TSTP Solution File: ARI340_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI340_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 : n032.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 17:47:41 EDT 2023
% Result : Theorem 6.57s 1.47s
% Output : Proof 21.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.08 % Problem : ARI340_1 : TPTP v8.1.2. Released v5.0.0.
% 0.05/0.09 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Tue Aug 29 18:26:16 EDT 2023
% 0.09/0.28 % CPUTime :
% 0.14/0.48 ________ _____
% 0.14/0.48 ___ __ \_________(_)________________________________
% 0.14/0.48 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.14/0.48 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.14/0.48 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.14/0.48
% 0.14/0.48 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.48 (2023-06-19)
% 0.14/0.48
% 0.14/0.48 (c) Philipp Rümmer, 2009-2023
% 0.14/0.48 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.48 Amanda Stjerna.
% 0.14/0.48 Free software under BSD-3-Clause.
% 0.14/0.48
% 0.14/0.48 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.48
% 0.14/0.48 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.14/0.49 Running up to 7 provers in parallel.
% 0.14/0.50 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.50 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.50 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.50 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.50 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.50 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.14/0.50 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.20/0.71 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.20/0.71 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.20/0.71 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.20/0.71 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.20/0.71 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.20/0.71 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.20/0.71 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.85/0.84 Prover 1: Preprocessing ...
% 1.85/0.84 Prover 4: Preprocessing ...
% 2.24/0.89 Prover 6: Preprocessing ...
% 2.24/0.89 Prover 0: Preprocessing ...
% 4.75/1.24 Prover 2: Preprocessing ...
% 4.75/1.27 Prover 5: Preprocessing ...
% 4.75/1.29 Prover 3: Preprocessing ...
% 6.01/1.42 Prover 6: Constructing countermodel ...
% 6.01/1.43 Prover 0: Constructing countermodel ...
% 6.57/1.45 Prover 1: Constructing countermodel ...
% 6.57/1.46 Prover 6: proved (965ms)
% 6.57/1.46
% 6.57/1.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.57/1.47
% 6.79/1.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.79/1.47 Prover 0: proved (981ms)
% 6.79/1.47
% 6.79/1.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.79/1.47
% 6.79/1.48 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.79/1.48 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.79/1.48 Prover 4: Constructing countermodel ...
% 6.79/1.48 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.79/1.51 Prover 8: Preprocessing ...
% 9.08/1.77 Prover 8: Warning: ignoring some quantifiers
% 9.08/1.78 Prover 7: Preprocessing ...
% 9.08/1.79 Prover 8: Constructing countermodel ...
% 9.08/1.81 Prover 1: Found proof (size 7)
% 9.08/1.81 Prover 1: proved (1316ms)
% 9.08/1.81 Prover 4: stopped
% 9.08/1.82 Prover 8: stopped
% 14.49/2.56 Prover 2: stopped
% 15.09/2.63 Prover 7: stopped
% 20.09/3.61 Prover 5: Constructing countermodel ...
% 20.09/3.61 Prover 5: stopped
% 21.39/3.86 Prover 3: Constructing countermodel ...
