TSTP Solution File: ARI552_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI552_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 : n017.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 17:48:21 EDT 2023
% Result : Theorem 7.31s 1.74s
% Output : Proof 12.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI552_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 : n017.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 17:46:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.68 ________ _____
% 0.21/0.68 ___ __ \_________(_)________________________________
% 0.21/0.68 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.68 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.68 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.68
% 0.21/0.68 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.68 (2023-06-19)
% 0.21/0.68
% 0.21/0.68 (c) Philipp Rümmer, 2009-2023
% 0.21/0.68 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.68 Amanda Stjerna.
% 0.21/0.68 Free software under BSD-3-Clause.
% 0.21/0.68
% 0.21/0.68 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.68
% 0.21/0.68 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.70 Running up to 7 provers in parallel.
% 0.21/0.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.71 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.71 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.71 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.71 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.71 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.66/1.00 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.66/1.00 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.66/1.00 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.66/1.00 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.66/1.00 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.66/1.00 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.66/1.00 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.26/1.09 Prover 1: Preprocessing ...
% 2.65/1.09 Prover 4: Preprocessing ...
% 3.09/1.16 Prover 6: Preprocessing ...
% 3.09/1.16 Prover 0: Preprocessing ...
% 3.91/1.32 Prover 2: Preprocessing ...
% 3.91/1.32 Prover 5: Preprocessing ...
% 3.91/1.32 Prover 3: Preprocessing ...
% 6.59/1.70 Prover 6: Constructing countermodel ...
% 7.31/1.72 Prover 0: Constructing countermodel ...
% 7.31/1.73 Prover 6: proved (1019ms)
% 7.31/1.73
% 7.31/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.31/1.74
% 7.31/1.75 Prover 0: proved (1031ms)
% 7.31/1.75
% 7.31/1.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.31/1.75
% 7.31/1.76 Prover 1: Constructing countermodel ...
% 7.31/1.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.31/1.76 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 7.31/1.76 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.31/1.76 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 7.31/1.77 Prover 8: Preprocessing ...
% 7.85/1.80 Prover 4: Constructing countermodel ...
% 7.85/1.85 Prover 7: Preprocessing ...
% 9.17/1.98 Prover 8: Warning: ignoring some quantifiers
% 9.36/2.01 Prover 8: Constructing countermodel ...
% 9.36/2.02 Prover 1: Found proof (size 7)
% 9.36/2.02 Prover 1: proved (1312ms)
% 9.56/2.02 Prover 4: stopped
% 9.56/2.05 Prover 8: stopped
% 9.56/2.06 Prover 2: stopped
% 10.75/2.24 Prover 7: stopped
% 11.74/2.39 Prover 5: Constructing countermodel ...
% 11.74/2.39 Prover 5: stopped
% 12.42/2.53 Prover 3: Constructing countermodel ...
