TSTP Solution File: SET929+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET929+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n004.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 15:27:05 EDT 2023
% Result : Theorem 4.27s 1.41s
% Output : Proof 6.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SET929+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 09:16:37 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.73/0.98 Prover 1: Preprocessing ...
% 1.73/0.98 Prover 4: Preprocessing ...
% 2.16/1.02 Prover 3: Preprocessing ...
% 2.16/1.02 Prover 5: Preprocessing ...
% 2.16/1.02 Prover 6: Preprocessing ...
% 2.16/1.02 Prover 0: Preprocessing ...
% 2.16/1.02 Prover 2: Preprocessing ...
% 3.15/1.16 Prover 1: Warning: ignoring some quantifiers
% 3.15/1.19 Prover 1: Constructing countermodel ...
% 3.15/1.20 Prover 3: Warning: ignoring some quantifiers
% 3.15/1.21 Prover 3: Constructing countermodel ...
% 3.15/1.21 Prover 5: Proving ...
% 3.15/1.22 Prover 4: Constructing countermodel ...
% 3.83/1.23 Prover 6: Proving ...
% 3.83/1.24 Prover 2: Proving ...
% 3.83/1.24 Prover 0: Proving ...
% 4.27/1.40 Prover 3: proved (742ms)
% 4.27/1.40
% 4.27/1.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.27/1.41
% 4.27/1.41 Prover 5: stopped
% 4.27/1.41 Prover 2: stopped
% 4.27/1.41 Prover 6: stopped
% 4.27/1.41 Prover 0: stopped
% 4.27/1.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.27/1.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.27/1.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.27/1.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.27/1.41 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.27/1.44 Prover 13: Preprocessing ...
% 4.27/1.44 Prover 11: Preprocessing ...
% 4.27/1.45 Prover 7: Preprocessing ...
% 5.39/1.46 Prover 8: Preprocessing ...
% 5.39/1.47 Prover 10: Preprocessing ...
% 5.65/1.51 Prover 7: Warning: ignoring some quantifiers
% 5.65/1.51 Prover 10: Warning: ignoring some quantifiers
% 5.65/1.51 Prover 7: Constructing countermodel ...
% 5.65/1.51 Prover 10: Constructing countermodel ...
% 5.65/1.52 Prover 8: Warning: ignoring some quantifiers
% 5.65/1.52 Prover 13: Warning: ignoring some quantifiers
% 5.65/1.53 Prover 13: Constructing countermodel ...
% 5.92/1.53 Prover 8: Constructing countermodel ...
% 5.92/1.54 Prover 4: Found proof (size 45)
% 5.92/1.54 Prover 4: proved (883ms)
% 5.92/1.54 Prover 10: stopped
% 5.92/1.54 Prover 7: stopped
% 5.92/1.54 Prover 13: stopped
% 5.92/1.54 Prover 1: stopped
% 5.92/1.54 Prover 8: stopped
% 5.92/1.55 Prover 11: Constructing countermodel ...
% 5.92/1.56 Prover 11: stopped
% 5.92/1.56
% 5.92/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.92/1.56
% 5.92/1.56 % SZS output start Proof for theBenchmark
% 5.92/1.57 Assumptions after simplification:
% 5.92/1.57 ---------------------------------
% 5.92/1.57
% 5.92/1.57 (commutativity_k2_tarski)
% 5.92/1.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) |
% 5.92/1.60 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i]
% 5.92/1.60 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) |
% 5.92/1.60 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 5.92/1.60
% 5.92/1.60 (t37_xboole_1)
% 5.92/1.61 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~
% 5.92/1.61 (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~
% 5.92/1.61 (v3 = 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 5.92/1.61 int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 5.92/1.61 $i] : ( ~ (v3 = empty_set) & set_difference(v0, v1) = v3 & $i(v3))) & !
