TSTP Solution File: SWW650_2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW650_2 : TPTP v8.1.2. Released v6.1.0.
% 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 : Fri Sep 1 00:51:00 EDT 2023
% Result : Theorem 7.94s 1.84s
% Output : Proof 9.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW650_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n026.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 : Sun Aug 27 18:28:34 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.94/1.15 Prover 1: Preprocessing ...
% 2.94/1.15 Prover 6: Preprocessing ...
% 2.94/1.15 Prover 3: Preprocessing ...
% 2.94/1.15 Prover 4: Preprocessing ...
% 2.94/1.15 Prover 2: Preprocessing ...
% 2.94/1.15 Prover 0: Preprocessing ...
% 2.94/1.15 Prover 5: Preprocessing ...
% 5.68/1.56 Prover 1: Warning: ignoring some quantifiers
% 5.68/1.57 Prover 3: Warning: ignoring some quantifiers
% 6.46/1.60 Prover 4: Warning: ignoring some quantifiers
% 6.46/1.62 Prover 3: Constructing countermodel ...
% 6.46/1.62 Prover 1: Constructing countermodel ...
% 6.46/1.63 Prover 6: Proving ...
% 6.46/1.64 Prover 4: Constructing countermodel ...
% 6.46/1.67 Prover 5: Proving ...
% 6.46/1.68 Prover 0: Proving ...
% 6.46/1.70 Prover 2: Proving ...
% 7.94/1.84 Prover 0: proved (1221ms)
% 7.94/1.84
% 7.94/1.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.94/1.84
% 7.94/1.84 Prover 6: stopped
% 7.94/1.84 Prover 3: stopped
% 7.94/1.84 Prover 5: stopped
% 7.94/1.84 Prover 2: stopped
% 7.94/1.85 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.94/1.85 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.94/1.85 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.94/1.85 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.94/1.85 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.67/1.95 Prover 11: Preprocessing ...
% 8.67/1.98 Prover 4: Found proof (size 22)
% 8.67/1.98 Prover 4: proved (1354ms)
% 8.67/1.98 Prover 1: stopped
% 8.67/1.98 Prover 8: Preprocessing ...
% 8.67/1.99 Prover 10: Preprocessing ...
% 8.67/1.99 Prover 7: Preprocessing ...
% 8.67/2.00 Prover 13: Preprocessing ...
% 8.67/2.00 Prover 11: stopped
% 9.23/2.01 Prover 7: stopped
% 9.23/2.01 Prover 10: stopped
% 9.23/2.03 Prover 13: stopped
% 9.23/2.06 Prover 8: Warning: ignoring some quantifiers
% 9.23/2.07 Prover 8: Constructing countermodel ...
% 9.23/2.07 Prover 8: stopped
% 9.23/2.07
% 9.23/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.23/2.07
% 9.23/2.08 % SZS output start Proof for theBenchmark
% 9.23/2.08 Assumptions after simplification:
% 9.23/2.08 ---------------------------------
% 9.23/2.08
% 9.23/2.08 (iter_1)
% 9.23/2.10 ! [v0: t1] : ! [v1: t1] : ( ~ (f1(v0) = v1) | ~ t1(v0) | (iter1(1, v0) = v1
