TSTP Solution File: SEU166+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU166+3 : TPTP v8.1.2. Released v3.2.0.
% 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 : Thu Aug 31 17:42:59 EDT 2023
% Result : Theorem 6.77s 1.69s
% Output : Proof 8.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU166+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n002.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 19:39:16 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.11/0.98 Prover 1: Preprocessing ...
% 2.11/0.98 Prover 4: Preprocessing ...
% 2.11/1.04 Prover 5: Preprocessing ...
% 2.11/1.04 Prover 6: Preprocessing ...
% 2.11/1.04 Prover 2: Preprocessing ...
% 2.11/1.04 Prover 3: Preprocessing ...
% 2.11/1.04 Prover 0: Preprocessing ...
% 4.05/1.34 Prover 1: Warning: ignoring some quantifiers
% 4.05/1.35 Prover 4: Warning: ignoring some quantifiers
% 4.05/1.35 Prover 3: Warning: ignoring some quantifiers
% 4.67/1.36 Prover 6: Proving ...
% 4.67/1.36 Prover 5: Proving ...
% 4.67/1.37 Prover 2: Proving ...
% 4.67/1.37 Prover 0: Proving ...
% 4.67/1.37 Prover 1: Constructing countermodel ...
% 4.67/1.37 Prover 3: Constructing countermodel ...
% 4.67/1.37 Prover 4: Constructing countermodel ...
% 6.77/1.69 Prover 3: proved (1058ms)
% 6.77/1.69
% 6.77/1.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.77/1.69
% 6.77/1.69 Prover 5: stopped
% 6.77/1.69 Prover 2: stopped
% 6.77/1.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.77/1.70 Prover 0: stopped
% 6.77/1.70 Prover 6: stopped
% 6.77/1.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.77/1.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.77/1.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.77/1.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.77/1.72 Prover 8: Preprocessing ...
% 6.77/1.73 Prover 10: Preprocessing ...
% 7.23/1.73 Prover 7: Preprocessing ...
% 7.23/1.73 Prover 13: Preprocessing ...
% 7.23/1.73 Prover 11: Preprocessing ...
% 7.46/1.79 Prover 10: Warning: ignoring some quantifiers
% 7.46/1.80 Prover 7: Warning: ignoring some quantifiers
% 7.46/1.80 Prover 8: Warning: ignoring some quantifiers
% 7.46/1.81 Prover 10: Constructing countermodel ...
% 7.46/1.81 Prover 7: Constructing countermodel ...
% 7.46/1.81 Prover 13: Warning: ignoring some quantifiers
% 7.46/1.82 Prover 8: Constructing countermodel ...
% 7.46/1.82 Prover 13: Constructing countermodel ...
% 7.98/1.84 Prover 4: Found proof (size 52)
% 7.98/1.84 Prover 4: proved (1205ms)
% 7.98/1.84 Prover 10: stopped
% 7.98/1.84 Prover 8: stopped
% 7.98/1.84 Prover 13: stopped
% 7.98/1.85 Prover 7: stopped
% 7.98/1.85 Prover 1: stopped
% 7.98/1.85 Prover 11: Warning: ignoring some quantifiers
% 7.98/1.85 Prover 11: Constructing countermodel ...
% 7.98/1.86 Prover 11: stopped
% 7.98/1.86
% 7.98/1.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.98/1.86
% 8.21/1.87 % SZS output start Proof for theBenchmark
% 8.21/1.87 Assumptions after simplification:
% 8.21/1.87 ---------------------------------
% 8.21/1.87
% 8.21/1.87 (d2_zfmisc_1)
% 8.21/1.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 8.21/1.91 $i] : ! [v6: $i] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~
% 8.21/1.91 (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ~ $i(v6) | ~ $i(v5) |
% 8.21/1.91 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any]
% 8.21/1.91 : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & !
% 8.21/1.91 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 8.21/1.91 (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~
% 8.21/1.91 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] :
% 8.21/1.91 (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0 & $i(v5) &
% 8.21/1.91 $i(v4))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 =
% 8.21/1.91 v0 | ~ (cartesian_product2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 8.21/1.91 $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 8.21/1.91 int] : ? [v9: int] : ? [v10: $i] : (in(v4, v0) = v5 & $i(v7) & $i(v6) &
% 8.21/1.91 $i(v4) & ( ~ (v5 = 0) | ! [v11: $i] : ! [v12: $i] : ( ~
% 8.21/1.91 (ordered_pair(v11, v12) = v4) | ~ $i(v12) | ~ $i(v11) | ? [v13:
% 8.21/1.91 any] : ? [v14: any] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~
% 8.21/1.91 (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 =
% 8.21/1.91 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0))))
% 8.21/1.91
% 8.21/1.91 (d3_tarski)
% 8.21/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 8.21/1.92 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 8.21/1.92 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 8.21/1.92 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 8.21/1.92 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 8.21/1.92 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 8.21/1.92 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 8.21/1.92 $i(v0) | in(v2, v1) = 0)
% 8.21/1.92
% 8.21/1.92 (t118_zfmisc_1)
% 8.21/1.92 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 8.21/1.92 any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : (subset(v6, v7) = v8 &
% 8.21/1.92 subset(v3, v4) = v5 & subset(v0, v1) = 0 & cartesian_product2(v2, v1) = v7 &
% 8.21/1.92 cartesian_product2(v2, v0) = v6 & cartesian_product2(v1, v2) = v4 &
% 8.21/1.92 cartesian_product2(v0, v2) = v3 & $i(v7) & $i(v6) & $i(v4) & $i(v3) & $i(v2)
% 8.21/1.92 & $i(v1) & $i(v0) & ( ~ (v8 = 0) | ~ (v5 = 0)))
% 8.21/1.92
% 8.21/1.92 (function-axioms)
% 8.21/1.92 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.21/1.92 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 8.21/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.21/1.92 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 8.21/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.21/1.92 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i]
% 8.21/1.92 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3,
% 8.21/1.92 v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 8.21/1.93 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 8.21/1.93 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 8.21/1.93 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 8.21/1.93 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 8.21/1.93 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 8.21/1.93
% 8.21/1.93 Further assumptions not needed in the proof:
% 8.21/1.93 --------------------------------------------
% 8.21/1.93 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, fc1_zfmisc_1,
% 8.21/1.93 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski
% 8.21/1.93
% 8.21/1.93 Those formulas are unsatisfiable:
% 8.21/1.93 ---------------------------------
% 8.21/1.93
% 8.21/1.93 Begin of proof
% 8.21/1.93 |
% 8.21/1.93 | ALPHA: (d2_zfmisc_1) implies:
% 8.21/1.93 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 8.21/1.93 | (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) |
% 8.21/1.93 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] :
% 8.21/1.93 | (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0 & $i(v5)
