TSTP Solution File: ARI345_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI345_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 : n010.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 17:47:42 EDT 2023
% Result : Theorem 6.47s 1.58s
% Output : Proof 10.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI345_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n010.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 18:36:48 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.59/0.62 ________ _____
% 0.59/0.62 ___ __ \_________(_)________________________________
% 0.59/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.59/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.59/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.59/0.62
% 0.59/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.59/0.62 (2023-06-19)
% 0.59/0.62
% 0.59/0.62 (c) Philipp Rümmer, 2009-2023
% 0.59/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.59/0.62 Amanda Stjerna.
% 0.59/0.62 Free software under BSD-3-Clause.
% 0.59/0.62
% 0.59/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.59/0.62
% 0.59/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.59/0.63 Running up to 7 provers in parallel.
% 0.59/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.59/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.59/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.59/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.59/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.59/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.59/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.29/0.91 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.29/0.91 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.29/0.91 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.29/0.91 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.29/0.91 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.29/0.91 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.29/0.91 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.90/0.97 Prover 4: Preprocessing ...
% 1.90/0.97 Prover 1: Preprocessing ...
% 2.38/1.02 Prover 6: Preprocessing ...
% 2.38/1.02 Prover 0: Preprocessing ...
% 3.02/1.09 Prover 3: Preprocessing ...
% 3.02/1.09 Prover 2: Preprocessing ...
% 3.02/1.10 Prover 5: Preprocessing ...
% 5.81/1.51 Prover 6: Constructing countermodel ...
% 6.47/1.54 Prover 1: Constructing countermodel ...
% 6.47/1.57 Prover 6: proved (930ms)
% 6.47/1.57
% 6.47/1.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.47/1.58
% 6.47/1.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.85/1.59 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 6.85/1.60 Prover 4: Constructing countermodel ...
% 6.85/1.61 Prover 0: Constructing countermodel ...
% 6.85/1.61 Prover 0: stopped
% 6.85/1.62 Prover 2: stopped
% 6.85/1.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.85/1.62 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 6.85/1.63 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.85/1.63 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 6.85/1.63 Prover 8: Preprocessing ...
% 7.37/1.66 Prover 7: Preprocessing ...
% 7.49/1.66 Prover 10: Preprocessing ...
% 7.89/1.79 Prover 8: Warning: ignoring some quantifiers
% 8.39/1.80 Prover 8: Constructing countermodel ...
% 8.39/1.83 Prover 4: Found proof (size 7)
% 8.39/1.83 Prover 4: proved (1191ms)
% 8.39/1.83 Prover 1: Found proof (size 7)
% 8.39/1.83 Prover 1: proved (1193ms)
% 8.39/1.83 Prover 8: stopped
% 9.07/1.89 Prover 10: stopped
% 9.07/1.91 Prover 7: stopped
% 9.53/1.95 Prover 5: Constructing countermodel ...
% 9.53/1.95 Prover 5: stopped
% 9.53/2.01 Prover 3: Constructing countermodel ...
% 9.53/2.01 Prover 3: stopped
% 9.53/2.01
% 9.53/2.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.53/2.01
% 9.87/2.01 % SZS output start Proof for theBenchmark
% 9.87/2.02 Assumptions after simplification:
% 9.87/2.02 ---------------------------------
% 9.87/2.02
% 9.87/2.02 (real_less_problem_1)
% 9.87/2.04 ? [v0: int] : ( ~ (v0 = 0) & real_$less(real_5/2, real_3) = v0)
% 9.87/2.04
% 9.87/2.04 (input)
% 10.10/2.07 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_3) & ~
% 10.10/2.07 (real_very_large = real_5/2) & ~ (real_very_large = real_0) & ~
% 10.10/2.07 (real_very_small = real_3) & ~ (real_very_small = real_5/2) & ~
