TSTP Solution File: SET937+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET937+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 : n003.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 15:27:07 EDT 2023
% Result : Theorem 10.85s 2.24s
% Output : Proof 13.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET937+1 : 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 : n003.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 : Sat Aug 26 09:22:24 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.15/1.02 Prover 4: Preprocessing ...
% 2.15/1.02 Prover 1: Preprocessing ...
% 2.85/1.08 Prover 6: Preprocessing ...
% 2.85/1.08 Prover 2: Preprocessing ...
% 2.85/1.08 Prover 0: Preprocessing ...
% 2.85/1.08 Prover 3: Preprocessing ...
% 2.85/1.08 Prover 5: Preprocessing ...
% 5.86/1.54 Prover 1: Warning: ignoring some quantifiers
% 5.86/1.55 Prover 3: Warning: ignoring some quantifiers
% 5.86/1.57 Prover 6: Proving ...
% 6.18/1.57 Prover 5: Proving ...
% 6.18/1.58 Prover 1: Constructing countermodel ...
% 6.18/1.59 Prover 3: Constructing countermodel ...
% 6.18/1.61 Prover 4: Warning: ignoring some quantifiers
% 6.18/1.63 Prover 2: Proving ...
% 6.75/1.65 Prover 4: Constructing countermodel ...
% 7.34/1.75 Prover 0: Proving ...
% 10.33/2.17 Prover 3: gave up
% 10.33/2.18 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.33/2.22 Prover 7: Preprocessing ...
% 10.85/2.24 Prover 0: proved (1613ms)
% 10.85/2.24
% 10.85/2.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.85/2.24
% 10.85/2.24 Prover 2: stopped
% 10.85/2.24 Prover 5: stopped
% 10.85/2.24 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.85/2.24 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.85/2.24 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.85/2.25 Prover 6: stopped
% 10.85/2.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.22/2.29 Prover 8: Preprocessing ...
% 11.22/2.29 Prover 10: Preprocessing ...
% 11.22/2.29 Prover 7: Warning: ignoring some quantifiers
% 11.22/2.30 Prover 11: Preprocessing ...
% 11.22/2.30 Prover 13: Preprocessing ...
% 11.22/2.32 Prover 7: Constructing countermodel ...
% 11.22/2.34 Prover 10: Warning: ignoring some quantifiers
% 11.80/2.35 Prover 10: Constructing countermodel ...
% 11.99/2.40 Prover 13: Warning: ignoring some quantifiers
% 11.99/2.41 Prover 8: Warning: ignoring some quantifiers
% 12.37/2.43 Prover 8: Constructing countermodel ...
% 12.37/2.43 Prover 13: Constructing countermodel ...
% 12.56/2.49 Prover 11: Warning: ignoring some quantifiers
% 12.56/2.50 Prover 4: Found proof (size 79)
% 12.56/2.50 Prover 4: proved (1872ms)
% 12.56/2.50 Prover 8: stopped
% 12.56/2.50 Prover 13: stopped
% 12.56/2.50 Prover 1: stopped
% 12.56/2.50 Prover 10: stopped
% 12.56/2.51 Prover 7: stopped
% 12.56/2.51 Prover 11: Constructing countermodel ...
% 12.56/2.52 Prover 11: stopped
% 12.56/2.52
% 12.56/2.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.06/2.52
% 13.06/2.53 % SZS output start Proof for theBenchmark
% 13.06/2.53 Assumptions after simplification:
% 13.06/2.53 ---------------------------------
% 13.06/2.53
% 13.06/2.53 (commutativity_k2_xboole_0)
% 13.06/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 13.06/2.56 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 13.06/2.56 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 13.06/2.56 | (set_union2(v1, v0) = v2 & $i(v2)))
% 13.06/2.56
% 13.06/2.56 (d1_tarski)
% 13.06/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 13.06/2.56 ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : !
% 13.06/2.56 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) =
% 13.06/2.56 v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 13.06/2.56 (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 13.06/2.56 [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 =
% 13.06/2.56 0 | v3 = v1)))
% 13.06/2.56
% 13.06/2.56 (d1_zfmisc_1)
% 13.06/2.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.06/2.57 (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 13.06/2.57 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0: $i] : !