% 12.42/2.53 Prover 3: stopped
% 12.42/2.53
% 12.42/2.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.42/2.53
% 12.42/2.54 % SZS output start Proof for theBenchmark
% 12.42/2.54 Assumptions after simplification:
% 12.42/2.54 ---------------------------------
% 12.42/2.54
% 12.42/2.54 (rat_combined_problem_12)
% 12.42/2.58 ? [v0: int] : ( ~ (v0 = 0) & rat_$less(rat_-35/4, rat_53/12) = v0)
% 12.42/2.58
% 12.42/2.58 (input)
% 12.42/2.62 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_53/12) & ~
% 12.42/2.62 (rat_very_large = rat_-53/12) & ~ (rat_very_large = rat_-35/4) & ~
% 12.42/2.62 (rat_very_large = rat_0) & ~ (rat_very_small = rat_53/12) & ~
% 12.42/2.62 (rat_very_small = rat_-53/12) & ~ (rat_very_small = rat_-35/4) & ~
% 12.42/2.62 (rat_very_small = rat_0) & ~ (rat_53/12 = rat_-53/12) & ~ (rat_53/12 =
% 12.42/2.62 rat_-35/4) & ~ (rat_53/12 = rat_0) & ~ (rat_-53/12 = rat_-35/4) & ~
% 12.42/2.62 (rat_-53/12 = rat_0) & ~ (rat_-35/4 = rat_0) & rat_$is_int(rat_53/12) = 1 &
% 12.42/2.62 rat_$is_int(rat_-53/12) = 1 & rat_$is_int(rat_-35/4) = 1 & rat_$is_int(rat_0)
% 12.42/2.62 = 0 & rat_$is_rat(rat_53/12) = 0 & rat_$is_rat(rat_-53/12) = 0 &
% 12.42/2.62 rat_$is_rat(rat_-35/4) = 0 & rat_$is_rat(rat_0) = 0 & rat_$floor(rat_0) =
% 12.42/2.62 rat_0 & rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_0) = rat_0 &
% 12.42/2.62 rat_$round(rat_0) = rat_0 & rat_$to_int(rat_53/12) = 4 &
% 12.42/2.62 rat_$to_int(rat_-53/12) = -5 & rat_$to_int(rat_-35/4) = -9 &
% 12.42/2.62 rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_53/12) = rat_53/12 &
% 12.42/2.62 rat_$to_rat(rat_-53/12) = rat_-53/12 & rat_$to_rat(rat_-35/4) = rat_-35/4 &
% 12.42/2.62 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_53/12) = real_53/12 &
% 12.42/2.62 rat_$to_real(rat_-53/12) = real_-53/12 & rat_$to_real(rat_-35/4) = real_-35/4
% 12.42/2.62 & rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_0,
% 12.42/2.62 rat_53/12) = rat_0 & rat_$quotient(rat_0, rat_-53/12) = rat_0 &
% 12.42/2.62 rat_$quotient(rat_0, rat_-35/4) = rat_0 & rat_$product(rat_53/12, rat_0) =
% 12.42/2.62 rat_0 & rat_$product(rat_-53/12, rat_0) = rat_0 & rat_$product(rat_-35/4,
% 12.42/2.62 rat_0) = rat_0 & rat_$product(rat_0, rat_53/12) = rat_0 &
% 12.42/2.62 rat_$product(rat_0, rat_-53/12) = rat_0 & rat_$product(rat_0, rat_-35/4) =
% 12.42/2.63 rat_0 & rat_$product(rat_0, rat_0) = rat_0 & rat_$difference(rat_53/12,
% 12.42/2.63 rat_53/12) = rat_0 & rat_$difference(rat_53/12, rat_0) = rat_53/12 &
% 12.42/2.63 rat_$difference(rat_-53/12, rat_-53/12) = rat_0 & rat_$difference(rat_-53/12,
% 12.42/2.63 rat_0) = rat_-53/12 & rat_$difference(rat_-35/4, rat_-35/4) = rat_0 &
% 12.42/2.63 rat_$difference(rat_-35/4, rat_0) = rat_-35/4 & rat_$difference(rat_0,
% 12.42/2.63 rat_53/12) = rat_-53/12 & rat_$difference(rat_0, rat_-53/12) = rat_53/12 &
% 12.42/2.63 rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_53/12) = rat_-53/12 &
