TSTP Solution File: SEU182+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU182+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 : n005.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 17:43:06 EDT 2023
% Result : Theorem 9.42s 3.01s
% Output : Proof 12.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU182+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 23 15:10:24 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.67 ________ _____
% 0.22/0.67 ___ __ \_________(_)________________________________
% 0.22/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.67
% 0.22/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.67 (2023-06-19)
% 0.22/0.67
% 0.22/0.67 (c) Philipp Rümmer, 2009-2023
% 0.22/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.67 Amanda Stjerna.
% 0.22/0.67 Free software under BSD-3-Clause.
% 0.22/0.67
% 0.22/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.67
% 0.22/0.67 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.68 Running up to 7 provers in parallel.
% 0.22/0.74 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.74 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.74 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.74 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.74 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.74 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.27/1.25 Prover 4: Preprocessing ...
% 2.27/1.25 Prover 1: Preprocessing ...
% 2.44/1.32 Prover 6: Preprocessing ...
% 2.44/1.32 Prover 3: Preprocessing ...
% 2.44/1.33 Prover 5: Preprocessing ...
% 2.44/1.33 Prover 2: Preprocessing ...
% 2.44/1.33 Prover 0: Preprocessing ...
% 5.73/2.06 Prover 1: Warning: ignoring some quantifiers
% 6.15/2.14 Prover 1: Constructing countermodel ...
% 6.15/2.18 Prover 5: Proving ...
% 6.15/2.24 Prover 6: Proving ...
% 6.15/2.25 Prover 3: Warning: ignoring some quantifiers
% 6.15/2.28 Prover 3: Constructing countermodel ...
% 6.15/2.33 Prover 4: Warning: ignoring some quantifiers
% 7.19/2.38 Prover 2: Proving ...
% 7.65/2.44 Prover 4: Constructing countermodel ...
% 7.65/2.47 Prover 0: Proving ...
% 9.42/3.00 Prover 3: proved (2273ms)
% 9.42/3.01
% 9.42/3.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.42/3.01
% 9.42/3.01 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.42/3.03 Prover 2: stopped
% 9.42/3.03 Prover 6: stopped
% 9.42/3.03 Prover 0: stopped
% 9.42/3.04 Prover 5: stopped
% 10.36/3.06 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.36/3.06 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.36/3.06 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.36/3.07 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.36/3.08 Prover 7: Preprocessing ...
% 10.36/3.08 Prover 10: Preprocessing ...
% 10.36/3.09 Prover 8: Preprocessing ...
% 10.36/3.13 Prover 13: Preprocessing ...
% 10.36/3.13 Prover 11: Preprocessing ...
% 11.44/3.24 Prover 10: Warning: ignoring some quantifiers
% 11.44/3.24 Prover 7: Warning: ignoring some quantifiers
% 11.44/3.25 Prover 10: Constructing countermodel ...
% 11.61/3.26 Prover 7: Constructing countermodel ...
% 11.61/3.27 Prover 8: Warning: ignoring some quantifiers
% 11.61/3.31 Prover 8: Constructing countermodel ...
% 11.61/3.32 Prover 13: Warning: ignoring some quantifiers
% 12.04/3.33 Prover 1: Found proof (size 75)
% 12.04/3.33 Prover 1: proved (2632ms)
% 12.04/3.34 Prover 4: stopped
% 12.04/3.34 Prover 13: Constructing countermodel ...
% 12.04/3.34 Prover 8: stopped
% 12.04/3.35 Prover 13: stopped
% 12.04/3.35 Prover 7: stopped
% 12.04/3.35 Prover 10: stopped
% 12.23/3.44 Prover 11: Warning: ignoring some quantifiers
% 12.49/3.46 Prover 11: Constructing countermodel ...
% 12.57/3.47 Prover 11: stopped
% 12.57/3.47
% 12.57/3.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.57/3.47
% 12.57/3.48 % SZS output start Proof for theBenchmark
% 12.57/3.49 Assumptions after simplification:
% 12.57/3.49 ---------------------------------
% 12.57/3.49
% 12.57/3.49 (d3_tarski)
% 12.77/3.54 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 12.77/3.54 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 12.77/3.54 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 12.77/3.54 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0)
% 12.77/3.54 = 0) | ~ $i(v2) | in(v2, v1) = 0))
% 12.77/3.54
% 12.77/3.54 (d4_relat_1)
% 12.77/3.54 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 12.77/3.55 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~
% 12.77/3.55 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~
% 12.77/3.55 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) =
% 12.77/3.55 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i]
% 12.77/3.55 : ? [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6)
% 12.77/3.55 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0
% 12.77/3.55 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 12.77/3.55 (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) &
% 12.77/3.55 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4:
% 12.77/3.55 $i] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) &
% 12.77/3.55 $i(v3)))))))
% 12.77/3.55
% 12.77/3.55 (d8_relat_1)
% 12.90/3.56 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] :
% 12.90/3.56 ( ~ (relation_composition(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3
% 12.90/3.56 = 0) & relation(v1) = v3) | ! [v3: $i] : ( ~ (relation(v3) = 0) | ~
% 12.90/3.56 $i(v3) | (( ~ (v3 = v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 12.90/3.56 [v7: int] : (v7 = 0 | ~ (ordered_pair(v4, v5) = v6) | ~ (in(v6,
% 12.90/3.56 v2) = v7) | ~ $i(v5) | ~ $i(v4) | ! [v8: $i] : ! [v9:
% 12.90/3.56 $i] : ( ~ (ordered_pair(v4, v8) = v9) | ~ (in(v9, v0) = 0) |
% 12.90/3.56 ~ $i(v8) | ? [v10: $i] : ? [v11: int] : ( ~ (v11 = 0) &
% 12.90/3.56 ordered_pair(v8, v5) = v10 & in(v10, v1) = v11 & $i(v10))))
% 12.90/3.56 & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v4,
% 12.90/3.56 v5) = v6) | ~ (in(v6, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ?
% 12.90/3.56 [v7: $i] : ? [v8: $i] : ? [v9: $i] : (ordered_pair(v7, v5) =
% 12.90/3.56 v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) = 0 & in(v8, v0) =
% 12.90/3.56 0 & $i(v9) & $i(v8) & $i(v7))))) & (v3 = v2 | ? [v4: $i] : ?
% 12.90/3.56 [v5: $i] : ? [v6: $i] : ? [v7: any] : (ordered_pair(v4, v5) = v6 &
% 12.90/3.56 in(v6, v3) = v7 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v7 = 0) | !