% 13.06/2.57 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (powerset(v0) = v1) | ~
% 13.06/2.57 (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~
% 13.06/2.57 (v4 = 0) & subset(v2, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 13.06/2.57 : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 13.06/2.57 ~ $i(v0) | in(v2, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 13.06/2.57 (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 13.06/2.57 $i(v0) | subset(v2, v0) = 0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2
% 13.06/2.57 = v0 | ~ (powerset(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 13.06/2.57 [v4: any] : ? [v5: any] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & $i(v3) &
% 13.06/2.57 ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 13.06/2.57
% 13.06/2.57 (d2_xboole_0)
% 13.30/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 13.30/2.58 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~
% 13.30/2.58 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0)
% 13.30/2.58 & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0: $i] : !
% 13.30/2.58 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 13.30/2.58 (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) |
% 13.30/2.58 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 &
% 13.30/2.58 in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 13.30/2.58 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (set_union2(v0, v1) =
% 13.30/2.58 v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 13.30/2.58 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5
% 13.30/2.58 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 13.30/2.58 $i] : ! [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) |
% 13.30/2.58 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 13.30/2.58 (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 =
% 13.30/2.58 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 13.30/2.58 [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) |
% 13.30/2.58 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3,
% 13.30/2.58 v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) &
% 13.30/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1)
% 13.30/2.58 = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 13.30/2.58 $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v1) = v5 & in(v3, v0) = v4 &
% 13.30/2.58 (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 13.30/2.58 $i] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 13.30/2.58 $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4,
% 13.30/2.58 v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | (
% 13.30/2.58 ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0)))
% 13.30/2.58
% 13.30/2.58 (d3_tarski)
% 13.30/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.30/2.58 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 13.30/2.58 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 13.30/2.58 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 13.30/2.58 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 13.30/2.58 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 13.30/2.58 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 13.30/2.58 $i(v0) | in(v2, v1) = 0)
% 13.30/2.58
% 13.30/2.58 (d4_xboole_0)
% 13.30/2.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 13.30/2.59 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~
% 13.30/2.59 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1) =
% 13.30/2.59 v6 & in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1:
% 13.30/2.59 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 13.30/2.59 (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2)
% 13.30/2.59 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v6 &
% 13.30/2.59 in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 13.30/2.59 ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ (set_difference(v0, v1) = v2) |
% 13.30/2.59 ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 13.30/2.59 [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0)
% 13.30/2.59 | (v6 = 0 & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 13.30/2.59 ! [v3: $i] : ! [v4: any] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0)
% 13.30/2.59 = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ?
% 13.30/2.59 [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~
% 13.30/2.59 (v6 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 13.30/2.59 ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~
% 13.30/2.59 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) =
% 13.30/2.59 v4 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 13.30/2.59 $i] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) |
% 13.30/2.59 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v2)
% 13.30/2.59 = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] :
% 13.30/2.59 ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ~
% 13.30/2.59 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] :
% 13.30/2.59 ? [v7: any] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4)
% 13.30/2.59 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 =
% 13.30/2.59 0)))))
% 13.30/2.59
% 13.30/2.59 (d7_xboole_0)
% 13.30/2.59 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~
% 13.30/2.59 (set_intersection2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : (
% 13.30/2.59 ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 13.30/2.59 int] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 13.30/2.59 [v3: $i] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3 & $i(v3)))
% 13.30/2.59 & ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~
% 13.30/2.59 $i(v0) | set_intersection2(v0, v1) = empty_set) & ! [v0: $i] : ! [v1: $i]
% 13.30/2.59 : ( ~ (set_intersection2(v0, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) |
% 13.30/2.59 disjoint(v0, v1) = 0)
% 13.30/2.59
% 13.30/2.59 (t1_xboole_1)
% 13.30/2.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.30/2.59 (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 13.30/2.59 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] :
% 13.30/2.59 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (subset(v0, v2) = v3)
% 13.30/2.59 | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int]
% 13.30/2.59 : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 13.30/2.59 $i] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~
% 13.30/2.59 $i(v1) | ~ $i(v0) | subset(v0, v2) = 0)
% 13.30/2.59
% 13.30/2.59 (t28_xboole_1)
% 13.30/2.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (set_intersection2(v0,
% 13.30/2.59 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 13.30/2.59 subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) =
% 13.30/2.59 0) | ~ $i(v1) | ~ $i(v0) | set_intersection2(v0, v1) = v0)
% 13.30/2.59
% 13.30/2.59 (t36_xboole_1)
% 13.30/2.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) |
% 13.30/2.59 ~ $i(v1) | ~ $i(v0) | subset(v2, v0) = 0)
% 13.30/2.59
% 13.30/2.59 (t63_xboole_1)
% 13.30/2.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.30/2.60 (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 13.30/2.60 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0:
% 13.30/2.60 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (disjoint(v0,
% 13.30/2.60 v2) = v3) | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 13.30/2.60 | ? [v4: int] : ( ~ (v4 = 0) & disjoint(v1, v2) = v4)) & ! [v0: $i] : !
