TSTP Solution File: SET934+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET934+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 : n010.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 7.71s 1.88s
% Output : Proof 10.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET934+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 16:24:35 EDT 2023
% 0.14/0.34 % 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 ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 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
% 2.38/1.04 Prover 1: Preprocessing ...
% 2.38/1.04 Prover 4: Preprocessing ...
% 2.38/1.08 Prover 3: Preprocessing ...
% 2.38/1.08 Prover 0: Preprocessing ...
% 2.38/1.08 Prover 2: Preprocessing ...
% 2.38/1.08 Prover 5: Preprocessing ...
% 2.38/1.08 Prover 6: Preprocessing ...
% 4.82/1.42 Prover 5: Proving ...
% 4.82/1.42 Prover 2: Proving ...
% 4.82/1.42 Prover 6: Proving ...
% 4.82/1.42 Prover 3: Warning: ignoring some quantifiers
% 4.82/1.43 Prover 1: Warning: ignoring some quantifiers
% 4.82/1.43 Prover 3: Constructing countermodel ...
% 4.82/1.44 Prover 4: Warning: ignoring some quantifiers
% 4.82/1.45 Prover 0: Proving ...
% 4.82/1.45 Prover 1: Constructing countermodel ...
% 4.82/1.47 Prover 4: Constructing countermodel ...
% 7.71/1.88 Prover 0: proved (1235ms)
% 7.71/1.88
% 7.71/1.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.71/1.88
% 7.71/1.88 Prover 2: stopped
% 7.71/1.88 Prover 5: stopped
% 7.71/1.88 Prover 3: stopped
% 7.71/1.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.71/1.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.71/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.36/1.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.36/1.89 Prover 6: stopped
% 8.36/1.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.36/1.91 Prover 11: Preprocessing ...
% 8.36/1.92 Prover 8: Preprocessing ...
% 8.36/1.92 Prover 7: Preprocessing ...
% 8.36/1.93 Prover 10: Preprocessing ...
% 8.36/1.93 Prover 13: Preprocessing ...
% 9.00/1.98 Prover 8: Warning: ignoring some quantifiers
% 9.00/1.99 Prover 7: Warning: ignoring some quantifiers
% 9.00/2.00 Prover 8: Constructing countermodel ...
% 9.00/2.00 Prover 7: Constructing countermodel ...
% 9.00/2.01 Prover 10: Warning: ignoring some quantifiers
% 9.00/2.03 Prover 10: Constructing countermodel ...
% 9.00/2.04 Prover 13: Warning: ignoring some quantifiers
% 9.00/2.06 Prover 13: Constructing countermodel ...
% 9.00/2.07 Prover 11: Warning: ignoring some quantifiers
% 9.00/2.08 Prover 11: Constructing countermodel ...
% 9.95/2.14 Prover 4: Found proof (size 76)
% 9.95/2.14 Prover 4: proved (1499ms)
% 9.95/2.14 Prover 13: stopped
% 9.95/2.14 Prover 8: stopped
% 9.95/2.14 Prover 11: stopped
% 9.95/2.14 Prover 1: stopped
% 9.95/2.14 Prover 7: stopped
% 9.95/2.14 Prover 10: stopped
% 9.95/2.14
% 9.95/2.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.95/2.14
% 9.95/2.15 % SZS output start Proof for theBenchmark
% 9.95/2.16 Assumptions after simplification:
% 9.95/2.16 ---------------------------------
% 9.95/2.16
% 9.95/2.16 (commutativity_k2_xboole_0)
% 9.95/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 9.95/2.19 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 9.95/2.19 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 9.95/2.19 | (set_union2(v1, v0) = v2 & $i(v2)))
% 9.95/2.19
% 9.95/2.19 (d1_zfmisc_1)
% 9.95/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 9.95/2.19 (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 9.95/2.19 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0: $i] : !
