TSTP Solution File: SEU162+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU162+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n022.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 : Thu Aug 31 17:42:55 EDT 2023
% Result : Theorem 4.64s 1.42s
% Output : Proof 6.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU162+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n022.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 : Wed Aug 23 14:37:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.62 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.93/0.98 Prover 4: Preprocessing ...
% 1.93/0.98 Prover 1: Preprocessing ...
% 1.93/1.03 Prover 6: Preprocessing ...
% 1.93/1.03 Prover 0: Preprocessing ...
% 1.93/1.03 Prover 5: Preprocessing ...
% 1.93/1.03 Prover 2: Preprocessing ...
% 1.93/1.03 Prover 3: Preprocessing ...
% 3.13/1.19 Prover 1: Constructing countermodel ...
% 3.13/1.19 Prover 5: Proving ...
% 3.13/1.19 Prover 3: Constructing countermodel ...
% 3.13/1.19 Prover 6: Constructing countermodel ...
% 3.13/1.20 Prover 2: Proving ...
% 3.13/1.21 Prover 4: Constructing countermodel ...
% 3.63/1.21 Prover 0: Proving ...
% 4.02/1.31 Prover 3: gave up
% 4.02/1.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.02/1.34 Prover 1: gave up
% 4.02/1.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.64/1.35 Prover 7: Preprocessing ...
% 4.64/1.36 Prover 8: Preprocessing ...
% 4.64/1.38 Prover 7: Warning: ignoring some quantifiers
% 4.64/1.38 Prover 7: Constructing countermodel ...
% 4.64/1.41 Prover 6: gave up
% 4.64/1.41 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 4.64/1.42 Prover 0: proved (782ms)
% 4.64/1.42
% 4.64/1.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.64/1.42
% 4.64/1.43 Prover 2: stopped
% 4.64/1.43 Prover 9: Preprocessing ...
% 4.64/1.43 Prover 5: stopped
% 4.64/1.44 Prover 7: gave up
% 4.64/1.44 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.64/1.44 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.64/1.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.64/1.44 Prover 8: Warning: ignoring some quantifiers
% 4.64/1.44 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.64/1.45 Prover 8: Constructing countermodel ...
% 4.64/1.45 Prover 16: Preprocessing ...
% 4.64/1.46 Prover 10: Preprocessing ...
% 4.64/1.46 Prover 13: Preprocessing ...
% 4.64/1.47 Prover 11: Preprocessing ...
% 4.93/1.50 Prover 10: Warning: ignoring some quantifiers
% 4.93/1.50 Prover 16: Warning: ignoring some quantifiers
% 4.93/1.51 Prover 16: Constructing countermodel ...
% 4.93/1.51 Prover 10: Constructing countermodel ...
% 4.93/1.51 Prover 13: Warning: ignoring some quantifiers
% 4.93/1.51 Prover 13: Constructing countermodel ...
% 4.93/1.53 Prover 4: Found proof (size 45)
% 4.93/1.53 Prover 4: proved (880ms)
% 4.93/1.53 Prover 10: stopped
% 4.93/1.53 Prover 13: stopped
% 4.93/1.53 Prover 8: stopped
% 4.93/1.54 Prover 16: stopped
% 4.93/1.54 Prover 9: Constructing countermodel ...
% 4.93/1.54 Prover 9: stopped
% 5.99/1.56 Prover 11: Constructing countermodel ...
