TSTP Solution File: PUZ060+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : PUZ060+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n006.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 13:22:59 EDT 2023
% Result : Theorem 3.83s 1.39s
% Output : Proof 5.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : PUZ060+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.31 % Computer : n006.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sat Aug 26 22:29:37 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.58 ________ _____
% 0.16/0.58 ___ __ \_________(_)________________________________
% 0.16/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.58
% 0.16/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.58 (2023-06-19)
% 0.16/0.58
% 0.16/0.58 (c) Philipp Rümmer, 2009-2023
% 0.16/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.58 Amanda Stjerna.
% 0.16/0.58 Free software under BSD-3-Clause.
% 0.16/0.58
% 0.16/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.58
% 0.16/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.16/0.60 Running up to 7 provers in parallel.
% 0.16/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.77/0.99 Prover 4: Preprocessing ...
% 1.77/0.99 Prover 1: Preprocessing ...
% 2.11/1.05 Prover 2: Preprocessing ...
% 2.11/1.05 Prover 5: Preprocessing ...
% 2.11/1.05 Prover 3: Preprocessing ...
% 2.11/1.05 Prover 0: Preprocessing ...
% 2.11/1.05 Prover 6: Preprocessing ...
% 2.58/1.14 Prover 2: Proving ...
% 2.58/1.15 Prover 5: Proving ...
% 3.02/1.21 Prover 3: Constructing countermodel ...
% 3.02/1.21 Prover 1: Constructing countermodel ...
% 3.02/1.22 Prover 4: Constructing countermodel ...
% 3.02/1.23 Prover 6: Proving ...
% 3.02/1.24 Prover 0: Proving ...
% 3.83/1.38 Prover 0: proved (775ms)
% 3.83/1.38
% 3.83/1.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.83/1.39
% 3.83/1.39 Prover 3: gave up
% 3.83/1.39 Prover 2: stopped
% 3.83/1.39 Prover 5: stopped
% 3.83/1.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.83/1.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.83/1.40 Prover 6: stopped
% 3.83/1.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.83/1.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.83/1.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.83/1.41 Prover 1: gave up
% 3.83/1.41 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 3.83/1.42 Prover 7: Preprocessing ...
% 3.83/1.43 Prover 4: Found proof (size 18)
% 3.83/1.43 Prover 4: proved (815ms)
% 3.83/1.44 Prover 10: Preprocessing ...
% 3.83/1.44 Prover 13: Preprocessing ...
% 3.83/1.44 Prover 8: Preprocessing ...
% 3.83/1.44 Prover 16: Preprocessing ...
% 3.83/1.45 Prover 11: Preprocessing ...
% 3.83/1.45 Prover 7: Warning: ignoring some quantifiers
% 3.83/1.46 Prover 7: Constructing countermodel ...
% 3.83/1.46 Prover 13: Warning: ignoring some quantifiers
% 3.83/1.46 Prover 10: Warning: ignoring some quantifiers
% 3.83/1.46 Prover 7: stopped
% 3.83/1.46 Prover 13: Constructing countermodel ...
% 3.83/1.46 Prover 10: Constructing countermodel ...
% 3.83/1.46 Prover 13: stopped
% 4.75/1.46 Prover 10: stopped
% 4.97/1.47 Prover 11: stopped
% 4.97/1.48 Prover 16: Warning: ignoring some quantifiers
% 4.97/1.48 Prover 16: Constructing countermodel ...
% 4.97/1.48 Prover 16: stopped
% 4.97/1.50 Prover 8: Warning: ignoring some quantifiers
% 4.97/1.51 Prover 8: Constructing countermodel ...
% 4.97/1.52 Prover 8: stopped
% 4.97/1.52
% 4.97/1.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.97/1.52
% 4.97/1.52 % SZS output start Proof for theBenchmark
% 4.97/1.52 Assumptions after simplification:
% 4.97/1.52 ---------------------------------
% 4.97/1.52
% 4.97/1.52 (prove_this)
% 5.51/1.58 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 5.51/1.58 $i] : ? [v6: int] : ( ~ (v6 = 0) & alive(v2) = 0 & eats(v2, v0) = 0 &
% 5.51/1.58 likes(v1, v0) = v6 & food(v5) = 0 & food(v4) = 0 & $i(v5) & $i(v4) & $i(v3)
% 5.51/1.58 & $i(v2) & $i(v1) & $i(v0) & ! [v7: $i] : ! [v8: $i] : ! [v9: int] : (v9
% 5.51/1.58 = 0 | ~ (alive(v7) = 0) | ~ (not_killed_by(v7, v8) = v9) | ~ $i(v8) |
% 5.51/1.58 ~ $i(v7)) & ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~
% 5.51/1.58 (not_killed_by(v9, v7) = 0) | ~ (food(v7) = v8) | ~ $i(v9) | ~ $i(v7) |
% 5.51/1.58 ? [v10: int] : ( ~ (v10 = 0) & eats(v9, v7) = v10)) & ! [v7: $i] : !