% 5.92/1.61 [v0: $i] : ! [v1: $i] : ( ~ (set_difference(v0, v1) = empty_set) | ~ $i(v1)
% 5.92/1.61 | ~ $i(v0) | subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 5.92/1.61 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | set_difference(v0, v1) =
% 5.92/1.61 empty_set)
% 5.92/1.61
% 5.92/1.61 (t38_zfmisc_1)
% 5.92/1.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 5.92/1.61 | ~ (subset(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ $i(v2) |
% 5.92/1.61 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v1, v2) = v6 &
% 5.92/1.61 in(v0, v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1:
% 5.92/1.61 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (subset(v3, v2) = 0) | ~
% 5.92/1.61 (unordered_pair(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1,
% 5.92/1.61 v2) = 0 & in(v0, v2) = 0))
% 5.92/1.61
% 5.92/1.61 (t73_zfmisc_1)
% 5.92/1.61 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 5.92/1.61 [v4: $i] : ? [v5: any] : ? [v6: any] : (set_difference(v3, v2) = v4 &
% 5.92/1.61 unordered_pair(v0, v1) = v3 & in(v1, v2) = v6 & in(v0, v2) = v5 & $i(v4) &
% 5.92/1.61 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v6 = 0 & v5 = 0 & ~ (v4 = empty_set))
% 5.92/1.61 | (v4 = empty_set & ( ~ (v6 = 0) | ~ (v5 = 0)))))
% 5.92/1.61
% 5.92/1.62 (function-axioms)
% 5.92/1.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.92/1.62 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 5.92/1.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 5.92/1.62 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 5.92/1.62 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.92/1.62 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 5.92/1.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 5.92/1.62 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 5.92/1.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 5.92/1.62 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 5.92/1.62
% 5.92/1.62 Further assumptions not needed in the proof:
% 5.92/1.62 --------------------------------------------
% 5.92/1.62 antisymmetry_r2_hidden, fc1_xboole_0, rc1_xboole_0, rc2_xboole_0,
% 5.92/1.62 reflexivity_r1_tarski
% 5.92/1.62
% 5.92/1.62 Those formulas are unsatisfiable:
% 5.92/1.62 ---------------------------------
% 5.92/1.62
% 5.92/1.62 Begin of proof
% 5.92/1.62 |
% 5.92/1.62 | ALPHA: (commutativity_k2_tarski) implies:
% 5.92/1.62 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) =
% 5.92/1.62 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 &
% 5.92/1.62 | $i(v2)))
% 5.92/1.62 |
% 5.92/1.62 | ALPHA: (t37_xboole_1) implies:
% 5.92/1.63 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (set_difference(v0, v1) = empty_set) |
% 5.92/1.63 | ~ $i(v1) | ~ $i(v0) | subset(v0, v1) = 0)
% 5.92/1.63 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~
% 5.92/1.63 | (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 5.92/1.63 | : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 5.92/1.63 |
% 5.92/1.63 | ALPHA: (t38_zfmisc_1) implies:
% 5.92/1.63 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (subset(v3,
% 5.92/1.63 | v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | ~ $i(v2) | ~
% 5.92/1.63 | $i(v1) | ~ $i(v0) | (in(v1, v2) = 0 & in(v0, v2) = 0))
% 5.92/1.63 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 5.92/1.63 | (v4 = 0 | ~ (subset(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) |