% 10.10/2.07 (real_very_small = real_0) & ~ (real_3 = real_5/2) & ~ (real_3 = real_0) &
% 10.10/2.07 ~ (real_5/2 = real_0) & real_$is_int(real_3) = 0 & real_$is_int(real_5/2) = 1
% 10.10/2.07 & real_$is_int(real_0) = 0 & real_$is_rat(real_3) = 0 & real_$is_rat(real_5/2)
% 10.10/2.07 = 0 & real_$is_rat(real_0) = 0 & real_$floor(real_3) = real_3 &
% 10.10/2.07 real_$floor(real_0) = real_0 & real_$ceiling(real_3) = real_3 &
% 10.10/2.07 real_$ceiling(real_5/2) = real_3 & real_$ceiling(real_0) = real_0 &
% 10.10/2.07 real_$truncate(real_3) = real_3 & real_$truncate(real_0) = real_0 &
% 10.10/2.07 real_$round(real_3) = real_3 & real_$round(real_5/2) = real_3 &
% 10.10/2.07 real_$round(real_0) = real_0 & real_$to_int(real_3) = 3 &
% 10.10/2.07 real_$to_int(real_5/2) = 2 & real_$to_int(real_0) = 0 & real_$to_rat(real_3) =
% 10.10/2.07 rat_3 & real_$to_rat(real_5/2) = rat_5/2 & real_$to_rat(real_0) = rat_0 &
% 10.10/2.07 real_$to_real(real_3) = real_3 & real_$to_real(real_5/2) = real_5/2 &
% 10.10/2.07 real_$to_real(real_0) = real_0 & int_$to_real(3) = real_3 & int_$to_real(0) =
% 10.10/2.07 real_0 & real_$quotient(real_0, real_3) = real_0 & real_$quotient(real_0,
% 10.10/2.07 real_5/2) = real_0 & real_$product(real_3, real_0) = real_0 &
% 10.10/2.07 real_$product(real_5/2, real_0) = real_0 & real_$product(real_0, real_3) =
% 10.10/2.07 real_0 & real_$product(real_0, real_5/2) = real_0 & real_$product(real_0,
% 10.10/2.07 real_0) = real_0 & real_$difference(real_3, real_3) = real_0 &
% 10.10/2.07 real_$difference(real_3, real_0) = real_3 & real_$difference(real_5/2,
% 10.10/2.07 real_5/2) = real_0 & real_$difference(real_5/2, real_0) = real_5/2 &
% 10.10/2.07 real_$difference(real_0, real_0) = real_0 & real_$uminus(real_0) = real_0 &
% 10.10/2.07 real_$sum(real_3, real_0) = real_3 & real_$sum(real_5/2, real_0) = real_5/2 &
% 10.10/2.07 real_$sum(real_0, real_3) = real_3 & real_$sum(real_0, real_5/2) = real_5/2 &
% 10.10/2.07 real_$sum(real_0, real_0) = real_0 & real_$greatereq(real_very_small,
% 10.10/2.07 real_very_large) = 1 & real_$greatereq(real_3, real_3) = 0 &
% 10.10/2.07 real_$greatereq(real_3, real_5/2) = 0 & real_$greatereq(real_3, real_0) = 0 &
% 10.10/2.07 real_$greatereq(real_5/2, real_3) = 1 & real_$greatereq(real_5/2, real_5/2) =
% 10.10/2.07 0 & real_$greatereq(real_5/2, real_0) = 0 & real_$greatereq(real_0, real_3) =
% 10.10/2.07 1 & real_$greatereq(real_0, real_5/2) = 1 & real_$greatereq(real_0, real_0) =
% 10.10/2.07 0 & real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_3,
% 10.10/2.07 real_3) = 0 & real_$lesseq(real_3, real_5/2) = 1 & real_$lesseq(real_3,
% 10.10/2.07 real_0) = 1 & real_$lesseq(real_5/2, real_3) = 0 & real_$lesseq(real_5/2,
% 10.10/2.07 real_5/2) = 0 & real_$lesseq(real_5/2, real_0) = 1 & real_$lesseq(real_0,
% 10.10/2.07 real_3) = 0 & real_$lesseq(real_0, real_5/2) = 0 & real_$lesseq(real_0,
% 10.10/2.07 real_0) = 0 & real_$greater(real_very_large, real_3) = 0 &
% 10.10/2.07 real_$greater(real_very_large, real_5/2) = 0 & real_$greater(real_very_large,
% 10.10/2.07 real_0) = 0 & real_$greater(real_very_small, real_very_large) = 1 &
% 10.10/2.07 real_$greater(real_3, real_very_small) = 0 & real_$greater(real_3, real_3) = 1
% 10.10/2.07 & real_$greater(real_3, real_5/2) = 0 & real_$greater(real_3, real_0) = 0 &
% 10.10/2.07 real_$greater(real_5/2, real_very_small) = 0 & real_$greater(real_5/2, real_3)
% 10.10/2.07 = 1 & real_$greater(real_5/2, real_5/2) = 1 & real_$greater(real_5/2, real_0)
% 10.10/2.07 = 0 & real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0,
% 10.10/2.07 real_3) = 1 & real_$greater(real_0, real_5/2) = 1 & real_$greater(real_0,
% 10.10/2.07 real_0) = 1 & real_$less(real_very_small, real_very_large) = 0 &
% 10.10/2.07 real_$less(real_very_small, real_3) = 0 & real_$less(real_very_small,
% 10.10/2.07 real_5/2) = 0 & real_$less(real_very_small, real_0) = 0 & real_$less(real_3,
% 10.10/2.07 real_very_large) = 0 & real_$less(real_3, real_3) = 1 & real_$less(real_3,
% 10.10/2.07 real_5/2) = 1 & real_$less(real_3, real_0) = 1 & real_$less(real_5/2,
% 10.10/2.07 real_very_large) = 0 & real_$less(real_5/2, real_3) = 0 &
% 10.10/2.08 real_$less(real_5/2, real_5/2) = 1 & real_$less(real_5/2, real_0) = 1 &
% 10.10/2.08 real_$less(real_0, real_very_large) = 0 & real_$less(real_0, real_3) = 0 &