% 5.51/1.58 [v8: int] : ! [v9: $i] : (v8 = 0 | ~ (eats(v9, v7) = 0) | ~ (food(v7) =
% 5.51/1.58 v8) | ~ $i(v9) | ~ $i(v7) | ? [v10: int] : ( ~ (v10 = 0) &
% 5.51/1.58 not_killed_by(v9, v7) = v10)) & ! [v7: $i] : ! [v8: int] : (v8 = 0 |
% 5.51/1.58 ~ (eats(v3, v7) = v8) | ~ $i(v7) | ? [v9: int] : ( ~ (v9 = 0) & eats(v2,
% 5.51/1.58 v7) = v9)) & ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ (likes(v1, v7)
% 5.51/1.58 = v8) | ~ $i(v7) | ? [v9: int] : ( ~ (v9 = 0) & food(v7) = v9)) & !
% 5.51/1.58 [v7: $i] : ( ~ (eats(v2, v7) = 0) | ~ $i(v7) | eats(v3, v7) = 0) & ! [v7:
% 5.51/1.58 $i] : ( ~ (food(v7) = 0) | ~ $i(v7) | likes(v1, v7) = 0))
% 5.51/1.58
% 5.51/1.58 Those formulas are unsatisfiable:
% 5.51/1.58 ---------------------------------
% 5.51/1.58
% 5.51/1.58 Begin of proof
% 5.51/1.58 |
% 5.51/1.58 | DELTA: instantiating (prove_this) with fresh symbols all_3_0, all_3_1,
% 5.51/1.58 | all_3_2, all_3_3, all_3_4, all_3_5, all_3_6 gives:
% 5.51/1.60 | (1) ~ (all_3_0 = 0) & alive(all_3_4) = 0 & eats(all_3_4, all_3_6) = 0 &
% 5.51/1.60 | likes(all_3_5, all_3_6) = all_3_0 & food(all_3_1) = 0 & food(all_3_2) =
% 5.51/1.60 | 0 & $i(all_3_1) & $i(all_3_2) & $i(all_3_3) & $i(all_3_4) & $i(all_3_5)
% 5.51/1.60 | & $i(all_3_6) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 5.51/1.60 | (alive(v0) = 0) | ~ (not_killed_by(v0, v1) = v2) | ~ $i(v1) | ~
% 5.51/1.60 | $i(v0)) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~
% 5.51/1.60 | (not_killed_by(v2, v0) = 0) | ~ (food(v0) = v1) | ~ $i(v2) | ~
% 5.51/1.60 | $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & eats(v2, v0) = v3)) & ! [v0:
% 5.51/1.60 | $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (eats(v2, v0) = 0) |
% 5.51/1.60 | ~ (food(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 =
% 5.51/1.60 | 0) & not_killed_by(v2, v0) = v3)) & ! [v0: $i] : ! [v1: int] :
% 5.51/1.60 | (v1 = 0 | ~ (eats(all_3_3, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~
% 5.51/1.60 | (v2 = 0) & eats(all_3_4, v0) = v2)) & ! [v0: $i] : ! [v1: int] :
% 5.51/1.60 | (v1 = 0 | ~ (likes(all_3_5, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~
% 5.51/1.60 | (v2 = 0) & food(v0) = v2)) & ! [v0: $i] : ( ~ (eats(all_3_4, v0) =
% 5.51/1.60 | 0) | ~ $i(v0) | eats(all_3_3, v0) = 0) & ! [v0: $i] : ( ~
% 5.51/1.60 | (food(v0) = 0) | ~ $i(v0) | likes(all_3_5, v0) = 0)
% 5.51/1.60 |
% 5.51/1.60 | ALPHA: (1) implies:
% 5.51/1.60 | (2) ~ (all_3_0 = 0)
% 5.51/1.60 | (3) $i(all_3_6)
% 5.51/1.60 | (4) $i(all_3_4)
% 5.51/1.61 | (5) likes(all_3_5, all_3_6) = all_3_0
% 5.51/1.61 | (6) eats(all_3_4, all_3_6) = 0
% 5.51/1.61 | (7) alive(all_3_4) = 0
% 5.51/1.61 | (8) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (likes(all_3_5, v0) = v1) |
% 5.51/1.61 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & food(v0) = v2))
% 5.51/1.61 | (9) ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (eats(v2, v0) =
% 5.51/1.61 | 0) | ~ (food(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : (
% 5.51/1.61 | ~ (v3 = 0) & not_killed_by(v2, v0) = v3))
% 5.51/1.61 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (alive(v0) =
% 5.51/1.61 | 0) | ~ (not_killed_by(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0))
% 5.51/1.61 |
% 5.51/1.61 | GROUND_INST: instantiating (8) with all_3_6, all_3_0, simplifying with (3),
% 5.51/1.61 | (5) gives:
% 5.51/1.61 | (11) all_3_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & food(all_3_6) = v0)
% 5.51/1.61 |
% 5.51/1.61 | BETA: splitting (11) gives:
% 5.51/1.61 |
% 5.51/1.61 | Case 1:
% 5.51/1.61 | |
% 5.51/1.61 | | (12) all_3_0 = 0
% 5.51/1.61 | |
% 5.51/1.61 | | REDUCE: (2), (12) imply:
% 5.51/1.61 | | (13) $false
% 5.51/1.62 | |
% 5.51/1.62 | | CLOSE: (13) is inconsistent.