% 9.23/2.10 & t1(v1))) & ! [v0: t1] : ! [v1: t1] : ( ~ (iter1(1, v0) = v1) | ~
% 9.23/2.10 t1(v0) | (f1(v0) = v1 & t1(v1)))
% 9.23/2.10
% 9.23/2.10 (iter_s)
% 9.23/2.10 ! [v0: int] : ! [v1: t1] : ! [v2: t1] : ! [v3: t1] : ( ~ ($lesseq(1, v0))
% 9.23/2.10 | ~ (f1(v1) = v2) | ~ (iter1($sum(v0, -1), v2) = v3) | ~ t1(v1) |
% 9.23/2.10 (iter1(v0, v1) = v3 & t1(v3))) & ! [v0: int] : ! [v1: t1] : ! [v2: t1] :
% 9.23/2.10 ( ~ ($lesseq(1, v0)) | ~ (iter1(v0, v1) = v2) | ~ t1(v1) | ? [v3: t1] :
% 9.23/2.10 (f1(v1) = v3 & iter1($sum(v0, -1), v3) = v2 & t1(v3) & t1(v2)))
% 9.23/2.10
% 9.23/2.10 (lambda_range)
% 9.23/2.10 $lesseq(1, lambda1)
% 9.23/2.10
% 9.23/2.10 (mu_range)
% 9.23/2.10 $lesseq(0, mu1)
% 9.23/2.10
% 9.23/2.10 (wP_parameter_tortoise_hare)
% 9.23/2.11 t1(x01) & ? [v0: t1] : ? [v1: t1] : (f1(v0) = v1 & f1(x01) = v0 & t1(v1) &
% 9.23/2.11 t1(v0) & ! [v2: int] : ( ~ ($lesseq(0, $sum($difference(lambda1, v2),
% 9.23/2.11 mu1))) | ~ ($lesseq(1, v2)) | ~ (iter1(v2, x01) = v0) | ? [v3:
% 9.23/2.11 any] : ? [v4: t1] : ? [v5: t1] : ((v5 = v4 & $lesseq(1,
% 9.23/2.11 $difference(v2, v3)) & $lesseq(1, v3) & iter1($product(2, v3), x01)
% 9.23/2.11 = v4 & iter1(v3, x01) = v4 & t1(v4)) | ( ~ (v3 = v1) &
% 9.23/2.11 iter1($product(2, v2), x01) = v3 & t1(v3)))) & ? [v2: int] : ( ~
% 9.23/2.11 ($lesseq(0, $sum($difference(lambda1, v2), mu1))) | ~ ($lesseq(1, v2)) |
% 9.23/2.11 ~ (iter1($product(2, v2), x01) = v1) | ? [v3: any] : ? [v4: t1] : ?
% 9.23/2.11 [v5: t1] : ((v5 = v4 & $lesseq(1, $difference(v2, v3)) & $lesseq(1, v3) &
% 9.23/2.11 iter1($product(2, v3), x01) = v4 & iter1(v3, x01) = v4 & t1(v4)) | ( ~
% 9.23/2.11 (v3 = v0) & iter1(v2, x01) = v3 & t1(v3)))))
% 9.23/2.11
% 9.23/2.11 (function-axioms)
% 9.23/2.11 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: bool1] :
% 9.23/2.11 ! [v5: ty] : (v1 = v0 | ~ (match_bool1(v5, v4, v3, v2) = v1) | ~
% 9.23/2.11 (match_bool1(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.23/2.11 MultipleValueBool] : ! [v2: t1] : ! [v3: t1] : (v1 = v0 | ~ (rel1(v3, v2)
% 9.23/2.11 = v1) | ~ (rel1(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2:
% 9.23/2.11 int] : ! [v3: int] : (v1 = v0 | ~ (dist1(v3, v2) = v1) | ~ (dist1(v3, v2)
% 9.23/2.11 = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 =
% 9.23/2.11 v0 | ~ (contents(v3, v2) = v1) | ~ (contents(v3, v2) = v0)) & ! [v0: uni]
% 9.23/2.11 : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (mk_ref(v3, v2) =
% 9.93/2.11 v1) | ~ (mk_ref(v3, v2) = v0)) & ! [v0: t1] : ! [v1: t1] : ! [v2: t1]
% 9.93/2.11 : ! [v3: int] : (v1 = v0 | ~ (iter1(v3, v2) = v1) | ~ (iter1(v3, v2) = v0))
% 9.93/2.11 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: uni] : !
% 9.93/2.11 [v3: ty] : (v1 = v0 | ~ (sort1(v3, v2) = v1) | ~ (sort1(v3, v2) = v0)) & !
