TSTP Solution File: ARI737_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI737_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 : n018.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 17:48:58 EDT 2023
% Result : Theorem 7.51s 1.86s
% Output : Proof 13.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : ARI737_1 : TPTP v8.1.2. Released v7.0.0.
% 0.08/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n018.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Aug 29 18:09:03 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.17/0.62 ________ _____
% 0.17/0.62 ___ __ \_________(_)________________________________
% 0.17/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.62
% 0.17/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.62 (2023-06-19)
% 0.17/0.62
% 0.17/0.62 (c) Philipp Rümmer, 2009-2023
% 0.17/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.62 Amanda Stjerna.
% 0.17/0.62 Free software under BSD-3-Clause.
% 0.17/0.62
% 0.17/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.62
% 0.17/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/0.63 Running up to 7 provers in parallel.
% 0.17/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.43/0.97 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.97 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.97 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.97 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.97 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.97 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.43/0.97 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 2.41/1.08 Prover 4: Preprocessing ...
% 2.41/1.08 Prover 1: Preprocessing ...
% 2.67/1.12 Prover 0: Preprocessing ...
% 2.67/1.12 Prover 6: Preprocessing ...
% 2.67/1.19 Prover 2: Preprocessing ...
% 2.67/1.19 Prover 5: Preprocessing ...
% 2.67/1.20 Prover 3: Preprocessing ...
% 7.48/1.76 Prover 6: Constructing countermodel ...
% 7.51/1.84 Prover 0: Constructing countermodel ...
% 7.51/1.86 Prover 6: proved (1192ms)
% 7.51/1.86 Prover 0: proved (1211ms)
% 7.51/1.86
% 7.51/1.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.51/1.86
% 7.51/1.87
% 7.51/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.51/1.87
% 7.51/1.88 Prover 1: Constructing countermodel ...
% 7.51/1.88 Prover 4: Constructing countermodel ...
% 7.51/1.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.51/1.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.51/1.88 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 7.51/1.89 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 7.51/1.91 Prover 8: Preprocessing ...
% 8.86/1.96 Prover 7: Preprocessing ...
% 10.73/2.22 Prover 8: Warning: ignoring some quantifiers
% 10.73/2.24 Prover 8: Constructing countermodel ...
% 11.09/2.27 Prover 2: Constructing countermodel ...
% 11.09/2.28 Prover 1: Found proof (size 7)
% 11.09/2.28 Prover 4: Found proof (size 7)
% 11.09/2.28 Prover 4: proved (1626ms)
% 11.09/2.28 Prover 1: proved (1632ms)
% 11.09/2.29 Prover 2: stopped
% 11.09/2.29 Prover 8: stopped
% 11.78/2.36 Prover 3: Constructing countermodel ...
% 11.78/2.36 Prover 3: stopped
% 12.37/2.49 Prover 7: Warning: ignoring some quantifiers
% 12.57/2.52 Prover 7: Constructing countermodel ...
% 13.05/2.57 Prover 7: stopped
% 13.05/2.61 Prover 5: Constructing countermodel ...