% 9.95/2.19 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (powerset(v0) = v1) | ~
% 9.95/2.19 (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~
% 9.95/2.19 (v4 = 0) & subset(v2, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 9.95/2.19 : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 9.95/2.19 ~ $i(v0) | in(v2, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 9.95/2.19 (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 9.95/2.19 $i(v0) | subset(v2, v0) = 0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2
% 9.95/2.19 = v0 | ~ (powerset(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 9.95/2.19 [v4: any] : ? [v5: any] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & $i(v3) &
% 9.95/2.20 ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 9.95/2.20
% 9.95/2.20 (d2_xboole_0)
% 10.47/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 10.47/2.21 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~
% 10.47/2.21 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0)
% 10.47/2.21 & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0: $i] : !
% 10.47/2.21 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 10.47/2.21 (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) |
% 10.47/2.21 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 &
% 10.47/2.21 in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 10.47/2.21 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (set_union2(v0, v1) =
% 10.47/2.21 v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 10.47/2.21 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5
% 10.47/2.21 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 10.47/2.21 $i] : ! [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) |
% 10.47/2.21 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 10.47/2.21 (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 =
% 10.47/2.21 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 10.47/2.21 [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) |
% 10.47/2.21 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3,
% 10.47/2.21 v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) &
% 10.47/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1)
% 10.47/2.21 = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 10.47/2.21 $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v1) = v5 & in(v3, v0) = v4 &
% 10.47/2.21 (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 10.47/2.21 $i] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 10.47/2.21 $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4,
% 10.47/2.21 v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | (
% 10.47/2.21 ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0)))
% 10.47/2.21
% 10.47/2.21 (d3_tarski)
% 10.47/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 10.47/2.21 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 10.47/2.21 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 10.47/2.21 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 10.47/2.21 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 10.47/2.21 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 10.47/2.21 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 10.47/2.21 $i(v0) | in(v2, v1) = 0)
