TSTP Solution File: DAT044_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT044_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 : n002.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 22:18:59 EDT 2023
% Result : Theorem 5.95s 1.53s
% Output : Proof 7.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT044_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 14:57:01 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.32/1.09 Prover 1: Preprocessing ...
% 2.32/1.09 Prover 4: Preprocessing ...
% 2.95/1.13 Prover 0: Preprocessing ...
% 2.95/1.13 Prover 3: Preprocessing ...
% 2.95/1.13 Prover 5: Preprocessing ...
% 2.95/1.13 Prover 2: Preprocessing ...
% 2.95/1.13 Prover 6: Preprocessing ...
% 4.90/1.38 Prover 5: Proving ...
% 4.96/1.38 Prover 6: Proving ...
% 5.13/1.40 Prover 1: Constructing countermodel ...
% 5.13/1.41 Prover 4: Constructing countermodel ...
% 5.13/1.42 Prover 3: Constructing countermodel ...
% 5.24/1.44 Prover 2: Proving ...
% 5.24/1.45 Prover 0: Proving ...
% 5.95/1.53 Prover 3: proved (892ms)
% 5.95/1.53
% 5.95/1.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.95/1.53
% 5.95/1.54 Prover 5: proved (893ms)
% 5.95/1.54
% 5.95/1.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.95/1.54
% 5.95/1.54 Prover 0: proved (900ms)
% 5.95/1.54
% 5.95/1.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.95/1.54
% 5.95/1.54 Prover 6: stopped
% 5.95/1.54 Prover 2: stopped
% 5.95/1.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.95/1.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.95/1.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.95/1.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.95/1.55 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.95/1.57 Prover 7: Preprocessing ...
% 5.95/1.58 Prover 10: Preprocessing ...
% 5.95/1.58 Prover 11: Preprocessing ...
% 5.95/1.58 Prover 13: Preprocessing ...
% 5.95/1.58 Prover 8: Preprocessing ...
% 6.53/1.64 Prover 10: Constructing countermodel ...
% 6.53/1.64 Prover 7: Constructing countermodel ...
% 6.53/1.67 Prover 8: Warning: ignoring some quantifiers
% 6.53/1.67 Prover 4: Found proof (size 60)
% 6.53/1.67 Prover 4: proved (1035ms)
% 6.53/1.67 Prover 10: stopped
% 7.17/1.67 Prover 7: stopped
% 7.17/1.67 Prover 1: stopped
% 7.17/1.68 Prover 8: Constructing countermodel ...
% 7.17/1.68 Prover 13: Warning: ignoring some quantifiers
% 7.21/1.68 Prover 11: Constructing countermodel ...
% 7.21/1.68 Prover 8: stopped
% 7.21/1.69 Prover 13: Constructing countermodel ...
% 7.21/1.69 Prover 11: stopped
% 7.21/1.69 Prover 13: stopped
% 7.21/1.69
% 7.21/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.21/1.69
% 7.34/1.70 % SZS output start Proof for theBenchmark
% 7.34/1.71 Assumptions after simplification:
% 7.34/1.71 ---------------------------------
% 7.34/1.71
% 7.34/1.71 (ax3)
% 7.42/1.73 ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 7.42/1.73 v2) | ~ collection(v1) | ? [v3: collection] : ? [v4: int] : (add(v0,
% 7.42/1.73 v1) = v3 & count(v3) = v4 & count(v1) = $sum(v4, -1) & collection(v3)))
% 7.42/1.73 & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0,
% 7.42/1.73 v1) = v2) | ~ collection(v1) | ? [v3: int] : ( ~ (v3 = 0) & in(v0, v2)
% 7.42/1.73 = v3)) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~
% 7.42/1.73 (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: any] : ? [v4: int] : ?
% 7.42/1.73 [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 &
% 7.42/1.73 ($difference(v5, v4) = -1 | v3 = 0))) & ! [v0: int] : ! [v1: collection]
% 7.42/1.73 : ! [v2: collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3:
% 7.42/1.74 int] : ? [v4: int] : ? [v5: any] : (count(v2) = v3 & count(v1) = v4 &
% 7.42/1.74 in(v0, v1) = v5 & ( ~ (v5 = 0) | ~ ($difference(v4, v3) = -1)))) & !
