TSTP Solution File: SEU275+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU275+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 : n015.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 17:43:48 EDT 2023
% Result : Theorem 4.55s 1.78s
% Output : Proof 5.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU275+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.32 % Computer : n015.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Aug 23 14:26:19 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.61 ________ _____
% 0.18/0.61 ___ __ \_________(_)________________________________
% 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.61
% 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.61 (2023-06-19)
% 0.18/0.61
% 0.18/0.61 (c) Philipp Rümmer, 2009-2023
% 0.18/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.61 Amanda Stjerna.
% 0.18/0.61 Free software under BSD-3-Clause.
% 0.18/0.61
% 0.18/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.61
% 0.18/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.62 Running up to 7 provers in parallel.
% 0.18/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.86/1.02 Prover 4: Preprocessing ...
% 1.86/1.05 Prover 1: Preprocessing ...
% 2.04/1.12 Prover 6: Preprocessing ...
% 2.04/1.12 Prover 2: Preprocessing ...
% 2.04/1.12 Prover 3: Preprocessing ...
% 2.04/1.12 Prover 0: Preprocessing ...
% 2.04/1.12 Prover 5: Preprocessing ...
% 3.12/1.45 Prover 5: Proving ...
% 3.44/1.47 Prover 2: Proving ...
% 3.44/1.48 Prover 6: Constructing countermodel ...
% 3.44/1.49 Prover 3: Constructing countermodel ...
% 3.44/1.50 Prover 1: Constructing countermodel ...
% 3.83/1.59 Prover 4: Constructing countermodel ...
% 4.34/1.72 Prover 0: Proving ...
% 4.55/1.78 Prover 5: proved (1134ms)
% 4.55/1.78
% 4.55/1.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.55/1.78
% 4.55/1.81 Prover 2: stopped
% 4.55/1.83 Prover 6: stopped
% 4.55/1.84 Prover 3: stopped
% 4.94/1.86 Prover 0: stopped
% 5.08/1.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.08/1.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.08/1.90 Prover 7: Preprocessing ...
% 5.08/1.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.08/1.90 Prover 8: Preprocessing ...
% 5.08/1.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.08/1.90 Prover 10: Preprocessing ...
% 5.08/1.90 Prover 11: Preprocessing ...
% 5.08/1.91 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.08/1.91 Prover 7: Constructing countermodel ...
% 5.08/1.92 Prover 10: Constructing countermodel ...
% 5.26/1.95 Prover 13: Preprocessing ...
% 5.26/1.98 Prover 7: Found proof (size 11)
% 5.26/1.98 Prover 7: proved (172ms)
% 5.26/1.98 Prover 1: stopped
% 5.26/1.98 Prover 4: stopped
% 5.26/2.00 Prover 10: stopped
% 5.26/2.00 Prover 13: stopped
% 5.26/2.00 Prover 8: Warning: ignoring some quantifiers
% 5.26/2.00 Prover 8: Constructing countermodel ...
% 5.26/2.00 Prover 8: stopped
% 5.26/2.00 Prover 11: stopped
% 5.26/2.00
% 5.26/2.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.26/2.00
% 5.26/2.00 % SZS output start Proof for theBenchmark
% 5.26/2.01 Assumptions after simplification:
% 5.26/2.01 ---------------------------------
% 5.26/2.01
% 5.26/2.01 (d4_wellord1)
% 5.26/2.01 ! [v0: $i] : ( ~ $i(v0) | ~ well_founded_relation(v0) | ~ connected(v0) |
% 5.26/2.02 ~ antisymmetric(v0) | ~ transitive(v0) | ~ reflexive(v0) | ~ relation(v0)
% 5.26/2.02 | well_ordering(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ well_ordering(v0) | ~
% 5.26/2.02 relation(v0) | well_founded_relation(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 5.26/2.02 well_ordering(v0) | ~ relation(v0) | connected(v0)) & ! [v0: $i] : ( ~
% 5.26/2.02 $i(v0) | ~ well_ordering(v0) | ~ relation(v0) | antisymmetric(v0)) & !
