TSTP Solution File: SEU157+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU157+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:42:51 EDT 2023
% Result : Theorem 4.41s 1.39s
% Output : Proof 6.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU157+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.09 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Wed Aug 23 16:17:56 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.14/0.52 ________ _____
% 0.14/0.52 ___ __ \_________(_)________________________________
% 0.14/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.14/0.53 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.14/0.53 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.14/0.53
% 0.14/0.53 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.53 (2023-06-19)
% 0.14/0.53
% 0.14/0.53 (c) Philipp Rümmer, 2009-2023
% 0.14/0.53 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.53 Amanda Stjerna.
% 0.14/0.53 Free software under BSD-3-Clause.
% 0.14/0.53
% 0.14/0.53 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.53
% 0.14/0.53 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.54 Running up to 7 provers in parallel.
% 0.14/0.55 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.55 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.55 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.55 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.14/0.55 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.55 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.92/0.86 Prover 4: Preprocessing ...
% 0.92/0.86 Prover 1: Preprocessing ...
% 2.05/0.90 Prover 2: Preprocessing ...
% 2.05/0.90 Prover 6: Preprocessing ...
% 2.05/0.90 Prover 3: Preprocessing ...
% 2.05/0.90 Prover 0: Preprocessing ...
% 2.05/0.90 Prover 5: Preprocessing ...
% 3.35/1.14 Prover 1: Warning: ignoring some quantifiers
% 3.35/1.15 Prover 3: Warning: ignoring some quantifiers
% 3.35/1.15 Prover 4: Warning: ignoring some quantifiers
% 3.35/1.16 Prover 6: Proving ...
% 3.35/1.16 Prover 5: Proving ...
% 3.35/1.16 Prover 3: Constructing countermodel ...
% 3.97/1.17 Prover 4: Constructing countermodel ...
% 3.97/1.17 Prover 1: Constructing countermodel ...
% 4.14/1.21 Prover 0: Proving ...
% 4.41/1.23 Prover 2: Proving ...
% 4.41/1.39 Prover 3: proved (847ms)
% 4.41/1.39
% 4.41/1.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.41/1.39
% 4.41/1.40 Prover 6: stopped
% 4.41/1.40 Prover 2: stopped
% 4.41/1.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.41/1.40 Prover 5: stopped
% 4.41/1.40 Prover 0: stopped
% 4.41/1.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.41/1.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.41/1.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.41/1.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.41/1.42 Prover 13: Preprocessing ...
% 4.41/1.43 Prover 8: Preprocessing ...
% 4.41/1.43 Prover 11: Preprocessing ...
% 4.41/1.44 Prover 10: Preprocessing ...
% 4.41/1.45 Prover 7: Preprocessing ...
% 5.05/1.51 Prover 7: Warning: ignoring some quantifiers
% 5.05/1.52 Prover 10: Warning: ignoring some quantifiers
% 6.32/1.52 Prover 7: Constructing countermodel ...
% 6.32/1.52 Prover 10: Constructing countermodel ...
% 6.32/1.53 Prover 1: Found proof (size 40)
% 6.32/1.53 Prover 1: proved (983ms)
% 6.32/1.53 Prover 4: stopped
% 6.32/1.53 Prover 7: stopped
% 6.32/1.53 Prover 11: Warning: ignoring some quantifiers
% 6.32/1.53 Prover 10: stopped
% 6.32/1.53 Prover 13: Warning: ignoring some quantifiers
% 6.32/1.53 Prover 8: Warning: ignoring some quantifiers
% 6.32/1.53 Prover 11: Constructing countermodel ...
% 6.32/1.54 Prover 8: Constructing countermodel ...
% 6.32/1.54 Prover 13: Constructing countermodel ...
% 6.32/1.54 Prover 11: stopped
% 6.32/1.54 Prover 8: stopped
% 6.32/1.55 Prover 13: stopped
% 6.32/1.55
% 6.32/1.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.32/1.55
% 6.32/1.55 % SZS output start Proof for theBenchmark
% 6.32/1.56 Assumptions after simplification:
% 6.32/1.56 ---------------------------------
% 6.32/1.56
% 6.32/1.56 (d2_zfmisc_1)
% 6.32/1.59 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 6.32/1.59 (cartesian_product2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 6.32/1.59 [v4: $i] : ? [v5: any] : (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ! [v6:
% 6.32/1.59 $i] : ! [v7: $i] : ( ~ (ordered_pair(v6, v7) = v4) | ~ $i(v7) | ~
% 6.32/1.59 $i(v6) | ? [v8: any] : ? [v9: any] : (in(v7, v2) = v9 & in(v6, v1) =
% 6.32/1.59 v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & (v5 = 0 | ? [v6: $i] : ?