% 7.42/1.74 [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~ collection(v1) |
% 7.42/1.74 ? [v2: collection] : ? [v3: int] : ? [v4: int] : ( ~ ($difference(v4, v3)
% 7.42/1.74 = -1) & add(v0, v1) = v2 & count(v2) = v3 & count(v1) = v4 &
% 7.42/1.74 collection(v2)))
% 7.42/1.74
% 7.42/1.74 (ax4)
% 7.42/1.75 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : !
% 7.42/1.75 [v4: int] : (v4 = 0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~
% 7.42/1.75 collection(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0:
% 7.42/1.75 int] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v3 = 0 |
% 7.42/1.75 ~ (add(v0, v1) = v2) | ~ (in(v0, v2) = v3) | ~ collection(v1)) & ! [v0:
% 7.42/1.75 int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : (v2 = v0 |
% 7.42/1.75 ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | in(v0, v1)
% 7.42/1.75 = 0) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~
% 7.42/1.75 (in(v0, v1) = v2) | ~ collection(v1) | ? [v3: collection] : ? [v4: int] :
% 7.42/1.75 ? [v5: int] : ( ~ (v5 = v4) & add(v0, v1) = v3 & count(v3) = v4 & count(v1)
% 7.42/1.75 = v5 & collection(v3))) & ! [v0: int] : ! [v1: collection] : ! [v2:
% 7.42/1.75 collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: any] : ?
% 7.42/1.75 [v4: int] : ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) =
% 7.42/1.75 v3 & ( ~ (v3 = 0) | v5 = v4))) & ! [v0: int] : ! [v1: collection] : !
% 7.42/1.75 [v2: collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: int] :
% 7.42/1.75 ? [v4: int] : ? [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1)
% 7.42/1.75 = v5 & ( ~ (v4 = v3) | v5 = 0))) & ! [v0: int] : ! [v1: collection] : (
% 7.42/1.75 ~ (in(v0, v1) = 0) | ~ collection(v1) | ? [v2: collection] : ? [v3: int]
% 7.42/1.75 : (add(v0, v1) = v2 & count(v2) = v3 & count(v1) = v3 & collection(v2)))
% 7.42/1.75
% 7.42/1.75 (co1)
% 7.42/1.75 ? [v0: collection] : ? [v1: int] : ? [v2: collection] : ? [v3: int] : ?
% 7.42/1.75 [v4: int] : ($lesseq(v3, v4) & add(v1, v0) = v2 & count(v2) = v3 & count(v0) =
% 7.42/1.75 v4 & collection(v2) & collection(v0) & ! [v5: int] : ( ~ ($lesseq(v1, v5))
% 7.42/1.75 | ~ (in(v5, v0) = 0)))
% 7.42/1.75
% 7.42/1.75 (function-axioms)
% 7.42/1.75 ! [v0: collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int]
% 7.42/1.75 : (v1 = v0 | ~ (remove(v3, v2) = v1) | ~ (remove(v3, v2) = v0)) & ! [v0:
% 7.42/1.75 collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v1
% 7.42/1.76 = v0 | ~ (add(v3, v2) = v1) | ~ (add(v3, v2) = v0)) & ! [v0:
% 7.42/1.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: collection] : !
% 7.42/1.76 [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 7.42/1.76 int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~ (count(v2) = v1) |
% 7.42/1.76 ~ (count(v2) = v0))
% 7.42/1.76
% 7.42/1.76 Further assumptions not needed in the proof:
% 7.42/1.76 --------------------------------------------
% 7.42/1.76 ax1, ax2, ax5, ax6, ax7
% 7.42/1.76
% 7.42/1.76 Those formulas are unsatisfiable:
% 7.42/1.76 ---------------------------------
% 7.42/1.76
% 7.42/1.76 Begin of proof
% 7.42/1.76 |
% 7.42/1.76 | ALPHA: (ax3) implies:
% 7.42/1.76 | (1) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0,
% 7.42/1.76 | v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ?