% 10.47/2.21
% 10.47/2.21 (t1_xboole_1)
% 10.47/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 10.47/2.21 (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 10.47/2.21 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] :
% 10.47/2.21 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (subset(v0, v2) = v3)
% 10.47/2.21 | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int]
% 10.47/2.21 : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 10.47/2.21 $i] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~
% 10.47/2.21 $i(v1) | ~ $i(v0) | subset(v0, v2) = 0)
% 10.47/2.21
% 10.47/2.21 (t7_xboole_1)
% 10.47/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~
% 10.47/2.21 $i(v1) | ~ $i(v0) | subset(v0, v2) = 0)
% 10.47/2.21
% 10.47/2.21 (t81_zfmisc_1)
% 10.47/2.21 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 10.47/2.21 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & powerset(v5) = v6 &
% 10.47/2.21 powerset(v1) = v3 & powerset(v0) = v2 & subset(v4, v6) = v7 & set_union2(v2,
% 10.47/2.21 v3) = v4 & set_union2(v0, v1) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 10.47/2.21 $i(v2) & $i(v1) & $i(v0))
% 10.47/2.21
% 10.47/2.21 (function-axioms)
% 10.47/2.22 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.47/2.22 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 10.47/2.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.47/2.22 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0:
% 10.47/2.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.47/2.22 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 10.47/2.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 10.47/2.22 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 10.47/2.22 [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 10.47/2.22
% 10.47/2.22 Further assumptions not needed in the proof:
% 10.47/2.22 --------------------------------------------
% 10.47/2.22 antisymmetry_r2_hidden, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0,
% 10.47/2.22 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski
% 10.47/2.22
% 10.47/2.22 Those formulas are unsatisfiable:
% 10.47/2.22 ---------------------------------
% 10.47/2.22
% 10.47/2.22 Begin of proof
% 10.47/2.22 |
% 10.47/2.22 | ALPHA: (commutativity_k2_xboole_0) implies:
% 10.47/2.22 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 10.47/2.22 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 10.47/2.22 |
% 10.47/2.22 | ALPHA: (d1_zfmisc_1) implies:
% 10.47/2.22 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 10.47/2.22 | (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 10.47/2.22 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v2, v0) = v4))
% 10.47/2.22 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 10.47/2.22 | (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ~ $i(v2) | ~
% 10.47/2.22 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v1) = v4))
% 10.47/2.22 |
% 10.47/2.22 | ALPHA: (d2_xboole_0) implies:
% 10.47/2.22 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.47/2.22 | (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~