% 12.90/3.56 [v8: $i] : ! [v9: $i] : ( ~ (ordered_pair(v4, v8) = v9) | ~
% 12.90/3.56 (in(v9, v0) = 0) | ~ $i(v8) | ? [v10: $i] : ? [v11: int] :
% 12.90/3.56 ( ~ (v11 = 0) & ordered_pair(v8, v5) = v10 & in(v10, v1) = v11
% 12.90/3.56 & $i(v10)))) & (v7 = 0 | ? [v8: $i] : ? [v9: $i] : ?
% 12.90/3.56 [v10: $i] : (ordered_pair(v8, v5) = v10 & ordered_pair(v4, v8) =
% 12.90/3.56 v9 & in(v10, v1) = 0 & in(v9, v0) = 0 & $i(v10) & $i(v9) &
% 12.90/3.56 $i(v8)))))))))
% 12.90/3.56
% 12.90/3.56 (dt_k5_relat_1)
% 12.90/3.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) =
% 12.90/3.56 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 12.90/3.56 (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) |
% 12.90/3.56 ~ (v3 = 0) | v5 = 0)))
% 12.90/3.56
% 12.90/3.56 (t44_relat_1)
% 12.90/3.56 ? [v0: $i] : ? [v1: $i] : (relation_dom(v0) = v1 & relation(v0) = 0 & $i(v1)
% 12.90/3.56 & $i(v0) & ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5
% 12.90/3.56 = 0) & relation_composition(v0, v2) = v3 & relation_dom(v3) = v4 &
% 12.90/3.56 relation(v2) = 0 & subset(v4, v1) = v5 & $i(v4) & $i(v3) & $i(v2)))
% 12.90/3.56
% 12.90/3.56 (function-axioms)
% 12.90/3.57 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.90/3.57 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 12.90/3.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.90/3.57 (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) =
% 12.90/3.57 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 12.90/3.57 ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0:
% 12.90/3.57 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.90/3.57 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 12.90/3.57 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.90/3.57 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 12.90/3.57 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.90/3.57 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 12.90/3.57 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 12.90/3.57 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 12.90/3.57 $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] :
% 12.90/3.57 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 12.90/3.57 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 12.90/3.57 ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0:
% 12.90/3.57 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 12.90/3.57 ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 12.90/3.57
% 12.90/3.57 Further assumptions not needed in the proof:
% 12.90/3.57 --------------------------------------------
% 12.90/3.57 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, dt_k1_relat_1,
% 12.90/3.57 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, dt_k4_tarski,
% 12.90/3.57 dt_m1_subset_1, existence_m1_subset_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1,
% 12.90/3.57 fc2_subset_1, fc3_subset_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0,
% 12.90/3.57 rc2_subset_1, rc2_xboole_0, reflexivity_r1_tarski, t1_subset, t2_subset,
% 12.90/3.57 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 12.90/3.57
% 12.90/3.57 Those formulas are unsatisfiable:
% 12.90/3.57 ---------------------------------
% 12.90/3.57
% 12.90/3.57 Begin of proof
% 12.90/3.57 |
% 12.90/3.57 | ALPHA: (d3_tarski) implies:
% 12.90/3.58 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 12.90/3.58 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 12.90/3.58 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 12.90/3.58 |
% 12.90/3.58 | ALPHA: (function-axioms) implies:
% 12.90/3.58 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.90/3.58 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 12.90/3.58 |
% 12.90/3.58 | DELTA: instantiating (t44_relat_1) with fresh symbols all_34_0, all_34_1
% 12.90/3.58 | gives:
% 12.90/3.58 | (3) relation_dom(all_34_1) = all_34_0 & relation(all_34_1) = 0 &
% 12.90/3.58 | $i(all_34_0) & $i(all_34_1) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 12.90/3.58 | ? [v3: int] : ( ~ (v3 = 0) & relation_composition(all_34_1, v0) = v1 &
% 12.90/3.58 | relation_dom(v1) = v2 & relation(v0) = 0 & subset(v2, all_34_0) = v3
% 12.90/3.58 | & $i(v2) & $i(v1) & $i(v0))
% 12.90/3.58 |
% 12.90/3.58 | ALPHA: (3) implies:
% 12.90/3.58 | (4) $i(all_34_1)
% 12.90/3.58 | (5) $i(all_34_0)
% 12.90/3.58 | (6) relation(all_34_1) = 0
% 12.90/3.58 | (7) relation_dom(all_34_1) = all_34_0
% 12.90/3.58 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 12.90/3.58 | relation_composition(all_34_1, v0) = v1 & relation_dom(v1) = v2 &
% 12.90/3.58 | relation(v0) = 0 & subset(v2, all_34_0) = v3 & $i(v2) & $i(v1) &
% 12.90/3.58 | $i(v0))
% 12.90/3.58 |
% 12.90/3.58 | DELTA: instantiating (8) with fresh symbols all_36_0, all_36_1, all_36_2,
% 12.90/3.59 | all_36_3 gives:
% 12.90/3.59 | (9) ~ (all_36_0 = 0) & relation_composition(all_34_1, all_36_3) = all_36_2
% 12.90/3.59 | & relation_dom(all_36_2) = all_36_1 & relation(all_36_3) = 0 &
% 12.90/3.59 | subset(all_36_1, all_34_0) = all_36_0 & $i(all_36_1) & $i(all_36_2) &
% 12.90/3.59 | $i(all_36_3)
% 12.90/3.59 |
% 12.90/3.59 | ALPHA: (9) implies:
% 12.90/3.59 | (10) ~ (all_36_0 = 0)
% 12.90/3.59 | (11) $i(all_36_3)
% 12.90/3.59 | (12) $i(all_36_2)
% 12.90/3.59 | (13) $i(all_36_1)
% 12.90/3.59 | (14) subset(all_36_1, all_34_0) = all_36_0
% 12.90/3.59 | (15) relation(all_36_3) = 0
% 12.90/3.59 | (16) relation_dom(all_36_2) = all_36_1
% 12.90/3.59 | (17) relation_composition(all_34_1, all_36_3) = all_36_2
% 12.90/3.59 |
% 12.90/3.59 | GROUND_INST: instantiating (1) with all_36_1, all_34_0, all_36_0, simplifying
% 12.90/3.59 | with (5), (13), (14) gives:
% 12.90/3.59 | (18) all_36_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 12.90/3.59 | all_36_1) = 0 & in(v0, all_34_0) = v1 & $i(v0))
