TSTP Solution File: KRS187+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS187+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n018.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 05:51:34 EDT 2023
% Result : Theorem 11.09s 2.24s
% Output : Proof 13.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS187+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 02:00:16 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.14/1.17 Prover 4: Preprocessing ...
% 3.14/1.17 Prover 1: Preprocessing ...
% 3.82/1.21 Prover 6: Preprocessing ...
% 3.82/1.21 Prover 3: Preprocessing ...
% 3.82/1.21 Prover 5: Preprocessing ...
% 3.82/1.21 Prover 0: Preprocessing ...
% 3.82/1.22 Prover 2: Preprocessing ...
% 8.28/1.86 Prover 2: Proving ...
% 8.28/1.89 Prover 5: Proving ...
% 9.44/2.05 Prover 6: Proving ...
% 9.44/2.06 Prover 3: Constructing countermodel ...
% 9.44/2.07 Prover 1: Constructing countermodel ...
% 10.43/2.15 Prover 0: Proving ...
% 10.43/2.16 Prover 4: Constructing countermodel ...
% 11.09/2.24 Prover 3: proved (1597ms)
% 11.09/2.24
% 11.09/2.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.09/2.24
% 11.09/2.24 Prover 5: stopped
% 11.09/2.24 Prover 0: stopped
% 11.09/2.24 Prover 2: stopped
% 11.09/2.24 Prover 6: stopped
% 11.09/2.24 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.09/2.24 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.09/2.24 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.09/2.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.09/2.25 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.60/2.32 Prover 10: Preprocessing ...
% 11.60/2.33 Prover 8: Preprocessing ...
% 11.60/2.35 Prover 11: Preprocessing ...
% 11.60/2.35 Prover 13: Preprocessing ...
% 11.60/2.35 Prover 1: Found proof (size 23)
% 11.60/2.35 Prover 1: proved (1720ms)
% 11.60/2.35 Prover 4: stopped
% 11.60/2.35 Prover 7: Preprocessing ...
% 11.60/2.36 Prover 10: stopped
% 12.28/2.39 Prover 13: stopped
% 12.28/2.39 Prover 7: stopped
% 12.46/2.42 Prover 11: stopped
% 12.99/2.52 Prover 8: Warning: ignoring some quantifiers
% 12.99/2.54 Prover 8: Constructing countermodel ...
% 12.99/2.56 Prover 8: stopped
% 12.99/2.56
% 12.99/2.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.99/2.56
% 12.99/2.56 % SZS output start Proof for theBenchmark
% 12.99/2.56 Assumptions after simplification:
% 12.99/2.56 ---------------------------------
% 12.99/2.56
% 12.99/2.56 (isa)
% 13.34/2.59 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (isa(v0, v1) = v2) |
% 13.34/2.59 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 =
% 13.34/2.59 0) & status(v3, v4, v1) = v5 & status(v3, v4, v0) = 0 & $i(v4) &
% 13.34/2.59 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (isa(v0, v1) = 0) | ~ $i(v1) |
% 13.34/2.59 ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (status(v2, v3, v0) = 0) | ~
% 13.34/2.59 $i(v3) | ~ $i(v2) | status(v2, v3, v1) = 0))
% 13.34/2.59
% 13.34/2.59 (isa_tac_thm)
% 13.34/2.59 $i(tac) & $i(thm) & ? [v0: int] : ( ~ (v0 = 0) & isa(tac, thm) = v0)
% 13.34/2.59
% 13.34/2.59 (tac)
% 13.34/2.60 $i(tac) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (status(v0,
% 13.34/2.60 v1, tac) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : (
% 13.34/2.60 ~ (v4 = 0) & model(v3, v1) = v4 & $i(v3)) | ! [v3: $i] : ( ~ (model(v3,
