TSTP Solution File: PHI013+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : PHI013+1 : TPTP v8.1.2. Released v7.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n031.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 12:56:40 EDT 2023
% Result : Theorem 5.35s 1.48s
% Output : Proof 7.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : PHI013+1 : TPTP v8.1.2. Released v7.2.0.
% 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 09:15:54 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.39/0.98 Prover 4: Preprocessing ...
% 2.39/0.99 Prover 1: Preprocessing ...
% 2.39/1.03 Prover 3: Preprocessing ...
% 2.39/1.03 Prover 2: Preprocessing ...
% 2.39/1.03 Prover 0: Preprocessing ...
% 2.39/1.03 Prover 6: Preprocessing ...
% 2.39/1.03 Prover 5: Preprocessing ...
% 4.00/1.24 Prover 2: Constructing countermodel ...
% 4.00/1.24 Prover 5: Constructing countermodel ...
% 4.00/1.30 Prover 1: Constructing countermodel ...
% 4.00/1.32 Prover 3: Constructing countermodel ...
% 4.00/1.32 Prover 6: Proving ...
% 5.35/1.44 Prover 4: Constructing countermodel ...
% 5.35/1.48 Prover 2: proved (844ms)
% 5.35/1.48
% 5.35/1.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.35/1.48
% 5.35/1.48 Prover 5: stopped
% 5.35/1.48 Prover 6: stopped
% 5.35/1.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.35/1.49 Prover 3: stopped
% 5.35/1.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.35/1.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.35/1.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.89/1.52 Prover 0: Proving ...
% 5.89/1.52 Prover 8: Preprocessing ...
% 5.89/1.52 Prover 0: stopped
% 5.89/1.53 Prover 10: Preprocessing ...
% 5.89/1.53 Prover 7: Preprocessing ...
% 5.89/1.54 Prover 11: Preprocessing ...
% 5.89/1.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.29/1.58 Prover 10: Constructing countermodel ...
% 6.29/1.59 Prover 13: Preprocessing ...
% 6.29/1.60 Prover 7: Constructing countermodel ...
% 6.29/1.64 Prover 10: Found proof (size 13)
% 6.29/1.64 Prover 10: proved (152ms)
% 6.29/1.64 Prover 4: stopped
% 6.29/1.64 Prover 1: stopped
% 6.29/1.64 Prover 7: stopped
% 6.29/1.64 Prover 8: Warning: ignoring some quantifiers
% 6.29/1.64 Prover 13: Constructing countermodel ...
% 6.29/1.65 Prover 13: stopped
% 6.29/1.65 Prover 8: Constructing countermodel ...
% 6.87/1.65 Prover 8: stopped
% 6.99/1.72 Prover 11: Constructing countermodel ...
% 7.20/1.72 Prover 11: stopped
% 7.20/1.73
% 7.20/1.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.20/1.73
% 7.20/1.73 % SZS output start Proof for theBenchmark
% 7.20/1.73 Assumptions after simplification:
% 7.20/1.73 ---------------------------------
% 7.20/1.73
% 7.20/1.73 (definition_god)
% 7.20/1.74 $i(god) & $i(none_greater) & is_the(god, none_greater)
% 7.20/1.74
% 7.20/1.74 (definition_none_greater)
% 7.30/1.74 $i(greater_than) & $i(conceivable) & $i(none_greater) & ! [v0: $i] : ! [v1:
% 7.30/1.74 $i] : ( ~ $i(v1) | ~ $i(v0) | ~ exemplifies_relation(greater_than, v1, v0)
% 7.30/1.74 | ~ exemplifies_property(conceivable, v1) | ~
% 7.30/1.74 exemplifies_property(none_greater, v0) | ~ object(v1) | ~ object(v0)) & !
% 7.30/1.74 [v0: $i] : ( ~ $i(v0) | ~ exemplifies_property(conceivable, v0) | ~
% 7.30/1.74 object(v0) | exemplifies_property(none_greater, v0) | ? [v1: $i] : ($i(v1)
% 7.30/1.74 & exemplifies_relation(greater_than, v1, v0) &
% 7.30/1.74 exemplifies_property(conceivable, v1) & object(v1))) & ! [v0: $i] : ( ~
% 7.30/1.74 $i(v0) | ~ exemplifies_property(none_greater, v0) | ~ object(v0) |
% 7.30/1.74 exemplifies_property(conceivable, v0))
% 7.30/1.74
% 7.30/1.74 (description_is_property_and_described_is_object)
% 7.30/1.74 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ is_the(v0, v1) |
% 7.30/1.74 object(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 7.30/1.74 is_the(v0, v1) | property(v1))
% 7.30/1.74
% 7.30/1.74 (description_theorem_2)
% 7.30/1.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 7.30/1.74 ~ is_the(v2, v0) | ~ is_the(v1, v0) | ~ object(v2) | ~ object(v1) | ~
% 7.30/1.74 property(v0) | exemplifies_property(v0, v1))
% 7.30/1.74
% 7.30/1.74 (god_exists)
% 7.30/1.74 $i(god) & $i(existence) & ~ exemplifies_property(existence, god)
% 7.30/1.74
% 7.30/1.74 (premise_2)
% 7.30/1.75 $i(existence) & $i(greater_than) & $i(conceivable) & $i(none_greater) & !