% 13.30/2.60 [v1: $i] : ! [v2: $i] : ( ~ (disjoint(v1, v2) = 0) | ~ (subset(v0, v1) = 0)
% 13.30/2.60 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | disjoint(v0, v2) = 0)
% 13.30/2.60
% 13.30/2.60 (t79_xboole_1)
% 13.30/2.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) |
% 13.30/2.60 ~ $i(v1) | ~ $i(v0) | disjoint(v2, v1) = 0)
% 13.30/2.60
% 13.30/2.60 (t84_zfmisc_1)
% 13.30/2.60 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 13.30/2.60 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 13.30/2.60 int] : ( ~ (v9 = 0) & set_difference(v5, v6) = v7 & set_difference(v1, v2) =
% 13.30/2.60 v3 & powerset(v3) = v4 & powerset(v2) = v6 & powerset(v1) = v5 & subset(v4,
% 13.30/2.60 v8) = v9 & singleton(empty_set) = v0 & set_union2(v0, v7) = v8 & $i(v8) &
% 13.30/2.60 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.30/2.60
% 13.30/2.60 (function-axioms)
% 13.30/2.60 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.30/2.60 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 13.30/2.60 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.30/2.60 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 13.30/2.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.30/2.60 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 13.30/2.60 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.30/2.60 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 13.30/2.60 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.30/2.60 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0:
% 13.30/2.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.30/2.60 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 13.30/2.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 13.30/2.60 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 13.30/2.60 [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & !
% 13.30/2.60 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 13.30/2.60 (singleton(v2) = v0))
% 13.30/2.60
% 13.30/2.60 Further assumptions not needed in the proof:
% 13.30/2.60 --------------------------------------------
% 13.30/2.60 antisymmetry_r2_hidden, commutativity_k3_xboole_0, fc1_xboole_0, fc2_xboole_0,
% 13.30/2.60 fc3_xboole_0, idempotence_k2_xboole_0, idempotence_k3_xboole_0, rc1_xboole_0,
% 13.30/2.60 rc2_xboole_0, reflexivity_r1_tarski, symmetry_r1_xboole_0
% 13.30/2.60
% 13.30/2.60 Those formulas are unsatisfiable:
% 13.30/2.60 ---------------------------------
% 13.30/2.60
% 13.30/2.60 Begin of proof
% 13.30/2.60 |
% 13.30/2.61 | ALPHA: (commutativity_k2_xboole_0) implies:
% 13.30/2.61 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 13.30/2.61 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 13.30/2.61 |
% 13.30/2.61 | ALPHA: (d1_tarski) implies:
% 13.30/2.61 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0)
% 13.30/2.61 | = v1) | ~ (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0))
% 13.30/2.61 |
% 13.30/2.61 | ALPHA: (d1_zfmisc_1) implies:
% 13.30/2.61 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) = v1) | ~
% 13.30/2.61 | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | subset(v2, v0)
% 13.30/2.61 | = 0)
% 13.30/2.61 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) = v1) | ~
% 13.30/2.61 | (subset(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1)
% 13.30/2.61 | = 0)
% 13.30/2.61 |
% 13.30/2.61 | ALPHA: (d2_xboole_0) implies:
% 13.30/2.61 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 13.30/2.61 | (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~
% 13.30/2.61 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 13.30/2.61 | int] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) =
% 13.30/2.61 | v5))
% 13.30/2.61 |
% 13.30/2.61 | ALPHA: (d3_tarski) implies:
% 13.30/2.61 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 13.30/2.61 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 13.30/2.61 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 13.30/2.61 |
% 13.30/2.61 | ALPHA: (d4_xboole_0) implies:
% 13.30/2.61 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 13.30/2.61 | (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~
% 13.30/2.61 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 13.30/2.61 | any] : (in(v3, v2) = v6 & in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 =
% 13.30/2.61 | 0)))
% 13.30/2.62 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 13.30/2.62 | (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~
% 13.30/2.62 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 13.30/2.62 | any] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 =
% 13.30/2.62 | 0)))
% 13.30/2.62 |
% 13.30/2.62 | ALPHA: (d7_xboole_0) implies:
% 13.30/2.62 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~
% 13.30/2.62 | $i(v0) | set_intersection2(v0, v1) = empty_set)
% 13.30/2.62 |
% 13.30/2.62 | ALPHA: (t1_xboole_1) implies:
% 13.30/2.62 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v1, v2) = 0) |
% 13.30/2.62 | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 13.30/2.62 | subset(v0, v2) = 0)
% 13.30/2.62 |
% 13.30/2.62 | ALPHA: (t28_xboole_1) implies:
% 13.30/2.62 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 13.30/2.62 | (set_intersection2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 13.30/2.62 | int] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 13.30/2.62 |
% 13.30/2.62 | ALPHA: (t63_xboole_1) implies:
% 13.30/2.62 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (disjoint(v1, v2) = 0) |
% 13.30/2.62 | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 13.30/2.62 | disjoint(v0, v2) = 0)
% 13.30/2.62 |
% 13.30/2.62 | ALPHA: (t84_zfmisc_1) implies:
% 13.30/2.62 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 13.30/2.62 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] :
% 13.30/2.62 | ( ~ (v9 = 0) & set_difference(v5, v6) = v7 & set_difference(v1, v2) =
% 13.30/2.62 | v3 & powerset(v3) = v4 & powerset(v2) = v6 & powerset(v1) = v5 &
% 13.30/2.62 | subset(v4, v8) = v9 & singleton(empty_set) = v0 & set_union2(v0, v7)
% 13.30/2.62 | = v8 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)
% 13.30/2.62 | & $i(v1) & $i(v0))
% 13.30/2.62 |
% 13.30/2.62 | ALPHA: (function-axioms) implies:
% 13.30/2.62 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 13.30/2.62 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 13.30/2.62 | v0))
% 13.30/2.62 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 13.30/2.62 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3,
% 13.30/2.62 | v2) = v0))
% 13.30/2.62 |
% 13.30/2.62 | DELTA: instantiating (13) with fresh symbols all_36_0, all_36_1, all_36_2,
% 13.30/2.62 | all_36_3, all_36_4, all_36_5, all_36_6, all_36_7, all_36_8, all_36_9
% 13.30/2.62 | gives:
% 13.30/2.62 | (16) ~ (all_36_0 = 0) & set_difference(all_36_4, all_36_3) = all_36_2 &
% 13.30/2.62 | set_difference(all_36_8, all_36_7) = all_36_6 & powerset(all_36_6) =
% 13.30/2.62 | all_36_5 & powerset(all_36_7) = all_36_3 & powerset(all_36_8) =
% 13.30/2.62 | all_36_4 & subset(all_36_5, all_36_1) = all_36_0 &
% 13.30/2.62 | singleton(empty_set) = all_36_9 & set_union2(all_36_9, all_36_2) =
% 13.30/2.62 | all_36_1 & $i(all_36_1) & $i(all_36_2) & $i(all_36_3) & $i(all_36_4) &
% 13.30/2.62 | $i(all_36_5) & $i(all_36_6) & $i(all_36_7) & $i(all_36_8) &
% 13.30/2.62 | $i(all_36_9)
% 13.30/2.62 |
% 13.30/2.62 | ALPHA: (16) implies:
% 13.30/2.62 | (17) ~ (all_36_0 = 0)
% 13.30/2.62 | (18) $i(all_36_9)
% 13.30/2.62 | (19) $i(all_36_8)
% 13.30/2.62 | (20) $i(all_36_7)
% 13.30/2.63 | (21) $i(all_36_6)
% 13.30/2.63 | (22) $i(all_36_5)
% 13.30/2.63 | (23) $i(all_36_4)
% 13.30/2.63 | (24) $i(all_36_3)
% 13.30/2.63 | (25) $i(all_36_2)
