TSTP Solution File: ALG211+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n023.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 : Wed Aug 30 16:39:57 EDT 2023
% Result : Theorem 7.66s 1.75s
% Output : Proof 10.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 03:46:25 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.50/0.58 ________ _____
% 0.50/0.58 ___ __ \_________(_)________________________________
% 0.50/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.50/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.50/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.50/0.58
% 0.50/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.50/0.58 (2023-06-19)
% 0.50/0.58
% 0.50/0.58 (c) Philipp Rümmer, 2009-2023
% 0.50/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.50/0.58 Amanda Stjerna.
% 0.50/0.58 Free software under BSD-3-Clause.
% 0.50/0.58
% 0.50/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.50/0.58
% 0.50/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.50/0.59 Running up to 7 provers in parallel.
% 0.50/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.50/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.50/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.50/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.50/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.50/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.50/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.92/0.99 Prover 1: Preprocessing ...
% 1.92/0.99 Prover 4: Preprocessing ...
% 2.36/1.03 Prover 6: Preprocessing ...
% 2.36/1.03 Prover 5: Preprocessing ...
% 2.36/1.03 Prover 0: Preprocessing ...
% 2.36/1.03 Prover 3: Preprocessing ...
% 2.36/1.03 Prover 2: Preprocessing ...
% 3.38/1.20 Prover 5: Proving ...
% 3.38/1.20 Prover 2: Proving ...
% 3.38/1.22 Prover 1: Constructing countermodel ...
% 3.38/1.22 Prover 3: Constructing countermodel ...
% 3.38/1.23 Prover 6: Proving ...
% 3.99/1.27 Prover 4: Constructing countermodel ...
% 4.33/1.30 Prover 0: Proving ...
% 4.74/1.34 Prover 3: gave up
% 4.74/1.34 Prover 1: gave up
% 4.74/1.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.74/1.36 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.84/1.38 Prover 8: Preprocessing ...
% 4.84/1.38 Prover 7: Preprocessing ...
% 5.25/1.42 Prover 7: Constructing countermodel ...
% 5.25/1.45 Prover 8: Warning: ignoring some quantifiers
% 5.53/1.45 Prover 8: Constructing countermodel ...
% 5.53/1.46 Prover 7: gave up
% 5.53/1.46 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 5.53/1.47 Prover 9: Preprocessing ...
% 5.53/1.51 Prover 8: gave up
% 5.53/1.52 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.53/1.53 Prover 10: Preprocessing ...
% 6.19/1.56 Prover 10: Constructing countermodel ...
% 6.54/1.59 Prover 9: Constructing countermodel ...
% 6.54/1.59 Prover 10: gave up
% 6.54/1.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.54/1.61 Prover 11: Preprocessing ...
% 7.66/1.73 Prover 11: Constructing countermodel ...
% 7.66/1.75 Prover 0: proved (1144ms)
% 7.66/1.75
% 7.66/1.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.66/1.75
% 7.66/1.75 Prover 9: stopped
% 7.66/1.75 Prover 6: stopped
% 7.85/1.75 Prover 5: stopped
% 7.85/1.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.85/1.75 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.85/1.75 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 7.85/1.76 Prover 16: Preprocessing ...
% 7.85/1.76 Prover 2: stopped
% 7.85/1.76 Prover 19: Preprocessing ...
% 7.85/1.77 Prover 13: Preprocessing ...
% 7.85/1.79 Prover 16: Warning: ignoring some quantifiers
% 7.85/1.79 Prover 16: Constructing countermodel ...
% 7.85/1.79 Prover 13: Warning: ignoring some quantifiers
% 7.85/1.80 Prover 13: Constructing countermodel ...
% 8.41/1.83 Prover 19: Warning: ignoring some quantifiers
% 8.41/1.83 Prover 19: Constructing countermodel ...
% 8.75/1.92 Prover 19: gave up
% 10.16/2.12 Prover 13: Found proof (size 25)
% 10.16/2.12 Prover 13: proved (368ms)
% 10.16/2.12 Prover 16: stopped
% 10.16/2.12 Prover 4: stopped
% 10.16/2.12 Prover 11: stopped
% 10.16/2.12
% 10.16/2.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.16/2.12
% 10.71/2.13 % SZS output start Proof for theBenchmark
% 10.71/2.13 Assumptions after simplification:
% 10.71/2.13 ---------------------------------
% 10.71/2.13
% 10.71/2.13 (basis_of)
% 10.71/2.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vec_to_class(v1) = v2) | ~
% 10.71/2.15 $i(v1) | ~ $i(v0) | ~ basis_of(v0, v1) | a_subset_of(v0, v2)) & ! [v0:
% 10.71/2.16 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vec_to_class(v1) = v2) | ~ $i(v1) |
% 10.71/2.16 ~ $i(v0) | ~ basis_of(v0, v1) | lin_ind_subset(v0, v1)) & ! [v0: $i] : !