% 12.90/3.59 |
% 12.90/3.59 | GROUND_INST: instantiating (d8_relat_1) with all_34_1, simplifying with (4),
% 12.90/3.59 | (6) gives:
% 12.90/3.60 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_composition(all_34_1, v0) =
% 12.90/3.60 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & relation(v0) = v2)
% 12.90/3.60 | | ! [v2: $i] : ( ~ (relation(v2) = 0) | ~ $i(v2) | (( ~ (v2 = v1)
% 12.90/3.60 | | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] :
% 12.90/3.60 | (v6 = 0 | ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v1) =
% 12.90/3.60 | v6) | ~ $i(v4) | ~ $i(v3) | ! [v7: $i] : ! [v8: $i]
% 12.90/3.60 | : ( ~ (ordered_pair(v3, v7) = v8) | ~ (in(v8, all_34_1) =
% 12.90/3.60 | 0) | ~ $i(v7) | ? [v9: $i] : ? [v10: int] : ( ~
% 12.90/3.60 | (v10 = 0) & ordered_pair(v7, v4) = v9 & in(v9, v0) =
% 12.90/3.60 | v10 & $i(v9)))) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 12.90/3.60 | $i] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v1) =
% 12.90/3.60 | 0) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : ? [v7: $i] :
% 12.90/3.60 | ? [v8: $i] : (ordered_pair(v6, v4) = v8 &
% 12.90/3.60 | ordered_pair(v3, v6) = v7 & in(v8, v0) = 0 & in(v7,
% 12.90/3.60 | all_34_1) = 0 & $i(v8) & $i(v7) & $i(v6))))) & (v2 =
% 12.90/3.60 | v1 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: any] :
% 12.90/3.60 | (ordered_pair(v3, v4) = v5 & in(v5, v2) = v6 & $i(v5) & $i(v4)
% 12.90/3.60 | & $i(v3) & ( ~ (v6 = 0) | ! [v7: $i] : ! [v8: $i] : ( ~
% 12.90/3.60 | (ordered_pair(v3, v7) = v8) | ~ (in(v8, all_34_1) = 0)
% 12.90/3.60 | | ~ $i(v7) | ? [v9: $i] : ? [v10: int] : ( ~ (v10 =
% 12.90/3.60 | 0) & ordered_pair(v7, v4) = v9 & in(v9, v0) = v10 &
% 12.90/3.60 | $i(v9)))) & (v6 = 0 | ? [v7: $i] : ? [v8: $i] : ?
% 12.90/3.60 | [v9: $i] : (ordered_pair(v7, v4) = v9 & ordered_pair(v3,
% 12.90/3.60 | v7) = v8 & in(v9, v0) = 0 & in(v8, all_34_1) = 0 &
% 12.90/3.60 | $i(v9) & $i(v8) & $i(v7))))))))
% 12.90/3.60 |
% 12.90/3.60 | GROUND_INST: instantiating (d4_relat_1) with all_34_1, all_34_0, simplifying
% 12.90/3.60 | with (4), (7) gives:
% 12.90/3.61 | (20) ? [v0: int] : ( ~ (v0 = 0) & relation(all_34_1) = v0) | ( ? [v0: any]
% 12.90/3.61 | : (v0 = all_34_0 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1,
% 12.90/3.61 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] :
% 12.90/3.61 | ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, all_34_1) = 0) |
% 12.90/3.61 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] :
% 12.90/3.61 | (ordered_pair(v1, v3) = v4 & in(v4, all_34_1) = 0 & $i(v4) &
% 12.90/3.61 | $i(v3))))) & ( ~ $i(all_34_0) | ( ! [v0: $i] : ! [v1: int]
% 12.90/3.61 | : (v1 = 0 | ~ (in(v0, all_34_0) = v1) | ~ $i(v0) | ! [v2: $i]
% 12.90/3.61 | : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3,
% 12.90/3.61 | all_34_1) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0,
% 12.90/3.61 | all_34_0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 12.90/3.61 | (ordered_pair(v0, v1) = v2 & in(v2, all_34_1) = 0 & $i(v2) &
% 12.90/3.61 | $i(v1))))))
% 12.90/3.61 |
% 12.90/3.61 | GROUND_INST: instantiating (d4_relat_1) with all_36_2, all_36_1, simplifying
% 12.90/3.61 | with (12), (16) gives:
% 12.90/3.61 | (21) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_2) = v0) | ( ? [v0: any]
% 12.90/3.61 | : (v0 = all_36_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1,
% 12.90/3.61 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] :
% 12.90/3.61 | ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, all_36_2) = 0) |
% 12.90/3.61 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] :
% 12.90/3.61 | (ordered_pair(v1, v3) = v4 & in(v4, all_36_2) = 0 & $i(v4) &
% 12.90/3.61 | $i(v3))))) & ( ~ $i(all_36_1) | ( ! [v0: $i] : ! [v1: int]
% 12.90/3.61 | : (v1 = 0 | ~ (in(v0, all_36_1) = v1) | ~ $i(v0) | ! [v2: $i]
% 12.90/3.61 | : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3,
% 12.90/3.61 | all_36_2) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0,
% 12.90/3.62 | all_36_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 12.90/3.62 | (ordered_pair(v0, v1) = v2 & in(v2, all_36_2) = 0 & $i(v2) &
% 12.90/3.62 | $i(v1))))))
% 12.90/3.62 |
% 12.90/3.62 | GROUND_INST: instantiating (dt_k5_relat_1) with all_34_1, all_36_3, all_36_2,
% 12.90/3.62 | simplifying with (4), (11), (17) gives:
% 12.90/3.62 | (22) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_36_2) = v2
% 12.90/3.62 | & relation(all_36_3) = v1 & relation(all_34_1) = v0 & ( ~ (v1 = 0) |
% 12.90/3.62 | ~ (v0 = 0) | v2 = 0))
% 12.90/3.62 |
% 12.90/3.62 | GROUND_INST: instantiating (19) with all_36_3, all_36_2, simplifying with
% 12.90/3.62 | (11), (17) gives:
% 12.90/3.63 | (23) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_3) = v0) | ! [v0: $i] :
% 12.90/3.63 | ( ~ (relation(v0) = 0) | ~ $i(v0) | (( ~ (v0 = all_36_2) | ( ! [v1:
% 12.90/3.63 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 |
% 12.90/3.63 | ~ (ordered_pair(v1, v2) = v3) | ~ (in(v3, all_36_2) = v4) |
% 12.90/3.63 | ~ $i(v2) | ~ $i(v1) | ! [v5: $i] : ! [v6: $i] : ( ~
% 12.90/3.63 | (ordered_pair(v1, v5) = v6) | ~ (in(v6, all_34_1) = 0) |
% 12.90/3.63 | ~ $i(v5) | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) &
% 12.90/3.63 | ordered_pair(v5, v2) = v7 & in(v7, all_36_3) = v8 &
% 12.90/3.63 | $i(v7)))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 12.90/3.63 | ~ (ordered_pair(v1, v2) = v3) | ~ (in(v3, all_36_2) = 0) |
% 12.90/3.63 | ~ $i(v2) | ~ $i(v1) | ? [v4: $i] : ? [v5: $i] : ? [v6:
% 12.90/3.63 | $i] : (ordered_pair(v4, v2) = v6 & ordered_pair(v1, v4) =
% 12.90/3.63 | v5 & in(v6, all_36_3) = 0 & in(v5, all_34_1) = 0 & $i(v6)
% 12.90/3.63 | & $i(v5) & $i(v4))))) & (v0 = all_36_2 | ? [v1: $i] : ?