% 21.39/3.86 Prover 3: stopped
% 21.39/3.86
% 21.39/3.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.39/3.86
% 21.39/3.86 % SZS output start Proof for theBenchmark
% 21.39/3.87 Assumptions after simplification:
% 21.39/3.87 ---------------------------------
% 21.39/3.87
% 21.39/3.87 (rat_combined_problem_6)
% 21.85/3.90 ? [v0: int] : ( ~ (v0 = 0) & rat_$less(rat_15/2, rat_77/10) = v0)
% 21.85/3.90
% 21.85/3.91 (input)
% 21.95/3.94 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_15/2) & ~
% 21.95/3.94 (rat_very_large = rat_77/10) & ~ (rat_very_large = rat_24/5) & ~
% 21.95/3.94 (rat_very_large = rat_29/10) & ~ (rat_very_large = rat_0) & ~
% 21.95/3.94 (rat_very_small = rat_15/2) & ~ (rat_very_small = rat_77/10) & ~
% 21.95/3.94 (rat_very_small = rat_24/5) & ~ (rat_very_small = rat_29/10) & ~
% 21.95/3.94 (rat_very_small = rat_0) & ~ (rat_15/2 = rat_77/10) & ~ (rat_15/2 =
% 21.95/3.94 rat_24/5) & ~ (rat_15/2 = rat_29/10) & ~ (rat_15/2 = rat_0) & ~
% 21.95/3.94 (rat_77/10 = rat_24/5) & ~ (rat_77/10 = rat_29/10) & ~ (rat_77/10 = rat_0) &
% 21.95/3.94 ~ (rat_24/5 = rat_29/10) & ~ (rat_24/5 = rat_0) & ~ (rat_29/10 = rat_0) &
% 21.95/3.94 rat_$is_int(rat_15/2) = 1 & rat_$is_int(rat_77/10) = 1 & rat_$is_int(rat_24/5)
% 21.95/3.94 = 1 & rat_$is_int(rat_29/10) = 1 & rat_$is_int(rat_0) = 0 &
% 21.95/3.94 rat_$is_rat(rat_15/2) = 0 & rat_$is_rat(rat_77/10) = 0 & rat_$is_rat(rat_24/5)
% 21.95/3.94 = 0 & rat_$is_rat(rat_29/10) = 0 & rat_$is_rat(rat_0) = 0 & rat_$floor(rat_0)
% 21.95/3.94 = rat_0 & rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_0) = rat_0 &
% 21.95/3.94 rat_$round(rat_0) = rat_0 & rat_$to_int(rat_15/2) = 7 & rat_$to_int(rat_77/10)
% 21.95/3.94 = 7 & rat_$to_int(rat_24/5) = 4 & rat_$to_int(rat_29/10) = 2 &
% 21.95/3.94 rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_15/2) = rat_15/2 &
% 21.95/3.94 rat_$to_rat(rat_77/10) = rat_77/10 & rat_$to_rat(rat_24/5) = rat_24/5 &
% 21.95/3.94 rat_$to_rat(rat_29/10) = rat_29/10 & rat_$to_rat(rat_0) = rat_0 &
% 21.95/3.95 rat_$to_real(rat_15/2) = real_15/2 & rat_$to_real(rat_77/10) = real_77/10 &
% 21.95/3.95 rat_$to_real(rat_24/5) = real_24/5 & rat_$to_real(rat_29/10) = real_29/10 &
% 21.95/3.95 rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_0,
% 21.95/3.95 rat_15/2) = rat_0 & rat_$quotient(rat_0, rat_77/10) = rat_0 &
% 21.95/3.95 rat_$quotient(rat_0, rat_24/5) = rat_0 & rat_$quotient(rat_0, rat_29/10) =
% 21.95/3.95 rat_0 & rat_$product(rat_15/2, rat_0) = rat_0 & rat_$product(rat_77/10, rat_0)
% 21.95/3.95 = rat_0 & rat_$product(rat_24/5, rat_0) = rat_0 & rat_$product(rat_29/10,
% 21.95/3.95 rat_0) = rat_0 & rat_$product(rat_0, rat_15/2) = rat_0 & rat_$product(rat_0,
% 21.95/3.95 rat_77/10) = rat_0 & rat_$product(rat_0, rat_24/5) = rat_0 &