% 9.93/2.11 [v0: ty] : ! [v1: ty] : ! [v2: ty] : (v1 = v0 | ~ (ref(v2) = v1) | ~
% 9.93/2.11 (ref(v2) = v0)) & ! [v0: t1] : ! [v1: t1] : ! [v2: t1] : (v1 = v0 | ~
% 9.93/2.11 (f1(v2) = v1) | ~ (f1(v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2:
% 9.93/2.11 ty] : (v1 = v0 | ~ (witness1(v2) = v1) | ~ (witness1(v2) = v0))
% 9.93/2.11
% 9.93/2.11 Further assumptions not needed in the proof:
% 9.93/2.11 --------------------------------------------
% 9.93/2.11 bool_inversion, compatOrderMult, contents_def1, contents_sort1, cycle,
% 9.93/2.11 cycle_induction, dist_def, distinct, iter_0, iter_s2, match_bool_False,
% 9.93/2.11 match_bool_True, match_bool_sort2, mk_ref_sort1, ref_inversion1, rel_def,
% 9.93/2.11 true_False, tuple0_inversion, witness_sort1
% 9.93/2.11
% 9.93/2.11 Those formulas are unsatisfiable:
% 9.93/2.11 ---------------------------------
% 9.93/2.11
% 9.93/2.11 Begin of proof
% 9.93/2.11 |
% 9.93/2.11 | ALPHA: (iter_s) implies:
% 9.93/2.12 | (1) ! [v0: int] : ! [v1: t1] : ! [v2: t1] : ! [v3: t1] : ( ~
% 9.93/2.12 | ($lesseq(1, v0)) | ~ (f1(v1) = v2) | ~ (iter1($sum(v0, -1), v2) =
% 9.93/2.12 | v3) | ~ t1(v1) | (iter1(v0, v1) = v3 & t1(v3)))
% 9.93/2.12 |
% 9.93/2.12 | ALPHA: (iter_1) implies:
% 9.93/2.12 | (2) ! [v0: t1] : ! [v1: t1] : ( ~ (f1(v0) = v1) | ~ t1(v0) | (iter1(1,
% 9.93/2.12 | v0) = v1 & t1(v1)))
% 9.93/2.12 |
% 9.93/2.12 | ALPHA: (wP_parameter_tortoise_hare) implies:
% 9.93/2.12 | (3) t1(x01)
% 9.93/2.12 | (4) ? [v0: t1] : ? [v1: t1] : (f1(v0) = v1 & f1(x01) = v0 & t1(v1) &
% 9.93/2.12 | t1(v0) & ! [v2: int] : ( ~ ($lesseq(0, $sum($difference(lambda1,
% 9.93/2.12 | v2), mu1))) | ~ ($lesseq(1, v2)) | ~ (iter1(v2, x01) =
% 9.93/2.12 | v0) | ? [v3: any] : ? [v4: t1] : ? [v5: t1] : ((v5 = v4 &
% 9.93/2.12 | $lesseq(1, $difference(v2, v3)) & $lesseq(1, v3) &
% 9.93/2.12 | iter1($product(2, v3), x01) = v4 & iter1(v3, x01) = v4 &
% 9.93/2.12 | t1(v4)) | ( ~ (v3 = v1) & iter1($product(2, v2), x01) = v3 &
% 9.93/2.12 | t1(v3)))) & ? [v2: int] : ( ~ ($lesseq(0,
% 9.93/2.12 | $sum($difference(lambda1, v2), mu1))) | ~ ($lesseq(1, v2)) |
% 9.93/2.12 | ~ (iter1($product(2, v2), x01) = v1) | ? [v3: any] : ? [v4: t1] :
% 9.93/2.12 | ? [v5: t1] : ((v5 = v4 & $lesseq(1, $difference(v2, v3)) &
% 9.93/2.12 | $lesseq(1, v3) & iter1($product(2, v3), x01) = v4 & iter1(v3,
