TSTP Solution File: PHI010+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : PHI010+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 : n010.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 12:56:39 EDT 2023
% Result : Theorem 4.38s 1.31s
% Output : Proof 6.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PHI010+1 : TPTP v8.1.2. Released v7.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 08:39:49 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.04/0.97 Prover 4: Preprocessing ...
% 2.04/0.97 Prover 1: Preprocessing ...
% 2.40/1.01 Prover 5: Preprocessing ...
% 2.40/1.01 Prover 0: Preprocessing ...
% 2.40/1.01 Prover 2: Preprocessing ...
% 2.40/1.01 Prover 6: Preprocessing ...
% 2.40/1.01 Prover 3: Preprocessing ...
% 3.47/1.21 Prover 2: Constructing countermodel ...
% 3.47/1.22 Prover 5: Constructing countermodel ...
% 3.47/1.22 Prover 1: Constructing countermodel ...
% 3.47/1.22 Prover 3: Constructing countermodel ...
% 3.47/1.22 Prover 6: Proving ...
% 4.38/1.30 Prover 5: proved (671ms)
% 4.38/1.30
% 4.38/1.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.38/1.31
% 4.38/1.31 Prover 3: stopped
% 4.38/1.31 Prover 2: stopped
% 4.38/1.32 Prover 6: stopped
% 4.38/1.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.38/1.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.38/1.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.38/1.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.38/1.34 Prover 7: Preprocessing ...
% 4.38/1.34 Prover 4: Constructing countermodel ...
% 4.38/1.35 Prover 8: Preprocessing ...
% 4.38/1.36 Prover 10: Preprocessing ...
% 4.38/1.36 Prover 11: Preprocessing ...
% 4.38/1.40 Prover 10: Constructing countermodel ...
% 4.38/1.40 Prover 0: Proving ...
% 4.38/1.41 Prover 7: Constructing countermodel ...
% 4.38/1.41 Prover 0: stopped
% 4.38/1.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.38/1.44 Prover 13: Preprocessing ...
% 4.96/1.45 Prover 1: Found proof (size 18)
% 4.96/1.45 Prover 7: Found proof (size 7)
% 4.96/1.45 Prover 10: Found proof (size 7)
% 4.96/1.45 Prover 1: proved (830ms)
% 4.96/1.45 Prover 10: proved (126ms)
% 4.96/1.45 Prover 7: proved (142ms)
% 4.96/1.45 Prover 4: stopped
% 5.55/1.47 Prover 8: Warning: ignoring some quantifiers
% 5.55/1.48 Prover 8: Constructing countermodel ...
% 5.55/1.48 Prover 8: stopped
% 5.55/1.49 Prover 13: Constructing countermodel ...
% 5.55/1.50 Prover 13: stopped
% 6.02/1.55 Prover 11: Constructing countermodel ...
% 6.02/1.56 Prover 11: stopped
% 6.02/1.56
% 6.02/1.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.02/1.56
% 6.02/1.56 % SZS output start Proof for theBenchmark
% 6.02/1.57 Assumptions after simplification:
% 6.02/1.57 ---------------------------------
% 6.02/1.57
% 6.02/1.57 (description_axiom_identity_instance)
% 6.02/1.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (is_the(v1, v0) =
% 6.02/1.60 v3) | ~ (object(v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 6.02/1.60 any] : ? [v5: any] : (property(v0) = v4 & object(v1) = v5 & ( ~ (v5 = 0)
% 6.02/1.60 | ~ (v4 = 0))) | (( ~ (v3 = 0) | ~ (v2 = v1) |