% 10.47/2.22 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 10.47/2.22 | (in(v3, v1) = v5 & in(v3, v0) = v4 & (v5 = 0 | v4 = 0)))
% 10.47/2.22 |
% 10.47/2.22 | ALPHA: (d3_tarski) implies:
% 10.47/2.22 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 10.47/2.22 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 10.47/2.22 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 10.47/2.22 |
% 10.47/2.22 | ALPHA: (t1_xboole_1) implies:
% 10.47/2.22 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 10.47/2.22 | (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ~ $i(v2) | ~
% 10.47/2.22 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) =
% 10.47/2.22 | v4))
% 10.47/2.22 |
% 10.47/2.22 | ALPHA: (function-axioms) implies:
% 10.47/2.22 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.47/2.22 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 10.47/2.22 |
% 10.47/2.23 | DELTA: instantiating (t81_zfmisc_1) with fresh symbols all_20_0, all_20_1,
% 10.47/2.23 | all_20_2, all_20_3, all_20_4, all_20_5, all_20_6, all_20_7 gives:
% 10.47/2.23 | (8) ~ (all_20_0 = 0) & powerset(all_20_2) = all_20_1 & powerset(all_20_6)
% 10.47/2.23 | = all_20_4 & powerset(all_20_7) = all_20_5 & subset(all_20_3, all_20_1)
% 10.47/2.23 | = all_20_0 & set_union2(all_20_5, all_20_4) = all_20_3 &
% 10.47/2.23 | set_union2(all_20_7, all_20_6) = all_20_2 & $i(all_20_1) & $i(all_20_2)
% 10.47/2.23 | & $i(all_20_3) & $i(all_20_4) & $i(all_20_5) & $i(all_20_6) &
% 10.47/2.23 | $i(all_20_7)
% 10.47/2.23 |
% 10.47/2.23 | ALPHA: (8) implies:
% 10.47/2.23 | (9) ~ (all_20_0 = 0)
% 10.47/2.23 | (10) $i(all_20_7)
% 10.47/2.23 | (11) $i(all_20_6)
% 10.47/2.23 | (12) $i(all_20_5)
% 10.47/2.23 | (13) $i(all_20_4)
% 10.47/2.23 | (14) $i(all_20_1)
% 10.47/2.23 | (15) set_union2(all_20_7, all_20_6) = all_20_2
% 10.47/2.23 | (16) set_union2(all_20_5, all_20_4) = all_20_3
% 10.47/2.23 | (17) subset(all_20_3, all_20_1) = all_20_0
% 10.47/2.23 | (18) powerset(all_20_7) = all_20_5
% 10.47/2.23 | (19) powerset(all_20_6) = all_20_4
% 10.47/2.23 | (20) powerset(all_20_2) = all_20_1
% 10.47/2.23 |
% 10.47/2.23 | GROUND_INST: instantiating (1) with all_20_6, all_20_7, all_20_2, simplifying
% 10.47/2.23 | with (10), (11), (15) gives:
% 10.47/2.23 | (21) set_union2(all_20_6, all_20_7) = all_20_2 & $i(all_20_2)
% 10.47/2.23 |
% 10.47/2.23 | ALPHA: (21) implies:
% 10.47/2.23 | (22) $i(all_20_2)
% 10.47/2.23 | (23) set_union2(all_20_6, all_20_7) = all_20_2
% 10.47/2.23 |
% 10.47/2.23 | GROUND_INST: instantiating (t7_xboole_1) with all_20_7, all_20_6, all_20_2,
% 10.47/2.23 | simplifying with (10), (11), (15) gives:
% 10.47/2.23 | (24) subset(all_20_7, all_20_2) = 0
% 10.47/2.23 |
% 10.47/2.23 | GROUND_INST: instantiating (1) with all_20_4, all_20_5, all_20_3, simplifying
% 10.47/2.23 | with (12), (13), (16) gives:
% 10.47/2.23 | (25) set_union2(all_20_4, all_20_5) = all_20_3 & $i(all_20_3)
% 10.47/2.23 |
% 10.47/2.23 | ALPHA: (25) implies:
% 10.47/2.23 | (26) $i(all_20_3)
% 10.47/2.23 | (27) set_union2(all_20_4, all_20_5) = all_20_3
% 10.47/2.23 |
% 10.47/2.23 | GROUND_INST: instantiating (5) with all_20_3, all_20_1, all_20_0, simplifying