% 12.90/3.63 | [v2: $i] : ? [v3: $i] : ? [v4: any] : (ordered_pair(v1, v2) =
% 12.90/3.63 | v3 & in(v3, v0) = v4 & $i(v3) & $i(v2) & $i(v1) & ( ~ (v4 = 0)
% 12.90/3.63 | | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v1, v5) =
% 12.90/3.63 | v6) | ~ (in(v6, all_34_1) = 0) | ~ $i(v5) | ? [v7:
% 12.90/3.63 | $i] : ? [v8: int] : ( ~ (v8 = 0) & ordered_pair(v5, v2)
% 12.90/3.63 | = v7 & in(v7, all_36_3) = v8 & $i(v7)))) & (v4 = 0 | ?
% 12.90/3.63 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : (ordered_pair(v5, v2)
% 12.90/3.63 | = v7 & ordered_pair(v1, v5) = v6 & in(v7, all_36_3) = 0 &
% 12.90/3.63 | in(v6, all_34_1) = 0 & $i(v7) & $i(v6) & $i(v5)))))))
% 12.90/3.63 |
% 12.90/3.63 | DELTA: instantiating (22) with fresh symbols all_47_0, all_47_1, all_47_2
% 12.90/3.63 | gives:
% 12.90/3.63 | (24) relation(all_36_2) = all_47_0 & relation(all_36_3) = all_47_1 &
% 12.90/3.63 | relation(all_34_1) = all_47_2 & ( ~ (all_47_1 = 0) | ~ (all_47_2 = 0)
% 12.90/3.63 | | all_47_0 = 0)
% 12.90/3.63 |
% 12.90/3.63 | ALPHA: (24) implies:
% 12.90/3.63 | (25) relation(all_34_1) = all_47_2
% 12.90/3.63 | (26) relation(all_36_3) = all_47_1
% 12.90/3.63 | (27) relation(all_36_2) = all_47_0
% 12.90/3.63 | (28) ~ (all_47_1 = 0) | ~ (all_47_2 = 0) | all_47_0 = 0
% 12.90/3.63 |
% 12.90/3.63 | BETA: splitting (18) gives:
% 12.90/3.63 |
% 12.90/3.63 | Case 1:
% 12.90/3.63 | |
% 12.90/3.63 | | (29) all_36_0 = 0
% 12.90/3.63 | |
% 12.90/3.63 | | REDUCE: (10), (29) imply:
% 12.90/3.63 | | (30) $false
% 12.90/3.63 | |
% 12.90/3.63 | | CLOSE: (30) is inconsistent.
% 12.90/3.63 | |
% 12.90/3.63 | Case 2:
% 12.90/3.63 | |
% 12.90/3.63 | | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_36_1) = 0 &
% 12.90/3.63 | | in(v0, all_34_0) = v1 & $i(v0))
% 12.90/3.63 | |
% 12.90/3.63 | | DELTA: instantiating (31) with fresh symbols all_53_0, all_53_1 gives:
% 12.90/3.64 | | (32) ~ (all_53_0 = 0) & in(all_53_1, all_36_1) = 0 & in(all_53_1,
% 12.90/3.64 | | all_34_0) = all_53_0 & $i(all_53_1)
% 12.90/3.64 | |
% 12.90/3.64 | | ALPHA: (32) implies:
% 12.90/3.64 | | (33) ~ (all_53_0 = 0)
% 12.90/3.64 | | (34) $i(all_53_1)
% 12.90/3.64 | | (35) in(all_53_1, all_34_0) = all_53_0
% 12.90/3.64 | | (36) in(all_53_1, all_36_1) = 0
% 12.90/3.64 | |
% 12.90/3.64 | | GROUND_INST: instantiating (2) with 0, all_47_2, all_34_1, simplifying with
% 12.90/3.64 | | (6), (25) gives:
% 12.90/3.64 | | (37) all_47_2 = 0
% 12.90/3.64 | |
% 12.90/3.64 | | GROUND_INST: instantiating (2) with 0, all_47_1, all_36_3, simplifying with
% 12.90/3.64 | | (15), (26) gives:
% 12.90/3.64 | | (38) all_47_1 = 0
% 12.90/3.64 | |
% 12.90/3.64 | | BETA: splitting (28) gives:
% 12.90/3.64 | |
% 12.90/3.64 | | Case 1:
% 12.90/3.64 | | |
% 12.90/3.64 | | | (39) ~ (all_47_1 = 0)
% 12.90/3.64 | | |
% 12.90/3.64 | | | REDUCE: (38), (39) imply:
% 12.90/3.64 | | | (40) $false
% 12.90/3.64 | | |
% 12.90/3.64 | | | CLOSE: (40) is inconsistent.