% 8.21/1.93 | & $i(v4)))
% 8.21/1.93 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 8.21/1.93 | ! [v5: $i] : ! [v6: $i] : (v4 = 0 | ~ (cartesian_product2(v0, v1) =
% 8.21/1.93 | v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ~
% 8.21/1.93 | $i(v6) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 8.21/1.93 | ? [v7: any] : ? [v8: any] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~
% 8.21/1.93 | (v8 = 0) | ~ (v7 = 0))))
% 8.21/1.93 |
% 8.21/1.93 | ALPHA: (d3_tarski) implies:
% 8.21/1.93 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 8.21/1.93 | (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) =
% 8.21/1.93 | 0)
% 8.21/1.93 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 8.21/1.93 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 8.21/1.93 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 8.54/1.93 |
% 8.54/1.93 | ALPHA: (function-axioms) implies:
% 8.54/1.94 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.54/1.94 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 8.54/1.94 |
% 8.54/1.94 | DELTA: instantiating (t118_zfmisc_1) with fresh symbols all_14_0, all_14_1,
% 8.54/1.94 | all_14_2, all_14_3, all_14_4, all_14_5, all_14_6, all_14_7, all_14_8
% 8.54/1.94 | gives:
% 8.54/1.94 | (6) subset(all_14_2, all_14_1) = all_14_0 & subset(all_14_5, all_14_4) =
% 8.54/1.94 | all_14_3 & subset(all_14_8, all_14_7) = 0 &
% 8.54/1.94 | cartesian_product2(all_14_6, all_14_7) = all_14_1 &
% 8.54/1.94 | cartesian_product2(all_14_6, all_14_8) = all_14_2 &
% 8.54/1.94 | cartesian_product2(all_14_7, all_14_6) = all_14_4 &
% 8.54/1.94 | cartesian_product2(all_14_8, all_14_6) = all_14_5 & $i(all_14_1) &
% 8.54/1.94 | $i(all_14_2) & $i(all_14_4) & $i(all_14_5) & $i(all_14_6) &
% 8.54/1.94 | $i(all_14_7) & $i(all_14_8) & ( ~ (all_14_0 = 0) | ~ (all_14_3 = 0))
% 8.54/1.94 |
% 8.54/1.94 | ALPHA: (6) implies:
% 8.54/1.94 | (7) $i(all_14_8)
% 8.54/1.94 | (8) $i(all_14_7)
% 8.54/1.94 | (9) $i(all_14_6)
% 8.54/1.94 | (10) $i(all_14_5)
% 8.54/1.94 | (11) $i(all_14_4)
% 8.54/1.94 | (12) $i(all_14_2)
% 8.54/1.94 | (13) $i(all_14_1)
% 8.54/1.94 | (14) cartesian_product2(all_14_8, all_14_6) = all_14_5
% 8.54/1.94 | (15) cartesian_product2(all_14_7, all_14_6) = all_14_4
% 8.54/1.94 | (16) cartesian_product2(all_14_6, all_14_8) = all_14_2
% 8.54/1.94 | (17) cartesian_product2(all_14_6, all_14_7) = all_14_1
% 8.54/1.94 | (18) subset(all_14_8, all_14_7) = 0
% 8.54/1.94 | (19) subset(all_14_5, all_14_4) = all_14_3
% 8.54/1.94 | (20) subset(all_14_2, all_14_1) = all_14_0
% 8.54/1.94 | (21) ~ (all_14_0 = 0) | ~ (all_14_3 = 0)
% 8.54/1.94 |
% 8.54/1.94 | GROUND_INST: instantiating (4) with all_14_5, all_14_4, all_14_3, simplifying
% 8.54/1.94 | with (10), (11), (19) gives:
% 8.54/1.94 | (22) all_14_3 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 8.54/1.94 | all_14_4) = v1 & in(v0, all_14_5) = 0 & $i(v0))
% 8.54/1.94 |
% 8.54/1.94 | GROUND_INST: instantiating (4) with all_14_2, all_14_1, all_14_0, simplifying
% 8.54/1.94 | with (12), (13), (20) gives:
% 8.54/1.94 | (23) all_14_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 8.54/1.94 | all_14_1) = v1 & in(v0, all_14_2) = 0 & $i(v0))
% 8.54/1.94 |
% 8.54/1.94 | BETA: splitting (21) gives:
% 8.54/1.94 |
% 8.54/1.95 | Case 1:
% 8.54/1.95 | |
% 8.54/1.95 | | (24) ~ (all_14_0 = 0)
% 8.54/1.95 | |
% 8.54/1.95 | | BETA: splitting (23) gives:
% 8.54/1.95 | |
% 8.54/1.95 | | Case 1:
% 8.54/1.95 | | |
% 8.54/1.95 | | | (25) all_14_0 = 0
% 8.54/1.95 | | |
% 8.54/1.95 | | | REDUCE: (24), (25) imply:
% 8.54/1.95 | | | (26) $false
% 8.54/1.95 | | |
% 8.54/1.95 | | | CLOSE: (26) is inconsistent.