% 5.99/1.56 Prover 11: stopped
% 5.99/1.56
% 5.99/1.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.99/1.56
% 5.99/1.57 % SZS output start Proof for theBenchmark
% 5.99/1.57 Assumptions after simplification:
% 5.99/1.57 ---------------------------------
% 5.99/1.57
% 5.99/1.57 (l25_zfmisc_1)
% 5.99/1.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v0) = v2) | ~
% 5.99/1.60 (disjoint(v2, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0)
% 5.99/1.60 & in(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) |
% 5.99/1.60 ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 5.99/1.60 singleton(v0) = v2 & disjoint(v2, v1) = v3 & $i(v2)))
% 5.99/1.60
% 5.99/1.60 (l28_zfmisc_1)
% 5.99/1.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 5.99/1.60 (singleton(v0) = v2) | ~ (disjoint(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) |
% 5.99/1.60 in(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 5.99/1.60 (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (singleton(v0) =
% 5.99/1.60 v3 & disjoint(v3, v1) = 0 & $i(v3)))
% 5.99/1.60
% 5.99/1.60 (symmetry_r1_xboole_0)
% 5.99/1.61 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v1, v0) =
% 5.99/1.61 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & disjoint(v0,
% 5.99/1.61 v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~
% 5.99/1.61 $i(v1) | ~ $i(v0) | disjoint(v1, v0) = 0)
% 5.99/1.61
% 5.99/1.61 (t65_zfmisc_1)
% 5.99/1.61 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] :
% 5.99/1.61 (set_difference(v0, v2) = v3 & singleton(v1) = v2 & in(v1, v0) = v4 & $i(v3) &
% 5.99/1.61 $i(v2) & $i(v1) & $i(v0) & ((v4 = 0 & v3 = v0) | ( ~ (v4 = 0) & ~ (v3 =
% 5.99/1.61 v0))))
% 5.99/1.61
% 5.99/1.61 (t83_xboole_1)
% 6.25/1.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (set_difference(v0,
% 6.25/1.61 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 6.25/1.61 disjoint(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 6.25/1.61 0 | ~ (disjoint(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~
% 6.25/1.61 (v3 = v0) & set_difference(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1:
% 6.25/1.61 $i] : ( ~ (set_difference(v0, v1) = v0) | ~ $i(v1) | ~ $i(v0) |
% 6.25/1.61 disjoint(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) =
% 6.25/1.61 0) | ~ $i(v1) | ~ $i(v0) | set_difference(v0, v1) = v0)
% 6.25/1.61
% 6.25/1.61 (function-axioms)
% 6.25/1.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.25/1.62 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 6.25/1.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 6.25/1.62 : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & !
% 6.25/1.62 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 6.25/1.62 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i]
% 6.25/1.62 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 6.25/1.62 (singleton(v2) = v0))
% 6.25/1.62
% 6.25/1.62 Further assumptions not needed in the proof:
% 6.25/1.62 --------------------------------------------