% 13.05/2.61 Prover 5: stopped
% 13.05/2.61
% 13.05/2.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.05/2.61
% 13.31/2.61 % SZS output start Proof for theBenchmark
% 13.31/2.61 Assumptions after simplification:
% 13.31/2.61 ---------------------------------
% 13.31/2.61
% 13.31/2.61 (g5)
% 13.47/2.65 ? [v0: int] : ( ~ (v0 = -1) & real_$to_int(real_-1) = v0)
% 13.47/2.65
% 13.47/2.65 (input)
% 13.47/2.70 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_-1) & ~
% 13.47/2.70 (real_very_large = real_-3/2) & ~ (real_very_large = real_3/2) & ~
% 13.47/2.70 (real_very_large = real_0) & ~ (real_very_small = real_-1) & ~
% 13.47/2.70 (real_very_small = real_-3/2) & ~ (real_very_small = real_3/2) & ~
% 13.47/2.70 (real_very_small = real_0) & ~ (real_-1 = real_-3/2) & ~ (real_-1 =
% 13.47/2.70 real_3/2) & ~ (real_-1 = real_0) & ~ (real_-3/2 = real_3/2) & ~
% 13.47/2.70 (real_-3/2 = real_0) & ~ (real_3/2 = real_0) & real_$is_int(real_-1) = 0 &
% 13.47/2.70 real_$is_int(real_-3/2) = 1 & real_$is_int(real_3/2) = 1 &
% 13.47/2.70 real_$is_int(real_0) = 0 & real_$is_rat(real_-1) = 0 & real_$is_rat(real_-3/2)
% 13.47/2.70 = 0 & real_$is_rat(real_3/2) = 0 & real_$is_rat(real_0) = 0 &
% 13.47/2.70 real_$floor(real_-1) = real_-1 & real_$floor(real_0) = real_0 &
% 13.47/2.70 real_$ceiling(real_-1) = real_-1 & real_$ceiling(real_-3/2) = real_-1 &
% 13.47/2.70 real_$ceiling(real_0) = real_0 & real_$truncate(real_-1) = real_-1 &
% 13.47/2.70 real_$truncate(real_-3/2) = real_-1 & real_$truncate(real_0) = real_0 &
% 13.47/2.70 real_$round(real_-1) = real_-1 & real_$round(real_-3/2) = real_-1 &
% 13.47/2.70 real_$round(real_0) = real_0 & real_$to_rat(real_-1) = rat_-1 &
% 13.47/2.70 real_$to_rat(real_-3/2) = rat_-3/2 & real_$to_rat(real_3/2) = rat_3/2 &
% 13.47/2.70 real_$to_rat(real_0) = rat_0 & real_$to_real(real_-1) = real_-1 &
% 13.47/2.70 real_$to_real(real_-3/2) = real_-3/2 & real_$to_real(real_3/2) = real_3/2 &
% 13.47/2.70 real_$to_real(real_0) = real_0 & int_$to_real(-1) = real_-1 & int_$to_real(0)
% 13.47/2.70 = real_0 & real_$quotient(real_-3/2, real_-1) = real_3/2 &
% 13.47/2.70 real_$quotient(real_-3/2, real_3/2) = real_-1 & real_$quotient(real_3/2,
% 13.47/2.70 real_-1) = real_-3/2 & real_$quotient(real_3/2, real_-3/2) = real_-1 &
% 13.47/2.70 real_$quotient(real_0, real_-1) = real_0 & real_$quotient(real_0, real_-3/2) =
% 13.47/2.70 real_0 & real_$quotient(real_0, real_3/2) = real_0 & real_$product(real_-1,
% 13.47/2.70 real_-3/2) = real_3/2 & real_$product(real_-1, real_3/2) = real_-3/2 &
% 13.47/2.70 real_$product(real_-1, real_0) = real_0 & real_$product(real_-3/2, real_-1) =
% 13.47/2.70 real_3/2 & real_$product(real_-3/2, real_0) = real_0 & real_$product(real_3/2,
% 13.47/2.70 real_-1) = real_-3/2 & real_$product(real_3/2, real_0) = real_0 &
% 13.47/2.70 real_$product(real_0, real_-1) = real_0 & real_$product(real_0, real_-3/2) =
% 13.47/2.70 real_0 & real_$product(real_0, real_3/2) = real_0 & real_$product(real_0,
% 13.47/2.70 real_0) = real_0 & real_$difference(real_-1, real_-1) = real_0 &
% 13.47/2.70 real_$difference(real_-1, real_0) = real_-1 & real_$difference(real_-3/2,
% 13.47/2.70 real_-3/2) = real_0 & real_$difference(real_-3/2, real_0) = real_-3/2 &
