/3.74 | |
% 19.70/3.74 | Case 2:
% 19.70/3.74 | |
% 19.70/3.74 | | (10) all_5_0 = rat_5/8
% 19.70/3.74 | |
% 19.70/3.74 | | REDUCE: (5), (10) imply:
% 19.70/3.74 | | (11) $false
% 19.70/3.74 | |
% 19.70/3.74 | | CLOSE: (11) is inconsistent.
% 19.70/3.74 | |
% 19.70/3.74 | End of split
% 19.70/3.74 |
% 19.70/3.74 End of proof
% 19.70/3.74 % SZS output end Proof for theBenchmark
% 19.70/3.74
% 19.70/3.74 3153ms
%------------------------------------------------------------------------------