% 10.10/2.08 real_$less(real_0, real_5/2) = 0 & real_$less(real_0, real_0) = 1 & ! [v0:
% 10.10/2.08 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] :
% 10.10/2.08 ( ~ (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] :
% 10.10/2.08 (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0: $real] : !
% 10.10/2.08 [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~
% 10.10/2.08 (real_$sum(v2, v3) = v4) | ~ (real_$sum(v1, v0) = v3) | ? [v5: $real] :
% 10.10/2.08 (real_$sum(v5, v0) = v4 & real_$sum(v2, v1) = v5)) & ! [v0: $real] : !
% 10.10/2.08 [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2,
% 10.10/2.08 v1) = 0) | ~ (real_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0)
% 10.10/2.08 & real_$lesseq(v1, v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.10/2.08 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~
% 10.10/2.08 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0)
% 10.10/2.08 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] :
% 10.10/2.08 (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ?
% 10.10/2.08 [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : !
% 10.10/2.08 [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1,
% 10.10/2.08 v0) = 0) | ~ (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) &
% 10.10/2.08 real_$less(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.10/2.08 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v1) = 0) | ~
% 10.10/2.08 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1,
% 10.10/2.08 v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3:
% 10.10/2.08 int] : (v3 = 0 | ~ (real_$less(v2, v0) = v3) | ~ (real_$less(v1, v0) = 0)
% 10.10/2.08 | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real]
% 10.10/2.08 : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ( ~ (real_$uminus(v0) =
% 10.10/2.08 v2) | ~ (real_$sum(v1, v2) = v3) | real_$difference(v1, v0) = v3) & !
% 10.10/2.08 [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~
% 10.10/2.08 (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1,
% 10.10/2.08 v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 |
% 10.10/2.08 ~ (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 10.10/2.08 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.10/2.08 int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 =
% 10.10/2.08 0) & real_$greatereq(v0, v1) = v3)) & ! [v0: $real] : ! [v1: $real] :
% 10.10/2.08 ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~
% 10.10/2.08 (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] :
% 10.10/2.08 ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~
% 10.10/2.08 (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] :
% 10.10/2.08 ! [v2: int] : (v2 = 0 | ~ (real_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3
% 10.10/2.08 = 0) & real_$greater(v0, v1) = v3)) & ! [v0: $real] : ! [v1: $real] :
% 10.10/2.08 ! [v2: $real] : (v0 = real_0 | ~ (real_$product(v1, v0) = v2) |
% 10.10/2.08 real_$quotient(v2, v0) = v1) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.10/2.08 $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) & !
% 10.10/2.08 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) =
% 10.10/2.08 v2) | real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : !
% 10.10/2.08 [v2: $real] : ( ~ (real_$difference(v1, v0) = v2) | ? [v3: $real] :
% 10.10/2.08 (real_$uminus(v0) = v3 & real_$sum(v1, v3) = v2)) & ! [v0: $real] : ! [v1:
% 10.10/2.08 $real] : ! [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0, v1) =
% 10.10/2.08 v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0,
% 10.10/2.08 v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] :
% 10.10/2.08 ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$lesseq(v1, v0) = 0)
% 10.10/2.08 | real_$lesseq(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.10/2.08 $real] : ( ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$less(v1, v0) = 0) |
% 10.10/2.08 real_$less(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 10.10/2.08 ( ~ (real_$lesseq(v1, v0) = 0) | ~ (real_$less(v2, v1) = 0) | real_$less(v2,
% 10.10/2.08 v0) = 0) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0,
% 10.10/2.08 real_0) = v1)) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~
% 10.10/2.08 (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = 0) & ! [v0: $real] : !