% 10.71/2.16 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ basis_of(v0, v1) | lin_ind_subset(v0,
% 10.71/2.16 v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 10.71/2.16 basis_of(v0, v1) | ? [v2: $i] : (vec_to_class(v1) = v2 & $i(v2) &
% 10.71/2.16 a_subset_of(v0, v2)))
% 10.71/2.16
% 10.71/2.16 (bg_2_2_5)
% 10.71/2.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 10.71/2.16 ~ lin_ind_subset(v0, v2) | ~ basis_of(v1, v2) | ? [v3: $i] : ? [v4: $i]
% 10.71/2.16 : (union(v0, v3) = v4 & $i(v4) & $i(v3) & a_subset_of(v3, v1) & basis_of(v4,
% 10.71/2.16 v2)))
% 10.71/2.16
% 10.71/2.16 (bg_2_4_2)
% 10.71/2.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vec_to_class(v0)
% 10.71/2.16 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ a_vector_subspace_of(v0,
% 10.71/2.16 v1) | ~ a_subset_of(v2, v3) | ~ lin_ind_subset(v2, v1) |
% 10.71/2.16 lin_ind_subset(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 10.71/2.16 $i] : ( ~ (vec_to_class(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 10.71/2.16 a_vector_subspace_of(v0, v1) | ~ a_subset_of(v2, v3) | ~
% 10.71/2.16 lin_ind_subset(v2, v0) | lin_ind_subset(v2, v1)) & ! [v0: $i] : ! [v1: $i]
% 10.71/2.16 : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 10.71/2.16 a_vector_subspace_of(v0, v1) | ~ lin_ind_subset(v2, v1) |
% 10.71/2.16 lin_ind_subset(v2, v0) | ? [v3: $i] : (vec_to_class(v0) = v3 & $i(v3) & ~
% 10.71/2.16 a_subset_of(v2, v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 10.71/2.16 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ a_vector_subspace_of(v0, v1) | ~
% 10.71/2.16 lin_ind_subset(v2, v0) | lin_ind_subset(v2, v1) | ? [v3: $i] :
% 10.71/2.16 (vec_to_class(v0) = v3 & $i(v3) & ~ a_subset_of(v2, v3)))
% 10.71/2.16
% 10.71/2.16 (bg_2_4_3)
% 10.71/2.17 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v3) & $i(v2) &
% 10.71/2.17 $i(v1) & $i(v0) & a_vector_subspace_of(v2, v3) & a_vector_subspace_of(v0,
% 10.71/2.17 v1) & a_vector_space(v3) & a_vector_space(v1) & ! [v4: $i] : ! [v5: $i]
% 10.71/2.17 : ! [v6: $i] : ( ~ (union(v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~
% 10.71/2.17 basis_of(v6, v3) | ~ basis_of(v4, v2)) & ? [v4: $i] : ! [v5: $i] : ( ~
% 10.71/2.17 $i(v5) | ~ $i(v4) | ~ basis_of(v5, v0) | ? [v6: $i] : (union(v5, v4) =
% 10.71/2.17 v6 & $i(v6) & ~ basis_of(v6, v1))))
% 10.71/2.17
% 10.71/2.17 (bg_2_4_a)
% 10.71/2.17 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 10.71/2.17 a_vector_subspace_of(v0, v1) | a_vector_space(v0))
% 10.71/2.17
% 10.71/2.17 (bg_remark_63_a)
% 10.71/2.17 ! [v0: $i] : ( ~ $i(v0) | ~ a_vector_space(v0) | ? [v1: $i] : ($i(v1) &
% 10.71/2.17 basis_of(v1, v0)))
% 10.71/2.17
% 10.71/2.17 Those formulas are unsatisfiable:
% 10.71/2.17 ---------------------------------
% 10.71/2.17
% 10.71/2.17 Begin of proof
% 10.71/2.17 |
% 10.71/2.17 | ALPHA: (basis_of) implies:
% 10.71/2.17 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ basis_of(v0,
% 10.71/2.17 | v1) | ? [v2: $i] : (vec_to_class(v1) = v2 & $i(v2) &
% 10.71/2.17 | a_subset_of(v0, v2)))
% 10.71/2.17 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ basis_of(v0,
% 10.71/2.17 | v1) | lin_ind_subset(v0, v1))
% 10.71/2.17 |
% 10.71/2.17 | ALPHA: (bg_2_4_2) implies:
% 10.71/2.17 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.71/2.17 | (vec_to_class(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 10.71/2.17 | a_vector_subspace_of(v0, v1) | ~ a_subset_of(v2, v3) | ~
% 10.71/2.17 | lin_ind_subset(v2, v0) | lin_ind_subset(v2, v1))
% 10.71/2.17 |
% 10.71/2.17 | DELTA: instantiating (bg_2_4_3) with fresh symbols all_8_0, all_8_1, all_8_2,
% 10.71/2.17 | all_8_3 gives:
% 10.98/2.18 | (4) $i(all_8_0) & $i(all_8_1) & $i(all_8_2) & $i(all_8_3) &
% 10.98/2.18 | a_vector_subspace_of(all_8_1, all_8_0) & a_vector_subspace_of(all_8_3,
% 10.98/2.18 | all_8_2) & a_vector_space(all_8_0) & a_vector_space(all_8_2) & !