% 21.95/3.95 rat_$product(rat_0, rat_29/10) = rat_0 & rat_$product(rat_0, rat_0) = rat_0 &
% 21.95/3.95 rat_$difference(rat_15/2, rat_15/2) = rat_0 & rat_$difference(rat_15/2, rat_0)
% 21.95/3.95 = rat_15/2 & rat_$difference(rat_77/10, rat_77/10) = rat_0 &
% 21.95/3.95 rat_$difference(rat_77/10, rat_24/5) = rat_29/10 & rat_$difference(rat_77/10,
% 21.95/3.95 rat_29/10) = rat_24/5 & rat_$difference(rat_77/10, rat_0) = rat_77/10 &
% 21.95/3.95 rat_$difference(rat_24/5, rat_24/5) = rat_0 & rat_$difference(rat_24/5, rat_0)
% 21.95/3.95 = rat_24/5 & rat_$difference(rat_29/10, rat_29/10) = rat_0 &
% 21.95/3.95 rat_$difference(rat_29/10, rat_0) = rat_29/10 & rat_$difference(rat_0, rat_0)
% 21.95/3.95 = rat_0 & rat_$uminus(rat_0) = rat_0 & rat_$sum(rat_15/2, rat_0) = rat_15/2 &
% 21.95/3.95 rat_$sum(rat_77/10, rat_0) = rat_77/10 & rat_$sum(rat_24/5, rat_29/10) =
% 21.95/3.95 rat_77/10 & rat_$sum(rat_24/5, rat_0) = rat_24/5 & rat_$sum(rat_29/10,
% 21.95/3.95 rat_24/5) = rat_77/10 & rat_$sum(rat_29/10, rat_0) = rat_29/10 &
% 21.95/3.95 rat_$sum(rat_0, rat_15/2) = rat_15/2 & rat_$sum(rat_0, rat_77/10) = rat_77/10
% 21.95/3.95 & rat_$sum(rat_0, rat_24/5) = rat_24/5 & rat_$sum(rat_0, rat_29/10) =
% 21.95/3.95 rat_29/10 & rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small,
% 21.95/3.95 rat_very_large) = 1 & rat_$greatereq(rat_15/2, rat_15/2) = 0 &
% 21.95/3.95 rat_$greatereq(rat_15/2, rat_77/10) = 1 & rat_$greatereq(rat_15/2, rat_24/5) =
% 21.95/3.95 0 & rat_$greatereq(rat_15/2, rat_29/10) = 0 & rat_$greatereq(rat_15/2, rat_0)
% 21.95/3.95 = 0 & rat_$greatereq(rat_77/10, rat_15/2) = 0 & rat_$greatereq(rat_77/10,
% 21.95/3.95 rat_77/10) = 0 & rat_$greatereq(rat_77/10, rat_24/5) = 0 &
% 21.95/3.95 rat_$greatereq(rat_77/10, rat_29/10) = 0 & rat_$greatereq(rat_77/10, rat_0) =
% 21.95/3.95 0 & rat_$greatereq(rat_24/5, rat_15/2) = 1 & rat_$greatereq(rat_24/5,
% 21.95/3.95 rat_77/10) = 1 & rat_$greatereq(rat_24/5, rat_24/5) = 0 &
% 21.95/3.95 rat_$greatereq(rat_24/5, rat_29/10) = 0 & rat_$greatereq(rat_24/5, rat_0) = 0
% 21.95/3.95 & rat_$greatereq(rat_29/10, rat_15/2) = 1 & rat_$greatereq(rat_29/10,
% 21.95/3.95 rat_77/10) = 1 & rat_$greatereq(rat_29/10, rat_24/5) = 1 &
% 21.95/3.95 rat_$greatereq(rat_29/10, rat_29/10) = 0 & rat_$greatereq(rat_29/10, rat_0) =
% 21.95/3.95 0 & rat_$greatereq(rat_0, rat_15/2) = 1 & rat_$greatereq(rat_0, rat_77/10) = 1
% 21.95/3.95 & rat_$greatereq(rat_0, rat_24/5) = 1 & rat_$greatereq(rat_0, rat_29/10) = 1 &
% 21.95/3.95 rat_$greatereq(rat_0, rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large)
% 21.95/3.95 = 0 & rat_$lesseq(rat_15/2, rat_15/2) = 0 & rat_$lesseq(rat_15/2, rat_77/10) =
