TSTP Solution File: SEU244+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU244+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 : n021.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 17:43:36 EDT 2023
% Result : Theorem 6.72s 1.66s
% Output : Proof 8.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU244+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n021.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 : Wed Aug 23 23:57:54 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.91/0.97 Prover 4: Preprocessing ...
% 1.91/0.97 Prover 1: Preprocessing ...
% 2.53/1.01 Prover 5: Preprocessing ...
% 2.53/1.01 Prover 3: Preprocessing ...
% 2.53/1.02 Prover 0: Preprocessing ...
% 2.53/1.02 Prover 2: Preprocessing ...
% 2.53/1.02 Prover 6: Preprocessing ...
% 4.01/1.35 Prover 1: Warning: ignoring some quantifiers
% 4.01/1.35 Prover 3: Warning: ignoring some quantifiers
% 4.01/1.36 Prover 5: Proving ...
% 4.01/1.37 Prover 6: Proving ...
% 4.01/1.37 Prover 1: Constructing countermodel ...
% 4.01/1.37 Prover 3: Constructing countermodel ...
% 4.01/1.38 Prover 2: Proving ...
% 5.75/1.54 Prover 4: Constructing countermodel ...
% 6.72/1.64 Prover 0: Proving ...
% 6.72/1.66 Prover 3: proved (1049ms)
% 6.72/1.66
% 6.72/1.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.72/1.66
% 6.72/1.66 Prover 5: stopped
% 6.72/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.72/1.67 Prover 2: stopped
% 6.72/1.67 Prover 0: stopped
% 6.72/1.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.72/1.68 Prover 6: stopped
% 6.72/1.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.72/1.69 Prover 8: Preprocessing ...
% 6.72/1.69 Prover 7: Preprocessing ...
% 6.72/1.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.72/1.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.33/1.71 Prover 11: Preprocessing ...
% 7.33/1.72 Prover 13: Preprocessing ...
% 7.33/1.72 Prover 10: Preprocessing ...
% 7.90/1.78 Prover 10: Constructing countermodel ...
% 7.90/1.79 Prover 8: Warning: ignoring some quantifiers
% 7.90/1.81 Prover 7: Constructing countermodel ...
% 7.90/1.81 Prover 13: Warning: ignoring some quantifiers
% 7.90/1.83 Prover 13: Constructing countermodel ...
% 7.90/1.83 Prover 8: Constructing countermodel ...
% 8.86/1.93 Prover 10: Found proof (size 36)
% 8.86/1.93 Prover 10: proved (244ms)
% 8.86/1.93 Prover 13: stopped
% 8.86/1.93 Prover 4: stopped
% 8.86/1.93 Prover 8: stopped
% 8.86/1.93 Prover 1: stopped
% 8.86/1.93 Prover 7: stopped
% 8.86/1.97 Prover 11: Constructing countermodel ...
% 8.86/1.98 Prover 11: stopped
% 8.86/1.98
% 8.86/1.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.86/1.98
% 8.86/1.99 % SZS output start Proof for theBenchmark
% 8.86/1.99 Assumptions after simplification:
% 8.86/1.99 ---------------------------------
% 8.86/1.99
% 8.86/1.99 (d12_relat_2)
% 8.86/2.02 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ~
% 8.86/2.02 is_antisymmetric_in(v0, v1) | ~ relation(v0) | antisymmetric(v0)) & ! [v0:
% 8.86/2.02 $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ~
% 8.86/2.02 antisymmetric(v0) | ~ relation(v0) | is_antisymmetric_in(v0, v1))
% 8.86/2.02
% 8.86/2.02 (d14_relat_2)
% 8.86/2.02 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ~
% 8.86/2.02 is_connected_in(v0, v1) | ~ relation(v0) | connected(v0)) & ! [v0: $i] :
% 8.86/2.02 ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ~ connected(v0) | ~
% 8.86/2.02 relation(v0) | is_connected_in(v0, v1))
% 8.86/2.02
% 8.86/2.02 (d16_relat_2)