% 7.42/1.76 | [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~
% 7.42/1.76 | (v5 = 0) | ~ ($difference(v4, v3) = -1))))
% 7.42/1.76 | (2) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0,
% 7.42/1.76 | v1) = v2) | ~ collection(v1) | ? [v3: any] : ? [v4: int] : ?
% 7.42/1.76 | [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 &
% 7.42/1.76 | ($difference(v5, v4) = -1 | v3 = 0)))
% 7.42/1.76 |
% 7.42/1.76 | ALPHA: (ax4) implies:
% 7.42/1.77 | (3) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0,
% 7.42/1.77 | v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ?
% 7.42/1.77 | [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~
% 7.42/1.77 | (v4 = v3) | v5 = 0)))
% 7.42/1.77 | (4) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0,
% 7.42/1.77 | v1) = v2) | ~ collection(v1) | ? [v3: any] : ? [v4: int] : ?
% 7.42/1.77 | [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 & ( ~
% 7.42/1.77 | (v3 = 0) | v5 = v4)))
% 7.42/1.77 |
% 7.42/1.77 | ALPHA: (function-axioms) implies:
% 7.42/1.77 | (5) ! [v0: int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~
% 7.42/1.77 | (count(v2) = v1) | ~ (count(v2) = v0))
% 7.42/1.77 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 7.42/1.77 | collection] : ! [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~
% 7.42/1.77 | (in(v3, v2) = v0))
% 7.42/1.77 |
% 7.42/1.77 | DELTA: instantiating (co1) with fresh symbols all_13_0, all_13_1, all_13_2,
% 7.42/1.77 | all_13_3, all_13_4 gives:
% 7.42/1.77 | (7) $lesseq(all_13_1, all_13_0) & add(all_13_3, all_13_4) = all_13_2 &
% 7.42/1.77 | count(all_13_2) = all_13_1 & count(all_13_4) = all_13_0 &
% 7.42/1.77 | collection(all_13_2) & collection(all_13_4) & ! [v0: int] : ( ~
% 7.42/1.77 | ($lesseq(all_13_3, v0)) | ~ (in(v0, all_13_4) = 0))
% 7.42/1.77 |
% 7.42/1.77 | ALPHA: (7) implies:
% 7.42/1.77 | (8) $lesseq(all_13_1, all_13_0)
% 7.42/1.77 | (9) collection(all_13_4)
% 7.42/1.77 | (10) count(all_13_4) = all_13_0
% 7.42/1.77 | (11) count(all_13_2) = all_13_1
% 7.42/1.77 | (12) add(all_13_3, all_13_4) = all_13_2
% 7.42/1.77 | (13) ! [v0: int] : ( ~ ($lesseq(all_13_3, v0)) | ~ (in(v0, all_13_4) =
% 7.42/1.77 | 0))
% 7.42/1.77 |
% 7.42/1.78 | GROUND_INST: instantiating (4) with all_13_3, all_13_4, all_13_2, simplifying
% 7.42/1.78 | with (9), (12) gives:
% 7.42/1.78 | (14) ? [v0: any] : ? [v1: int] : ? [v2: int] : (count(all_13_2) = v1 &
% 7.42/1.78 | count(all_13_4) = v2 & in(all_13_3, all_13_4) = v0 & ( ~ (v0 = 0) |
% 7.42/1.78 | v2 = v1))
% 7.42/1.78 |
% 7.42/1.78 | GROUND_INST: instantiating (2) with all_13_3, all_13_4, all_13_2, simplifying
% 7.42/1.78 | with (9), (12) gives:
% 7.42/1.78 | (15) ? [v0: any] : ? [v1: int] : ? [v2: int] : (count(all_13_2) = v1 &