% 21.95/3.95 0 & rat_$lesseq(rat_15/2, rat_24/5) = 1 & rat_$lesseq(rat_15/2, rat_29/10) = 1
% 21.95/3.95 & rat_$lesseq(rat_15/2, rat_0) = 1 & rat_$lesseq(rat_77/10, rat_15/2) = 1 &
% 21.95/3.95 rat_$lesseq(rat_77/10, rat_77/10) = 0 & rat_$lesseq(rat_77/10, rat_24/5) = 1 &
% 21.95/3.95 rat_$lesseq(rat_77/10, rat_29/10) = 1 & rat_$lesseq(rat_77/10, rat_0) = 1 &
% 21.95/3.95 rat_$lesseq(rat_24/5, rat_15/2) = 0 & rat_$lesseq(rat_24/5, rat_77/10) = 0 &
% 21.95/3.95 rat_$lesseq(rat_24/5, rat_24/5) = 0 & rat_$lesseq(rat_24/5, rat_29/10) = 1 &
% 21.95/3.95 rat_$lesseq(rat_24/5, rat_0) = 1 & rat_$lesseq(rat_29/10, rat_15/2) = 0 &
% 21.95/3.95 rat_$lesseq(rat_29/10, rat_77/10) = 0 & rat_$lesseq(rat_29/10, rat_24/5) = 0 &
% 21.95/3.95 rat_$lesseq(rat_29/10, rat_29/10) = 0 & rat_$lesseq(rat_29/10, rat_0) = 1 &
% 21.95/3.95 rat_$lesseq(rat_0, rat_15/2) = 0 & rat_$lesseq(rat_0, rat_77/10) = 0 &
% 21.95/3.95 rat_$lesseq(rat_0, rat_24/5) = 0 & rat_$lesseq(rat_0, rat_29/10) = 0 &
% 21.95/3.95 rat_$lesseq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, rat_15/2) = 0 &
% 21.95/3.95 rat_$greater(rat_very_large, rat_77/10) = 0 & rat_$greater(rat_very_large,
% 21.95/3.95 rat_24/5) = 0 & rat_$greater(rat_very_large, rat_29/10) = 0 &
% 21.95/3.95 rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small,
% 21.95/3.95 rat_very_large) = 1 & rat_$greater(rat_15/2, rat_very_small) = 0 &
% 21.95/3.95 rat_$greater(rat_15/2, rat_15/2) = 1 & rat_$greater(rat_15/2, rat_77/10) = 1 &
% 21.95/3.95 rat_$greater(rat_15/2, rat_24/5) = 0 & rat_$greater(rat_15/2, rat_29/10) = 0 &
% 21.95/3.95 rat_$greater(rat_15/2, rat_0) = 0 & rat_$greater(rat_77/10, rat_very_small) =
% 21.95/3.95 0 & rat_$greater(rat_77/10, rat_15/2) = 0 & rat_$greater(rat_77/10, rat_77/10)
% 21.95/3.95 = 1 & rat_$greater(rat_77/10, rat_24/5) = 0 & rat_$greater(rat_77/10,
% 21.95/3.95 rat_29/10) = 0 & rat_$greater(rat_77/10, rat_0) = 0 & rat_$greater(rat_24/5,
% 21.95/3.95 rat_very_small) = 0 & rat_$greater(rat_24/5, rat_15/2) = 1 &
% 21.95/3.95 rat_$greater(rat_24/5, rat_77/10) = 1 & rat_$greater(rat_24/5, rat_24/5) = 1 &
% 21.95/3.95 rat_$greater(rat_24/5, rat_29/10) = 0 & rat_$greater(rat_24/5, rat_0) = 0 &
% 21.95/3.95 rat_$greater(rat_29/10, rat_very_small) = 0 & rat_$greater(rat_29/10,
% 21.95/3.95 rat_15/2) = 1 & rat_$greater(rat_29/10, rat_77/10) = 1 &
% 21.95/3.95 rat_$greater(rat_29/10, rat_24/5) = 1 & rat_$greater(rat_29/10, rat_29/10) = 1
% 21.95/3.95 & rat_$greater(rat_29/10, rat_0) = 0 & rat_$greater(rat_0, rat_very_small) = 0
% 21.95/3.95 & rat_$greater(rat_0, rat_15/2) = 1 & rat_$greater(rat_0, rat_77/10) = 1 &
% 21.95/3.95 rat_$greater(rat_0, rat_24/5) = 1 & rat_$greater(rat_0, rat_29/10) = 1 &
% 21.95/3.95 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0