% 13.34/2.60 v0) = 0) | ~ $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (status(v0,
% 13.34/2.60 v1, tac) = 0) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] :
% 13.34/2.60 (v3 = 0 | ~ (model(v2, v1) = v3) | ~ $i(v2)) & ? [v2: $i] : (model(v2,
% 13.34/2.60 v0) = 0 & $i(v2))))
% 13.34/2.60
% 13.34/2.60 (thm)
% 13.34/2.60 $i(thm) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (status(v0,
% 13.34/2.60 v1, thm) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : (
% 13.34/2.60 ~ (v4 = 0) & model(v3, v1) = v4 & model(v3, v0) = 0 & $i(v3))) & ! [v0:
% 13.34/2.60 $i] : ! [v1: $i] : ( ~ (status(v0, v1, thm) = 0) | ~ $i(v1) | ~ $i(v0) |
% 13.34/2.60 ! [v2: $i] : ( ~ (model(v2, v0) = 0) | ~ $i(v2) | model(v2, v1) = 0))
% 13.34/2.60
% 13.34/2.60 Further assumptions not needed in the proof:
% 13.34/2.60 --------------------------------------------
% 13.34/2.60 cax, completeness, contradiction, csa, eqv, esa, eth, mighta, mixed_pair,
% 13.34/2.60 nevera, noc, non_thm_spt, not, nota, sap, sat, sat_non_taut_pair, satisfiable,
% 13.34/2.60 sca, tau, tautology, tca, unp, uns, wca, wec, wtc, wth, xora
% 13.34/2.60
% 13.34/2.60 Those formulas are unsatisfiable:
% 13.34/2.60 ---------------------------------
% 13.34/2.60
% 13.34/2.60 Begin of proof
% 13.34/2.60 |
% 13.34/2.60 | ALPHA: (thm) implies:
% 13.34/2.60 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (status(v0, v1,
% 13.34/2.60 | thm) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 13.34/2.60 | ( ~ (v4 = 0) & model(v3, v1) = v4 & model(v3, v0) = 0 & $i(v3)))
% 13.34/2.60 |
% 13.34/2.60 | ALPHA: (tac) implies:
% 13.34/2.60 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (status(v0, v1, tac) = 0) | ~ $i(v1) |
% 13.34/2.60 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (model(v2, v1)
% 13.34/2.60 | = v3) | ~ $i(v2)) & ? [v2: $i] : (model(v2, v0) = 0 &
% 13.34/2.60 | $i(v2))))
% 13.34/2.60 |
% 13.34/2.61 | ALPHA: (isa) implies:
% 13.34/2.61 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (isa(v0, v1) =
% 13.34/2.61 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 13.34/2.61 | int] : ( ~ (v5 = 0) & status(v3, v4, v1) = v5 & status(v3, v4, v0)
% 13.34/2.61 | = 0 & $i(v4) & $i(v3)))
% 13.34/2.61 |
% 13.34/2.61 | ALPHA: (isa_tac_thm) implies:
% 13.34/2.61 | (4) $i(thm)
% 13.34/2.61 | (5) $i(tac)
% 13.34/2.61 | (6) ? [v0: int] : ( ~ (v0 = 0) & isa(tac, thm) = v0)
% 13.34/2.61 |
% 13.34/2.61 | DELTA: instantiating (6) with fresh symbol all_30_0 gives:
% 13.34/2.61 | (7) ~ (all_30_0 = 0) & isa(tac, thm) = all_30_0
% 13.34/2.61 |
% 13.34/2.61 | ALPHA: (7) implies:
% 13.34/2.61 | (8) ~ (all_30_0 = 0)
% 13.34/2.61 | (9) isa(tac, thm) = all_30_0
% 13.34/2.61 |
% 13.34/2.61 | GROUND_INST: instantiating (3) with tac, thm, all_30_0, simplifying with (4),
% 13.34/2.61 | (5), (9) gives:
% 13.34/2.61 | (10) all_30_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0)
% 13.34/2.61 | & status(v0, v1, tac) = 0 & status(v0, v1, thm) = v2 & $i(v1) &
% 13.34/2.61 | $i(v0))
% 13.34/2.61 |
% 13.34/2.61 | BETA: splitting (10) gives:
% 13.34/2.61 |
% 13.34/2.61 | Case 1:
% 13.34/2.61 | |
% 13.34/2.61 | | (11) all_30_0 = 0
% 13.34/2.61 | |
% 13.34/2.61 | | REDUCE: (8), (11) imply:
% 13.34/2.61 | | (12) $false
% 13.34/2.61 | |
% 13.34/2.61 | | CLOSE: (12) is inconsistent.