% 5.92/1.63 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 5.92/1.63 | (in(v1, v2) = v6 & in(v0, v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 5.92/1.63 |
% 5.92/1.63 | ALPHA: (t73_zfmisc_1) implies:
% 5.92/1.63 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 5.92/1.63 | ? [v5: any] : ? [v6: any] : (set_difference(v3, v2) = v4 &
% 5.92/1.63 | unordered_pair(v0, v1) = v3 & in(v1, v2) = v6 & in(v0, v2) = v5 &
% 5.92/1.63 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v6 = 0 & v5 = 0 & ~
% 5.92/1.63 | (v4 = empty_set)) | (v4 = empty_set & ( ~ (v6 = 0) | ~ (v5 =
% 5.92/1.63 | 0)))))
% 5.92/1.63 |
% 5.92/1.63 | ALPHA: (function-axioms) implies:
% 5.92/1.63 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.92/1.63 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 5.92/1.63 |
% 5.92/1.63 | DELTA: instantiating (6) with fresh symbols all_13_0, all_13_1, all_13_2,
% 5.92/1.63 | all_13_3, all_13_4, all_13_5, all_13_6 gives:
% 6.41/1.64 | (8) set_difference(all_13_3, all_13_4) = all_13_2 &
% 6.41/1.64 | unordered_pair(all_13_6, all_13_5) = all_13_3 & in(all_13_5, all_13_4)
% 6.41/1.64 | = all_13_0 & in(all_13_6, all_13_4) = all_13_1 & $i(all_13_2) &
% 6.41/1.64 | $i(all_13_3) & $i(all_13_4) & $i(all_13_5) & $i(all_13_6) & ((all_13_0
% 6.41/1.64 | = 0 & all_13_1 = 0 & ~ (all_13_2 = empty_set)) | (all_13_2 =
% 6.41/1.64 | empty_set & ( ~ (all_13_0 = 0) | ~ (all_13_1 = 0))))
% 6.41/1.64 |
% 6.41/1.64 | ALPHA: (8) implies:
% 6.41/1.64 | (9) $i(all_13_6)
% 6.41/1.64 | (10) $i(all_13_5)
% 6.41/1.64 | (11) $i(all_13_4)
% 6.41/1.64 | (12) in(all_13_6, all_13_4) = all_13_1
% 6.41/1.64 | (13) in(all_13_5, all_13_4) = all_13_0
% 6.41/1.64 | (14) unordered_pair(all_13_6, all_13_5) = all_13_3
% 6.41/1.64 | (15) set_difference(all_13_3, all_13_4) = all_13_2
% 6.41/1.64 | (16) (all_13_0 = 0 & all_13_1 = 0 & ~ (all_13_2 = empty_set)) | (all_13_2
% 6.41/1.64 | = empty_set & ( ~ (all_13_0 = 0) | ~ (all_13_1 = 0)))
% 6.41/1.64 |
% 6.41/1.64 | GROUND_INST: instantiating (1) with all_13_5, all_13_6, all_13_3, simplifying
% 6.41/1.64 | with (9), (10), (14) gives:
% 6.41/1.64 | (17) unordered_pair(all_13_5, all_13_6) = all_13_3 & $i(all_13_3)
% 6.41/1.64 |
% 6.41/1.64 | ALPHA: (17) implies:
% 6.41/1.64 | (18) $i(all_13_3)
% 6.41/1.64 |
% 6.41/1.64 | GROUND_INST: instantiating (3) with all_13_3, all_13_4, all_13_2, simplifying
% 6.41/1.64 | with (11), (15), (18) gives:
% 6.41/1.64 | (19) all_13_2 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & subset(all_13_3,
% 6.41/1.64 | all_13_4) = v0)
% 6.41/1.64 |
% 6.41/1.64 | BETA: splitting (16) gives:
% 6.41/1.64 |
% 6.41/1.64 | Case 1:
% 6.41/1.64 | |
% 6.41/1.64 | | (20) all_13_0 = 0 & all_13_1 = 0 & ~ (all_13_2 = empty_set)
% 6.41/1.64 | |
% 6.41/1.64 | | ALPHA: (20) implies:
% 6.41/1.64 | | (21) all_13_1 = 0
% 6.41/1.64 | | (22) all_13_0 = 0
% 6.41/1.64 | | (23) ~ (all_13_2 = empty_set)
% 6.41/1.64 | |
% 6.41/1.64 | | REDUCE: (13), (22) imply:
% 6.41/1.64 | | (24) in(all_13_5, all_13_4) = 0
% 6.41/1.64 | |
% 6.41/1.64 | | REDUCE: (12), (21) imply:
% 6.41/1.64 | | (25) in(all_13_6, all_13_4) = 0
% 6.41/1.64 | |
% 6.41/1.64 | | BETA: splitting (19) gives:
% 6.41/1.64 | |
% 6.41/1.64 | | Case 1:
% 6.41/1.64 | | |
% 6.41/1.64 | | | (26) all_13_2 = empty_set
% 6.41/1.64 | | |
% 6.41/1.64 | | | REDUCE: (23), (26) imply:
% 6.41/1.64 | | | (27) $false
% 6.41/1.65 | | |
% 6.41/1.65 | | | CLOSE: (27) is inconsistent.