% 8.86/2.02 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ~
% 8.86/2.02 is_transitive_in(v0, v1) | ~ relation(v0) | transitive(v0)) & ! [v0: $i] :
% 8.86/2.02 ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ~ transitive(v0) |
% 8.86/2.02 ~ relation(v0) | is_transitive_in(v0, v1))
% 8.86/2.02
% 8.86/2.02 (d4_wellord1)
% 8.86/2.03 ! [v0: $i] : ( ~ $i(v0) | ~ well_founded_relation(v0) | ~ reflexive(v0) |
% 8.86/2.03 ~ transitive(v0) | ~ connected(v0) | ~ antisymmetric(v0) | ~ relation(v0)
% 8.86/2.03 | well_ordering(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ well_ordering(v0) | ~
% 8.86/2.03 relation(v0) | well_founded_relation(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 8.86/2.03 well_ordering(v0) | ~ relation(v0) | reflexive(v0)) & ! [v0: $i] : ( ~
% 8.86/2.03 $i(v0) | ~ well_ordering(v0) | ~ relation(v0) | transitive(v0)) & ! [v0:
% 8.86/2.03 $i] : ( ~ $i(v0) | ~ well_ordering(v0) | ~ relation(v0) | connected(v0)) &
% 8.86/2.03 ! [v0: $i] : ( ~ $i(v0) | ~ well_ordering(v0) | ~ relation(v0) |
% 8.86/2.03 antisymmetric(v0))
% 8.86/2.03
% 8.86/2.03 (d5_wellord1)
% 8.86/2.03 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ is_well_founded_in(v0,
% 8.86/2.03 v1) | ~ is_reflexive_in(v0, v1) | ~ is_transitive_in(v0, v1) | ~
% 8.86/2.03 is_connected_in(v0, v1) | ~ is_antisymmetric_in(v0, v1) | ~ relation(v0) |
% 8.86/2.03 well_orders(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 8.86/2.03 ~ well_orders(v0, v1) | ~ relation(v0) | is_well_founded_in(v0, v1)) & !
% 8.86/2.03 [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ well_orders(v0, v1) | ~
% 8.86/2.03 relation(v0) | is_reflexive_in(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.86/2.03 $i(v1) | ~ $i(v0) | ~ well_orders(v0, v1) | ~ relation(v0) |
% 8.86/2.03 is_transitive_in(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 8.86/2.03 $i(v0) | ~ well_orders(v0, v1) | ~ relation(v0) | is_connected_in(v0, v1))
% 8.86/2.03 & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ well_orders(v0, v1)
% 8.86/2.03 | ~ relation(v0) | is_antisymmetric_in(v0, v1))
% 8.86/2.03
% 8.86/2.03 (d9_relat_2)
% 8.86/2.04 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ~
% 8.86/2.04 is_reflexive_in(v0, v1) | ~ relation(v0) | reflexive(v0)) & ! [v0: $i] :
% 8.86/2.04 ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ~ reflexive(v0) | ~
% 8.86/2.04 relation(v0) | is_reflexive_in(v0, v1))
% 8.86/2.04
% 8.86/2.04 (t5_wellord1)
% 8.86/2.04 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ~
% 8.86/2.04 is_well_founded_in(v0, v1) | ~ relation(v0) | well_founded_relation(v0)) &
% 8.86/2.04 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ~
% 8.86/2.04 well_founded_relation(v0) | ~ relation(v0) | is_well_founded_in(v0, v1))
% 8.86/2.04
% 8.86/2.04 (t8_wellord1)
% 8.86/2.04 ? [v0: $i] : ? [v1: $i] : (relation_field(v0) = v1 & $i(v1) & $i(v0) &
% 8.86/2.04 relation(v0) & ((well_orders(v0, v1) & ~ well_ordering(v0)) |
% 8.86/2.04 (well_ordering(v0) & ~ well_orders(v0, v1))))
% 8.86/2.04
% 8.86/2.04 Further assumptions not needed in the proof:
% 8.86/2.04 --------------------------------------------
% 8.86/2.04 commutativity_k2_xboole_0, d6_relat_1, dt_k1_relat_1, dt_k2_relat_1,
% 8.86/2.04 dt_k2_xboole_0, dt_k3_relat_1, idempotence_k2_xboole_0
% 8.86/2.04
% 8.86/2.04 Those formulas are unsatisfiable:
% 8.86/2.04 ---------------------------------
% 8.86/2.04
% 8.86/2.04 Begin of proof
% 8.86/2.04 |
% 8.86/2.04 | ALPHA: (d12_relat_2) implies:
% 8.86/2.04 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) |