% 8.54/1.95 | | |
% 8.54/1.95 | | Case 2:
% 8.54/1.95 | | |
% 8.54/1.95 | | | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_14_1) = v1
% 8.54/1.95 | | | & in(v0, all_14_2) = 0 & $i(v0))
% 8.54/1.95 | | |
% 8.54/1.95 | | | DELTA: instantiating (27) with fresh symbols all_29_0, all_29_1 gives:
% 8.54/1.95 | | | (28) ~ (all_29_0 = 0) & in(all_29_1, all_14_1) = all_29_0 &
% 8.54/1.95 | | | in(all_29_1, all_14_2) = 0 & $i(all_29_1)
% 8.54/1.95 | | |
% 8.54/1.95 | | | ALPHA: (28) implies:
% 8.54/1.95 | | | (29) ~ (all_29_0 = 0)
% 8.54/1.95 | | | (30) $i(all_29_1)
% 8.54/1.95 | | | (31) in(all_29_1, all_14_2) = 0
% 8.54/1.95 | | | (32) in(all_29_1, all_14_1) = all_29_0
% 8.54/1.95 | | |
% 8.54/1.95 | | | GROUND_INST: instantiating (1) with all_14_6, all_14_8, all_14_2,
% 8.54/1.95 | | | all_29_1, simplifying with (7), (9), (12), (16), (30), (31)
% 8.54/1.95 | | | gives:
% 8.54/1.95 | | | (33) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_29_1 &
% 8.54/1.95 | | | in(v1, all_14_8) = 0 & in(v0, all_14_6) = 0 & $i(v1) & $i(v0))
% 8.54/1.95 | | |
% 8.54/1.95 | | | DELTA: instantiating (33) with fresh symbols all_38_0, all_38_1 gives:
% 8.54/1.95 | | | (34) ordered_pair(all_38_1, all_38_0) = all_29_1 & in(all_38_0,
% 8.54/1.95 | | | all_14_8) = 0 & in(all_38_1, all_14_6) = 0 & $i(all_38_0) &
% 8.54/1.95 | | | $i(all_38_1)
% 8.54/1.95 | | |
% 8.54/1.95 | | | ALPHA: (34) implies:
% 8.54/1.95 | | | (35) $i(all_38_1)
% 8.54/1.95 | | | (36) $i(all_38_0)
% 8.54/1.95 | | | (37) in(all_38_1, all_14_6) = 0
% 8.54/1.95 | | | (38) in(all_38_0, all_14_8) = 0
% 8.54/1.95 | | | (39) ordered_pair(all_38_1, all_38_0) = all_29_1
% 8.54/1.95 | | |
% 8.54/1.95 | | | GROUND_INST: instantiating (3) with all_14_8, all_14_7, all_38_0,
% 8.54/1.95 | | | simplifying with (7), (8), (18), (36), (38) gives:
% 8.54/1.95 | | | (40) in(all_38_0, all_14_7) = 0
% 8.54/1.95 | | |
% 8.54/1.96 | | | GROUND_INST: instantiating (2) with all_14_6, all_14_7, all_14_1,
% 8.54/1.96 | | | all_29_1, all_29_0, all_38_1, all_38_0, simplifying with (8),
% 8.54/1.96 | | | (9), (13), (17), (30), (32), (35), (36), (39) gives:
% 8.54/1.96 | | | (41) all_29_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_38_0,
% 8.54/1.96 | | | all_14_7) = v1 & in(all_38_1, all_14_6) = v0 & ( ~ (v1 = 0) |
% 8.54/1.96 | | | ~ (v0 = 0)))
% 8.54/1.96 | | |
% 8.54/1.96 | | | BETA: splitting (41) gives:
% 8.54/1.96 | | |
% 8.54/1.96 | | | Case 1:
% 8.54/1.96 | | | |
% 8.54/1.96 | | | | (42) all_29_0 = 0
% 8.54/1.96 | | | |
% 8.54/1.96 | | | | REDUCE: (29), (42) imply:
% 8.54/1.96 | | | | (43) $false
% 8.54/1.96 | | | |
% 8.54/1.96 | | | | CLOSE: (43) is inconsistent.