% 6.41/1.65 | | |
% 6.41/1.65 | | Case 2:
% 6.41/1.65 | | |
% 6.41/1.65 | | | (28) ? [v0: int] : ( ~ (v0 = 0) & subset(all_13_3, all_13_4) = v0)
% 6.41/1.65 | | |
% 6.41/1.65 | | | DELTA: instantiating (28) with fresh symbol all_32_0 gives:
% 6.41/1.65 | | | (29) ~ (all_32_0 = 0) & subset(all_13_3, all_13_4) = all_32_0
% 6.41/1.65 | | |
% 6.41/1.65 | | | ALPHA: (29) implies:
% 6.41/1.65 | | | (30) ~ (all_32_0 = 0)
% 6.41/1.65 | | | (31) subset(all_13_3, all_13_4) = all_32_0
% 6.41/1.65 | | |
% 6.41/1.65 | | | GROUND_INST: instantiating (5) with all_13_6, all_13_5, all_13_4,
% 6.41/1.65 | | | all_13_3, all_32_0, simplifying with (9), (10), (11), (14),
% 6.41/1.65 | | | (31) gives:
% 6.41/1.65 | | | (32) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_13_5,
% 6.41/1.65 | | | all_13_4) = v1 & in(all_13_6, all_13_4) = v0 & ( ~ (v1 = 0) |
% 6.41/1.65 | | | ~ (v0 = 0)))
% 6.41/1.65 | | |
% 6.41/1.65 | | | BETA: splitting (32) gives:
% 6.41/1.65 | | |
% 6.41/1.65 | | | Case 1:
% 6.41/1.65 | | | |
% 6.41/1.65 | | | | (33) all_32_0 = 0
% 6.41/1.65 | | | |
% 6.41/1.65 | | | | REDUCE: (30), (33) imply:
% 6.41/1.65 | | | | (34) $false
% 6.41/1.65 | | | |
% 6.41/1.65 | | | | CLOSE: (34) is inconsistent.
% 6.41/1.65 | | | |
% 6.41/1.65 | | | Case 2:
% 6.41/1.65 | | | |
% 6.41/1.65 | | | | (35) ? [v0: any] : ? [v1: any] : (in(all_13_5, all_13_4) = v1 &
% 6.41/1.65 | | | | in(all_13_6, all_13_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.41/1.65 | | | |
% 6.41/1.65 | | | | DELTA: instantiating (35) with fresh symbols all_47_0, all_47_1 gives:
% 6.41/1.65 | | | | (36) in(all_13_5, all_13_4) = all_47_0 & in(all_13_6, all_13_4) =
% 6.41/1.65 | | | | all_47_1 & ( ~ (all_47_0 = 0) | ~ (all_47_1 = 0))
% 6.41/1.65 | | | |
% 6.41/1.65 | | | | ALPHA: (36) implies:
% 6.41/1.65 | | | | (37) in(all_13_6, all_13_4) = all_47_1
% 6.41/1.65 | | | | (38) in(all_13_5, all_13_4) = all_47_0
% 6.41/1.65 | | | | (39) ~ (all_47_0 = 0) | ~ (all_47_1 = 0)
% 6.41/1.65 | | | |
% 6.41/1.65 | | | | GROUND_INST: instantiating (7) with 0, all_47_1, all_13_4, all_13_6,
% 6.41/1.65 | | | | simplifying with (25), (37) gives:
% 6.41/1.65 | | | | (40) all_47_1 = 0
% 6.41/1.65 | | | |
% 6.41/1.65 | | | | GROUND_INST: instantiating (7) with 0, all_47_0, all_13_4, all_13_5,
% 6.41/1.65 | | | | simplifying with (24), (38) gives:
% 6.41/1.65 | | | | (41) all_47_0 = 0
% 6.41/1.65 | | | |
% 6.41/1.65 | | | | BETA: splitting (39) gives:
% 6.41/1.65 | | | |
% 6.41/1.65 | | | | Case 1:
% 6.41/1.65 | | | | |
% 6.41/1.65 | | | | | (42) ~ (all_47_0 = 0)
% 6.41/1.65 | | | | |
% 6.41/1.65 | | | | | REDUCE: (41), (42) imply:
% 6.41/1.65 | | | | | (43) $false
% 6.41/1.65 | | | | |
% 6.41/1.65 | | | | | CLOSE: (43) is inconsistent.
