TSTP Solution File: PHI012+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : PHI012+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 : n022.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 8.09s 1.91s
% Output : Proof 12.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : PHI012+1 : TPTP v8.1.2. Released v7.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 08:51:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 ________ _____
% 0.20/0.58 ___ __ \_________(_)________________________________
% 0.20/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.58
% 0.20/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.58 (2023-06-19)
% 0.20/0.58
% 0.20/0.58 (c) Philipp Rümmer, 2009-2023
% 0.20/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.58 Amanda Stjerna.
% 0.20/0.58 Free software under BSD-3-Clause.
% 0.20/0.58
% 0.20/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.58
% 0.20/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.59 Running up to 7 provers in parallel.
% 0.20/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 1.95/0.99 Prover 1: Preprocessing ...
% 1.95/1.00 Prover 4: Preprocessing ...
% 2.35/1.06 Prover 0: Preprocessing ...
% 2.35/1.06 Prover 3: Preprocessing ...
% 2.35/1.06 Prover 6: Preprocessing ...
% 2.35/1.06 Prover 5: Preprocessing ...
% 2.35/1.06 Prover 2: Preprocessing ...
% 3.09/1.18 Prover 5: Constructing countermodel ...
% 3.09/1.18 Prover 2: Constructing countermodel ...
% 3.09/1.24 Prover 1: Constructing countermodel ...
% 3.09/1.24 Prover 6: Proving ...
% 3.56/1.25 Prover 3: Constructing countermodel ...
% 4.06/1.34 Prover 4: Constructing countermodel ...
% 4.06/1.44 Prover 0: Proving ...
% 8.09/1.91 Prover 0: proved (1302ms)
% 8.09/1.91
% 8.09/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.09/1.91
% 8.09/1.92 Prover 2: stopped
% 8.09/1.93 Prover 5: stopped
% 8.09/1.93 Prover 3: stopped
% 8.09/1.93 Prover 6: stopped
% 8.09/1.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.09/1.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.09/1.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.09/1.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.09/1.93 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.39/1.96 Prover 7: Preprocessing ...
% 8.39/1.96 Prover 11: Preprocessing ...
% 8.39/1.96 Prover 8: Preprocessing ...
% 8.39/1.97 Prover 10: Preprocessing ...
% 8.39/1.97 Prover 13: Preprocessing ...
% 8.39/1.98 Prover 7: Constructing countermodel ...
% 8.39/1.99 Prover 10: Constructing countermodel ...
% 8.39/2.01 Prover 13: Constructing countermodel ...
% 8.39/2.02 Prover 8: Warning: ignoring some quantifiers
% 8.39/2.04 Prover 8: Constructing countermodel ...
% 9.13/2.09 Prover 11: Constructing countermodel ...
% 12.45/2.58 Prover 13: Found proof (size 19)
% 12.45/2.58 Prover 13: proved (647ms)
% 12.45/2.59 Prover 7: stopped
% 12.45/2.59 Prover 11: stopped
% 12.45/2.59 Prover 10: stopped
% 12.45/2.59 Prover 8: stopped
% 12.45/2.59 Prover 4: stopped
% 12.45/2.59 Prover 1: stopped
% 12.45/2.59
% 12.45/2.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.45/2.59
% 12.45/2.59 % SZS output start Proof for theBenchmark
% 12.45/2.60 Assumptions after simplification:
% 12.45/2.60 ---------------------------------
% 12.45/2.60
% 12.45/2.60 (connectedness_of_greater_than)
% 12.45/2.60 $i(greater_than) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~
% 12.45/2.60 $i(v0) | ~ object(v1) | ~ object(v0) | exemplifies_relation(greater_than,
% 12.45/2.60 v1, v0) | exemplifies_relation(greater_than, v0, v1))
% 12.45/2.60
% 12.45/2.60 (definition_none_greater)
% 12.45/2.61 $i(greater_than) & $i(conceivable) & $i(none_greater) & ! [v0: $i] : ! [v1:
% 12.45/2.61 $i] : ( ~ $i(v1) | ~ $i(v0) | ~ exemplifies_relation(greater_than, v1, v0)
% 12.45/2.61 | ~ exemplifies_property(conceivable, v1) | ~
% 12.45/2.61 exemplifies_property(none_greater, v0) | ~ object(v1) | ~ object(v0)) & !