% 8.86/2.04 | ~ antisymmetric(v0) | ~ relation(v0) | is_antisymmetric_in(v0, v1))
% 8.86/2.05 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) |
% 8.86/2.05 | ~ is_antisymmetric_in(v0, v1) | ~ relation(v0) | antisymmetric(v0))
% 8.86/2.05 |
% 8.86/2.05 | ALPHA: (d14_relat_2) implies:
% 8.86/2.05 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) |
% 8.86/2.05 | ~ connected(v0) | ~ relation(v0) | is_connected_in(v0, v1))
% 8.86/2.05 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) |
% 8.86/2.05 | ~ is_connected_in(v0, v1) | ~ relation(v0) | connected(v0))
% 8.86/2.05 |
% 8.86/2.05 | ALPHA: (d16_relat_2) implies:
% 8.86/2.05 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) |
% 8.86/2.05 | ~ transitive(v0) | ~ relation(v0) | is_transitive_in(v0, v1))
% 8.86/2.05 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) |
% 8.86/2.05 | ~ is_transitive_in(v0, v1) | ~ relation(v0) | transitive(v0))
% 8.86/2.05 |
% 8.86/2.05 | ALPHA: (d4_wellord1) implies:
% 8.86/2.05 | (7) ! [v0: $i] : ( ~ $i(v0) | ~ well_ordering(v0) | ~ relation(v0) |
% 8.86/2.05 | antisymmetric(v0))
% 8.86/2.05 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ well_ordering(v0) | ~ relation(v0) |
% 8.86/2.05 | connected(v0))
% 8.86/2.05 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ well_ordering(v0) | ~ relation(v0) |
% 8.86/2.05 | transitive(v0))
% 8.86/2.05 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ well_ordering(v0) | ~ relation(v0) |
% 8.86/2.05 | reflexive(v0))
% 8.86/2.05 | (11) ! [v0: $i] : ( ~ $i(v0) | ~ well_ordering(v0) | ~ relation(v0) |
% 8.86/2.05 | well_founded_relation(v0))
% 8.86/2.05 | (12) ! [v0: $i] : ( ~ $i(v0) | ~ well_founded_relation(v0) | ~
% 8.86/2.05 | reflexive(v0) | ~ transitive(v0) | ~ connected(v0) | ~
% 8.86/2.05 | antisymmetric(v0) | ~ relation(v0) | well_ordering(v0))
% 8.86/2.05 |
% 8.86/2.05 | ALPHA: (d5_wellord1) implies:
% 8.86/2.05 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 8.86/2.05 | well_orders(v0, v1) | ~ relation(v0) | is_antisymmetric_in(v0, v1))
% 8.86/2.06 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 8.86/2.06 | well_orders(v0, v1) | ~ relation(v0) | is_connected_in(v0, v1))
% 8.86/2.06 | (15) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 8.86/2.06 | well_orders(v0, v1) | ~ relation(v0) | is_transitive_in(v0, v1))
% 8.86/2.06 | (16) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 8.86/2.06 | well_orders(v0, v1) | ~ relation(v0) | is_reflexive_in(v0, v1))
% 8.86/2.06 | (17) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 8.86/2.06 | well_orders(v0, v1) | ~ relation(v0) | is_well_founded_in(v0, v1))
% 8.86/2.06 | (18) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 8.86/2.06 | is_well_founded_in(v0, v1) | ~ is_reflexive_in(v0, v1) | ~
% 8.86/2.06 | is_transitive_in(v0, v1) | ~ is_connected_in(v0, v1) | ~
% 8.86/2.06 | is_antisymmetric_in(v0, v1) | ~ relation(v0) | well_orders(v0, v1))
% 8.86/2.06 |
% 8.86/2.06 | ALPHA: (d9_relat_2) implies:
% 8.86/2.06 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0)
% 8.86/2.06 | | ~ reflexive(v0) | ~ relation(v0) | is_reflexive_in(v0, v1))
% 8.86/2.06 | (20) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0)
% 8.86/2.06 | | ~ is_reflexive_in(v0, v1) | ~ relation(v0) | reflexive(v0))
% 8.86/2.06 |
% 8.86/2.06 | ALPHA: (t5_wellord1) implies:
% 8.86/2.06 | (21) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0)
% 8.86/2.06 | | ~ well_founded_relation(v0) | ~ relation(v0) |
% 8.86/2.06 | is_well_founded_in(v0, v1))