% 8.54/1.96 | | | |
% 8.54/1.96 | | | Case 2:
% 8.54/1.96 | | | |
% 8.54/1.96 | | | | (44) ? [v0: any] : ? [v1: any] : (in(all_38_0, all_14_7) = v1 &
% 8.54/1.96 | | | | in(all_38_1, all_14_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 8.54/1.96 | | | |
% 8.54/1.96 | | | | DELTA: instantiating (44) with fresh symbols all_58_0, all_58_1 gives:
% 8.54/1.96 | | | | (45) in(all_38_0, all_14_7) = all_58_0 & in(all_38_1, all_14_6) =
% 8.54/1.96 | | | | all_58_1 & ( ~ (all_58_0 = 0) | ~ (all_58_1 = 0))
% 8.54/1.96 | | | |
% 8.54/1.96 | | | | ALPHA: (45) implies:
% 8.54/1.96 | | | | (46) in(all_38_1, all_14_6) = all_58_1
% 8.54/1.96 | | | | (47) in(all_38_0, all_14_7) = all_58_0
% 8.54/1.96 | | | | (48) ~ (all_58_0 = 0) | ~ (all_58_1 = 0)
% 8.54/1.96 | | | |
% 8.54/1.96 | | | | GROUND_INST: instantiating (5) with 0, all_58_1, all_14_6, all_38_1,
% 8.54/1.96 | | | | simplifying with (37), (46) gives:
% 8.54/1.96 | | | | (49) all_58_1 = 0
% 8.54/1.96 | | | |
% 8.54/1.96 | | | | GROUND_INST: instantiating (5) with 0, all_58_0, all_14_7, all_38_0,
% 8.54/1.96 | | | | simplifying with (40), (47) gives:
% 8.54/1.96 | | | | (50) all_58_0 = 0
% 8.54/1.96 | | | |
% 8.54/1.96 | | | | BETA: splitting (48) gives:
% 8.54/1.96 | | | |
% 8.54/1.96 | | | | Case 1:
% 8.54/1.96 | | | | |
% 8.54/1.96 | | | | | (51) ~ (all_58_0 = 0)
% 8.54/1.96 | | | | |
% 8.54/1.96 | | | | | REDUCE: (50), (51) imply:
% 8.54/1.96 | | | | | (52) $false
% 8.54/1.96 | | | | |
% 8.54/1.96 | | | | | CLOSE: (52) is inconsistent.
% 8.54/1.96 | | | | |
% 8.54/1.96 | | | | Case 2:
% 8.54/1.96 | | | | |
% 8.54/1.96 | | | | | (53) ~ (all_58_1 = 0)
% 8.54/1.96 | | | | |
% 8.54/1.96 | | | | | REDUCE: (49), (53) imply:
% 8.54/1.96 | | | | | (54) $false
% 8.54/1.96 | | | | |
% 8.54/1.96 | | | | | CLOSE: (54) is inconsistent.
% 8.54/1.96 | | | | |
% 8.54/1.96 | | | | End of split
% 8.54/1.96 | | | |
% 8.54/1.96 | | | End of split
% 8.54/1.96 | | |
% 8.54/1.96 | | End of split
% 8.54/1.96 | |
% 8.54/1.96 | Case 2:
% 8.54/1.96 | |
% 8.54/1.96 | | (55) ~ (all_14_3 = 0)
% 8.54/1.96 | |
% 8.54/1.96 | | BETA: splitting (22) gives:
% 8.54/1.96 | |
% 8.54/1.96 | | Case 1:
% 8.54/1.96 | | |
% 8.54/1.96 | | | (56) all_14_3 = 0
% 8.54/1.96 | | |
% 8.54/1.96 | | | REDUCE: (55), (56) imply:
% 8.54/1.96 | | | (57) $false
% 8.54/1.96 | | |
% 8.54/1.96 | | | CLOSE: (57) is inconsistent.