% 10.10/2.08 [v1: int] : (v1 = 0 | ~ (real_$lesseq(v0, v0) = v1)) & ! [v0: $real] : !
% 10.10/2.08 [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0:
% 10.10/2.08 $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$sum(v0, v1) =
% 10.10/2.08 real_0) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$greatereq(v0, v1) =
% 10.10/2.08 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 10.10/2.08 (real_$lesseq(v1, v0) = 0) | real_$greatereq(v0, v1) = 0) & ! [v0: $real] :
% 10.10/2.08 ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) &
% 10.10/2.08 ! [v0: $real] : ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) |
% 10.10/2.08 real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 10.10/2.08 (real_$less(v1, v0) = 0) | real_$greater(v0, v1) = 0) & ! [v0: $real] : !
% 10.10/2.08 [v1: MultipleValueBool] : ( ~ (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0)
% 10.10/2.08 = 0) & ! [v0: $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0))
% 10.10/2.08
% 10.10/2.08 (function-axioms)
% 10.10/2.09 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 |
% 10.10/2.09 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & !
% 10.10/2.09 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 10.10/2.09 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0:
% 10.10/2.09 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 10.10/2.09 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & !
% 10.10/2.09 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 10.10/2.09 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0:
% 10.10/2.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 10.10/2.09 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~
% 10.10/2.09 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.10/2.09 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 10.10/2.09 (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, v2) = v0)) & ! [v0:
% 10.10/2.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 10.10/2.09 $real] : (v1 = v0 | ~ (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3,
% 10.10/2.09 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 10.10/2.09 ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~
% 10.10/2.09 (real_$less(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.10/2.09 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1)
% 10.10/2.09 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.10/2.09 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1)
% 10.10/2.09 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.10/2.09 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) &
% 10.10/2.09 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 10.10/2.09 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] :
% 10.10/2.09 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~
% 10.10/2.09 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 10.10/2.09 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) &
% 10.10/2.09 ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2)
% 10.10/2.09 = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : !
% 10.10/2.09 [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) =
% 10.10/2.09 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 10.10/2.09 (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] :
% 10.10/2.09 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~
% 10.10/2.09 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real]
% 10.10/2.09 : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0))
% 10.10/2.09
% 10.10/2.09 Those formulas are unsatisfiable:
% 10.10/2.09 ---------------------------------
% 10.10/2.09
% 10.10/2.09 Begin of proof
% 10.10/2.09 |
% 10.10/2.09 | ALPHA: (function-axioms) implies:
% 10.10/2.09 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.10/2.09 | $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) |
% 10.10/2.09 | ~ (real_$less(v3, v2) = v0))
% 10.10/2.09 |
% 10.10/2.09 | ALPHA: (input) implies:
% 10.10/2.09 | (2) real_$less(real_5/2, real_3) = 0
% 10.10/2.09 |
% 10.10/2.09 | DELTA: instantiating (real_less_problem_1) with fresh symbol all_5_0 gives:
% 10.10/2.10 | (3) ~ (all_5_0 = 0) & real_$less(real_5/2, real_3) = all_5_0
% 10.10/2.10 |
% 10.10/2.10 | ALPHA: (3) implies:
% 10.10/2.10 | (4) ~ (all_5_0 = 0)
% 10.10/2.10 | (5) real_$less(real_5/2, real_3) = all_5_0
% 10.10/2.10 |
% 10.10/2.10 | GROUND_INST: instantiating (1) with 0, all_5_0, real_3, real_5/2, simplifying
% 10.10/2.10 | with (2), (5) gives:
% 10.10/2.10 | (6) all_5_0 = 0
% 10.10/2.10 |
% 10.10/2.10 | REDUCE: (4), (6) imply:
% 10.10/2.10 | (7) $false
% 10.10/2.10 |
% 10.10/2.10 | CLOSE: (7) is inconsistent.
% 10.10/2.10 |
% 10.10/2.10 End of proof
% 10.10/2.10 % SZS output end Proof for theBenchmark
% 10.10/2.10
% 10.10/2.10 1481ms
%------------------------------------------------------------------------------