% 6.32/1.59 [v7: $i] : (ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0
% 6.32/1.59 & $i(v7) & $i(v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 6.32/1.59 (cartesian_product2(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( !
% 6.32/1.59 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | !
% 6.32/1.59 [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v6) = v3) | ~ $i(v6) |
% 6.32/1.59 ~ $i(v5) | ? [v7: any] : ? [v8: any] : (in(v6, v1) = v8 & in(v5, v0)
% 6.32/1.59 = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))) & ! [v3: $i] : ( ~ (in(v3,
% 6.32/1.59 v2) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: $i] : (ordered_pair(v4,
% 6.32/1.59 v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0 & $i(v5) & $i(v4)))))
% 6.32/1.59
% 6.32/1.59 (l55_zfmisc_1)
% 6.32/1.60 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 6.32/1.60 $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] : (cartesian_product2(v2,
% 6.32/1.60 v3) = v5 & ordered_pair(v0, v1) = v4 & in(v4, v5) = v6 & in(v1, v3) = v8 &
% 6.32/1.60 in(v0, v2) = v7 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v8
% 6.32/1.60 = 0 & v7 = 0 & ~ (v6 = 0)) | (v6 = 0 & ( ~ (v8 = 0) | ~ (v7 = 0)))))
% 6.32/1.60
% 6.32/1.60 (t33_zfmisc_1)
% 6.32/1.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 6.32/1.60 (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4) | ~ $i(v3) |
% 6.32/1.60 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (v3 = v1 & v2 = v0))
% 6.32/1.60
% 6.32/1.60 (function-axioms)
% 6.32/1.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.32/1.60 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 6.32/1.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.32/1.60 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i]
% 6.32/1.60 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3,
% 6.32/1.60 v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 6.32/1.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 6.32/1.60 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 6.32/1.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 6.32/1.60 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 6.32/1.60 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 6.32/1.60
% 6.32/1.60 Further assumptions not needed in the proof:
% 6.32/1.60 --------------------------------------------
% 6.32/1.61 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, dt_k1_tarski,
% 6.32/1.61 dt_k2_tarski, dt_k2_zfmisc_1, dt_k4_tarski, fc1_zfmisc_1, rc1_xboole_0,
% 6.32/1.61 rc2_xboole_0
% 6.32/1.61
% 6.32/1.61 Those formulas are unsatisfiable:
% 6.32/1.61 ---------------------------------
% 6.32/1.61
% 6.32/1.61 Begin of proof
% 6.32/1.61 |
% 6.32/1.61 | ALPHA: (d2_zfmisc_1) implies:
% 6.82/1.61 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0,
% 6.82/1.61 | v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : !
% 6.82/1.61 | [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ! [v5:
% 6.82/1.61 | $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v6) = v3) | ~ $i(v6)
% 6.82/1.61 | | ~ $i(v5) | ? [v7: any] : ? [v8: any] : (in(v6, v1) = v8 &
% 6.82/1.61 | in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))) & ! [v3:
% 6.82/1.61 | $i] : ( ~ (in(v3, v2) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5:
% 6.82/1.61 | $i] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0)
% 6.82/1.61 | = 0 & $i(v5) & $i(v4)))))
% 6.82/1.61 |
% 6.82/1.61 | ALPHA: (function-axioms) implies:
% 6.82/1.61 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.82/1.61 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.82/1.61 |
% 6.82/1.61 | DELTA: instantiating (l55_zfmisc_1) with fresh symbols all_13_0, all_13_1,
% 6.82/1.61 | all_13_2, all_13_3, all_13_4, all_13_5, all_13_6, all_13_7, all_13_8