% 13.47/2.70 real_$difference(real_3/2, real_3/2) = real_0 & real_$difference(real_3/2,
% 13.47/2.70 real_0) = real_3/2 & real_$difference(real_0, real_-3/2) = real_3/2 &
% 13.47/2.70 real_$difference(real_0, real_3/2) = real_-3/2 & real_$difference(real_0,
% 13.47/2.70 real_0) = real_0 & real_$uminus(real_-3/2) = real_3/2 &
% 13.47/2.70 real_$uminus(real_3/2) = real_-3/2 & real_$uminus(real_0) = real_0 &
% 13.47/2.70 real_$sum(real_-1, real_0) = real_-1 & real_$sum(real_-3/2, real_3/2) = real_0
% 13.47/2.70 & real_$sum(real_-3/2, real_0) = real_-3/2 & real_$sum(real_3/2, real_-3/2) =
% 13.47/2.70 real_0 & real_$sum(real_3/2, real_0) = real_3/2 & real_$sum(real_0, real_-1) =
% 13.47/2.70 real_-1 & real_$sum(real_0, real_-3/2) = real_-3/2 & real_$sum(real_0,
% 13.47/2.70 real_3/2) = real_3/2 & real_$sum(real_0, real_0) = real_0 &
% 13.47/2.70 real_$greatereq(real_very_small, real_very_large) = 1 &
% 13.47/2.70 real_$greatereq(real_-1, real_-1) = 0 & real_$greatereq(real_-1, real_-3/2) =
% 13.47/2.70 0 & real_$greatereq(real_-1, real_3/2) = 1 & real_$greatereq(real_-1, real_0)
% 13.47/2.70 = 1 & real_$greatereq(real_-3/2, real_-1) = 1 & real_$greatereq(real_-3/2,
% 13.47/2.70 real_-3/2) = 0 & real_$greatereq(real_-3/2, real_3/2) = 1 &
% 13.47/2.70 real_$greatereq(real_-3/2, real_0) = 1 & real_$greatereq(real_3/2, real_-1) =
% 13.47/2.70 0 & real_$greatereq(real_3/2, real_-3/2) = 0 & real_$greatereq(real_3/2,
% 13.47/2.70 real_3/2) = 0 & real_$greatereq(real_3/2, real_0) = 0 &
% 13.47/2.70 real_$greatereq(real_0, real_-1) = 0 & real_$greatereq(real_0, real_-3/2) = 0
% 13.47/2.70 & real_$greatereq(real_0, real_3/2) = 1 & real_$greatereq(real_0, real_0) = 0
% 13.47/2.71 & real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_-1,
% 13.47/2.71 real_-1) = 0 & real_$lesseq(real_-1, real_-3/2) = 1 & real_$lesseq(real_-1,
% 13.47/2.71 real_3/2) = 0 & real_$lesseq(real_-1, real_0) = 0 & real_$lesseq(real_-3/2,
% 13.47/2.71 real_-1) = 0 & real_$lesseq(real_-3/2, real_-3/2) = 0 &
% 13.47/2.71 real_$lesseq(real_-3/2, real_3/2) = 0 & real_$lesseq(real_-3/2, real_0) = 0 &
% 13.47/2.71 real_$lesseq(real_3/2, real_-1) = 1 & real_$lesseq(real_3/2, real_-3/2) = 1 &
% 13.47/2.71 real_$lesseq(real_3/2, real_3/2) = 0 & real_$lesseq(real_3/2, real_0) = 1 &
% 13.47/2.71 real_$lesseq(real_0, real_-1) = 1 & real_$lesseq(real_0, real_-3/2) = 1 &
% 13.47/2.71 real_$lesseq(real_0, real_3/2) = 0 & real_$lesseq(real_0, real_0) = 0 &
% 13.47/2.71 real_$greater(real_very_large, real_-1) = 0 & real_$greater(real_very_large,
% 13.47/2.71 real_-3/2) = 0 & real_$greater(real_very_large, real_3/2) = 0 &
% 13.47/2.71 real_$greater(real_very_large, real_0) = 0 & real_$greater(real_very_small,
% 13.47/2.71 real_very_large) = 1 & real_$greater(real_-1, real_very_small) = 0 &
% 13.47/2.71 real_$greater(real_-1, real_-1) = 1 & real_$greater(real_-1, real_-3/2) = 0 &
% 13.47/2.71 real_$greater(real_-1, real_3/2) = 1 & real_$greater(real_-1, real_0) = 1 &
% 13.47/2.71 real_$greater(real_-3/2, real_very_small) = 0 & real_$greater(real_-3/2,
% 13.47/2.71 real_-1) = 1 & real_$greater(real_-3/2, real_-3/2) = 1 &
% 13.47/2.71 real_$greater(real_-3/2, real_3/2) = 1 & real_$greater(real_-3/2, real_0) = 1