% 7.30/1.75 [v0: $i] : ( ~ $i(v0) | ~ is_the(v0, none_greater) | ~ object(v0) |
% 7.30/1.75 exemplifies_property(existence, v0) | ? [v1: $i] : ($i(v1) &
% 7.30/1.75 exemplifies_relation(greater_than, v1, v0) &
% 7.30/1.75 exemplifies_property(conceivable, v1) & object(v1)))
% 7.30/1.75
% 7.30/1.75 Further assumptions not needed in the proof:
% 7.30/1.75 --------------------------------------------
% 7.30/1.75 description_theorem_1, lemma_2, premise_1
% 7.30/1.75
% 7.30/1.75 Those formulas are unsatisfiable:
% 7.30/1.75 ---------------------------------
% 7.30/1.75
% 7.30/1.75 Begin of proof
% 7.30/1.75 |
% 7.30/1.75 | ALPHA: (god_exists) implies:
% 7.30/1.75 | (1) ~ exemplifies_property(existence, god)
% 7.30/1.75 |
% 7.30/1.75 | ALPHA: (definition_god) implies:
% 7.30/1.75 | (2) is_the(god, none_greater)
% 7.30/1.75 | (3) $i(god)
% 7.30/1.75 |
% 7.30/1.75 | ALPHA: (premise_2) implies:
% 7.30/1.75 | (4) ! [v0: $i] : ( ~ $i(v0) | ~ is_the(v0, none_greater) | ~ object(v0)
% 7.30/1.75 | | exemplifies_property(existence, v0) | ? [v1: $i] : ($i(v1) &
% 7.30/1.75 | exemplifies_relation(greater_than, v1, v0) &
% 7.30/1.75 | exemplifies_property(conceivable, v1) & object(v1)))
% 7.30/1.75 |
% 7.30/1.75 | ALPHA: (definition_none_greater) implies:
% 7.30/1.75 | (5) $i(none_greater)
% 7.30/1.75 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 7.30/1.75 | exemplifies_relation(greater_than, v1, v0) | ~
% 7.30/1.75 | exemplifies_property(conceivable, v1) | ~
% 7.30/1.75 | exemplifies_property(none_greater, v0) | ~ object(v1) | ~
% 7.30/1.75 | object(v0))
% 7.30/1.75 |
% 7.30/1.75 | ALPHA: (description_is_property_and_described_is_object) implies:
% 7.30/1.75 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ is_the(v0, v1)
% 7.30/1.75 | | property(v1))
% 7.30/1.75 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ is_the(v0, v1)
% 7.30/1.75 | | object(v0))
% 7.30/1.75 |
% 7.30/1.76 | GROUND_INST: instantiating (8) with god, none_greater, simplifying with (2),
% 7.30/1.76 | (3), (5) gives:
% 7.30/1.76 | (9) object(god)
% 7.30/1.76 |
% 7.30/1.76 | GROUND_INST: instantiating (7) with god, none_greater, simplifying with (2),
% 7.30/1.76 | (3), (5) gives:
% 7.30/1.76 | (10) property(none_greater)
% 7.30/1.76 |
% 7.30/1.76 | GROUND_INST: instantiating (description_theorem_2) with none_greater, god,
% 7.30/1.76 | god, simplifying with (2), (3), (5), (9), (10) gives:
% 7.30/1.76 | (11) exemplifies_property(none_greater, god)
% 7.30/1.76 |
% 7.30/1.76 | GROUND_INST: instantiating (4) with god, simplifying with (1), (2), (3), (9)
% 7.30/1.76 | gives:
% 7.30/1.76 | (12) ? [v0: $i] : ($i(v0) & exemplifies_relation(greater_than, v0, god) &
% 7.30/1.76 | exemplifies_property(conceivable, v0) & object(v0))
% 7.30/1.76 |
% 7.30/1.76 | DELTA: instantiating (12) with fresh symbol all_24_0 gives:
% 7.30/1.76 | (13) $i(all_24_0) & exemplifies_relation(greater_than, all_24_0, god) &
% 7.30/1.76 | exemplifies_property(conceivable, all_24_0) & object(all_24_0)
% 7.30/1.76 |
% 7.30/1.76 | ALPHA: (13) implies:
% 7.30/1.76 | (14) object(all_24_0)
% 7.30/1.76 | (15) exemplifies_property(conceivable, all_24_0)
% 7.30/1.76 | (16) exemplifies_relation(greater_than, all_24_0, god)
% 7.30/1.76 | (17) $i(all_24_0)
% 7.30/1.76 |
% 7.30/1.76 | GROUND_INST: instantiating (6) with god, all_24_0, simplifying with (3), (9),
% 7.30/1.76 | (11), (14), (15), (16), (17) gives:
% 7.30/1.76 | (18) $false
% 7.30/1.76 |
% 7.30/1.76 | CLOSE: (18) is inconsistent.
% 7.30/1.76 |
% 7.30/1.76 End of proof
% 7.30/1.76 % SZS output end Proof for theBenchmark
% 7.30/1.76
% 7.30/1.76 1147ms
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