% 12.42/2.63 rat_$uminus(rat_-53/12) = rat_53/12 & rat_$uminus(rat_0) = rat_0 &
% 12.42/2.63 rat_$sum(rat_53/12, rat_-53/12) = rat_0 & rat_$sum(rat_53/12, rat_0) =
% 12.42/2.63 rat_53/12 & rat_$sum(rat_-53/12, rat_53/12) = rat_0 & rat_$sum(rat_-53/12,
% 12.42/2.63 rat_0) = rat_-53/12 & rat_$sum(rat_-35/4, rat_0) = rat_-35/4 &
% 12.42/2.63 rat_$sum(rat_0, rat_53/12) = rat_53/12 & rat_$sum(rat_0, rat_-53/12) =
% 12.42/2.63 rat_-53/12 & rat_$sum(rat_0, rat_-35/4) = rat_-35/4 & rat_$sum(rat_0, rat_0) =
% 12.42/2.63 rat_0 & rat_$greatereq(rat_very_small, rat_very_large) = 1 &
% 12.42/2.63 rat_$greatereq(rat_53/12, rat_53/12) = 0 & rat_$greatereq(rat_53/12,
% 12.42/2.63 rat_-53/12) = 0 & rat_$greatereq(rat_53/12, rat_-35/4) = 0 &
% 12.42/2.63 rat_$greatereq(rat_53/12, rat_0) = 0 & rat_$greatereq(rat_-53/12, rat_53/12) =
% 12.42/2.63 1 & rat_$greatereq(rat_-53/12, rat_-53/12) = 0 & rat_$greatereq(rat_-53/12,
% 12.42/2.63 rat_-35/4) = 0 & rat_$greatereq(rat_-53/12, rat_0) = 1 &
% 12.42/2.63 rat_$greatereq(rat_-35/4, rat_53/12) = 1 & rat_$greatereq(rat_-35/4,
% 12.42/2.63 rat_-53/12) = 1 & rat_$greatereq(rat_-35/4, rat_-35/4) = 0 &
% 12.42/2.63 rat_$greatereq(rat_-35/4, rat_0) = 1 & rat_$greatereq(rat_0, rat_53/12) = 1 &
% 12.42/2.63 rat_$greatereq(rat_0, rat_-53/12) = 0 & rat_$greatereq(rat_0, rat_-35/4) = 0 &
% 12.42/2.63 rat_$greatereq(rat_0, rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large)
% 12.42/2.63 = 0 & rat_$lesseq(rat_53/12, rat_53/12) = 0 & rat_$lesseq(rat_53/12,
% 12.42/2.63 rat_-53/12) = 1 & rat_$lesseq(rat_53/12, rat_-35/4) = 1 &
% 12.42/2.63 rat_$lesseq(rat_53/12, rat_0) = 1 & rat_$lesseq(rat_-53/12, rat_53/12) = 0 &
% 12.42/2.63 rat_$lesseq(rat_-53/12, rat_-53/12) = 0 & rat_$lesseq(rat_-53/12, rat_-35/4) =
% 12.42/2.63 1 & rat_$lesseq(rat_-53/12, rat_0) = 0 & rat_$lesseq(rat_-35/4, rat_53/12) = 0
% 12.42/2.63 & rat_$lesseq(rat_-35/4, rat_-53/12) = 0 & rat_$lesseq(rat_-35/4, rat_-35/4) =
% 12.42/2.63 0 & rat_$lesseq(rat_-35/4, rat_0) = 0 & rat_$lesseq(rat_0, rat_53/12) = 0 &
% 12.42/2.63 rat_$lesseq(rat_0, rat_-53/12) = 1 & rat_$lesseq(rat_0, rat_-35/4) = 1 &
% 12.42/2.63 rat_$lesseq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, rat_53/12) = 0 &
% 12.42/2.63 rat_$greater(rat_very_large, rat_-53/12) = 0 & rat_$greater(rat_very_large,
% 12.42/2.63 rat_-35/4) = 0 & rat_$greater(rat_very_large, rat_0) = 0 &
% 12.42/2.63 rat_$greater(rat_very_small, rat_very_large) = 1 & rat_$greater(rat_53/12,
% 12.42/2.63 rat_very_small) = 0 & rat_$greater(rat_53/12, rat_53/12) = 1 &
% 12.42/2.63 rat_$greater(rat_53/12, rat_-53/12) = 0 & rat_$greater(rat_53/12, rat_-35/4) =
% 12.42/2.63 0 & rat_$greater(rat_53/12, rat_0) = 0 & rat_$greater(rat_-53/12,
% 12.42/2.63 rat_very_small) = 0 & rat_$greater(rat_-53/12, rat_53/12) = 1 &
% 12.42/2.63 rat_$greater(rat_-53/12, rat_-53/12) = 1 & rat_$greater(rat_-53/12, rat_-35/4)
% 12.42/2.63 = 0 & rat_$greater(rat_-53/12, rat_0) = 1 & rat_$greater(rat_-35/4,