% 10.47/2.23 | with (14), (17), (26) gives:
% 10.47/2.23 | (28) all_20_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 10.47/2.23 | all_20_1) = v1 & in(v0, all_20_3) = 0 & $i(v0))
% 10.47/2.23 |
% 10.47/2.23 | BETA: splitting (28) gives:
% 10.47/2.23 |
% 10.47/2.23 | Case 1:
% 10.47/2.23 | |
% 10.47/2.23 | | (29) all_20_0 = 0
% 10.47/2.23 | |
% 10.47/2.23 | | REDUCE: (9), (29) imply:
% 10.47/2.23 | | (30) $false
% 10.47/2.23 | |
% 10.47/2.23 | | CLOSE: (30) is inconsistent.
% 10.47/2.23 | |
% 10.47/2.24 | Case 2:
% 10.47/2.24 | |
% 10.47/2.24 | | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_20_1) = v1 &
% 10.47/2.24 | | in(v0, all_20_3) = 0 & $i(v0))
% 10.47/2.24 | |
% 10.47/2.24 | | DELTA: instantiating (31) with fresh symbols all_42_0, all_42_1 gives:
% 10.47/2.24 | | (32) ~ (all_42_0 = 0) & in(all_42_1, all_20_1) = all_42_0 & in(all_42_1,
% 10.47/2.24 | | all_20_3) = 0 & $i(all_42_1)
% 10.47/2.24 | |
% 10.47/2.24 | | ALPHA: (32) implies:
% 10.47/2.24 | | (33) ~ (all_42_0 = 0)
% 10.47/2.24 | | (34) $i(all_42_1)
% 10.47/2.24 | | (35) in(all_42_1, all_20_3) = 0
% 10.47/2.24 | | (36) in(all_42_1, all_20_1) = all_42_0
% 10.47/2.24 | |
% 10.47/2.24 | | GROUND_INST: instantiating (4) with all_20_5, all_20_4, all_20_3, all_42_1,
% 10.47/2.24 | | simplifying with (12), (13), (16), (26), (34), (35) gives:
% 10.47/2.24 | | (37) ? [v0: any] : ? [v1: any] : (in(all_42_1, all_20_4) = v1 &
% 10.47/2.24 | | in(all_42_1, all_20_5) = v0 & (v1 = 0 | v0 = 0))
% 10.47/2.24 | |
% 10.47/2.24 | | GROUND_INST: instantiating (2) with all_20_2, all_20_1, all_42_1, all_42_0,
% 10.47/2.24 | | simplifying with (14), (20), (22), (34), (36) gives:
% 10.47/2.24 | | (38) all_42_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_42_1,
% 10.47/2.24 | | all_20_2) = v0)
% 10.47/2.24 | |
% 10.47/2.24 | | GROUND_INST: instantiating (t7_xboole_1) with all_20_6, all_20_7, all_20_2,
% 10.47/2.24 | | simplifying with (10), (11), (23) gives:
% 10.47/2.24 | | (39) subset(all_20_6, all_20_2) = 0
% 10.47/2.24 | |
% 10.47/2.24 | | GROUND_INST: instantiating (4) with all_20_4, all_20_5, all_20_3, all_42_1,
% 10.47/2.24 | | simplifying with (12), (13), (26), (27), (34), (35) gives:
% 10.47/2.24 | | (40) ? [v0: any] : ? [v1: any] : (in(all_42_1, all_20_4) = v0 &
% 10.47/2.24 | | in(all_42_1, all_20_5) = v1 & (v1 = 0 | v0 = 0))
% 10.47/2.24 | |
% 10.47/2.24 | | DELTA: instantiating (40) with fresh symbols all_62_0, all_62_1 gives:
% 10.47/2.24 | | (41) in(all_42_1, all_20_4) = all_62_1 & in(all_42_1, all_20_5) =
% 10.47/2.24 | | all_62_0 & (all_62_0 = 0 | all_62_1 = 0)
% 10.47/2.24 | |
% 10.47/2.24 | | ALPHA: (41) implies:
% 10.47/2.24 | | (42) in(all_42_1, all_20_5) = all_62_0
% 10.47/2.24 | | (43) in(all_42_1, all_20_4) = all_62_1
% 10.47/2.24 | |
% 10.47/2.24 | | DELTA: instantiating (37) with fresh symbols all_66_0, all_66_1 gives:
% 10.47/2.24 | | (44) in(all_42_1, all_20_4) = all_66_0 & in(all_42_1, all_20_5) =
% 10.47/2.24 | | all_66_1 & (all_66_0 = 0 | all_66_1 = 0)
% 10.47/2.24 | |
% 10.47/2.24 | | ALPHA: (44) implies:
% 10.47/2.24 | | (45) in(all_42_1, all_20_5) = all_66_1
% 10.47/2.24 | | (46) in(all_42_1, all_20_4) = all_66_0