% 13.47/2.71 & real_$greater(real_3/2, real_very_small) = 0 & real_$greater(real_3/2,
% 13.47/2.71 real_-1) = 0 & real_$greater(real_3/2, real_-3/2) = 0 &
% 13.47/2.71 real_$greater(real_3/2, real_3/2) = 1 & real_$greater(real_3/2, real_0) = 0 &
% 13.47/2.71 real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0, real_-1) =
% 13.47/2.71 0 & real_$greater(real_0, real_-3/2) = 0 & real_$greater(real_0, real_3/2) = 1
% 13.47/2.71 & real_$greater(real_0, real_0) = 1 & real_$less(real_very_small,
% 13.47/2.71 real_very_large) = 0 & real_$less(real_very_small, real_-1) = 0 &
% 13.47/2.71 real_$less(real_very_small, real_-3/2) = 0 & real_$less(real_very_small,
% 13.47/2.71 real_3/2) = 0 & real_$less(real_very_small, real_0) = 0 &
% 13.47/2.71 real_$less(real_-1, real_very_large) = 0 & real_$less(real_-1, real_-1) = 1 &
% 13.47/2.71 real_$less(real_-1, real_-3/2) = 1 & real_$less(real_-1, real_3/2) = 0 &
% 13.47/2.71 real_$less(real_-1, real_0) = 0 & real_$less(real_-3/2, real_very_large) = 0 &
% 13.47/2.71 real_$less(real_-3/2, real_-1) = 0 & real_$less(real_-3/2, real_-3/2) = 1 &
% 13.47/2.71 real_$less(real_-3/2, real_3/2) = 0 & real_$less(real_-3/2, real_0) = 0 &
% 13.47/2.71 real_$less(real_3/2, real_very_large) = 0 & real_$less(real_3/2, real_-1) = 1
% 13.47/2.71 & real_$less(real_3/2, real_-3/2) = 1 & real_$less(real_3/2, real_3/2) = 1 &
% 13.47/2.71 real_$less(real_3/2, real_0) = 1 & real_$less(real_0, real_very_large) = 0 &
% 13.47/2.71 real_$less(real_0, real_-1) = 1 & real_$less(real_0, real_-3/2) = 1 &
% 13.47/2.71 real_$less(real_0, real_3/2) = 0 & real_$less(real_0, real_0) = 1 &
% 13.47/2.71 real_$to_int(real_-1) = -1 & real_$to_int(real_-3/2) = -2 &
% 13.47/2.71 real_$to_int(real_3/2) = 1 & real_$to_int(real_0) = 0 & ! [v0: $real] : !
% 13.47/2.71 [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~
% 13.47/2.71 (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] :
% 13.47/2.71 (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0: $real] : !
% 13.47/2.71 [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~
% 13.47/2.71 (real_$quotient(v2, v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0:
% 13.47/2.71 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~
% 13.47/2.71 (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] :
% 13.47/2.71 ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real]
% 13.47/2.71 : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, v0) = 0) | ~
% 13.47/2.71 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2, v1)
% 13.47/2.71 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real]
% 13.47/2.71 : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) |
% 13.47/2.71 real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 13.47/2.71 $real] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) =
% 13.47/2.71 v2)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~
% 13.47/2.71 (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 13.47/2.71 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 13.47/2.71 int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3:
% 13.47/2.71 int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & ! [v0: $real] : !