% 12.42/2.63 rat_very_small) = 0 & rat_$greater(rat_-35/4, rat_53/12) = 1 &
% 12.42/2.63 rat_$greater(rat_-35/4, rat_-53/12) = 1 & rat_$greater(rat_-35/4, rat_-35/4) =
% 12.42/2.63 1 & rat_$greater(rat_-35/4, rat_0) = 1 & rat_$greater(rat_0, rat_very_small) =
% 12.42/2.63 0 & rat_$greater(rat_0, rat_53/12) = 1 & rat_$greater(rat_0, rat_-53/12) = 0 &
% 12.42/2.63 rat_$greater(rat_0, rat_-35/4) = 0 & rat_$greater(rat_0, rat_0) = 1 &
% 12.42/2.63 rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small,
% 12.42/2.63 rat_53/12) = 0 & rat_$less(rat_very_small, rat_-53/12) = 0 &
% 12.42/2.63 rat_$less(rat_very_small, rat_-35/4) = 0 & rat_$less(rat_very_small, rat_0) =
% 12.42/2.63 0 & rat_$less(rat_53/12, rat_very_large) = 0 & rat_$less(rat_53/12, rat_53/12)
% 12.42/2.63 = 1 & rat_$less(rat_53/12, rat_-53/12) = 1 & rat_$less(rat_53/12, rat_-35/4) =
% 12.42/2.63 1 & rat_$less(rat_53/12, rat_0) = 1 & rat_$less(rat_-53/12, rat_very_large) =
% 12.42/2.63 0 & rat_$less(rat_-53/12, rat_53/12) = 0 & rat_$less(rat_-53/12, rat_-53/12) =
% 12.42/2.63 1 & rat_$less(rat_-53/12, rat_-35/4) = 1 & rat_$less(rat_-53/12, rat_0) = 0 &
% 12.42/2.63 rat_$less(rat_-35/4, rat_very_large) = 0 & rat_$less(rat_-35/4, rat_53/12) = 0
% 12.42/2.63 & rat_$less(rat_-35/4, rat_-53/12) = 0 & rat_$less(rat_-35/4, rat_-35/4) = 1 &
% 12.42/2.63 rat_$less(rat_-35/4, rat_0) = 0 & rat_$less(rat_0, rat_very_large) = 0 &
% 12.42/2.63 rat_$less(rat_0, rat_53/12) = 0 & rat_$less(rat_0, rat_-53/12) = 1 &
% 12.42/2.63 rat_$less(rat_0, rat_-35/4) = 1 & rat_$less(rat_0, rat_0) = 1 & ! [v0: $rat]
% 12.42/2.63 : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~
% 12.42/2.63 (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] :
% 12.42/2.63 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1:
% 12.42/2.63 $rat] : ! [v2: $rat] : ! [v3: $rat] : (v3 = v1 | v0 = rat_0 | ~
% 12.42/2.63 (rat_$quotient(v2, v0) = v3) | ~ (rat_$product(v1, v0) = v2)) & ! [v0:
% 12.42/2.63 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~
% 12.42/2.63 (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : (
% 12.42/2.64 ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] :
% 12.42/2.64 ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~
% 12.42/2.64 (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) =
% 12.42/2.64 v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~
% 12.42/2.64 (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1,
% 12.42/2.64 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v2 = rat_0 |
% 12.42/2.64 ~ (rat_$uminus(v0) = v1) | ~ (rat_$sum(v0, v1) = v2)) & ! [v0: $rat] : !
% 12.42/2.64 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ?
% 12.42/2.64 [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : !
% 12.42/2.64 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ( ~ (v1
% 12.42/2.64 = v0) & ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3))) & !