% 12.90/3.64 | | |
% 12.90/3.64 | | Case 2:
% 12.90/3.64 | | |
% 12.90/3.64 | | | (41) ~ (all_47_2 = 0) | all_47_0 = 0
% 12.90/3.64 | | |
% 12.90/3.64 | | | BETA: splitting (20) gives:
% 12.90/3.64 | | |
% 12.90/3.64 | | | Case 1:
% 12.90/3.64 | | | |
% 12.90/3.64 | | | | (42) ? [v0: int] : ( ~ (v0 = 0) & relation(all_34_1) = v0)
% 12.90/3.64 | | | |
% 12.90/3.64 | | | | DELTA: instantiating (42) with fresh symbol all_67_0 gives:
% 12.90/3.64 | | | | (43) ~ (all_67_0 = 0) & relation(all_34_1) = all_67_0
% 12.90/3.64 | | | |
% 12.90/3.64 | | | | ALPHA: (43) implies:
% 12.90/3.64 | | | | (44) ~ (all_67_0 = 0)
% 12.90/3.64 | | | | (45) relation(all_34_1) = all_67_0
% 12.90/3.64 | | | |
% 12.90/3.64 | | | | GROUND_INST: instantiating (2) with 0, all_67_0, all_34_1, simplifying
% 12.90/3.64 | | | | with (6), (45) gives:
% 12.90/3.64 | | | | (46) all_67_0 = 0
% 12.90/3.64 | | | |
% 12.90/3.64 | | | | REDUCE: (44), (46) imply:
% 12.90/3.64 | | | | (47) $false
% 12.90/3.64 | | | |
% 12.90/3.64 | | | | CLOSE: (47) is inconsistent.
% 12.90/3.64 | | | |
% 12.90/3.65 | | | Case 2:
% 12.90/3.65 | | | |
% 12.90/3.65 | | | | (48) ? [v0: any] : (v0 = all_34_0 | ~ $i(v0) | ? [v1: $i] : ?
% 12.90/3.65 | | | | [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3:
% 12.90/3.65 | | | | $i] : ! [v4: $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~
% 12.90/3.65 | | | | (in(v4, all_34_1) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3:
% 12.90/3.65 | | | | $i] : ? [v4: $i] : (ordered_pair(v1, v3) = v4 & in(v4,
% 12.90/3.65 | | | | all_34_1) = 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_34_0)
% 12.90/3.65 | | | | | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_34_0)
% 12.90/3.65 | | | | = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 12.90/3.65 | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_34_1) = 0)
% 12.90/3.65 | | | | | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_34_0) = 0)
% 12.90/3.65 | | | | | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 12.90/3.65 | | | | (ordered_pair(v0, v1) = v2 & in(v2, all_34_1) = 0 & $i(v2)
% 12.90/3.65 | | | | & $i(v1)))))
% 12.90/3.65 | | | |
% 12.90/3.65 | | | | ALPHA: (48) implies:
% 12.90/3.65 | | | | (49) ~ $i(all_34_0) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 12.90/3.65 | | | | (in(v0, all_34_0) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3:
% 12.90/3.65 | | | | $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3,
% 12.90/3.65 | | | | all_34_1) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~
% 12.90/3.65 | | | | (in(v0, all_34_0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 12.90/3.65 | | | | $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_34_1) = 0 &
% 12.90/3.65 | | | | $i(v2) & $i(v1))))
% 12.90/3.65 | | | |
% 12.90/3.65 | | | | BETA: splitting (23) gives:
% 12.90/3.65 | | | |
% 12.90/3.65 | | | | Case 1:
% 12.90/3.65 | | | | |
% 12.90/3.65 | | | | | (50) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_3) = v0)
% 12.90/3.65 | | | | |
% 12.90/3.65 | | | | | DELTA: instantiating (50) with fresh symbol all_66_0 gives:
% 12.90/3.65 | | | | | (51) ~ (all_66_0 = 0) & relation(all_36_3) = all_66_0
% 12.90/3.65 | | | | |
% 12.90/3.65 | | | | | ALPHA: (51) implies:
% 12.90/3.65 | | | | | (52) ~ (all_66_0 = 0)
% 12.90/3.65 | | | | | (53) relation(all_36_3) = all_66_0
% 12.90/3.65 | | | | |
% 12.90/3.65 | | | | | GROUND_INST: instantiating (2) with 0, all_66_0, all_36_3, simplifying
% 12.90/3.65 | | | | | with (15), (53) gives:
% 12.90/3.65 | | | | | (54) all_66_0 = 0
% 12.90/3.65 | | | | |
% 12.90/3.65 | | | | | REDUCE: (52), (54) imply:
% 12.90/3.65 | | | | | (55) $false
% 12.90/3.65 | | | | |
% 12.90/3.65 | | | | | CLOSE: (55) is inconsistent.
% 12.90/3.65 | | | | |
% 12.90/3.65 | | | | Case 2:
% 12.90/3.65 | | | | |
% 12.90/3.66 | | | | | (56) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | (( ~ (v0 =
% 12.90/3.66 | | | | | all_36_2) | ( ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 12.90/3.66 | | | | | ! [v4: int] : (v4 = 0 | ~ (ordered_pair(v1, v2) =
% 12.90/3.66 | | | | | v3) | ~ (in(v3, all_36_2) = v4) | ~ $i(v2) | ~
% 12.90/3.66 | | | | | $i(v1) | ! [v5: $i] : ! [v6: $i] : ( ~
% 12.90/3.66 | | | | | (ordered_pair(v1, v5) = v6) | ~ (in(v6, all_34_1)
% 12.90/3.66 | | | | | = 0) | ~ $i(v5) | ? [v7: $i] : ? [v8: int] :
% 12.90/3.66 | | | | | ( ~ (v8 = 0) & ordered_pair(v5, v2) = v7 & in(v7,
% 12.90/3.66 | | | | | all_36_3) = v8 & $i(v7)))) & ! [v1: $i] : !
% 12.90/3.66 | | | | | [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v1, v2) =
% 12.90/3.66 | | | | | v3) | ~ (in(v3, all_36_2) = 0) | ~ $i(v2) | ~
% 12.90/3.66 | | | | | $i(v1) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 12.90/3.66 | | | | | (ordered_pair(v4, v2) = v6 & ordered_pair(v1, v4) =
% 12.90/3.66 | | | | | v5 & in(v6, all_36_3) = 0 & in(v5, all_34_1) = 0 &
% 12.90/3.66 | | | | | $i(v6) & $i(v5) & $i(v4))))) & (v0 = all_36_2 | ?