% 13.47/2.71 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ?
% 13.47/2.71 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : !
% 13.47/2.71 [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = v2) |
% 13.47/2.71 real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 13.47/2.71 $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0:
% 13.47/2.71 $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) |
% 13.47/2.71 ~ (real_$less(v1, v0) = 0) | real_$less(v2, v0) = 0) & ! [v0: $real] : !
% 13.47/2.71 [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! [v0: $real] :
% 13.47/2.71 ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0)
% 13.47/2.71 = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) |
% 13.47/2.71 real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 13.47/2.71 (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $real] :
% 13.47/2.71 ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) &
% 13.47/2.71 ! [v0: $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0))
% 13.47/2.71
% 13.47/2.71 (function-axioms)
% 13.47/2.73 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 |
% 13.47/2.73 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & !
% 13.47/2.73 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 13.47/2.73 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0:
% 13.47/2.73 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 13.47/2.73 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & !
% 13.47/2.73 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 13.47/2.73 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0:
% 13.47/2.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 13.47/2.73 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~
% 13.47/2.73 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.47/2.73 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 13.47/2.73 (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, v2) = v0)) & ! [v0:
% 13.47/2.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 13.47/2.73 $real] : (v1 = v0 | ~ (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3,
% 13.47/2.73 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 13.47/2.73 ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~
% 13.47/2.73 (real_$less(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.47/2.73 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1)
% 13.47/2.73 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.47/2.73 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1)
% 13.47/2.73 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 13.47/2.73 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) &
% 13.47/2.73 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 13.47/2.73 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] :
% 13.47/2.73 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~
% 13.47/2.73 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 13.47/2.73 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) &
% 13.47/2.73 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $real] : (v1 = v0 | ~
% 13.47/2.73 (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: $real] : !
% 13.47/2.73 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~
% 13.47/2.73 (real_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] :
% 13.47/2.73 (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = v0)) & ! [v0:
% 13.47/2.73 $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$uminus(v2) =
% 13.47/2.73 v1) | ~ (real_$uminus(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2:
% 13.47/2.73 $real] : (v1 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0))
% 13.47/2.73
% 13.47/2.73 Those formulas are unsatisfiable:
% 13.47/2.73 ---------------------------------
% 13.47/2.73
% 13.47/2.73 Begin of proof
% 13.47/2.73 |
% 13.47/2.73 | ALPHA: (function-axioms) implies:
% 13.47/2.73 | (1) ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~
% 13.47/2.73 | (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0))
% 13.47/2.73 |
% 13.47/2.73 | ALPHA: (input) implies:
% 13.47/2.73 | (2) real_$to_int(real_-1) = -1
% 13.47/2.73 |
% 13.90/2.74 | DELTA: instantiating (g5) with fresh symbol all_5_0 gives:
% 13.90/2.74 | (3) ~ (all_5_0 = -1) & real_$to_int(real_-1) = all_5_0
% 13.90/2.74 |
% 13.90/2.74 | ALPHA: (3) implies:
% 13.90/2.74 | (4) ~ (all_5_0 = -1)
% 13.90/2.74 | (5) real_$to_int(real_-1) = all_5_0
% 13.90/2.74 |
% 13.90/2.74 | GROUND_INST: instantiating (1) with -1, all_5_0, real_-1, simplifying with
% 13.90/2.74 | (2), (5) gives:
% 13.90/2.74 | (6) all_5_0 = -1
% 13.90/2.74 |
% 13.90/2.74 | REDUCE: (4), (6) imply:
% 13.90/2.74 | (7) $false
% 13.90/2.74 |
% 13.90/2.74 | CLOSE: (7) is inconsistent.
% 13.90/2.74 |
% 13.90/2.74 End of proof
% 13.90/2.74 % SZS output end Proof for theBenchmark
% 13.90/2.74
% 13.90/2.74 2123ms
%------------------------------------------------------------------------------