% 9.93/2.12 | x01) = v4 & t1(v4)) | ( ~ (v3 = v0) & iter1(v2, x01) = v3 &
% 9.93/2.12 | t1(v3)))))
% 9.93/2.12 |
% 9.93/2.12 | ALPHA: (function-axioms) implies:
% 9.93/2.12 | (5) ! [v0: t1] : ! [v1: t1] : ! [v2: t1] : ! [v3: int] : (v1 = v0 | ~
% 9.93/2.12 | (iter1(v3, v2) = v1) | ~ (iter1(v3, v2) = v0))
% 9.93/2.12 |
% 9.93/2.12 | DELTA: instantiating (4) with fresh symbols all_36_0, all_36_1 gives:
% 9.93/2.12 | (6) f1(all_36_1) = all_36_0 & f1(x01) = all_36_1 & t1(all_36_0) &
% 9.93/2.12 | t1(all_36_1) & ! [v0: int] : ( ~ ($lesseq(0, $sum($difference(lambda1,
% 9.93/2.12 | v0), mu1))) | ~ ($lesseq(1, v0)) | ~ (iter1(v0, x01) =
% 9.93/2.12 | all_36_1) | ? [v1: any] : ? [v2: t1] : ? [v3: t1] : ((v3 = v2 &
% 9.93/2.12 | $lesseq(1, $difference(v0, v1)) & $lesseq(1, v1) &
% 9.93/2.12 | iter1($product(2, v1), x01) = v2 & iter1(v1, x01) = v2 & t1(v2))
% 9.93/2.12 | | ( ~ (v1 = all_36_0) & iter1($product(2, v0), x01) = v1 &
% 9.93/2.12 | t1(v1)))) & ? [v0: int] : ( ~ ($lesseq(0,
% 9.93/2.12 | $sum($difference(lambda1, v0), mu1))) | ~ ($lesseq(1, v0)) | ~
% 9.93/2.13 | (iter1($product(2, v0), x01) = all_36_0) | ? [v1: any] : ? [v2: t1]
% 9.93/2.13 | : ? [v3: t1] : ((v3 = v2 & $lesseq(1, $difference(v0, v1)) &
% 9.93/2.13 | $lesseq(1, v1) & iter1($product(2, v1), x01) = v2 & iter1(v1,
% 9.93/2.13 | x01) = v2 & t1(v2)) | ( ~ (v1 = all_36_1) & iter1(v0, x01) = v1
% 9.93/2.13 | & t1(v1))))
% 9.93/2.13 |
% 9.93/2.13 | ALPHA: (6) implies:
% 9.93/2.13 | (7) f1(x01) = all_36_1
% 9.93/2.13 | (8) f1(all_36_1) = all_36_0
% 9.93/2.13 | (9) ! [v0: int] : ( ~ ($lesseq(0, $sum($difference(lambda1, v0), mu1))) |
% 9.93/2.13 | ~ ($lesseq(1, v0)) | ~ (iter1(v0, x01) = all_36_1) | ? [v1: any] :
% 9.93/2.13 | ? [v2: t1] : ? [v3: t1] : ((v3 = v2 & $lesseq(1, $difference(v0,
% 9.93/2.13 | v1)) & $lesseq(1, v1) & iter1($product(2, v1), x01) = v2 &
% 9.93/2.13 | iter1(v1, x01) = v2 & t1(v2)) | ( ~ (v1 = all_36_0) &
% 9.93/2.13 | iter1($product(2, v0), x01) = v1 & t1(v1))))
% 9.93/2.13 |
% 9.93/2.13 | GROUND_INST: instantiating (2) with x01, all_36_1, simplifying with (3), (7)
% 9.93/2.13 | gives:
% 9.93/2.13 | (10) iter1(1, x01) = all_36_1 & t1(all_36_1)
% 9.93/2.13 |
% 9.93/2.13 | ALPHA: (10) implies:
% 9.93/2.13 | (11) t1(all_36_1)
% 9.93/2.13 | (12) iter1(1, x01) = all_36_1