% 13.30/2.63 | (26) set_union2(all_36_9, all_36_2) = all_36_1
% 13.30/2.63 | (27) singleton(empty_set) = all_36_9
% 13.30/2.63 | (28) subset(all_36_5, all_36_1) = all_36_0
% 13.30/2.63 | (29) powerset(all_36_8) = all_36_4
% 13.30/2.63 | (30) powerset(all_36_7) = all_36_3
% 13.30/2.63 | (31) powerset(all_36_6) = all_36_5
% 13.30/2.63 | (32) set_difference(all_36_8, all_36_7) = all_36_6
% 13.30/2.63 | (33) set_difference(all_36_4, all_36_3) = all_36_2
% 13.30/2.63 |
% 13.30/2.63 | GROUND_INST: instantiating (1) with all_36_2, all_36_9, all_36_1, simplifying
% 13.30/2.63 | with (18), (25), (26) gives:
% 13.30/2.63 | (34) set_union2(all_36_2, all_36_9) = all_36_1 & $i(all_36_1)
% 13.30/2.63 |
% 13.30/2.63 | ALPHA: (34) implies:
% 13.30/2.63 | (35) $i(all_36_1)
% 13.30/2.63 | (36) set_union2(all_36_2, all_36_9) = all_36_1
% 13.30/2.63 |
% 13.30/2.63 | GROUND_INST: instantiating (6) with all_36_5, all_36_1, all_36_0, simplifying
% 13.30/2.63 | with (22), (28), (35) gives:
% 13.30/2.63 | (37) all_36_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 13.30/2.63 | all_36_1) = v1 & in(v0, all_36_5) = 0 & $i(v0))
% 13.30/2.63 |
% 13.30/2.63 | GROUND_INST: instantiating (t79_xboole_1) with all_36_8, all_36_7, all_36_6,
% 13.30/2.63 | simplifying with (19), (20), (32) gives:
% 13.30/2.63 | (38) disjoint(all_36_6, all_36_7) = 0
% 13.30/2.63 |
% 13.30/2.63 | GROUND_INST: instantiating (t36_xboole_1) with all_36_8, all_36_7, all_36_6,
% 13.30/2.63 | simplifying with (19), (20), (32) gives:
% 13.30/2.63 | (39) subset(all_36_6, all_36_8) = 0
% 13.30/2.63 |
% 13.30/2.63 | BETA: splitting (37) gives:
% 13.30/2.63 |
% 13.30/2.63 | Case 1:
% 13.30/2.63 | |
% 13.30/2.63 | | (40) all_36_0 = 0
% 13.30/2.63 | |
% 13.30/2.63 | | REDUCE: (17), (40) imply:
% 13.30/2.63 | | (41) $false
% 13.30/2.63 | |
% 13.30/2.63 | | CLOSE: (41) is inconsistent.
% 13.30/2.63 | |
% 13.30/2.63 | Case 2:
% 13.30/2.63 | |
% 13.30/2.63 | | (42) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_36_1) = v1 &
% 13.30/2.63 | | in(v0, all_36_5) = 0 & $i(v0))
% 13.30/2.63 | |
% 13.30/2.63 | | DELTA: instantiating (42) with fresh symbols all_52_0, all_52_1 gives:
% 13.30/2.63 | | (43) ~ (all_52_0 = 0) & in(all_52_1, all_36_1) = all_52_0 & in(all_52_1,
% 13.30/2.63 | | all_36_5) = 0 & $i(all_52_1)
% 13.30/2.63 | |
% 13.30/2.63 | | ALPHA: (43) implies:
% 13.30/2.63 | | (44) ~ (all_52_0 = 0)
% 13.30/2.63 | | (45) $i(all_52_1)
% 13.30/2.63 | | (46) in(all_52_1, all_36_5) = 0
% 13.30/2.63 | | (47) in(all_52_1, all_36_1) = all_52_0
% 13.30/2.63 | |
% 13.30/2.63 | | GROUND_INST: instantiating (3) with all_36_6, all_36_5, all_52_1,
% 13.30/2.63 | | simplifying with (21), (22), (31), (45), (46) gives:
% 13.30/2.63 | | (48) subset(all_52_1, all_36_6) = 0
% 13.30/2.63 | |
% 13.30/2.63 | | GROUND_INST: instantiating (5) with all_36_9, all_36_2, all_36_1, all_52_1,
% 13.30/2.63 | | all_52_0, simplifying with (18), (25), (26), (35), (45), (47)
% 13.30/2.63 | | gives:
% 13.30/2.64 | | (49) all_52_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 =
% 13.30/2.64 | | 0) & in(all_52_1, all_36_2) = v1 & in(all_52_1, all_36_9) = v0)
% 13.30/2.64 | |
% 13.30/2.64 | | GROUND_INST: instantiating (5) with all_36_2, all_36_9, all_36_1, all_52_1,
% 13.30/2.64 | | all_52_0, simplifying with (18), (25), (35), (36), (45), (47)
% 13.30/2.64 | | gives:
% 13.30/2.64 | | (50) all_52_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 =
% 13.30/2.64 | | 0) & in(all_52_1, all_36_2) = v0 & in(all_52_1, all_36_9) = v1)
% 13.30/2.64 | |
% 13.30/2.64 | | BETA: splitting (50) gives:
% 13.30/2.64 | |
% 13.30/2.64 | | Case 1:
% 13.30/2.64 | | |
% 13.30/2.64 | | | (51) all_52_0 = 0
% 13.30/2.64 | | |
% 13.30/2.64 | | | REDUCE: (44), (51) imply:
% 13.30/2.64 | | | (52) $false
% 13.30/2.64 | | |
% 13.30/2.64 | | | CLOSE: (52) is inconsistent.