% 10.98/2.18 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~
% 10.98/2.18 | $i(v1) | ~ $i(v0) | ~ basis_of(v2, all_8_0) | ~ basis_of(v0,
% 10.98/2.18 | all_8_1)) & ? [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 10.98/2.18 | basis_of(v1, all_8_3) | ? [v2: $i] : (union(v1, v0) = v2 & $i(v2) &
% 10.98/2.18 | ~ basis_of(v2, all_8_2)))
% 10.98/2.18 |
% 10.98/2.18 | ALPHA: (4) implies:
% 10.98/2.18 | (5) a_vector_space(all_8_0)
% 10.98/2.18 | (6) a_vector_subspace_of(all_8_1, all_8_0)
% 10.98/2.18 | (7) $i(all_8_1)
% 10.98/2.18 | (8) $i(all_8_0)
% 10.98/2.18 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~
% 10.98/2.18 | $i(v1) | ~ $i(v0) | ~ basis_of(v2, all_8_0) | ~ basis_of(v0,
% 10.98/2.18 | all_8_1))
% 10.98/2.18 |
% 10.98/2.18 | GROUND_INST: instantiating (bg_remark_63_a) with all_8_0, simplifying with
% 10.98/2.18 | (5), (8) gives:
% 10.98/2.18 | (10) ? [v0: $i] : ($i(v0) & basis_of(v0, all_8_0))
% 10.98/2.18 |
% 10.98/2.18 | GROUND_INST: instantiating (bg_2_4_a) with all_8_1, all_8_0, simplifying with
% 10.98/2.18 | (6), (7), (8) gives:
% 10.98/2.18 | (11) a_vector_space(all_8_1)
% 10.98/2.18 |
% 10.98/2.18 | DELTA: instantiating (10) with fresh symbol all_19_0 gives:
% 10.98/2.18 | (12) $i(all_19_0) & basis_of(all_19_0, all_8_0)
% 10.98/2.18 |
% 10.98/2.18 | ALPHA: (12) implies:
% 10.98/2.18 | (13) basis_of(all_19_0, all_8_0)
% 10.98/2.18 | (14) $i(all_19_0)
% 10.98/2.18 |
% 10.98/2.18 | GROUND_INST: instantiating (2) with all_19_0, all_8_0, simplifying with (8),
% 10.98/2.18 | (13), (14) gives:
% 10.98/2.18 | (15) lin_ind_subset(all_19_0, all_8_0)
% 10.98/2.18 |
% 10.98/2.18 | GROUND_INST: instantiating (bg_remark_63_a) with all_8_1, simplifying with
% 10.98/2.18 | (7), (11) gives:
% 10.98/2.18 | (16) ? [v0: $i] : ($i(v0) & basis_of(v0, all_8_1))
% 10.98/2.18 |
% 10.98/2.18 | DELTA: instantiating (16) with fresh symbol all_29_0 gives:
% 10.98/2.18 | (17) $i(all_29_0) & basis_of(all_29_0, all_8_1)
% 10.98/2.18 |
% 10.98/2.18 | ALPHA: (17) implies:
% 10.98/2.18 | (18) basis_of(all_29_0, all_8_1)
% 10.98/2.18 | (19) $i(all_29_0)
% 10.98/2.18 |
% 10.98/2.18 | GROUND_INST: instantiating (2) with all_29_0, all_8_1, simplifying with (7),
% 10.98/2.18 | (18), (19) gives:
% 10.98/2.18 | (20) lin_ind_subset(all_29_0, all_8_1)
% 10.98/2.18 |
% 10.98/2.18 | GROUND_INST: instantiating (1) with all_29_0, all_8_1, simplifying with (7),
% 10.98/2.18 | (18), (19) gives:
% 10.98/2.18 | (21) ? [v0: $i] : (vec_to_class(all_8_1) = v0 & $i(v0) &
% 10.98/2.19 | a_subset_of(all_29_0, v0))
% 10.98/2.19 |