% 6.25/1.62 antisymmetry_r2_hidden, dt_k1_tarski, dt_k4_xboole_0
% 6.25/1.62
% 6.25/1.62 Those formulas are unsatisfiable:
% 6.25/1.62 ---------------------------------
% 6.25/1.62
% 6.25/1.62 Begin of proof
% 6.25/1.62 |
% 6.25/1.62 | ALPHA: (l25_zfmisc_1) implies:
% 6.25/1.62 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~
% 6.25/1.62 | $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & singleton(v0) =
% 6.25/1.62 | v2 & disjoint(v2, v1) = v3 & $i(v2)))
% 6.25/1.62 |
% 6.25/1.62 | ALPHA: (l28_zfmisc_1) implies:
% 6.25/1.62 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 6.25/1.62 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (singleton(v0) = v3 &
% 6.25/1.62 | disjoint(v3, v1) = 0 & $i(v3)))
% 6.25/1.62 |
% 6.25/1.62 | ALPHA: (symmetry_r1_xboole_0) implies:
% 6.25/1.63 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~
% 6.25/1.63 | $i(v0) | disjoint(v1, v0) = 0)
% 6.25/1.63 |
% 6.25/1.63 | ALPHA: (t83_xboole_1) implies:
% 6.25/1.63 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (set_difference(v0, v1) = v0) | ~
% 6.25/1.63 | $i(v1) | ~ $i(v0) | disjoint(v0, v1) = 0)
% 6.25/1.63 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 6.25/1.63 | (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 6.25/1.63 | : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 6.25/1.63 |
% 6.25/1.63 | ALPHA: (function-axioms) implies:
% 6.25/1.63 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2)
% 6.25/1.63 | = v1) | ~ (singleton(v2) = v0))
% 6.25/1.63 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.25/1.63 | ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3,
% 6.25/1.63 | v2) = v0))
% 6.25/1.63 |
% 6.25/1.63 | DELTA: instantiating (t65_zfmisc_1) with fresh symbols all_8_0, all_8_1,
% 6.25/1.63 | all_8_2, all_8_3, all_8_4 gives:
% 6.25/1.63 | (8) set_difference(all_8_4, all_8_2) = all_8_1 & singleton(all_8_3) =
% 6.25/1.63 | all_8_2 & in(all_8_3, all_8_4) = all_8_0 & $i(all_8_1) & $i(all_8_2) &
% 6.25/1.63 | $i(all_8_3) & $i(all_8_4) & ((all_8_0 = 0 & all_8_1 = all_8_4) | ( ~
% 6.25/1.63 | (all_8_0 = 0) & ~ (all_8_1 = all_8_4)))
% 6.25/1.63 |
% 6.25/1.63 | ALPHA: (8) implies:
% 6.25/1.63 | (9) $i(all_8_4)
% 6.25/1.63 | (10) $i(all_8_3)
% 6.25/1.63 | (11) $i(all_8_2)
% 6.25/1.63 | (12) $i(all_8_1)
% 6.25/1.63 | (13) in(all_8_3, all_8_4) = all_8_0
% 6.25/1.63 | (14) singleton(all_8_3) = all_8_2
% 6.25/1.63 | (15) set_difference(all_8_4, all_8_2) = all_8_1
% 6.25/1.64 | (16) (all_8_0 = 0 & all_8_1 = all_8_4) | ( ~ (all_8_0 = 0) & ~ (all_8_1 =
% 6.25/1.64 | all_8_4))
% 6.25/1.64 |
% 6.25/1.64 | GROUND_INST: instantiating (2) with all_8_3, all_8_4, all_8_0, simplifying
% 6.25/1.64 | with (9), (10), (13) gives:
% 6.25/1.64 | (17) all_8_0 = 0 | ? [v0: $i] : (singleton(all_8_3) = v0 & disjoint(v0,
% 6.25/1.64 | all_8_4) = 0 & $i(v0))
% 6.25/1.64 |
% 6.25/1.64 | GROUND_INST: instantiating (5) with all_8_4, all_8_2, all_8_1, simplifying
% 6.25/1.64 | with (9), (11), (15) gives:
% 6.25/1.64 | (18) all_8_1 = all_8_4 | ? [v0: int] : ( ~ (v0 = 0) & disjoint(all_8_4,
% 6.25/1.64 | all_8_2) = v0)
% 6.25/1.64 |
% 6.25/1.64 | BETA: splitting (16) gives:
% 6.25/1.64 |
% 6.25/1.64 | Case 1:
% 6.25/1.64 | |
% 6.25/1.64 | | (19) all_8_0 = 0 & all_8_1 = all_8_4
% 6.25/1.64 | |
% 6.25/1.64 | | ALPHA: (19) implies:
% 6.25/1.64 | | (20) all_8_1 = all_8_4
% 6.25/1.64 | | (21) all_8_0 = 0
% 6.25/1.64 | |
% 6.25/1.64 | | REDUCE: (15), (20) imply:
% 6.25/1.64 | | (22) set_difference(all_8_4, all_8_2) = all_8_4
% 6.25/1.64 | |
% 6.25/1.64 | | REDUCE: (13), (21) imply:
% 6.25/1.64 | | (23) in(all_8_3, all_8_4) = 0
% 6.25/1.64 | |
% 6.25/1.64 | | GROUND_INST: instantiating (1) with all_8_3, all_8_4, simplifying with (9),
% 6.25/1.64 | | (10), (23) gives:
% 6.25/1.64 | | (24) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & singleton(all_8_3) = v0
% 6.25/1.64 | | & disjoint(v0, all_8_4) = v1 & $i(v0))
% 6.25/1.64 | |
% 6.25/1.64 | | GROUND_INST: instantiating (4) with all_8_4, all_8_2, simplifying with (9),
% 6.25/1.64 | | (11), (22) gives:
% 6.25/1.64 | | (25) disjoint(all_8_4, all_8_2) = 0
% 6.25/1.64 | |
% 6.25/1.64 | | DELTA: instantiating (24) with fresh symbols all_25_0, all_25_1 gives:
% 6.25/1.64 | | (26) ~ (all_25_0 = 0) & singleton(all_8_3) = all_25_1 &
% 6.25/1.64 | | disjoint(all_25_1, all_8_4) = all_25_0 & $i(all_25_1)
% 6.25/1.64 | |
% 6.25/1.64 | | ALPHA: (26) implies:
% 6.25/1.64 | | (27) ~ (all_25_0 = 0)
% 6.25/1.64 | | (28) $i(all_25_1)
% 6.25/1.64 | | (29) disjoint(all_25_1, all_8_4) = all_25_0
% 6.25/1.64 | | (30) singleton(all_8_3) = all_25_1
% 6.25/1.64 | |
% 6.25/1.64 | | GROUND_INST: instantiating (6) with all_8_2, all_25_1, all_8_3, simplifying
% 6.25/1.64 | | with (14), (30) gives:
% 6.25/1.64 | | (31) all_25_1 = all_8_2
% 6.25/1.64 | |
% 6.25/1.64 | | REDUCE: (29), (31) imply:
% 6.25/1.64 | | (32) disjoint(all_8_2, all_8_4) = all_25_0
% 6.25/1.64 | |
% 6.25/1.64 | | GROUND_INST: instantiating (3) with all_8_4, all_8_2, simplifying with (9),
% 6.25/1.64 | | (11), (25) gives:
% 6.25/1.65 | | (33) disjoint(all_8_2, all_8_4) = 0
% 6.25/1.65 | |
% 6.25/1.65 | | GROUND_INST: instantiating (7) with all_25_0, 0, all_8_4, all_8_2,
% 6.25/1.65 | | simplifying with (32), (33) gives:
% 6.25/1.65 | | (34) all_25_0 = 0
% 6.25/1.65 | |
% 6.25/1.65 | | REDUCE: (27), (34) imply:
% 6.25/1.65 | | (35) $false
% 6.25/1.65 | |
% 6.25/1.65 | | CLOSE: (35) is inconsistent.
% 6.25/1.65 | |
% 6.25/1.65 | Case 2:
% 6.25/1.65 | |
% 6.25/1.65 | | (36) ~ (all_8_0 = 0) & ~ (all_8_1 = all_8_4)
% 6.25/1.65 | |
% 6.25/1.65 | | ALPHA: (36) implies:
% 6.25/1.65 | | (37) ~ (all_8_1 = all_8_4)
% 6.25/1.65 | | (38) ~ (all_8_0 = 0)
% 6.25/1.65 | |
% 6.25/1.65 | | BETA: splitting (17) gives:
% 6.25/1.65 | |
% 6.25/1.65 | | Case 1:
% 6.25/1.65 | | |
% 6.25/1.65 | | | (39) all_8_0 = 0
% 6.25/1.65 | | |
% 6.25/1.65 | | | REDUCE: (38), (39) imply:
% 6.25/1.65 | | | (40) $false
% 6.25/1.65 | | |
% 6.25/1.65 | | | CLOSE: (40) is inconsistent.