% 10.47/2.24 | | (47) all_66_0 = 0 | all_66_1 = 0
% 10.47/2.24 | |
% 10.47/2.24 | | BETA: splitting (38) gives:
% 10.47/2.24 | |
% 10.47/2.24 | | Case 1:
% 10.47/2.24 | | |
% 10.47/2.24 | | | (48) all_42_0 = 0
% 10.47/2.24 | | |
% 10.47/2.24 | | | REDUCE: (33), (48) imply:
% 10.47/2.24 | | | (49) $false
% 10.47/2.24 | | |
% 10.47/2.24 | | | CLOSE: (49) is inconsistent.
% 10.47/2.24 | | |
% 10.47/2.24 | | Case 2:
% 10.47/2.24 | | |
% 10.47/2.24 | | | (50) ? [v0: int] : ( ~ (v0 = 0) & subset(all_42_1, all_20_2) = v0)
% 10.47/2.25 | | |
% 10.47/2.25 | | | DELTA: instantiating (50) with fresh symbol all_72_0 gives:
% 10.47/2.25 | | | (51) ~ (all_72_0 = 0) & subset(all_42_1, all_20_2) = all_72_0
% 10.47/2.25 | | |
% 10.47/2.25 | | | ALPHA: (51) implies:
% 10.47/2.25 | | | (52) ~ (all_72_0 = 0)
% 10.47/2.25 | | | (53) subset(all_42_1, all_20_2) = all_72_0
% 10.47/2.25 | | |
% 10.47/2.25 | | | GROUND_INST: instantiating (7) with all_62_0, all_66_1, all_20_5,
% 10.47/2.25 | | | all_42_1, simplifying with (42), (45) gives:
% 10.47/2.25 | | | (54) all_66_1 = all_62_0
% 10.47/2.25 | | |
% 10.47/2.25 | | | GROUND_INST: instantiating (7) with all_62_1, all_66_0, all_20_4,
% 10.47/2.25 | | | all_42_1, simplifying with (43), (46) gives:
% 10.47/2.25 | | | (55) all_66_0 = all_62_1
% 10.47/2.25 | | |
% 10.47/2.25 | | | GROUND_INST: instantiating (6) with all_42_1, all_20_7, all_20_2,
% 10.47/2.25 | | | all_72_0, simplifying with (10), (22), (24), (34), (53)
% 10.47/2.25 | | | gives:
% 10.47/2.25 | | | (56) all_72_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_42_1,
% 10.47/2.25 | | | all_20_7) = v0)
% 10.47/2.25 | | |
% 10.47/2.25 | | | GROUND_INST: instantiating (6) with all_42_1, all_20_6, all_20_2,
% 10.47/2.25 | | | all_72_0, simplifying with (11), (22), (34), (39), (53)
% 10.47/2.25 | | | gives:
% 10.47/2.25 | | | (57) all_72_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_42_1,
% 10.47/2.25 | | | all_20_6) = v0)
% 10.47/2.25 | | |
% 10.47/2.25 | | | BETA: splitting (57) gives:
% 10.47/2.25 | | |
% 10.47/2.25 | | | Case 1:
% 10.47/2.25 | | | |
% 10.47/2.25 | | | | (58) all_72_0 = 0
% 10.47/2.25 | | | |
% 10.47/2.25 | | | | REDUCE: (52), (58) imply:
% 10.47/2.25 | | | | (59) $false
% 10.47/2.25 | | | |
% 10.47/2.25 | | | | CLOSE: (59) is inconsistent.
% 10.47/2.25 | | | |
% 10.47/2.25 | | | Case 2:
% 10.47/2.25 | | | |
% 10.47/2.25 | | | | (60) ? [v0: int] : ( ~ (v0 = 0) & subset(all_42_1, all_20_6) = v0)
% 10.47/2.25 | | | |
% 10.47/2.25 | | | | DELTA: instantiating (60) with fresh symbol all_95_0 gives:
% 10.47/2.25 | | | | (61) ~ (all_95_0 = 0) & subset(all_42_1, all_20_6) = all_95_0
% 10.47/2.25 | | | |
% 10.47/2.25 | | | | ALPHA: (61) implies:
% 10.47/2.25 | | | | (62) ~ (all_95_0 = 0)
% 10.47/2.25 | | | | (63) subset(all_42_1, all_20_6) = all_95_0
% 10.47/2.25 | | | |
% 10.47/2.25 | | | | BETA: splitting (56) gives:
% 10.47/2.25 | | | |
% 10.47/2.25 | | | | Case 1:
% 10.47/2.25 | | | | |
% 10.47/2.25 | | | | | (64) all_72_0 = 0
% 10.47/2.25 | | | | |
% 10.47/2.25 | | | | | REDUCE: (52), (64) imply:
% 10.47/2.25 | | | | | (65) $false
% 10.47/2.25 | | | | |
% 10.47/2.25 | | | | | CLOSE: (65) is inconsistent.