% 10.98/2.19 | GROUND_INST: instantiating (bg_2_2_5) with all_19_0, all_19_0, all_8_0,
% 10.98/2.19 | simplifying with (8), (13), (14), (15) gives:
% 10.98/2.19 | (22) ? [v0: $i] : ? [v1: $i] : (union(all_19_0, v0) = v1 & $i(v1) &
% 10.98/2.19 | $i(v0) & a_subset_of(v0, all_19_0) & basis_of(v1, all_8_0))
% 10.98/2.19 |
% 10.98/2.19 | DELTA: instantiating (21) with fresh symbol all_43_0 gives:
% 10.98/2.19 | (23) vec_to_class(all_8_1) = all_43_0 & $i(all_43_0) &
% 10.98/2.19 | a_subset_of(all_29_0, all_43_0)
% 10.98/2.19 |
% 10.98/2.19 | ALPHA: (23) implies:
% 10.98/2.19 | (24) a_subset_of(all_29_0, all_43_0)
% 10.98/2.19 | (25) vec_to_class(all_8_1) = all_43_0
% 10.98/2.19 |
% 10.98/2.19 | DELTA: instantiating (22) with fresh symbols all_47_0, all_47_1 gives:
% 10.98/2.19 | (26) union(all_19_0, all_47_1) = all_47_0 & $i(all_47_0) & $i(all_47_1) &
% 10.98/2.19 | a_subset_of(all_47_1, all_19_0) & basis_of(all_47_0, all_8_0)
% 10.98/2.19 |
% 10.98/2.19 | ALPHA: (26) implies:
% 10.98/2.19 | (27) basis_of(all_47_0, all_8_0)
% 10.98/2.19 | (28) $i(all_47_0)
% 10.98/2.19 |
% 10.98/2.19 | GROUND_INST: instantiating (3) with all_8_1, all_8_0, all_29_0, all_43_0,
% 10.98/2.19 | simplifying with (6), (7), (8), (19), (20), (24), (25) gives:
% 10.98/2.19 | (29) lin_ind_subset(all_29_0, all_8_0)
% 10.98/2.19 |
% 10.98/2.19 | GROUND_INST: instantiating (bg_2_2_5) with all_29_0, all_47_0, all_8_0,
% 10.98/2.19 | simplifying with (8), (19), (27), (28), (29) gives:
% 10.98/2.19 | (30) ? [v0: $i] : ? [v1: $i] : (union(all_29_0, v0) = v1 & $i(v1) &
% 10.98/2.19 | $i(v0) & a_subset_of(v0, all_47_0) & basis_of(v1, all_8_0))
% 10.98/2.19 |
% 10.98/2.19 | DELTA: instantiating (30) with fresh symbols all_105_0, all_105_1 gives:
% 10.98/2.19 | (31) union(all_29_0, all_105_1) = all_105_0 & $i(all_105_0) & $i(all_105_1)
% 10.98/2.19 | & a_subset_of(all_105_1, all_47_0) & basis_of(all_105_0, all_8_0)
% 10.98/2.19 |
% 10.98/2.19 | ALPHA: (31) implies:
% 10.98/2.19 | (32) basis_of(all_105_0, all_8_0)
% 10.98/2.19 | (33) $i(all_105_1)
% 10.98/2.19 | (34) union(all_29_0, all_105_1) = all_105_0
% 10.98/2.19 |
% 10.98/2.19 | GROUND_INST: instantiating (9) with all_29_0, all_105_1, all_105_0,
% 10.98/2.19 | simplifying with (18), (19), (32), (33), (34) gives:
% 10.98/2.19 | (35) $false
% 10.98/2.19 |
% 10.98/2.19 | CLOSE: (35) is inconsistent.
% 10.98/2.19 |
% 10.98/2.19 End of proof
% 10.98/2.19 % SZS output end Proof for theBenchmark
% 10.98/2.19
% 10.98/2.19 1609ms
%------------------------------------------------------------------------------