% 8.54/1.96 | | |
% 8.54/1.96 | | Case 2:
% 8.54/1.96 | | |
% 8.69/1.96 | | | (58) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_14_4) = v1
% 8.69/1.96 | | | & in(v0, all_14_5) = 0 & $i(v0))
% 8.69/1.96 | | |
% 8.69/1.96 | | | DELTA: instantiating (58) with fresh symbols all_29_0, all_29_1 gives:
% 8.69/1.96 | | | (59) ~ (all_29_0 = 0) & in(all_29_1, all_14_4) = all_29_0 &
% 8.69/1.96 | | | in(all_29_1, all_14_5) = 0 & $i(all_29_1)
% 8.69/1.96 | | |
% 8.69/1.96 | | | ALPHA: (59) implies:
% 8.69/1.97 | | | (60) ~ (all_29_0 = 0)
% 8.69/1.97 | | | (61) $i(all_29_1)
% 8.69/1.97 | | | (62) in(all_29_1, all_14_5) = 0
% 8.69/1.97 | | | (63) in(all_29_1, all_14_4) = all_29_0
% 8.69/1.97 | | |
% 8.69/1.97 | | | GROUND_INST: instantiating (1) with all_14_8, all_14_6, all_14_5,
% 8.69/1.97 | | | all_29_1, simplifying with (7), (9), (10), (14), (61), (62)
% 8.69/1.97 | | | gives:
% 8.69/1.97 | | | (64) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_29_1 &
% 8.69/1.97 | | | in(v1, all_14_6) = 0 & in(v0, all_14_8) = 0 & $i(v1) & $i(v0))
% 8.69/1.97 | | |
% 8.69/1.97 | | | DELTA: instantiating (64) with fresh symbols all_38_0, all_38_1 gives:
% 8.69/1.97 | | | (65) ordered_pair(all_38_1, all_38_0) = all_29_1 & in(all_38_0,
% 8.69/1.97 | | | all_14_6) = 0 & in(all_38_1, all_14_8) = 0 & $i(all_38_0) &
% 8.69/1.97 | | | $i(all_38_1)
% 8.69/1.97 | | |
% 8.69/1.97 | | | ALPHA: (65) implies:
% 8.69/1.97 | | | (66) $i(all_38_1)
% 8.69/1.97 | | | (67) $i(all_38_0)
% 8.69/1.97 | | | (68) in(all_38_1, all_14_8) = 0
% 8.69/1.97 | | | (69) in(all_38_0, all_14_6) = 0
% 8.69/1.97 | | | (70) ordered_pair(all_38_1, all_38_0) = all_29_1
% 8.69/1.97 | | |
% 8.69/1.97 | | | GROUND_INST: instantiating (3) with all_14_8, all_14_7, all_38_1,
% 8.69/1.97 | | | simplifying with (7), (8), (18), (66), (68) gives:
% 8.69/1.97 | | | (71) in(all_38_1, all_14_7) = 0
% 8.69/1.97 | | |
% 8.69/1.97 | | | GROUND_INST: instantiating (2) with all_14_7, all_14_6, all_14_4,
% 8.69/1.97 | | | all_29_1, all_29_0, all_38_1, all_38_0, simplifying with (8),
% 8.69/1.97 | | | (9), (11), (15), (61), (63), (66), (67), (70) gives:
% 8.69/1.97 | | | (72) all_29_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_38_0,
% 8.69/1.97 | | | all_14_6) = v1 & in(all_38_1, all_14_7) = v0 & ( ~ (v1 = 0) |
% 8.69/1.97 | | | ~ (v0 = 0)))
% 8.69/1.97 | | |
% 8.69/1.97 | | | BETA: splitting (72) gives:
% 8.69/1.97 | | |
% 8.69/1.97 | | | Case 1:
% 8.69/1.97 | | | |
% 8.69/1.97 | | | | (73) all_29_0 = 0
% 8.69/1.97 | | | |
% 8.69/1.97 | | | | REDUCE: (60), (73) imply:
% 8.69/1.97 | | | | (74) $false
% 8.69/1.97 | | | |
% 8.69/1.97 | | | | CLOSE: (74) is inconsistent.