% 13.34/2.61 | |
% 13.34/2.61 | Case 2:
% 13.34/2.61 | |
% 13.34/2.61 | | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & status(v0,
% 13.34/2.61 | | v1, tac) = 0 & status(v0, v1, thm) = v2 & $i(v1) & $i(v0))
% 13.34/2.61 | |
% 13.34/2.61 | | DELTA: instantiating (13) with fresh symbols all_73_0, all_73_1, all_73_2
% 13.34/2.61 | | gives:
% 13.34/2.61 | | (14) ~ (all_73_0 = 0) & status(all_73_2, all_73_1, tac) = 0 &
% 13.34/2.61 | | status(all_73_2, all_73_1, thm) = all_73_0 & $i(all_73_1) &
% 13.34/2.61 | | $i(all_73_2)
% 13.34/2.61 | |
% 13.34/2.61 | | ALPHA: (14) implies:
% 13.34/2.61 | | (15) ~ (all_73_0 = 0)
% 13.34/2.61 | | (16) $i(all_73_2)
% 13.34/2.61 | | (17) $i(all_73_1)
% 13.34/2.62 | | (18) status(all_73_2, all_73_1, thm) = all_73_0
% 13.34/2.62 | | (19) status(all_73_2, all_73_1, tac) = 0
% 13.34/2.62 | |
% 13.34/2.62 | | GROUND_INST: instantiating (1) with all_73_2, all_73_1, all_73_0,
% 13.34/2.62 | | simplifying with (16), (17), (18) gives:
% 13.34/2.62 | | (20) all_73_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & model(v0,
% 13.34/2.62 | | all_73_1) = v1 & model(v0, all_73_2) = 0 & $i(v0))
% 13.34/2.62 | |
% 13.34/2.62 | | GROUND_INST: instantiating (2) with all_73_2, all_73_1, simplifying with
% 13.34/2.62 | | (16), (17), (19) gives:
% 13.34/2.62 | | (21) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (model(v0, all_73_1) = v1)
% 13.34/2.62 | | | ~ $i(v0)) & ? [v0: $i] : (model(v0, all_73_2) = 0 & $i(v0))
% 13.34/2.62 | |
% 13.34/2.62 | | ALPHA: (21) implies:
% 13.34/2.62 | | (22) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (model(v0, all_73_1) = v1)
% 13.34/2.62 | | | ~ $i(v0))
% 13.34/2.62 | |
% 13.34/2.62 | | BETA: splitting (20) gives:
% 13.34/2.62 | |
% 13.34/2.62 | | Case 1:
% 13.34/2.62 | | |
% 13.34/2.62 | | | (23) all_73_0 = 0
% 13.34/2.62 | | |
% 13.34/2.62 | | | REDUCE: (15), (23) imply:
% 13.34/2.62 | | | (24) $false
% 13.34/2.62 | | |
% 13.34/2.62 | | | CLOSE: (24) is inconsistent.
% 13.34/2.62 | | |
% 13.34/2.62 | | Case 2:
% 13.34/2.62 | | |
% 13.34/2.62 | | | (25) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & model(v0, all_73_1) =
% 13.34/2.62 | | | v1 & model(v0, all_73_2) = 0 & $i(v0))
% 13.34/2.62 | | |
% 13.34/2.62 | | | DELTA: instantiating (25) with fresh symbols all_87_0, all_87_1 gives:
% 13.34/2.62 | | | (26) ~ (all_87_0 = 0) & model(all_87_1, all_73_1) = all_87_0 &
% 13.34/2.62 | | | model(all_87_1, all_73_2) = 0 & $i(all_87_1)
% 13.34/2.62 | | |
% 13.34/2.62 | | | ALPHA: (26) implies:
% 13.34/2.62 | | | (27) ~ (all_87_0 = 0)
% 13.34/2.62 | | | (28) $i(all_87_1)
% 13.34/2.62 | | | (29) model(all_87_1, all_73_1) = all_87_0
% 13.34/2.62 | | |
% 13.34/2.62 | | | GROUND_INST: instantiating (22) with all_87_1, all_87_0, simplifying with
% 13.34/2.62 | | | (28), (29) gives:
% 13.34/2.62 | | | (30) all_87_0 = 0
% 13.34/2.62 | | |
% 13.34/2.62 | | | REDUCE: (27), (30) imply:
% 13.34/2.62 | | | (31) $false
% 13.34/2.62 | | |
% 13.34/2.62 | | | CLOSE: (31) is inconsistent.
% 13.34/2.62 | | |
% 13.34/2.62 | | End of split
% 13.34/2.62 | |
% 13.34/2.62 | End of split
% 13.34/2.62 |
% 13.34/2.62 End of proof
% 13.34/2.62 % SZS output end Proof for theBenchmark
% 13.34/2.62
% 13.34/2.62 2009ms
%------------------------------------------------------------------------------