% 21.95/3.95 & rat_$less(rat_very_small, rat_15/2) = 0 & rat_$less(rat_very_small,
% 21.95/3.95 rat_77/10) = 0 & rat_$less(rat_very_small, rat_24/5) = 0 &
% 21.95/3.95 rat_$less(rat_very_small, rat_29/10) = 0 & rat_$less(rat_very_small, rat_0) =
% 21.95/3.95 0 & rat_$less(rat_15/2, rat_very_large) = 0 & rat_$less(rat_15/2, rat_15/2) =
% 21.95/3.95 1 & rat_$less(rat_15/2, rat_77/10) = 0 & rat_$less(rat_15/2, rat_24/5) = 1 &
% 21.95/3.95 rat_$less(rat_15/2, rat_29/10) = 1 & rat_$less(rat_15/2, rat_0) = 1 &
% 21.95/3.95 rat_$less(rat_77/10, rat_very_large) = 0 & rat_$less(rat_77/10, rat_15/2) = 1
% 21.95/3.95 & rat_$less(rat_77/10, rat_77/10) = 1 & rat_$less(rat_77/10, rat_24/5) = 1 &
% 21.95/3.95 rat_$less(rat_77/10, rat_29/10) = 1 & rat_$less(rat_77/10, rat_0) = 1 &
% 21.95/3.95 rat_$less(rat_24/5, rat_very_large) = 0 & rat_$less(rat_24/5, rat_15/2) = 0 &
% 21.95/3.95 rat_$less(rat_24/5, rat_77/10) = 0 & rat_$less(rat_24/5, rat_24/5) = 1 &
% 21.95/3.95 rat_$less(rat_24/5, rat_29/10) = 1 & rat_$less(rat_24/5, rat_0) = 1 &
% 21.95/3.95 rat_$less(rat_29/10, rat_very_large) = 0 & rat_$less(rat_29/10, rat_15/2) = 0
% 21.95/3.95 & rat_$less(rat_29/10, rat_77/10) = 0 & rat_$less(rat_29/10, rat_24/5) = 0 &
% 21.95/3.95 rat_$less(rat_29/10, rat_29/10) = 1 & rat_$less(rat_29/10, rat_0) = 1 &
% 21.95/3.95 rat_$less(rat_0, rat_very_large) = 0 & rat_$less(rat_0, rat_15/2) = 0 &
% 21.95/3.95 rat_$less(rat_0, rat_77/10) = 0 & rat_$less(rat_0, rat_24/5) = 0 &
% 21.95/3.95 rat_$less(rat_0, rat_29/10) = 0 & rat_$less(rat_0, rat_0) = 1 & ! [v0: $rat]
% 21.95/3.95 : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~
% 21.95/3.95 (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] :
% 21.95/3.95 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1:
% 21.95/3.95 $rat] : ! [v2: $rat] : ! [v3: $rat] : (v3 = v1 | v0 = rat_0 | ~
% 21.95/3.95 (rat_$quotient(v2, v0) = v3) | ~ (rat_$product(v1, v0) = v2)) & ! [v0:
% 21.95/3.95 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~
% 21.95/3.95 (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : (
% 21.95/3.95 ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] :
% 21.95/3.95 ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~
% 21.95/3.95 (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) =
% 21.95/3.95 v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~
% 21.95/3.95 (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1,
% 21.95/3.95 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v2 = rat_0 |
% 21.95/3.95 ~ (rat_$uminus(v0) = v1) | ~ (rat_$sum(v0, v1) = v2)) & ! [v0: $rat] : !
% 21.95/3.95 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ?
% 21.95/3.95 [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : !
% 21.95/3.95 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ( ~ (v1
% 21.95/3.96 = v0) & ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3))) & !
% 21.95/3.96 [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greater(v0, v1)
% 21.95/3.96 = v2) | ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0:
% 21.95/3.96 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) |
% 21.95/3.96 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 21.95/3.96 ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1:
% 21.95/3.96 $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1,
% 21.95/3.96 v0) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : (v1
% 21.95/3.96 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1: $rat] : (v1
% 21.95/3.96 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat]
% 21.95/3.96 : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0:
% 21.95/3.96 $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1,
% 21.95/3.96 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0)
% 21.95/3.96 | rat_$less(v1, v0) = 0) & ! [v0: $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0)
% 21.95/3.96 = v0))
% 21.95/3.96
% 21.95/3.96 (function-axioms)
% 21.95/3.96 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 21.95/3.96 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0:
% 21.95/3.96 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 21.95/3.96 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0:
% 21.95/3.96 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 21.95/3.96 (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & !
% 21.95/3.96 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 21.95/3.96 (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0:
% 21.95/3.96 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 21.95/3.96 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3,
% 21.95/3.96 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 21.95/3.96 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~
% 21.95/3.96 (rat_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 21.95/3.96 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 21.95/3.96 (rat_$greater(v3, v2) = v1) | ~ (rat_$greater(v3, v2) = v0)) & ! [v0:
% 21.95/3.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 21.95/3.97 $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) =
% 21.95/3.97 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 21.95/3.97 $rat] : (v1 = v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) &
% 21.95/3.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 =
% 21.95/3.97 v0 | ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat]
% 21.95/3.97 : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~
% 21.95/3.97 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1
% 21.95/3.97 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0:
% 21.95/3.97 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) =
% 21.95/3.97 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : !
% 21.95/3.97 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) &
% 21.95/3.97 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) =
% 21.95/3.97 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 21.95/3.97 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) &
% 21.95/3.97 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~
% 21.95/3.97 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : !
% 21.95/3.97 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~
% 21.95/3.97 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 21.95/3.97 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0))
% 21.95/3.97
% 21.95/3.97 Those formulas are unsatisfiable:
% 21.95/3.97 ---------------------------------
% 21.95/3.97
% 21.95/3.97 Begin of proof
% 21.95/3.97 |
% 21.95/3.97 | ALPHA: (function-axioms) implies:
% 21.95/3.97 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat]
% 21.95/3.97 | : ! [v3: $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~
% 21.95/3.97 | (rat_$less(v3, v2) = v0))
% 21.95/3.97 |
% 21.95/3.97 | ALPHA: (input) implies:
% 21.95/3.97 | (2) rat_$less(rat_15/2, rat_77/10) = 0
% 21.95/3.97 |
% 21.95/3.97 | DELTA: instantiating (rat_combined_problem_6) with fresh symbol all_5_0 gives:
% 21.95/3.97 | (3) ~ (all_5_0 = 0) & rat_$less(rat_15/2, rat_77/10) = all_5_0
% 21.95/3.97 |
% 21.95/3.97 | ALPHA: (3) implies:
% 21.95/3.97 | (4) ~ (all_5_0 = 0)
% 21.95/3.97 | (5) rat_$less(rat_15/2, rat_77/10) = all_5_0
% 21.95/3.97 |
% 21.95/3.97 | GROUND_INST: instantiating (1) with 0, all_5_0, rat_77/10, rat_15/2,
% 21.95/3.97 | simplifying with (2), (5) gives:
% 21.95/3.98 | (6) all_5_0 = 0
% 21.95/3.98 |
% 21.95/3.98 | REDUCE: (4), (6) imply:
% 21.95/3.98 | (7) $false
% 21.95/3.98 |
% 21.95/3.98 | CLOSE: (7) is inconsistent.
% 21.95/3.98 |
% 21.95/3.98 End of proof
% 21.95/3.98 % SZS output end Proof for theBenchmark
% 21.95/3.98
% 21.95/3.98 3499ms
%------------------------------------------------------------------------------