% 12.45/2.61 [v0: $i] : ( ~ $i(v0) | ~ exemplifies_property(conceivable, v0) | ~
% 12.45/2.61 object(v0) | exemplifies_property(none_greater, v0) | ? [v1: $i] : ($i(v1)
% 12.45/2.61 & exemplifies_relation(greater_than, v1, v0) &
% 12.45/2.61 exemplifies_property(conceivable, v1) & object(v1))) & ! [v0: $i] : ( ~
% 12.45/2.61 $i(v0) | ~ exemplifies_property(none_greater, v0) | ~ object(v0) |
% 12.45/2.61 exemplifies_property(conceivable, v0))
% 12.45/2.61
% 12.45/2.61 (lemma_2)
% 12.45/2.61 $i(none_greater) & ? [v0: $i] : ($i(v0) & exemplifies_property(none_greater,
% 12.45/2.61 v0) & object(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 12.45/2.61 exemplifies_property(none_greater, v1) | ~ object(v1) | ? [v2: $i] : ( ~
% 12.45/2.61 (v2 = v1) & $i(v2) & exemplifies_property(none_greater, v2) &
% 12.45/2.61 object(v2))))
% 12.45/2.61
% 12.45/2.61 Those formulas are unsatisfiable:
% 12.45/2.61 ---------------------------------
% 12.45/2.61
% 12.45/2.61 Begin of proof
% 12.45/2.61 |
% 12.45/2.61 | ALPHA: (lemma_2) implies:
% 12.45/2.61 | (1) ? [v0: $i] : ($i(v0) & exemplifies_property(none_greater, v0) &
% 12.45/2.61 | object(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 12.45/2.61 | exemplifies_property(none_greater, v1) | ~ object(v1) | ? [v2:
% 12.45/2.61 | $i] : ( ~ (v2 = v1) & $i(v2) & exemplifies_property(none_greater,
% 12.45/2.61 | v2) & object(v2))))
% 12.45/2.61 |
% 12.45/2.61 | ALPHA: (connectedness_of_greater_than) implies:
% 12.45/2.61 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 12.45/2.61 | object(v1) | ~ object(v0) | exemplifies_relation(greater_than, v1,
% 12.45/2.61 | v0) | exemplifies_relation(greater_than, v0, v1))
% 12.45/2.61 |
% 12.45/2.61 | ALPHA: (definition_none_greater) implies:
% 12.45/2.62 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ exemplifies_property(none_greater, v0) |
% 12.45/2.62 | ~ object(v0) | exemplifies_property(conceivable, v0))
% 12.45/2.62 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 12.45/2.62 | exemplifies_relation(greater_than, v1, v0) | ~
% 12.45/2.62 | exemplifies_property(conceivable, v1) | ~
% 12.45/2.62 | exemplifies_property(none_greater, v0) | ~ object(v1) | ~
% 12.45/2.62 | object(v0))
% 12.45/2.62 |
% 12.45/2.62 | DELTA: instantiating (1) with fresh symbol all_5_0 gives:
% 12.45/2.62 | (5) $i(all_5_0) & exemplifies_property(none_greater, all_5_0) &
% 12.45/2.62 | object(all_5_0) & ! [v0: $i] : ( ~ $i(v0) | ~
% 12.45/2.62 | exemplifies_property(none_greater, v0) | ~ object(v0) | ? [v1: $i]
% 12.45/2.62 | : ( ~ (v1 = v0) & $i(v1) & exemplifies_property(none_greater, v1) &
% 12.45/2.62 | object(v1)))
% 12.45/2.62 |
% 12.45/2.62 | ALPHA: (5) implies:
% 12.45/2.62 | (6) object(all_5_0)
% 12.45/2.62 | (7) exemplifies_property(none_greater, all_5_0)
% 12.45/2.62 | (8) $i(all_5_0)
% 12.45/2.62 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ exemplifies_property(none_greater, v0) |
% 12.45/2.62 | ~ object(v0) | ? [v1: $i] : ( ~ (v1 = v0) & $i(v1) &
% 12.45/2.62 | exemplifies_property(none_greater, v1) & object(v1)))