% 8.69/1.97 | | | |
% 8.69/1.97 | | | Case 2:
% 8.69/1.97 | | | |
% 8.69/1.97 | | | | (75) ? [v0: any] : ? [v1: any] : (in(all_38_0, all_14_6) = v1 &
% 8.69/1.97 | | | | in(all_38_1, all_14_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 8.69/1.97 | | | |
% 8.69/1.97 | | | | DELTA: instantiating (75) with fresh symbols all_58_0, all_58_1 gives:
% 8.69/1.97 | | | | (76) in(all_38_0, all_14_6) = all_58_0 & in(all_38_1, all_14_7) =
% 8.69/1.97 | | | | all_58_1 & ( ~ (all_58_0 = 0) | ~ (all_58_1 = 0))
% 8.69/1.97 | | | |
% 8.69/1.97 | | | | ALPHA: (76) implies:
% 8.69/1.97 | | | | (77) in(all_38_1, all_14_7) = all_58_1
% 8.69/1.98 | | | | (78) in(all_38_0, all_14_6) = all_58_0
% 8.69/1.98 | | | | (79) ~ (all_58_0 = 0) | ~ (all_58_1 = 0)
% 8.69/1.98 | | | |
% 8.69/1.98 | | | | GROUND_INST: instantiating (5) with 0, all_58_1, all_14_7, all_38_1,
% 8.69/1.98 | | | | simplifying with (71), (77) gives:
% 8.69/1.98 | | | | (80) all_58_1 = 0
% 8.69/1.98 | | | |
% 8.69/1.98 | | | | GROUND_INST: instantiating (5) with 0, all_58_0, all_14_6, all_38_0,
% 8.69/1.98 | | | | simplifying with (69), (78) gives:
% 8.69/1.98 | | | | (81) all_58_0 = 0
% 8.69/1.98 | | | |
% 8.69/1.98 | | | | BETA: splitting (79) gives:
% 8.69/1.98 | | | |
% 8.69/1.98 | | | | Case 1:
% 8.69/1.98 | | | | |
% 8.69/1.98 | | | | | (82) ~ (all_58_0 = 0)
% 8.69/1.98 | | | | |
% 8.69/1.98 | | | | | REDUCE: (81), (82) imply:
% 8.69/1.98 | | | | | (83) $false
% 8.69/1.98 | | | | |
% 8.69/1.98 | | | | | CLOSE: (83) is inconsistent.
% 8.69/1.98 | | | | |
% 8.69/1.98 | | | | Case 2:
% 8.69/1.98 | | | | |
% 8.69/1.98 | | | | | (84) ~ (all_58_1 = 0)
% 8.69/1.98 | | | | |
% 8.69/1.98 | | | | | REDUCE: (80), (84) imply:
% 8.69/1.98 | | | | | (85) $false
% 8.69/1.98 | | | | |
% 8.69/1.98 | | | | | CLOSE: (85) is inconsistent.
% 8.69/1.98 | | | | |
% 8.69/1.98 | | | | End of split
% 8.69/1.98 | | | |
% 8.69/1.98 | | | End of split
% 8.69/1.98 | | |
% 8.69/1.98 | | End of split
% 8.69/1.98 | |
% 8.69/1.98 | End of split
% 8.69/1.98 |
% 8.69/1.98 End of proof
% 8.69/1.98 % SZS output end Proof for theBenchmark
% 8.69/1.98
% 8.69/1.98 1367ms
%------------------------------------------------------------------------------