% 13.30/2.64 | | |
% 13.30/2.64 | | Case 2:
% 13.30/2.64 | | |
% 13.30/2.64 | | | (53) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 13.30/2.64 | | | in(all_52_1, all_36_2) = v0 & in(all_52_1, all_36_9) = v1)
% 13.30/2.64 | | |
% 13.30/2.64 | | | DELTA: instantiating (53) with fresh symbols all_74_0, all_74_1 gives:
% 13.30/2.64 | | | (54) ~ (all_74_0 = 0) & ~ (all_74_1 = 0) & in(all_52_1, all_36_2) =
% 13.30/2.64 | | | all_74_1 & in(all_52_1, all_36_9) = all_74_0
% 13.30/2.64 | | |
% 13.30/2.64 | | | ALPHA: (54) implies:
% 13.30/2.64 | | | (55) in(all_52_1, all_36_9) = all_74_0
% 13.30/2.64 | | | (56) in(all_52_1, all_36_2) = all_74_1
% 13.30/2.64 | | |
% 13.30/2.64 | | | BETA: splitting (49) gives:
% 13.30/2.64 | | |
% 13.30/2.64 | | | Case 1:
% 13.30/2.64 | | | |
% 13.30/2.64 | | | | (57) all_52_0 = 0
% 13.30/2.64 | | | |
% 13.30/2.64 | | | | REDUCE: (44), (57) imply:
% 13.30/2.64 | | | | (58) $false
% 13.30/2.64 | | | |
% 13.30/2.64 | | | | CLOSE: (58) is inconsistent.
% 13.30/2.64 | | | |
% 13.30/2.64 | | | Case 2:
% 13.30/2.64 | | | |
% 13.30/2.64 | | | | (59) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 13.30/2.64 | | | | in(all_52_1, all_36_2) = v1 & in(all_52_1, all_36_9) = v0)
% 13.30/2.64 | | | |
% 13.30/2.64 | | | | DELTA: instantiating (59) with fresh symbols all_79_0, all_79_1 gives:
% 13.30/2.64 | | | | (60) ~ (all_79_0 = 0) & ~ (all_79_1 = 0) & in(all_52_1, all_36_2) =
% 13.30/2.64 | | | | all_79_0 & in(all_52_1, all_36_9) = all_79_1
% 13.30/2.64 | | | |
% 13.30/2.64 | | | | ALPHA: (60) implies:
% 13.30/2.64 | | | | (61) ~ (all_79_1 = 0)
% 13.30/2.64 | | | | (62) ~ (all_79_0 = 0)
% 13.30/2.64 | | | | (63) in(all_52_1, all_36_9) = all_79_1
% 13.30/2.64 | | | | (64) in(all_52_1, all_36_2) = all_79_0
% 13.30/2.64 | | | |
% 13.30/2.64 | | | | GROUND_INST: instantiating (14) with all_74_0, all_79_1, all_36_9,
% 13.30/2.64 | | | | all_52_1, simplifying with (55), (63) gives:
% 13.30/2.64 | | | | (65) all_79_1 = all_74_0
% 13.30/2.64 | | | |
% 13.30/2.64 | | | | GROUND_INST: instantiating (14) with all_74_1, all_79_0, all_36_2,
% 13.30/2.64 | | | | all_52_1, simplifying with (56), (64) gives:
% 13.30/2.64 | | | | (66) all_79_0 = all_74_1
% 13.30/2.64 | | | |
% 13.30/2.64 | | | | REDUCE: (62), (66) imply:
% 13.30/2.64 | | | | (67) ~ (all_74_1 = 0)
% 13.30/2.64 | | | |
% 13.30/2.64 | | | | REDUCE: (61), (65) imply:
% 13.30/2.64 | | | | (68) ~ (all_74_0 = 0)
% 13.30/2.64 | | | |
% 13.30/2.64 | | | | GROUND_INST: instantiating (8) with all_36_4, all_36_3, all_36_2,
% 13.30/2.64 | | | | all_52_1, all_74_1, simplifying with (23), (24), (25),
% 13.30/2.64 | | | | (33), (45), (56) gives:
% 13.30/2.64 | | | | (69) all_74_1 = 0 | ? [v0: any] : ? [v1: any] : (in(all_52_1,
% 13.30/2.64 | | | | all_36_3) = v1 & in(all_52_1, all_36_4) = v0 & ( ~ (v0 = 0)
% 13.30/2.64 | | | | | v1 = 0))
% 13.30/2.64 | | | |
% 13.30/2.64 | | | | GROUND_INST: instantiating (12) with all_52_1, all_36_6, all_36_7,
% 13.30/2.64 | | | | simplifying with (20), (21), (38), (45), (48) gives:
% 13.30/2.64 | | | | (70) disjoint(all_52_1, all_36_7) = 0
% 13.30/2.64 | | | |
% 13.30/2.64 | | | | GROUND_INST: instantiating (10) with all_52_1, all_36_6, all_36_8,
% 13.30/2.64 | | | | simplifying with (19), (21), (39), (45), (48) gives:
% 13.30/2.64 | | | | (71) subset(all_52_1, all_36_8) = 0
% 13.30/2.64 | | | |
% 13.30/2.64 | | | | BETA: splitting (69) gives:
% 13.30/2.64 | | | |
% 13.30/2.64 | | | | Case 1:
% 13.30/2.64 | | | | |
% 13.30/2.64 | | | | | (72) all_74_1 = 0
% 13.30/2.64 | | | | |
% 13.30/2.64 | | | | | REDUCE: (67), (72) imply:
% 13.30/2.64 | | | | | (73) $false
% 13.30/2.64 | | | | |
% 13.30/2.64 | | | | | CLOSE: (73) is inconsistent.