% 8.86/2.06 | (22) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0)
% 8.86/2.06 | | ~ is_well_founded_in(v0, v1) | ~ relation(v0) |
% 8.86/2.06 | well_founded_relation(v0))
% 8.86/2.06 |
% 8.86/2.06 | DELTA: instantiating (t8_wellord1) with fresh symbols all_13_0, all_13_1
% 8.86/2.06 | gives:
% 8.86/2.06 | (23) relation_field(all_13_1) = all_13_0 & $i(all_13_0) & $i(all_13_1) &
% 8.86/2.06 | relation(all_13_1) & ((well_orders(all_13_1, all_13_0) & ~
% 8.86/2.06 | well_ordering(all_13_1)) | (well_ordering(all_13_1) & ~
% 8.86/2.06 | well_orders(all_13_1, all_13_0)))
% 8.86/2.06 |
% 8.86/2.06 | ALPHA: (23) implies:
% 8.86/2.06 | (24) relation(all_13_1)
% 8.86/2.06 | (25) $i(all_13_1)
% 8.86/2.06 | (26) $i(all_13_0)
% 8.86/2.06 | (27) relation_field(all_13_1) = all_13_0
% 8.86/2.06 | (28) (well_orders(all_13_1, all_13_0) & ~ well_ordering(all_13_1)) |
% 8.86/2.06 | (well_ordering(all_13_1) & ~ well_orders(all_13_1, all_13_0))
% 8.86/2.07 |
% 8.86/2.07 | BETA: splitting (28) gives:
% 8.86/2.07 |
% 8.86/2.07 | Case 1:
% 8.86/2.07 | |
% 8.86/2.07 | | (29) well_orders(all_13_1, all_13_0) & ~ well_ordering(all_13_1)
% 8.86/2.07 | |
% 8.86/2.07 | | ALPHA: (29) implies:
% 8.86/2.07 | | (30) ~ well_ordering(all_13_1)
% 8.86/2.07 | | (31) well_orders(all_13_1, all_13_0)
% 8.86/2.07 | |
% 8.86/2.07 | | GROUND_INST: instantiating (17) with all_13_1, all_13_0, simplifying with
% 8.86/2.07 | | (24), (25), (26), (31) gives:
% 8.86/2.07 | | (32) is_well_founded_in(all_13_1, all_13_0)
% 8.86/2.07 | |
% 8.86/2.07 | | GROUND_INST: instantiating (16) with all_13_1, all_13_0, simplifying with
% 8.86/2.07 | | (24), (25), (26), (31) gives:
% 8.86/2.07 | | (33) is_reflexive_in(all_13_1, all_13_0)
% 8.86/2.07 | |
% 8.86/2.07 | | GROUND_INST: instantiating (15) with all_13_1, all_13_0, simplifying with
% 8.86/2.07 | | (24), (25), (26), (31) gives:
% 8.86/2.07 | | (34) is_transitive_in(all_13_1, all_13_0)
% 8.86/2.07 | |
% 8.86/2.07 | | GROUND_INST: instantiating (14) with all_13_1, all_13_0, simplifying with
% 8.86/2.07 | | (24), (25), (26), (31) gives:
% 8.86/2.07 | | (35) is_connected_in(all_13_1, all_13_0)
% 8.86/2.07 | |
% 8.86/2.07 | | GROUND_INST: instantiating (13) with all_13_1, all_13_0, simplifying with
% 8.86/2.07 | | (24), (25), (26), (31) gives:
% 8.86/2.07 | | (36) is_antisymmetric_in(all_13_1, all_13_0)
% 8.86/2.07 | |
% 8.86/2.07 | | GROUND_INST: instantiating (2) with all_13_1, all_13_0, simplifying with
% 8.86/2.07 | | (24), (25), (27), (36) gives:
% 8.86/2.07 | | (37) antisymmetric(all_13_1)
% 8.86/2.07 | |
% 8.86/2.07 | | GROUND_INST: instantiating (4) with all_13_1, all_13_0, simplifying with
% 8.86/2.07 | | (24), (25), (27), (35) gives:
% 8.86/2.07 | | (38) connected(all_13_1)
% 8.86/2.07 | |
% 8.86/2.07 | | GROUND_INST: instantiating (6) with all_13_1, all_13_0, simplifying with
% 8.86/2.07 | | (24), (25), (27), (34) gives:
% 8.86/2.07 | | (39) transitive(all_13_1)
% 8.86/2.07 | |
% 8.86/2.07 | | GROUND_INST: instantiating (20) with all_13_1, all_13_0, simplifying with
% 8.86/2.07 | | (24), (25), (27), (33) gives:
% 8.86/2.07 | | (40) reflexive(all_13_1)
% 8.86/2.07 | |
% 8.86/2.07 | | GROUND_INST: instantiating (22) with all_13_1, all_13_0, simplifying with
% 8.86/2.07 | | (24), (25), (27), (32) gives:
% 8.86/2.07 | | (41) well_founded_relation(all_13_1)
% 8.86/2.07 | |
% 8.86/2.07 | | GROUND_INST: instantiating (12) with all_13_1, simplifying with (24), (25),
% 8.86/2.07 | | (30), (37), (38), (39), (40), (41) gives:
% 8.86/2.07 | | (42) $false
% 8.86/2.08 | |
% 8.86/2.08 | | CLOSE: (42) is inconsistent.