% 6.02/1.60 (exemplifies_property(v0, v1) = 0 & object(v1) = 0 & ! [v4: $i] : (v4 =
% 6.02/1.60 v1 | ~ (exemplifies_property(v0, v4) = 0) | ~ $i(v4) | ? [v5:
% 6.02/1.60 int] : ( ~ (v5 = 0) & object(v4) = v5)))) & ( ~
% 6.02/1.60 (exemplifies_property(v0, v2) = 0) | ? [v4: $i] : ( ~ (v4 = v2) &
% 6.02/1.60 exemplifies_property(v0, v4) = 0 & object(v4) = 0 & $i(v4)) | (v3 = 0
% 6.02/1.60 & v2 = v1))))
% 6.02/1.60
% 6.02/1.60 (lemma_1)
% 6.02/1.60 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & is_the(v0, v1) = 0 &
% 6.02/1.60 exemplifies_property(v1, v0) = v2 & property(v1) = 0 & object(v0) = 0 &
% 6.02/1.60 $i(v1) & $i(v0))
% 6.02/1.60
% 6.02/1.60 (function-axioms)
% 6.02/1.61 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 6.02/1.61 [v3: $i] : (v1 = v0 | ~ (is_the(v3, v2) = v1) | ~ (is_the(v3, v2) = v0)) &
% 6.02/1.61 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 6.02/1.61 $i] : (v1 = v0 | ~ (exemplifies_property(v3, v2) = v1) | ~
% 6.02/1.61 (exemplifies_property(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.02/1.61 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (property(v2) = v1) | ~
% 6.02/1.61 (property(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.02/1.61 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (object(v2) = v1) | ~
% 6.02/1.61 (object(v2) = v0))
% 6.02/1.61
% 6.02/1.61 Further assumptions not needed in the proof:
% 6.02/1.61 --------------------------------------------
% 6.02/1.61 description_is_property_and_described_is_object,
% 6.02/1.61 exemplifier_is_object_and_exemplified_is_property, objects_are_not_properties
% 6.02/1.61
% 6.02/1.61 Those formulas are unsatisfiable:
% 6.02/1.61 ---------------------------------
% 6.02/1.61
% 6.02/1.61 Begin of proof
% 6.02/1.61 |
% 6.02/1.61 | ALPHA: (function-axioms) implies:
% 6.02/1.61 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.02/1.61 | (v1 = v0 | ~ (object(v2) = v1) | ~ (object(v2) = v0))
% 6.02/1.61 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.02/1.61 | (v1 = v0 | ~ (property(v2) = v1) | ~ (property(v2) = v0))
% 6.02/1.61 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.02/1.61 | ! [v3: $i] : (v1 = v0 | ~ (exemplifies_property(v3, v2) = v1) | ~
% 6.02/1.61 | (exemplifies_property(v3, v2) = v0))
% 6.02/1.61 |
% 6.02/1.61 | DELTA: instantiating (lemma_1) with fresh symbols all_7_0, all_7_1, all_7_2
% 6.02/1.61 | gives:
% 6.02/1.61 | (4) ~ (all_7_0 = 0) & is_the(all_7_2, all_7_1) = 0 &
% 6.02/1.61 | exemplifies_property(all_7_1, all_7_2) = all_7_0 & property(all_7_1) =
% 6.02/1.61 | 0 & object(all_7_2) = 0 & $i(all_7_1) & $i(all_7_2)
% 6.02/1.61 |
% 6.02/1.61 | ALPHA: (4) implies:
% 6.02/1.61 | (5) ~ (all_7_0 = 0)
% 6.02/1.62 | (6) $i(all_7_2)
% 6.02/1.62 | (7) $i(all_7_1)
% 6.02/1.62 | (8) object(all_7_2) = 0
% 6.02/1.62 | (9) property(all_7_1) = 0
% 6.02/1.62 | (10) exemplifies_property(all_7_1, all_7_2) = all_7_0
% 6.02/1.62 | (11) is_the(all_7_2, all_7_1) = 0
% 6.02/1.62 |
% 6.02/1.62 | GROUND_INST: instantiating (description_axiom_identity_instance) with all_7_1,