% 12.90/3.66 | | | | | [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] :
% 12.90/3.66 | | | | | (ordered_pair(v1, v2) = v3 & in(v3, v0) = v4 & $i(v3) &
% 12.90/3.66 | | | | | $i(v2) & $i(v1) & ( ~ (v4 = 0) | ! [v5: $i] : ! [v6:
% 12.90/3.66 | | | | | $i] : ( ~ (ordered_pair(v1, v5) = v6) | ~ (in(v6,
% 12.90/3.66 | | | | | all_34_1) = 0) | ~ $i(v5) | ? [v7: $i] : ?
% 12.90/3.66 | | | | | [v8: int] : ( ~ (v8 = 0) & ordered_pair(v5, v2) =
% 12.90/3.66 | | | | | v7 & in(v7, all_36_3) = v8 & $i(v7)))) & (v4 = 0
% 12.90/3.66 | | | | | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 12.90/3.66 | | | | | (ordered_pair(v5, v2) = v7 & ordered_pair(v1, v5) =
% 12.90/3.66 | | | | | v6 & in(v7, all_36_3) = 0 & in(v6, all_34_1) = 0 &
% 12.90/3.67 | | | | | $i(v7) & $i(v6) & $i(v5)))))))
% 12.90/3.67 | | | | |
% 12.90/3.67 | | | | | BETA: splitting (41) gives:
% 12.90/3.67 | | | | |
% 12.90/3.67 | | | | | Case 1:
% 12.90/3.67 | | | | | |
% 12.90/3.67 | | | | | | (57) ~ (all_47_2 = 0)
% 12.90/3.67 | | | | | |
% 12.90/3.67 | | | | | | REDUCE: (37), (57) imply:
% 12.90/3.67 | | | | | | (58) $false
% 12.90/3.67 | | | | | |
% 12.90/3.67 | | | | | | CLOSE: (58) is inconsistent.
% 12.90/3.67 | | | | | |
% 12.90/3.67 | | | | | Case 2:
% 12.90/3.67 | | | | | |
% 12.90/3.67 | | | | | | (59) all_47_0 = 0
% 12.90/3.67 | | | | | |
% 12.90/3.67 | | | | | | REDUCE: (27), (59) imply:
% 12.90/3.67 | | | | | | (60) relation(all_36_2) = 0
% 12.90/3.67 | | | | | |
% 12.90/3.67 | | | | | | BETA: splitting (21) gives:
% 12.90/3.67 | | | | | |
% 12.90/3.67 | | | | | | Case 1:
% 12.90/3.67 | | | | | | |
% 12.90/3.67 | | | | | | | (61) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_2) = v0)
% 12.90/3.67 | | | | | | |
% 12.90/3.67 | | | | | | | DELTA: instantiating (61) with fresh symbol all_77_0 gives:
% 12.90/3.67 | | | | | | | (62) ~ (all_77_0 = 0) & relation(all_36_2) = all_77_0
% 12.90/3.67 | | | | | | |
% 12.90/3.67 | | | | | | | ALPHA: (62) implies:
% 12.90/3.67 | | | | | | | (63) ~ (all_77_0 = 0)
% 12.90/3.67 | | | | | | | (64) relation(all_36_2) = all_77_0
% 12.90/3.67 | | | | | | |
% 12.90/3.67 | | | | | | | GROUND_INST: instantiating (2) with 0, all_77_0, all_36_2,
% 12.90/3.67 | | | | | | | simplifying with (60), (64) gives:
% 12.90/3.67 | | | | | | | (65) all_77_0 = 0
% 12.90/3.67 | | | | | | |
% 12.90/3.67 | | | | | | | REDUCE: (63), (65) imply:
% 12.90/3.67 | | | | | | | (66) $false
% 12.90/3.67 | | | | | | |
% 12.90/3.67 | | | | | | | CLOSE: (66) is inconsistent.
% 12.90/3.67 | | | | | | |
% 12.90/3.67 | | | | | | Case 2:
% 12.90/3.67 | | | | | | |
% 12.90/3.68 | | | | | | | (67) ? [v0: any] : (v0 = all_36_1 | ~ $i(v0) | ? [v1: $i] :
% 12.90/3.68 | | | | | | | ? [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) |
% 12.90/3.68 | | | | | | | ! [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v1,
% 12.90/3.68 | | | | | | | v3) = v4) | ~ (in(v4, all_36_2) = 0) | ~
% 12.90/3.68 | | | | | | | $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] :
% 12.90/3.68 | | | | | | | (ordered_pair(v1, v3) = v4 & in(v4, all_36_2) = 0 &
% 12.90/3.68 | | | | | | | $i(v4) & $i(v3))))) & ( ~ $i(all_36_1) | ( ! [v0:
% 12.90/3.68 | | | | | | | $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_36_1)
% 12.90/3.68 | | | | | | | = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : (
% 12.90/3.68 | | | | | | | ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3,
% 12.90/3.68 | | | | | | | all_36_2) = 0) | ~ $i(v2))) & ! [v0: $i] : (
% 12.90/3.68 | | | | | | | ~ (in(v0, all_36_1) = 0) | ~ $i(v0) | ? [v1: $i] :
% 12.90/3.68 | | | | | | | ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2,
% 12.90/3.69 | | | | | | | all_36_2) = 0 & $i(v2) & $i(v1)))))
% 12.90/3.69 | | | | | | |
% 12.90/3.69 | | | | | | | ALPHA: (67) implies:
% 12.90/3.69 | | | | | | | (68) ~ $i(all_36_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 |
% 12.90/3.69 | | | | | | | ~ (in(v0, all_36_1) = v1) | ~ $i(v0) | ! [v2: $i] :
% 12.90/3.69 | | | | | | | ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~
% 12.90/3.69 | | | | | | | (in(v3, all_36_2) = 0) | ~ $i(v2))) & ! [v0: $i] :
% 12.90/3.69 | | | | | | | ( ~ (in(v0, all_36_1) = 0) | ~ $i(v0) | ? [v1: $i] :
% 12.90/3.69 | | | | | | | ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2,
% 12.90/3.69 | | | | | | | all_36_2) = 0 & $i(v2) & $i(v1))))
% 12.90/3.69 | | | | | | |
% 12.90/3.69 | | | | | | | BETA: splitting (49) gives:
% 12.90/3.69 | | | | | | |
% 12.90/3.69 | | | | | | | Case 1:
% 12.90/3.69 | | | | | | | |
% 12.90/3.69 | | | | | | | | (69) ~ $i(all_34_0)
% 12.90/3.69 | | | | | | | |
% 12.90/3.69 | | | | | | | | PRED_UNIFY: (5), (69) imply:
% 12.90/3.69 | | | | | | | | (70) $false
% 12.90/3.69 | | | | | | | |
% 12.90/3.69 | | | | | | | | CLOSE: (70) is inconsistent.