% 7.42/1.78 | count(all_13_4) = v2 & in(all_13_3, all_13_4) = v0 &
% 7.42/1.78 | ($difference(v2, v1) = -1 | v0 = 0))
% 7.42/1.78 |
% 7.42/1.78 | GROUND_INST: instantiating (1) with all_13_3, all_13_4, all_13_2, simplifying
% 7.42/1.78 | with (9), (12) gives:
% 7.42/1.78 | (16) ? [v0: int] : ? [v1: int] : ? [v2: any] : (count(all_13_2) = v0 &
% 7.42/1.78 | count(all_13_4) = v1 & in(all_13_3, all_13_4) = v2 & ( ~ (v2 = 0) |
% 7.42/1.78 | ~ ($difference(v1, v0) = -1)))
% 7.42/1.78 |
% 7.42/1.78 | GROUND_INST: instantiating (3) with all_13_3, all_13_4, all_13_2, simplifying
% 7.42/1.78 | with (9), (12) gives:
% 7.42/1.78 | (17) ? [v0: int] : ? [v1: int] : ? [v2: any] : (count(all_13_2) = v0 &
% 7.42/1.78 | count(all_13_4) = v1 & in(all_13_3, all_13_4) = v2 & ( ~ (v1 = v0) |
% 7.42/1.78 | v2 = 0))
% 7.42/1.78 |
% 7.42/1.78 | DELTA: instantiating (14) with fresh symbols all_23_0, all_23_1, all_23_2
% 7.42/1.78 | gives:
% 7.42/1.78 | (18) count(all_13_2) = all_23_1 & count(all_13_4) = all_23_0 & in(all_13_3,
% 7.42/1.78 | all_13_4) = all_23_2 & ( ~ (all_23_2 = 0) | all_23_0 = all_23_1)
% 7.42/1.78 |
% 7.42/1.78 | ALPHA: (18) implies:
% 7.42/1.78 | (19) in(all_13_3, all_13_4) = all_23_2
% 7.42/1.78 | (20) count(all_13_4) = all_23_0
% 7.42/1.78 | (21) count(all_13_2) = all_23_1
% 7.42/1.78 |
% 7.42/1.78 | DELTA: instantiating (17) with fresh symbols all_25_0, all_25_1, all_25_2
% 7.42/1.78 | gives:
% 7.42/1.78 | (22) count(all_13_2) = all_25_2 & count(all_13_4) = all_25_1 & in(all_13_3,
% 7.42/1.78 | all_13_4) = all_25_0 & ( ~ (all_25_1 = all_25_2) | all_25_0 = 0)
% 7.42/1.78 |
% 7.42/1.78 | ALPHA: (22) implies:
% 7.42/1.78 | (23) in(all_13_3, all_13_4) = all_25_0
% 7.42/1.79 | (24) count(all_13_4) = all_25_1
% 7.42/1.79 | (25) count(all_13_2) = all_25_2
% 7.42/1.79 |
% 7.42/1.79 | DELTA: instantiating (16) with fresh symbols all_27_0, all_27_1, all_27_2
% 7.42/1.79 | gives:
% 7.42/1.79 | (26) count(all_13_2) = all_27_2 & count(all_13_4) = all_27_1 & in(all_13_3,
% 7.42/1.79 | all_13_4) = all_27_0 & ( ~ (all_27_0 = 0) | ~
% 7.42/1.79 | ($difference(all_27_1, all_27_2) = -1))
% 7.42/1.79 |
% 7.42/1.79 | ALPHA: (26) implies:
% 7.42/1.79 | (27) in(all_13_3, all_13_4) = all_27_0
% 7.42/1.79 | (28) count(all_13_4) = all_27_1
% 7.42/1.79 | (29) count(all_13_2) = all_27_2
% 7.42/1.79 |
% 7.42/1.79 | DELTA: instantiating (15) with fresh symbols all_29_0, all_29_1, all_29_2
% 7.42/1.79 | gives:
% 7.42/1.79 | (30) count(all_13_2) = all_29_1 & count(all_13_4) = all_29_0 & in(all_13_3,
% 7.42/1.79 | all_13_4) = all_29_2 & ($difference(all_29_0, all_29_1) = -1 |
% 7.42/1.79 | all_29_2 = 0)
% 7.42/1.79 |
% 7.42/1.79 | ALPHA: (30) implies:
% 7.42/1.79 | (31) in(all_13_3, all_13_4) = all_29_2
% 7.42/1.79 | (32) count(all_13_4) = all_29_0
% 7.42/1.79 | (33) count(all_13_2) = all_29_1
% 7.42/1.79 | (34) $difference(all_29_0, all_29_1) = -1 | all_29_2 = 0
% 7.42/1.79 |
% 7.42/1.79 | GROUND_INST: instantiating (6) with all_23_2, all_27_0, all_13_4, all_13_3,
% 7.42/1.79 | simplifying with (19), (27) gives:
% 7.42/1.79 | (35) all_27_0 = all_23_2
% 7.42/1.79 |
% 7.42/1.79 | GROUND_INST: instantiating (6) with all_27_0, all_29_2, all_13_4, all_13_3,
% 7.42/1.79 | simplifying with (27), (31) gives:
% 7.42/1.79 | (36) all_29_2 = all_27_0
% 7.42/1.79 |
% 7.42/1.79 | GROUND_INST: instantiating (6) with all_25_0, all_29_2, all_13_4, all_13_3,
% 7.42/1.79 | simplifying with (23), (31) gives:
% 7.42/1.79 | (37) all_29_2 = all_25_0
% 7.42/1.79 |
% 7.42/1.79 | GROUND_INST: instantiating (5) with all_13_0, all_27_1, all_13_4, simplifying
% 7.42/1.79 | with (10), (28) gives:
% 7.42/1.79 | (38) all_27_1 = all_13_0
% 7.42/1.79 |
% 7.42/1.79 | GROUND_INST: instantiating (5) with all_25_1, all_27_1, all_13_4, simplifying
% 7.42/1.79 | with (24), (28) gives:
% 7.42/1.79 | (39) all_27_1 = all_25_1
% 7.42/1.79 |
% 7.42/1.79 | GROUND_INST: instantiating (5) with all_27_1, all_29_0, all_13_4, simplifying
% 7.42/1.79 | with (28), (32) gives:
% 7.42/1.79 | (40) all_29_0 = all_27_1
% 7.42/1.79 |
% 7.42/1.79 | GROUND_INST: instantiating (5) with all_23_0, all_29_0, all_13_4, simplifying
% 7.42/1.79 | with (20), (32) gives:
% 7.42/1.79 | (41) all_29_0 = all_23_0
% 7.42/1.79 |
% 7.42/1.79 | GROUND_INST: instantiating (5) with all_23_1, all_27_2, all_13_2, simplifying
% 7.42/1.79 | with (21), (29) gives:
% 7.42/1.79 | (42) all_27_2 = all_23_1
% 7.42/1.79 |
% 7.42/1.79 | GROUND_INST: instantiating (5) with all_13_1, all_29_1, all_13_2, simplifying
% 7.42/1.79 | with (11), (33) gives:
% 7.42/1.79 | (43) all_29_1 = all_13_1
% 7.42/1.79 |
% 7.42/1.79 | GROUND_INST: instantiating (5) with all_27_2, all_29_1, all_13_2, simplifying
% 7.42/1.79 | with (29), (33) gives:
% 7.42/1.79 | (44) all_29_1 = all_27_2
% 7.42/1.79 |
% 7.42/1.79 | GROUND_INST: instantiating (5) with all_25_2, all_29_1, all_13_2, simplifying
% 7.42/1.79 | with (25), (33) gives:
% 7.42/1.79 | (45) all_29_1 = all_25_2
% 7.42/1.79 |
% 7.42/1.79 | COMBINE_EQS: (40), (41) imply:
% 7.42/1.79 | (46) all_27_1 = all_23_0
% 7.42/1.79 |
% 7.42/1.79 | SIMP: (46) implies:
% 7.42/1.79 | (47) all_27_1 = all_23_0
% 7.42/1.79 |
% 7.42/1.79 | COMBINE_EQS: (44), (45) imply:
% 7.42/1.79 | (48) all_27_2 = all_25_2
% 7.42/1.79 |
% 7.42/1.79 | SIMP: (48) implies:
% 7.42/1.79 | (49) all_27_2 = all_25_2
% 7.42/1.79 |
% 7.42/1.79 | COMBINE_EQS: (43), (45) imply:
% 7.42/1.79 | (50) all_25_2 = all_13_1
% 7.42/1.79 |
% 7.42/1.80 | COMBINE_EQS: (36), (37) imply:
% 7.42/1.80 | (51) all_27_0 = all_25_0
% 7.42/1.80 |
% 7.42/1.80 | SIMP: (51) implies:
% 7.42/1.80 | (52) all_27_0 = all_25_0
% 7.42/1.80 |
% 7.42/1.80 | COMBINE_EQS: (35), (52) imply:
% 7.42/1.80 | (53) all_25_0 = all_23_2
% 7.42/1.80 |
% 7.42/1.80 | SIMP: (53) implies:
% 7.42/1.80 | (54) all_25_0 = all_23_2
% 7.42/1.80 |
% 7.42/1.80 | COMBINE_EQS: (39), (47) imply:
% 7.42/1.80 | (55) all_25_1 = all_23_0
% 7.42/1.80 |
% 7.42/1.80 | COMBINE_EQS: (38), (39) imply:
% 7.42/1.80 | (56) all_25_1 = all_13_0
% 7.42/1.80 |
% 7.42/1.80 | COMBINE_EQS: (42), (49) imply:
% 7.42/1.80 | (57) all_25_2 = all_23_1
% 7.42/1.80 |
% 7.42/1.80 | SIMP: (57) implies:
% 7.42/1.80 | (58) all_25_2 = all_23_1
% 7.42/1.80 |
% 7.42/1.80 | COMBINE_EQS: (55), (56) imply:
% 7.42/1.80 | (59) all_23_0 = all_13_0
% 7.42/1.80 |
% 7.42/1.80 | COMBINE_EQS: (50), (58) imply:
% 7.42/1.80 | (60) all_23_1 = all_13_1
% 7.42/1.80 |
% 7.42/1.80 | COMBINE_EQS: (37), (54) imply:
% 7.42/1.80 | (61) all_29_2 = all_23_2
% 7.42/1.80 |
% 7.42/1.80 | COMBINE_EQS: (41), (59) imply:
% 7.42/1.80 | (62) all_29_0 = all_13_0
% 7.42/1.80 |
% 7.42/1.80 | BETA: splitting (34) gives:
% 7.42/1.80 |
% 7.42/1.80 | Case 1:
% 7.42/1.80 | |
% 7.42/1.80 | | (63) all_29_2 = 0
% 7.42/1.80 | |
% 7.42/1.80 | | COMBINE_EQS: (61), (63) imply:
% 7.42/1.80 | | (64) all_23_2 = 0
% 7.42/1.80 | |
% 7.42/1.80 | | REDUCE: (19), (64) imply:
% 7.42/1.80 | | (65) in(all_13_3, all_13_4) = 0
% 7.42/1.80 | |
% 7.42/1.80 | | GROUND_INST: instantiating (13) with all_13_3, simplifying with (65) gives:
% 7.42/1.80 | | (66) $false
% 7.42/1.80 | |
% 7.42/1.80 | | CLOSE: (66) is inconsistent.
% 7.42/1.80 | |
% 7.42/1.80 | Case 2:
% 7.42/1.80 | |
% 7.42/1.80 | | (67) $difference(all_29_0, all_29_1) = -1
% 7.42/1.80 | |
% 7.42/1.80 | | COMBINE_EQS: (62), (67) imply:
% 7.42/1.80 | | (68) $difference(all_29_1, all_13_0) = 1
% 7.42/1.80 | |
% 7.42/1.80 | | SIMP: (68) implies:
% 7.42/1.80 | | (69) $difference(all_29_1, all_13_0) = 1
% 7.42/1.80 | |
% 7.42/1.80 | | COMBINE_EQS: (43), (69) imply:
% 7.42/1.80 | | (70) $difference(all_13_0, all_13_1) = -1
% 7.42/1.80 | |
% 7.42/1.80 | | SIMP: (70) implies:
% 7.42/1.80 | | (71) $difference(all_13_0, all_13_1) = -1
% 7.42/1.80 | |
% 7.42/1.80 | | REDUCE: (8), (71) imply:
% 7.42/1.80 | | (72) $false
% 7.42/1.80 | |
% 7.42/1.80 | | CLOSE: (72) is inconsistent.
% 7.42/1.80 | |
% 7.42/1.80 | End of split
% 7.42/1.80 |
% 7.42/1.80 End of proof
% 7.42/1.80 % SZS output end Proof for theBenchmark
% 7.42/1.80
% 7.42/1.80 1186ms
%------------------------------------------------------------------------------