TSTP Solution File: ARI272_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI272_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 : n026.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 17:47:31 EDT 2023
% Result : Theorem 6.04s 1.55s
% Output : Proof 6.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ARI272_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.35 % Computer : n026.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue Aug 29 18:59:35 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.35/0.91 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.35/0.91 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.35/0.91 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.35/0.91 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.35/0.91 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.35/0.91 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.35/0.91 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.16/1.00 Prover 1: Preprocessing ...
% 2.16/1.00 Prover 4: Preprocessing ...
% 2.52/1.04 Prover 5: Preprocessing ...
% 2.52/1.04 Prover 2: Preprocessing ...
% 2.52/1.05 Prover 3: Preprocessing ...
% 2.52/1.05 Prover 6: Preprocessing ...
% 2.52/1.05 Prover 0: Preprocessing ...
% 4.59/1.43 Prover 6: Proving ...
% 4.59/1.44 Prover 5: Proving ...
% 4.59/1.44 Prover 1: Constructing countermodel ...
% 4.59/1.44 Prover 2: Proving ...
% 4.59/1.46 Prover 3: Constructing countermodel ...
% 4.59/1.47 Prover 4: Constructing countermodel ...
% 5.60/1.51 Prover 0: Proving ...
% 6.04/1.55 Prover 5: proved (898ms)
% 6.04/1.55
% 6.04/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.04/1.55
% 6.04/1.55 Prover 2: proved (903ms)
% 6.04/1.55
% 6.04/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.04/1.55
% 6.04/1.55 Prover 0: stopped
% 6.04/1.55 Prover 6: stopped
% 6.04/1.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.04/1.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.04/1.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.04/1.55 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.04/1.56 Prover 3: stopped
% 6.04/1.56 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.04/1.56 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.04/1.56 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.04/1.56 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.04/1.56 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.04/1.56 Prover 7: Preprocessing ...
% 6.04/1.56 Prover 10: Preprocessing ...
% 6.04/1.57 Prover 11: Preprocessing ...
% 6.04/1.57 Prover 8: Preprocessing ...
% 6.04/1.57 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.04/1.57 Prover 1: Found proof (size 3)
% 6.04/1.57 Prover 1: proved (927ms)
% 6.04/1.58 Prover 13: Preprocessing ...
% 6.04/1.59 Prover 4: Found proof (size 3)
% 6.04/1.59 Prover 4: proved (932ms)
% 6.04/1.59 Prover 7: stopped
% 6.04/1.59 Prover 10: stopped
% 6.35/1.61 Prover 11: stopped
% 6.35/1.61 Prover 13: stopped
% 6.62/1.66 Prover 8: Warning: ignoring some quantifiers
% 6.62/1.67 Prover 8: Constructing countermodel ...
% 6.62/1.68 Prover 8: stopped
% 6.62/1.68
% 6.62/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.62/1.68
% 6.62/1.68 % SZS output start Proof for theBenchmark
% 6.62/1.69 Assumptions after simplification:
% 6.62/1.69 ---------------------------------
% 6.62/1.69
% 6.62/1.69 (rat_sum_problem_27)
% 6.90/1.71 ! [v0: $rat] : ~ (rat_$sum(v0, rat_0) = v0)
% 6.90/1.71
% 6.90/1.71 (input)
% 6.90/1.74 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_0) & ~
% 6.90/1.74 (rat_very_small = rat_0) & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_0) = 0 &
% 6.90/1.74 rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_0)
% 6.90/1.74 = rat_0 & rat_$round(rat_0) = rat_0 & rat_$to_int(rat_0) = 0 &
% 6.90/1.74 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_0) = real_0 & int_$to_rat(0) =
% 6.90/1.74 rat_0 & rat_$product(rat_0, rat_0) = rat_0 & rat_$difference(rat_0, rat_0) =
% 6.90/1.74 rat_0 & rat_$uminus(rat_0) = rat_0 & rat_$greatereq(rat_very_small,
% 6.90/1.74 rat_very_large) = 1 & rat_$greatereq(rat_0, rat_0) = 0 &
% 6.90/1.74 rat_$lesseq(rat_very_small, rat_very_large) = 0 & rat_$lesseq(rat_0, rat_0) =
% 6.90/1.74 0 & rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small,
% 6.90/1.74 rat_very_large) = 1 & rat_$greater(rat_0, rat_very_small) = 0 &
% 6.90/1.74 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0
% 6.90/1.74 & rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_0, rat_very_large) = 0
% 6.90/1.74 & rat_$less(rat_0, rat_0) = 1 & rat_$sum(rat_0, rat_0) = rat_0 & ! [v0: $rat]
% 6.90/1.74 : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~
% 6.90/1.74 (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] :
% 6.90/1.74 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1:
% 6.90/1.74 $rat] : ! [v2: $rat] : ! [v3: $rat] : (v3 = v1 | v0 = rat_0 | ~
% 6.90/1.74 (rat_$quotient(v2, v0) = v3) | ~ (rat_$product(v1, v0) = v2)) & ! [v0:
% 6.90/1.74 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~
% 6.90/1.74 (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : (
% 6.90/1.74 ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] :
% 6.90/1.74 ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~
% 6.90/1.74 (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) =
% 6.90/1.74 v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~
% 6.90/1.74 (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1,
% 6.90/1.74 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v2 = rat_0 |
% 6.90/1.74 ~ (rat_$uminus(v0) = v1) | ~ (rat_$sum(v0, v1) = v2)) & ! [v0: $rat] : !
% 6.90/1.74 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ?
% 6.90/1.74 [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : !
% 6.90/1.74 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ( ~ (v1
% 6.90/1.74 = v0) & ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3))) & !
% 6.90/1.74 [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greater(v0, v1)
% 6.90/1.74 = v2) | ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0:
% 6.90/1.74 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) |
% 6.90/1.74 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 6.90/1.74 ( ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1, v0) = 0) | rat_$less(v2, v0)
% 6.90/1.74 = 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1)
% 6.90/1.74 = v2) | rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0
% 6.90/1.74 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] : !
% 6.90/1.74 [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : !
% 6.90/1.74 [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0:
% 6.90/1.74 $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1,
% 6.90/1.74 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0)
% 6.90/1.74 | rat_$less(v1, v0) = 0) & ! [v0: $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0)
% 6.90/1.74 = v0))
% 6.90/1.74
% 6.90/1.74 Those formulas are unsatisfiable:
% 6.90/1.74 ---------------------------------
% 6.90/1.74
% 6.90/1.74 Begin of proof
% 6.90/1.74 |
% 6.90/1.74 | ALPHA: (input) implies:
% 6.90/1.74 | (1) rat_$sum(rat_0, rat_0) = rat_0
% 6.90/1.74 |
% 6.90/1.75 | GROUND_INST: instantiating (rat_sum_problem_27) with rat_0, simplifying with
% 6.90/1.75 | (1) gives:
% 6.90/1.75 | (2) $false
% 6.90/1.75 |
% 6.90/1.75 | CLOSE: (2) is inconsistent.
% 6.90/1.75 |
% 6.90/1.75 End of proof
% 6.90/1.75 % SZS output end Proof for theBenchmark
% 6.90/1.75
% 6.90/1.75 1119ms
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