% 13.30/2.64 | | | | |
% 13.30/2.64 | | | | Case 2:
% 13.30/2.64 | | | | |
% 13.30/2.64 | | | | | (74) ? [v0: any] : ? [v1: any] : (in(all_52_1, all_36_3) = v1 &
% 13.30/2.64 | | | | | in(all_52_1, all_36_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 13.30/2.64 | | | | |
% 13.30/2.64 | | | | | DELTA: instantiating (74) with fresh symbols all_101_0, all_101_1
% 13.30/2.64 | | | | | gives:
% 13.30/2.64 | | | | | (75) in(all_52_1, all_36_3) = all_101_0 & in(all_52_1, all_36_4) =
% 13.30/2.64 | | | | | all_101_1 & ( ~ (all_101_1 = 0) | all_101_0 = 0)
% 13.30/2.64 | | | | |
% 13.30/2.64 | | | | | ALPHA: (75) implies:
% 13.30/2.64 | | | | | (76) in(all_52_1, all_36_4) = all_101_1
% 13.30/2.64 | | | | | (77) in(all_52_1, all_36_3) = all_101_0
% 13.30/2.64 | | | | | (78) ~ (all_101_1 = 0) | all_101_0 = 0
% 13.30/2.64 | | | | |
% 13.30/2.65 | | | | | GROUND_INST: instantiating (7) with all_36_4, all_36_3, all_36_2,
% 13.30/2.65 | | | | | all_52_1, all_101_0, simplifying with (23), (24), (25),
% 13.30/2.65 | | | | | (33), (45), (77) gives:
% 13.30/2.65 | | | | | (79) all_101_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_52_1,
% 13.30/2.65 | | | | | all_36_2) = v1 & in(all_52_1, all_36_4) = v0 & ( ~ (v0 =
% 13.30/2.65 | | | | | 0) | v1 = 0))
% 13.30/2.65 | | | | |
% 13.30/2.65 | | | | | GROUND_INST: instantiating (4) with all_36_8, all_36_4, all_52_1,
% 13.30/2.65 | | | | | simplifying with (19), (23), (29), (45), (71) gives:
% 13.30/2.65 | | | | | (80) in(all_52_1, all_36_4) = 0
% 13.30/2.65 | | | | |
% 13.30/2.65 | | | | | GROUND_INST: instantiating (9) with all_52_1, all_36_7, simplifying
% 13.30/2.65 | | | | | with (20), (45), (70) gives:
% 13.30/2.65 | | | | | (81) set_intersection2(all_52_1, all_36_7) = empty_set
% 13.30/2.65 | | | | |
% 13.30/2.65 | | | | | BETA: splitting (79) gives:
% 13.30/2.65 | | | | |
% 13.30/2.65 | | | | | Case 1:
% 13.30/2.65 | | | | | |
% 13.30/2.65 | | | | | | (82) all_101_0 = 0
% 13.30/2.65 | | | | | |
% 13.30/2.65 | | | | | | REDUCE: (77), (82) imply:
% 13.30/2.65 | | | | | | (83) in(all_52_1, all_36_3) = 0
% 13.30/2.65 | | | | | |
% 13.30/2.65 | | | | | | GROUND_INST: instantiating (3) with all_36_7, all_36_3, all_52_1,
% 13.30/2.65 | | | | | | simplifying with (20), (24), (30), (45), (83) gives:
% 13.30/2.65 | | | | | | (84) subset(all_52_1, all_36_7) = 0
% 13.30/2.65 | | | | | |
% 13.30/2.65 | | | | | | GROUND_INST: instantiating (11) with all_52_1, all_36_7, empty_set,
% 13.30/2.65 | | | | | | simplifying with (20), (45), (81) gives:
% 13.30/2.65 | | | | | | (85) all_52_1 = empty_set | ? [v0: int] : ( ~ (v0 = 0) &
% 13.30/2.65 | | | | | | subset(all_52_1, all_36_7) = v0)
% 13.30/2.65 | | | | | |
% 13.30/2.65 | | | | | | BETA: splitting (85) gives:
% 13.30/2.65 | | | | | |
% 13.30/2.65 | | | | | | Case 1:
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | (86) all_52_1 = empty_set
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | REDUCE: (55), (86) imply:
% 13.30/2.65 | | | | | | | (87) in(empty_set, all_36_9) = all_74_0
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | REDUCE: (45), (86) imply:
% 13.30/2.65 | | | | | | | (88) $i(empty_set)