% 12.42/2.64 [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greater(v0, v1)
% 12.42/2.64 = v2) | ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0:
% 12.42/2.64 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) |
% 12.42/2.64 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 12.42/2.64 ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1:
% 12.42/2.64 $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1,
% 12.42/2.64 v0) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : (v1
% 12.42/2.64 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1: $rat] : (v1
% 12.42/2.64 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat]
% 12.42/2.64 : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0:
% 12.42/2.64 $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1,
% 12.42/2.64 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0)
% 12.42/2.64 | rat_$less(v1, v0) = 0) & ! [v0: $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0)
% 12.42/2.64 = v0))
% 12.42/2.64
% 12.42/2.64 (function-axioms)
% 12.42/2.65 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 12.42/2.65 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0:
% 12.42/2.65 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 12.42/2.65 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0:
% 12.42/2.65 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 12.42/2.65 (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & !
% 12.42/2.65 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 12.42/2.65 (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0:
% 12.42/2.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 12.42/2.65 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3,
% 12.42/2.65 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 12.42/2.65 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~
% 12.42/2.65 (rat_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.42/2.65 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 12.42/2.65 (rat_$greater(v3, v2) = v1) | ~ (rat_$greater(v3, v2) = v0)) & ! [v0:
% 12.42/2.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 12.42/2.65 $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) =
% 12.42/2.65 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 12.42/2.65 $rat] : (v1 = v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) &
% 12.42/2.65 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 =
% 12.42/2.65 v0 | ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat]
% 12.42/2.65 : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~
% 12.42/2.65 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1
% 12.42/2.65 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0:
% 12.42/2.65 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) =
% 12.42/2.65 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : !
% 12.42/2.65 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) &
% 12.42/2.65 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) =
% 12.42/2.65 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 12.42/2.65 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) &
% 12.42/2.65 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~
% 12.42/2.65 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : !
% 12.42/2.65 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~
% 12.42/2.65 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 12.42/2.65 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0))
% 12.42/2.65
% 12.42/2.65 Those formulas are unsatisfiable:
% 12.42/2.65 ---------------------------------
% 12.42/2.65
% 12.42/2.65 Begin of proof
% 12.42/2.65 |
% 12.42/2.65 | ALPHA: (function-axioms) implies:
% 12.42/2.65 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat]
% 12.42/2.65 | : ! [v3: $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~
% 12.42/2.65 | (rat_$less(v3, v2) = v0))
% 12.42/2.65 |
% 12.42/2.65 | ALPHA: (input) implies:
% 12.42/2.65 | (2) rat_$less(rat_-35/4, rat_53/12) = 0
% 12.42/2.65 |
% 12.42/2.66 | DELTA: instantiating (rat_combined_problem_12) with fresh symbol all_5_0
% 12.42/2.66 | gives:
% 12.42/2.66 | (3) ~ (all_5_0 = 0) & rat_$less(rat_-35/4, rat_53/12) = all_5_0
% 12.42/2.66 |
% 12.42/2.66 | ALPHA: (3) implies:
% 12.42/2.66 | (4) ~ (all_5_0 = 0)
% 12.42/2.66 | (5) rat_$less(rat_-35/4, rat_53/12) = all_5_0
% 12.42/2.66 |
% 12.42/2.66 | GROUND_INST: instantiating (1) with 0, all_5_0, rat_53/12, rat_-35/4,
% 12.42/2.66 | simplifying with (2), (5) gives:
% 12.42/2.66 | (6) all_5_0 = 0
% 12.42/2.66 |
% 12.42/2.66 | REDUCE: (4), (6) imply:
% 12.42/2.66 | (7) $false
% 12.42/2.66 |
% 12.42/2.66 | CLOSE: (7) is inconsistent.
% 12.42/2.66 |
% 12.42/2.66 End of proof
% 12.42/2.66 % SZS output end Proof for theBenchmark
% 12.42/2.66
% 12.42/2.66 1976ms
%------------------------------------------------------------------------------