% 5.26/2.02 [v0: $i] : ( ~ $i(v0) | ~ well_ordering(v0) | ~ relation(v0) |
% 5.26/2.02 transitive(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ well_ordering(v0) | ~
% 5.26/2.02 relation(v0) | reflexive(v0))
% 5.26/2.02
% 5.26/2.02 (dt_k1_wellord2)
% 5.26/2.04 ! [v0: $i] : ! [v1: $i] : ( ~ (inclusion_relation(v0) = v1) | ~ $i(v0) |
% 5.26/2.04 relation(v1))
% 5.26/2.04
% 5.26/2.04 (t2_wellord2)
% 5.26/2.04 ! [v0: $i] : ! [v1: $i] : ( ~ (inclusion_relation(v0) = v1) | ~ $i(v0) |
% 5.26/2.04 reflexive(v1))
% 5.26/2.04
% 5.26/2.04 (t3_wellord2)
% 5.26/2.05 ! [v0: $i] : ! [v1: $i] : ( ~ (inclusion_relation(v0) = v1) | ~ $i(v0) |
% 5.26/2.05 transitive(v1))
% 5.26/2.05
% 5.26/2.05 (t4_wellord2)
% 5.26/2.05 ! [v0: $i] : ! [v1: $i] : ( ~ (inclusion_relation(v0) = v1) | ~ $i(v0) | ~
% 5.26/2.05 ordinal(v0) | connected(v1))
% 5.26/2.05
% 5.26/2.05 (t5_wellord2)
% 5.26/2.05 ! [v0: $i] : ! [v1: $i] : ( ~ (inclusion_relation(v0) = v1) | ~ $i(v0) |
% 5.26/2.05 antisymmetric(v1))
% 5.26/2.05
% 5.26/2.05 (t6_wellord2)
% 5.26/2.05 ! [v0: $i] : ! [v1: $i] : ( ~ (inclusion_relation(v0) = v1) | ~ $i(v0) | ~
% 5.26/2.05 ordinal(v0) | well_founded_relation(v1))
% 5.26/2.05
% 5.26/2.05 (t7_wellord2)
% 5.26/2.05 ? [v0: $i] : ? [v1: $i] : (inclusion_relation(v0) = v1 & $i(v1) & $i(v0) &
% 5.26/2.05 ordinal(v0) & ~ well_ordering(v1))
% 5.26/2.05
% 5.26/2.05 Further assumptions not needed in the proof:
% 5.26/2.05 --------------------------------------------
% 5.26/2.05 cc1_ordinal1, cc2_ordinal1, rc1_ordinal1
% 5.26/2.05
% 5.26/2.05 Those formulas are unsatisfiable:
% 5.26/2.05 ---------------------------------
% 5.26/2.05
% 5.26/2.05 Begin of proof
% 5.26/2.05 |
% 5.26/2.05 | ALPHA: (d4_wellord1) implies:
% 5.26/2.05 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ well_founded_relation(v0) | ~
% 5.26/2.05 | connected(v0) | ~ antisymmetric(v0) | ~ transitive(v0) | ~
% 5.26/2.05 | reflexive(v0) | ~ relation(v0) | well_ordering(v0))
% 5.26/2.05 |
% 5.26/2.06 | DELTA: instantiating (t7_wellord2) with fresh symbols all_14_0, all_14_1
% 5.26/2.06 | gives:
% 5.26/2.06 | (2) inclusion_relation(all_14_1) = all_14_0 & $i(all_14_0) & $i(all_14_1) &
% 5.26/2.06 | ordinal(all_14_1) & ~ well_ordering(all_14_0)
% 5.26/2.06 |
% 5.26/2.06 | ALPHA: (2) implies:
% 5.26/2.06 | (3) ~ well_ordering(all_14_0)
% 5.26/2.06 | (4) ordinal(all_14_1)
% 5.26/2.06 | (5) $i(all_14_1)
% 5.26/2.06 | (6) $i(all_14_0)
% 5.26/2.06 | (7) inclusion_relation(all_14_1) = all_14_0
% 5.26/2.06 |
% 5.26/2.06 | GROUND_INST: instantiating (t6_wellord2) with all_14_1, all_14_0, simplifying
% 5.26/2.06 | with (4), (5), (7) gives:
% 5.26/2.06 | (8) well_founded_relation(all_14_0)
% 5.26/2.06 |
% 5.26/2.06 | GROUND_INST: instantiating (t4_wellord2) with all_14_1, all_14_0, simplifying
% 5.26/2.06 | with (4), (5), (7) gives:
% 5.26/2.06 | (9) connected(all_14_0)
% 5.26/2.06 |
% 5.26/2.06 | GROUND_INST: instantiating (t5_wellord2) with all_14_1, all_14_0, simplifying
% 5.26/2.06 | with (5), (7) gives:
% 5.26/2.06 | (10) antisymmetric(all_14_0)
% 5.26/2.06 |
% 5.26/2.06 | GROUND_INST: instantiating (t3_wellord2) with all_14_1, all_14_0, simplifying
% 5.26/2.06 | with (5), (7) gives:
% 5.26/2.06 | (11) transitive(all_14_0)
% 5.26/2.06 |
% 5.26/2.06 | GROUND_INST: instantiating (t2_wellord2) with all_14_1, all_14_0, simplifying
% 5.26/2.06 | with (5), (7) gives:
% 5.26/2.06 | (12) reflexive(all_14_0)
% 5.26/2.06 |
% 5.26/2.06 | GROUND_INST: instantiating (dt_k1_wellord2) with all_14_1, all_14_0,
% 5.26/2.06 | simplifying with (5), (7) gives:
% 5.26/2.06 | (13) relation(all_14_0)
% 5.26/2.06 |
% 5.26/2.06 | GROUND_INST: instantiating (1) with all_14_0, simplifying with (3), (6), (8),
% 5.26/2.06 | (9), (10), (11), (12), (13) gives:
% 5.26/2.07 | (14) $false
% 5.26/2.07 |
% 5.26/2.07 | CLOSE: (14) is inconsistent.
% 5.26/2.07 |
% 5.26/2.07 End of proof
% 5.26/2.07 % SZS output end Proof for theBenchmark
% 5.26/2.07
% 5.26/2.07 1454ms
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