% 12.45/2.62 |
% 12.45/2.62 | GROUND_INST: instantiating (3) with all_5_0, simplifying with (6), (7), (8)
% 12.45/2.62 | gives:
% 12.45/2.62 | (10) exemplifies_property(conceivable, all_5_0)
% 12.45/2.62 |
% 12.45/2.62 | GROUND_INST: instantiating (9) with all_5_0, simplifying with (6), (7), (8)
% 12.45/2.62 | gives:
% 12.45/2.62 | (11) ? [v0: any] : ( ~ (v0 = all_5_0) & $i(v0) &
% 12.45/2.62 | exemplifies_property(none_greater, v0) & object(v0))
% 12.45/2.62 |
% 12.45/2.62 | DELTA: instantiating (11) with fresh symbol all_14_0 gives:
% 12.45/2.62 | (12) ~ (all_14_0 = all_5_0) & $i(all_14_0) &
% 12.45/2.62 | exemplifies_property(none_greater, all_14_0) & object(all_14_0)
% 12.45/2.62 |
% 12.45/2.62 | ALPHA: (12) implies:
% 12.45/2.62 | (13) ~ (all_14_0 = all_5_0)
% 12.45/2.62 | (14) object(all_14_0)
% 12.45/2.62 | (15) exemplifies_property(none_greater, all_14_0)
% 12.45/2.62 | (16) $i(all_14_0)
% 12.45/2.62 |
% 12.45/2.63 | GROUND_INST: instantiating (2) with all_5_0, all_14_0, simplifying with (6),
% 12.45/2.63 | (8), (14), (16) gives:
% 12.45/2.63 | (17) all_14_0 = all_5_0 | exemplifies_relation(greater_than, all_14_0,
% 12.45/2.63 | all_5_0) | exemplifies_relation(greater_than, all_5_0, all_14_0)
% 12.45/2.63 |
% 12.45/2.63 | GROUND_INST: instantiating (3) with all_14_0, simplifying with (14), (15),
% 12.45/2.63 | (16) gives:
% 12.45/2.63 | (18) exemplifies_property(conceivable, all_14_0)
% 12.45/2.63 |
% 12.45/2.63 | BETA: splitting (17) gives:
% 12.45/2.63 |
% 12.45/2.63 | Case 1:
% 12.45/2.63 | |
% 12.45/2.63 | | (19) exemplifies_relation(greater_than, all_14_0, all_5_0)
% 12.45/2.63 | |
% 12.45/2.63 | | GROUND_INST: instantiating (4) with all_5_0, all_14_0, simplifying with (6),
% 12.45/2.63 | | (7), (8), (14), (16), (18), (19) gives:
% 12.45/2.63 | | (20) $false
% 12.45/2.63 | |
% 12.45/2.63 | | CLOSE: (20) is inconsistent.
% 12.45/2.63 | |
% 12.45/2.63 | Case 2:
% 12.45/2.63 | |
% 12.45/2.63 | | (21) all_14_0 = all_5_0 | exemplifies_relation(greater_than, all_5_0,
% 12.45/2.63 | | all_14_0)
% 12.45/2.63 | |
% 12.45/2.63 | | BETA: splitting (21) gives:
% 12.45/2.63 | |
% 12.45/2.63 | | Case 1:
% 12.45/2.63 | | |
% 12.45/2.63 | | | (22) exemplifies_relation(greater_than, all_5_0, all_14_0)
% 12.45/2.63 | | |
% 12.45/2.63 | | | GROUND_INST: instantiating (4) with all_14_0, all_5_0, simplifying with
% 12.45/2.63 | | | (6), (8), (10), (14), (15), (16), (22) gives:
% 12.45/2.63 | | | (23) $false
% 12.45/2.63 | | |
% 12.45/2.63 | | | CLOSE: (23) is inconsistent.
% 12.45/2.63 | | |
% 12.45/2.63 | | Case 2:
% 12.45/2.63 | | |
% 12.45/2.63 | | | (24) all_14_0 = all_5_0
% 12.45/2.63 | | |
% 12.45/2.63 | | | REDUCE: (13), (24) imply:
% 12.45/2.63 | | | (25) $false
% 12.45/2.63 | | |
% 12.45/2.63 | | | CLOSE: (25) is inconsistent.
% 12.45/2.63 | | |
% 12.45/2.63 | | End of split
% 12.45/2.63 | |
% 12.45/2.63 | End of split
% 12.45/2.63 |
% 12.45/2.63 End of proof
% 12.45/2.63 % SZS output end Proof for theBenchmark
% 12.45/2.63
% 12.45/2.63 2048ms
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