% 6.41/1.65 | | | | |
% 6.41/1.65 | | | | Case 2:
% 6.41/1.65 | | | | |
% 6.41/1.65 | | | | | (44) ~ (all_47_1 = 0)
% 6.41/1.65 | | | | |
% 6.41/1.65 | | | | | REDUCE: (40), (44) imply:
% 6.41/1.65 | | | | | (45) $false
% 6.41/1.65 | | | | |
% 6.41/1.65 | | | | | CLOSE: (45) is inconsistent.
% 6.41/1.65 | | | | |
% 6.41/1.65 | | | | End of split
% 6.41/1.65 | | | |
% 6.41/1.65 | | | End of split
% 6.41/1.65 | | |
% 6.41/1.65 | | End of split
% 6.41/1.65 | |
% 6.41/1.65 | Case 2:
% 6.41/1.65 | |
% 6.41/1.65 | | (46) all_13_2 = empty_set & ( ~ (all_13_0 = 0) | ~ (all_13_1 = 0))
% 6.41/1.65 | |
% 6.41/1.65 | | ALPHA: (46) implies:
% 6.41/1.65 | | (47) all_13_2 = empty_set
% 6.41/1.66 | | (48) ~ (all_13_0 = 0) | ~ (all_13_1 = 0)
% 6.41/1.66 | |
% 6.41/1.66 | | REDUCE: (15), (47) imply:
% 6.41/1.66 | | (49) set_difference(all_13_3, all_13_4) = empty_set
% 6.41/1.66 | |
% 6.41/1.66 | | GROUND_INST: instantiating (2) with all_13_3, all_13_4, simplifying with
% 6.41/1.66 | | (11), (18), (49) gives:
% 6.41/1.66 | | (50) subset(all_13_3, all_13_4) = 0
% 6.41/1.66 | |
% 6.41/1.66 | | GROUND_INST: instantiating (4) with all_13_6, all_13_5, all_13_4, all_13_3,
% 6.41/1.66 | | simplifying with (9), (10), (11), (14), (50) gives:
% 6.41/1.66 | | (51) in(all_13_5, all_13_4) = 0 & in(all_13_6, all_13_4) = 0
% 6.41/1.66 | |
% 6.41/1.66 | | ALPHA: (51) implies:
% 6.41/1.66 | | (52) in(all_13_6, all_13_4) = 0
% 6.41/1.66 | | (53) in(all_13_5, all_13_4) = 0
% 6.41/1.66 | |
% 6.41/1.66 | | GROUND_INST: instantiating (7) with all_13_1, 0, all_13_4, all_13_6,
% 6.41/1.66 | | simplifying with (12), (52) gives:
% 6.41/1.66 | | (54) all_13_1 = 0
% 6.41/1.66 | |
% 6.41/1.66 | | GROUND_INST: instantiating (7) with all_13_0, 0, all_13_4, all_13_5,
% 6.41/1.66 | | simplifying with (13), (53) gives:
% 6.41/1.66 | | (55) all_13_0 = 0
% 6.41/1.66 | |
% 6.41/1.66 | | BETA: splitting (48) gives:
% 6.41/1.66 | |
% 6.41/1.66 | | Case 1:
% 6.41/1.66 | | |
% 6.41/1.66 | | | (56) ~ (all_13_0 = 0)
% 6.41/1.66 | | |
% 6.41/1.66 | | | REDUCE: (55), (56) imply:
% 6.41/1.66 | | | (57) $false
% 6.41/1.66 | | |
% 6.41/1.66 | | | CLOSE: (57) is inconsistent.
% 6.41/1.66 | | |
% 6.41/1.66 | | Case 2:
% 6.41/1.66 | | |
% 6.41/1.66 | | | (58) ~ (all_13_1 = 0)
% 6.41/1.66 | | |
% 6.41/1.66 | | | REDUCE: (54), (58) imply:
% 6.41/1.66 | | | (59) $false
% 6.41/1.66 | | |
% 6.41/1.66 | | | CLOSE: (59) is inconsistent.
% 6.41/1.66 | | |
% 6.41/1.66 | | End of split
% 6.41/1.66 | |
% 6.41/1.66 | End of split
% 6.41/1.66 |
% 6.41/1.66 End of proof
% 6.41/1.66 % SZS output end Proof for theBenchmark
% 6.41/1.66
% 6.41/1.66 1030ms
%------------------------------------------------------------------------------