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | GROUND_INST: instantiating (2) with empty_set, all_36_9, all_74_0,
% 13.30/2.65 | | | | | | | simplifying with (18), (27), (87), (88) gives:
% 13.30/2.65 | | | | | | | (89) all_74_0 = 0
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | REDUCE: (68), (89) imply:
% 13.30/2.65 | | | | | | | (90) $false
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | CLOSE: (90) is inconsistent.
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | Case 2:
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | (91) ? [v0: int] : ( ~ (v0 = 0) & subset(all_52_1, all_36_7) =
% 13.30/2.65 | | | | | | | v0)
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | DELTA: instantiating (91) with fresh symbol all_153_0 gives:
% 13.30/2.65 | | | | | | | (92) ~ (all_153_0 = 0) & subset(all_52_1, all_36_7) =
% 13.30/2.65 | | | | | | | all_153_0
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | ALPHA: (92) implies:
% 13.30/2.65 | | | | | | | (93) ~ (all_153_0 = 0)
% 13.30/2.65 | | | | | | | (94) subset(all_52_1, all_36_7) = all_153_0
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | GROUND_INST: instantiating (15) with 0, all_153_0, all_36_7,
% 13.30/2.65 | | | | | | | all_52_1, simplifying with (84), (94) gives:
% 13.30/2.65 | | | | | | | (95) all_153_0 = 0
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | REDUCE: (93), (95) imply:
% 13.30/2.65 | | | | | | | (96) $false
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | CLOSE: (96) is inconsistent.
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | End of split
% 13.30/2.65 | | | | | |
% 13.30/2.65 | | | | | Case 2:
% 13.30/2.65 | | | | | |
% 13.30/2.65 | | | | | | (97) ~ (all_101_0 = 0)
% 13.30/2.65 | | | | | |
% 13.30/2.65 | | | | | | BETA: splitting (78) gives:
% 13.30/2.65 | | | | | |
% 13.30/2.65 | | | | | | Case 1:
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | (98) ~ (all_101_1 = 0)
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | GROUND_INST: instantiating (14) with all_101_1, 0, all_36_4,
% 13.30/2.65 | | | | | | | all_52_1, simplifying with (76), (80) gives:
% 13.30/2.65 | | | | | | | (99) all_101_1 = 0
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | REDUCE: (98), (99) imply:
% 13.30/2.65 | | | | | | | (100) $false
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | CLOSE: (100) is inconsistent.
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | Case 2:
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | (101) all_101_0 = 0
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | REDUCE: (97), (101) imply:
% 13.30/2.65 | | | | | | | (102) $false
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | | CLOSE: (102) is inconsistent.
% 13.30/2.65 | | | | | | |
% 13.30/2.65 | | | | | | End of split
% 13.30/2.65 | | | | | |
% 13.30/2.65 | | | | | End of split
% 13.30/2.65 | | | | |
% 13.30/2.65 | | | | End of split
% 13.30/2.65 | | | |
% 13.30/2.65 | | | End of split
% 13.30/2.65 | | |
% 13.30/2.65 | | End of split
% 13.30/2.65 | |
% 13.30/2.65 | End of split
% 13.30/2.65 |
% 13.30/2.65 End of proof
% 13.30/2.65 % SZS output end Proof for theBenchmark
% 13.30/2.65
% 13.30/2.65 2045ms
%------------------------------------------------------------------------------