% 6.82/1.61 | gives:
% 6.82/1.61 | (3) cartesian_product2(all_13_6, all_13_5) = all_13_3 &
% 6.82/1.61 | ordered_pair(all_13_8, all_13_7) = all_13_4 & in(all_13_4, all_13_3) =
% 6.82/1.61 | all_13_2 & in(all_13_7, all_13_5) = all_13_0 & in(all_13_8, all_13_6) =
% 6.82/1.61 | all_13_1 & $i(all_13_3) & $i(all_13_4) & $i(all_13_5) & $i(all_13_6) &
% 6.82/1.61 | $i(all_13_7) & $i(all_13_8) & ((all_13_0 = 0 & all_13_1 = 0 & ~
% 6.82/1.61 | (all_13_2 = 0)) | (all_13_2 = 0 & ( ~ (all_13_0 = 0) | ~ (all_13_1
% 6.82/1.61 | = 0))))
% 6.82/1.61 |
% 6.82/1.61 | ALPHA: (3) implies:
% 6.82/1.62 | (4) $i(all_13_8)
% 6.82/1.62 | (5) $i(all_13_7)
% 6.82/1.62 | (6) $i(all_13_6)
% 6.82/1.62 | (7) $i(all_13_5)
% 6.82/1.62 | (8) $i(all_13_4)
% 6.82/1.62 | (9) $i(all_13_3)
% 6.82/1.62 | (10) in(all_13_8, all_13_6) = all_13_1
% 6.82/1.62 | (11) in(all_13_7, all_13_5) = all_13_0
% 6.82/1.62 | (12) in(all_13_4, all_13_3) = all_13_2
% 6.82/1.62 | (13) ordered_pair(all_13_8, all_13_7) = all_13_4
% 6.82/1.62 | (14) cartesian_product2(all_13_6, all_13_5) = all_13_3
% 6.82/1.62 | (15) (all_13_0 = 0 & all_13_1 = 0 & ~ (all_13_2 = 0)) | (all_13_2 = 0 & (
% 6.82/1.62 | ~ (all_13_0 = 0) | ~ (all_13_1 = 0)))
% 6.82/1.62 |
% 6.82/1.62 | GROUND_INST: instantiating (1) with all_13_6, all_13_5, all_13_3, simplifying
% 6.82/1.62 | with (6), (7), (9), (14) gives:
% 6.82/1.62 | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_13_3) = v1) | ~
% 6.82/1.62 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) = v0)
% 6.82/1.62 | | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : (in(v3,
% 6.82/1.62 | all_13_5) = v5 & in(v2, all_13_6) = v4 & ( ~ (v5 = 0) | ~ (v4
% 6.82/1.62 | = 0))))) & ! [v0: $i] : ( ~ (in(v0, all_13_3) = 0) | ~
% 6.82/1.62 | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v2) = v0 &
% 6.82/1.62 | in(v2, all_13_5) = 0 & in(v1, all_13_6) = 0 & $i(v2) & $i(v1)))
% 6.82/1.62 |
% 6.82/1.62 | ALPHA: (16) implies:
% 6.82/1.62 | (17) ! [v0: $i] : ( ~ (in(v0, all_13_3) = 0) | ~ $i(v0) | ? [v1: $i] :
% 6.82/1.62 | ? [v2: $i] : (ordered_pair(v1, v2) = v0 & in(v2, all_13_5) = 0 &
% 6.82/1.62 | in(v1, all_13_6) = 0 & $i(v2) & $i(v1)))
% 6.82/1.62 | (18) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_13_3) = v1) | ~
% 6.82/1.62 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) = v0)
% 6.82/1.62 | | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : (in(v3,
% 6.82/1.63 | all_13_5) = v5 & in(v2, all_13_6) = v4 & ( ~ (v5 = 0) | ~ (v4
% 6.82/1.63 | = 0)))))
% 6.82/1.63 |
% 6.82/1.63 | GROUND_INST: instantiating (18) with all_13_4, all_13_2, simplifying with (8),
% 6.82/1.63 | (12) gives:
% 6.82/1.63 | (19) all_13_2 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) =
% 6.82/1.63 | all_13_4) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 6.82/1.63 | (in(v1, all_13_5) = v3 & in(v0, all_13_6) = v2 & ( ~ (v3 = 0) | ~
% 6.82/1.63 | (v2 = 0))))
% 6.82/1.63 |
% 6.82/1.63 | BETA: splitting (15) gives:
% 6.82/1.63 |
% 6.82/1.63 | Case 1:
% 6.82/1.63 | |
% 6.82/1.63 | | (20) all_13_0 = 0 & all_13_1 = 0 & ~ (all_13_2 = 0)
% 6.82/1.63 | |
% 6.82/1.63 | | ALPHA: (20) implies:
% 6.82/1.63 | | (21) all_13_1 = 0
% 6.82/1.63 | | (22) all_13_0 = 0
% 6.82/1.63 | | (23) ~ (all_13_2 = 0)
% 6.82/1.63 | |
% 6.82/1.63 | | REDUCE: (11), (22) imply:
% 6.82/1.63 | | (24) in(all_13_7, all_13_5) = 0
% 6.82/1.63 | |
% 6.82/1.63 | | REDUCE: (10), (21) imply:
% 6.82/1.63 | | (25) in(all_13_8, all_13_6) = 0
% 6.82/1.63 | |
% 6.82/1.63 | | BETA: splitting (19) gives:
% 6.82/1.63 | |
% 6.82/1.63 | | Case 1:
% 6.82/1.63 | | |
% 6.82/1.63 | | | (26) all_13_2 = 0
% 6.82/1.63 | | |
% 6.82/1.63 | | | REDUCE: (23), (26) imply:
% 6.82/1.63 | | | (27) $false
% 6.82/1.63 | | |
% 6.82/1.63 | | | CLOSE: (27) is inconsistent.