% 12.90/3.69 | | | | | | | |
% 12.90/3.69 | | | | | | | Case 2:
% 12.90/3.69 | | | | | | | |
% 12.90/3.70 | | | | | | | | (71) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 12.90/3.70 | | | | | | | | all_34_0) = v1) | ~ $i(v0) | ! [v2: $i] : !
% 12.90/3.70 | | | | | | | | [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~
% 12.90/3.70 | | | | | | | | (in(v3, all_34_1) = 0) | ~ $i(v2))) & ! [v0: $i] :
% 12.90/3.70 | | | | | | | | ( ~ (in(v0, all_34_0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 12.90/3.70 | | | | | | | | ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2,
% 12.90/3.70 | | | | | | | | all_34_1) = 0 & $i(v2) & $i(v1)))
% 12.90/3.70 | | | | | | | |
% 12.90/3.70 | | | | | | | | ALPHA: (71) implies:
% 12.90/3.70 | | | | | | | | (72) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 12.90/3.70 | | | | | | | | all_34_0) = v1) | ~ $i(v0) | ! [v2: $i] : !
% 12.90/3.70 | | | | | | | | [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~
% 12.90/3.70 | | | | | | | | (in(v3, all_34_1) = 0) | ~ $i(v2)))
% 12.90/3.70 | | | | | | | |
% 12.90/3.70 | | | | | | | | BETA: splitting (68) gives:
% 12.90/3.70 | | | | | | | |
% 12.90/3.70 | | | | | | | | Case 1:
% 12.90/3.70 | | | | | | | | |
% 12.90/3.70 | | | | | | | | | (73) ~ $i(all_36_1)
% 12.90/3.70 | | | | | | | | |
% 12.90/3.70 | | | | | | | | | PRED_UNIFY: (13), (73) imply:
% 12.90/3.70 | | | | | | | | | (74) $false
% 12.90/3.70 | | | | | | | | |
% 12.90/3.70 | | | | | | | | | CLOSE: (74) is inconsistent.
% 12.90/3.70 | | | | | | | | |
% 12.90/3.70 | | | | | | | | Case 2:
% 12.90/3.70 | | | | | | | | |
% 12.90/3.70 | | | | | | | | | (75) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 12.90/3.70 | | | | | | | | | all_36_1) = v1) | ~ $i(v0) | ! [v2: $i] : !
% 12.90/3.70 | | | | | | | | | [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~
% 12.90/3.70 | | | | | | | | | (in(v3, all_36_2) = 0) | ~ $i(v2))) & ! [v0: $i]
% 12.90/3.70 | | | | | | | | | : ( ~ (in(v0, all_36_1) = 0) | ~ $i(v0) | ? [v1: $i]
% 12.90/3.70 | | | | | | | | | : ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2,
% 12.90/3.70 | | | | | | | | | all_36_2) = 0 & $i(v2) & $i(v1)))
% 12.90/3.70 | | | | | | | | |
% 12.90/3.70 | | | | | | | | | ALPHA: (75) implies:
% 12.90/3.70 | | | | | | | | | (76) ! [v0: $i] : ( ~ (in(v0, all_36_1) = 0) | ~ $i(v0) |
% 12.90/3.70 | | | | | | | | | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) =
% 12.90/3.70 | | | | | | | | | v2 & in(v2, all_36_2) = 0 & $i(v2) & $i(v1)))
% 12.90/3.70 | | | | | | | | |
% 12.90/3.70 | | | | | | | | | GROUND_INST: instantiating (72) with all_53_1, all_53_0,
% 12.90/3.70 | | | | | | | | | simplifying with (34), (35) gives:
% 12.90/3.70 | | | | | | | | | (77) all_53_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~
% 12.90/3.70 | | | | | | | | | (ordered_pair(all_53_1, v0) = v1) | ~ (in(v1,
% 12.90/3.70 | | | | | | | | | all_34_1) = 0) | ~ $i(v0))
% 12.90/3.70 | | | | | | | | |
% 12.90/3.70 | | | | | | | | | GROUND_INST: instantiating (76) with all_53_1, simplifying with
% 12.90/3.70 | | | | | | | | | (34), (36) gives:
% 12.90/3.70 | | | | | | | | | (78) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_53_1,
% 12.90/3.70 | | | | | | | | | v0) = v1 & in(v1, all_36_2) = 0 & $i(v1) & $i(v0))
% 12.90/3.70 | | | | | | | | |
% 12.90/3.70 | | | | | | | | | GROUND_INST: instantiating (56) with all_36_2, simplifying with
% 12.90/3.70 | | | | | | | | | (12), (60) gives:
% 12.90/3.70 | | | | | | | | | (79) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int]
% 12.90/3.70 | | | | | | | | | : (v3 = 0 | ~ (ordered_pair(v0, v1) = v2) | ~
% 12.90/3.70 | | | | | | | | | (in(v2, all_36_2) = v3) | ~ $i(v1) | ~ $i(v0) | !
% 12.90/3.70 | | | | | | | | | [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v0, v4) =
% 12.90/3.70 | | | | | | | | | v5) | ~ (in(v5, all_34_1) = 0) | ~ $i(v4) | ?
% 12.90/3.70 | | | | | | | | | [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) &
% 12.90/3.70 | | | | | | | | | ordered_pair(v4, v1) = v6 & in(v6, all_36_3) =
% 12.90/3.70 | | | | | | | | | v7 & $i(v6)))) & ! [v0: $i] : ! [v1: $i] : !