% 5.51/1.62 | |
% 5.51/1.62 | Case 2:
% 5.51/1.62 | |
% 5.51/1.62 | | (14) ? [v0: int] : ( ~ (v0 = 0) & food(all_3_6) = v0)
% 5.51/1.62 | |
% 5.51/1.62 | | DELTA: instantiating (14) with fresh symbol all_16_0 gives:
% 5.51/1.62 | | (15) ~ (all_16_0 = 0) & food(all_3_6) = all_16_0
% 5.51/1.62 | |
% 5.51/1.62 | | ALPHA: (15) implies:
% 5.51/1.62 | | (16) ~ (all_16_0 = 0)
% 5.51/1.62 | | (17) food(all_3_6) = all_16_0
% 5.51/1.62 | |
% 5.51/1.62 | | GROUND_INST: instantiating (9) with all_3_6, all_16_0, all_3_4, simplifying
% 5.51/1.62 | | with (3), (4), (6), (17) gives:
% 5.51/1.62 | | (18) all_16_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & not_killed_by(all_3_4,
% 5.51/1.62 | | all_3_6) = v0)
% 5.51/1.62 | |
% 5.51/1.62 | | BETA: splitting (18) gives:
% 5.51/1.62 | |
% 5.51/1.62 | | Case 1:
% 5.51/1.62 | | |
% 5.51/1.62 | | | (19) all_16_0 = 0
% 5.51/1.62 | | |
% 5.51/1.62 | | | REDUCE: (16), (19) imply:
% 5.51/1.62 | | | (20) $false
% 5.51/1.62 | | |
% 5.51/1.62 | | | CLOSE: (20) is inconsistent.
% 5.51/1.62 | | |
% 5.51/1.62 | | Case 2:
% 5.51/1.62 | | |
% 5.51/1.62 | | | (21) ? [v0: int] : ( ~ (v0 = 0) & not_killed_by(all_3_4, all_3_6) =
% 5.51/1.62 | | | v0)
% 5.51/1.62 | | |
% 5.51/1.62 | | | DELTA: instantiating (21) with fresh symbol all_31_0 gives:
% 5.51/1.62 | | | (22) ~ (all_31_0 = 0) & not_killed_by(all_3_4, all_3_6) = all_31_0
% 5.51/1.62 | | |
% 5.51/1.62 | | | ALPHA: (22) implies:
% 5.51/1.62 | | | (23) ~ (all_31_0 = 0)
% 5.51/1.62 | | | (24) not_killed_by(all_3_4, all_3_6) = all_31_0
% 5.51/1.62 | | |
% 5.51/1.62 | | | GROUND_INST: instantiating (10) with all_3_4, all_3_6, all_31_0,
% 5.51/1.62 | | | simplifying with (3), (4), (7), (24) gives:
% 5.51/1.62 | | | (25) all_31_0 = 0
% 5.51/1.62 | | |
% 5.51/1.63 | | | REDUCE: (23), (25) imply:
% 5.51/1.63 | | | (26) $false
% 5.51/1.63 | | |
% 5.51/1.63 | | | CLOSE: (26) is inconsistent.
% 5.51/1.63 | | |
% 5.51/1.63 | | End of split
% 5.51/1.63 | |
% 5.51/1.63 | End of split
% 5.51/1.63 |
% 5.51/1.63 End of proof
% 5.73/1.63 % SZS output end Proof for theBenchmark
% 5.73/1.63
% 5.73/1.63 1040ms
%------------------------------------------------------------------------------