% 6.25/1.65 | | |
% 6.25/1.65 | | Case 2:
% 6.25/1.65 | | |
% 6.25/1.65 | | | (41) ? [v0: $i] : (singleton(all_8_3) = v0 & disjoint(v0, all_8_4) = 0
% 6.25/1.65 | | | & $i(v0))
% 6.25/1.65 | | |
% 6.25/1.65 | | | DELTA: instantiating (41) with fresh symbol all_21_0 gives:
% 6.25/1.65 | | | (42) singleton(all_8_3) = all_21_0 & disjoint(all_21_0, all_8_4) = 0 &
% 6.25/1.65 | | | $i(all_21_0)
% 6.25/1.65 | | |
% 6.25/1.65 | | | ALPHA: (42) implies:
% 6.25/1.65 | | | (43) $i(all_21_0)
% 6.25/1.65 | | | (44) disjoint(all_21_0, all_8_4) = 0
% 6.25/1.65 | | | (45) singleton(all_8_3) = all_21_0
% 6.25/1.65 | | |
% 6.25/1.65 | | | BETA: splitting (18) gives:
% 6.25/1.65 | | |
% 6.25/1.65 | | | Case 1:
% 6.25/1.65 | | | |
% 6.25/1.65 | | | | (46) all_8_1 = all_8_4
% 6.25/1.65 | | | |
% 6.25/1.65 | | | | REDUCE: (37), (46) imply:
% 6.25/1.65 | | | | (47) $false
% 6.25/1.65 | | | |
% 6.25/1.65 | | | | CLOSE: (47) is inconsistent.
% 6.25/1.65 | | | |
% 6.25/1.65 | | | Case 2:
% 6.25/1.65 | | | |
% 6.45/1.65 | | | | (48) ? [v0: int] : ( ~ (v0 = 0) & disjoint(all_8_4, all_8_2) = v0)
% 6.45/1.65 | | | |
% 6.45/1.65 | | | | DELTA: instantiating (48) with fresh symbol all_27_0 gives:
% 6.45/1.65 | | | | (49) ~ (all_27_0 = 0) & disjoint(all_8_4, all_8_2) = all_27_0
% 6.45/1.65 | | | |
% 6.45/1.65 | | | | ALPHA: (49) implies:
% 6.45/1.65 | | | | (50) ~ (all_27_0 = 0)
% 6.45/1.65 | | | | (51) disjoint(all_8_4, all_8_2) = all_27_0
% 6.45/1.65 | | | |
% 6.45/1.65 | | | | GROUND_INST: instantiating (6) with all_8_2, all_21_0, all_8_3,
% 6.45/1.65 | | | | simplifying with (14), (45) gives:
% 6.45/1.65 | | | | (52) all_21_0 = all_8_2
% 6.45/1.65 | | | |
% 6.45/1.65 | | | | REDUCE: (44), (52) imply:
% 6.45/1.65 | | | | (53) disjoint(all_8_2, all_8_4) = 0
% 6.45/1.65 | | | |
% 6.45/1.65 | | | | GROUND_INST: instantiating (3) with all_8_2, all_8_4, simplifying with
% 6.45/1.65 | | | | (9), (11), (53) gives:
% 6.45/1.65 | | | | (54) disjoint(all_8_4, all_8_2) = 0
% 6.45/1.65 | | | |
% 6.45/1.66 | | | | GROUND_INST: instantiating (7) with all_27_0, 0, all_8_2, all_8_4,
% 6.45/1.66 | | | | simplifying with (51), (54) gives:
% 6.45/1.66 | | | | (55) all_27_0 = 0
% 6.45/1.66 | | | |
% 6.45/1.66 | | | | REDUCE: (50), (55) imply:
% 6.45/1.66 | | | | (56) $false
% 6.45/1.66 | | | |
% 6.45/1.66 | | | | CLOSE: (56) is inconsistent.
% 6.45/1.66 | | | |
% 6.45/1.66 | | | End of split
% 6.45/1.66 | | |
% 6.45/1.66 | | End of split
% 6.45/1.66 | |
% 6.45/1.66 | End of split
% 6.45/1.66 |
% 6.45/1.66 End of proof
% 6.45/1.66 % SZS output end Proof for theBenchmark
% 6.45/1.66
% 6.45/1.66 1038ms
%------------------------------------------------------------------------------