% 6.82/1.63 | | |
% 6.82/1.63 | | Case 2:
% 6.82/1.63 | | |
% 6.82/1.63 | | | (28) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) = all_13_4)
% 6.82/1.63 | | | | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in(v1,
% 6.82/1.63 | | | all_13_5) = v3 & in(v0, all_13_6) = v2 & ( ~ (v3 = 0) | ~
% 6.82/1.63 | | | (v2 = 0))))
% 6.82/1.63 | | |
% 6.82/1.63 | | | GROUND_INST: instantiating (28) with all_13_8, all_13_7, simplifying with
% 6.82/1.63 | | | (4), (5), (13) gives:
% 6.82/1.63 | | | (29) ? [v0: any] : ? [v1: any] : (in(all_13_7, all_13_5) = v1 &
% 6.82/1.63 | | | in(all_13_8, all_13_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.82/1.63 | | |
% 6.82/1.63 | | | DELTA: instantiating (29) with fresh symbols all_37_0, all_37_1 gives:
% 6.82/1.63 | | | (30) in(all_13_7, all_13_5) = all_37_0 & in(all_13_8, all_13_6) =
% 6.82/1.63 | | | all_37_1 & ( ~ (all_37_0 = 0) | ~ (all_37_1 = 0))
% 6.82/1.63 | | |
% 6.82/1.63 | | | ALPHA: (30) implies:
% 6.82/1.63 | | | (31) in(all_13_8, all_13_6) = all_37_1
% 6.82/1.63 | | | (32) in(all_13_7, all_13_5) = all_37_0
% 6.82/1.63 | | | (33) ~ (all_37_0 = 0) | ~ (all_37_1 = 0)
% 6.82/1.63 | | |
% 6.82/1.63 | | | GROUND_INST: instantiating (2) with 0, all_37_1, all_13_6, all_13_8,
% 6.82/1.63 | | | simplifying with (25), (31) gives:
% 6.82/1.63 | | | (34) all_37_1 = 0
% 6.82/1.63 | | |
% 6.82/1.63 | | | GROUND_INST: instantiating (2) with 0, all_37_0, all_13_5, all_13_7,
% 6.82/1.63 | | | simplifying with (24), (32) gives:
% 6.82/1.63 | | | (35) all_37_0 = 0
% 6.82/1.63 | | |
% 6.82/1.63 | | | BETA: splitting (33) gives:
% 6.82/1.63 | | |
% 6.82/1.63 | | | Case 1:
% 6.82/1.63 | | | |
% 6.82/1.63 | | | | (36) ~ (all_37_0 = 0)
% 6.82/1.63 | | | |
% 6.82/1.63 | | | | REDUCE: (35), (36) imply:
% 6.82/1.63 | | | | (37) $false
% 6.82/1.63 | | | |
% 6.82/1.63 | | | | CLOSE: (37) is inconsistent.
% 6.82/1.63 | | | |
% 6.82/1.63 | | | Case 2:
% 6.82/1.64 | | | |
% 6.82/1.64 | | | | (38) ~ (all_37_1 = 0)
% 6.82/1.64 | | | |
% 6.82/1.64 | | | | REDUCE: (34), (38) imply:
% 6.82/1.64 | | | | (39) $false
% 6.82/1.64 | | | |
% 6.82/1.64 | | | | CLOSE: (39) is inconsistent.