% 10.47/2.25 | | | | |
% 10.47/2.25 | | | | Case 2:
% 10.47/2.25 | | | | |
% 10.47/2.25 | | | | | (66) ? [v0: int] : ( ~ (v0 = 0) & subset(all_42_1, all_20_7) = v0)
% 10.47/2.25 | | | | |
% 10.47/2.25 | | | | | DELTA: instantiating (66) with fresh symbol all_100_0 gives:
% 10.47/2.25 | | | | | (67) ~ (all_100_0 = 0) & subset(all_42_1, all_20_7) = all_100_0
% 10.47/2.25 | | | | |
% 10.47/2.25 | | | | | ALPHA: (67) implies:
% 10.47/2.25 | | | | | (68) ~ (all_100_0 = 0)
% 10.47/2.25 | | | | | (69) subset(all_42_1, all_20_7) = all_100_0
% 10.47/2.25 | | | | |
% 10.47/2.25 | | | | | GROUND_INST: instantiating (3) with all_20_7, all_20_5, all_42_1,
% 10.47/2.25 | | | | | all_100_0, simplifying with (10), (12), (18), (34), (69)
% 10.47/2.25 | | | | | gives:
% 10.47/2.25 | | | | | (70) all_100_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_42_1,
% 10.47/2.25 | | | | | all_20_5) = v0)
% 10.47/2.25 | | | | |
% 10.47/2.25 | | | | | GROUND_INST: instantiating (3) with all_20_6, all_20_4, all_42_1,
% 10.47/2.25 | | | | | all_95_0, simplifying with (11), (13), (19), (34), (63)
% 10.47/2.25 | | | | | gives:
% 10.47/2.25 | | | | | (71) all_95_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_42_1,
% 10.47/2.25 | | | | | all_20_4) = v0)
% 10.47/2.25 | | | | |
% 10.47/2.26 | | | | | BETA: splitting (70) gives:
% 10.47/2.26 | | | | |
% 10.47/2.26 | | | | | Case 1:
% 10.47/2.26 | | | | | |
% 10.47/2.26 | | | | | | (72) all_100_0 = 0
% 10.47/2.26 | | | | | |
% 10.47/2.26 | | | | | | REDUCE: (68), (72) imply:
% 10.47/2.26 | | | | | | (73) $false
% 10.47/2.26 | | | | | |
% 10.47/2.26 | | | | | | CLOSE: (73) is inconsistent.
% 10.47/2.26 | | | | | |
% 10.47/2.26 | | | | | Case 2:
% 10.47/2.26 | | | | | |
% 10.47/2.26 | | | | | | (74) ? [v0: int] : ( ~ (v0 = 0) & in(all_42_1, all_20_5) = v0)
% 10.47/2.26 | | | | | |
% 10.47/2.26 | | | | | | DELTA: instantiating (74) with fresh symbol all_117_0 gives:
% 10.47/2.26 | | | | | | (75) ~ (all_117_0 = 0) & in(all_42_1, all_20_5) = all_117_0
% 10.47/2.26 | | | | | |
% 10.47/2.26 | | | | | | ALPHA: (75) implies:
% 10.47/2.26 | | | | | | (76) ~ (all_117_0 = 0)
% 10.47/2.26 | | | | | | (77) in(all_42_1, all_20_5) = all_117_0
% 10.47/2.26 | | | | | |
% 10.47/2.26 | | | | | | BETA: splitting (71) gives:
% 10.47/2.26 | | | | | |
% 10.47/2.26 | | | | | | Case 1:
% 10.47/2.26 | | | | | | |
% 10.47/2.26 | | | | | | | (78) all_95_0 = 0
% 10.47/2.26 | | | | | | |
% 10.47/2.26 | | | | | | | REDUCE: (62), (78) imply:
% 10.47/2.26 | | | | | | | (79) $false
% 10.47/2.26 | | | | | | |
% 10.47/2.26 | | | | | | | CLOSE: (79) is inconsistent.