% 6.02/1.62 | all_7_2, all_7_2, 0, simplifying with (6), (7), (8), (11) gives:
% 6.02/1.62 | (12) ? [v0: any] : ? [v1: any] : (property(all_7_1) = v0 &
% 6.02/1.62 | object(all_7_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) |
% 6.02/1.62 | (exemplifies_property(all_7_1, all_7_2) = 0 & ! [v0: any] : (v0 =
% 6.02/1.62 | all_7_2 | ~ (exemplifies_property(all_7_1, v0) = 0) | ~ $i(v0) |
% 6.02/1.62 | ? [v1: int] : ( ~ (v1 = 0) & object(v0) = v1)))
% 6.02/1.62 |
% 6.02/1.62 | BETA: splitting (12) gives:
% 6.02/1.62 |
% 6.02/1.62 | Case 1:
% 6.02/1.62 | |
% 6.02/1.62 | | (13) ? [v0: any] : ? [v1: any] : (property(all_7_1) = v0 &
% 6.02/1.62 | | object(all_7_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.02/1.62 | |
% 6.02/1.62 | | DELTA: instantiating (13) with fresh symbols all_19_0, all_19_1 gives:
% 6.02/1.62 | | (14) property(all_7_1) = all_19_1 & object(all_7_2) = all_19_0 & ( ~
% 6.02/1.62 | | (all_19_0 = 0) | ~ (all_19_1 = 0))
% 6.02/1.62 | |
% 6.02/1.62 | | ALPHA: (14) implies:
% 6.02/1.62 | | (15) object(all_7_2) = all_19_0
% 6.02/1.62 | | (16) property(all_7_1) = all_19_1
% 6.02/1.62 | | (17) ~ (all_19_0 = 0) | ~ (all_19_1 = 0)
% 6.02/1.62 | |
% 6.02/1.62 | | GROUND_INST: instantiating (1) with 0, all_19_0, all_7_2, simplifying with
% 6.02/1.62 | | (8), (15) gives:
% 6.02/1.62 | | (18) all_19_0 = 0
% 6.02/1.62 | |
% 6.02/1.62 | | GROUND_INST: instantiating (2) with 0, all_19_1, all_7_1, simplifying with
% 6.02/1.62 | | (9), (16) gives:
% 6.02/1.63 | | (19) all_19_1 = 0
% 6.02/1.63 | |
% 6.02/1.63 | | BETA: splitting (17) gives:
% 6.02/1.63 | |
% 6.02/1.63 | | Case 1:
% 6.02/1.63 | | |
% 6.02/1.63 | | | (20) ~ (all_19_0 = 0)
% 6.02/1.63 | | |
% 6.02/1.63 | | | REDUCE: (18), (20) imply:
% 6.02/1.63 | | | (21) $false
% 6.02/1.63 | | |
% 6.02/1.63 | | | CLOSE: (21) is inconsistent.
% 6.02/1.63 | | |
% 6.02/1.63 | | Case 2:
% 6.02/1.63 | | |
% 6.02/1.63 | | | (22) ~ (all_19_1 = 0)
% 6.02/1.63 | | |
% 6.02/1.63 | | | REDUCE: (19), (22) imply:
% 6.02/1.63 | | | (23) $false
% 6.02/1.63 | | |
% 6.02/1.63 | | | CLOSE: (23) is inconsistent.
% 6.02/1.63 | | |
% 6.02/1.63 | | End of split
% 6.02/1.63 | |
% 6.02/1.63 | Case 2:
% 6.02/1.63 | |
% 6.02/1.63 | | (24) exemplifies_property(all_7_1, all_7_2) = 0 & ! [v0: any] : (v0 =
% 6.02/1.63 | | all_7_2 | ~ (exemplifies_property(all_7_1, v0) = 0) | ~ $i(v0) |
% 6.02/1.63 | | ? [v1: int] : ( ~ (v1 = 0) & object(v0) = v1))
% 6.02/1.63 | |
% 6.02/1.63 | | ALPHA: (24) implies:
% 6.02/1.63 | | (25) exemplifies_property(all_7_1, all_7_2) = 0
% 6.02/1.63 | |
% 6.02/1.63 | | GROUND_INST: instantiating (3) with all_7_0, 0, all_7_2, all_7_1,
% 6.02/1.63 | | simplifying with (10), (25) gives:
% 6.02/1.63 | | (26) all_7_0 = 0
% 6.02/1.63 | |
% 6.02/1.63 | | REDUCE: (5), (26) imply:
% 6.02/1.63 | | (27) $false
% 6.02/1.63 | |
% 6.02/1.63 | | CLOSE: (27) is inconsistent.
% 6.02/1.63 | |
% 6.02/1.63 | End of split
% 6.02/1.63 |
% 6.02/1.63 End of proof
% 6.02/1.63 % SZS output end Proof for theBenchmark
% 6.02/1.63
% 6.02/1.63 1028ms
%------------------------------------------------------------------------------