% 6.82/1.64 | | | |
% 6.82/1.64 | | | End of split
% 6.82/1.64 | | |
% 6.82/1.64 | | End of split
% 6.82/1.64 | |
% 6.82/1.64 | Case 2:
% 6.82/1.64 | |
% 6.82/1.64 | | (40) all_13_2 = 0 & ( ~ (all_13_0 = 0) | ~ (all_13_1 = 0))
% 6.82/1.64 | |
% 6.82/1.64 | | ALPHA: (40) implies:
% 6.82/1.64 | | (41) all_13_2 = 0
% 6.82/1.64 | | (42) ~ (all_13_0 = 0) | ~ (all_13_1 = 0)
% 6.82/1.64 | |
% 6.82/1.64 | | REDUCE: (12), (41) imply:
% 6.82/1.64 | | (43) in(all_13_4, all_13_3) = 0
% 6.82/1.64 | |
% 6.82/1.64 | | GROUND_INST: instantiating (17) with all_13_4, simplifying with (8), (43)
% 6.82/1.64 | | gives:
% 6.82/1.64 | | (44) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_13_4 &
% 6.82/1.64 | | in(v1, all_13_5) = 0 & in(v0, all_13_6) = 0 & $i(v1) & $i(v0))
% 6.82/1.64 | |
% 6.82/1.64 | | DELTA: instantiating (44) with fresh symbols all_39_0, all_39_1 gives:
% 6.82/1.64 | | (45) ordered_pair(all_39_1, all_39_0) = all_13_4 & in(all_39_0, all_13_5)
% 6.82/1.64 | | = 0 & in(all_39_1, all_13_6) = 0 & $i(all_39_0) & $i(all_39_1)
% 6.82/1.64 | |
% 6.82/1.64 | | ALPHA: (45) implies:
% 6.82/1.64 | | (46) $i(all_39_1)
% 6.82/1.64 | | (47) $i(all_39_0)
% 6.82/1.64 | | (48) in(all_39_1, all_13_6) = 0
% 6.82/1.64 | | (49) in(all_39_0, all_13_5) = 0
% 6.82/1.64 | | (50) ordered_pair(all_39_1, all_39_0) = all_13_4
% 6.82/1.64 | |
% 6.82/1.64 | | GROUND_INST: instantiating (t33_zfmisc_1) with all_13_8, all_13_7, all_39_1,
% 6.82/1.64 | | all_39_0, all_13_4, simplifying with (4), (5), (13), (46),
% 6.82/1.64 | | (47), (50) gives:
% 6.82/1.64 | | (51) all_39_0 = all_13_7 & all_39_1 = all_13_8
% 6.82/1.64 | |
% 6.82/1.64 | | ALPHA: (51) implies:
% 6.82/1.64 | | (52) all_39_1 = all_13_8
% 6.82/1.64 | | (53) all_39_0 = all_13_7
% 6.82/1.64 | |
% 6.82/1.64 | | REDUCE: (49), (53) imply:
% 6.82/1.64 | | (54) in(all_13_7, all_13_5) = 0
% 6.82/1.64 | |
% 6.82/1.64 | | REDUCE: (48), (52) imply:
% 6.82/1.64 | | (55) in(all_13_8, all_13_6) = 0
% 6.82/1.64 | |
% 6.82/1.64 | | GROUND_INST: instantiating (2) with all_13_1, 0, all_13_6, all_13_8,
% 6.82/1.64 | | simplifying with (10), (55) gives:
% 6.82/1.64 | | (56) all_13_1 = 0
% 6.82/1.64 | |
% 6.82/1.64 | | GROUND_INST: instantiating (2) with all_13_0, 0, all_13_5, all_13_7,
% 6.82/1.64 | | simplifying with (11), (54) gives:
% 6.82/1.64 | | (57) all_13_0 = 0
% 6.82/1.64 | |
% 6.82/1.64 | | BETA: splitting (42) gives:
% 6.82/1.64 | |
% 6.82/1.64 | | Case 1:
% 6.82/1.64 | | |
% 6.82/1.64 | | | (58) ~ (all_13_0 = 0)
% 6.82/1.64 | | |
% 6.82/1.64 | | | REDUCE: (57), (58) imply:
% 6.82/1.64 | | | (59) $false
% 6.82/1.64 | | |
% 6.82/1.64 | | | CLOSE: (59) is inconsistent.
% 6.82/1.64 | | |
% 6.82/1.64 | | Case 2:
% 6.82/1.64 | | |
% 6.82/1.64 | | | (60) ~ (all_13_1 = 0)
% 6.82/1.64 | | |
% 6.82/1.64 | | | REDUCE: (56), (60) imply:
% 6.82/1.64 | | | (61) $false
% 6.82/1.64 | | |
% 6.82/1.64 | | | CLOSE: (61) is inconsistent.
% 6.82/1.64 | | |
% 6.82/1.64 | | End of split
% 6.82/1.64 | |
% 6.82/1.64 | End of split
% 6.82/1.64 |
% 6.82/1.64 End of proof
% 6.82/1.64 % SZS output end Proof for theBenchmark
% 6.82/1.64
% 6.82/1.64 1118ms
%------------------------------------------------------------------------------