% 9.93/2.13 |
% 9.93/2.13 | GROUND_INST: instantiating (2) with all_36_1, all_36_0, simplifying with (8),
% 9.93/2.13 | (11) gives:
% 9.93/2.13 | (13) iter1(1, all_36_1) = all_36_0 & t1(all_36_0)
% 9.93/2.13 |
% 9.93/2.13 | ALPHA: (13) implies:
% 9.93/2.13 | (14) iter1(1, all_36_1) = all_36_0
% 9.93/2.13 |
% 9.93/2.13 | GROUND_INST: instantiating (9) with 1, simplifying with (12) gives:
% 9.93/2.13 | (15) ~ ($lesseq(1, $sum(lambda1, mu1))) | ? [v0: any] : ( ~ (v0 =
% 9.93/2.13 | all_36_0) & iter1(2, x01) = v0 & t1(v0))
% 9.93/2.13 |
% 9.93/2.13 | GROUND_INST: instantiating (1) with 2, x01, all_36_1, all_36_0, simplifying
% 9.93/2.13 | with (3), (7), (14) gives:
% 9.93/2.13 | (16) iter1(2, x01) = all_36_0 & t1(all_36_0)
% 9.93/2.13 |
% 9.93/2.13 | ALPHA: (16) implies:
% 9.93/2.13 | (17) iter1(2, x01) = all_36_0
% 9.93/2.13 |
% 9.93/2.13 | BETA: splitting (15) gives:
% 9.93/2.13 |
% 9.93/2.13 | Case 1:
% 9.93/2.13 | |
% 9.93/2.13 | | (18) $lesseq(mu1, $product(-1, lambda1))
% 9.93/2.13 | |
% 9.93/2.13 | | COMBINE_INEQS: (18), (lambda_range) imply:
% 9.93/2.13 | | (19) $lesseq(mu1, -1)
% 9.93/2.13 | |
% 9.93/2.13 | | COMBINE_INEQS: (19), (mu_range) imply:
% 9.93/2.13 | | (20) $false
% 9.93/2.13 | |
% 9.93/2.13 | | CLOSE: (20) is inconsistent.
% 9.93/2.13 | |
% 9.93/2.13 | Case 2:
% 9.93/2.13 | |
% 9.93/2.13 | | (21) ? [v0: any] : ( ~ (v0 = all_36_0) & iter1(2, x01) = v0 & t1(v0))
% 9.93/2.13 | |
% 9.93/2.13 | | DELTA: instantiating (21) with fresh symbol all_73_0 gives:
% 9.93/2.13 | | (22) ~ (all_73_0 = all_36_0) & iter1(2, x01) = all_73_0 & t1(all_73_0)
% 9.93/2.13 | |
% 9.93/2.13 | | ALPHA: (22) implies:
% 9.93/2.13 | | (23) ~ (all_73_0 = all_36_0)
% 9.93/2.13 | | (24) iter1(2, x01) = all_73_0
% 9.93/2.13 | |
% 9.93/2.14 | | GROUND_INST: instantiating (5) with all_36_0, all_73_0, x01, 2, simplifying
% 9.93/2.14 | | with (17), (24) gives:
% 9.93/2.14 | | (25) all_73_0 = all_36_0
% 9.93/2.14 | |
% 9.93/2.14 | | REDUCE: (23), (25) imply:
% 9.93/2.14 | | (26) $false
% 9.93/2.14 | |
% 9.93/2.14 | | CLOSE: (26) is inconsistent.
% 9.93/2.14 | |
% 9.93/2.14 | End of split
% 9.93/2.14 |
% 9.93/2.14 End of proof
% 9.93/2.14 % SZS output end Proof for theBenchmark
% 9.93/2.14
% 9.93/2.14 1538ms
%------------------------------------------------------------------------------