% 10.47/2.26 | | | | | | |
% 10.47/2.26 | | | | | | Case 2:
% 10.47/2.26 | | | | | | |
% 10.47/2.26 | | | | | | | (80) ? [v0: int] : ( ~ (v0 = 0) & in(all_42_1, all_20_4) = v0)
% 10.47/2.26 | | | | | | |
% 10.47/2.26 | | | | | | | DELTA: instantiating (80) with fresh symbol all_138_0 gives:
% 10.47/2.26 | | | | | | | (81) ~ (all_138_0 = 0) & in(all_42_1, all_20_4) = all_138_0
% 10.47/2.26 | | | | | | |
% 10.47/2.26 | | | | | | | ALPHA: (81) implies:
% 10.47/2.26 | | | | | | | (82) ~ (all_138_0 = 0)
% 10.47/2.26 | | | | | | | (83) in(all_42_1, all_20_4) = all_138_0
% 10.47/2.26 | | | | | | |
% 10.47/2.26 | | | | | | | GROUND_INST: instantiating (7) with all_62_0, all_117_0, all_20_5,
% 10.47/2.26 | | | | | | | all_42_1, simplifying with (42), (77) gives:
% 10.47/2.26 | | | | | | | (84) all_117_0 = all_62_0
% 10.47/2.26 | | | | | | |
% 10.47/2.26 | | | | | | | GROUND_INST: instantiating (7) with all_62_1, all_138_0, all_20_4,
% 10.47/2.26 | | | | | | | all_42_1, simplifying with (43), (83) gives:
% 10.47/2.26 | | | | | | | (85) all_138_0 = all_62_1
% 10.47/2.26 | | | | | | |
% 10.47/2.26 | | | | | | | REDUCE: (82), (85) imply:
% 10.47/2.26 | | | | | | | (86) ~ (all_62_1 = 0)
% 10.47/2.26 | | | | | | |
% 10.47/2.26 | | | | | | | REDUCE: (76), (84) imply:
% 10.47/2.26 | | | | | | | (87) ~ (all_62_0 = 0)
% 10.47/2.26 | | | | | | |
% 10.47/2.26 | | | | | | | BETA: splitting (47) gives:
% 10.47/2.26 | | | | | | |
% 10.47/2.26 | | | | | | | Case 1:
% 10.47/2.26 | | | | | | | |
% 10.47/2.26 | | | | | | | | (88) all_66_0 = 0
% 10.47/2.26 | | | | | | | |
% 10.47/2.26 | | | | | | | | COMBINE_EQS: (55), (88) imply:
% 10.47/2.26 | | | | | | | | (89) all_62_1 = 0
% 10.47/2.26 | | | | | | | |
% 10.47/2.26 | | | | | | | | SIMP: (89) implies:
% 10.47/2.26 | | | | | | | | (90) all_62_1 = 0
% 10.47/2.26 | | | | | | | |
% 10.47/2.26 | | | | | | | | REDUCE: (86), (90) imply:
% 10.47/2.26 | | | | | | | | (91) $false
% 10.47/2.26 | | | | | | | |
% 10.47/2.26 | | | | | | | | CLOSE: (91) is inconsistent.
% 10.47/2.26 | | | | | | | |
% 10.47/2.26 | | | | | | | Case 2:
% 10.47/2.26 | | | | | | | |
% 10.47/2.26 | | | | | | | | (92) all_66_1 = 0
% 10.47/2.26 | | | | | | | |
% 10.47/2.26 | | | | | | | | COMBINE_EQS: (54), (92) imply:
% 10.47/2.26 | | | | | | | | (93) all_62_0 = 0
% 10.47/2.26 | | | | | | | |
% 10.47/2.26 | | | | | | | | SIMP: (93) implies:
% 10.47/2.26 | | | | | | | | (94) all_62_0 = 0
% 10.47/2.26 | | | | | | | |
% 10.47/2.26 | | | | | | | | REDUCE: (87), (94) imply:
% 10.47/2.26 | | | | | | | | (95) $false
% 10.47/2.26 | | | | | | | |
% 10.47/2.26 | | | | | | | | CLOSE: (95) is inconsistent.
% 10.47/2.26 | | | | | | | |
% 10.47/2.26 | | | | | | | End of split
% 10.47/2.26 | | | | | | |
% 10.47/2.26 | | | | | | End of split
% 10.47/2.26 | | | | | |
% 10.47/2.26 | | | | | End of split
% 10.47/2.26 | | | | |
% 10.47/2.26 | | | | End of split
% 10.47/2.26 | | | |
% 10.47/2.26 | | | End of split
% 10.47/2.26 | | |
% 10.47/2.26 | | End of split
% 10.47/2.26 | |
% 10.47/2.26 | End of split
% 10.47/2.26 |
% 10.47/2.26 End of proof
% 10.47/2.26 % SZS output end Proof for theBenchmark
% 10.47/2.26
% 10.47/2.26 1648ms
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