% 12.90/3.70 | | | | | | | | | [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~
% 12.90/3.70 | | | | | | | | | (in(v2, all_36_2) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 12.90/3.70 | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 12.90/3.70 | | | | | | | | | (ordered_pair(v3, v1) = v5 & ordered_pair(v0, v3) =
% 12.90/3.70 | | | | | | | | | v4 & in(v5, all_36_3) = 0 & in(v4, all_34_1) = 0 &
% 12.90/3.70 | | | | | | | | | $i(v5) & $i(v4) & $i(v3)))
% 12.90/3.70 | | | | | | | | |
% 12.90/3.70 | | | | | | | | | ALPHA: (79) implies:
% 12.90/3.70 | | | | | | | | | (80) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 12.90/3.70 | | | | | | | | | (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_36_2) =
% 12.90/3.71 | | | | | | | | | 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 12.90/3.71 | | | | | | | | | $i] : ? [v5: $i] : (ordered_pair(v3, v1) = v5 &
% 12.90/3.71 | | | | | | | | | ordered_pair(v0, v3) = v4 & in(v5, all_36_3) = 0 &
% 12.90/3.71 | | | | | | | | | in(v4, all_34_1) = 0 & $i(v5) & $i(v4) & $i(v3)))
% 12.90/3.71 | | | | | | | | |
% 12.90/3.71 | | | | | | | | | DELTA: instantiating (78) with fresh symbols all_94_0,
% 12.90/3.71 | | | | | | | | | all_94_1 gives:
% 12.90/3.71 | | | | | | | | | (81) ordered_pair(all_53_1, all_94_1) = all_94_0 &
% 12.90/3.71 | | | | | | | | | in(all_94_0, all_36_2) = 0 & $i(all_94_0) &
% 12.90/3.71 | | | | | | | | | $i(all_94_1)
% 12.90/3.71 | | | | | | | | |
% 12.90/3.72 | | | | | | | | | ALPHA: (81) implies:
% 12.90/3.72 | | | | | | | | | (82) $i(all_94_1)
% 12.90/3.72 | | | | | | | | | (83) in(all_94_0, all_36_2) = 0
% 12.90/3.72 | | | | | | | | | (84) ordered_pair(all_53_1, all_94_1) = all_94_0
% 12.90/3.72 | | | | | | | | |
% 12.90/3.72 | | | | | | | | | BETA: splitting (77) gives:
% 12.90/3.72 | | | | | | | | |
% 12.90/3.72 | | | | | | | | | Case 1:
% 12.90/3.72 | | | | | | | | | |
% 12.90/3.72 | | | | | | | | | | (85) all_53_0 = 0
% 12.90/3.72 | | | | | | | | | |
% 12.90/3.72 | | | | | | | | | | REDUCE: (33), (85) imply:
% 12.90/3.72 | | | | | | | | | | (86) $false
% 12.90/3.72 | | | | | | | | | |
% 12.90/3.72 | | | | | | | | | | CLOSE: (86) is inconsistent.
% 12.90/3.72 | | | | | | | | | |
% 12.90/3.72 | | | | | | | | | Case 2:
% 12.90/3.72 | | | | | | | | | |
% 12.90/3.72 | | | | | | | | | | (87) ! [v0: $i] : ! [v1: $i] : ( ~
% 12.90/3.72 | | | | | | | | | | (ordered_pair(all_53_1, v0) = v1) | ~ (in(v1,
% 12.90/3.72 | | | | | | | | | | all_34_1) = 0) | ~ $i(v0))
% 12.90/3.72 | | | | | | | | | |
% 12.90/3.72 | | | | | | | | | | GROUND_INST: instantiating (80) with all_53_1, all_94_1,
% 12.90/3.72 | | | | | | | | | | all_94_0, simplifying with (34), (82), (83), (84)
% 12.90/3.72 | | | | | | | | | | gives:
% 12.90/3.73 | | | | | | | | | | (88) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 12.90/3.73 | | | | | | | | | | (ordered_pair(v0, all_94_1) = v2 &
% 12.90/3.73 | | | | | | | | | | ordered_pair(all_53_1, v0) = v1 & in(v2, all_36_3)
% 12.90/3.73 | | | | | | | | | | = 0 & in(v1, all_34_1) = 0 & $i(v2) & $i(v1) &
% 12.90/3.73 | | | | | | | | | | $i(v0))
% 12.90/3.73 | | | | | | | | | |
% 12.90/3.73 | | | | | | | | | | DELTA: instantiating (88) with fresh symbols all_112_0,
% 12.90/3.73 | | | | | | | | | | all_112_1, all_112_2 gives:
% 12.90/3.73 | | | | | | | | | | (89) ordered_pair(all_112_2, all_94_1) = all_112_0 &
% 12.90/3.73 | | | | | | | | | | ordered_pair(all_53_1, all_112_2) = all_112_1 &
% 12.90/3.73 | | | | | | | | | | in(all_112_0, all_36_3) = 0 & in(all_112_1,
% 12.90/3.73 | | | | | | | | | | all_34_1) = 0 & $i(all_112_0) & $i(all_112_1) &
% 12.90/3.73 | | | | | | | | | | $i(all_112_2)
% 12.90/3.73 | | | | | | | | | |
% 12.90/3.73 | | | | | | | | | | ALPHA: (89) implies:
% 12.90/3.73 | | | | | | | | | | (90) $i(all_112_2)
% 12.90/3.73 | | | | | | | | | | (91) in(all_112_1, all_34_1) = 0
% 12.90/3.73 | | | | | | | | | | (92) ordered_pair(all_53_1, all_112_2) = all_112_1
% 12.90/3.73 | | | | | | | | | |
% 12.90/3.73 | | | | | | | | | | GROUND_INST: instantiating (87) with all_112_2, all_112_1,
% 12.90/3.73 | | | | | | | | | | simplifying with (90), (91), (92) gives:
% 12.90/3.73 | | | | | | | | | | (93) $false
% 12.90/3.73 | | | | | | | | | |
% 12.90/3.73 | | | | | | | | | | CLOSE: (93) is inconsistent.
% 12.90/3.73 | | | | | | | | | |
% 12.90/3.73 | | | | | | | | | End of split
% 12.90/3.73 | | | | | | | | |
% 12.90/3.73 | | | | | | | | End of split
% 12.90/3.73 | | | | | | | |
% 12.90/3.73 | | | | | | | End of split
% 12.90/3.73 | | | | | | |
% 12.90/3.73 | | | | | | End of split
% 12.90/3.73 | | | | | |
% 12.90/3.73 | | | | | End of split
% 12.90/3.73 | | | | |
% 12.90/3.73 | | | | End of split
% 12.90/3.73 | | | |
% 12.90/3.73 | | | End of split
% 12.90/3.73 | | |
% 12.90/3.73 | | End of split
% 12.90/3.73 | |
% 12.90/3.73 | End of split
% 12.90/3.73 |
% 12.90/3.73 End of proof
% 12.90/3.73 % SZS output end Proof for theBenchmark
% 12.90/3.73
% 12.90/3.73 3057ms
%------------------------------------------------------------------------------