% 8.86/2.08 | |
% 8.86/2.08 | Case 2:
% 8.86/2.08 | |
% 8.86/2.08 | | (43) well_ordering(all_13_1) & ~ well_orders(all_13_1, all_13_0)
% 8.86/2.08 | |
% 8.86/2.08 | | ALPHA: (43) implies:
% 8.86/2.08 | | (44) ~ well_orders(all_13_1, all_13_0)
% 8.86/2.08 | | (45) well_ordering(all_13_1)
% 8.86/2.08 | |
% 8.86/2.08 | | GROUND_INST: instantiating (11) with all_13_1, simplifying with (24), (25),
% 8.86/2.08 | | (45) gives:
% 8.86/2.08 | | (46) well_founded_relation(all_13_1)
% 8.86/2.08 | |
% 8.86/2.08 | | GROUND_INST: instantiating (10) with all_13_1, simplifying with (24), (25),
% 8.86/2.08 | | (45) gives:
% 8.86/2.08 | | (47) reflexive(all_13_1)
% 8.86/2.08 | |
% 8.86/2.08 | | GROUND_INST: instantiating (9) with all_13_1, simplifying with (24), (25),
% 8.86/2.08 | | (45) gives:
% 8.86/2.08 | | (48) transitive(all_13_1)
% 8.86/2.08 | |
% 8.86/2.08 | | GROUND_INST: instantiating (8) with all_13_1, simplifying with (24), (25),
% 8.86/2.08 | | (45) gives:
% 8.86/2.08 | | (49) connected(all_13_1)
% 8.86/2.08 | |
% 8.86/2.08 | | GROUND_INST: instantiating (7) with all_13_1, simplifying with (24), (25),
% 8.86/2.08 | | (45) gives:
% 8.86/2.08 | | (50) antisymmetric(all_13_1)
% 8.86/2.08 | |
% 8.86/2.08 | | GROUND_INST: instantiating (1) with all_13_1, all_13_0, simplifying with
% 8.86/2.08 | | (24), (25), (27), (50) gives:
% 8.86/2.08 | | (51) is_antisymmetric_in(all_13_1, all_13_0)
% 8.86/2.08 | |
% 8.86/2.08 | | GROUND_INST: instantiating (3) with all_13_1, all_13_0, simplifying with
% 8.86/2.08 | | (24), (25), (27), (49) gives:
% 8.86/2.08 | | (52) is_connected_in(all_13_1, all_13_0)
% 8.86/2.08 | |
% 8.86/2.08 | | GROUND_INST: instantiating (5) with all_13_1, all_13_0, simplifying with
% 8.86/2.08 | | (24), (25), (27), (48) gives:
% 8.86/2.08 | | (53) is_transitive_in(all_13_1, all_13_0)
% 8.86/2.08 | |
% 8.86/2.08 | | GROUND_INST: instantiating (19) with all_13_1, all_13_0, simplifying with
% 8.86/2.08 | | (24), (25), (27), (47) gives:
% 8.86/2.08 | | (54) is_reflexive_in(all_13_1, all_13_0)
% 8.86/2.08 | |
% 8.86/2.08 | | GROUND_INST: instantiating (21) with all_13_1, all_13_0, simplifying with
% 8.86/2.08 | | (24), (25), (27), (46) gives:
% 8.86/2.08 | | (55) is_well_founded_in(all_13_1, all_13_0)
% 8.86/2.08 | |
% 8.86/2.08 | | GROUND_INST: instantiating (18) with all_13_1, all_13_0, simplifying with
% 8.86/2.08 | | (24), (25), (26), (44), (51), (52), (53), (54), (55) gives:
% 8.86/2.08 | | (56) $false
% 8.86/2.08 | |
% 8.86/2.08 | | CLOSE: (56) is inconsistent.
% 8.86/2.08 | |
% 8.86/2.08 | End of split
% 8.86/2.08 |
% 8.86/2.08 End of proof
% 8.86/2.08 % SZS output end Proof for theBenchmark
% 8.86/2.08
% 8.86/2.08 1493ms
%------------------------------------------------------------------------------